MISCELLANEOUS PAPERS 
 
 CONNECTED WITH 
 
 PHYSICAL SCIENCE 
 
 BY 
 
 HUMPHREY LLOYD, D.D., D.C.L., 
 
 PHOTOS! OF TRINITY COLLEGE, DUBLIN ; 
 FORMERLY PROFESSOR OF NATURAL PHILOSOPHY IN THE UNIVERSITY. 
 
 REIMUXTED FROM THE TRANSACTIONS OP THE ROYAL IRISH ACADEMY ; THE REPORTS OK 
 THE BRITISH ASSOCIATION FOR THE ADVANCEMENT OF SCIENCE ; ETC. 
 
 LONDON: 
 LONGMANS, GREEN, AND CO. 
 
 1877.
 
 BUBLIK : 
 
 t ^nifrmitg $**x
 
 ' . 
 
 CONTENTS. 
 
 PAGE. 
 
 I. On the Phenomena presented by Light in its passage along the 
 
 Axes of Biaxal Crystals, 1 
 
 II. Report on the Progress and Present State of Physical Optics, . 19 
 
 III. On a new case of Interference of the Rays of Light, . . .149 
 
 IV. On the Light reflected and transmitted by Thin Plates, . .157 
 
 V. Observations of the Direction and Intensity of the Terrestrial 
 
 Magnetic Force in Ireland, . . . . . . .170 
 
 VI. On the position of the Isogonal Lines in Ireland, deduced from 
 
 the Observations of CAPTAIN SIR JAMES CLARKE Ross, R. N., . 217 
 
 VII. On a New Magnetical Instrument, for the measurement of the 
 
 Inclination, and its Changes, 221 
 
 VIII. Remarks on the theory of the Compound Magnetic Needle, . 231 
 IX. On the Mean Results of Observations, 233 
 
 X. On the determination of the Horizontal Intensity of the Earth's 
 
 Magnetic Force in absolute measure, ..... 246 
 
 XI. On the determination of the Total Intensity of the Earth's Mag- 
 netic Force in absolute measure, by means of the Dip-circle, . 260 
 
 XII. On Earth-currents, and their connexion with the Diurnal Changes 
 
 of the Horizontal Magnetic Needle, 271 
 
 XIII. On Earth-currents, in connexion with Magnetic Disturbances, . 295 
 
 XIV. On the probable causes of the Earth-currents, .... 299 
 
 XV. On the direct Magnetic Influence of a distant Luminary upon the 
 Diurnal Variations of the Magnetic Force at the Earth's sur- 
 face, 30(5
 
 IV CONTENTS. 
 
 PAGE. 
 
 XVI. On the Storm of the 18th of April, 1850, . . . .312 
 
 XVII. Notes on the Meteorology of Ireland, deduced from the Observa- 
 tions made in the year 1851, under the direction of the Royal 
 Irish Academy, . . . 317 
 
 XVIII. The Climate of Ireland, and the Currents of the Atlantic. 
 (Lecture delivered before the Dublin Young Men's Christian 
 Association, October 25, 1865), 381 
 
 XIX. On the rise and progress of Mechanical Philosophy. (Intro- 
 ductory Lecture delivered in the Philosophy School of Trinity 
 College, in Hilary Term, 1834), 414 
 
 XX. The Applied Sciences, and the mode of Teaching them. (Preelec- 
 tion delivered on the occasion of the Opening of the School of 
 Engineering in the University of Dublin, November 15, 1841), 437 
 
 XXI. Address delivered at a Meeting of the Royal Irish Academy, held 
 
 April 13, 1846, on the occasion of taking the Chair, . . 454 
 
 XXII. Address delivered at a Meeting of the Royal Irish Academy, held 
 June 26, 1848, on the occasion of the presentation of the Medals 
 awarded by the Council, 468 
 
 XXIII. Address delivered at the Opening Meeting of the British Asso- 
 ciation for the Advancement of Science, held in Dublin, 
 August 26, 1857, 485 
 
 NOTES. 
 
 Note to Table VI., p. 289, 511 
 
 Note to Tables V. and VIII., pp. 286 and 291, . . . .511
 
 PLATES. 
 
 MAGNETIC CHART OF IRELAND . . - opposite page 216 
 
 EARTH CURRENTS. PLATES 1 and 2 . 294 
 
 METEOROLOGY OF IRELAND. PLATKS 1, 2, 3, 
 
 and 4 
 
 380
 
 MISCELLANEOUS PAPERS. 
 
 I. ON THE PHENOMENA PEESENTED BY LIGHT IN ITS 
 PASSAGE ALONG THE AXES OF BIAXAL CEYSTALS. 
 
 Transactions of the Royal Irish Academy, Vol. XVII. 
 
 IT is well known that when a ray of light is incident upon certain 
 crystals, such as Iceland spar and quartz, it is in general divided 
 into two pencils, of which one is refracted according to the known 
 law of the sines, while the direction of the other is determined by a 
 new and extraordinary law, first assigned by Huygens. 
 
 These laws were long supposed to apply to all doubly -refracting 
 substances ; and it was not until the subject was examined by the 
 ablest advocate of the undulatory theory, that the problem of 
 double refraction was solved in all its generality. Setting out 
 from the hypothesis, that the elasticity of the vibrating medium 
 within the crystal is unequal in three rectangular directions, Fresnel 
 has shown that the surface of the wave is not, in general, either a 
 sphere or spheroid, as in the Huygenian law, but a surface of the 
 fourth order, consisting of two sheets ; and that the directions of 
 the two refracted rays are determined by tangent planes drawn to 
 these surfaces under known conditions. Such crystals have, in 
 general, two optic axes, and are thence denominated bia.rnL When
 
 'J CONICAL REFRACTION. 
 
 the elasticity of the medium is the same in two of the three direc- 
 tions, the equation of the wave-surface is resolvable into two, which 
 represent the sphere and spheroid of the Huygenian law. The 
 two optic axes in this case coincide ; and the law of Huygens is 
 thus proved to be a case of a more general law, and shown to 
 belong to uniaxal crystals only. Finally, when the elasticity is 
 the same in all the three directions, the wave-surface becomes a 
 sphere ; and the refraction is single, and takes place according to 
 the ordinary law of the sines. This case comprises a few of the 
 crystallized, and most uncrystallized substances. 
 
 There are two remarkable cases, however, in this elegant and 
 profound theory, which its author seems to have overlooked, if 
 not to have misapprehended. In a communication made to the 
 Academy at its last meeting, Professor Hamilton has supplied 
 these omissions in the theory of Fresnel, and has been thus led to 
 results in the highest degree novel and remarkable. 
 
 To understand these conclusions, it may be useful to revert for 
 a moment to the original theory of Fresnel. The general form 
 of the wave-surface is determined by the equation 
 
 (a 2 cos 2 a + tf cos 2 /3 + c 2 cos 2 -y)r 4 
 
 _ |y (ja + c 2 ) C os 2 a + & 2 ( 2 + c 2 ) cos 2 /3 4 c 2 (a 2 + ft 2 ) cos 2 7 ] r 2 
 + a 2 b 2 c 2 = ; 
 
 in which a, j3, 7, denote the angles made by the radius- vector with 
 the three axes, and a 2 , 6 2 , c 2 , the elasticities of the medium in these 
 directions. If now we make cos /3 = in this equation, so as to 
 obtain the section of the surface made by the plane of ars, the result 
 is reducible to the form 
 
 (r z - V] [( 2 cos 2 a + c 2 sin 2 a) r z - V] = 0. 
 
 So that the surface intersects the plane of xz in a circle and ellipse, 
 whose equations are 
 
 r = ft, (a- cos 2 a + c 2 sin 2 a) r 2 = V. 
 
 Now b, the radius of the circle, being intermediate between a 
 and c, the semiaxes of the ellipse, it is obvious that the two curves 
 must intersect in four points, or cusps, as represented in (fig. 1) ; 
 and the angle which the radius-vector OP, drawn to the cusp,
 
 CONICAL REFRACTION. 
 
 3 
 
 makes with the axis of x, is found by eliminating r between the 
 two equations, by wliich means we obtain 
 
 Fig. 1. 
 
 At each of the points thus determined there will be two tangents 
 to tho plane section ; and consequently the ray OP, proceeding 
 within the crystal to one of these points, 
 might be supposed to be divided at emer- 
 gence into two, whose directions are deter- 
 mined by those of the tangents. 
 
 Such seems to have been Fresnel's con- 
 ception of this case. Professor Hamilton has 
 shown, however, that there is a cusp at each 
 of these points, not only in this particular 
 section, but in every section of the wave- 
 surface passing through the line OP ; or, in 
 other words, that there is a conoidal cusp on 
 the general wave-surface at the four points 
 of intersection of the circle and ellipse ; so 
 that there must be an infinite number of tangent planes at each 
 of these points, and consequently a single rat/, such as OP, pro- 
 ceeding from a point within the crystal to one of these points, 
 must be divided into an infinite number of emergent rays, constitut- 
 ing a conical surface.* 
 
 It is evident further, that the circle and ellipse will have four 
 common tangents, such as MN (fig. 1). The planes passing 
 through these tangents, and parallel to the third or mean axis, 
 are parallel to the circular sections of the surface of elastic it;/ of 
 Fresnel's theory, or perpendicular to the optic axes. Fresnel seems 
 to have concluded that these planes touched the wave-surface only 
 in the two points just mentioned ; and, consequently, that a single 
 ray, incident upon a biaxal crystal in such a manner that one of 
 the refracted rays should coincide with an optic axis, would be 
 divided into two, determined by the points of contact. This result, 
 if verified by experience, would place a remarkable distinction 
 between the phenomena of uniaxal and biaxal crystals ; but though 
 the case was examined by M. Biot, no corresponding appearances 
 were observed.
 
 4 CONICAL REFRACTION. 
 
 Professor Hamilton has shown that the four planes of which 
 we have spoken touch the wave-surface, not in two points only, 
 but in an infinite number of points, constituting each a small 
 circle of contact, whose plane is parallel to one of the two circular 
 sections of the surface of elasticity ; and that, consequently, a 
 single ray of common light, incident externally in the above- 
 mentioned direction, should be divided within the crystal into an 
 infinite number of refracted rays, constituting a conical surface. 
 
 Here, then, are two singular and unexpected consequences of 
 the undulatory theory, not only unsupported by any facts hitherto 
 observed, but even opposed to all the analogies derived from ex- 
 perience. If confirmed by experiment, they would furnish new 
 and almost convincing proofs of the truth of that theory ; and if 
 disproved, on the other hand, it is evident that the theory must be 
 abandoned or modified. 
 
 Being naturally anxious to submit the undulatory hypothesis 
 to this delicate test, and to establish or disprove these new results 
 of theory, Professor Hamilton requested me to institute a series of 
 experiments with that view. I accordingly applied myself to this 
 interesting research with all the attention which the subject so 
 well merited, and have fortunately succeeded in verifying both 
 cases of conical refraction. The substance I employed in these 
 experiments was arragonite, which is well known to be a biaxal 
 crystal, whose axes are inclined at an angle of nearly 20. I 
 selected it partly on account of the magnitude of its biaxal energy, 
 and partly also because the optical elements 6f this mineral have 
 been determined, apparently with great care, by Professor Rudberg ; 
 and therefore the results of theory could be applied to it at once 
 without further examination. The specimen I used was one of 
 considerable size and purity, procured for me by Mr. Dollond, 
 and cut with its parallel faces perpendicular to the line bisecting 
 the optic axes. 
 
 The first-mentioned species of conical refraction, it has been 
 observed, takes place in air, when a ray of common light is trans- 
 mitted within the crystal in the direction of the line joining two 
 opposite cusps of the wave. If we suppose such a ray to pass in 
 both directions out of the crystal, it is evident that it must emerge 
 similarly at both surfaces ; consequently, the rays which are trans- 
 mitted along this line within the crystal, and form a diverging 
 cone at emergence at the second surface, must be incident in a
 
 CONICAL REFRACTION. Q 
 
 converging cone at the first. Having therefore nearly ascertained 
 the required direction by means of the system of rings in polarized 
 light, I placed a lens of short focus at its focal distance from the 
 first surface, and in such a position that the central part of the 
 pencil might have an incidence nearly corresponding to the cusp- 
 ray within. Then looking through the crystal at the light of a 
 lamp placed at a considerable distance, I observed in the expected 
 direction a point more luminous than the space immediately about 
 it, and surrounded by something resembling a stellar radiation. 
 Fearing that this singular appearance might have arisen from 
 some imperfection in the crystal, I transmitted the light in the 
 same manner through several different parts of its substance, and 
 always with the same result. The connexion of the phenomenon 
 with the optic axis was proved by the system of rings which 
 appeared in the same direction, when the light was examined with 
 a polarizing and analyzing plate. 
 
 This result is of some interest in itself, independently of its 
 connexion with theory. It has been hitherto supposed that the 
 only method of determining experimentally the direction of the 
 optic axes, in most doubly-refracting substances, consisted in 
 observing the system of coloured rings, which appear around them 
 when the incident and emergent light is polarized. Here, how- 
 ever, we find that common, or unpolarized light, undergoes such 
 modifications in the neighbourhood of one of the optic axes, that 
 the apparent direction of that axis may be at once determined, 
 and with the aid of the simplest contrivance.* 
 
 But to examine the emergent cone, it was necessary to exclude 
 the light which passed through the crystal in all but one direction. 
 For this purpose, a plate of thin metal, having a minute aperture, 
 was placed on the surface of the crystal next the eye, and the 
 position of the aperture so adjusted, that the line connecting it 
 with the luminous point on the first surface might be, as nearly as 
 possible, in the direction of the cusp-ray. The exact adjustment 
 to this direction was made by subsequent trial. The phenomenon 
 
 * This fact is here mentioned, rather as a matter of curiosity than as one likely co 
 be of practical value in determining the optical elements of crystals. It is to be 
 observed, moreover, that the direction thus determined is that of the normal to the 
 circular section of the ellipsoid of Fresnel's theory ; while the rings (there is strong 
 reason to believe) are related to the normals to the circular sections of the surface 
 iif elasticity.
 
 6 CONICAL REFRACTION. 
 
 which presented itself when this disposition was complete was in 
 the highest degree curious. There appeared at first a luminous 
 circle, with a small dark space in the centre ; and in this dark 
 central space were two bright points, separated by a narrow and 
 well-defined dark line. These appearances are represented in 
 (figs, a and b). When the aperture in the plate was slightly 
 
 Fig. a. Fig. 
 
 shifted, the phenomena rapidly changed, assuming in succession 
 the forms represented in (figs, c, d, e). In the first stage of its 
 change, the central dark space became greatly enlarged, and a 
 double sector appeared in the centre. The circle was reduced to 
 about a quadrant, and was separated by a dark interval from the 
 sector just mentioned. This is represented in (fig. c.) The 
 remote sector then disappeared, and the circular arch diminished, 
 
 Fig. c. Fig. d. Fig. e. 
 
 as in (fig. d) ; and as the inclination of the internal ray to the 
 cusp-ray was further increased, these two luminous portions 
 merged gradually into the two pencils, into which a single ray is 
 divided in the other parts of the crystal. This change is repre- 
 sented in (fig. e). 
 
 Similar observations were made without the lens, by bringing 
 the flame of the lamp near the first surface of the crystal, and 
 forming the converging cone by covering that surface also with a 
 thin metallic plate, perforated with a minute aperture. In this 
 case the line connecting the two minute apertures was adjusted 
 as before, and the phenomena were the same as in the former
 
 CONICAL REFRACTION. 7 
 
 instance, the rays which passed along this line within the crystal 
 forming a diverging cone at emergence. 
 
 In all these experiments the emergent rays were received 
 directly by the eye placed close to the aperture on the second 
 surface. It was obviously desirable, however, to receive them on 
 a screen, and thus to observe the section of the cone at different 
 distances from its summit. After some trials, I effected this with 
 the sun's light, the light of a lamp being too weak for the purpose. 
 The emergent cone being made to fall on a screen of roughened 
 glass, I was enabled to observe its sections at various distances, 
 and therefore with all the advantages of enlargement. The light 
 was sufficiently bright, and the appearance distinct, when the 
 diameter of the section was between one and two inches. 
 
 On examining the emergent cone with a tourmaline plate, I 
 was surprised to observe that one radius only of the circular section* 
 vanished in a given position of the axis of the tourmaline, and 
 that the ray which disappeared ranged through 360 as the 
 tourmaline plate was turned through 180. Thus it appeared that 
 all the rays of the cone are polarized in different planes. 
 
 On examining this curious phenomenon more attentively, I 
 discovered the remarkable law, " that the angle between the planes 
 of polarization of any two rays of the cone is half the angle between 
 the planes containing the rays themselves and the axis" 
 
 Having assured myself of the near truth of this law by experi- 
 ment, I was naturally led to inquire how far it was in accordance 
 with theory ; and on examining Fresnel's theory with this view, I 
 was gratified to find that it led to the very same result. 
 
 According to the known rule, the plane of polarization of any 
 one ray of the emergent cone must bisect the angle contained by 
 the planes passing through tho corresponding normal to the front 
 of the wave and the two optic axes. Now, it can be easily shown 
 that the normals to the wave, at the cusp, surround one of the 
 optic axes, and are inclined to it all round at small angles. For 
 the tangent of the angle which the normals to the circle and 
 ellipse in the plane of xz make with one another is 
 
 ac 
 
 * These sections are not mathematically circular, the line being, in fact, one of the 
 
 fourth order.
 
 8 CONICAL REFEACTION. 
 
 and it can be easily shown that the tangent of the angle which the 
 optic axis makes with the normal to the circle, or the cusp-ray, is 
 
 Now, this is about half the former, since b* = ac, nearly; and 
 
 consequently the optic axis nearly bisects the angle contained by 
 
 the extreme normals in the plane of xz. Hence if A and B be 
 
 the intersections of the two optic axes with the sphere whose 
 
 centre is at the cusp, and 
 
 N the intersection of one 
 
 of the normals at that point 
 
 with the same (fig. 2), the 
 
 angle NA C ranges through 
 
 every magnitude between 
 
 and 360, the arc NA being 
 
 all the time very small. Let the angle NAC be denoted by a, 
 
 and NPC by w, NP being the arch bisecting the angle N\ then 
 
 in the triangle APN, we have 
 
 
 or, since AN is very small, and therefore cos^jY = 1, nearly, 
 cos o> = cos (a - i-ZV), and ta = a- ^N, nearly. 
 
 But, when any side of a spherical triangle is very small in com- 
 parison with the other two, the adjacent angles are together equal 
 to 180 q.p. Consequently, 
 
 N = a, and w = Ja, nearly. 
 
 From this it appears that the angle, which the plane of polari- 
 zation of any ray makes with the plane of the optic axes, is half 
 the angle which the plane passing through the normal and the 
 , near axis makes with the same plane. But this latter angle, it 
 may be easily shown, is very nearly the same as that which the 
 plane passing through the emergent ray and the axis of the cone 
 makes with the plane of the optic axes. Consequently the angle, 
 which the plane of polarization of any ray of the emergent cone
 
 CONICAL REFRACTION. 9 
 
 makes with the plane of the optic axes, is half of that which the 
 plane containing that ray and the axis of the cone' forms with the 
 same plane. 
 
 The general phenomena being observed, it remained to ex- 
 amine the magnitude and position of the emergent cone, and to 
 compare the results with those furnished by theory. For this 
 purpose I viewed the aperture in the second plate through a small 
 telescope, which was moved in a plane nearly perpendicular to the 
 axis of the emergent cone ; and by noting the points at which the 
 light failed, I obtained the magnitude of the section of the cone 
 made by that plane. The distance of this section from the crystal 
 being then measured, the angle of the cone was obtained from the 
 trigonometrical tables, and was found to be very nearly 6. I 
 then placed the flame of a wax taper at the centre of the section, 
 and removing the plate from the second surface of the crystal, 
 found the direction of the ray reflected from the surface. A well 
 defined mark was then placed on this line, at a considerable dis- 
 tance, and the angular distance between the centre of the flame 
 and the mark measured by a sextant, whose centre was brought 
 exactly to the place of the crystal. This angle was found to be 
 31 56' ; and consequently the angle of emergence corresponding 
 to the central rays of the cone was 15 58'. 
 
 Now to compare these results with those of theory. It is a 
 well-known principle of the theory of waves that the direction of 
 a ray incident upon or emergent from a crystal, and the normal 
 to the front of the wave, are always in the same plane perpen- 
 dicular to the surface of incidence or emergence ; and the angles 
 which these two lines make with the perpendicular to the surface, 
 are connected by the known law of the sines ; the index of refrac- 
 tion being the reciprocal of the normal velocity of the wave, or of 
 the perpendicular upon the tangent plane. Now, at the cusp, 
 there are an infinite number of normals to the wave, and conse- 
 quently an infinite number of corresponding emergent rays. Of 
 these the two rays in the plane of the optic axes form the greatest 
 angle, and their directions are determined by those of the normals 
 to the circle and ellipse, which constitute the section of the wave- 
 surface in that plane. If then p' and /" denote the angles of 
 emergence of these rays, t the angle which the normal to the 
 ircle, or cusp-ray, makes with the perpendicular to the surface, 
 a the angle contained by the normals to the circle and ellipse,
 
 10 CONICAL REFRACTION. 
 
 and p the perpendicular from the centre on the tangent to the 
 ellipse at the cusp, we have 
 
 sin p' = - sin t, sin p" = - sin (t - a) ; 
 
 Now in arragonite, according to the determination of M. 
 Rudberg, 
 
 - = 1.5326, i = 1.6863, - = 1.6908 ; 
 a b c 
 
 and substituting these values we find 
 
 - = 1.68708, a - 144'48". 
 P 
 
 These values being introduced in the first two equations, p' and p" 
 will be determined for any given surface of emergence. In this 
 manner Professor Hamilton has found that when t = 0, or the 
 surface of emergence perpendicular to the cusp-ray, p' = 0, and 
 p" = 2 56' 51". And when i = 9 56' 27", or the surface perpen- 
 dicular to the line bisecting the optic axes, p' = 16 55' 27", and 
 p" = 13 54' 49". Accordingly, the difference of these angles, 
 p' - p", which is the extreme angle of the emergent cone, is in the 
 former case 2 56' 51",* and in the latter 3 0' 38". Also, half 
 the sum of these angles, which is the angle of emergence corres- 
 ponding to the axis of the cone, is 15 25' 8". 
 
 Comparing these with the results of observation, it will be 
 seen that they agree nearly with respect to the mean angle of 
 emergence, the difference amounting only to 33' ; whereas the 
 angle of the cone determined by experiment is about double of 
 that furnished by calculation. 
 
 I also measured the angle of the cone by tracing the outline 
 of its section on a screen of roughened glass, when the sun's light 
 was employed instead of that of a lamp. The mean diameter of 
 this section being then accurately ascertained, and the distance of 
 the screen from the aperture measured, the angle was given by 
 
 " It is easily shown that the sine of the angle of the cone, in this case, is generally 
 expressed by the formula
 
 CONICAL REFRACTION. 11 
 
 the tables. Measurements taken in this manner gave for the 
 value of the angle, 6 24', 5 56', 6 22', respectively ; and the 
 mean of these is 6 14', which, like the former measurement, 
 differs very little from the double of the calculated angle. 
 
 The results of observation thus appeared to be at variance 
 with those of theory in two important particulars. In the first 
 place, the emergent rays appeared to form a solid cone, instead of 
 a conical surface ; and in the next, the magnitude of this cone 
 was about double of the expected magnitude. Conceiving that 
 these discrepancies might probably be owing to the rays which are 
 inclined to the cusp-ray at small angles, and which pass by the 
 edge of the aperture, I determined to ascertain the fact by trying 
 the effects of apertures of various sizes. 
 
 I found accordingly that when the aperture was at all con- 
 siderable, such as that formed by a large-sized pin, two concentric 
 circles were seen to surround the axis, the interior of which had 
 about double the brightness of the exterior annulus. And it was 
 remarkable that the light of the interior circle was unpolarized, 
 while that of the surrounding annulus was polarized according to 
 the law already explained. When smaller apertures were used, 
 the inner circle contracted, the breadth of the exterior annulus 
 remaining nearly the same ; until the former was finally reduced 
 to a point in the centre of a fainter circle. When the aperture 
 was still further diminished, a dark space sprung up in the centre, 
 enlarging as the aperture decreased ; until finally, with a very 
 minute aperture, the breadth of this central space increased to 
 about f ths of the entire diameter. 
 
 The phenomena exhibited in these cases assumed the forms 
 represented in figures (/) and (</). (Fig. h) represents the ap- 
 
 O O O 
 
 Fig-/ Fig.y. Fig- A- 
 
 pearance of the section when the line connecting the aperture 
 with the luminous point on the first surface was slightly inclined 
 to the cusp-ray.
 
 12 
 
 CONICAL REFRACTION. 
 
 It is easy to render an account of these various appearances. 
 When the aperture mn (fig. 3) is at all considerable, the rays cm, 
 en, proceeding to its circumference from a point on the first surface, 
 will be sensibly inclined to the cusp-ray, which we shall suppose to 
 be'the line co, connecting the point on the first surface with the 
 
 Fig. 3. 
 
 centre of the aperture. Consequently the interior refracted rays, 
 mq, nr, as well as the exterior, mp, ns, will be inclined outwards ; 
 and it is obvious that there will be a central bright space, limited 
 by the lines mq, nr, each point of which will be illuminated by one 
 interior and one exterior ray. The light in this space, therefore, will 
 have double the intensity of that of the surrounding space ; and 
 as the rays which combine to form it are polarized in planes at 
 
 right-angles to'one another, the resulting light will be unpolarized. 
 When the aperture is diminished, the inclination of the rays mq, 
 nr, to one another is lessened, until finally they are reduced to 
 parallelism, and the central bright space contracts to a point. 
 This is represented in (fig. 4). When the aperture is still further
 
 SICAL KK FRACTION. 13 
 
 diminished, the rays mq, nr, become inclined inwards, and cross 
 (fig. 5). It is obvious that beyond the point of intersection there 
 will be a dark space illumined by no ray whatever ; and as in the 
 surrounding annulus there is no meeting of rays oppositely 
 polarized, the whole of the light icitt le polarized, and according to 
 the law already explained. With a yet diminished aperture, the 
 
 Fig. 5. 
 
 rays mq, nr, approach to parallelism with the exterior rays, ns, mp; 
 and the central dark space enlarges, and approaches to equality 
 with the outer and limiting cone. Thus the annulus of light in 
 any section is diminished indefinitely in breadth, and the cone 
 approaches to a mathematical surface. 
 
 Now, if we assume that the divergence of the two refracted rays 
 in this plane, corresponding severally to the rays cm, co, en, is the 
 same, as must be nearly the case, it will follow that the angle of 
 the true cone, which would arise from the single ray co, is half the 
 sum of the angles of the exterior and interior surfaces of the conical 
 annulus ; and that when a bright circle appears in the centre, as 
 is the case with a considerable aperture, the dark space must be 
 considered as negative, and the true angle is half the difference of 
 the observed angles. 
 
 From this it follows that when the central bright space is re- 
 duced to a point, the true angle is just half the observed. Now 
 this was very nearly the case in the experiments from which the 
 measures were taken ; consequently the corrected angle, deduced 
 from these measures, coincides very nearly with that assigned by 
 theory. 
 
 Two other measurements, taken since with a more direct refer- 
 ence to this correction, were as follows : 
 
 1. Distance of screen from the aperture on the second surface 
 of the crystal = 19 - 3 half inches. Mean diameter of section of
 
 14 CONICAL REFRACTION. 
 
 exterior cone = 1 '27. Mean diameter of interior = 0'55. Corrected 
 angle of cone thence computed = 2 44'. 
 
 2. Distance of screen = 11*9. Mean diameter of section of ex- 
 terior cone = 0*93. Mean diameter of interior = 0'41. Computed 
 angle of cone = 3 14'. 
 
 The mean of these two measurements is 2 59'. 
 
 Inasmuch as the cusp-ray, within the crystal, corresponds to a 
 cone of rays without, it is evident that there must be a converging 
 cone incident on the first surface, equal to that which diverges 
 from the second. With a view to determine its magnitude, I 
 placed a kind of rough micrometer, consisting of two moveable 
 metallic plates, immediately before the lens ; and closed the plates 
 until, on looking through the aperture on the second surface, I 
 could see them touching the circumference of the annular section. 
 The diameters of the interior and exterior circumferences of this 
 section, at the distance of the lens, being thus ascertained, and the 
 focal length of the lens measured, the corrected angle of the cone 
 was found. The mean of three measurements taken in this manner 
 gave for this angle 3 47'. But the methods by which this last 
 result was obtained do not seem susceptible of much accuracy. 
 
 Before I conclude this part of the subject, I may observe that 
 an interesting variation in the phenomena is obtained by substitut- 
 ing a narrow linear aperture for the small circular one, in the plate 
 which covers the first surface of the crystal that surface being 
 close to the lamp. The linear aperture is to be so fixed, that the 
 plane passing through it and the aperture in the plate next the 
 eye shall be the plane of the optic axes. In this case, according 
 to the received theory, all the rays transmitted through the two 
 apertures should be refracted doubly in the plane of the optic axes, 
 so that no part of the line should appear enlarged in breadth on 
 looking through the second aperture ; whereas, according to Pro- 
 fessor Hamilton's beautiful conclusion from the same theory, the 
 (Hisp-ray should be refracted in every possible azimuth. I found 
 accordingly that the luminous line was un-dilated, except in the 
 direction corresponding to that of the cusp-ray ; and that in the 
 neighbourhood of this direction its boundaries were no longer rec- 
 tilinear, but swelled out in the form of an oval curve (fig. i}. 
 
 When a very minute aperture was used on the surface next the 
 eye, in this experiment, the phenomenon was rendered much more 
 remarkable. The swelling curves in this case were separated by a
 
 CONICAL REFRACTION. 15 
 
 considerable dark interval, and the luminous line was prolonged 
 into this dark space, terminating abruptly near its centre. This 
 
 Fig. i. 
 
 appearance is represented in (fig. k). When the plate next the 
 eye was slightly shifted, so that the plane passing through the two 
 
 Fig. *. 
 
 apertures no longer coincided accurately with the plane of the optic 
 axes, the curves rapidly changed, preserving however, in all cases, 
 
 Fig. I. 
 
 the form of the conchoid, whose pole was the projection of the axis 
 of the emergent cone, and asymptote the line on the first surface 
 
 Fig. m. 
 
 ifigs. /, m). It is easy to show that these results are in accordance 
 with theory.
 
 16 CONICAL REFRACTION. 
 
 The second kind of conical refraction, whose existence has been 
 anticipated by Professor Hamilton, depends (it will be remembered) 
 on the mathematical fact, that the wave-surface is touched in an 
 infinite number of points, constituting a small circle of contact, by 
 a single plane parallel to one of the circular sections of the surface 
 of elasticity. It takes place when a single external ray falls upon a 
 biaxal crystal in such a manner that one refracted ray may coin- 
 cide with an optic axis. When this is the case, there will be a cone 
 of rays within the crystal, determined by lines connecting the 
 centre of the wave with the points of the periphery of the circle of 
 contact. The angle of this cone is equal to 
 
 tang 
 
 and its numerical value in the case of arragonite is 1 55', assum- 
 ing the values of the three indices as determined for the ray E by 
 Professor Eudberg (see page 10). 
 
 As the rays constituting this cone will be refracted at emer- 
 gence in a direction parallel to the incident ray, they will form a 
 small cylinder of rays in air. This cylinder, it will be seen, is in 
 all cases extremely small ; for the diameter of its section made by 
 the surface of emergence subtends an angle of 1 55' only, at a dis- 
 tance equal to the thickness of the crystal. Hence the experiments 
 required to detect its existence and measure its magnitude demand 
 more care and precision than those already described. The inci- 
 dent light was that of a lamp placed at some distance ; and in 
 order to reduce as much as possible the breadth of the incident 
 beam, it was constrained to pass through two small apertures, the 
 first of which was in a screen placed near the flame, and the second 
 perforated in a thin metallic plate adjoining to the first surface of 
 the crystal. Under ordinary circumstances, it is obvious, the inci- 
 dent rays will be divided into two within the crystal, and these will 
 emerge parallel from the second surface. I was able to distinguish 
 these two rays by the aid of a lens ; and turning the crystal 
 slowly, so as to vary the incidence gradually, I at length observed 
 that there was a position in which the two rays changed their rela- 
 tive places rapidly, on any slight change of incidence, and appeared 
 at times to revolve round one another, as the incidence was altered. 
 Being convinced that the ray was now near the critical incidence, 
 I changed the position of the crystal, with respect to the incident
 
 CONICAL REFRACTION. 17 
 
 ray, very slowly ; and after much care in the adjustment, I at last 
 saw the two rays spread into a continuous circle, whose diameter 
 was apparently equal to their former interval. 
 
 This phenomenon was exceedingly striking. It looked like a 
 small ring of gold viewed upon a dark ground ; and the sudden and 
 almost magical change of the appearance, from two luminous points 
 to a perfect luminous ring, contributed not a little to enhance the 
 interest. 
 
 The emergent light, in this experiment, being too faint to be 
 reflected from a screen, I repeated the experiment with the sun's 
 light, and received the emergent cylinder upon a small piece of 
 silver-paper. I could detect no sensible difference in the mag- 
 nitude of the circular sections at different distances from the 
 crystal. 
 
 When the adjustment was perfect, the light of the entire an- 
 nulus was white, and of equal intensity throughout. But when 
 there was a very slight deviation from the exact position, two 
 opposite quadrants of the circle appeared more faint than the other 
 two, and the two pairs were of complementary colours.* The light 
 of the circle was polarized, according to the law which I had be- 
 fore observed in the other case of conical refraction. In this in- 
 stance, however, the law was anticipated from theory by Professor 
 Hamilton. 
 
 I measured the angle of incidence by a method similar to that 
 already employed for the emergent ray in the former case ; and 
 found it to be 15 40'. This determination is, for many reasons, 
 capable of much greater accuracy than the other ; and was probably, 
 in this instance, very near the truth. 
 
 In order to compare it with the result of theory, it is to be 
 observed that the optic axis is a normal to the wave-surface, and, 
 therefore, the corresponding incident ray will be given by the 
 ordinary law of the sines, the index of refraction being the mean 
 jin/c.r of the crystal. Now, the angle which the normal to the cir- 
 cular section of the surface of elasticity, or the optic axis, makes 
 with the axis of x, or the perpendicular to the surface, is equal to 
 
 tan' 1 / C T ; and its numerical value, in the case of arragonite, 
 
 \fl a -b-i 
 
 * This part of the phenomenon appears to be explained by the non-coincidence of tho 
 optic axes for the rays of different colours. 
 

 
 18 CONICAL REFRACTION. 
 
 is 9 1'. We have then sin t = T6863 sin (9 1') ; from which we 
 find i = 1519'. The difference between this and the observed 
 angle is 21'. 
 
 In order to measure the angle of the cone, I was compelled to 
 employ a method somewhat indirect, but, I think, susceptible of 
 considerable accuracy. As the aperture on the first surface of the 
 crystal must have some physical magnitude, it is obvious that, 
 instead of a cone of mathematical rays within the crystal, there 
 will be in all cases a cone of cylindrical pencils, overlapping one 
 another near the point of divergence ; and that the diameter of 
 these pencils will be equal to the diameter of the aperture. Now, 
 I tried a number of apertures, until I found one with which these 
 cylindrical pencils just separated at the second surface of the 
 crystal. It is evident that, in this case, the interval between the 
 axes of the cylinders at the surface of emergence is just equal to 
 the diameter of one of them, or to the diameter of the aperture. I 
 had then only to measure the aperture itself. This was effected 
 by the aid of a micrometer divided to the l-500th of an inch, 
 placed along with the aperture before a compound microscope ; and 
 it was found to be '016 of an inch. This therefore was the diameter 
 of the oblique section of the cone made by the surface of emergence ; 
 and the diameter of the circular section at the same distance was 
 016 cos 9, since the axis of the cone makes an angle of 9 with 
 the normal to the faces of the crystal. The perpendicular thick- 
 ness of the crystal was 0'49 of an inch ; and therefore the thickness 
 
 0*4Q 
 
 estimated in the direction of the axis of the cone was -5-. 
 
 cos 9 
 
 From these data the angle of the cone was calculated by the tables, 
 and found to be 1 50' ; a result which differs from the theoretical 
 angle by 5' only.
 
 II. REPORT OX THE PROGRESS AND PRESENT STATE OF 
 PHYSICAL OPTICS. 
 
 Report of the British Association for the Advancement of Science for 1834. 
 
 Ix the Report which I have the honour to submit to the Associa- 
 tion, I have attempted to consider in some detail the present state 
 of our knowledge with regard to the physical theory of light, and 
 the successive advances which have, in late years, been made 
 towards its establishment. The method which I have thought 
 it expedient to adopt in this review has been to take, in the first 
 instance, a rapid survey of the several leading classes of optical 
 phenomena, which the labours of experimental philosophers have 
 wrought out in such rich profusion, and afterwards to examine 
 how far they are reducible to one or other of the two rival 
 theories which have alone advanced any claim to our considera- 
 tion. This is, in fact, the only way in which the truth of a 
 physical theory can be established ; and the argument in its favour 
 is essentially cumulative. 
 
 But in making this comparison it is not enough to rest in 
 vague explanations which may be moulded to suit any theory. 
 Whatever be the apparent simplicity of an hypothesis whatever 
 its analogy to known laws it is only when it admits of mathe- 
 matical expression, and when its mathematical consequences 
 can be numerically compared with established facts, that its 
 truth can be fully and finally ascertained.* Considered in this 
 point of view, the wave-theory of light seems now to have reached 
 
 * C'est en tirant des formules les consequences les plus subtiles et les plus eloigne'es 
 des principes, puis allant les verifier par 1' experience, que 1'on peut r6ellement s' assurer 
 si une theorie est vraie ou fausse, et si Ton doit s'y confier comme & un guide fidele, 
 ou la rejeter comme un systeme trompeur. Biot, Traite de Physique, torn, i., p. xiv. 
 
 c2
 
 20 REPORT ON PHYSICAL OPTICS. 
 
 a point almost, if not entirely, as advanced as that to which the 
 theory of universal gravitation was pushed by the single-handed 
 efforts of Newton. Varied and comprehensive classes of phenomena 
 have been embraced in its deductions ; and where its progress has 
 been arrested, it has been owing in a great degree to the imper- 
 fections of that intricate branch of analysis by which it was to 
 be unfolded. The principles of the theory of emission, on the 
 other hand, have in comparatively few instances been mathemati- 
 cally expressed and developed ; and accordingly this theory pre- 
 sents but rarely those points of contact with experimental truth by 
 which alone it can be judged. 
 
 This signal difference in the present state of the two theories 
 has been by some ascribed to a difference in the intellectual power 
 by which they have been worked ; and it has been said that had 
 the Newtonian theory been cultivated with the same zeal and 
 talent as the Huygenian, it might have had equal triumphs to 
 boast of. This position, I confess, appears to me altogether un- 
 tenable. With respect to the implied fact, it may be enough to 
 observe that Newton and Laplace were both engaged on one side 
 of the question ; and I believe I may add that among the sup- 
 porters of the wave-theory of light there are few who have not had 
 to encounter early predilections in favour of the theory of emission. 
 The nature and laws of projectile movement are far more familiar 
 to every lover of mechanical philosophy than those of vibratory 
 propagation ; and the triumphant career of the former branch of 
 this science, in its application to the movements of the heavenly 
 bodies, is in itself sufficient to induce everyone to lean to a theory 
 which proposes to account for the phenomena of light on similar 
 principles. As to the opinion itself, it seems highly improbable, to 
 say the least, that two theories so widely separated should run hand 
 in hand in their explanation of phenomena. There is indeed one case, 
 and that a striking one, of this kind : the fundamental laws of 
 reflexion and refraction are exact and necessary consequences of 
 each of these theories; but I believe their history affords no 
 parallel instance. 
 
 An unfruitful theory may, however, be fertilized by the addi- 
 tion of new hypotheses. By such subsidiary principles it may be 
 brought up to the level of experimental science, and appear to 
 meet the accumulating weight of evidence furnished by new phe- 
 nomena. But a theory thus overloaded does not merit the name.
 
 REPORT ON PHYSICAL OPTICS. 21 
 
 It is a union of unconnected principles, which can at best be con- 
 sidered but as supplying the materials for a higher generalization. 
 Its very complexity furnishes a presumption against its truth ; for 
 the higher we are permitted to ascend in the scale of physical in- 
 duction, the more we perceive of that harmony, and unity, and 
 order, which must reign in the works of One Supreme Author. 
 The theory of emission, in its present state, exhibits all these 
 symptoms of unsoundness ; but there is something stronger than 
 mere presumption against it. It will appear, I think, upon a fair 
 review, that in almost every instance in which it has been de- 
 veloped, its consequences are at variance with facts ; and the proof 
 of its insufficiency seems even stronger than the positive evidence 
 in favour of the rival theory. 
 
 In proceeding to the consideration of these arguments, I have 
 found it necessary to deviate from the arrangement which a strictly 
 theoretical view of the subject would naturally suggest. The re- 
 lation of theory to phenomena, which I propose to consider, obliges 
 me to examine the latter in the groups in which they have been 
 usually brought together, and under which their laws have been 
 investigated. I propose, therefore, to divide the following Eeport 
 into two parts, of which the first will treat of unpolarized, and the 
 second of polarized light. In the former I shall consider sepa- 
 rately 
 
 1. The propagation of light, and the principle of interference ; 
 
 2. The reflexion and refraction of light ; 
 
 3. Diffraction; 
 
 4. The colours of thin and thick plates^ 
 
 The second part will comprise 
 
 1. The polarization of light, and the principle of transversal mira- 
 
 tions ; 
 
 2. The reflexion and refraction of polarized light; 
 
 3. Double refraction ; 
 
 4. The colours of crystallized plates. 
 
 Many subjects of high interest are omitted in this arrangement, 
 as being but remotely connected with the leading object of the 
 present Report. I have left wholly untouched, for this reason, 
 that branch of optical science which is sometimes denominated 
 " mathematical optics," or the development of the fundamental
 
 22 REPORT ON PHYSICAL OPTICS. 
 
 laws of reflexion and refraction. The phenomena of vision have 
 been in like manner omitted, as involving also the science of phy- 
 siology ; and the relations of light to other agents, as heat, elec- 
 tricity, and magnetism, because these relations are as yet little 
 understood, and in the present state of the kindred sciences, the 
 science of light can hope to derive little aid from their examina- 
 tion. These interesting subjects would, each of them, well merit a 
 separate consideration. 
 
 PART I. UNPOLARIZED LIGHT. 
 I. Propagation of Light. Principle of Interference. 
 
 The first property of light which claims our notice is its pro- 
 gressive movement. Light, we know, travels from one point of 
 space to another in time, with a velocity of about 195,000 miles 
 in a second. The inquiry concerning the mode of this propaga- 
 tion involves that respecting the nature of light itself. 
 
 There are two distinct and intelligible ways of conceiving such 
 a motion. Either it is the self -same body which is found at dif- 
 ferent times in distant points of space ; or there are a multitude 
 of moving bodies, occupying the entire interval, each of which 
 vibrates continually within certain limits, while the vibratory mo- 
 tion is communicated from one to another, and so advances uni- 
 formly. Nature affords numerous examples of each of these modes 
 of propagated movement ; and in adopting one or other to account 
 for the phenomena of light, we fall upon one or other of the two 
 rival systems the theories of Newton and of Huygens. 
 
 The Newtonian theory, in the shape in which it is usually pre- 
 sented, is undoubtedly simpler in conception than its rival ; but 
 this simplicity is only apparent. Newton himself was far too 
 clear-sighted to suppose that the forces of attraction and repulsion, 
 by which the molecules of light were supposed to be refracted and 
 reflected, were adequate to account for all the phenomena ; and it 
 is remarkable that, when he proceeds to speculate on the physical 
 theory of light, he has found it necessary to admit all the appa- 
 ratus required in the theory of waves. In fact, Newton felt, and 
 distinctly stated, that the vibrations of an ethereal medium were 
 necessary in his hypothesis,* although he denied that those vibra- 
 
 * Phi!. Tram. 1672.
 
 PROPAGATION OF LIGHT PRINCIPLE OF INTERFERENCE.' 23 
 
 tions constituted light. He has even gone further, and asserted 
 that they were the chief and essential parts of that hypothesis, 
 the molecules emitted from luminous bodies only performing the 
 office of exciting these vibrations, as stones flung into water pro- 
 duce waves.* On the other hand, the molecules themselves are 
 supposed to be emitted by a vibratory motion of the parts of the 
 luminous body f the same vibratory movement, though acting 
 with a different energy, in which he supposes heat to consist. It 
 would appear, then, that Newton assumed too much, and that he 
 erred against his own valuable rule " Causas rerum naturalium 
 -non plut'cs admitti debere" &c. Had he simply left out the mole- 
 cular part of his hypothesis, and supposed that the vibrations of 
 his ethereal medium were directly excited by those of the luminous 
 body, his theory would have resolved itself into that of Huygens 
 and of Hooke. It may be observed, in connexion with this sub- 
 ject, that Newton seems actually to have admitted the wave-theory 
 with respect to radiant heat ; and that he supposed it to be pro- 
 pagated, not by the translation of material particles, but by the 
 vibrations of an ethereal medium.^ 
 
 The peculiar part of the theory of emission the supposition 
 that the rays of light are bodies projected with a great velocity 
 would seem to offer an easy criterion of its truth. If the weight 
 of a molecule of light amounted to one grain, its momentum would 
 equal that of a cannon ball 150 pounds in weight, and moving 
 with the velocity of 1000 feet in a second. The weight of a single 
 molecule may be supposed many millions of times less than this ; 
 but, on the other hand, millions of such molecules may be made to 
 act together, by concentrating them in the foci of lenses or mirrors, 
 and the effects of their impulse might, it was expected, be thus 
 rendered sensible. This easy test of the materiality of light was long 
 since appealed to. The experiments of Homberg seemed to have 
 established the existence of a sensible impulsive effect ; but when 
 these experiments were repeated with more caution by Mairan and 
 l)ufay, they conducted to the opposite conclusion. The results 
 
 * " Were I to assume an hypothesis, it should be this, if propounded more gene-- 
 rallyso as not to determine what light is, further than that it is something or other 
 capable of exciting vibrations in the ether : for thus it will become so general, and compre- 
 hensive of other hypotheses, as to leave little room for new ones to be invented." 
 Hirch's II i*tr>/ <>f the I{ ;/1 .SV /<///, vol. Hi. p. 249. 
 
 f Opt ',<*, Query S. ; Oy,//V.s, (Jui-ry IS.
 
 24 REPORT ON PHYSICAL OPTICS. 
 
 obtained by Michell at a later period, and with the aid of a more 
 sensitive apparatus than any before employed, seemed to be de- 
 cisive in favour of the materiality of light.* The effects observed 
 in these experiments, however, have been with much probability 
 referred to aerial currents, produced by unequal temperature, or 
 even to a difference in the elastic force of the air in contact with 
 the opposite surfaces of the body acted on. f The subsequent ex- 
 periments of Mr. Bennett were made under circumstances far more 
 favourable ; and in particular, having been repeated in a vacuum, 
 they are independent of the sources of error now alluded to. Their 
 result was conclusive as to the non-existence of a sensible effect. + 
 
 The objection to the materiality of light, arising from its want 
 of sensible momentum, was first urged by Franklin. Horsley at- 
 tempted to remove the difficulty ; but his laborious arithmetical 
 calculations only go to prove that the particles of light, if ma- 
 terial, must be of extreme minuteness. It must at the same time 
 be confessed that objections of this nature are entitled to little 
 weight. It is easy to attribute to the molecules of light a minute- 
 ness sufficient to evade any means that we possess of detecting 
 their inertia by their effects upon other bodies; and in whatever 
 point of view we regard the phenomena of optics, we are forced to 
 contemplate quantities immeasurably smaller than any to which the 
 imagination has been accustomed. 
 
 The aberration of the light of the fixed stars, resulting from the 
 motion of the earth and that of light, is an easy consequence of 
 the theory of emission, in which these motions are conceived to 
 subsist independently. In order to account for the phenomenon 
 in the theory of waves, it seems necessary to assume that the ether 
 which encompasses our globe does not participate in its motion ; so 
 that the ethereal current produced by this relative motion must be 
 supposed to 'have a free passage through the solid mass of the 
 earth; or that, in the words of Young, "the luminiferous ether 
 pervades the substance of all material bodies with little or no re- 
 sistance, as freely perhaps as the wind passes through a grove of 
 trees." || Fresnel has maintained the same opinion, and, startling 
 
 * Priestley's History of Optics, p. 387. 
 
 t Young " On the Theory of Light and Colours," Phil. Trans. 1801. 
 
 t Phil. Tram. 1792. 
 
 I Ibid. 1770. I. 
 
 II " Experiments and Calculations relative to Physical Optics," Phil. Trans. 1803.
 
 PROPAGATION OF LIGHT PRINCIPLE OF INTERFERENCE. 25 
 
 as the position seems at first, he has very clearly shown that no 
 fair argument can be advanced against it, founded on the opacity 
 of the mass which the ether is supposed to permeate.* 
 
 The discoveries of Bradley and Roemer, when compared toge- 
 ther, have led to a further and most important conclusion respect- 
 ing light namely, that its velocity is one and the same, whatever 
 be the luminous origin, the light of the sun, the fixed stars, the 
 planets and their satellites, being all propagated with the same 
 swiftness. This conclusion must be allowed to present a for- 
 midable difficulty in the theory of emission. Laplace has shown 
 that if the diameter of a fixed star were 250 times as great as that 
 of our sun, its density being the same, its attraction would be suf- 
 ficient to destroy the whole momentum of the emitted molecules, 
 and the star would be invisible at great distances, f With a 
 smaller mass there will be a corresponding retardation ; so that 
 the final velocities will be different, whatever be the initial. The 
 suggestion of M. Arago seems to offer the only means of avoiding 
 this difficulty. It may be supposed that the molecules of light are 
 originally projected with very different velocities ; but that among 
 these velocities there is but one which is adapted to our organs of 
 vision, and which produces the sensation of light. This supposi- 
 tion seems to be supported by the discoveries of Herschel, Wol- 
 laston, and Bitter, respecting the invisible rays of the spectrum ; 
 but it does not appear to be easily reconciled with any hypothesis 
 which we are able to frame respecting the nature of vision. This 
 uniformity of velocity, on the other hand, is a necessary conse- 
 quence of the principles of the wave-theory. The velocity with 
 which vibratory movement is propagated in an elastic medium de- 
 pends solely on the elasticity of that medium, and on its density ; 
 and if these be uniform in the vast spaces which intervene between 
 the material bodies of the universe and it is not easy to suppose it 
 otherwise the velocity must be the same, whatever be the origi- 
 nating source. 
 
 The rectilinear motion of light has long been urged in favour 
 of the theory of emission, and against the theory of waves. If 
 light consists in the undulations of an elastic fluid, it has been said, 
 it should be propagated in all directions from every new centre, 
 
 * " Sur 1' Influence du Mouvement terrestre dans quelqut-8 Phcnomenes d'Optiquo, " 
 Annales de C/iitnie, torn. ix. 
 t Zach, Ephem. t iv. 1.
 
 26 REPORT ON PHYSICAL OPTICS. 
 
 and so bend round interposed obstacles. Thus, luminous objects 
 should be visible, "*even when an opaque body is between them and 
 the eye, just as sounding bodies are heard, though a dense body 
 intervene between them and the ear. To this objection, which 
 was first insisted on by Newton, * a full answer has been given. 
 The phenomena of diffraction, and especially the interior fringes 
 in the shadow of narrow opaque bodies, prove that light does bend 
 round obstacles, and deviate perceptibly from the rectilinear course. 
 When the obstacle is of considerable dimensions, the intensity of 
 the light decreases, indeed, very rapidly within the edge of the 
 geometric shadow ; so that at a very small distance from that 
 edge it is no longer perceptible. But the darkness does not arise 
 from the absence of luminiferous waves, but from the mutual 
 destruction of those sent there. In fact, if the surface of the wave 
 when it reaches the obstacle be divided into any number of small 
 portions, the motion of the ether at any point behind it is, by the 
 principle of Huygens, the sum of all the motions produced there 
 by these several portions, considered as separate centres of dis- 
 turbance ; and it is easy to show that, when the distance of the 
 point in question from the obstacle is a large multiple of the 
 length of a wave, the magnitude of this resultant must diminish 
 rapidly within the shadow, and the light become insensible when 
 the line drawn from that point to the edge of the screen is in- 
 clined at a small angle to the normal to the front of the wave. 
 The accurate calculation of the intensity, in this and other similar 
 cases, has been made by Fresnel by the aid of the principle of 
 interference, and the result is found to agree in the most complete 
 manner with observation, f 
 
 The same principles apply to the aerial waves which constitute 
 sound ; and these too should present analogous phenomena. But 
 the scale is widely different. The length of an aerial wave is more 
 than 10,000 times greater than that of an ethereal undulation ; 
 and the distance of the ear from the obstacle must be augmented 
 in the same proportion, in order that the same conclusions may be 
 applicable to the two cases. 
 
 According to this account, then, the right-lined propagation of 
 the rays of light is a consequence of the principle of interference, 
 combined with the principle of Huygens. A very different view 
 
 * Optics, Query 28. 
 
 t " Memoire sur la Diffraction," Memoires de V Ltxtitut, torn. v.
 
 PROPAGATION OP LIGHT PRINCIPLE OF INTERFERENCE. 27 
 
 of the subject, however, has been presented by M. Poisson, in a 
 memoir on the propagation of motion in elastic fluids read before 
 the French Academy in the year 1823.* The elasticity of the 
 fluid being supposed the same in all directions, the velocity of 
 propagation will be also the same, and consequently the waves 
 spherical. The absolute velocities of the molecules themselves, 
 however, will be very different. M. Poisson finds that when the 
 original disturbance takes place only in one direction, the velocity 
 of the molecules will be indefinitely small in all directions inclined 
 to it at finite angles, so that the motion will not be sensibly pro- 
 pagated except in that direction. This diminution of intensity, he 
 finds, will be greater the more rapid the velocity of propagation ; 
 and it is in this manner only, he concludes, that we can account 
 for the rectilinear motion of light in the wave-theory. This con- 
 clusion, however, M. Fresnel has shown, is contradicted by the 
 ordinary phenomena of diffraction ; and he has adduced theoretical 
 reasons, drawn from the principle of the coexistence of small mo- 
 tions, to prove that it cannot hold in any fluid whatever, but that 
 the molecules are in all cases disturbed in a sensible manner in 
 directions very much inclined to that of the original vibrations.f 
 
 The principle of the superposition of small motions, which has 
 been more than once adverted to, is an immediate consequence of 
 the linearity of the original equation of partial differences which 
 determines the law of vibration of an ethereal particle. The 
 complete integral of this question will contain, in general, a term 
 for every distinct original disturbance ; and the total disturbance 
 will be the sum of all the partial disturbances due to each cause 
 acting separately. The partial disturbances may, however, con- 
 spire, or be opposed ; so that in the case of two such disturbances, 
 for example, the second may have the effect either of augmenting 
 or diminishing the first, and the absolute velocity of the ethereal 
 molecules may be increased, or lessened, or even wholly destroyed 
 by the union. In fact, if the form of the function which expresses 
 the wave-disturbance be assumeo} to be that by which the law of 
 vibration of the cycloidal pendulum is represented, the sum of 
 two coexisting disturbances will be a single disturbance of the 
 same form, provided the component undulations have the same 
 length ; and the effect of two such coexisting undulations will be a 
 single undulation of the same length, but differing in the position 
 
 * Aiinnlex de Chiinie, torn. xxii. t /*W. torn, xxiii.
 
 28 REPORT ON PHYSICAL OPTICS. 
 
 and magnitude of the space of greatest vibration from either of 
 the components. The magnitude of the resulting vibration may be 
 the sum, or difference, of those of the component vibrations, or it 
 may have any value intermediate to these limits. When the com- 
 ponent vibrations are equal, the resultant may even vanish altoge- 
 ther ; and two lights of equal intensity, when added together, will 
 produce darkness, provided that the interval of retardation of 
 one wave on the other is an odd multiple of the length of half a 
 wave. 
 
 This important consequence of the theory of waves the princi- 
 ple of interference of the rays of light was first distinctly stated 
 and established by Dr. Thomas Young, although some of the facts 
 by which its truth is experimentally confirmed were known to 
 Grimaldi.* The general calculation of the intensity of the result- 
 ing light, for any relative position of the interfering waves, is due to 
 Fresnel, and has been followed out and developed by Sir John 
 Herschel in his valuable Essay on Light. When a beam of homo- 
 geneous light is transmitted through two small apertures in a 
 card, or plate of metal, the light will diverge from each as from a 
 new centre. If the two apertures are close together, and the 
 diverging pencils received on a reflecting surface, a series of 
 parallel straight bands is observed, perpendicular to the line con- 
 necting the apertures, and separated by intervals absolutely dark. 
 That these alternations of light and darkness are produced by the 
 mutual action of the two pencils, Young proved by the fact that 
 when one of the beams is intercepted, the whole system of fringes 
 instantly disappears, and the dark intervals recover their former 
 brightness. 
 
 The experiment of Fresnel is still more satisfactory. In this 
 important and instructive experiment, the fact of interference is 
 placed beyond all question. The two pencils proceed from one 
 common origin, and are separated simply by reflexion at plane 
 surfaces, without any attending circumstance which can, by possi- 
 bility, be supposed to influence the result. The phenomenon is 
 thus divested of everything non-essential, and it becomes impos- 
 sible to hesitate about its nature. But the accordance of theory 
 and experiment is maintained, not only in the general features of 
 
 * This ingenious philosopher even stated explicitly that an illuminated body may 
 be rendered darker by the addition of light, and adduced a simple experiment in proof 
 of it. Phyiico-Mathesis de Lumine. Bologna, 1665.
 
 PROPAGATION OF LIGHT PRINCIPLE OP INTERFERENCE. 29 
 
 the phenomenon, but even in its minutest details. The distances 
 of the points of each fringe from the two foci of reflected rays 
 should, according to theory, differ by a constant quantity that 
 constant being an odd multiple of the length of half a wave for 
 the dark fringes, and an even multiple of the same quantity for 
 the bright ones. Hence the fringes should be propagated in 
 hyperbolic lines, whose foci are the foci of the reflected pencils ; 
 and the most accurate measurements have shown that it is so. 
 The constant differences just alluded to are far too minute to be 
 directly measured ; but they can be calculated with great accu- 
 racy, when the distances of the successive bands from the central 
 one have been obtained. The latter distances have been deter- 
 mined by Fresnel with much nicety by micrometrical measure- 
 ments; and the lengths of the waves of each species of simple 
 light, thence computed, agree in the most satisfactory manner with 
 the values of the same quantities as deduced from the observation 
 of Newton's rings. 
 
 The central fringe is formed at those points in arriving at 
 which the two pencils have traversed equal paths ; and as its posi- 
 tion is therefore independent of the length of a wave, the rays of 
 all colours will be united there, and the fringe itself will be ichite, 
 or colourless. Such is the fact, as described by Fresnel himself, 
 and by most observers who have repeated the experiment. Mr. 
 Potter states, however, as the result of his observations, that the 
 central fringe may be seen both black and white, although more 
 frequently the former ; and he urges the fact in opposition to the 
 wave -theory.* But it seems premature to draw any inference 
 from such experiments, until the circumstances which have oc- 
 casioned the variation in the results have been fully investigated 
 and understood. 
 
 The interference of the rays of light has, since the decisive ex- 
 periment of Fresnel, been admitted on all hands ; and the phe- 
 nomena which were previously explained on the Newtonian 
 hypothesis of the " fits of easy reflexion and transmission" are 
 now, by most of the advocates of the Newtonian theory, referred 
 to this simpler and more fertile principle. This principle is, it 
 has been stated, an immediate and necessary consequence of the 
 wave-theory, and its experimental establishment must be regarded 
 as a weighty argument in favour of that theory. It now remains 
 
 Phil. Mag. (3rd Series), vol. ii. p. 280.
 
 :)() REPORT ON PHYSICAL OPTICS. 
 
 to inquire whether an account can be given of it in the theory of 
 emission. 
 
 The molecules of light cannot be supposed to exert any mutual 
 influence ; for the regularity of the laws of reflexion and refraction 
 compels us to consider them as independent, and each, separately, 
 the subject of those forces from which, in the theory of emission, 
 these laws are derived. The phenomenon of interference may, 
 however, be plausibly accounted for by the vibrations of the optic 
 nerve, produced by the impulse of the rays of light upon the re- 
 tina, and by the accordance or discordance of these vibrations 
 when caused by two interfering pencils. On this supposition, 
 which was suggested by Dr. Toung himself, the intensity of the 
 light will depend on the relation between the time of vibration of 
 the optic nerve and the interval of the impulses of the succeeding 
 particles. If this interval be equal to the time of vibration, or to 
 any multiple of it, the second impulse will add its effect to that of 
 the first, and the motion be accumulated. It will, on the other 
 hand, be destroyed, if the second impulse follows the first at an in- 
 terval equal to half that time. 
 
 It is here assumed that the emitted particles succeed one 
 another at equal intervals, as will be the case if their emission be 
 owing (as Newton supposed it to be) to a vibratory motion of the 
 parts of the luminous body. But we must assume further that the 
 intervals of emission vary with the nature of the particles, in the 
 light of different colours ; or that all the red-making particles (to 
 use an expression of Newton) are emitted at one certain interval 
 all the blue-making at another and so for each different species of 
 simple light. Hence the vibrations of the parts of the luminous 
 body must be of different periods for the light of different colours. 
 This is, in truth, a part, and a necessary, part, of the theory of 
 waves ; but it has no connexion whatever with the principles of the 
 rival theory. 
 
 II. Reflexion and Refraction of Light. 
 
 To account for the phenomena of reflexion and refraction it is 
 supposed, in the Newtonian theory, that the particles of bodies and 
 those of light exert a mutual action ; that, when they are nearly 
 in contact, this action is attractive that at a distance a little 
 greater, the attractive force is changed into a repulsive one, and 
 that these attractive and repulsive forces succeed one another pro-
 
 REFLEXION AND REFRACTION OF LIGHT. IU 
 
 bably for many alternations. The absolute values, or intensities, 
 of these forces are different in different bodies; but the form of 
 the law, or the function of the distance by which they are ex- 
 pressed, is assumed to be the same for all. * From these postu- 
 lates Newton has rigorously deduced the laws of reflexion and 
 refraction. The problem is the first in which the effects of that 
 important class of forces acting only at insensible distances have 
 been submitted to calculation ; and the solution is regarded by 
 M. Poisson as forming an era in the history of science. 
 
 The reflexion of light at the exterior surface of dense media is 
 ascribed to the repulsive force ; refraction, and internal reflexion, 
 to that inner attractive force which extends up to actual contact. 
 The outermost sphere of action of every body, in this theory, is ne- 
 cessarily attractive, as well as the inmost ; for, were it otherwise, 
 no ray could enter, or emerge from, the medium at an extreme 
 incidence. Sir David Brewster has made an ingenious use of this 
 principle to explain the remarkable fact noticed by Bouguer, that 
 water is more reflective than glass at oblique incidences. 
 
 But though the theory of emission is perfectly successful in 
 explaining the laws of reflexion and refraction, considered as dis- 
 tinct phenomena, yet it is by no means equally so in accounting 
 for their connexion and mutual dependence. When a beam of 
 light is incident on the surface of any transparent medium, part is 
 in all cases transmitted, and part reflected. The intensity of the 
 reflexion is in general less, the less the difference of the refractive 
 indices of the two media ; and accordingly the reflective and re- 
 fractive forces (if such be the cause of the phenomena) are related 
 to one another in all media, so that one increases or diminishes 
 along with the other.f But how is it that some of the molecules 
 obey the influence of the repulsive force, and are reflected, while 
 others yield to the attractive force, and are refracted? To 
 account 'for this Newton was obliged to have recourse to a new 
 hypothesis. The molecules of light are supposed to pass through 
 certain periodical states, called " fits of easy reflexion and trans- 
 
 * This assumption is tacitly made by Newton, when he takes the function 
 
 as the measure of the refractive power. See Herschel's " Essay on Light,' ' Encyc. Metrop. 
 
 t The reader will find much novel and interesting matter connected with this suh- 
 
 ject in a paper hy Sir David Brewster, " On the Reflexion and Decomposition of 
 
 Light at the separating surface of media of the same and of different refractive powers," 
 
 /'/'/. Trans. 1829. '
 
 32 REPORT ON PHYSICAL OPTICS. 
 
 mission," which modify the effects of the attractive and repulsive 
 forces, and in which they are disposed to yield alternately to one 
 or the other. The actual determination of the particle will de- 
 pend, partly on the phase of the fit, and partly on the obliquity 
 under which it meets the bounding surface. Now the molecules 
 composing a beam of light are supposed to be in every possible 
 phase of their fits when they reach the surface : some of them 
 consequently will be reflected, and others refracted ; and the pro- 
 portion of the former to the latter will depend on the incidence. 
 
 As to the fits themselves, Newton thought that they must be 
 referred to a vibratory motion in the ether, excited by the rays 
 themselves, just as a stone flung into water raises waves on its 
 surface. This vibratory motion is supposed to be propagated 
 faster than light itself, and thus to overtake the molecules, and 
 impress upon them the disposition in question by conspiring with 
 or opposing their progressive motion. In one of his queries New- 
 ton has even calculated the lesser limit of the elasticity of the 
 ether, as compared with that of air, in order that it should have 
 so great a velocity of propagation.* The hypothesis of Mr. Mel- 
 ville and M. Biot is more in accordance with the spirit of the 
 theory of emission. The molecules of light are supposed, in this 
 hypothesis, to have a rotatory motion round their centres of gra- 
 vity, which continues along with the progressive motion, and in 
 virtue of which they present attracting and repelling poles alter- 
 nately during their progress in space.f Boscovich imagined a 
 vibratory motion in the parts of the ray itself, which it received 
 at the moment of emission, and retained in its progress.* 
 
 The theory of the fits has now lost much of its credit, since 
 the phenomena of the colours of thin plates phenomena which 
 first suggested it to the mind of Newton have been shown to be 
 irreconcilable with it. The explanation which it gives of the 
 facts now under consideration is, as was observed by Young and 
 Fresnel, inconsistent with the regularity of refraction. In fact, 
 the molecules which are transmitted are not all in the maximum 
 of the fit of transmission, but are supposed to reach the surface in 
 very different phases of this, which may be denominated the posi- 
 tive fit. Now as a change of the fit from positive to negative is, 
 
 * Optics, Query 21. 
 
 t Phil Trans. 1753. Traite de Physique, iv. p. 245. 
 
 \ Philosophies Naturatis Theoria.
 
 REFLEXION AND REFRACTION OF LIGHT. 33 
 
 in general, sufficient to overcome altogether the effect of the 
 attractive force, and subject the molecule to the repulsive, it is 
 obvious that the phase of the fit must modify the effects of these 
 forces in every intermediate degree ; and that the molecules which 
 do obey the attractive force must have their velocities augmented 
 in different degrees, depending on the phase. Consequently, as 
 the direction of the refracted ray depends on its velocity, the 
 transmitted beam will consist of rays refracted in widely different 
 angles, and will be scattered and irregular. 
 
 In some of his writings, Newton attributes the reflexion and 
 refraction of light to a difference in the density of the ether within 
 and without bodies ; or rather he refers the attractive and repul- 
 sive forces to this, as to a more general principle. The ether is 
 supposed to be rarer within dense bodies than without ; and the 
 rays of light, in crossing the bounding surface, are pushed from 
 the side of the denser ether, so that their motion is accelerated if 
 they pass from the rarer to the denser body, and retarded in the 
 opposite case. Reflexion at the surface of the rarer medium is ex- 
 plained on the same suppositions ; but to account for the ordinary 
 reflexion by a denser medium, Newton was obliged to introduce 
 new and gratuitous hypotheses respecting the constitution of the 
 ether at the confines of two media in which its density is different.* 
 
 The velocity of propagation, in the wave-theory of light, de- 
 pends solely on the elasticity of the vibrating medium as compared 
 with its density. If, then, a plane wave be incident obliquely on 
 the bounding surface of two media, it is obvious that its several 
 portions will reach that surface at different moments of time ; 
 and each of these portions will become the centre of two spherical 
 waves, one of which will be propagated in the first medium with 
 the original velocity, while the other will be propagated in the 
 new medium, and with the velocity which belongs to it. But, by 
 the principle of the coexistence of small motions, the agitation of 
 any particle of either medium is the sum of the agitations sent 
 there at the same instant from these several centres of disturbance ; 
 and the surfaces on which they are accumulated at any instant 
 will be the reflected and refracted waves. These surfaces are 
 those which touch all the small spherical waves at any instant. 
 It is easy to see that they are both plane ; and that the reflected 
 
 * Birch's History of the Royal Society, vol. iii. p. Ml. Optics, Query 19. 
 D
 
 34 REPORT ON PHYSICAL OPTICS. 
 
 wave is inclined to the surface at the same angle as the incident 
 wave, while the sine of the angle of inclination of the refracted 
 wave is to that of the incident in the constant ratio of the veloci- 
 ties of propagation in the two media. 
 
 Such is the demonstration of the laws of reflexion and refrac- 
 tion given by Huygens.* The composition of the grand, or 
 primary wave, by the union of the several secondary or partial 
 waves, in this demonstration, has been denominated the principle 
 of Huygens; and it is obviously a case of the more general prin- 
 ciple of the coexistence of small motions. It easily follows from 
 this mode of composition, that the surface of the primary wave 
 must mark the extreme limits to which the vibratory movement 
 is propagated in any direction, in any given time ; so that light, 
 according to this theory, is propagated from any one point to 
 another in the least possible time. This is the well-known law of 
 Fermat, the law of swiftest propagation ; and it will readily appear 
 that it holds, whatever be the number of modifications which the 
 course of the light may undergo by reflexion or refraction, as 
 likewise, whatever be the form of the elementary wave. 
 
 The demonstration of Huygens has been thrown into an ana- 
 lytical form by Lagrange,f but he has added nothing to its rigour 
 or perspicuity. An important supplement to the demonstration 
 was, however, given by Fresnel. From the reasoning of Huy- 
 gens it did not appear what became of those portions of the 
 secondary waves which did not conspire in the formation of the 
 grand wave. The crossing of these in all directions ought to give 
 rise to a weak diffused light, filling the entire space between the 
 grand wave and the reflecting or refracting surface ; and, in fact, 
 Huygens supposed that such a light did actually exist, but was 
 too feeble to affect the eye. Fresnel has shown, however, that all 
 those portions which do not conspire in the formation of the grand 
 wave, are destroyed by interference so that the formation of one 
 grand wave, by the union of an indefinite number of lesser waves, 
 
 The total reflexion of light at the surface of a rarer medium 
 )een urged by Newton against the wave-theory, and the 
 
 * Traite de la Lumiere. 
 
 t ' Star la Theorie de la Lunuere d' Huygens."- Annales de CMm., torn. xxi. 
 
 a! XI i Kefracfaon dans la Systeme des Ondes."-^^ do Chimie,
 
 REFLEXION AND REFRACTION OF LIGHT. U5 
 
 apparent difficulty seems to have had much weight in inducing 
 him to reject that theory. It is, in fact, not easy to perceive at 
 first view why the disturbance of the ether within the denser 
 medium should not be communicated to the external ether, and a 
 wave be thus propagated to the eye, whatever be the obliquity of 
 the incident wave. To this it may be enough to reply, that the 
 law of refraction itself, in all its generality, is a necessary conse- 
 quence of the wave-theory ; and therefore that the phenomenon 
 of total reflexion, which is a particular case of that law, is likewise 
 accounted for. But the principle of interference furnishes a direct 
 answer to the difficulty. It can be shown that the elementary 
 waves, which are propagated into the rarer medium from the 
 several points of the bounding surface, destroy one another by 
 interference, when the sine of the angle of incidence is greater 
 than the ratio of the velocities of propagation in the two media, or 
 the angle itself greater than the limiting angle of total reflexion.* 
 It is here supposed that the distance from the refracting surface is 
 a large multiple of the length of a wave. The conclusion does 
 not apply to points very near that surface ; and for such points, 
 there is reason to think, the law of refraction is more complicated. 
 Experience shows, in fact, that light may issue from the denser 
 medium, to an appreciable distance, when the incidence exceeds 
 the limiting angle of total reflexion. If two prisms, whose bases 
 are slightly convex, be put together, and the inclination of these 
 bases gradually changed while we look through them, it will be 
 observed that, beyond the limiting angle, the light will still be trans- 
 mitted in the neighbourhood of the parts in contact. By mea- 
 suring the breadth of this space, and comparing it to the diameters 
 of the coloured rings, Fresnel found that the interval of the 
 glasses, through which this deviation from the ordinary law of re- 
 fraction occurred, exceeded the length of the wave.f The analysis of 
 M. Poisson points also to the same result, and it is proved that the 
 second medium will be agitated in the part immediately in contact 
 with the first, this agitation decreasing rapidly, and becoming 
 insensible, at a very minute distance from the surface. 
 
 The laws of reflexion and refraction, then, follow from the 
 theory of waves, whether we suppose the vibrating medium in 
 
 * See Fresnel, " Sur le Syateme dcs Vibrations lumineuses." Bibliotkique Univer- 
 selle, torn. xxii. 
 t Ibid. 
 
 D2
 
 36 REPORT ON PHYSICAL OPTICS. 
 
 dense bodies to be the body itself, the ether within it, or both con- 
 jointly. Euler maintained the first of these opinions, and believed 
 that light was propagated through the gross particles alone, in the 
 same manner as sound. But this hypothesis is contradicted by 
 the most obvious facts ; and according to it, as Dr. Young has 
 observed, the refraction of the rays of light in our atmosphere 
 should be a million times greater than it is. Of the other two 
 opinions, Young seems to have held the latter, and to have 
 thought that the molecules of the body formed, together with 
 those of the ether within it, a compound vibrating medium, which 
 was denser than the ether alone, but not more elastic. Others, 
 lastly, attribute the propagation of light in transparent bodies to- 
 the vibrations of the ether alone, that fluid being retained by the 
 attraction of the body in a state of greater density within it than 
 in free space. 
 
 A very different view of this subject has been recently main- 
 tained by Mr. Challis. Assuming that the density of the ether 
 is the same in solid media as in free space an assumption which 
 he seems to think required by the phenomenon of aberration this 
 mathematician conceives that the reflexion of light, and its re- 
 tardation in the denser medium, may be both accounted for by 
 the reflexions which the ethereal waves undergo from the solid 
 particles of the medium which they encounter in their progress.* 
 lie shows, in fact, that the absolute velocities impressed upon the- 
 ethereal particles by such reflexion may be resolved into two parts, 
 one of which is propagated uniformly, and is accompanied by a 
 change of density ; while the other is propagated instantaneously r 
 without change of density. t The former of these, he thinks, will 
 account for the reflexion of light, the latter for the diminished 
 velocity of transmission.^ This ingenious theory has the advan- 
 
 * This manner of conceiving the reflexion of light, in the wave-theory, was that 
 originally entertained by Fresnel, and was put forward in a memoir read to the French 
 Academy in 1819. 
 
 t Phil Mag., New Series, vol. xi. 
 
 I The mean effect of these reflexions, Mr. Challis shows, is equivalent to that of a 
 retarding force ; and, by a certain supposition respecting its value, he has arrived at 
 the following simple formula for the determination of the ratio of the velocities of 
 propagation in free space and in the medium 
 
 M 3 - 1 = tf X; 
 
 in which 5 denotes the density of the medium, and H a constant proportional to 
 he mean retarding effect of a given number of its molecules. For the gases, then, the
 
 REFLEXION AM) REFRACTION OF LIGHT. 37 
 
 tage of connecting the velocity of propagation in dense bodies 
 directly with their constitution, and so of advancing a step in the 
 process of physical induction. On the other hand, it requires us 
 to admit that the particles of ether and those of gross bodies 
 exert no mutual action of any kind. We know too little of the 
 ether, or of its properties, to deny this, simply because it is unsup- 
 ported by any of the properties of matter hitherto revealed ; but it 
 must at the same time be admitted that the violation of such 
 analogies furnishes an argument of some weight against the theory 
 which demands them. 
 
 Whatever supposition we may frame respecting the constitution 
 -of bodies, or of the ether within them, in the wave-theory, it must be 
 such that the velocity of propagation is less in the denser medium. 
 In the theory of emission, on the other hand, it is the reverse ; so 
 that although it conducts to the same result, it does so by an 
 opposite route. Here, then, the rival theories are at issue upon a 
 matter of fact ; and we have only to ascertain this fact, in order 
 to be able to decide between them. This seemed to be accom- 
 plished by the reasonings of Young. From the laws of inter- 
 ference it appears that homogeneous light, in its progress in space, 
 passes through certain periodically returning states, the intervals 
 -of which are constant in the same medium; while in different 
 media they are proportional to the velocities of propagation, 
 since the number of such intervals in a given quantity of light can- 
 not be supposed to vary. Now, it followed from the experiments 
 of Newton, that the intervals, by which he explained the pheno- 
 mena of thin plates, were diminished in the denser medium ; and 
 as these intervals have been shown by Young to be identical with 
 those deduced from the law of interference, it followed that the 
 velocity of light was slower in the denser medium.* Newton had 
 even found the ratio of the magnitudes of the intervals to be the 
 same with that of the sines of incidence and refraction ; and this 
 is precisely as it should be on the principles of the wave-theory. 
 
 But the retardation of light in the denser medium has been 
 
 quantity ~ is nearly constant, whatever be the compression. This result i a 
 
 very simple consequence of the theory of emission ; its experimental truth has been 
 -established by MM. Biot and Arngo. Phil. Mag., New Series, vol. vii. 
 
 * "Experiments and Calculations relative to Physical Optics." Phd. Tram., 
 1803.
 
 38 REPORT ON PHYSICAL OPTICS. 
 
 directly established by M. Arago. If two pencils be made to in- 
 terfere and produce fringes, as in the experiment of Fresnel, and 
 if a thin plate of a denser medium be interposed in the path of one 
 of them, the whole system of fringes will be shifted to one side or 
 the other, according as the light has been accelerated or retarded 
 within the plate. The result of this important and decisive expe- 
 riment was in favour of the theory of waves.* 
 
 The refractive index being equal to the ratio of the velocities of 
 light in the two media, direct or inverse, it follows, whichever 
 theory we adopt, that any change in the velocity of the incident 
 ray must cause a variation in the amount of refraction, unless the 
 velocity of the refracted ray be altered proportionally. Now, the 
 relative velocity of the light of a star is altered by the earth's 
 motion ; and the amount of the change is obviously the resolved 
 part of the earth's velocity in the direction of the star. It was 
 therefore a matter of much interest to determine how, and in what 
 degree, this change affected the refraction. By the observation of 
 this effect, it was hoped, we should have an easy and accurate 
 method of determining the constant of aberration ; we should be 
 enabled to compare the light of different stars, and detect any 
 difference which might exist in their velocities; and, lastly, we 
 might compare these velocities with that of light emanating from 
 other sources. The experiment was undertaken by M. Arago, at 
 the request of Laplace, f An achromatic prism was attached in 
 front of the object-glass of the telescope of a repeating circle, so as 
 to cover only a portion of the lens. The star being then observed 
 directly through the uncovered part of the lens, and afterwards in 
 the direction in which its light was deviated by the prism, the 
 difference of the angles read off gave the deviation. The stars 
 selected for observation were those in the ecliptic, which passed the 
 meridian nearly at 6 A.M. and 6 P.M., the velocity of the earth 
 being added to that of the star in the former case, and subtracted 
 from it in the latter. No difference whatever was observed in the 
 deviations ; and the result was the same whatever was the origin 
 
 * Amulet de Chimie, torn. i. See also the account of Mr. Potter's repetition of 
 this experiment. Phil. Mag., vol. iii. p. 333. 
 
 t The idea of detecting a difference in the velocity of the light of the fixed stars, 
 by its effect upon the amount of refraction, seems to have first occurred to Mr. Michell. 
 Such a difference of velocity, he conceived, must, necessarily arise from the different 
 attractions of the stars upon the emitted molecules, and he has computed the dimi- 
 nution of the original velocity of emission arising from this cause. Phil.Traiu., 1784..
 
 REFLEXION AND REFRACTION OF LIGHT. 39 
 
 of the light.* Fraunhofer has likewise compared the light of 
 several of the fixed stars with respect to its refrangibility. No 
 difference whatever was observed, although the method employed 
 was adequate to the detection of a difference so small as the 
 10,000th part of the whole refraction nearly.f 
 
 This remarkable and unexpected result can be reconciled to 
 the theory of emission,:}: as M. Arago has observed, only by the 
 hypothesis already adverted to namely, that the molecules are 
 emitted from the luminous body with various velocities ; but that 
 among these velocities there is but one which is adapted to our 
 organs of vision, and which produces the sensation of light. The 
 wave-theory has been more successful in its explanation. If the 
 ether which encompasses our globe were like its atmosphere, and 
 partook of its motion, the refraction would be precisely the same as 
 if the whole were at rest. This, however, we have seen, cannot be 
 the case ; and the phenomena of aberration compel us to admit 
 that the ethereal medium which encompasses the earth is not dis- 
 placed by its motion. This being assumed, it follows that the ether 
 which is carried along by the refracting medium, is that which con- 
 stitutes the excess of its density above that of the surrounding ether. 
 On this supposition Fresnel has calculated the length of a wave in 
 the moving medium, and thence also the actual change in the 
 direction of the refracted ray produced by the earth's motion. 
 This change is found to be opposite, and exactly equal to that pro- 
 duced by the same cause in the apparent direction of the ray ; so 
 that the ray is actually seen in the same direction as if the earth 
 were at rest, and the apparent refraction is unaltered by the earth's 
 motion. These results, it may be observed, are precisely the same 
 for terrestrial objects, the velocity of wave-propagation being inde- 
 pendent of the motion of the luminous body. 
 
 * Biot, Astronomic Physique, vol. iii. 
 
 f Edinb. Journ. of Science, viii. p. 7. 
 
 J M. Prevost has endeavoured to reconcile the experimental result of M. Arago 
 with the ordinary suppositions of the theory of emission, and to show that a change in 
 the relative velocity in the light of the stars, caused by the motion of the refracting 
 plane, does not affect the refraction in the same manner as an equal change in the 
 absolute velocity. " De 1'Effet duMouvement d'un plan refringcnt sur laEefraction. "- 
 Geneva Memoirs, vol. i. His reasonings do not appear to be conclusive. 
 
 The sine of the change is to the sine of the total deviation of the ray in the ratio 
 of the velocity of the earth to that of light. Fresnel's result is much more com- 
 plicated, but it will be easily seen to reduce itself to this. " Sur I'Infltience du Mouve- 
 ment terrestre dans quelques Phenomenes d'Optique." Annales de Chimie, torn. ix.
 
 40 REPORT ON PHYSICAL OPTICS. 
 
 Newton thought that the different refrangibility of the rays of 
 light could be explained by supposing simply that they were bodies 
 of different sizes, the red being greatest and the violet least. It is 
 obvious, however, that this supposition can have no reference to 
 the simple projectile hypothesis held by his followers, or to the 
 demonstration of the law of refraction given in the Principia. It 
 is connected with that more complex theory, in which the mole- 
 cules of light are supposed to excite the vibrations of the ether in 
 the bodies which they meet. 
 
 M. de Courtivron and Mr. Melville proposed to account for the 
 dispersion of light by a difference in the initial velocity of the 
 molecules, the red being swiftest and the violet slowest. But 
 were such the cause of the phenomenon, the dispersion should be 
 proportionate to the mean refraction. Indeed, the hypothesis was 
 abandoned almost as soon as proposed. Its authors had foreseen the 
 consequence that, in the eclipses of Jupiter's satellites, the colour of 
 the light should vary just before immersion, and after emersion ; and 
 the existence of such an effect, in the degree indicated by theory,* 
 was completely disproved by the observations of Mr. Short, t 
 Another consequence of such a difference in the initial velocities of 
 the light of different colours is, that the aberration of the fixed 
 stars should also vary with the nature of the light, and each star 
 appear as a coloured spectrum, whose length is parallel to the 
 direction of the earth's motion. 
 
 According to the modern advocates of the theory of emission, 
 the molecules of light are heterogeneous ; and the attractions 
 exerted on them by bodies vary with their nature, and are, in 
 this respect, analogous to chemical affinities. This supposition, 
 however, as Dr. Young has justly observed, is but veiling our 
 inability to assign a mechanical cause for the phenomenon. 
 
 It is remarkable that Newton himself was the first to suggest 
 that part of the wave-theory, in which the colour of the light is 
 supposed to be determined by the frequency of the ethereal vibra- 
 
 * The duration of this change, according to Mr. Melville, should amount to thirty- 
 two seconds, the velocity of the light of different colours being inversely as their re- 
 fractive indices. (**. Trans., 1753.) This principle, however, as M. Clairaut has 
 shown (Phil. ZYww.,1764), is obviously incorrect. It will easily appear that the initial 
 velocities must vary inversely as the quantity v/M^ 7 !, in order to account for dis- 
 persion ; and that the duration of the expected phenomenon must be even greater than 
 that assigned by Mr. MelviUe. 
 
 t PhU. Trans., 1753.
 
 REFLEXION AND REFRACTION OF LIGHT. 41 
 
 tions, or by the length of the wave ;* and the addition has been 
 received by all its supporters. But observation proves that the 
 refractive index, or the ratio of the velocities of propagation, 
 in the two media, is different for the light of different colours. 
 The advocates of the wave-theory, therefore, are forced to con- 
 clude that the velocity of propagation in refracting media varies 
 with the length of the wave. Here, then, we encounter a difficulty 
 in this theory, which has been regarded as the most formidable 
 obstacle to its reception. Theory indicates that the velocity of 
 wave-propagation is constant in the same medium, depending 
 solely on the elasticity of the medium as compared with its density. 
 That velocity, therefore, should be the same for light of all colours, 
 as it is found to be for sound of all notes. 
 
 Various attempts have been made to solve this difficulty, f 
 Euler thought that the successive waves underwent an increase of 
 velocity arising from their mutual action ; and this increase he 
 supposed to vary with their length, the waves of greatest length 
 undergoing the least augmentation of velocity, and being there- 
 fore most refracted. J But the phenomena of coloured rings, as 
 Euler perceived, compel us, on the contrary, to suppose that the 
 lengths of the waves diminish as the refrangibility increases ; and 
 he seems himself to have abandoned his first conjecture. 
 
 Dr. Young accounted for dispersion by the supposition that 
 the solid particles of the refracting substance vibrate, as well as 
 the particles of the ether within it ; and that the former vibra- 
 tions affect the latter, and affect them differently according to 
 their frequency. Mr. Challis has adopted and developed this 
 hypothesis. According to this author, it has been already ob- 
 served, the diminished velocity of transmission in the denser 
 medium may be explained by the obstacle which the solid par- 
 ticles of the medium offer to the free movement of the ethereal 
 particles. If the former be supposed to be immovable, the ratio 
 of the velocities of propagation, in free space and in the medium, 
 
 * Phil. Trans., 1672. 
 
 t It is scarcely necessary to advert here to the law proposed by M. Rudberg, to 
 connect the lengths of an undulation, or the velocities of propagation, in different 
 media ; for this law is purely hypothetical, and its apparent consistency with obser- 
 vation has arisen solely from the adaptation of the arbitrary constants which enter 
 the expression. Annales de Chimie, torn, xxxvi., xxxvii. 
 
 J Opuscula varii Aryiimcnti, torn. i. p. 217.
 
 42 REPORT ON PHYSICAL OPTICS. 
 
 a simple function of the density of the latter, and in a 
 
 gven medium its value will be constant; but when the particles 
 of the medium vibrate, the value of this ratio will depend also on 
 the length of the wave, and will therefore vary with the colour o 
 
 the light.* 
 
 The solution suggested by Professor Airy is more closely con- 
 nected with received principles. It is now generally admitted 
 that part of the velocity of sound depends on a change of elasticity 
 which the air undergoes during its vibrations, in consequence of 
 the development of latent heat by compression. If this heat 
 required time for its development, the quantity developed, and 
 therefore the elastic force, must vary with the time of vibration. 
 Consequently, the velocity of propagation should also vary with 
 the time, and be different for waves of different lengths. Pro- 
 fessor Airy imagines something similar to this in the case of light ; 
 and conceives that the elasticity of the ether, in refracting media, 
 may consequently undergo a change whose amount depends on 
 the time of vibration. 
 
 But the explanation offered by Fresnel seems to be the sim- 
 plest and most natural. The conclusion of analysis that the 
 velocity of wave-propagation is constant in the same homogeneous 
 medium is deduced on the particular supposition that the sphere 
 of action of the molecules of the medium is indefinitely small 
 compared with the length of a wave. If this restriction be re- 
 moved, we have no longer any ground for concluding that waves 
 of different lengths will be propagated with the same velocity. 
 Fresnel states that he has demonstrated that, when the mutual 
 action of the ethereal molecules extends to a sensible distance as 
 compared with the length of a wave, the waves of different lengths 
 will be propagated with different velocities ; the elasticity of the 
 medium, and therefore also the velocity, increasing with the length 
 of the wave.f Here, then, the constancy of the velocity of wave- 
 propagation is regarded but as the approximate result of an 
 incomplete analysis. The problem presented itself to M. Cauchy 
 in a similar point of view. In the profound researches of this 
 
 * " An attempt to explain theoretically the different Refrangibility of the Rays of 
 Light, according to the hypothesis of Undulations." Phil. Mag., New Series, vol. viii. 
 
 t This demonstration is more than once referred to by the author, as contained in 
 a note appended to his memoir on double refraction. The note, however, probably by 
 some oversight, h*s never been printed.
 
 KEFLEXION AND KEFRACTION OF LIGHT. 43 
 
 mathematician relating to light, the ether is considered as a sys- 
 tem of particles solicited by mutual attractions or repulsions ; and 
 from the partial differential equations which represent their move- 
 ment, he had deduced the laws of propagation in crystallized as 
 well as in homogeneous media. These equations, however, were 
 but approximate, and derived from others of greater generality by 
 the omission of the terms containing the higher powers of the 
 displacements, and of their derivatives with respect to the co- 
 ordinates. Eesuming the problem of the propagation of a plane 
 wave, with the aid of the more general equations, he has finally 
 demonstrated the existence of a relation between the velocity of 
 propagation and the length of the wave.* 
 
 The opacity of bodies is ascribed by Newton to the discon- 
 tinuity of their parts, and to the multitude of internal reflexions 
 which the rays of light undergo within them.f We have many 
 reasons for believing this to be the case ; but as yet we are far from 
 a complete account of the phenomenon. If the reflexions and 
 refractions, which thus arise at each new bounding surface, be 
 similar to those which take place at the outer surfaces of bodies, 
 the molecules of light will indeed be scattered in every direction, 
 but they should undergo no diminution of velocity. How, then, 
 is it that they do not emerge finally from the body as readily as 
 they entered it, and thus render it visible in all directions, not by 
 a superficial reflexion, but by a secondary emission ? To account 
 for the extinction of light, in the theory of emission, we must sup- 
 pose it united to the body which it enters ; and the simplest mode 
 in which we can conceive this union to be brought about is by the 
 direct impact of the molecules of light on those of bodies, whereby 
 they are brought within the sphere of those interior attractive 
 forces to which chemical combinations are referred. This appears 
 to have been the opinion of Newton. " Are not gross bodies and 
 light," says he, "convertible into one another, and may not 
 bodies receive much of their activity from the particles of light 
 which enter their composition ? For all fixed bodies being heated 
 emit light, so long as they continue sufficiently hot, and light 
 
 * Mtmoire sur la Dispersion de la Zumiere.llie attention of the Mathematical 
 Section of the British Association was drawn to this theory by Professor Powell, at 
 the last meeting, chiefly in reference to a limitation which seemed to he required in 
 the physical hypothesis. See Report of Proceedings. 
 
 t Optics, hook 2, part 3.
 
 44 REPORT ON PHYSICAL OPTICS. 
 
 mutually stops in bodies as often as its rays strike upon their 
 parts."* 
 
 When from the simple fact of absorption we proceed to con- 
 sider its law, as depending on the nature of the light, the difficul- 
 ties increase at every step. The intensity of the transmitted 
 light, considered as a function of its refrangibility, appears to be 
 subject to no law, or to a law so complicated as completely to 
 baffle all attempts to embrace it in an empirical rule. The maxima 
 and minima are often actually numberless ; and the variable does 
 not reach them gradually, but by what seems to be an abrupt 
 violation of the law of continuity. These apparently capricious 
 changes were observed long since by Dr. Young, in the light 
 transmitted through the common smalt-blue glass. Sir David 
 Brewster has recently directed his attention to the same subject, 
 and examined a great number of coloured bodies with reference 
 to their absorptive properties. He has found, in particular, that 
 a very remarkable definite action is exercised upon the rays of the 
 spectrum by the green liquids obtained by extracting the colour- 
 ing-matter of the leaves of plants in alcohol ; and this action does 
 not cease altogether even when the liquid has become perfectly 
 colourless.f But the absorbing properties of .nitrous-acid gas, 
 observed by the same author, are by far the most remarkable ever 
 noticed. "When the light transmitted through this gas is analyzed 
 by a prism, it is found that about 2000 portions of the beam are 
 stopped, and 2000 dark spaces, or abrupt deficiencies of light, 
 appear in the spectrum. These increase in number and magni- 
 tude with the temperature of the gas, until, by a sufficient eleva- 
 tion of temperature, this rare body becomes perfectly opaque, and 
 refuses to transmit a single ray of the brightest sunshine. J Pro- 
 fessor Miller and Professor Daniell have found some analogous 
 properties in other gases. In the spectrum produced by the 
 light transmitted through the vapours of bromine and iodine, 
 more than one hundred dark lines are visible, disposed at equal 
 distances.! 
 
 To account for the selection of certain classes of rays by 
 
 * Optics. Query 30. 
 
 t " On the Colours of Natural Bodies." Edln. Trans., vol xii 
 
 " On the Lines of the Solar Spectrum," & K .-Edin. Trans., vol. xii. 
 t French translation of Herschel's Essay on Light, Supplement, p. 455.
 
 REFLEXION AND REFRACTION OF LIGHT. 45 
 
 coloured media, in the theory of emission, it seems necessary to 
 suppose that an attractive force is exerted at a distance between 
 the molecules of the tody and those of light, and that the absolute 
 value of this force varies with the colour. It does not seem easy 
 to reconcile these suppositions to the Newtonian account of refrac- 
 tion ; and the difficulty is still further increased when we proceed 
 to apply the same considerations to the absorption of definite 
 rays, and introduce the hypothesis of specific actions, varying in 
 the most abrupt and irregular manner with the refrangibility of 
 the ray.* 
 
 The absorption of light, and the opacity of bodies, were long 
 since urged by Halley as difficulties in the wave-theory. The ether 
 is supposed to penetrate all bodies freely, and why not also the 
 undulatory motion in which light consists ? To this difficulty we 
 find a full and complete solution in the principle of interference. 
 When a wave enters a discontinuous substance, it will be broken 
 up, and its parts undergo continued 'subdivision by internal re- 
 flexions ; so that when these parts reach the second surface of the 
 body, they are found in every possible phase, and must destroy one 
 another by interference. The phenomenon, as has been observed 
 by Sir John Herschel, is analogous to the impeded propagation of 
 sound in a mixture of gases differing much in elasticity as com- 
 pared with their density. 
 
 The same writer has given an ingenious and natural account 
 of the absorption of specific rays on the principles of the wave- 
 theory, in a paper read before the Association last year, f He con- 
 siders the molecules of the body and those of the ether as forming, 
 conjointly, compound vibrating systems, which are more disposed 
 to transmit vibrations of some determinate period than others. 
 Other vibrations, however, not in unison with these systems, may 
 be propagated through them. These forced vibrations, as he calls 
 them, will be obstructed in their progress, and their amplitudes 
 diminished by the mutual influence of the motions of the parts 
 of the systems ; and he shows that it is possible to conceive sys- 
 tems, which will be wholly impervious to a vibration of a par- 
 ticular period, while they freely transmit others not differing from 
 
 * See Sir David Brewster's Report on Optics. 
 
 t "On the Absorption of Light by coloured Media, viewed in connexion with tho 
 Undulatory Theory." Phil. Mag., Third Series, vol. iii.
 
 46 EEPOKT ON PHYSICAL OPTICS. 
 
 them materially in their frequency * But these important and 
 interesting speculations, it must be remembered, are advanced by 
 their author solely with the view of removing an imagined incon- 
 sistency between the phenomena of absorption and the mechanical 
 laws of vibratory movement. We are still far from a precise 
 theory of absorption. When such a theory shall have been estab- 
 lished, there seems reason to believe that it will bring with it also 
 an insight into the internal constitution of bodies even yet more 
 close than that afforded by the affections of polarized light ; and 
 that the laws of molecular action may perhaps, at some future day, 
 be studied in the phenomena of transmitted light. 
 
 The properties of solar phosphori, which attracted so much of 
 the attention of experimental philosophers of the last century, 
 seem at first view to favour the account of absorption suggested 
 by the theory of emission, and to arise from the disengagement of 
 the light which had become united to the body. Canton observed 
 that light may remain in these bodies, as it were in a latent state, 
 for several months, until its re-emission is determined by the action 
 of heat. But it must be observed, in the first place, that the 
 feeble light emitted from the phosphori bears a very small propor- 
 tion to that which they are supposed to receive by absorption. 
 Dessaignes has remarked that most of these substances emit the 
 same kind of light, whatever be the species of light to which they 
 have been exposed.! The same fact has been observed by M. 
 Grotthouss+ and other subsequent inquirers ; and in some of the 
 diamonds possessing the property of phosphorescence, the most 
 efficacious exciting light is of a different colour from that excited. 
 These facts seem to be inexplicable in the theory of emission. In 
 
 * An interesting interference experiment, similar in some respects to that indicated 
 by Sir John Herschel in this paper, has been recently made by Mr. Kane. A com- 
 pound tube, whose branches of 9 and 13 J inches united at the two extremities, was 
 made to sound by the languette of an organ pipe. Each of the tubes, separately, gave 
 its own fundamental note, and all its harmonics ; and when a free communication was 
 opened between them, the system gave all the notes of the two series, with the excep- 
 tion of those whose waves were in complete discordance. Thus, the fundamental note 
 of the short tube was stopped altogether, while its octave was given with remarkable 
 clearness ; the two waves being in complete discordance in the former case, and in 
 complete accordance in the latter. 
 
 t Mem. Inst, torn. xi. 
 
 Journal, 18 15. The same observer discovered the curious fact, 
 that the electric current restored the property of phosphorescence, in many cases 
 where it appeared to have been destroyed by the action of violent heat.
 
 REFLEXION AND REFRACTION OF LIGHT. 47 
 
 the wave-theory, on the other hand, the phenomenon is easily 
 comprehended. As the vibrations of the air excite those of sound- 
 ing bodies, and communicate to them a motion which continues 
 for some time after the exciting cause has ceased to act, so it 
 must also be with the undulations of the ether. When the body 
 is in unison with the incident light, their vibrations will continue 
 isochronous, and the undulations of the ether excited by the body 
 will be of the same length as those by which it is itself excited. 
 In the other case, the period of vibration, and consequently the 
 length of the wave, will be altered, and the excited and exciting 
 lights will be of different colours. The fact observed by Canton 
 is indeed not so easily explained. Young supposed that the vibra- 
 tions of the body may be abruptly suspended by cold, and may 
 proceed anew when released from this restraint, like a string 
 which has been stopped and detained in any part of its vibration 
 on either side of the centre. 
 
 The fixed lines in the solar spectrum first noticed by Wollaston, 
 and afterwards more minutely traced by Fraunhofer, have lately 
 been examined with great care, and with his usual success, by Sir 
 David Brewster ; and he has observed a remarkable coincidence 
 between these lines and the dark bands of the spectrum of the 
 nitrous-acid gas.* Sir David Brewster has also studied, in' con- 
 nexion with the same subject, the definite absorbing effects of the 
 earth's atmosphere. This has been effected by examining the 
 solar spectrum, when the sun was near the horizon ; and it has 
 been found that most of the dark bands thus developed belonged 
 to the fixed lines of Fraunhofer, which were thus, as it were, 
 widened and brought out by the absorptive action of the atmo- 
 sphere. A similar result has been arrived at in other cases, and it 
 has been found that the points of the spectrum on which absorbing 
 bodies exert the strongest specific actions are generally coincident 
 with the deficient rays of solar light, t This singular connexion 
 gives considerable weight to the speculations of Sir David Brew- 
 ster respecting the latter phenomena. + 
 
 The observation of the fixed lines in the solar spectrum led 
 Fraunhofer to examine the optical characters of the lights ema- 
 
 * " On the Lines of the Solar Spectrum." Edin. Tram., vol. lii. 
 t "On the Colours of Natural Bodies." Edin. Traits., voL xii. 
 J Report on Optics.
 
 4 g REPORT ON PHYSICAL OPTICS. 
 
 nating from other sources. He thus arrived at the interesting 
 d sov g ery, that the system of bands in the "h"**^ 
 light wb ich he examined varied with the source ; while it was 
 cottaltlv the same in the number of the bands, and the* relate 
 o the coloured spaces, in the light of the same source however 
 Codified. In the light of Sirius there are three broad band 
 which have no resemblance to those of solar light. The light o 
 the electric spark, on the other hand, when analyzed by the prism, 
 is found to have several bright lines, of which that in the green is 
 remarkably brilliant. Similar phenomena were observed in the 
 light of artificial flames-the flame of an oil lamp, for example, 
 exhibiting a well-defined bright band between the red and yel- 
 low and another not so distinct in the green * This, however, is 
 not universally the case. In the red flame of strontia, as was 
 observed by Dr. Faraday and Mr. Talbot, there are a number oi 
 red rays separated from each other by dark bands ; and in the 
 flame of cyanogen, when similarly analyzed, the violet is found to 
 be divided into three distinct portions, with broad dark intervals.f 
 It is easy to account for the general fact of the deficiency of 
 certain classes of rays in certain lights. "When a body violently 
 heated begins to shine, the phenomenon is simply accounted for, 
 in the wave-theory, by an increase in the frequency of its vibra- 
 tions. In the same manner it seems natural to suppose, generally, 
 that the mechanical agencies at work during combustion accelerate 
 or retard, in various ways, the rate of vibration, and so alter the 
 character of the emitted lights. The light emitted in weak or 
 incipient combustion is generally blue. Sir John Herschel ob- 
 served that when sulphur burns with a feeble flame, its light con- 
 tains all the rays of the spectrum, and particularly the blue and 
 violet ; while, in vivid combustion, these disappear entirely, and 
 the light is a yellow of almost perfect homogeneity.* The various 
 shades of colour in the flame of a common candle from the deep 
 blue of the lower part, which is found by prismatic analysis to 
 consist of five distinct portions, to the yellowish white in the 
 centre, and thence to the dusky red at the apex of the flame 
 seem to be referrible to the same principle, Fraunhofer and Sir 
 
 Munich Memoirs. 
 
 t Phil. Mag., Third Series, vol. iv. p. 114. 
 
 J " On Absorption of Light in coloured Media." Edin. Tram., vol. ix.
 
 KEFLEXION AND REFRACTION OF LIGHT. 49 
 
 David Brewster have both remarked that the flame of oil, urged 
 by the blowpipe, consists chiefly or wholly of yellow rays. The 
 same fact was long since observed by Mr. Melville with respect to 
 the flame of alcohol into which nitre, muriate of soda, and other 
 salts had been introduced ;* and Sir David Brewster has found 
 that the quantity of yellow light given out by burning bodies 
 increases with their humidity, the flame of alcohol diluted with 
 water being nearly a homogeneous yellow, f It is more important 
 to remark, however, in illustration of the undulatory view of the 
 phenomenon of emission, that the colour of flames is often found 
 to depend on the presence of something which is itself unaltered 
 in the process of combustion. Thus Mr. Talbot has remarked, 
 that when a small quantity of muriate of lime was placed on the 
 wick of a spirit lamp, it gave out red and green rays during an 
 entire evening, though the salt was not sensibly diminished. J 
 The absence of definite rays in certain lights, and the fixed lines of 
 the solar spectrum, have been referred by Sir John Herschel to 
 the same principle by which he has explained the absorption of 
 specific rays. 
 
 In what has preceded we have assumed the truth of the re- 
 ceived theory with respect to the composition of solar light, and 
 the connexion between the colour of a ray and its refrangibility. 
 This theory, however, has been recently opposed by Sir David 
 Brewster. According to this philosopher, white light consists of 
 but three simple colours red, yellow, and blue ; and the solar 
 spectrum is composed of three overlapping spectra of these colours, 
 the intensity of each of which is greatest at the point where that 
 colour is strongest in the compound spectrum. According to this 
 view, then, all the colours in the solar spectrum are compound, and 
 consist of red, yellow, and blue light, in different proportions. 
 These compound colours cannot be analyzed by the prism, inas- 
 much as the rays of Which they consist at any point of the spec- 
 trum have the same refrangibility ; and it is only by the different 
 action of absorbing media on their constituent elements that their 
 compound nature can be detected. Each of them may be con- 
 
 * Edinb. Estays. 
 
 t On a Monochromatic Lamp, Ibid. 
 
 I Edinb. Journ. of Science, v. 77. 
 
 Phil. Mag., Third Series, vol. iii. p. 407.
 
 50 EEPOKT ON PHYSICAL OPTICS. 
 
 ceived to consist of a certain quantity of white light, and of an 
 excess of the light of two of the simple colours ; and if this excess 
 be absorbed, a white light will be the result, which will be inde- 
 composable by the prism. This result of his hypothesis has been 
 experimentally confirmed by Sir David Brewster.* 
 
 These views, if finally established, sever the connexion be- 
 tween the colour of a ray and its refrangibility, laid down by 
 Newton ; and the former must be supposed to depend not on the 
 length of the wave but on some other element of the vibratory 
 movement. 
 
 III. Diffraction. 
 
 It has been already stated that Newton considered the undu- 
 lations of an ethereral medium to be a necessary part of his theory, 
 and that that theory, as maintained by its author, differed from 
 the theory of Huygens and of Hooke only by the addition of a 
 new hypothesis. The necessity of something extraneous to the 
 undulations of the ether seems to have been admitted by Newton, 
 mainly to account for the right-lined propagation of the rays of 
 light ; and a careful consideration of his optical writings leaves 
 the impression, that had the wave-theory alone appeared to ex- 
 plain this fact, Newton would not have hesitated to embrace it. 
 This explanation has been spoken of in another place, and it has 
 been shown to follow from that theory, that the light which en- 
 counters an obstacle must diminish rapidly in intensity within the 
 edge of the geometric shadow. It now remains to consider the 
 other phenomena which arise under these circumstances ; and it 
 will be found that the same theory affords the most complete 
 account, not only of their general characters, but even of their 
 numerical details. 
 
 In order to understand the theory of shadows, it is necessary to 
 investigate their laws in the simple case in which the magnitude 
 of the luminous body is reduced to a point. The effects thus pre- 
 sented were first observed by Grimaldi, and they have been since 
 studied as a separate branch of optical science, under the title of 
 diffraction or inflexion. Grimaldi found that when a small opaque 
 body was placed in the cone of light, admitted into a dark cham- 
 
 * " On a New Analysis of Solar Light." Edin. Trans., 1831.
 
 DIFFRACTION. 51 
 
 ber through a very small aperture, its shadow was much larger 
 than its geometric projection, so that the light suffered some devia- 
 tion from its rectilinear course in passing by the edge. Observing 
 these shadows more attentively, he found that they were bordered 
 with three iris-coloured fringes, which decreased in breadth and 
 intensity in the order of their distances from the edge of the sha- 
 dow, preserving the same distance from the edge throughout its 
 entire extent, unless where the body terminated in a sharp angle. 
 Similar fringes were observed under favourable circumstances 
 within the shadows of narrow bodies.* 
 
 The phenomena of diffraction were subsequently examined by 
 Hooke, and by Newton. The first observations of Newton were 
 but repetitions of those of Grrimaldi ; and it is remarkable that he 
 altogether overlooked the important phenomenon of the interior 
 fringes noticed by the Italian philosopher. But to Newton we 
 owe the analysis of the phenomena, so far as they depended on the 
 nature of the light. When the different species of simple light, 
 into which the sun's rays were divided by a prism, were cast in suc- 
 cession on the diffracting body, Newton observed that the fringes 
 formed were broadest in the red light, narrowest in the violet, 
 and of intermediate magnitude in the light of mean refrangibility, 
 so that the iris-coloured fringes which are formed in white light 
 are but the fringes of different colours superposed. But the ob- 
 servations of Newton most closely connected with his physical 
 theory are those in which the light is made to pass between two 
 near knife-edges, whether parallel or inclined. From these obser- 
 vations Newton concluded that the light of the first fringe passed 
 by the edge, at a distance greater than the 800th of an inch, that 
 of the second and third fringes passing at still greater distances. 
 These distances, however, were not the same wherever the fringes 
 were formed ; and it appeared to follow from the experiments that 
 the light of the same fringe was not the same light at all distances, 
 but that each fringe was, as it were, a caustic formed by the in- 
 tersection of the rays passing at different distances from the edge ; 
 the portion of the fringe near the knives being formed of light 
 which passed nearest to the edge and was most bent.f 
 
 To account for these phenomena, Newton supposed the rays of 
 
 * Physieo-Mathesis de Luminc, Bologna, 1665. 
 f Optics, Book iii. 
 
 E2
 
 52 REPORT ON PHYSICAL OPTICS. 
 
 light to be inflected in passing by the edges of bodies, by the ope- 
 ration of the attractive and repulsive forces which the molecules 
 of bodies were conceived to exert on those of light at sensible 
 distances. Thus, the rays passing by the edges of a narrow 
 opaque body are supposed to be turned aside by its repulsion ; 
 and as this force decreases rapidly as the distance increases, the 
 rays which pass at a distance from the body will be. less deflected 
 than those which pass close to it. The caustic formed by the in- 
 tersection of these deflected rays will be concave inwards ; and 
 as none of the rays pass within it, it will form the boundary of 
 the visible shadow. To explain the alternations of darkness and 
 light beyond this, Newton appears to have supposed that the 
 attractive and repulsive forces succeed one another for some alter- 
 nations; and that the molecules composing each ray, in their 
 passage by the body, are bent to and fro by these forces, " with a 
 motion like that of an eel," and are finally thrown off at one or 
 other of the points of contrary flexure. The separation of white 
 light into its elements is explained, by supposing that the rays 
 which differ in refrangibility differ also in inflexibility, the body 
 acting alike upon the less refrangible rays at a greater distance, 
 and upon the more refrangible at a less distance.* In one of his 
 letters to Oldenburgh,f Newton advances a more refined theory of 
 diffraction. The bending of the ray near the edge of the obstacle 
 ne conceived to arise from a variation in the density of the ether 
 in the neighbourhood of the body ; and, following the analogy of 
 thin plates, he endeavoured to account for the coloured fringes by 
 the vibrations of the ether, which are propagated faster than the 
 rays themselves, and overtake them at the middle of the curved 
 portion of the trajectory they describe. 
 
 It is needless to comment upon the vagueness of these expla- 
 nations. Newton himself was dissatisfied with them, and the 
 subject fell from his hands unfinished. Still, however, the mere 
 guesses of such a mind as that of Newton must possess a high 
 interest, and we are not to wonder that among his followers more 
 weight should be attached to these explanations than he himself 
 ever gave them. It seems necessary therefore to advert to some 
 
 the circumstances of these phenomena, which are not only 
 
 * Optia, Book iii., Queries 1, 2, 3, 4. 
 
 t December 21, W5.-JKreh; History tf the Royal Society, vol. iii.
 
 DIFFRACTION. 53 
 
 unexplained by this theory, but which seem moreover irrecon- 
 cileably at variance with it. 
 
 If the phenomena of inflexion be the effects of attractive and 
 repulsive forces emanating from the interposed body, and if these 
 forces are the same with, or even analogous to, those to which the 
 reflexion and refraction of light are ascribed in the theory of 
 emission, it will follow that they must exist in different bodies in 
 very different degrees ; so that the amount of bending of the rays, 
 and therefore the position of the diffracted fringes, should vary 
 with the mass, the nature, and the form of the inflecting body. 
 Now it is clearly ascertained, on the contrary, that all bodies, 
 whatever be their nature or the form of their edge, produce under 
 the same circumstances fringes identically the same; and in fact 
 the partial interception of light, caused by the interposition of an 
 obstacle of any kind, seems to be the only condition on which the 
 character of the phenomenon depends. Grravesende seems to have 
 first observed that the nature or density of the body had no effect 
 upon the magnitude of the diffracted fringes ; and the fact has 
 since been confirmed in the fullest manner by almost every inquirer 
 in this branch of experimental science. One of the ablest suppor- 
 ters of the theory of emission has admitted that the inflecting 
 forces, if such exist, must be independent of the chemical nature 
 of the inflecting body, and altogether different in their nature 
 from those to which, in the same theory, the phenomena of re- 
 flexion and refraction are ascribed.* To ascertain whether the 
 form of the edge had any effect upon the fringes, Fresnel took two 
 plates of steel, the edge of each of which was rounded in one half 
 of its length and sharp in the remaining half, and placed the 
 rounded portion of one edge opposite the angular part of the 
 other, and vice versa. If, then, the position of the fringes depended 
 on the form of the surface, the effect would thus be doubled, and 
 the fringes appear broken in the middle. They were found, on 
 the contrary, to be perfectly straight throughout their entire 
 length.f 
 
 Biot, Precis elementaire, Tol. ii. p. 473, 3 Edit. 
 
 t Me'moire sur la Dif, -action, p. 370. The Bulletin Unirersrl for February, 1828, 
 contains some animadversions on this part of Fresnel's optical labours, in a ; 
 signed by the secretary of the Academy of Sciences of St. Pctersburgh, and purporting 
 to be an official reply to some remarks in a former number of the Bulletin .on the pro- 
 gramme of the prize questions proposed by the Academy. The writers hare con-
 
 54 REPORT ON PHYSICAL OPTICS. 
 
 Again, the inflecting forces though they must be supposed to 
 vary in intensity, with the form and mass of the body, and with 
 the distance of the luminous molecule from the edge cannot be 
 conceived to depend in any way upon the distance previously tra- 
 versed by the molecule, before it arrives in the neighbourhood of 
 that edge ; so that the magnitude and position of the fringes, in 
 this hypothesis, cannot vary in any way with the distance of the 
 inflecting edge from the luminous point. But this conclusion is 
 the reverse of fact : the fringes dilate in breadth, and their mutual 
 inclination is increased, as the screen approaches the luminous 
 origin. There seems to be but one way of avoiding the inference 
 drawn from this fact against the theory of emission. It may be 
 supposed that the bands have their origin at some sensible distance 
 from the edge of the body, and thus that the obliquity of the 
 incident ray varies as the edge approaches the luminous point. 
 Such was the conjecture of Du Tour, who noticed the fact. Fresnel 
 calculated the breadth of the fringes according to this suppo- 
 sition, and found that the computed and experimental results do 
 not agree.* But, in point of fact, the bands may be supposed 
 without sensible error to have their origin at the edge itself. 
 Fresnel found by direct measurement that the distance of the third 
 band" from the edge of the shadow, at its origin, was less than the 
 100th part of a millimetre. 
 
 The objections just considered seem to apply equally to the 
 hypothesis of Mairan and Du Tour, in which the phenomena of 
 diffraction are referred to the reflexions and refractions of an 
 atmosphere supposed to encompass all bodies. For if such an 
 atmosphere be retained around the body by its attraction, and 
 this seems to be the only mode of accounting for its presence, its 
 density and its form must vary with those of the body itself, and 
 consequently its effects upon the rays of light must vary also. 
 But the experiments of M. Haldat seem to leave no tenable 
 ground for these hypotheses. Every agent has been tried which 
 
 founded two experiments of Fresnel which were instituted with different views, and 
 differently reasoned upon. Fresnel's object, in this experiment, was simply to show 
 diffract o f ^ Pr dUCed D GffeCt UPOD the Mn Ses, as * 5 to do if 
 
 from boles'"! r^r a v tiVe ^ rePUldVe fOTCeS eXtendi "S to Se ^ ^stances 
 
 fe intke ml JeCtl DS *** * *" Same " a ^ ainst the wave-theory 
 
 rise, in lite manner, in misconception. 
 
 Memoire sur la Diffraction de la Lumiere."-^ m . de PItutiMf tom> y< p ^
 
 DIFFRACTION. 55 
 
 could be conceived capable of modifying the attractive force of the 
 body, or the density of the imagined atmosphere, and without 
 effect. The metallic wires and plates which produced the fringes 
 were heated to redness, and cooled down below the freezing-point ; 
 they were traversed by voltaic currents, and the charges of power- 
 ful batteries transmitted through them ; but in whatever manner the 
 condition of the diffracting body was varied, no change whatever 
 was perceived either in the intensity or dimensions of the diffracted 
 fringes.* 
 
 Although the phenomena of diffraction were studied by many 
 diligent observers! after the publication of the Optics, no material 
 accession was made to the knowledge of their laws until the prin- 
 ciples of the wave-theory were applied to their explanation by 
 Young. The exterior fringes, formed without the shadows of 
 bodies, were ascribed by Young to the interference of two portions 
 of light, one of which passed by the body, and was more or less 
 inflected, while the other was obliquely reflected from its edge, the 
 latter losing half an undulation at the instant of reflexion.* The 
 fringes formed by narrow apertures were, in like manner, sup- 
 posed to arise from the interference of the two pencils reflected 
 from the opposite edges ; while the interior fringes, within the 
 shadows of narrow bodies, were accounted for by the interference 
 of the pencils which passed on either side of the body at an insen- 
 sible distance, and were inflected into the shadow. The observed 
 facts closely correspond with the calculated results of this theory ; 
 and in the case last mentioned Young proved that the phenomena 
 admitted of no other explanation. Placing a small opaque screen 
 on either side of the diffracting body, so as to intercept the portion 
 of light which passed by one of its edges, the bands immediately 
 disappeared, although the light passing by the other edge was un- 
 modified. The same effect was produced, and by the same means, 
 upon the crested fringes of Grimaldi, formed within the shadows of 
 bodies having a rectangular termination. Thus the phenomena 
 
 * " Sur les Causes de la Diffraction," Annales de Chimie, torn. xli. Similar ex- 
 periments had been made some time before by Mayer, and with the same result. 
 (jt;iqen Memoir*, vol. iv. 
 
 t Maraldi (Mem. Acad. Par. 1723), Mairan (Ibid. 1738), Du Tour (JMM*tt 
 xentcs, torn, v.), Mr. Brougham (Phil. Trans. 1796-7), and Mr. Jordan (New Obterta. 
 tions concerning the Inflexion of Light. London, 1795). 
 
 t " On the Theory of Light and Colours." TV'tf. Trans., 1802. 
 
 " Experiments and Calculations relative to Physical Optics." PAH. Tram*. 180*.
 
 56 KEPORT ON PHYSICAL OPTICS. 
 
 of the fringes, or the alternations of light and darkness, were 
 shown to be cases of the more general principle of interference ; 
 and the connexion is now admitted by some of the warmest ad- 
 vocates of the Newtonian theory.* The bending of the light into 
 the shadow, or the fact of inflexion itself, was at first ascribed by 
 Young to the refraction of an ethereal atmosphere encompassing 
 bodies, and decreasing in density with the distance. He afterwards, 
 however, adopted the simpler doctrine of Huygens and Grimaldi, 
 and referred the phenomenon to the fundamental property of 
 waves. 
 
 But perhaps the most important of the labours of Young on 
 this subject is that in which he descends into numerical details, and, 
 taking the observations of Newton, as well as his own, calculates 
 the differences of the lengths of the paths traversed by the two 
 pencils, when they destroy or reinforce one another by interference. 
 These intervals he found to constitute an arithmetical progression 
 for the successive bands, the first term of which was the same 
 in the same species of light, whatever be the distance at which the 
 fringes are received, or the other conditions of the experiment. 
 And, finally, comparing these constants with the similar intervals 
 of the two pencils reflected by the surfaces of a thin plate, as 
 deduced from the experiments of Newton, he found that their 
 difference was within the limits of error to which such observa- 
 tions are liable, and that we are warranted in concluding that 
 the two classes of phenomena are to be referred to one simple prin- 
 ciple.! It is true that, in these calculations, Young starts from an 
 erroneous principle respecting the lights which form the diffracted 
 fringes by their interference, and he has remarked some discord- 
 ances in his results which have, no doubt, their origin in that 
 circumstance ; but the results of the exact theory are not greatly 
 different from that which he adopted, and the more complete 
 analysis of Fresnel has only tended to confirm the conclusion ob- 
 tained by Young. 
 
 The important experiment of Young, on the disappearance of 
 
 the fringes in the shadow of a narrow opaque body, when the light 
 
 ffifflg by one of its edges was intercepted, was that which first 
 
 d him to the principle of interference. An instructive variation 
 
 ' Biot, Precit elementaire, vol. ii. p. 472, 3 Edit. 
 
 'Experiments and Calculations relative to Physical Optics." Phil. Trans.
 
 DIFFRACTION. 57 
 
 in this experiment was made by M. Arago. The interior fringes 
 were found to disappear likewise, when the light passing by one of 
 the edges was transmitted through a plate of some transparent 
 substance ; and, by varying the thickness of the interposed plate, 
 M. Arago discovered that the disappearance of the fringes in this 
 case arose from their displacement, the bands being always trans- 
 ferred to the side on which the plate was interposed. From this 
 it followed that the light was retarded in the denser medium.* 
 M. Arago afterwards produced the same modification in the inter- 
 ference bands formed by two mirrors ; and the experiment, in this 
 form, is a complete crucial instance, as applied to the two theories 
 of light. The amount of the displacement determines the velo- 
 city of light in the medium, and therefore the refractive index, 
 with an accuracy unattainable by any other method. Professor 
 Powell has suggested a very elegant modification of this experi- 
 ment, which at once establishes the truth of the law that the 
 velocity of light is inversely as the refractive index of the medium 
 traversed, f 
 
 The experimental laws of the diffracted fringes were next 
 examined by MM. Biot and Pouillet. In the case of a narrow 
 rectilinear aperture which was that chiefly studied they found 
 that the deviations produced in the different species of simple 
 light, or the distances of the bands from the axis of the pencil, 
 were in all cases proportional to the lengths of the Jits, the magni- 
 tude of the aperture remaining the same. The same analogy was 
 preserved in different media, the deviations varying in the inverse 
 ratio of the refractive indices of the media, or in the direct ratio of 
 the fits.J M. Pouillet adds, that they were unable to explain 
 these laws, having adopted the theory of emission. They are all 
 simple consequences of the wave-theory. The interval of the fits is 
 exactly half the length of a wave ; and the true connexion between 
 the place of the fringes and the latter quantity had been already 
 pointed out by Young. 
 
 Mayer afterwards studied the phenomena of diffraction, but 
 without adding any new facts to those already known. As to the 
 
 * "Sur un Phenomena remarquable qui s'observe dans la Diffraction de la Lu- 
 mierc." Annaletde Chimie, torn. i. 
 
 t Phil. Jfaff., Second Series, vol. xi. p. 6. 
 
 t Biot, Trait* de Physique, torn. iv. Supplement a 1'Optique. 
 
 { Siemens de Physique, torn. ii. p. 437.
 
 58 KEPORT ON PHYSICAL OPTICS. 
 
 theory, he adopted that of Newton, with some modifications. With 
 Newton, he ascribed the inflexion of light into the shadow to the 
 operation of an attractive force ; but, unwilling to admit the ex- 
 istence of a repulsive force, he attempted to account for deflexion 
 by the impact of the molecules reflected from the edge against 
 those which passed by it.* 
 
 Fresnel at first adopted and developed Young's theory of dif- 
 fraction, and found that the general laws of the fringes the 
 dependence of their magnitude upon the length of a wave, and 
 upon the distances of the luminous origin and of the screen were 
 thus fully explained. It was shown that, as the position of the 
 screen is varied, the successive points at which the same fringe 
 is formed are not in a right line, but constitute an hyperbola ; and 
 that when the distance of the luminous origin is lessened, the 
 inclination of these hyperbolic branches, considered as coincident 
 with their asymptots, augments, and the fringes dilate in breadth, f 
 Fresnel, however, was soon dissatisfied with this theory. If the 
 exterior bands had their origin in the interference of the direct 
 and reflected light, their intensity should depend on the curvature 
 of the edge ; it is found, on the contrary, that the fringes formed 
 by the back and by the edge of a razor are precisely alike in every 
 respect. As to the other cases of diffraction, there were many 
 phenomena, and especially those exhibited in Newton's experi- 
 ment with the two knife-edges, which proved that the rays grazing 
 the edges of the body were not the only rays concerned in the 
 production of the fringes, but that the light which passed by those 
 edges at sensible distances was also deviated, and concurred in 
 their formation.* 
 
 Fresnel was thus led to seek a broader foundation for his 
 theory, and the result of his investigations is given in the able 
 memoir which was crowned by the French Academy in 1819. In 
 this memoir the laws of diffraction are derived from the two prin- 
 ciples to which the laws of reflexion and refraction are them- 
 selves referred the principle of interference and the principle of 
 Huygens. To apply these principles to the present case, Fresnel 
 supposes the surface of the wave, when it reaches the obstacle, to 
 
 * Comm. Soc. G'Mingensis Recentiores, vol. iv. p. 49. 
 
 t Annales de Chimie, torn. i. p. 239. 
 
 J Memoires sur la Diffraction de la Lumitre, p. 368.
 
 DIFFRACTION. 59 
 
 be subdivided into an indefinite number of equal portions, and he 
 applies the mathematical laws of interference, unfolded in this 
 memoir, to determine the resultant of all the elementary waves 
 sent by them at the same instant to any point. This resultant is 
 expressed by means of two integrals, which are to be taken within 
 limits determined by the particular nature of the problem. Its 
 square is the measure of the intensity of the light ; and it is found 
 that its value has several maxima, and minima, which correspond 
 to the intensities of the light in the bright and dark bands. 
 
 The problem of diffraction was thus completely solved ; and it 
 only remained to apply the solution to the principal cases, and 
 to compare the results with those of observation. The cases of 
 diffraction selected by Fresnel are : 1st. the phenomena produced 
 by a single straight edge ; 2nd. by an aperture terminated by 
 parallel straight edges; and 3rd. by a narrow opaque body of 
 the same form. The agreement of observation and theory is so 
 complete, that the computed places of the several bands seldom 
 differ from those observed by more than the hundredth part of a 
 millimetre, the case of diffraction by narrow apertures alone ex- 
 cepted. The small differences between observation and theory, 
 in this case, Fresnel ascribes to a false judgment of the eye as to 
 the position of the centre of the dark bands, occasioned by the 
 different intensities of the bright bands on either side, the mini- 
 mum always appearing nearer to the brighter light than it really 
 is. The computed places of the bands, in the first case of diffrac- 
 tion, were found to differ from those deduced from the hypothesis 
 of Young by a small numerical quantity, the distance of the first 
 dark band being less in the former theory, in the ratio of '936 to 
 unity ; but small as the difference is, the measures of Fresnel 
 completely decide the question.* 
 
 M. Poisson applied Fresnel's integral to the case of diffraction 
 by an opaque circular disc, and arrived at the singular result, that 
 the intensity of the light in the centre of the shadow is precisely 
 the same as if the disc were removed. This remarkable anticipa- 
 tion of theory has been verified by the observation of M. Arago.f 
 Fresnel himself solved the problem in the analogous case of a 
 circular aperture, and arrived at the result, that the intensity of 
 the light of any simple colour, at the central spot, will be the 
 
 * Hilmoire stir la Diffraction de la Lumu-re, p. 420. t /**., P- 460.
 
 60 REPORT ON PHYSICAL OPTICS. 
 
 same as that reflected by a plate of air, whose thickness bears a 
 certain simple relation to the radius of the aperture, and to its 
 distances from the luminous origin and from the eye. With 
 homogeneous light, therefore, the illumination of the central spot 
 vanishes periodically, as the distance of the eye from the aperture 
 is varied ; and in white light it assumes in succession the most 
 vivid and beautiful hues, coinciding with those of the reflected 
 rings of thin plates. These interesting phenomena were observed 
 about the same time by Sir John Herschel, and their laws deduced, 
 independently, from observation.* 
 
 With the exception of the observations now referred to, no 
 attempt has been made to verify the theory, by comparing the 
 intensity of the light in the fringes with that deduced from the 
 formulae ; and indeed it is obvious that a comparison of this nature 
 is ill calculated to afford any conclusive evidence on the question. 
 Fresnel thought, however, that the expression for the intensity 
 might be indirectly verified, by superposing two sets of fringes 
 (such as the interior and exterior fringes of a narrow opaque body), 
 by means of double refraction, and then examining the position of 
 the new maxima and minima. This ingenious suggestion does not 
 appear to have been acted on. 
 
 The intensity of the light in the partial waves sent from each 
 point of the primary wave, considered as a distinct centre of 
 disturbance, will necessarily be different in different directions, 
 depending on the angle which these directions form with the front 
 of the original wave ; and to solve the problem of diffraction in 
 its most general form, it would be necessary to know the law of 
 this variation. Fresnel has shown, however, that the rays whose 
 directions are inclined at sensible angles to the normal to the 
 front of the primary wave, destroy one another by interference ; 
 so that the actual effect is produced by rays indefinitely near that 
 normal, and which therefore may be regarded as of equal inten- 
 sity. The truth of this assumption, however, is disputed by M. 
 Poisson. From his theory of the propagation of motion in fluid 
 media, this mathematician inferred that the absolute velocities of 
 the molecules are insensible in directions making finite angles 
 with the direction of the original vibrations. He concludes, 
 therefore, that these velocities, or the intensity of the light in the 
 
 * Essay on Light, Art. 729.
 
 DIFFRACTION. 61 
 
 partial waves, cannot be regarded as sensibly equal in directions 
 inclined to it at very small angles.* Fresnel's reply to this part of 
 M. Poisson's theory has been already referred to. The principle 
 of Huygens itself, which forms the basis of Fresnel's theory, 
 though not denied by M. Poisson, is yet objected to as introducing 
 a needless complication into the question ; and indeed it does not 
 seem easy to understand, at first view, why each point of the pri- 
 mary wave in this mode of composition should not give rise to a 
 retrograde as well as to a direct wave.f 
 
 An objection of a different nature has been raised against 
 Fresnel's theory, derived from its supposed discordance with phe- 
 nomena. It is a consequence of that theory, when applied to the 
 case of diffraction by a narrow aperture bounded by parallel 
 straight edges, that if a point be taken in the axis of the pencil, 
 whose distances measured from the centre and edge of the aperture 
 differ by half a wave, that point will be the limit within which all 
 the interior fringes are confined ; and beyond that point the centre 
 of the image will be always white. This result is confirmed by the 
 previous experiments of M. Biot ; by the observations of Fresnel 
 himself ; and by those of Professors Airy and Powell, by whom 
 they have been since repeated. M. Biot found that the central 
 band was dark and white alternately, to a certain distance from 
 the aperture ; after which it was always white. He remarks that 
 when this limit is attained, we may diminish the breadth of the 
 aperture, and even bring its sides into actual contact, without any 
 change in the central band, except its enlargement and consequent 
 diminution of intensity. J 
 
 Newton's celebrated experiment with the two knife-edges has 
 been adduced in opposition to these results. Newton found that 
 when the distance of these edges was the 400th part of an inch, 
 the light which passed between the knives parted in the middle, 
 
 * It may be necessary to state that it was part of M. Poisson's theory, that tho 
 vibrations are normal to the wave. 
 
 t See Annales de Chimie, torn. xxii. p. 270 ; and Airy's Mathematical Tracts, 
 p. 267. 
 
 } Traits de Physiqut, torn. iy. pp. 749, 760. The description of the phenomenon 
 given by Mayer is very similar : " Prout ilia distantia acierum semper magis magisque 
 imminuitur, fasciae adeo evanescunt, ita ut denique non nisi fascia media remaneat ; 
 sed ad dextram atque sinistram adeo in latitudinem extensa, ut non nisi lumen langui- 
 dum, a medio spectri initialis utrinquc instar caudse cometce sese dilatans, represents." 
 G'dttingen Memoirs, vol. iv. p. 61.
 
 (52 REPORT ON PHYSICAL OPTICS. 
 
 and left a dark space in the centre * The experiment has been 
 repeated by Mr. Barton, and with a similar result. t These ex- 
 periments, however, were made with curved edges; and as Professor 
 Powell has observed, we have no ground for supposing that the 
 phenomenon may not be modified by this change in the conditions 
 under which it is presented. The theory of Fresnel has not been 
 applied to the more complex problem of an aperture with curvi- 
 linear edges, and the analytical difficulties of the problem seem to 
 be insuperable. There seems to be some uncertainty, however, 
 with respect to the phenomenon itself. Professor Powell repeated 
 the experiment with edges of various curvatures, and always 
 found that the centre was a point of relative brightness, as com- 
 pared with other points in the line perpendicular to the length of 
 the aperture. J As to Newton's experiment, it seems certain, as 
 the same writer has observed, that we are not acquainted with all 
 its conditions ; and it is apparent from many passages that the 
 illustrious observer himself was far from being assured with respect 
 to the real nature and circumstances of these phenomena.! 
 
 But there is another essential circumstance to be taken into 
 account, in comparing the experiments of Newton with the results 
 of Fresnel's theory. In that theory the origin of light is supposed 
 to be a point ; and this condition is practically fulfilled by making 
 the light to diverge from the focus of a lens of high power, the 
 origin of the light in that case being (by the principles of the 
 wave-theory) the minute image of the sun in the focus. In 
 Newton's experiments, however, the sun's light was made to pass 
 through a hole of sensible magnitude; and in the remarkable 
 experiment now referred to, that hole was a quarter of an inch in 
 diameter. The problem of diffraction in this case is one of much 
 greater complexity. It is necessary to determine the joint effect 
 produced at any point of the diffracting aperture by the several 
 indefinitely small portions of a wave transmitted through the ex- 
 
 * Optics, Book iii., Obs. vi. and vii. 
 
 t- Phil. Mag., vol. ii. p. 268. 
 
 J Ibid., p. 429, &c. 
 
 " The subject of the third book I have also left imperfect, not having tried all 
 the experiments which I intended when I was about these matters, nor repeated some 
 of those I did try until I had satisfied myself about all their circumstances. To com- 
 municate what I have tried, and leave the rest to others for further inquiry, is all my 
 design in publishing these papers." Optics, Advertisement 1. See also latter part of 
 Obs. 11, Book iii.
 
 DIFFRACTION. 63 
 
 ternal hole ; and, considering each of these as a new centre of 
 disturbance, to find their total resultant at any point of the screen 
 on which the fringes are received. The method of solution has 
 been pointed out by Professor Airy ; and he has shown that when 
 the external hole is a rectangular parallelogram, and the diffract- 
 ing aperture of the same form, and similarly placed, the law of 
 illumination at any point of a screen will be similar to that pro- 
 duced by a rhomboidal aperture, in Fresnel'a method of obser- 
 vation; the dimensions and distances in the two cases being 
 connected by certain relations.* From these investigations Pro- 
 fessor Airy concludes that the size of the external hole could 
 not account for the dark central shadow mentioned by Newton 
 in the sixth observation. He has confirmed this conclusion by 
 experiment ; and employing holes of various magnitudes, he found 
 the central band in all cases bright. The effect recorded by New- 
 ton is ascribed by Professor Airy to the influence of contrast on 
 the retina. 
 
 A remarkable class of phenomena arise when a lens is placed 
 close to an aperture of any form, and the light received on a screen 
 at its focus, or on an eye-glass at its own focal distance from 
 it. In fact, the phenomena of diffraction are in this manner pro- 
 duced with holes of considerable dimensions, and were observed by 
 Sir W. Herschel, with the undiminished apertures of his great 
 telescopes ; the stars being seen encompassed by several dark and 
 bright rings, succeeding one another at equal intervals, when a 
 high magnifying power was employed. But the phenomena be- 
 come more distinct when the aperture is limited by a diaphragm 
 of moderate size, the diameters of the rings varying inversely as 
 those of the apertures. The effects produced by diaphragms of dif- 
 ferent sizes and forms have been examined in much detail by Sir 
 John Herschel and M. Arago.f 
 
 The phenomena produced by minute apertures, when combined 
 with a lens in the manner now spoken of, have been studied with 
 much zeal and success by Fraunhofer. The most remarkable of 
 these phenomena are those produced by a fine grating, such as may 
 be formed by stretching a fine wire between two parallel screws of 
 
 * " On the Calculation of Newton's Experiments on Diffraction." Camli<l<j<- 
 Trans., vol. v. part 2. 
 
 t Professor Amici has also noticed some phenomena of the same class. See EdiM. 
 Journal of Science, vol. iv. p. 306.
 
 64: REPORT ON PHYSICAL OPTICS. 
 
 equal thread. When such a grating is placed before the object- 
 glass of a telescope, and a narrow slit, whose length is parallel 
 to the wires of the grating, viewed through it, the direct image of 
 the slit is bordered on either side by a succession of richly-coloured 
 diffracted images, which increase in breadth and diminish in bright- 
 ness as they recede from the centre. The first pair of spectra are 
 separated from the central image by a space absolutely black, and 
 a similar interval occurs between the first and second pair. Fraun- 
 hofer observed, under favourable circumstances, thirteen such spectra 
 on either side of the central image. He has measured with great 
 accuracy the angular deviations of the rays of each colour from the 
 axis ; and he has found that the experimental laws thus deduced 
 agree in the most complete manner with the results of the prin- 
 ciple of interference.* The results are the same, both by theory 
 and experiment, in the case of reflexion from ruled surfaces.f 
 
 The optical phenomena of gratings are interesting in many 
 points of view. The appearance of lateral spectra, produced by 
 simply intercepting a part of the light, proves that the light actually 
 diverges in all directions from the front of the grand wave where 
 it meets the lens, and that it is to the interference of this light 
 with that intercepted by the grating that we are to ascribe its 
 want of sensible effect under ordinary circumstances.* Another 
 very remarkable circumstance of these phenomena is the purity of 
 the light of each simple colour, which is such that the fixed lines 
 
 The angular deviation, 0,,, of any ray from the axis is expressed by the formula 
 
 n\ 
 
 sin 8 n = , 
 
 in which n denotes the order of the spectrum, \ the length of an undulation, and 6 the 
 interval of the axes of the wires. The value of e is obtained with great precision, so 
 that the measurement of the angular deviations of the rays of each simple colour affords 
 the most exact data for the determination of the lengths of their waves. Fraunhofer 
 has in this manner computed the lengths of the waves, corresponding to the seven 
 principal fixed lines in the spectrum ; and the resulting values are perhaps the most 
 exact optical constants we possess. It is a remarkable consequence of the expression 
 above given, that when e is less than \, the angle 6 will be imaginary. In this cast', 
 then, there can be no coloured spectra ; and it follows that scratches or inequalities on. 
 any polished surface, whose interval is less than the length of a wave, do not disturb 
 the regularity of reflexion and refraction. 
 
 t Fraunhofer's researches on diffraction are published in the Memoirs of the Bava- 
 rian Academy of Sciences, vol. viii. A very full analysis of them is given in the 
 Edinburgh Encyclopedia, art. OPTICS; and in Sir J. Herschel's "Essay on Li-ht " 
 Encyc. Metrop. 
 
 J Airy's Math. Traett, p. 331.
 
 DIFFRACTION. 65 
 
 may be discerned in the spectra. The distances of these lines, in 
 the diffracted spectrum, are always proportional, whatever be the 
 diffracting substance ; while the ratios of their intervals, or the 
 breadths of the coloured spaces, in the spectra formed by refrac- 
 tion, vary with the nature of the prism. This fact appears to be 
 decisive against the Newtonian theory of inflexion, in which in- 
 flexion and refraction are referred to the same cause. 
 
 The analytical investigation of the problem of diffraction in the 
 cases last alluded to those, namely, in which a lens is combined 
 with the aperture, and the intensity of the light is sought at any 
 point of a parallel plane passing through the focus is far more 
 manageable than in most other cases. The general expression of 
 the displacement is at once integrated with respect to one of the 
 variables, and the complete integral can, in many cases, be exactly 
 found. Professor Airy has given the solution of this problem in 
 his valuable tract on the Undulatory Theory,* and in applying it 
 to the phenomenon last mentioned has deduced all the appearances 
 observed by Fraunhofer. The remarkable appearance of the six- 
 rayed star, observed by Sir John Herschel, when a triangular 
 diaphragm was placed before the object-glass of a telescope, has 
 been likewise deduced as another case of the same problem. 
 
 The same effects, as Fraunhofer observed, were produced by 
 reflexion from grooved surfaces ; and their theory is to be referred 
 to the same principles, the light reflected from the surfaces be- 
 tween the grooves interfering in a manner precisely analogous to 
 that admitted through the apertures of the gratings. The colours 
 exhibited by such surfaces under ordinary circumstances were ob- 
 served by Boyle and Grimaldi ; Young showed that they were 
 consequences of the principle of interference, and determined the 
 law of their recurrence depending on the incidence ;f and Sir 
 David Brewster seems to have been the^ first to observe that the 
 spectra formed in these cases of multiplied diffraction approached 
 the solar spectrum in purity far more nearly than the ordinary 
 diffracted bands, or the coloured rings of Newton. These phe- 
 nomena indicate the superficial structure more unerringly, perhaps, 
 than the most powerful microscopes. Among the most important 
 and beautiful instances of this application of optical science may 
 
 * Math. Tracts, p. 321, See. 
 
 t " On the Theory of Light and Colours. "Phil. Tran$. 1801.
 
 QQ REPORT ON PHYSICAL OPTICS. 
 
 be ranked the analysis of the colours of mother-of-pearl,* and the 
 investigation of the structure of the crystalline lenses of the eyes 
 of fishes and other animals, by Sir David Brewster.f The same 
 author has also described a new series of periodical colours, which 
 are exhibited by some of the plates of grooved steel constructed by 
 Mr. Barton, and which succeed one another in a plane at right 
 angles to that in which the usual spectra are developed.? The 
 theory of this phenomenon remains yet to be developed. In the 
 solution of the analogous problem, given by Professor Airy, a 
 periodical variation in the intensity of the light in the direction of 
 the apertures of the grating is indeed pointed out ; but that varia- 
 tion, it is easily seen, will not account for the facts last mentioned. 
 
 IV. Colours of thin Plates. 
 
 The earliest observations on record, in which the colours of thin 
 plates were made the subject of experimental research, are those 
 of Boyle. This diligent observer remarked the fact, that most 
 transparent substances exhibit colour by reflected light when suf- 
 ficiently reduced in thickness ; and that these tints varied in the 
 same substance, and therefore did not depend essentially upon its 
 chemical nature. The observations of Boyle were made on the 
 bubbles of various liquids, and he even succeeded in blowing glass 
 sufficiently thin to exhibit similar phenomena. 
 
 The vivid and varying colours of the soap bubble also engaged 
 the attention of Hooke ;|| but the most important of the observa- 
 tions of this philosopher, connected with the subject of thin plates, 
 are those recorded in his Micrographia, which was published in the 
 year 1665. In this work he shows that the colours of laminae of 
 mica are dependent on their thickness, and appear only when that 
 thickness is comprised within certain limits; that when the tint 
 exhibited by a given plate is uniform over its entire surface, the 
 plate is also uniformly thick ; and that the colour presented by 
 two plates superposed is different from those of either beparately. 
 Hooke has also the merit of producing the phenomena of thin 
 
 * Phil. Trans. 1814. 
 
 f Ibid. 1833. 
 
 J Phil. Trans. 1829. 
 
 Experiments and Observations upon Colours, 1663. 
 
 II Birch's History of the Royal Society, vol. iii. p. 29.
 
 COLOURS OP THIN PLATES. 67 
 
 plates in the instructive form in which their laws have since been 
 studied, namely, by placing two object-glasses in contact ; and he 
 found that any transparent fluid introduced between the lenses 
 furnished a succession of colours as well as air ; the colour, how- 
 ever, being more vivid, the more the refractive power of the plate 
 differed from that of the glasses within which it was inclosed. 
 
 The attention of Newton was soon after directed to the same 
 subject ; and his investigations, which ended in the complete dis- 
 covery of the laws of the phenomena, will ever be considered as a 
 model of experimental inquiry. A convex lens of glass being laid 
 upon a plane surface of the same material, after the manner of 
 Hooke, the bands of the same colour are arranged round the point 
 of nearest approach in concentric circles ; and the diameters of 
 these circles will be obviously as the square roots of the thicknesses 
 of the plate of air at the points at which they are exhibited. In 
 order to investigate the relation between the colour and the thick- 
 ness, then, it was only necessary to measure the diameters of these 
 rings in the different species of simple light ; and taking similar 
 measurements when the other circumstances of the phenomena 
 were varied, Newton deduced their laws, as they depended on the 
 substance of the reflecting plate, and on the obliquity of the inci- 
 dent pencil. Newton observed, moreover, that there was a second 
 system of rings formed by transmission. The transmitted rings 
 were found to observe the same laws with this remarkable excep- 
 tion, that the colour transmitted at any particular thickness of the 
 plate was always complementary to that reflected at the same 
 thickness, so that in homogeneous light, the bright transmitted 
 ring is always found at the same distance from the centre as the 
 corresponding dark one of the reflected system. 
 
 The observations of Mariotte,* Mazeas,f and Du Tour, have 
 added nothing essential to the laws discovered by Newton. Most 
 of these observations, in fact, related to the colours exhibited by 
 the plate of air inclosed between two plane glasses, and in circum- 
 stances, therefore, much less favourable to the analysis of the 
 phenomenon than those selected by Newton. Perhaps the most 
 interesting of the facts noticed by Mazeas are the effects produced 
 
 * Traite de la Lumiere et des Couleurs. 
 f Memoires presentes, torn. ii. 
 Ibid., torn. iv. v. vi. 
 
 r2
 
 (J3 REPORT ON PHYSICAL OPTICS. - 
 
 on the coloured bands by the application of heat to the glasses, the 
 colours retreating to the edges of the plates, and the bands dimi- 
 nishing in breadth as the temperature was increased. The same 
 author also found that no sensible change took place in the phe- 
 nomenon when the air was withdrawn by the air-pump. 
 
 In the observations of Du Tour, the reflected and the transmit- 
 ted tints were observed at the same time, the latter being reflected 
 from the second surface of the lower glass, and returning to the 
 eye through the entire system. This latter set of rings is rendered 
 more distinct, when the shadow of an opaque body is passed over 
 the upper surface. In this manner the phenomenon was observed 
 by Sir William Herschel ; and it was found that additional sets of 
 rings became visible by increasing the number of reflecting faces. 
 Sir William Herschel observed, likewise, that the primary reflected 
 system was produced when a lens was laid upon a metallic re- 
 flector ; and he remarks that, in this case, the transmitted system 
 must be conceived to be absorbed by the metal. The same author 
 has described a remarkable set of coloured bands adjacent to the 
 iris, at the limit of total reflexion, when a prism is in contact with 
 a plane surface.* The analysis of this phenomenon has been given 
 by Sir John Herschel in his Essay on Light.f 
 
 The important observations of M. Arago are the next to de- 
 mand our notice. J Viewing the rings through a rhomboid of 
 Iceland spar, whose principal section was parallel or perpendicular 
 to the plane of incidence, this philosopher observed that the inten- 
 sity of the light in one of the images varied with the incidence, 
 and that it vanished altogether when the rays made an angle of 
 35 with the surface. It was further observed that the same 
 image vanished, and at the same angle, whether the rings were 
 formed by reflexion or transmission. Thus, the light of the trans- 
 mitted, as well as of the reflected rings, was wholly polarized in 
 the plane of incidence, and at the usual angle for glass. M. Arago 
 has further shown, that the colours of the reflected and transmitted 
 rings are not only complementary, but that their intensities are 
 also precisely the same ; for, when the two systems are superposed, 
 they completely neutralize each other. 
 
 * "Experiments for investigating the Cause of the Coloured Rings," &c.Phil. 
 Trans. 1807, 1809, 1810. 
 t Articles 641, 642. 
 J " Sur les Couleurs des Lames minces." Memoires d'Jrmeil, torn. iii.
 
 COLOURS OF THIN PLATES. 69 
 
 But the most remarkable of the results obtained by this author 
 relate to the rings formed by the plate of air inclosed between a 
 lens of glass and a metallic reflector. When these were observed 
 in the manner already alluded to, one of the images vanished, as 
 before, at the polarizing angle of glass ; while its appearance, at 
 angles above and below the polarizing angle, presented a remark- 
 able contrast. When the incidence was less than this angle, the 
 two images seen through the double refracting crystal differed 
 only in intensity ; the dimensions and colours of the rings were 
 the same in both. Beyond the polarizing angle, however, the 
 rings in the two images were of complementary colours ; so that if 
 the series in one commenced from a black centre, in the other it 
 began from a white one. The dimensions of the rings of the same 
 order in the two images were also different. Similar phenomena 
 were produced when the thin plate was of a density intermediate 
 to those of the two substances between which it was contained. 
 I shall hereafter have occasion to refer to the observations and 
 deductions of Professor Airy connected with these phenomena. 
 
 When the metallic reflector was slightly tarnished, a second 
 system of rings was visible to the naked eye. The formation of 
 these rings depended on the light irregularly dispersed at. the 
 surface of the metal ; and they were visible, in whatever manner 
 the eye was placed with respect to the incident light. Their tints 
 were complementary to those of the regular series. 
 
 It was soon felt that the phenomena of thin plates were closely 
 connected with some new and fundamental property of light,* 
 and that it was in their application to these phenomena that all 
 theories of light were to be judged. For their explanation, it has 
 been already stated, Newton invented his celebrated doctrine of 
 the " fits of easy reflexion and transmission," a doctrine which will 
 always hold a prominent place in the page of philosophical history. 
 Its application is obvious. The ray is in a fit of easy transmission 
 in its passage through the first surface ; this is succeeded by a fit 
 of easy reflexion, and so alternately. On arriving at the second 
 surface, then, the ray will be in a fit of easy transmission or easy 
 
 * It is unnecessary to refer to the theories of Sir William Herschel, or of M. Par- 
 rot, in both of which the laws of thin plates have been referred to those of reflexion 
 and refraction ; or to that of Mayer, who attempted to reduce them to inflexion. None 
 of these theories have had supporters, and they are all of them inconsistent with 
 oLvious facts.
 
 70 REPORT ON PHYSICAL OPTICS. 
 
 reflexion, according as the interval of the surfaces, or the thickness 
 of the plate, is an even or an odd multiple of the length of the fit. 
 Thus the alternate succession of bright and dark rings in homo- 
 geneous light, and the arithmetical progression of the thicknesses 
 at which they are exhibited, are satisfactorily explained. To 
 explain the variation in the dimensions of the rings depending on 
 the nature of the light, it is necessary to suppose that the length 
 of the fits varies with the colour being greatest in red light, 
 least in violet, and of intermediate magnitude for the rays of inter- 
 mediate refrangibility. Newton determined the absolute lengths 
 of these fits for the rays of each simple colour, and found that 
 they bore a remarkable numerical relation to the lengths of the 
 chords sounding the octave. These results are even yet referred 
 to as fundamental data in optical inquiries. 
 
 To account for the remaining laws Newton was constrained to 
 make new suppositions, and to attribute properties to the fits 
 which seem inconsistent with every physical account which has 
 been given of them. Thus, to explain the dilatation of the rings 
 with the increasing obliquity of the incident pencil, he assumed 
 that the length of the fits augmented with the incidence, and 
 according to a complicated law. This assumption is at entire 
 variance with the physical theory. If the fits are produced by 
 the vibrations of the ether, which are propagated faster than the 
 rays, and which alternately conspire with and oppose their pro- 
 gressive motion, their lengths should continue the same in the 
 same medium, whatever be the incidence. No attempt, that I am 
 aware of, has been made to reconcile this law with the physical 
 hypothesis of Mr. Melville and M. Biot. 
 
 The same may be said of the variation of the dimensions of 
 the rings with the substance of the reflecting plate. Newton found 
 that when a drop of water was introduced between the glasses, the 
 rings contracted ; and by comparing their diameters in air and in 
 water, he found that the corresponding thicknesses of the plate 
 were as 4 to 3, or in the inverse ratio of the refractive indices. It 
 was necessary to suppose, therefore, that in different media, the 
 lengths of the fits varied in the same proportion ; and, since in the 
 Newtonian theory the refractive indices are directly as the veloci- 
 ties of propagation, it followed that as the velocities augmented, 
 3 spaces traversed by the ray in the interval of its periodical 
 states must diminish, and in the same ratio.
 
 COLOURS OF THIN PLATES. 71 
 
 But the facts observed by M. Arago and Professor Airy seem 
 to overturn altogether this part of the theory of emission. The 
 rings formed by a plate of air, inclosed between a lens of glass 
 and a metallic reflector, vanish altogether when the light is 
 polarized perpendicularly to the plane of incidence, and is incident 
 at the polarizing angle of glass. Under these circumstances, no 
 light is reflected from the upper surface of the plate ; but as it is 
 abundantly reflected from the lower, the disappearance of the rings 
 proves that the light reflected from the upper surface is essential to 
 their production. That the light reflected from the lower surface 
 also concurs in their formation, appears from the effects observed 
 by M. Arago, when the metallic plate was tarnished ; and we are 
 thus driven to the conclusion, that the phenomena arise from the 
 union and mutual influence of the pencils reflected from the two 
 surfaces. 
 
 This mode of explaining the colours of thin plates was pointed 
 out by Hooke, in a remarkable passage in his Micrographia, some 
 years before the subject was taken up by Newton. In this passage 
 he very clearly describes the manner in which the rings of succes- 
 sive orders depend on the interval of retardation of the second 
 " pulse," or wave, on the first, and therefore on the thickness of 
 the plate. But he does not seem to have had any distinct idea of 
 the principle of interference itself ; and his conception of the mode 
 in which the colours resulted from this "duplicated pulse" is 
 entirely erroneous. Euler was the next who attempted to connect 
 the phenomena of thin plates with the wave-theory of light ; but 
 the attempt, like all the physical speculations of this great mathe- 
 matician, was signally unsuccessful. Euler thought, in fact, that 
 the colours of thin plates, as well as those of natural bodies, 
 arose from emitted, and not from reflected light. The incident 
 light was supposed to excite the vibrations of the plate, the fre- 
 quency of which depended on its thickness, in the same manner as 
 the frequency of the vibrations of the column of air in a tube 
 depends on its length. These vibrations again were believed to 
 excite those of the luminiferous ether, and thus to produce the 
 sensation of various colours, the red corresponding to the less 
 frequent vibrations, and the violet to the most frequent.* 
 
 The subject remained in this unsatisfactory state until the 
 
 * Mem. Acad. Berlin, 1752.
 
 72 REPORT ON PHYSICAL OPTICS. 
 
 principle of interference was discovered by Young. When this 
 principle was combined with the suggestion of Hooke, the whole 
 mystery vanished. The application was made by Young himself; 
 and all the principal laws of the reflected rings were readily and 
 simply explained, by the interference of the two portions of light 
 which are reflected at the two surfaces of the plate.* In applying 
 this principle, however, Young perceived that the interval of re- 
 tardation was not simply that due to the difference of the paths 
 traversed by the two pencils ; but that one of them must be sup- 
 posed to undergo a change of phase, amounting to half an undula- 
 tion, at the instant of reflexion. Young clearly pointed out the 
 accordance of this effect with mechanical principles ; and the con- 
 nexion has been fully confirmed by the more complete investiga- 
 tions of Fresnel. In fact, the two reflexions take place under 
 opposite circumstances, one of the portions being reflected at the 
 surface of a rarer, and the other at that of a denser, medium ; and 
 the laws of impact of elastic bodies indicate that the direction of 
 the vibratory movement must be reversed by reflexion in the one 
 case, while in the other it is unchanged. Young had the satis- 
 faction of putting this principle to the test in a remarkable man- 
 ner. It followed from it that, if the thin plate were of a refractive 
 density intermediate to those of the two media within which it 
 was inclosed, the laws of the phenomenon would be determined 
 by the difference of the paths alone, the reflexion being of the 
 same kind at the two surfaces. Young accordingly predicted that 
 in this case the rings should commence from a white centre, instead 
 of a black one, and the prediction was soon after verified on trial, f 
 The transmitted rings are accounted for, in the wave-theory, 
 by the interference of the direct light with that which has under- 
 gone two reflexions within the plate ; and it follows from the pre- 
 ceding considerations that their colours must be complementary 
 to those of the reflected system. This origin at once shows the 
 reason of the fact observed by M. Arago, that the light of the 
 transmitted rings is polarized in the plane of reflexion. M. Biot 
 has laboured to reconcile this fact to the theory of emission, with 
 which it appears, at first view, at utter variance. The account 
 which he has given of the phenomenon will, I think, be hardly 
 deemed satisfactory.? 
 
 ^ On the Theory of Light and Colours." Phil. Trans. 1802. 
 h "Account of some Cases of the Production of Colours." .PM. Trans. 1802. 
 t See Biot's " TraiU de Physique," torn. iv. pp. 308, et *eq.
 
 COLOURS OF THIN PLATES. 73 
 
 The theory of thin plates, as it came from the hands of Young, 
 was however incomplete. It is obvious that the intensity of the 
 two portions of light reflected from the upper and under surfaces 
 of the plate can never be the same, the light incident on the 
 second surface being already weakened by partial reflexion at the 
 first. These two portions therefore cannot wholly destroy one 
 another by interference ; and the intensity of the light in the dark 
 rings should never entirely vanish, as it appears to do when homo- 
 geneous light is employed. M. Poisson was the first to point out, 
 and to remedy, this defect of the theory. It is evident, in fact, 
 that there must be an infinite number of partial reflexions within 
 the plate, at each of which a portion is transmitted ; and that it is 
 the sum of all these portions, and not the two first terms of the 
 series only, which is to be considered in the calculation of the 
 effect. Taking up the problem in this more general form, and 
 employing the formula obtained by himself and Young for the 
 intensity of the light reflected and transmitted at a perpendicular 
 incidence, M. Poisson has proved that at this incidence, and at 
 points for which the thickness of the plate is an exact multiple of 
 the length of half a wave the intensity of the reflected and 
 transmitted lights will be the same as if the plate were suppressed 
 altogether, and the bounding media in absolute contact ; so that 
 when these media are of the same refractive power, the reflected 
 light must vanish altogether, and the transmitted light be equal to 
 the incident.* Fresnel afterwards showed that the result was 
 independent of the expression for the intensity of the reflected 
 light ; and by the aid of the property discovered by M. Arago, 
 namely, that the light is reflected in the same proportion at the 
 first and second surfaces of a transparent plate he extended 
 the conclusion to all incidences.! The general expression of the 
 intensity of the light in any part of the reflected or transmitted 
 rings has been given by Professor Airy.J 
 
 Here, then, we have reached a point with respect to which the 
 two theories are completely opposed. According to both, a cer- 
 
 * " Sur le Phenomcnedes Anneaux Colores." Annales de Chimit, torn. xxii. p. 33 
 M. Poisson has further shown that rings absolutely black will be formed at points 
 corresponding to the bright rings in the ordinary case, when the velocity of propa- 
 gation within the plate is a mean proportional to the velocities in the bounding media. 
 
 t Annales de Chimie, torn, xxiii. p. 129. 
 
 I Math. Tracts, p. 302, &c.
 
 74 REPORT ON PHYSICAL OPTICS. 
 
 tain portion of light is reflected from the first surface of the plate. 
 This, in the Newtonian theory, is left in all cases to produce its full 
 effect ; while in the wave-theory it is, at certain intervals, wholly 
 destroyed by the interference of the other pencil, and the dark 
 rings should he absolutely black in homogeneous light. The latter 
 of these conclusions seems to accord with phenomena, while the 
 former is obviously at variance with them. This is clearly shown 
 by an experiment of Fresnel. A prism was laid upon a lens 
 having its lower surface blackened, a portion of the base of the 
 prism being suffered to extend beyond the lens. The light re- 
 flected from this portion, according to the Newtonian theory, 
 should not surpass in intensity that of the dark rings. The rough- 
 est trial is sufficient to show that the intensity of the light in the 
 two cases is widely different, and to prove that the dark rings 
 cannot arise (as they are supposed to do in the theory of fits) from 
 the suppression of the second reflexion.* 
 
 Mr. Potter has applied a new method of " photometry by com- 
 parison " to determine the relative intensities of the light in the 
 bright and dark rings of the transmitted system. In this method 
 the ratio of the intensities of the light reflected from two plane 
 glasses is varied, by varying the incidence, until it is judged to be 
 equal to the ratio of the light in the bright and dark rings. The 
 former ratio is then deduced from the incidence by means of an 
 empirical formula. In this manner Mr, Potter concludes that the 
 ratio of the light in the rings, at a perpendicular incidence, is 2'48 
 for green light, and 3*49 for red.f The ratio deduced from the 
 principles of the wave-theory is about 1-20 in the case of crown 
 glass. But, independently of the uncertainty connected with the 
 empirical law, which is taken by Mr. Potter as the basis of his com- 
 putation in these deductions, the photometrical method itself seems 
 to be open to objection. It appears to be assumed, in the appli- 
 cation of that method, that where the quantity of light incident 
 upon an irregularly reflecting surface is given, the quantity of 
 reflected light will be the same in its entire amount, and in all 
 directions, whatever be the incidence. This seems to be contra- 
 dicted by obvious facts. There is yet another difficulty in the 
 application of this method, which appears to leave room for some 
 
 * Memoire sur la Diffraction, p. 347. 
 t Phil. Mag., 3rd Series, vol. i. p. 174.
 
 COLOURS OF THIN PLATES. 75 
 
 uncertainty in the results. Where luminous objects are so small 
 that the eye cannot readily distinguish parts, the absolute quan- 
 tity and the intensity of the light are confounded. I am not 
 aware how far this may have been the case in Mr. Potter's instru- 
 ment ; but it is remarkable that, if we suppose the quantities of 
 light reflected from the two glasses to have been taken as the 
 terms of comparison, the calculated results will accord very closely 
 with theory.* 
 
 When a beam of light falls upon two plates superposed, some 
 of the many portions into which it is divided by partial reflexion 
 at the bounding surfaces are often in a condition to interfere and 
 exhibit colour. Thus, when light is transmitted through two 
 parallel plates, slightly differing in thickness, the colour produced 
 will be that corresponding to the difference, and will be indepen- 
 dent of the interval of the plates. This phenomenon was ob- 
 served by Mr. Nicholson,! and was shown by Dr. Young to arise 
 from the interference of two pencils, one of which is twice reflected 
 within the first glass, and the other twice reflected in the second. 
 Sir David Brewster observed a similar case of interference pro- 
 duced by two plates of equal thickness, slightly inclined, the thick- 
 ness traversed in the two plates being altered by their inclination. 
 In both these cases, however, the interfering pencils are mixed 
 up with, and overpowered by, the light directly transmitted, and 
 some contrivance is necessary to make the fringes visible. The 
 phenomena are much more obvious in the light reflected by both 
 plates, which, on account of their inclination, is separated from 
 the direct light. It is obvious, in fact, that the direct image 
 of a luminous object seen through the glasses will be accom- 
 panied by several lateral images, formed by two, four, six, etc., 
 reflexions. These images Sir David Brewster observed to be 
 richly coloured. The bands are parallel to the line of junction of 
 the two glasses, and their breadth is greater the less the inclination 
 of the plates. J The colours in the first lateral image are produced 
 by the interference of the pencils which have undergone two re- 
 flexions, one of them being reflected internally by the first plate 
 and externally by the second, while the other is reflected inter- 
 
 See Phil. Mag. vol. v. p. 441. 
 
 f Nicholson's Journal, vol. ii. p. 312. 
 
 I Edinb. Trans., vol. vii. p. 435.
 
 76 REPORT ON PHYSICAL OPTICS. 
 
 nally by the second, and externally by the first. The routes of 
 these portions differ only by reason of the different inclinations 
 at which they traverse the intervals of the surfaces. M. Pouillet 
 has observed a phenomenon of the same kind, when a thick plate 
 of glass is placed above a metallic mirror, and in a direction nearly 
 parallel to its surface.* The interfering rays in this case appear 
 to be those which have undergone two reflexions within the plate, 
 and one at the surface of the mirror, the reflexion from the mirror 
 preceding the others in the case of one pencil, and following them 
 for the other. The routes of two such pencils will slightly differ, 
 owing to the different obliquity under which they traverse the 
 plate. 
 
 The remarkable phenomena observed by Mr. Knox, when a 
 double-convex lens was combined with two plane glasses, one 
 adjacent to each surface, have been explained by Young on the 
 same principles. In addition to the rings exhibited by each plate 
 of air, a third system of concentric rings is formed in this case, the 
 dimensions of which are greater than those of either of the pri- 
 mary systems. The diameters of these rings increase indefinitely 
 as those of the primary systems approach to equality ; until finally 
 the circles become straight lines when they are equal, f It is 
 easily seen, in fact, that each ring is the locus of the points for 
 which the difference of the thicknesses of the two plates of air 
 is constant ; and that this locus is a circle, whose diameter will 
 depend on the curvatures of the surfaces, and on the interval of 
 the centres of the two primary systems. The fringes formed by 
 " double plates " have been observed under another form by Mr. 
 Talbot, when two films of thin blown glass were superposed. 
 
 The "colours of thick plates" are perhaps of too unusual 
 occurrence to entitle them to be studied as a separate class of 
 optical phenomena; the attention which they have received is 
 owing to the investigations of Newton. In the experiment of 
 Newton a beam of light is admitted through a small aperture, 
 and received on a concavo-convex mirror with parallel surfaces, 
 the second of which is silvered. When a screen of white paper is 
 then held at the centre of the mirror, having a hole in the middle 
 to allow the beam to pass and repass, a set of broad coloured rings 
 
 * Element de Physique, torn. ii. p. 478. 
 t Phil. Trans., 1815, p. 161.
 
 COLOURS OF THIN PLATES. 77 
 
 will be depicted on it, similar to the transmitted rings of thin 
 plates, the diameters of the rings varying inversely as the square 
 roots of the thicknesses of the mirrors. The Duo de Chaulnes 
 observed that similar phenomena were produced when a metallic 
 mirror was substituted for the glass one, and the rays transmitted 
 through a semi-transparent plate of any kind, or even through a 
 screen of gauze placed at a short distance in front of the mirror.* 
 Sir W. Herschel found that the rings could be produced by scat- 
 tering fine powder in the air before the mirror ;f and M. Pouillet 
 has ascertained that similar rings are formed, when the light inci- 
 dent on the mirror is simply transmitted through an aperture of 
 any form in an opaque screen.^. More recently, Mr. Whewell and 
 M. Quetelet have observed a set of coloured bands, which are 
 formed when the image of a candle is viewed in a plane glass 
 mirror, the candle being held at a short distance in front of the 
 eye, so that the incident and reflected rays may make a small 
 angle. M. Quetelet appears to think, however, that this pheno- 
 menon is to be referred to a different class from those last con- 
 sidered. 
 
 Newton very ingeniously accounted for the colours observed 
 in his experiments, by the fits of easy reflexion and transmission 
 of that [portion of light which is scattered in all directions at the 
 first surface of the glass; and M. Biot has extended the expla- 
 nation to the analogous phenomena observed by the Duo de 
 Chaulnes. Young showed that they could be explained by the 
 interference of the two portions of light which are scattered in the 
 passing and repassing of the ray through the refracting surf ace. || 
 The complete investigation, as far as relates to the dimensions of 
 the successive rings, is given by Sir John Herschel; and the 
 formula obtained is found to agree precisely with Newton's 
 measures.lf 
 
 When the interval between two glasses is filled with different 
 substances, such as water and air, or water and oil, in a finely 
 
 * Mem. Acad. Par. 1755. 
 t Phil. Trans. 1807. 
 J Elemens de Physique, torn. ii. p. 476. 
 
 Correspondance Matketnatiquf, torn. V. p. 6, et torn. vi. p. 1. 
 || " On the Theory of Light and Colours." PM. Trans. ; and Encyel. Brit., Art. 
 CHUOMATICS. 
 
 U Essay on Light , Art. 679, ct seq.
 
 78 KEPORT ON PHYSICAL OPTICS. 
 
 subdivided state, the portions of light which have traversed them 
 are in a condition to interfere, the interval of retardation depend- 
 ing on the difference of the velocities of light in the two media. 
 Accordingly, coloured rings will be seen when a luminous object 
 is viewed through the glasses; the rings being similar to those 
 usually seen by transmission, but much larger. But when a dark 
 object is behind the glasses, and the incident light somewhat 
 oblique, the rings immediately change their character, and re- 
 semble those of the ordinary reflected system ; one of the portions 
 in this case being reflected, and therefore suffering a loss of half 
 an undulation. These phenomena were observed and explained 
 by Young,* and have been denominated by him the " colours of 
 mixed plates." Young also observed some similar phenomena of 
 colour in an unconfined medium. Thus, when the dust of the 
 lycoperdon is mixed with water, the mixture exhibits a green tint 
 by direct light, and a purple tint when the light is indirect ; and 
 the colours rise in the series when the difference of the refractive 
 densities is lessened by adding salt to the water. The interval of 
 retardation in this case depends also on the magnitude of the 
 transparent particle, f 
 
 In closing the review of this part of the subject, I would 
 observe that any well-imagined theory may be accommodated to 
 phenomena, and seem to explain them, if only we increase the 
 number of its postulates, so as still to embrace each new class of 
 phenomena as it arises. In a certain sense, and to a certain ex- 
 tent, such a theory may be said to be true, so far as it is the mere 
 expression of known laws. But it is no longer a physical theory, 
 whose very essence it is to connect these laws together, and to 
 demonstrate their dependence on some higher principle : it is an 
 aggregate of separate principles, whose mutual relations are un- 
 known. Thus the cycles and epicycles of the Ptolemaic system 
 represented with fidelity the more obvious movements of the plane- 
 tary bodies ; but when the refinements of astronomical research 
 laid bare new laws, new epicycles were added to the system, until 
 at length its complication rendered it useless as a guide. Such 
 appears to be the present state of the theory of emission; and so 
 
 "Account of some Cases of the Production of Colours."-PM. Trans. 1802. 
 Abbe Mazeas noticed many fact 
 . Memoiret presentes, vol. ii. 
 t Introduction to Medical Literature, p. 5,56. 
 
 W*MIWU ui Colours. rim. 
 
 Abbe Mazeas noticed many facts which appear to be referrible to the same pnnci- 
 pies. Memoires prtsente's, vol. ii.
 
 POLARIZATION TRANSVERSAL VIBRATIONS. 79 
 
 glaringly does this blemish show itself in that part of the theory 
 which has been last under consideration, that one of its advocates 
 says, " Bevera illae vices reflexionis et transitus, cum omnibus 
 additamentis fictitiis, mirabiliores adhuc sunt quam phenomenon 
 ipsuin, ad cujus explicationem in usum sunt vocatse."* The same 
 attribute appears in the broader divisions of the science. The 
 several classes of phenomena do not flow from the theory as from 
 one common source ; but each has its separate and independent 
 head, and its separate and independent data. In the wave-theory, 
 on the other hand, not only the individual laws, but the classes of 
 phenomena are related ; and to calculate, numerically, the laws of 
 refraction, the varied phenomena of diffraction, and those of thin 
 plates, we only need to borrow one result from experience, the 
 length of a wave of light in each medium. There is thus estab- 
 lished that connexion and harmony in its parts which is the never- 
 failing attribute of truth. But powerful as is the weight of this 
 intrinsic evidence in favour of the wave-theory, it has yet stronger 
 claims to our assent. These claims are grounded on the vast body 
 of new phenomena which it explains, and explains (it is to be 
 remembered) not in a vague and general manner, but in the pre- 
 cise language of analysis, and with an accuracy which the refine- 
 ments of modern observation have not been able to impugn. It 
 may be confidently said that it possesses characters which no false 
 theory ever possessed before. 
 
 PART II. POLARIZED LIGHT. 
 I. Polarization. Transversal Vibrations. 
 
 In the various phenomena which have been hitherto described 
 as taking place when a ray of light encounters the surface of a new 
 medium, it has been assumed that the direction, and the intensity 
 of the several portions into which it is subdivided, are wholly inde- 
 pendent of the manner in which the ray is presented to the bound- 
 ing surface, the direction of the ray remaining unchanged. In 
 other words, it was taken for granted that a ray of light had no 
 relation to space, with the exception of that dependent on its direc- 
 
 * Mayer on Newton's Rings. GWingen Memoirs, vol. v. p. 22.
 
 30 REPOKT ON PHYSICAL OPTICS. 
 
 tion ; that around that direction its properties were on all sicks 
 alike; and that if the ray were supposed to revolve round that line 
 as an axis, the resulting phenomena would be unaltered. 
 
 Huygens was the first to observe that this was not always the 
 case. In the course of his researches on the law of double refrac- 
 tion, he found that when a ray of solar light is received upon a 
 rhomb of Iceland crystal,* in any but one direction, it is always 
 subdivided into two of equal intensity. But on transmitting 
 these rays through a second rhomb, he was surprised to observe 
 that the two portions into which each of them was subdivided 
 were no longer equally intense ; that their relative brightness 
 depended on the position of the second rhomb with regard to the 
 first ; and that there were two such positions in which one of the 
 rays vanished altogether. 
 
 From this " wonderful phenomenon," as Huygens justly called 
 it, it appeared that each of the rays refracted by the first rhomb 
 had acquired properties which distinguished it altogether from 
 solar light. It had, in fact, acquired sides ; and it was evident 
 that the phenomena of refraction depended, in some unknown 
 manner, on the relation of these sides to certain planes within the 
 crystal. Such was the conclusion of Newton : " This argues," 
 says he, "a virtue or disposition in those sides of the rays, which 
 answers to, and sympathizes with, that virtue or disposition of the 
 crystal, as the poles of two magnets answer to one another." 
 
 This conception was followed out by Malus, whose varied and 
 important discoveries respecting the nature and laws of polarized 
 light have justly placed him in the rank of founder in this most 
 interesting branch of science. The molecules of a polarized ray 
 were supposed by him to have all their homologous sides turned 
 in the same directions. He adopted the term "polarization" to 
 express the phenomenon, and compared the effect to that of a 
 magnet which turns the poles of a series of needles all to the same 
 side. M. Biot has modified the hypothesis of Malus in order to 
 embrace the other phenomena of light, and assumes that there is 
 one line, or axis, similarly placed in each molecule, and that these 
 axes in a polarized ray are all turned in the same direction. 
 The molecules, however, are at liberty to revolve round these 
 axes, and thus to assume different dispositions with respect to the 
 attracting or repelling forces to which they are exposed when they 
 encounter the surface of a new medium.
 
 POLARIZATION TRANSVERSAL VIBRATIONS. 81 
 
 The phenomenon of polarization seems to have had much 
 weight with Newton in forcing him to reject the theory proposed 
 by Huygens. "It is difficult," he says, " to conceive how the 
 rays of light, unless they be bodies, can have a permanent virtue 
 in two of their sides, which is not in their other sides, and this 
 without any regard to their position to the space or medium 
 through which they pass."* " Are not all hypotheses erroneous," 
 he adds in another place, " in which light is supposed to consist in 
 pression or motion, propagated through a fluid medium ? . . . . 
 Pressions or motions, propagated from a shining body through an 
 uniform medium, must be on all sides alike ; whereas by those 
 experiments it appears that the rays of light have different proper- 
 ties in their different sides."f In this objection Newton seems to 
 have fixed his thoughts upon that species of undulatory propaga- 
 tion whose laws he himself had so sagaciously divined. When 
 sound is propagated through air or water, the vibrations of the 
 particles of the fluid are performed in the direction in which the 
 wave advances ; and if the vibrations of the ether, which are sup- 
 posed to constitute light, were of the same kind, the objection 
 would seem to be insuperable. But the case is altered, if, as is now- 
 assumed, the vibrations of the ethereal particles be transverse to the 
 direction of the ray's progress. And though we were unable to 
 render any account of this hypothesis, or even to show that it is 
 consistent with mechanical principles ; yet the numerous classes of 
 phenomena which it has explained, and the striking and exact 
 manner in which its predictions have been verified on trial, com- 
 pel us to admit, that if the law to which we have thus reduced so 
 various and such complicated facts be not itself a law of nature, it 
 is at least coordinate with it, in such a sense that we may take it 
 as the representative of actual existence, and reason from it as we 
 would from an established physical law. 
 
 The hypothesis of transversal vibrations first occurred to Dr. 
 Thomas Young, who illustrated it by the propagation of undu- 
 lations along a stretched cord agitated at one of its extremities. 
 Young seems to have been led to this principle while considering 
 the results arrived at by Sir David Brewster, in his researches 
 on the laws of double refraction in biaxal crystals. The principle 
 was soon after raised above the rank of a mere hypothesis, and 
 
 * Optics, book iii. Query 29. t Query 28.
 
 82 EEPOET ON PHYSICAL OPTICS. 
 
 shown to be a necessary consequence of the laws of interference of 
 polarized light, if the theory of waves be admitted at all. It fol- 
 lows, in fact, from the laws of composition of vibrations, that the 
 intensity of the light resulting from the union of two rays oppo- 
 sitely polarized will be constant, and independent of the phase as 
 was proved to be the case in the experimental researches of MM. 
 Arago and Fresnel only when the vibrations normal to the wave 
 are evanescent. It appears from the same investigation that the 
 actual vibrations are either parallel or perpendicular to the plane 
 of polarization. As far as the phenomena of interference are 
 concerned, it is indifferent which of these results be assumed to be 
 the fact. But the theory of transversal vibrations itself, when 
 applied to the laws of double-refraction, leads to the conclusion 
 that the vibrations which constitute the ordinary ray in uniaxal 
 crystals are perpendicular to the principal plane ; and this being its 
 plane of polarization, Fresnel concluded that the vibrations of a 
 polarized ray are on the surface of the wave, and perpendicular to 
 the plane of polarization* 
 
 The principle of transversal vibrations, thus deduced from the 
 phenomena of interference of polarized light, is easily extended to 
 the case of common or unpolarized light. For when a ray of such 
 light falls perpendicularly upon a double-refracting crystal, it is 
 divided into two polarized pencils, neither of which, it appears 
 from the preceding, can contain vibrations normal to the surface 
 of the wave. If, then, there were any such in the incident ray, 
 they would be destroyed by refraction, and there would ensue a loss 
 of vis viva, and consequently a diminution in the intensity of 
 the light ; in other words, the sum of the intensities of the two 
 refracted pencils would be less than that of the incident, which is 
 contrary to observation. In unpolarized light, therefore, as in 
 polarized, the vibrations are only on the surface of the waves ; and 
 we must conceive such light to consist of a rapid succession of sys- 
 tems of waves polarized in every possible plane passing through 
 the normal to the front of the wave. The phenomenon of po- 
 larization then, in this theory, consists simply in the resolution 
 of the vibrations into two sets, in two rectangular directions, and 
 the subsequent separation of the two Systems of waves thus pro- 
 duced. 
 
 * " Memoira sur la Double Refraction.' 1 Mem. Inst., 
 
 torn. vii.
 
 POLARIZATION TRANSVERSAL VIBRATIONS. 8.'] 
 
 The erroneous views of mathematicians on this subject, accord- 
 ing to Fresnel, have arisen from the imperfect physical conceptions 
 which they have made the basis of their reasoning. Elastic fluids 
 have been represented as composed of particles in contact, capable 
 only of condensation and dilatation ; and accordingly the accelerat- 
 ing forces have been conceived to arise solely from the difference 
 of density of the consecutive shells of the fluid. In this case, it is 
 evident that if any row of particles is displaced in the direction of 
 the connecting line, this row will slide upon the succeeding one, 
 and the motion will be resisted by no elastic force. But when we 
 regard these bodies as they really are composed of molecules 
 separated by intervals which are probably considerable as compared 
 with their magnitude, and acting on one another according to 
 some law varying with the distance, the whole question is altered. 
 When any row or line of such molecules is similarly displaced, and 
 through a space which is small compared with the separating 
 intervals, the molecules of the succeeding row will be moved in the 
 same direction by the forces which are thus developed with the 
 change of distance ; so that the vibrations of the particles compos- 
 ing the first row will be communicated to those of the second, and 
 thus the vibratory motion will be propagated in a direction per- 
 pendicular to that in which it takes place.* The rapidity of the 
 propagation will depend on the magnitude of the force developed by 
 the displacement. To account for the fact that there are no sen- 
 sible vibrations in a direction normal to the wave, we have only to 
 suppose the repulsive force between the molecules to be very great, 
 or the resistance to compression very considerable ; for in this case, 
 it will be seen, the force which resists the approach of two strata 
 of the fluid is much greater than that which opposes their sliding 
 on one another. Fresnel's views on this subject are contained in 
 a short paper, entitled "Considerations mecaniques sur la po- 
 larisation de la lumiere,t" and in his celebrated memoir on 
 double refraction.* 
 
 The principle of transversal vibrations, however, has not been 
 
 * The existence of transversal vibrations has been fully established in other cases 
 of vibratory motion. M. Savart and Mr. Wheatstone have shown that in many 
 instances the elementary motions of the molecules of bodies which transmit sound 
 are transverse to the direction of the propagation. 
 
 t Bulletin de la Soc. Philom., 1824. 
 
 t Mt'moires dc I'lnstitut, torn. vii. 
 
 r, 2
 
 84 REPORT ON PHYSICAL OPTICS. 
 
 received without much discussion ; and even to this hour the- 
 opinion of the mathematical world is not entirely at rest upon the 
 subject. In a memoir on the propagation of motion in elastic 
 fluids, read before the Academy of Sciences in the year 1823, 
 M. Poisson arrived at the conclusion that the vibratory motions of 
 the particles finally become normal to the wave, whatever be the 
 direction of the original disturbance * To this Fresnel replied 
 that the equations of motion of elastic fluids employed by M. 
 Poisson are but a mathematical abstraction, which do not apply to 
 anything actually existing ; that, in fact, these fluids are assumed 
 to be composed of contiguous elements, capable of compression in a 
 degree proportionate to the pressure exerted ; that this hypothesis 
 is untrue ; and that, although it may accord with the statical pro- 
 perties of these fluids, it can never lead to the discovery of their 
 dynamical laws.f 
 
 M. Poisson seems to have felt the full force of this objection ; 
 for in his memoirs on the same subject, read to the Academy in 
 the years 1828 and 1830, he has resumed the whole theory, and 
 reared it upon its firmer basis. In the former of these memoirs he 
 has formed the differential equations of equilibrium and motion of 
 elastic bodies, these bodies being supposed to consist of molecules 
 attracting or repelling one another according to some function of 
 the distance.^: In the latter he proceeds to integrate these equations 
 generally, and to deduce the laws of propagation of waves at a consi- 
 derable distance from the origin of disturbance. In the case of fluids 
 he arrives at the conclusion which he had before obtained, namely, 
 that when the distance from the origin of disturbance is very great 
 compared with the length of a wave, the motion of the particles, in 
 any fluid, is normal to the surface of the wave, whatever be the 
 initial motions. He admits, however, that the fundamental equa- 
 tions of the motion of fluids, and therefore also the consequences 
 deduced from them, will probably require modification in the case 
 of very rapid motions, such as those of the luminif erous ether ; 
 there being a finite interval of time, whose magnitude depends on 
 
 * Annales de Chtmie, torn. xxii. 
 t Ibid., torn xxiii. 
 
 J "Memoire sur 1'Equilibre et le Mouvement des Corps Elastiques." J/e'. Insf.,. 
 torn. viii. 
 
 $ " Memoire sur la Propagation du Mouvement dans les Milieux' Elastiques." 
 M<im. In*t., torn. x.
 
 POLAEIZATION TRANSVERSAL VIBRATIONS. 85 
 
 the nature of the fluid, during which the pressure is not the same 
 in all directions. In the case of very rapid motions this time must 
 be taken into account, and the equations of motion of fluids will no 
 longer be those furnished by the principle of D'Alembert.* 
 
 M. Poisson has shown also that a disturbance produced in a 
 limited portion of a solid body will give rise to two waves, which 
 will be propagated with different velocities. He proves further 
 that, whatever be the initial motions of the disturbed particles, the 
 vibrations in one of these waves will finally be radial, or in the 
 direction of the motion propagated, while those of the other are 
 perpendicular to that direction, or transversal. The first are at- 
 tended with dilatations proportionate to the absolute velocities of 
 the molecules, and the waves thus propagated are similar to 
 those which take place in fluids. The transversal vibrations, on 
 the other hand, are unaccompanied by any change of density in 
 the medium. M. Poisson does not seem to think that this result 
 can justify the hypothesis of transversal vibrations in the ethereal 
 fluid; though he admits that the properties attributed to the ether 
 are in some respects analogous to those of a solid body. 
 
 The propagation of transversal vibrations appears to be now 
 established, as a necessary consequence of dynamical principles, by 
 the able researches of M. Cauchy.f I shall shortly have occasion 
 to allude more particularly to the important conclusions arrived at 
 by this mathematician, in applying the general laws of the propa- 
 gation of motion in elastic media to the case of light. For the 
 present it will be sufficient to observe that the form of the wave- 
 surface, obtained in the course of these investigations, is a curved 
 surface of three sheets ; and that, consequently, a ray of light on 
 entering any medium will be, in general, subdivided into three 
 rays, the directions of the vibrations being determined in each. 
 When the elasticity of the ether, in this medium, is the same in all 
 directions, these three rays will have a common direction, and two 
 of them a common velocity. They are thus reduced to two a 
 single and a double ray coincident in direction, the vibrations of 
 the former being parallel to that direction, and those of the latter 
 perpendicular to it. If the initial vibrations in the system in ques- 
 tion are contained in a plane perpendicular to the direction of the 
 
 * Annales da CJiimie, torn. xliv. 
 
 f " Memoire sur la Theorie de la Lumicrc." Mm. Inst., torn. x.
 
 80 REPORT ON PHYSICAL OPTICS. 
 
 rays, the single ray will vanish, and the vibrations of the mole- 
 cules of the double ray will be constantly parallel to the direction 
 of the initial displacements. This condition therefore reduces the 
 three rays to one, which is unpolarized; and as this is known by 
 experience to be the case in media in which the light is propagated 
 in all directions with the same velocity, it follows that the propa- 
 gation of transversal vibrations is a necessary consequence of the 
 general theory. 
 
 Thus the theory of Young and Fresnel has received the 
 strongest possible confirmation ; and when we consider the nu- 
 merous and important conclusions which have been reproduced and 
 confirmed by M. Cauchy in the development of his analysis, it is 
 scarcely possible to believe that there is anything defective in its 
 principle. There is one important and fundamental difference, 
 however, between the theories of M. Cauchy and Fresnel a dif- 
 ference which seems to mark the limits to which we have attained 
 in this branch of mathematical physics. According to the latter 
 author, it has been already stated, the vibrations are perpendicular 
 to the plane of polarization, as it is usually defined : according to 
 M. Cauchy they are parallel to that plane. I am inclined to think 
 that the field on which this question between the two theories 
 must be decided is their application to the laws of reflexion of 
 polarized light ; and, if so, there seems already reason for believing 
 that the hypothesis of Fresnel is the true one. 
 
 II. Reflexion and Refraction of Polarized Light. 
 
 Although the phenomenon discovered by Huygens was one- 
 of the highest interest in itself, and in its bearings of such im- 
 portance, in the mind of Newton, as to force him to admit the- 
 existence of properties in the rays of light which until then had 
 never been imagined ; yet the result remained for more than one- 
 hundred years a unique fact in science, and the kindred pheno- 
 menathe properties which light acquires in a greater or less 
 degree in almost every modification which it undergoes re- 
 mained unnoticed until the beginning of the present century. 
 In the year 1808, while Malus was engaged in his experimental 
 researches on the Huygenian law of double refraction, he dis- 
 covered the important fact, that when a ray of light is reflected 
 from the surface of glass or water at certain angles, the reflected
 
 EEFLEXION AND REFEACTION OF POLARIZED LIGHT. 87 
 
 ray acquires all the characters which had been found to belong to 
 one of the pencils produced by double refraction. "When received 
 upon a rhomb of Iceland spar, one of the two pencils into which it 
 is generally divided vanished in two positions of the principal sec- 
 tion with respect to the plane of reflexion ; while in intermediate 
 positions these pencils varied in intensity through every possible 
 gradation.* The same variations were observed when it underwent 
 a second reflexion at the same angle at which the effect was pro- 
 duced by the first; the twice-reflected light being a maximum 
 when the plane of the second reflexion coincided with that of the 
 first, and vanishing altogether when it was perpendicular to it, 
 the whole light in that case passing into the refracted pencil. To 
 represent the intensity of the reflected light, in any position of 
 the plane of the second reflexion with regard to the first, Malus 
 assumed it to vary as the square of the cosine of the angle which 
 these planes formed with one another.f The accuracy of this law 
 has since been verified by the observations of M. Arago and others. 
 
 From this law it follows that a beam of common light may be 
 represented as composed of two polarized beams of equal intensity, 
 whose planes of polarization are at right angles ; for when such a 
 compound beam is received upon a reflecting surface at the po- 
 larizing angle, the intensity of the reflected light will be constant, 
 and independent of the position of the plane of reflexion. But 
 though this compound beam so far exhibits the character of com- 
 mon or unpolarized light, it must not be regarded as it seems to 
 be by many writers as its physical representative. It appears, in 
 fact, from the theory of the composition of vibrations, that two 
 rays of equal intensity polarized at right angles compound a single 
 ray polarized in a single plane, when the difference of their phases 
 is nothing, or equal to any integer number of semi-undulations ; 
 while in intermediate cases the polarization of the resulting light 
 is either circular or elliptic. These indications of theory have 
 been confirmed in the fullest manner by a beautiful experiment of 
 Fresnel. 
 
 On pursuing his inquiries Malus found that all other transpa- 
 rent substances impressed upon the reflected light the same modifi- 
 cation ; and that the angle of incidence at which this effect was 
 
 Memoirea fArcueil, torn. ii. p. 143. 
 t Ibid., p. 264.
 
 88 REPORT ON PHYSICAL OPTICS. 
 
 produced, and which he called the angle of polarization, was in 
 general different for every different substance. He ascertained, 
 moreover, the relation between the angles of polarization at the 
 first and second surfaces of the same transparent medium, and 
 found that their sines were in the ratio of the sines of incidence 
 and refraction ; so that when the medium is bounded by parallel 
 surfaces, and the light incident on the first at its polarizing angle, 
 the transmitted portion will meet the second surface also at Us 
 polarizing angle, and the light reflected from both will be wholly 
 polarized.* Malus was unable, however, to discover any con- 
 nexion between the polarizing angle and the other properties of 
 the substances; and he concluded that the power of polarizing 
 light by reflexion, which different bodies possessed at different 
 angles, was wholly independent of their other modes of action 
 upon light. 
 
 Sir David Brewster commenced, not long after, an extensive 
 series of experiments, with the view of determining the angles of 
 polarization of different media, and of connecting them by a law. 
 These researches terminated in the discovery of the law perhaps 
 the most beautiful in the whole range of this interesting science 
 that " the tangent of the angle of polarization is equal to the 
 refractive index." This law, when translated into geometrical 
 language, declares that, when the ray is wholly polarized by re- 
 flexion, the angles of incidence and refraction are complementary, 
 so that the reflected and refracted rays form a right angle. The 
 law applies to the case of reflexion from the surface of the rarer, as 
 well as that of the denser medium; and it follows from it that 
 the two angles of polarization at the bounding surface of the same 
 two media are complementary, f 
 
 Malus observed that when the angle of incidence was either 
 greater or less than the polarizing angle, the properties already 
 described were only in part developed in the reflected pencil. 
 
 Me'moire* fArcueil, torn. ii. p. 1 52. M. Arago has extended the same law to the 
 case of partial polarization, and has found that the sines of the angles at which the 
 first and second surfaces of a transparent medium polarized light hy reflexion in an 
 equal degree are to one another in the ratio of the sines of incidence and refraction ; so 
 that the pencils reflected from the two surfaces of a parallel plate, at any incidence, 
 contain the same proportion of polarized light. 
 
 t " On the Laws which regulate the Polarization of Light hy Reflexion from 
 transparent Bodies." Phil. Tram. 1815.
 
 REFLEXION AND REFRACTION OF POLARIZED LIGHT. 89 
 
 Neither of the two pencils, into which it was divided by a rhomb 
 of Iceland spar, ever wholly vanished ; but they varied in inten- 
 sity between certain limits, these limits being closer the more 
 remote the incidence from the angle of complete polarization. 
 Prom this he naturally concluded that, in these circumstances, 
 a portion only of the reflected pencil had received the modifi- 
 cation to which he had given the name of polarization, that 
 portion increasing as the incidence approached the polarizing 
 angle ; and that the remaining portion was unmodified, or in 
 the state of common light. In this supposition Malus has been 
 followed by most subsequent philosophers. A different view of 
 the phenomenon of partial polarization has been taken by Sir 
 David Brewster, to which I shall have occasion presently to allude ; 
 and he has employed his theory to explain a phenomenon which 
 he seems to have been the first to observe, namely, that com- 
 mon light may be polarized by a sufficient number of reflexions 
 &i any angle, the number of reflexions required to produce the 
 effect being greater the more remote the incidence is from the 
 polarizing angle.* 
 
 Examining the transmitted pencil, Malus found that it was par- 
 tially polarized ; and that its plane of polarization was not,, like 
 that of the reflected pencil, coincident with the plane of reflexion, 
 but perpendicular to it.f The two portions of light thus polarized 
 in opposite planes he observed to be intimately connected ; and in 
 a subsequent memoir he announced the fact that, whenever we pro- 
 duce by any contrivance a ray polarized in any plane, there is 
 produced at the same time a second ray polarized in the opposite 
 plane. These two polarized rays follow separate paths, and their 
 quantities are always proportionate. The connexion, however, is 
 still more strict than was supposed by Malus ; for the quantities of 
 polarized light in the reflected and transmitted pencils are not 
 only proportionate, but absolutely equal. This remarkable law 
 was discovered by M. Arago. 
 
 When a ray, which is partially polarized by transmission 
 through a plate of glass, is received upon a second plate at the 
 same angle, the portion of common light which it contains under- 
 goes a new subdivision; and so continually, whatever be the 
 
 * Phil. Trans. 1815. 
 f Mtm. Inst. 1810.
 
 90 REPORT ON PHYSICAL OPTICS. 
 
 number of plates. Hence, when that number is sufficiently great, 
 the transmitted light will be, as to sense, completely polarized ; and 
 the whole light is thus subdivided into two pencils oppositely 
 polarized, one of which is reflected from, and the other transmitted 
 through, the pile. These facts were also observed by Malus. 
 The laws of the phenomena have since been investigated, in much 
 detail, by Sir David Brewster ; and he has arrived at the con- 
 clusion, that when a ray of light is transmitted successively through 
 any number of parallel plates, the tangent of the angle at 
 which the polarization of the refracted pencil appears complete is 
 inversely as their number.* 
 
 I may now proceed to consider these phenomena in their rela- 
 tion to the two theories of light. 
 
 Newton proved that the fundamental laws of reflexion and 
 refraction could be derived from the operation of attractive and 
 repulsive forces exerted by the molecules of body on those of light.. 
 The phenomena of polarization, however, show that these forces 
 are exerted in very different degrees, according to the position of 
 the sides of the ray with respect to the plane of reflexion or refrac- 
 tion; and we are now to consider the additional hypotheses which 
 become necessary in the theory of emission in order to render an 
 account of these new facts. 
 
 It has been already mentioned that, in the theory of M. Biot, 
 a polarized ray was one in which certain axes (called the axes of 
 polarization) of all the molecules were turned in the same direction. 
 This effect is ascribed to the operation of certain forces emanating 
 from the molecules of the body. These forces M. Biot denominates 
 polarizing forces ; and he considers them as distinct from the re- 
 flecting and refracting forces, although intimately connected with 
 them. The effect of a polarizing force is to give a rotation to the 
 axes of the molecules ; and that which impresses the property of 
 polarization upon the reflected ray is assumed to act in the plane 
 of reflexion. This being supposed, since a ray of common light 
 is polarized by reflexion when incident at a certain angle, we are 
 obliged to admit that, at this angle, the polarizing force turns the 
 axes of polarization of all the molecules, and brings them into the- 
 plane of reflexion ; and, since this takes place for all the molecules* 
 
 Iol4. 
 
 "On the Polarization of Light by oblique Transmission," ic.-PM. 
 
 4
 
 REFLEXION AND REFKACTION OF POLARIZED LIGHT. 91 
 
 of the reflected ray, such an arrangement of the axes is conceived 
 to be a necessary condition of reflexion at that incidence. 
 
 Now, let such a polarized ray fall upon a second reflecting 
 surface at the polarizing angle, and let the plane of the second 
 reflexion be perpendicular to that of the first. Then the axes of 
 polarization of the molecules, in their incidence on the second plate, 
 are perpendicular to the plane of reflexion ; and consequently, the 
 polarizing force, acting in that plane, affects equally the two halves 
 of the axis, and cannot therefore turn it into the plane of re- 
 flexion, a condition which is assumed to be necessary to reflexion 
 at that angle. No light therefore is reflected. But when the 
 plane of the second reflexion is inclined to that of the first at any 
 angle less than 90, the polarizing force of the second plate no 
 longer acts symmetrically on the two halves of the axes of the 
 molecules : it may therefore turn these axes so as to make them 
 coincide with the plane of reflexion, and thus subject the mole- 
 cules to the action of the reflecting force. The effect of the- 
 polarizing force increases as the inclination of the two planes of 
 reflexion diminishes ; and consequently the number of molecules 
 reflected by the second plate increases likewise. 
 
 But here it is necessary to make another supposition. In 
 any position of the plane of the second reflexion with respect to 
 the first, except the perpendicular one, experience proves that a 
 portion of the light is reflected, and another portion refracted. Ac- 
 cording to this theory, then, some of the molecules obey the 
 polarizing force, and have their axes brought into the plane of re- 
 flexion, while others do not. To account for this diversity of 
 effect there must be some diversity of condition in the molecules 
 themselves. The theory of M. Biot supplies this by attributing to 
 them an oscillatory movement round their axes of polarization, 
 the molecules yielding to the polarizing force, or not, according to 
 the phase of the oscillation in which they are found at the moment 
 they reach the surface. 
 
 The force which impresses the property of polarization upon the 
 refracted pencil is supposed by M. Biot to act also in the plane of 
 incidence, its operation however being to turn the axes of po- 
 larization of the luminous molecules in a direction p*rp*HKe*t*r to 
 that plane. Thus, when a ray of light traverses the surface of a 
 plate of glass at the polarizing angle, it is subjected to the action 
 of two forces, one tending to bring the axes of polarization of the-
 
 92 REPORT ON PHYSICAL OPTICS. 
 
 molecules into the plane of incidence, the other to turn them at 
 right angles to it ; and the molecules themselves yield to one or 
 other of these forces according to the phases of their fits. For the 
 manner in which this may be supposed to take place we must refer 
 to the Traite de Physique* The whole quantities of light oppo- 
 sitely polarized by the two forces M. Biot supposes to be equal ; 
 but he conceives that the force which polarizes the reflected pencil 
 is exerted on a much greater number of molecules than those 
 which actually undergo reflexion. These molecules, thus polarized 
 in the plane of incidence, enter into the transmitted beam 
 neutralize an equal number of molecules polarized by refraction in 
 the opposite plane, and compound with them a beam of com- 
 mon light. The whole quantities of light polarized by the two 
 forces being then equal, the remaining portions effectively polarized 
 will still be equal, conformably to the law discovered by M. Arago. 
 
 I have endeavoured to present the theory of M. Biot as fully 
 as the limits of the present paper will permit, because it appears to 
 me that the number and the nature of the hypotheses required, in 
 order to render any account of the phenomena of polarization in 
 the theory of emission, furnish in themselves a sufficient argument 
 against it. But let all these be admitted, and how far can we be 
 said to have advanced towards an explanation of the phenomena ? 
 The assumed forces and the known laws have not been connected, 
 in any one instance, by the sure processes of mathematical deduc- 
 tion ; and we are therefore unable to state how far the explanation 
 offered is competent to express even the general facts, far less can 
 we calculate them numerically, and compare the results with those 
 of observation. 
 
 The first attempt to connect the modifications of reflected light 
 with the theory of waves was made by Dr. Thomas Young. This 
 sagacious philosopher succeeded in solving the problem of reflexion 
 in the case of perpendicular incidence, and showed that the inten- 
 sity of the reflected light in that case was represented by a simple 
 function of the refractive index.f This formula was afterwards 
 reproduced as the result of a more refined analysis by M. Poisson, 
 in a memoir on the simultaneous motions of two elastic fluids in 
 contact, read to the French Academy in 18174 In that memoir, 
 
 * Book vi. chap. i. vol. iv. 
 
 t Encyc. Brit. Supp., Art. CitaoMATics. 
 
 % M<im. Inst., torn. ii.
 
 REFLEXION AND REFEACTION OF POLARIZED LIGHT. 93 
 
 however, the author had considered only the case of perpendicular 
 incidence, or the law of propagation of a plane wave parallel to 
 the bounding surface of the two media. In a subsequent memoir, 
 to which I have already alluded, and which was read to the 
 Academy in the year 1823,* he has resumed the problem gener- 
 ally, and examined the modifications produced in the intensity as 
 well as the direction of a wave, or series of waves, in passing from 
 one fluid to another of the same elasticity, but of a different den- 
 sity. The expressions obtained for the intensity of the reflected 
 and refracted waves are functions of the angle of incidence, and of 
 the ratio of the velocities of propagation in the two media. When 
 the wave is incident upon the surface of the denser medium, the 
 expression for the intensity of the reflected wave vanishes at a cer- 
 tain angle, whose tangent is equal to the ratio of the velocities of 
 propagation. At this angle, which is the angle of complete polari- 
 zation, objects should therefore cease to be visible by reflected 
 light ; a ^result which is contradicted by all experience, and is 
 only true when the light is polarized in a plane perpendicular to 
 the plane of reflexion. When the wave is reflected at the surface 
 of the rarer medium, there are two expressions for the intensity, 
 for incidences above and below the limiting angle of total reflexion, 
 respectively. There are also in this case two angles of evanescence. 
 These conclusions, which apply to the case of sound as well as 
 light, are sufficient to show the physical inapplicability of the 
 theory. 
 
 The theory of waves, however, when combined with the prin- 
 ciple of transversal vibrations, has afforded the complete solution 
 of the problem we have been considering. In this development 
 of his theory the character of Fresnel's genius is strongly marked. 
 Our imperfect knowledge of the precise physical conditions of the 
 question is supplied by bold, but highly probable assumptions : the 
 meaning of analysis is, as it were, intuitively discerned, where its 
 language has failed to guide ; and the conclusions thus sagaciously 
 reached are finally confirmed by experiments chosen in such a man- 
 ner as to force Nature to bear testimony to the truth or falsehood 
 of the theory.f 
 
 * Only a portion of this memoir has been printed in the Memoirs of the Institute, 
 under the title " Memoire sur le Mouvement de deux Fluides elastiques superposes," 
 torn. x. 
 
 t Fresnel's theory of reflexion is contained in a memoir read to the Academy of
 
 ^ 4 REPORT ON PHYSICAL OPTICS. 
 
 It is evident that the strata of ether in the two media, which 
 nre adjacent to the hounding surface, must undergo equal displace- 
 Lents parallel to that surface, inasmuch as one of them cannot 
 Ide on L other. Consequently the amplitude of the ^ration, 
 resolved in a direction parallel to the surface, must be the same in 
 the two media. Fresnel assumes that this equality at the bound- 
 ing surface is maintained at all distances ; and this furnishes him 
 with one relation among the amplitudes of vibration of the inci- 
 dent reflected, and refracted waves. A second relation among the 
 same' quantities is afforded by the law of the ** viva; but to apply 
 this it is necessary to know the relative densities of the ether in 
 the two media. Here Fresnel assumes that the elasticity of the 
 ether in these media is the same * but the density different ; and 
 this being taken for granted, it follows that "the two densities are 
 to one another inversely as the squares of the velocities of propa- 
 gation, and that therefore their ratio is given when the refractive 
 index is known. The amplitudes of the reflected and refracted 
 vibrations, and therefore also the intensities of the light in the two 
 pencils, are obtained by simple elimination between the equations 
 just mentioned. 
 
 The expressions for the intensity of the light in the reflected ray 
 are different, according as the incident light is polarized in the plane 
 of reflexion or in the perpendicular plane.f The intensity of the 
 reflected light in the latter case vanishes when the sum of the 
 angles of incidence and refraction is a right angle ; and thus was 
 solved the difficulty, which in the opinion of Young, pronounced 
 but three years before" would probably long remain, to mortify 
 the vanity of an ambitious philosophy, completely unresolved by 
 any theory." "When common, or unpolarized light, therefore, is 
 
 Sciences in the year 1823, entitled, " Memoire sur la Loi des Modifications que la Ee- 
 flexion imprime a la Lumiere polarisee." An incomplete extract of this memoir was 
 published in the Anvales de Chimie, 1825. The original paper was mislaid, and for a 
 time supposed to he lost ; it has lately, however, heen recovered among the papers of 
 M. Fourier, and has heen printed in the llth vol. of the Memoirs of the Institute. 
 
 * Fresnel states that he had solved the problem of reflexion in the general suppo- 
 sition that the two media differ in elasticity as well as density, in the case of rays 
 polarized in the plane of reflexion ; and that the resulting formula was the same as 
 that at which he had already arrived on the more limited hypothesis. An, Chim., 
 torn, xxiii. 
 
 t These two formula; were first published in the Atmales de Chimie, 1821 ; the 
 *econd without demonstration.
 
 EEFLEXION AND REFRACTION OF POLARIZED LIGHT. 95 
 
 incident at an angle whose tangent is equal to the refractive index, 
 the reflected light will be wholly polarized in the plane of reflexion ; 
 and the beautiful law of Brewster is among the first fruits of the 
 theory of Fresnel. The remarkable law obtained by M. Arago is 
 also a necessary consequence of the same formulae ; and it is easily 
 inferred that the quantities of polarized light in the reflected and 
 refracted pencils are equal, whatever be the incidence. 
 
 In the case of perpendicular incidence, these formulae are both 
 reduced to the simple expression obtained by Young and Poisson ; 
 and when the incidence is 90, or the ray grazes the surface, the 
 intensity of the reflected light is equal to that of the incident, or 
 the whole of the light is reflected whatever be the reflecting me- 
 dium. The latter conclusion has been verified by the observation 
 of the bands produced by the interference of direct light with that 
 which is reflected at an incidence of nearly 90. The first dark 
 band appears to be perfectly black ; and therefore the two lights 
 are, as to sense, of equal intensity.* 
 
 We are thus furnished with the solution of a problem which 
 has long baffled the labours of experimentalists, namely, the 
 determination of the law of intensity of reflected light as depend- 
 ent on the incidence. The formulae obtained have not been com- 
 pared with experiment by Fresnel except in the case of two 
 observations of M. Arago, the observations of Bouguer and Lam- 
 bert being confessedly inaccurate. The result of the comparison 
 alluded to has been given in the Annales de Chimierf and the 
 agreement is as satisfactory as can be expected in observations of 
 the kind. 
 
 Mr. Potter has recently examined the intensity of the light 
 reflected from diamond and glass of antimony, at various incidences.* 
 The photometrical method employed in these observations con- 
 sisted in comparing the light reflected at any incidence from the 
 substance examined with that reflected from a piece of crown- 
 glass, and then varying the incidence on the latter until the inten- 
 sities are observed to be equal. The intensity of the light reflected 
 from crown-glass at various incidences had been already ob- 
 tained from a detailed series of experiments, and the results em- 
 
 * "On a New Case of Interference." Tram. Royal In\h Ac.nlany, voL xvii. 
 
 f Tom. xvii. p. 190. 
 
 ; I'hil Mag., Third Series, vol. i. p. 17'J ; vol. ii. p. G.
 
 96 REPORT ON PHYSICAL OPTICS. 
 
 bodied in an empirical law, in which the intensity is represented 
 by the ordinate of a rectangular hyperbola, the corresponding 
 abscissa being the sine of incidence. This formula then gives the 
 intensity of the light reflected from crown-glass, and therefore also 
 from the substance examined, at the corresponding incidences. Mr. 
 Potter concludes, in this manner, that the intensity of the light 
 reflected from diamond at a perpendicular incidence is 9-3, and 
 that from glass of antimony 8-2, the intensity of the incident 
 light being represented by 100. The intensities calculated from 
 the refractive indices, by the formulae of Young, Poisson, and 
 Fresnel, are 18-36, and 13'33, respectively. This variance in the 
 results of theory and experiment is undoubtedly beyond the limits 
 of the errors of observation; and, were it otherwise, the partial 
 results obtained by Mr. Potter, in these and other experiments of 
 the same nature, agree too closely to permit us to refer the dis- 
 crepancy to such a source. The principle of the method, however, 
 appears (to say the least) uncertain ; and it cannot but be wished 
 that some of the various photometrical methods recently proposed 
 should be applied to the examination of this interesting question. 
 
 The formulae of Fresnel supply the account of the remarkable 
 phenomenon observed by M. Arago ; namely, that when New- 
 ton's rings are formed between a lens of glass and a metallic re- 
 flector, one of the two images into which they are divided by a 
 double-refracting crystal, whose principal section is parallel or per- 
 pendicular to the plane of reflexion, changes its character as the 
 incidence passes the polarizing angle of the glass ; the colours 
 being the same as in the other image when the incidence is less 
 than the polarizing angle, but complementary to them when it is 
 greater. In fact, when the incident light* is polarized perpen- 
 dicularly to the plane of reflexion, the amplitude of the reflected 
 vibration (which vanishes at the angle whose tangent is equal to 
 the refractive index) changes sign in passing through zero, being 
 negative when the incidence is less than that angle, and positive 
 when it is greater. Consequently, if the wave reflected from the 
 glass, at the central spot, is in complete discordance with that re- 
 flected from the metal in the former case, it will be in complete 
 accordance with it in the latter; and the centre, which before was 
 black, will then be white. For the same reason the whole system 
 
 * The effect is the same whether the light be polarized before or after reflexion.
 
 REFLEXION AND REFRACTION OF POLARIZED LIGHT. 97 
 
 will be complementary to that which it was before. Professor 
 Airy was led to anticipate this result from the consideration of 
 Fresnel's expressions, and afterwards verified it on trial,* appa- 
 rently without any knowledge of the facts observed by M. Arago. 
 A similar confirmation of the same principles may be obtained by 
 combining, in Fresnel's experiment, a metallic reflector with one 
 of glass. The light being polarized perpendicularly to the plane 
 of reflexion, the central band will be white, when the angle of inci- 
 dence is below the polarizing angle of the glass ; at the polarizing 
 angle, the interference bars will vanish altogether ; and beyond 
 that incidence they will reappear with a dark centre, instead of a 
 white one. This .method of observation would seem to be pecu- 
 liarly adapted to the investigation of the change of phase produced 
 by metallic reflexion at various incidences. 
 
 By the same considerations Professor Airy was led to expect 
 that when Newton's rings were formed between two transparent 
 substances of different refractive powers the light being polarized 
 perpendicularly to the plane of incidence, the rings should be 
 black-centred, when the incidence was less than the polarizing 
 angle of the low-refracting substance, or greater than that of the 
 high-refracting substance ; while they should appear with a white 
 centre, when it was intermediate to these angles ; the vibrations 
 of the waves reflected from the two surfaces being of opposite signs 
 in the former case, and of the same sign in the latter. All these 
 expectations were fully confirmed by experiment.! The sub- 
 stances selected by Professor Airy for these observations were 
 plate-glass and diamond, these substances differing very widely 
 in their refractive powers ; and in the course of his experiments 
 he has noticed certain peculiarities in the phenomena, from which 
 he has drawn some highly interesting conclusions respecting the 
 nature of reflexion from diamond. Had this been subjected to 
 the ordinary laws, the reflexion should cease, and the rings dis- 
 appear, at the polarizing angles of both substances. This however 
 was not the case. The rings did not vanish at the polarizing 
 angle of the diamond ; but the first black ring contracted, as the 
 incidence was gradually increased, and finally usurped the place 
 
 * "On a Remarkable Modification of Newton's Rings." Cambridge Trans. 1832. 
 t " On the Phenomena of Newton's Kings, when formed between two tram-parcn 
 substances of different refractive powers." Cambridge Trans. 1832. 
 
 H
 
 9& REPORT OX PHYSICAL OPTICS. 
 
 of the central white spot. A portion of the light is therefore still 
 reflected at the maximum polarizing angle of diamond ; and it is 
 evident from the phenomenon that the transition from a white to 
 a black centre is owing to a gradual change of phase of the reflected 
 vibration, amounting to nearly 180, while the coefficient of the 
 vibration itself is not much altered. The diamond therefore has 
 no angle of complete polarization ; and Professor Airy concludes 
 that the nature of the reflexion from this singular substance, in 
 the neighbourhood of the angle of maximum polarization, is differ- 
 ent from any that has been hitherto described. 
 
 Fresnel's theory of reflexion has received experimental confir- 
 mation of a different kind, and to an extent which leaves little 
 ground to doubt of its truth. When a ray polarized in any plane 
 falls upon a reflecting surface at any angle, the reflected ray is 
 still polarized, but its plane of polarization is changed the 
 amount of the change depending on the incidence. The law of 
 this change is at once furnished by the theory of Fresnel ; for the 
 tangent of the inclination of the plane of polarization of the re- 
 flected ray to the plane of incidence is equal to the ratio |of the 
 displacements in the plane of incidence and in the perpendicular 
 plane. The formula thus deduced has been verified in the most 
 complete manner by the observations of Fresnel himself, and more 
 fully since by those of M. Arago and Sir David Brewster.* 
 
 The views of the latter philosopher respecting the nature of 
 partially-polarized light are founded upon the phenomenon of the 
 change of the plane of polarization by reflexion. If common light 
 be conceived to consist of two pencils oppositely polarized, in planes 
 inclined 45 on either side of the plane of reflexion, the effect of 
 reflexion, it is obvious, will be to bring each of these planes nearer 
 to the plane of incidence ; so that the planes of polarization of the 
 two pencils will approach each other, and form an acute angle 
 after reflexion. Partially-polarized light, then, according to Sir D. 
 Brewster, consists of two polarized pencils, whose planes of polari- 
 zation form an acute angle; and no portion of it is in the condition 
 of ordinary light.f This hypothesis receives some support from 
 
 * Annales de Chimie, torn. xvii. ; Phil. Tram. 1830. 
 
 t Sir David Brewster has computed, on these principles, the quantity of light ap- 
 parently polarized in the plane of incidence, hy a single reflexion at-any angle, adopt- 
 ing Fresnel's expression for the intensity of the reflected ray. The agreement of the
 
 REFLEXION AND REFRACTION OF POLARIZED LIGHT. 99 
 
 the explanation which it affords of the effects of successive reflexions. 
 When light thus constituted is received upon a second reflecting 
 surface, in the same plane of incidence, the planes of polarization 
 of the two pencils will be brought nearer, and so continually; 
 until by a sufficient number of reflexions, these planes will, as to 
 sense, coincide with the plane of incidence, and the resulting light 
 will appear to be wholly polarized in that plane. 
 
 This ingenious theory seems open to an objection already 
 noticed, namely, that the light resulting from the union of two 
 oppositely polarized pencils cannot, in all respects, be taken as the 
 physical representative of common or unpolarized light. It also 
 involves this further difficulty, that the positions of the planes of 
 polarization of the two oppositely-polarized portions are entirely 
 arbitrary ; and that if they be differently assumed, the results will 
 be physically different. Thus, for example, if the two planes be 
 taken, one coincident with the plane of reflexion itself, and the 
 other with the perpendicular plane, neither of these planes will be 
 changed by reflexion, although the intensities of the corresponding 
 pencils will. 
 
 Sir David Brewster has also investigated experimentally the 
 effect of refraction upon the plane of polarization of the refracted 
 ray ; and he has found that the law of the change may be ex- 
 pressed by a very simple and elegant formula.* This formula is a 
 necessary consequence of Fresnel's theory, although Fresnel him- 
 self does not seem to have observed it. Its discovery by Sir David 
 Brewster adds one to the many instances of rare sagacity by which 
 this philosopher is guided in his experimental inquiries. The par- 
 tial polarization of light by refraction has been considered by Sir 
 David Brewster in the same memoir. In the investigation of the 
 quantity of polarized light in the refracted pencil, he employs a 
 principle similar to that which he had already applied to the re- 
 flected ray; and he arrives at the result that the quantities of 
 
 formula with the observations of M. Arago is found to be as near as can be expected in 
 such comparisons. " On the Law of PartialPolarization of Light by Reflexion." Phil. 
 Trans. 1830. 
 
 * a and ' being the azimuths of the planes of polarization of the incident and re- 
 fracted rays, estimated from the plane of reflexion, and i and i' the angles of incidence 
 and refraction, 
 
 cot a' = cot a cos (* ') 
 
 " On the Laws of the Polarization of Light by Refraction." Ph il. Tram. 1830. 
 H2
 
 100 REPORT ON PHYSICAL OPTICS. 
 
 polarized light in the reflected and refracted pencils are precisely 
 equal, whatever be the incidence, conformably to the law of 
 M. Arago. The effects produced by successive refractions are 
 accounted for on the same principles. 
 
 Sir David Brewster seems to have been the first who studied 
 the effects produced by total reflexion upon polarized light ; and he 
 observed, in particular, the complementary colours which the light 
 thus reflected furnished when analyzed with a rhomb of Iceland 
 spar.* At this time both he and Dr. Young concurred in thinking 
 that these phenomena arose from the interference of two portions 
 of light, which were reflected at unequal depths ; one portion, ac- 
 cording to Dr. Young, beginning to be refracted, and being then 
 turned back by the continued exercise of the same power.f 
 
 Fresnel had likewise observed, at an early period of his inqui- 
 ries, that when a ray, polarized in a plane inclined at an angle of 
 45 to the plane of incidence, undergoes total reflexion, it is in 
 part depolarized; and that this depolarization is rendered complete 
 by two total reflexions at an incidence of about 50. The reflected 
 light being then circularly-polarized is, according to theory, com- 
 posed of two equal pencils, one polarized in the plane of incidence, 
 and the other in the perpendicular plane, and differing in their 
 origin by a quarter of a wave. From this it followed that the 
 two pencils into which the incident light may be resolved, polar- 
 ized in these two planes, are not reflected at the same depth, or 
 that they have undergone unequal changes of phase at the moment 
 of reflexion, so that after reflexion one of them is in advance of 
 the other. After many ineffectual attempts to discover in what 
 manner this difference of phase depended on the incidence, Fresnel 
 was at length led to the solution of the problem by the discus- 
 sion of the formulae for the intensity of the reflected light already 
 noticed. 
 
 When the angle of incidence exceeds the angle of total re- 
 flexion, the light passing from the denser into the rarer medium, 
 these formulae become imaginary. It is evident, however, from 
 the law of the vis viva, that the intensity of the reflected light in 
 this case is simply equal to that of the incident. How, then, are 
 the imaginary expressions to be interpreted ? They signify, ac- 
 
 * Journ. Royal /.?<., vol. iii. 
 
 t Suppl. Encyc. Brit., Art. CHROMATICS.
 
 REFLEXION AND REFRACTION OF POLARIZED LIGHT. 101 
 
 cording to Fresnel, that the periods of vibration of the incident 
 and reflected waves, which had been assumed to coincide at the 
 reflecting surface, no longer coincide there when the reflexion is 
 total ; or, in other words, that the ray undergoes a change of phase 
 at the moment of reflexion. The amount of this change is deduced, 
 by a train of the most ingenious reasoning, from the general ex- 
 pressions. Now when a ray, polarized in any azimuth, is incident 
 upon the reflecting surface at an angle greater than the angle of 
 total reflexion, it may be resolved into two one polarized in the 
 plane of incidence, and the other in the perpendicular plane. The 
 intensities of these two portions will not be altered by reflexion ; 
 but their phases will, and each by a different amount. The re- 
 flected vibration, therefore, will be the resultant of two rectangular 
 vibrations differing in phase. This vibration, consequently, will 
 be elliptic, and the reflected light will be ellipticaUy-polarizcd. 
 When the azimuth of the plane of polarization of the incident ray 
 is 45, the intensities of the resolved portions are equal ; and if, 
 moreover, their difference of phase, after reflexion, is equal to a 
 quarter of an undulation, the ellipse will become a circle, and the 
 light will be circularly-polarized. 
 
 Eeducing his formulae to numbers, in the case of St. Gobain glass, 
 Fresnel found that the difference of phase of the two portions of the 
 reflected light amounted exactly to one-eighth of an undulation, 
 when the angle of incidence was 54 37'. Polishing, therefore, a 
 parallelepiped of this glass, whose faces of incidence and emergence 
 were inclined to the other sides at these angles, it followed that a 
 ray incident perpendicularly on one of these faces, and once re- 
 flected at each of the sides, should emerge perpendicularly at the 
 opposite face, the difference of phase in the two portions of the 
 twice-reflected ray amounting to a quarter of an undulation. If, 
 then, the incident ray be polarized in a plane inclined at an angle 
 of 45 to the plane of reflexion, the emergent light will be cin-n- 
 lat-ly-polarized. This was found to be the case on trial ; and the 
 parallelepiped thus constructed and which is known under the 
 name of Frcsnel's rhomb is of essential service in experiments on 
 -circular and elliptic polarization. The results of this remarkable 
 theory have been confirmed by Fresnel by other well-chosen ex- 
 periments ; so that, although the reasoning on which it is based is 
 far from rigorous, there can remain little doubt of its general truth. 
 Fresnel was himself fully aware of the incompleteness of his solu-
 
 102 REPORT ON PHYSICAL OPTICS. 
 
 tion, considered in an analytical point of view. In his memoir he 
 has adverted to the method to be adopted in order to obtain an 
 exact solution of the problem, unlimited by any arbitrary hypo- 
 thesis ; and he proposed himself to resume the question. But his 
 brilliant career of discovery was cut short by an untimely death. 
 
 The problem of the reflexion and refraction of polarized light 
 has also engaged the attention of M. Cauchy.* The solution given 
 by this mathematician is derived from a consideration of the con- 
 ditions which must be fulfilled at the separating surface of the two 
 media ; and it assumes that the density of the ether is the same in 
 both. The expressions obtained for the amplitudes of the vibra- 
 tions in the reflected wave agree with those of Fresnel. The cor- 
 responding quantities for the refracted wave differ from those 
 deduced from Fresnel's theory, by the simple inversion of the 
 ratio of the sines of incidence and refraction, which occurs as a 
 factor in both cases ; and, thus, although the formulae are different, 
 their consequences agree in many instances, as, for example, in 
 the determination of the plane of polarization of the refracted 
 pencil. It is important to observe, however, that according to the 
 formulae of M. Cauchy, the velocities of the ethereal molecules in 
 the refracted wave are greater than in the incident ; so that the 
 law of the vis viva is violated. This is not the case in Fresnel's. 
 results, which are in fact derived from that law. 
 
 The phenomena of metallic reflexion remain yet to be noticed in 
 connexion with this division of the science of light. 
 
 The effects produced upon light by reflexion at the surfaces 
 of metals did not escape the scrutiny of Malus. From his first ex- 
 periments upon the subject, Malus concluded that metals had no 
 effect in polarizing the light. He soon, however, modified this 
 opinion, and found that the phenomenon of polarization was par- 
 tially produced, the effect increasing to a maximum as the inci- 
 dence approached a certain angle. But the most instructive mode 
 of studying these phenomena is to let fall upon the metallic re- 
 flector a ray polarized in a plane inclined at an angle of 45 to the 
 plane of reflexion, and to analyze the reflected pencil by a double- 
 refracting prism. Proceeding in this manner, Malus found that 
 when the incidence was very small, or very great, the reflected ray 
 was still* polarized ; while at moderate incidences it was depolarized,. 
 
 * Bullttin Universe!, torn. xiv. p. 6.
 
 REFLEXION AND REFRACTION OF POLARIZED LIGHT. 103 
 
 and the pencil was divided into two in every position of the rhomb. 
 Prom these facts Mains concluded that the difference between 
 metals and transparent bodies consisted in this: that the latter 
 reflect all the light which is polarized in one plane, and refract all 
 the light polarized in the opposite plane ; while metals, on the 
 other hand, reflect light which is polarized in both planes. 
 
 The subject of metallic polarization was next examined by Sir 
 David Brewster ; and his labours on this subject constitute the 
 most important addition which has been recently made to our 
 knowledge of the laws of polarized light.* When light reflected 
 at a metallic surface is analyzed by a double-refracting crystal, 
 it is observed to be partially polarized in the plane of reflexion. 
 The effect is greatest in galena, and least in silver; and the angle 
 at which it is a maximum is about 74, but varies with the metal. 
 Ey successive reflexions in the same plane, Sir David Brewster 
 found that the proportion of polarized light was increased ; and 
 that by a sufficient number of reflexions the light became, as to 
 sense, wholly polarized in the plane of incidence. The number of 
 reflexions required to produce this effect varied widely in different 
 metals. 
 
 In order to determine the nature and laws of this phenomenon, 
 it is necessary to examine the effect produced upon polarized light. 
 Adopting, then, the method of Malus, Sir David Brewster found 
 that when a ray of light, polarized in the azimuth of 45, was re- 
 ceived upon a metallic reflector at an incidence greater than 40, 
 and less than 86, the reflected light was partly depolarized. The 
 effect produced was greatest at an angle of about 74 ; and when 
 the light underwent a second reflexion in the same plane, and at 
 the same angle, it was restored to light polarized in a single plane. 
 This new plane lies always on the other side of the plane of 
 reflexion ; and its azimuth varies within the limits and 45, 
 being greatest for silver, and least for galena. It is evident, then, 
 that the light produced by a single reflexion cannot be common 
 light. Neither is it plane-polarized light, because it does not 
 vanish in any position of the analyzing rhomb. Sir David Brewster 
 concludes that this light has received a species of polarization 
 hitherto unrecognised, intermediate between plane and circular 
 polarization. He calls it elliptic polarization, because the angles of 
 
 * " On the Phenomena and Laws of Elliptic Polarisation, as exhibited in the 
 Action of Metals upon Light." Phil. Tran*. 1830.
 
 104 REPORT ON PHYSICAL OPTICS. 
 
 reflexion at which this light is restored to plane-polarized light, in 
 any azimuth of the plane of the second reflexion with regard to the 
 first, may be represented by the variable radii of an ellipse ; while 
 these angles are equal in all azimuths in the case of light circu- 
 larly-polarized. 
 
 Sir David Brewster seems to have been led to employ the term 
 " elliptic polarization " in this manner, in his desire to avoid as 
 much as possible all reference to theory. The laws which he has 
 obtained, however, belong to elliptically-polarized light, in the 
 sense in which the term was introduced by Fresnel. It appears, 
 in fact, from the theory of the composition of vibrations, as laid 
 down by this author, that the vibration resulting from the union 
 of two rectilinear and rectangular vibrations will be in general 
 elliptic; so that two oppositely-polarized pencils compound in 
 general a pencil elliptically-polarized the ellipse becoming a right 
 line, when the difference of phase of the two portions is an integer 
 multiple of 180. When, therefore, by the effect of reflexion, two 
 such pencils are made to differ 90 in phase as Sir David Brewster 
 has shown to be the case when a ray polarized in the azimuth of 45 
 is incident at the maximum polarizing angle of the metal a 
 second reflexion, in the same plane and at the same angle, will raise 
 the difference to 180, and the resulting light will be plane-polarized. 
 In other parts of his memoir, however, Sir David Brewster seems 
 to acknowledge that theory, for he speaks of elliptic polarization 
 as produced by the interference of two unequal portions of oppo- 
 sitely-polarized light, and even calculates their difference of phase 
 for any incidence. 
 
 The identity of the light produced by metallic reflexion with 
 the elliptically-polarized light of the wave-theory seems to be 
 placed beyond all doubt by an observation of Professor Airy. 
 When Newton's rings are formed between glass and metal the 
 incident light being polarized, and the angle of incidence exceed- 
 ing the polarizing angle of the glass it is found that the rings 
 dilate, as the azimuth of the plane of polarization with respect to 
 the plane of reflexion is increased ; the dilatation being a maxi- 
 mum when these two planes become perpendicular. In order to 
 account for this fact, Professor Airy has shown that if the vibra- 
 tions of the incident pencil be resolved into two, one in the plane 
 of incidence, and the other in the perpendicular plane, it is neces- 
 sary to assume that their phases are unequally changed by reflexion;
 
 REFLEXION AND REFRACTION OF POLARIZED LIGHT. 105 
 
 the phases of the vibrations in the plane of reflexion Toeing more 
 retarded than in the perpendicular plane. The two oppositely 
 polarized portions, therefore, will differ in phase after reflexion, 
 and will therefore compound a pencil elliptically -polarized. Pro- 
 fessor Airy has observed a similar phenomenon when Newton's 
 rings were formed between diamond and plate-glass, the angle of 
 incidence being a few degrees less than the maximum polarizing 
 angle of diamond ; and he concludes that, for such incidences, 
 the nature of reflexion from diamond is analogous to metallic 
 reflexion. 
 
 Sir David Brewster has extended his researches on the subject 
 of metallic reflexion to a great variety of cases, and has traced the 
 effects of successive reflexions in the same, or in different planes ; 
 and at the same, or different angles. When the light which has 
 been restored to plane-polarized light, by two reflexions in the same 
 plane, and at the maximum polarizing angle, undergoes a third 
 reflexion under the same circumstances, it becomes again ellipti- 
 cally-polarized. By a fourth reflexion it is again restored to plane- 
 polarized light, the plane of polarization being, however, brought 
 nearer to the plane of reflexion. This continued approach of the 
 plane of polarization to the plane of reflexion enables the author 
 to explain, according to his peculiar views, the effect of successive 
 reflexions upon common light. 
 
 It remains, further, to extend the theory of Fresnel to reflexion 
 at the surface of a medium in which the elasticity of the ether is 
 different in different directions. All that we know on this interest- 
 ing subject we owe to the unwearied zeal of Sir David Brewster. 
 It had been supposed by Malus, and the opinion seems to have 
 passed current with succeeding philosophers, that the exterior sur- 
 faces of crystallized substances acted upon the reflected light 
 -exactly in the same manner as the surfaces of ordinary media ; or, 
 in the language of the theory of emission, that the reflecting forces 
 extended beyond the limits of the polarizing forces of the crystal. 
 Sir David Brewster was led to doubt this opinion ; and in the year 
 1819 he undertook an extensive series of experiments on the sub- 
 ject of crystalline reflexion. One of the first results at which he 
 arrived was, that the angle of complete polarization on the same 
 surface varies with the inclination of the plane of reflexion to the 
 principal section of the crystal ; being least when the plane of re- 
 flexion coincides with the principal section, and greatest when it is
 
 106 REPORT ON PHYSICAL OPTICS. 
 
 perpendicular to it ; and that with different surfaces the variation 
 depended on the inclination of the surface to the axis of the crystal. 
 The difference of the greatest and least angles in the case of Iceland 
 spar, and on one of the cleavage planes of the crystal, was found to 
 amount to more than 2. 
 
 But the effects produced upon the plane of polarization are still 
 more remarkable. On weakening the reflecting force, by causing 
 the reflexion to take place at the surface of contact of the crystal 
 and some fluid such as oil of cassia which had nearly the same 
 refractive power, Sir David Brewster found that the ray was no 
 longer polarized in the plane of reflexion ; and that the deviation 
 of the plane of polarization from the plane of reflexion depended on 
 the angle which the incident ray formed with the axis of the crystal. 
 This relation Sir David Brewster found to be expressed by the 
 law, that the sine of half the deviation varied as the square-root 
 of the sine of inclination of the incident ray to the axis.* 
 
 It is much to be desired that the attention of analysts should 
 be directed to the problem of reflexion at the surface of extraordi- 
 nary media. It is one of the very few important provinces of the 
 science of light, which has not yet yielded its tribute to the wave- 
 theory ; and we can hardly conceive a finer subject for the exercise- 
 of mathematical and physical skill.f 
 
 * " On the action of Crystallized Surfaces upon Light." Phil. Trans. 1819. 
 
 t Since the preceding was written, Mr. M'Cullagb. has arrived at an expression fcr 
 the angle of polarization at the surface of crystallized media, in the case in which the 
 plane of reflexion coincides with one of the principal sections of Fresnel's ellipsoid ;. 
 and he has found that the law, which he has extended by analogy to all cases, repre- 
 sents with much exactness the observations of Sir David Brewster. If a and b denote 
 the semiaxes of the elliptic section formed by the intersection of the plane of reflexion 
 with the ellipsoid of indices (or the ellipsoid whose axes coincide in direction with the- 
 axes of elasticity of the medium, and are equal to its three principal indices), and r the 
 radius of the same section coinciding with the face of the crystal, the angle of 
 polarization, *-, will be the same at whichsoever aide of the perpendicular the ray is 
 incident, its value being given by the formula,
 
 DOUBLE REFRACTION. 1Q7 
 
 III. Double Refract ion. 
 
 The phenomenon of double refraction was first discovered by 
 Erasmus Bartholinus, in Iceland spar. After a long series of ob- 
 servations, he found that one of the rays within the crystal observed 
 the known law of refraction discovered by Snellius, while the other 
 was bent according to a new and extraordinary law. An account 
 of these experiments was published at Copenhagen in the year 
 1669, under the title " Evperimenta Crystalli Islandici Disdiactastici, 
 quibus mira et insolita refract io deteyitur." 
 
 The success of Huygens in deriving the laws of ordinary re- 
 fraction from the hypothesis of waves naturally led him to examine 
 whether these new phenomena could be reconciled to the same 
 theory ; and in his desire to assimilate the two classes of pheno- 
 mena, he was happily led to assign the true law of extraordinary 
 refraction. Huygens had already shown that the direction of the 
 refracted ray, in glass and other uncrystallized substances, could 
 be deduced from the supposition that the ethereal wave within the- 
 substance was a sphere, or, in other words, that the velocity of 
 undulatory propagation was the same in all directions. One of 
 the rays in Iceland crystal, too, was found to obey the same law ; 
 and judging that the law which governed the other, though not so- 
 simple, was yet next in simplicity, he assumed the form of its 
 wave to be the spheroid of revolution, the greater and the lesser axis 
 of the generating ellipse being in the ratio of the greatest and 
 least index of refraction. The form of the wave being known, the 
 law of refraction is derived from the principle of the superposition 
 of small motions. Conceive three surfaces having their common 
 centre at the point of incidence, and representing respectively the 
 simultaneous positions of three waves diverging from that point, 
 the first in air, the other two within the crystal. Let the incident 
 ray be produced to meet the air icave, and at the point of intersec- 
 tion let a tangent plane be drawn. Through the line of intersection 
 of this plane with the refracting surface let planes be drawn 
 touching the two refracted waves ; the lines connecting the centre 
 with the points of contact are the directions of the two refracted 
 rays. This beautiful construction, and the other speculations of 
 Huygens on the subject of extraordinary refraction, are contained 
 in the fifth chapter of his Traite de la Lin// fire.
 
 108 REPORT ON PHYSICAL OPTICS. 
 
 Huygens was unable to reconcile the existence of a double 
 wave within the crystal with the supposition of a single vibrating 
 medium ; and ho was accordingly forced to assume the existence 
 of two such media the spherical wave being propagated by the 
 vibrations of the ether alone, while the spheroidal wave arose 
 from the vibrations of the crystal and of the ether jointly. 
 
 For the construction of Huygens Newton substituted another, 
 without stating the theoretical grounds on which he formed it, or 
 even advancing a single experiment in its confirmation.* In this 
 unsatisfactory position the problem of double refraction was suffered 
 to rest for nearly a century ; and it was not until the period of the 
 revival of physical optics in the hands of Young, that any new 
 light was thrown upon the question. This sagacious philosopher 
 was led by the theory of waves to assume the truth of the law of 
 Huygens ; and it was by his advice that Dr. Wollaston undertook 
 the experimental examination! which recalled to it the attention 
 of the scientific world, and ended in its universal admission. The 
 French Institute soon after proposed the question of double refrac- 
 tion as the subject of their prize essay, and the successful memoir 
 of Malus left no doubt remaining as to the accuracy of the Huy- 
 genian law.J 
 
 The examination of Malus was chiefly directed to the case of 
 Iceland spar ; but he made a few similar measurements, also, in 
 quartz, sulphate of barytes, and arragonite. In the first of these 
 crystals he mistook the ordinary for the extraordinary ray ; and 
 the faces which he chose for examination in the two latter not 
 happening to be well adapted to the discovery of their properties, 
 he was satisfied with a hasty generalization of the law observed in 
 Iceland spar, and concluded that it belonged to all double-refract- 
 ing bodies. Malus entered largely, in the same memoir, into 
 several questions connected with the problem of double refraction ; 
 and he showed, in particular, that the laws of extraordinary reflexion 
 at the second surfaces of crystals are deducible from the law of 
 Huygens. In a memoir presented to the Institute, in the follow- 
 ing year, he extended considerably the list of bodies possessing 
 
 * Optics, Look iii., query 25. 
 
 t " On the Oblique Refraction of Iceland Crystal." Phil Trans. 1802. 
 
 ' Theorie de la Double Refraction." Mem. List. 
 
 " Sur 1'Axe de Refraction des Cristaux et des Substances organisce,."-^. 
 Jntt. 1811.
 
 DOUBLE REFRACTION. 109 
 
 the property of double refraction ; and arrived at the conclusion 
 that this property belonged to all crystals, excepting those whose 
 primitive form was the cube or regular octahedron. Most organized 
 substances, whether vegetable or animal, were found to possess the 
 same properties. 
 
 In Iceland spar the extraordinary refractive index is less than 
 the ordinary. The extraordinary ray consequently is always re- 
 fracted from the axis of the crystal ; and the same law had been 
 supposed to belong to all double-refracting substances. M. Biot 
 made the important discovery that, in many crystals, the extra- 
 ordinary index was greater than the ordinary, and the extraordi- 
 nary ray therefore refracted towards the axis. Crystals of the latter 
 kind he called attractive, while those of the former were called re- 
 puhive ; the extraordinary refraction being ascribed, in the theory 
 of emission, to attractive or repulsive forces which act as if they 
 emanated from the axis.* These crystals are now generally dis- 
 tinguished by the denominations positive and negative. The Huy- 
 genian law applies to positive as well as to negative crystals ; the 
 spheroid being prolate in the former case, and oblate in the latter. 
 
 The construction given by Huygens for the direction of the 
 two refracted rays is, it has been stated, an immediate consequence 
 of the assumed form of the wave-surface. It easily appears, from 
 the principle of Huygens already adverted to, that the same con- 
 struction will apply in all cases, whatever be the form of the wave, 
 or the law of the velocity of propagation within the crystal ; so 
 that the law of direction is determined when that of velocity is 
 known. A similar connexion between the velocity of the molecule 
 and its path is established, in the theory of emission, by the law 
 of least action. This principle, we know, holds generally in the 
 motion of a point subjected to the action of attracting or repelling 
 forces; and in applying it to the case of a luminous molecule, 
 acted on by forces emanating from the particles of the body which 
 it meets, we may leave out of consideration the insensible curvi- 
 linear portion of the trajectory described in the passage from one 
 medium into another of different density, provided we assume, 
 with Newton, that the forces exerted by the molecules of body on 
 those of light are sensible only at insensible distances. In this 
 simplification of the problem we have to deal only with straight 
 
 * Jffiii. Intl. 1814.
 
 HO REPORT ON PHYSICAL OPTICS. 
 
 lines and uniform velocities; and when the dependence of these 
 velocities on the directions is assumed, or given, the principle in 
 question furnishes a relation between the directions of the two 
 portions of the trajectory. Such was the problem whose solution 
 was given by Laplace, in his memoir on the motion of light in 
 transparent media ;* and he has arrived at two equations in which 
 that solution is completely contained. Laplace applied these re- 
 sults to two cases : one in which the difference of the squares of 
 the velocities of the incident and refracted rays is constant, and 
 the other in which that difference is equal to a constant quantity, 
 plus another varying as the square of the cosine of the inclination 
 of the refracted ray to the optic axis. In the former of these 
 cases he obtained the known law of Snellius ; and the formulae of 
 refraction at which he arrived in the latter were found to be iden- 
 tical with those furnished by the construction of Huygens. 
 
 The velocity of the extraordinary ray, assumed by Laplace, is 
 the reciprocal of the radius-vector of the ellipsoid of Huygens, and 
 therefore the inverse of the assumed velocity in the wave-theory. 
 But Laplace himself has shown that the construction suggested by 
 that theory, and employed by Huygens for the determination of 
 the direction of the refracted ray, resolves itself into the principle 
 of least time, and that whatever be the form of the wave-surface ; 
 and as the law of least action and that of least time are identical, 
 provided the assumed velocities be reciprocal, it ceases to be strange 
 that two such very different methods should lead precisely to the 
 same result. The difference between Huygens and Laplace, as to 
 the mode of deducing the law of extraordinary refraction, is in 
 fact precisely the same as that which existed formerly between 
 Fermat and Maupertuis with regard to the ordinary law of the 
 sines. 
 
 This identity of the results afforded by the two theories has 
 since been more distinctly pointed out by M. Ampere. By means 
 of the principle of least action he has arrived at the following 
 general conclusion, whatever be the assumed law of the veloci- 
 ties, that if from the point of incidence on any extraordinary 
 medium, as centre, two surfaces be described whose radii- vectores 
 are inversely as the velocities of the incident and refracted rays in 
 their directions, and if the incident and refracted rays be pro- 
 
 * Mem. Inst. 1809.
 
 DOUBLE REFRACTION. Ill 
 
 duced to meet these surfaces, and tangent planes be drawn at the 
 points of meeting, the line of intersection of these planes will be on 
 the separating surface of the two media.* Hence the position of 
 the refracted ray is determined when that of the incident ray is 
 known ; and the construction thus supplied for its determination 
 is obviously the generalization of the construction of Huygens 
 already alluded to, if only the radii- vectores be taken in the direct 
 ratio of the velocities, instead of the inverse. 
 
 It is obvious, then, that the problem of double refraction, con- 
 sidered as a physical question, resolves itself into the determination 
 of the law of velocities. Newton showed that the constant ratio 
 of the velocities in ordinary media, and therefore the law of the 
 sines, could be explained on the supposition that the luminous 
 molecules are solicited by attracting forces emanating from the 
 molecules of the refracting body, and sensible only at very small 
 distances. The phenomenon of extraordinary refraction, in like 
 manner, was ascribed by Laplace to the operation of similar forces 
 emanating from the molecules of the crystal, but modified by the 
 form of these molecules and those of light, and by the manner in 
 which they are presented to each other. No attempt, however, 
 has been made in the theory of emission to advance beyond the 
 point at which Newton arrived, and to deduce the velocity of the 
 extraordinary ray in crystallized media from any assumed consti- 
 tution of the molecular forces ;t and, indeed, when the condition 
 of polarity is to be superadded to the laws of such forces, the theory 
 seems embarrassed in inextricable difficulties. The refraction which 
 a polarized ray undergoes in a crystal depends upon its plane of 
 polarization ; and, by a simple change of that plane, the refracted 
 ray may be converted from an extraordinary to an ordinary ray. 
 The extraordinary force then, it appears from the phenomena, 
 exerts no effect upon a ray polarized parallel to the principal 
 plane. Its effect is greatest upon a ray polarized in the perpen- 
 dicular plane ; and it must be supposed to act in every intermediate 
 
 * Mem. Inst. 1816. 
 
 t Fresncl states, in the commencement of his memoir on double refraction, that 
 Laplace had derived the velocity of the extraordinary ray, in uniaxal crystals, from 
 the hypothesis of a resultant force acting in a direction perpendicular to the optic axis, 
 and varying as the square of the sine of the angle which the ray makes with that line. 
 I have not been able to discover, in any of Laplace's writings, the discussion thus 
 adverted to.
 
 112 REPORT ON PHYSICAL OPTICS. 
 
 degree upon rays polarized in intermediate planes. Now a ray 
 of common light, in the theory of emission, is composed of mole- 
 cules whose planes of polarization are turned in all azimuths ; and 
 these molecules, consequently, should feel the influence of the ex- 
 traordinary force in every possible degree. Instead, therefore, of 
 two refracted rays, such a ray should be divided into an infinite 
 number, inclined in every possible angle between the limiting 
 directions of the ordinary and extraordinary rays. 
 
 It had been hitherto assumed, that no crystal had more than 
 one optic axis. While examining the rings which surround these 
 axes in polarized light, Sir David Brewster made the important 
 discovery that the greater number of crystals possess two optic 
 axes; and he soon after discovered the connexion between these 
 diversities of optical character and the crystalline form.* 
 
 The optic axes, however, as Sir David Brewster has shown, 
 cannot be regarded in general as the fundamental axes of the 
 double-refracting medium. He calls them apparent axes; and 
 considers them as the resultants of others, which he denominates 
 true or polarizing axes, and from which the forces which produce 
 the phenomena of polarization and double refraction are conceived 
 to emanate. The polarizing force proceeding from a single axis 
 is measured by the difference of the squares of the velocities of the 
 ordinary and extraordinary rays, and is supposed to vary as the 
 square of the sine of the angle which the direction of the ray 
 within the crystal contains with it; and when two such axes 
 cooperate, it is assumed that the increment of the square of the 
 velocity, arising from their joint action, is equal to the diagonal 
 of a parallelogram whose sides are the increments of the squares of 
 the velocities produced by each separately, and whose angle is double 
 of that formed by the two planes passing through the ray and the 
 axes.f From this hypothesis it followed that two rectangular 
 polarizing axes of equal intensity, and both positive or both 
 negative, compound a single resultant axis at right angles to both. 
 This axis is of the same intensity as the component axes, but of an 
 opposite character ; and, accordingly, three equal rectangular axes 
 of the same character balance each other's effects, and have no 
 
 * The important relations here alluded to have heen already brought under the 
 attention of the Association, in the able Report on Mineralogy, by Mr. Whewell. 
 
 t " On the laws of Polarization and Double Refraction in regularly crystallized 
 Bodies." Phil. Trans. 1818.
 
 DOUBLE REFRACTION . 113 
 
 resultant. Thus, then, the laws of uniaxal crystals, as well as of 
 singly-refracting media, are embraced in this hypothesis The case 
 of two resultant axes is reducible to that of two unequal polariz- 
 ing axes ; and it has been shown to be a consequence of the rule, 
 that the difference of the squares of the velocities of the ordinary 
 and extraordinary rays within the crystal is proportional to the 
 product of the sines of the angles which the latter makes with the 
 resultant axes. M. Biot was led to the discovery of this beautiful 
 law by analogy,* and he afterwards observed that it was implicitly 
 contained in the law proposed by Sir David Brewster. 
 
 The term " polarizing force" seems to have been adopted by 
 Sir David Brewster without any reference to the law which go- 
 verned the planes of polarization of the two pencils, a law 
 which, in biaxal crystals, still remained unknown. In the case 
 of uniaxal crystals, it could not fail to be observed, the plane of 
 polarization of one of the pencils contained the direction of the 
 ray and the axis ; while that of the other was a plane passing 
 through the ray at right angles to the former. Conceiving that 
 these planes, in biaxal crystals, must be symmetrically placed with 
 respect to the planes passing through the ray and the two axes, 
 M. Biot was led to the simple and elegant law that the plane 
 of polarization of one of the pencils was that passing through the 
 ray, and bisecting the dihedral angle contained by these planes ; 
 while that of the other was perpendicular to the former, or bisected 
 the supplemental dihedral angle.f 
 
 When a ray of light enters a crystal, the component molecules 
 are supposed, in the theory of M. Biot, to receive different motions 
 round their centres of gravity, dependent on the nature of the 
 forces exerted upon them by the particles of the body. Sometimes 
 the molecules of the ray are turned by the operation of these 
 forces, so as to have certain lines in each, denominated axes of 
 polarization, all in the same direction ; and this arrangement of 
 the molecules is maintained throughout the whole of their future 
 progress. There are other cases, however, according to this author, 
 in which the molecules oscillate round their centres of gravity in 
 certain periods, during their entire progress through the crystal ; 
 
 * " Memoire aur lea Lois generates dc la Double Refraction, &c.," &* /'> 
 torn. iii. 
 t Ibid. 
 
 I
 
 114 REPORT ON PHYSICAL OPTICS. 
 
 while in others, finally, they receive a motion of continued rotation. 
 To the two latter cases I shall have occasion to advert hereafter. 
 
 The phenomena of fixed polarization are ascribed by M. Biot 
 to the operation of certain forces, which he denominates polarizing 
 forces. In the case of uniaxal crystals these forces are supposed 
 to act in the planes containing the two rays and the axis of the 
 crystal, the ordinary polarizing force tending to arrange the 
 axes of the molecules in the plane containing the ray and the 
 axis, while the extraordinary polarizing force draws them towards 
 the perpendicular plane. If the molecules were similarly circum- 
 stanced in every respect, they would necessarily obey the stronger 
 of these forces, and there would be but one plane of polarization. 
 This, however, is supposed not to be the case. Owing to the 
 different phases of their fits, at their incidence upon the crystal, 
 the molecules are disposed to yield more readily to one or other of 
 these forces ; so that when a polarized ray meets a double-refracting 
 medium, some of the molecules fall under the influence of the 
 ordinary polarizing force, and have their axes of polarization 
 turned into the plane containing the ray and the axis of the 
 crystal, while others are actuated by the extraordinary force, and 
 have their axes arranged in the perpendicular plane. The number 
 of molecules which yield to one or other of these forces, or the 
 intensity of the two polarized rays, is supposed to depend on the 
 angle which the plane of primitive polarization makes with the two 
 planes just mentioned. When the plane of polarization coincides 
 with the former, the extraordinary force has no effect, and the ray 
 receives only the ordinary polarization ; the converse takes place 
 when the plane of polarization coincides with the perpendicular 
 plane. Similar suppositions were made to account for the phe- 
 nomena of polarization in biaxal crystals. 
 
 Such was the state of the theory of double refraction when the 
 subject was taken up by Fresnel. The law of refraction, we have 
 seen, whether in the theory of emission or in that of waves, was 
 intimately connected with, and dependent on the law of velocities ; 
 so that, considered as a physical question, the problem resolved 
 itself into the determination of the latter. With the exception, 
 however, of the reasonings of Young respecting the form of the 
 wave-surface in a medium compressed or dilated in a given 
 direction,* no attempt had been made to deduce the velocity of the 
 
 * Quarterly Seview, vol. ii.
 
 DOUBLE REFRACTION. 115 
 
 -extraordinary ray from the principles of either theory. Indeed 
 the general law of the velocities was itself unknown, even as an 
 experimental fact, although an important relation between the 
 velocities of the two pencils had been discovered by the labours of 
 Sir David Brewster and M. Biot. But this was not all. It was 
 evident that no physical theory of double refraction could be re- 
 garded as complete, which did not at the same time account for 
 the attendant phenomenon of polarization. In this branch of the 
 subject, however, nothing had been accomplished; and all that 
 had been said in explanation of the phenomenon of polarization 
 did not go further than some vague speculations as to its cause. 
 The theory of Fresnel to which I now proceed, and which not 
 only embraces all the known phenomena, but has even outstripped 
 observation, and predicted consequences which were afterwards 
 fully verified, will, I am persuaded, be regarded as the finest 
 generalization in physical science which has been made since the 
 discovery of universal gravitation. 
 
 Fresnel* sets out from the supposition that the elastic force 
 -of the vibrating medium is, in general, different in different 
 directions. This is, in fact, the most general supposition that can 
 be made; and whether we suppose that the vibrating medium 
 is the ether within the crystal, or that the molecules of the body 
 itself partake of the vibratory movement, there will be obviously 
 such a connexion, and mutual dependence, of the parts of the solid 
 and those of the medium in question, that we cannot hesitate to 
 admit for the one what has been already established on the clearest 
 evidence for the other.f Now if a disturbance be produced in a 
 medium so constituted, and any particle displaced from its position 
 of rest, the resultant of the elastic forces which resist the displace- 
 ment will not, in general, act in the direction of that displacement 
 (as in the case of a medium uniformly elastic), and therefore will 
 not drive the displaced particle directly back to its position of 
 equilibrium. Fresnel has shown, however, that there are three 
 directions at right angles to each other, in any of which, if the 
 particles are displaced, the elastic forces do act in the direction 
 
 * " Mcmoire sur la Double Refraction," Mem. Inst., torn. vii. 
 
 t M. Savart has shown that the elasticity of crystals, determined by means of 
 their sonorous vibrations, is, in general, different in different directions. The optic 
 axis of Iceland spar is the axis of least elasticity: that of rock crystal is the axis of 
 
 greatest elasticity. 
 
 1 2
 
 116 REPORT ON PHYSICAL OPTICS. 
 
 of the displacement, whatever be the nature or laws of the mole- 
 cular action ; and the only assumption which he makes is that these 
 three directions are parallel all throughout the crystal.* These 
 directions Fresnel denominates axes of elasticity. He conceives 
 that they ought also to he axes of symmetry with respect to the 
 crystalline form ; but observes that M. Mitscherlich has noticed 
 some crystals in which this does not hold.f If on each of these 
 axes, and on every line diverging from the same origin, portions 
 be taken which are as the square roots of the elastic forces in their 
 direction, the locus of the extremities of these portions will be a 
 surface which Fresnel calls the surface of elasticity. This surface 
 determines the velocity of propagation of the wave, when the 
 direction of its vibrations is given. For the velocity of undu- 
 latory propagation in an elastic medium, being as the square root 
 of the elastic force, must be represented by the radius- vector of the 
 surface of elasticity in the direction of the vibrations. 
 
 Now let us conceive a plane wave advancing within the crystal. 
 By the principle of transversal vibrations the movements of the 
 ethereal molecules are all parallel to the wave. But the motion 
 of each displaced particle is resisted by the elastic force of the 
 medium, and that force is, in general, oblique to the direction of 
 the displacement. Fresnel shows, however, that the displacement 
 may be resolved in two directions in the plane of the wave, such 
 that the elastic force called into action by each component will be 
 the resultant of two forces, one of which acts in the direction of 
 the displacement itself, while the other is normal to the wave* 
 The latter, by the principle of transversal vibrations, can produce 
 no effect ; and the former will give rise to a wave propagated 
 with a constant velocity. These two directions, he finds, are those 
 of the greatest and least diameters of the section of the surface of 
 elasticity made by the plane of the wave ; and if the original 
 displacement be resolved into two, parallel to them, each component 
 will give rise to a plane wave whose velocity of propagation is 
 
 * This will be the case, if the homologous lines of the groups of particles are all 
 parallel ; an arrangement at once the simplest and most natural, and which appears to 
 be observed in most crystallized bodies. Fresnel admits, however, the possibility of 
 other regular arrangements ; and he conceives that the phenomena of circular polari- 
 zation in rock crystal oblige us to suppose that its molecules are arranged according to 
 some less simple law. 
 
 t See Bulletin de la, Socie'tt Phikmafhi.jne, March, 1824.
 
 DOUBLE REFRACTION. 117 
 
 represented by that diameter, and the vibrations in each wave will 
 preserve constantly the same direction. 
 
 Thus it appears that a polarized plane wave will be resolved 
 into two within the crystal ; and these will be propagated with 
 different velocities, and consequently follow different paths. The 
 amplitudes of the component vibrations are as the cosines of the 
 angles which the direction of the original vibration contains with 
 the two fixed rectangular directions ; and as the squares of these 
 amplitudes represent the intensities of the two pencils, the law 
 of Malus respecting these intensities follows as an immediate 
 consequence.* Again, the planes perpendicular to these two 
 directions are the planes of polarization of the two pencils ; and 
 it is easily inferred that one of them must bisect the dihedral 
 angle contained by the two planes passing through the normal to 
 the wave, and the normals to the circular sections of the surface of 
 elasticity, while the other is perpendicular to it. This conclusion 
 does not coincide mathematically with the experimental law of 
 M. Biot : but the differences are much within the limits of the 
 errors of observation, and the results of experiment must be 
 regarded as confirmatory of the theory. 
 
 The velocity of propagation of a plane wave in any direction 
 being known, the form of the wave-surface diverging from any 
 point within the crystal may be found. For if we conceive an 
 indefinite number of plane waves, which, at the commencement of 
 the time, all pass through the point which is considered as the 
 centre of disturbance, the wave-surface will be that touched by all 
 these planes at any instant. This surface is of the fourth order. 
 Fresnel has deduced its equation, although in an indirect manner ; 
 and he has shown that it may be geometrically constructed by 
 means of an ellipsoid whose semiaxes are the same as those of the 
 surface of elasticity. The form of the wave-surface being known, 
 the directions of the two refracted rays are given by the construc- 
 tion of Huygens. 
 
 From the construction now alluded to it appears that there 
 
 * Young seems to have been the first to observe that the law of the square of the 
 cosine could be derivecTfrom the hypothesis of transversal vibrations, (Encyc. Brtt., 
 CHROMATICS, p. 161). The subject of the experimental confirmation of this importan 
 law has been recently brought before the French Academy by M. Arago, and he has 
 indicated the practical results which mny be derive 1 from this law in its application to 
 photometry. llersclicr* Essay on Lijht : French Transaeion, Suppl., p. 690.
 
 118 REPORT ON PHYSICAL OPTICS. 
 
 are two directions the normals, namely, to the two circular sec- 
 tions of the ellipsoid, in which the velocity of the two rays is 
 the same. These directions are called by Fresnel the optic axes r 
 although he sometimes applies this term to the normals to the 
 circular sections of the surface of elasticity, or the directions in 
 which a plane wave is propagated with a single velocity. It thus 
 appears that crystals have in general two optic axes, and can have 
 no more. When two of the three principal elasticities are equal, 
 the two optic axes unite, and the wave-surface resolves itself into 
 the sphere and spheroid of revolution. Thus the form of the wave 
 in uniaxal crystals, which Huygens assumed as the most natural, 
 comes out as a simple corollary from the general theory of FresneL 
 When, lastly, the three elasticities are all equal, the wave-surface 
 becomes a sphere; the velocity is accordingly the same in all 
 directions, and the law of refraction is reduced to the known law 
 of Snellius. 
 
 It was easily shown to follow from the general construction, 
 that the difference of the squares of the reciprocal velocities of the 
 two rays, in biaxal crystals, is proportional to the product of the 
 sines of the angles which their common direction within the crystal 
 contains with the two axes; so that the remarkable law of Sir 
 David Brewster and M. Biot is brought under the same theory. 
 But it appeared further, from that theory, that the velocity of 
 neither of the rays is constant, and that the refraction of both is 
 performed according to a new law. This conclusion was at variance 
 with all the received notions upon the subject ; and indeed the ex- 
 periments of M. Biot on limpid topaz* seemed to warrant his- 
 assumption that the refraction of one of the rays followed the 
 ordinary law of the sines. It became, therefore, a matter of much 
 interest to decide this question by accurate experiment. This has 
 been done by Fresnel himself by the ordinary method of prismatic 
 refraction, as well as by the nicer means afforded by the dis- 
 placement of the diffracted fringes ; and the result in both cases 
 has been conclusive in favour of his theory. The numerical data 
 afforded by the observations of M. Biot on topaz enabled Fresnel 
 to compute, according to the principles of that theory, the velocity 
 of the ray in different directions ; and the observed variation was- 
 found to agree with that deduced. 
 
 * Mem. Iml., torn. iii.
 
 DOUBLE REFRACTION. 119 
 
 The phenomenon of dispersion, in singly-refracting substances, 
 proves that the elasticity of the vibrating medium varies with the 
 length of the wave. The same thing must take place in double- 
 refracting media, in which the elasticity is different in different 
 directions ; and as we have no reason for supposing that the elas- 
 ticities should vary in the same proportion in the direction of the 
 three axes of elasticity, it will follow that in general each refractive 
 index will have its appropriate dispersive ratio. Sir David Brew- 
 ster first showed that this was actually the case, and that Iceland 
 spar and other double-refracting substances had two dispersive 
 powers.* M. Rudberg has recently examined the laws of dis- 
 persion in double-refracting media with much care, following the 
 accurate method of Fraunhof er. He has in this manner determined 
 the greatest and least refractive index, corresponding to the seven 
 principal dark lines of the spectrum, in Iceland spar and rock 
 crystal, and the three principal indices in arragonite and topaz ; 
 and has found, in accordance with the discovery of Sir David 
 Brewster, that the ratio of these indices increased with the refran- 
 gibility of the light.f The experiments of M. Budberg confirm 
 also the fundamental position of Fresnel's theory- namely, that 
 the velocity of a ray in a given medium is the same as long as its 
 plane of polarization is unchanged. 
 
 The angle contained by the optic axes, in biaxal crystals, is a 
 simple function of the three principal elasticities; and if their 
 ratio vary with the colour of the light, the inclination of the axes 
 must likewise vary. Such a variation has been established by the 
 observations of Sir John Herschel ; and it has been found that the 
 inclination of the axes is greater in red than in violet light for 
 some crystals, while in others it is less.J In the case of Rochelle 
 salt, the angle between the optic axes of the red and violet rays 
 
 * Treatise on New Philosophical Instruments, Edin. 1813. 
 
 t Annales de C/iimie, torn, xlviii. For the calculation of the phenomena of double 
 refraction in biaxal crystals, according to Fresnel's theory, it is necessary to know the 
 three principal refractive indices, or the velocities of propagation of rays whose vibra- 
 tions are parallel to the three axes of elasticity. Beside the researches of M. Rudberg, 
 I do not know that we possess any other in which all those data have been directly 
 determined. It is true that if we know the greatest and least index, and the an* 
 contained by the optic axes, the mean index can bo deduced. But the 11 
 of the optic axes cannot be determined experimentally with the same prec 
 other elements. 
 
 J Phil. Trans. 1820.
 
 120 EEPORT ON PHYSICAL OPTICS. 
 
 amounts to 10. Generally the position of the three axes of elas- 
 ticity is invariable, and the optic axes for all colours are confined 
 to one plane ; but Sir John Herschel has lately observed that, in 
 borax, the optic axes belonging to different colours lie in different 
 planes ; and we are compelled to conclude that the direction of the 
 axes of elasticity in this, and probably in many other crystals, 
 varies with the colour. 
 
 The first addition to the theory of Fresnel was made by M. 
 Ampere. The results alluded to are contained in two short papers 
 read to the French Academy in the year 1828, and since embodied 
 into one, and published in the Annales de Chimie* Fresnel had 
 arrived at the equation which belongs to all the tangent planes of 
 the wave-surface, and had shown in what manner the equation of 
 the surface itself might be thence deduced by differentiation and 
 elimination. This direct process, however, he seemed to think 
 would involve complicated and embarrassing calculations. The 
 method which he substituted for it consisted in verifying the 
 equation, to which he was led by reasonings not altogether rigo- 
 rous, and proving (by calculations which he found too tedious to 
 transcribe) that it satisfied the conditions already assigned. M. 
 Ampere has supplied the direct demonstration, and deduced the 
 equation of the wave-surface in the manner originally pointed out 
 by Fresnel. From this equation he has derived also the beautiful 
 geometrical construction given by Fresnel, and which the latter 
 had obtained indirectly. 
 
 A very concise demonstration of the same theorem, and of the 
 other principal points of Fresnel's theory, was given not long after 
 by Mr. M'CuHagh.f This writer has shown that both the magni- 
 tude and direction of the resultant elastic force, called into action 
 by any displacement, may be represented by means of an ellipsoid 
 whose semiaxes are the three principal refractive indices of the 
 medium ; and from this ellipsoid, by the aid of a few geometrical 
 lemmas, he has deduced in a clear and simple manner the leading 
 
 * " Memoire sur la Ddtermination'de la Surface courbe des Ondes lumineuses," 
 
 &C., t 
 
 t " On the Double Refraction of Light in a crystallized medium, according to the 
 principles of Fresnel," Transactions of the Royal Irish Academy, vol. xvi. A further 
 development of the principles of this memoir has been recently given by the author in 
 the 17th vol. of the same Transactions, under the title Geometrical Propositions 
 applied to the Wave-theory of Light."
 
 DOUBLE REFRACTION. 121 
 
 results arrived at by Fresnel. The axes of this ellipsoid coincide 
 in direction with, and are inversely proportional to, the axes of 
 Fresnel's generating ellipsoid; and Mr. M'Cullagh has demon- 
 strated the truth of Fresnel's construction for the wave-surface, by 
 means of a simple geometrical relation between its tangent planes 
 and the sections of the two ellipsoids. 
 
 In the third supplement to his " Essay on the Theory of Systems 
 of Rays"* Professor Hamilton has presented that portion of Fres- 
 nel's theory, which relates to the fundamental problem of the 
 determination of the velocity and polarization of a plane wave, in 
 a very elegant analytical form ; and from the velocity and direction 
 of the wave he deduces those of the ray, and therefore the form of 
 the wave-surface, by means of the general relations suggested by 
 his view of mathematical optics. 
 
 In this system, of which the author gave a brief sketch at the 
 late meeting of the Association, the laws of reflexion and refraction, 
 ordinary or extraordinary, are comprised in two fundamental ex- 
 pressions, which state that the partial differential coefficients of the 
 first order of a certain function taken with respect to two final 
 coordinates in the plane which touches the reflecting or refracting 
 surface at the point of incidence, are not altered by reflexion or 
 refraction. The function here considered is the characteristic func- 
 tion of the author, whose particular form may be considered as 
 characterizing the optical system, and on whose properties, he finds, 
 all the problems of mathematical optics may be made to depend. 
 On the principles of the wave-theory, this function is equal to the 
 undulatory time of propagation of light, from any one assumed 
 point to another, in the same or in a different medium ; and the 
 expressions just alluded to signify simply that the components of 
 normal slowness of the wave parallel to the bounding surface, or the 
 reciprocals of the velocities of wave-propagation resolved in the 
 direction of that surface, are not changed by reflexion or refraction. 
 The normal slowness of wave-propagation is, then, of fundamental 
 importance in this theory ; and if it be represented in magnitude 
 by a line taken in its direction, there is obtained for its expression 
 a curved surface which, on the principles of Fresnel, is found to be 
 a surface of two sheets, connected with the wave-surface by a 
 remarkable relation of reciprocity. When this relation is com- 
 
 * Transactions of the Royal Irish Academy, vol. xvii.
 
 122 REPORT ON PHYSICAL OPTICS. 
 
 bined with the laws of reflexion and refraction just alluded to, they 
 lead to a very elegant construction for the reflected or refracted 
 ray, which is, in most cases, more convenient than that of Huy- 
 gens. Thus, when a ray proceeds from air into any crystal, we 
 have only to construct the surfaces of wave-slowness belonging to the- 
 two media, and having their common centre at the point of inci- 
 . dence. Let the incident ray be then produced to meet the sphere, 
 which represents the normal slowness of the wave in air ; and 
 from the point of intersection let a perpendicular be drawn to the 
 reflecting or refracting surface. This will cut the surface of slow- 
 ness of the reflected or refracted waves in general in two points. 
 The lines connecting these points with the centre will represent 
 the direction and normal slowness of the waves ; while the perpen- 
 diculars from the centre on the tangent planes at the same points 
 will represent the direction and slowness of the rays themselves. 
 
 This important curved surface presented itself also to M. Cau- 
 chy in his able researches on the propagation of waves in elastic 
 media, although he does not seem to have been aware of all its 
 properties. The properties of the same surface, and its use in 
 constructing the direction of a reflected or a refracted ray, were 
 also discovered, independently, by Mr. M'Cullagh, who has re- 
 cently applied them to the geometrical development of the theory 
 of double refraction.* 
 
 The relations between the surface of wave-slowness, and that of 
 the wave, have led Professor Hamilton to the discovery of some 
 new geometrical properties of the latter. These properties are 
 demonstrated by means of certain transformations of the equation 
 of the wave-surface ; and it is shown that this surface has four 
 conoidal cusps, at the extremities of the lines of single ray-velocity, 
 at each of which the wave is touched (not by two planes as Fres- 
 nel supposed, but) by an infinite number forming a tangent cone 
 of the second degree ; while, at the extremities of the lines of single 
 wave-velocity, there axe four circles of plane contact, in every point of 
 each of which the wave-surface is touched by a single plane. 
 These singular properties have led Professor Hamilton to anticipate 
 two new laws of refraction called by him conical refraction, be- 
 cause in each case a single ray is refracted into an infinite number 
 
 ''Geometrical Propositions applied to the Wave-theory of Light," Transactions 
 of the Royal Irish Academy, vol. xvii.
 
 DOUBLE REFRACTION. 123 
 
 forming a species of cone. External conical refraction corresponds 
 to the cusp on the wave-surface ; and takes place without, when a 
 single internal ray coincides with either of the lines of single ray- 
 velocity. Internal conical refraction, on the other hand, takes 
 place within the crystal, when a single ray is incident externally 
 at an angle corresponding to the line of single wave-velocity 
 within. In this latter case, if the crystal be hounded by parallel 
 planes, all the rays of the cone will emerge at the second surface 
 parallel to the ray incident on the first, so as to form a small 
 elliptic cylinder, whose magnitude will depend upon the angle of 
 the cone and the thickness of the crystal. All these remarkable 
 conclusions have been verified in the fullest manner by experi- 
 ment.* 
 
 I shall now proceed to give a brief account of the labours of 
 M. Cauchy in this interesting department of analysis. The 
 researches of this eminent mathematician, on the propagation of 
 motion in elastic media, are scattered through various livraisons of 
 the Exercices de Mathematiques ; and he has given a valuable sum- 
 mary of the results of these investigations, as applied to the wave- 
 theory of light, in a memoir read to the French Academy in the 
 year 1830.f 
 
 Having assigned the general equations of motion of a system 
 of molecules, acting on one another by attracting or repelling 
 forces which vary according to any function of the distance, M. 
 Cauchy observes that it is not necessary to have recourse to their 
 general integrals in order to determine the laws of undulatory 
 propagation. It is sufficient, in fact, to determine the law of 
 propagation of a plane wave. For if we consider a great number 
 of plane waves inclined to one another at small angles, and which 
 are at first superposed in the neighbourhood of the point which is 
 considered as the origin of the disturbance, the vibrations in the 
 elementary waves, to which each of these gives rise, may be sup- 
 posed too small to affect the sense separately, and these waves 
 become efficacious only by superposition. Consequently the general 
 wave-surface will be the locus of all the points in which the 
 elementary plane waves are superposed ; and will therefore be the 
 
 * " On the Phenomena presented by Light in its passage along the axes of biaxal 
 Crystals," Transactions of the Royal Irish Academy, vol. xvii. 
 
 t " Mcmoire sur la Theorie de la Lumiere," Mem. List., torn. x.
 
 124 EEPOET ON PHYSICAL OPTICS. 
 
 surface touched by them all at any instant.* Hence the problem 
 is reduced to the determination of the law of propagation of a 
 plane wave. 
 
 M. Cauchy then shows that a disturbance, confined originally 
 to a given plane, will in general give rise to three pairs of plane 
 waves parallel to the original plane, and propagated with uniform 
 velocities, the two waves of each pair moving with equal velocities 
 in opposite directions. The velocities of propagation of the separate 
 pairs, he proves, may be represented by the reciprocals of the axes 
 of a certain ellipsoid, whose form depends upon the position of the 
 plane wave and upon the nature of the system ; and the absolute 
 displacements of the molecules will be parallel to the directions of 
 these axes. Accordingly, a system of plane waves, superposed at 
 first at the point of original disturbance, will be subdivided into 
 three corresponding systems; and these, by their superposition, 
 will generate a curved surface of three sheets, each sheet being 
 touched by all the plane waves of the same system. From these 
 principles it follows that a single ray of light will be, in general, 
 subdivided into three polarized rays; a ray being said, in this 
 theory, to be polarized parallel to a certain line or plane, when the 
 vibrations of the ethereal molecules are parallel to that line or 
 plane. M. Cauchy does not state the precise physical condition 
 on which the existence of the third ray depends. It would seem, 
 however, that it must arise from the circumstance that the vibration 
 normal to the wave is not absolutely insensible, or that the actual 
 vibrations are not accurately in the plane of the wave. He states 
 that the intensity of this ray will be in all cases very small, and 
 that its observation therefore will be a matter of difficulty ; and he 
 promises in a future communication to point out the means of 
 manifesting its existence. 
 
 The formulae, on which the solution of the general problem 
 depends, may be reduced to contain nine constant coefficients 
 depending on the law of distribution of the molecules in space. 
 Three of these represent the pressures sustained in the natural 
 condition of the medium by any three planes parallel to those of 
 the three coordinates ; and these (M. Cauchy afterwards concludes) 
 
 * M. Poisson does not admit the legitimacy of this conception of the wave-surface : 
 id he thinks that an assemblage of indefinite plane waves, having a small part in 
 common at the origin of the motion, cannot represent the initial condition of a medium 
 disturbed at that point.
 
 DOUBLE REFRACTION. 125 
 
 vanish of themselves. When the general theory is applied to the 
 case in which the elasticity is the same in all directions round any 
 line parallel to one of the axes of coordinates, M. Cauchy finds 
 that the nine coefficients are reduced to five ; and that two sheets 
 of the wave-surface become the sphere and spheroid of the Huy- 
 genian law, provided that the remaining constants fulfil two 
 assigned equations of condition. In the general case, in which the 
 elasticity is unequal in all directions, he investigates the sections 
 of the wave-surface made by the planes of the three coordinates ; 
 and he finds that for two sheets of that surface they are 
 reduced to the circle and ellipse of FresneFs theory, provided that 
 the constants fulfil three assigned equations of condition. The 
 wave-surface itself differs a little from the surface of the fourth 
 order obtained by Fresnel ; but is reducible to it when the excen- 
 tricities of the ellipses just mentioned are small, as is the case in 
 all known crystals. 
 
 Thus the results obtained by M. Cauchy embrace and confirm 
 those of Fresnel ; and the mathematical laws of the propagation 
 of light are shown to be particular cases of the more general laws 
 of the propagation of vibratory motion in any elastic medium 
 composed of attracting and repelling molecules. Considered,, 
 however, simply with reference to the theory of light, the solution 
 given by M. Cauchy cannot, I conceive, be considered as a com- 
 plete physical solution. In other words, the phenomena of light 
 are not connected directly with any given physical hypothesis ; but 
 are shown to be comprehended in the results of the general theory, 
 in virtue of certain assumed relations among the constants which 
 that theory involves. If, indeed, we were able to assign the 
 precise physical meaning of these equations of condition, we should 
 have nothing more to desire in the general theory of light ; for 
 these equations must necessarily express the characteristic properties 
 of the vibrating medium. In this point of view their discussion 
 becomes a subject of the highest interest ; and it is probable that 
 the important conclusions of which we have yet to speak may in 
 this manner be confirmed and extended. 
 
 These conclusions are contained in a memoir presented to the 
 French Academy by M. Lame, in the spring of the present year,* 
 
 * " Memoire sur les Lois dc 1'Equilibre dc 1'Ether dans les Corps dinphanes." A full 
 account of this paper is given in the Annaki de Chimie for March. The memoir iUelf 
 is not yet published.
 
 126 REPORT ON PHYSICAL OPTICS. 
 
 in which the author has proposed to determine the laws accord- 
 ing to which the molecules of bodies act on those of the ether, 
 and the molecules of the ether on one another. Setting out from 
 the existence of transversal vibrations, as established by the fact 
 of the non-interference of rays oppositely-polarized, the author 
 supposes a disturbance of the ether to take place in vacuum that 
 is, in a space devoid of all ponderable matter, and proceeds to 
 consider what will be the result when that disturbance reaches the 
 ether contained in a transparent body. Assuming the property of 
 transversal vibrations noticed by Fresnel, and more explicitly 
 stated by M. Poisson namely, that they are propagated without 
 any attendant change of density, M. Lame then seeks the conditions 
 to be satisfied by the function, which represents the mutual action 
 of the molecules of the ether and those of the solid body, in order 
 that this property may subsist. Introducing, accordingly, this 
 principle into the partial differential equations, which express the 
 laws of the vibratory movement generally, he arrives finally at an 
 equation of condition, from which he concludes that " the action 
 of ponderable matter on the ether varies in the inverse ratio of the 
 square of the distance ; and that the elasticity of the ether itself is 
 proportional to its density." 
 
 In order to determine the sign of this action that is to say, 
 whether it is attractive or repulsive, it is necessary to integrate 
 the differential equations. After certain transformations of these 
 equations tending to facilitate their examination, he obtains their^ 
 integral in the case of a single spherical and homogeneous mole- 
 cule of the body, around which the ether is distributed in spheri- 
 cal shells. The conclusions deduced from this case being combined 
 with the established fact, that the velocity of light is less in 
 transparent bodies than in vacuum, he arrives at the result, that 
 the mean density of the ether is less in the former, or that 
 the action of the molecules of these bodies on those of the ether is 
 rr-pukive. M. Lame concludes also from the examination of the 
 same case, that the retardation of the vibratory motion, in pene- 
 trating into a dense body, will be greater, the less the length of 
 an undulation, so that the refraction will be greater for waves of 
 shorter length. This he conceives to be the true explanation of 
 the phenomenon of dispersion. 
 
 M. Lame has likewise endeavoured to connect the phenomena 
 of double refraction with an assumed constitution of the ethereal
 
 DOUBLE REFRACTION. 127 
 
 fluid. He takes the case in which the ether is supposed to be 
 distributed round the molecules of the body in confocal ellip- 
 soidal shells; and he concludes that a vibratory movement, 
 propagated from vacuum into a body so constituted, will be 
 separated at its entrance into two component movements, which 
 will advance with different velocities. The two component vibra- 
 tions, he finds, will be at right angles, and parallel to the 
 lines of greatest and least curvature of the elementary ellipsoids. 
 Thus, the bifurcation of a ray of light on entering a crystallized 
 medium, and the opposite polarization of the two pencils, are 
 found to be consistent with a molecular constitution such as that 
 described. 
 
 These results are of the highest interest ; and will, no doubt, 
 receive an early examination from those engaged in the same 
 department of analysis. Their author seems to be persuaded that 
 his methods will lead him to the mathematical laws of other phe- 
 nomena, which he conceives to depend, in like manner, on the 
 motions of the ethereal fluid.* 
 
 I cannot close this division of the present Report without 
 referring to the phenomena of absorption by crystallized media, 
 although the laws of these phenomena are as yet wholly without 
 the pale of theory. Dr. Wollaston seems to have been the first 
 who noticed any facts connected with this interesting subject. 
 The absorbing properties of crystals were found to vary with 
 the direction : certain crystals of palladium, for example, appear- 
 ing of a deep red colour when viewed along the axis, and of 
 a yellowish green in a transverse direction. Tourmalines were 
 observed also to possess analogous properties.! Similar obser- 
 vations were afterwards made by M. Cordier and the Count de 
 Bournon. 
 
 The next step of any importance in this new field of research 
 
 * In a continuation of this memoir, recently read to the French Academy, 
 M. Lame has considered particularly the mode of vibration of the particles of 
 the ether which are disposed round the ponderable particles of body in concentric 
 spherical shells of decreasing density. Transparent homogeneous bodies are supposed 
 to consist of a multitude of such particles distributed uniformly In space, and at 
 -distances incomparably greater than their diameters ; and he conceives that the waves 
 propagated from the particles adjoining to the surface of emergence will, by their 
 interference, give rise to phenomena resembling the fixed lines in the spectrum. 
 Ann. Chim., torn. Ivii. 
 
 t Phil. Trans. 1804.
 
 128 REPORT ON PHYSICAL OPTICS. 
 
 was made by Sir David Brewster. This philosopher observed 
 that in some double-refracting crystals, as carbonate of barytes, 
 the two pencils were differently coloured ;* while in others their 
 intensity was widely different.! The unequal absorption of the 
 two pencils is most remarkable in tourmaline, in which it was 
 observed, nearly at the same time, by M. Biot and Dr. Seebeck ; 
 and the former philosopher inferred from the phenomena that 
 the more refrangible rays of the spectrum are more easily ab- 
 sorbed by the mineral, when polarized parallel to its axis, than 
 when perpendicularly.^ 
 
 Sir David Brewster, to whom we owe the greater part of our 
 knowledge on this subject, has shown that similar properties 
 belong, in a greater or less degree, to most coloured crystals which 
 possess double refraction ; and that the absorption of light by 
 such media varies, in general, both with the colour of the light 
 and with the position of the plane of polarization. When a ray 
 of common light therefore enters a plate of such a crystal, the 
 two pencils into which it is divided will be unequally absorbed, 
 and the emergent light will be partially polarized, the differ- 
 ence of the intensities of the oppositely-polarized portions in- 
 creasing with the thickness of the medium traversed. But the 
 two pencils differ, in general, in colour as well as in intensity ; 
 and this difference, in uniaxal crystals, Sir David Brewster 
 found to depend on the inclination of the ray to the axis, 
 vanishing when the ray coincided with the axis, and becoming 
 a maximum when it was perpendicular to it. A ray of common 
 light, therefore, transmitted perpendicularly through a plate of 
 such a crystal, will emerge coloured; and the resulting colour 
 will, in general, vary with the inclination of the surface to the 
 axis. Thus the phenomena of dichroism, observed by Wollas- 
 ton and others, are reduced to the more general laws of absorp- 
 tion. Analogous properties belong to biaxal crystals, and depend 
 in like manner on the planes of polarization of the two pencils, and 
 on the direction of the ray. These properties Sir David Brewster 
 found could be modified by heat ; and were even communicated by 
 such influences to crystals in which they did not naturally reside. 
 
 * Edin. Trans., vol. vii. ^ p hi i fi. anSf 1814> 
 
 I Traite de Physique, torn, iv., 313. 
 
 " On the Laws which regulate the Absorption of Polarized Light by double- 
 refracting Crystals," Phil. Trant. 1819.
 
 COLOURS OF CRYSTALLINE PLATES. 129 
 
 Notwithstanding the important labours of Sir David Brewster, 
 much remains to be done connected with this subject. Sir John 
 Herschel has proposed empirical formulae to represent the in- 
 tensity of the transmitted light as dependent on its direction; 
 and the results of the formulae present a general accordance 
 with observed facts.* It is much to be desired that these laws 
 should be placed beyond doubt by an extensive series of expe- 
 riments directed to this specific object. Although the laws of 
 absorption by crystallized media are necessarily more compli- 
 cated than those of ordinary media, yet they bear an evident 
 and close relation to the well-known laws of double refraction, 
 which seems to hold out a clue to their discovery; and I feel 
 persuaded that it is in the phenomena of dichroism that the 
 physical theory of absorption will first take its rise, and seek 
 its confirmation. 
 
 IV. Colours of Crystalline Plat<>*. 
 
 If a beam of light, polarized by reflexion, be received upon 
 a second reflecting plate at the polarizing angle, it is wholly 
 transmitted when the second plane of incidence is perpendicular 
 to the first. But if between the polarizing and analyzing plates, 
 as they are termed, there be interposed a plate of any double- 
 refracting crystal, a portion of the light is reflected, whose quan- 
 tity depends on the position of the interposed crystal. In order 
 to analyze the phenomenon, the crystalline plate may be placed 
 so as to receive the polarized beam perpendicularly, and then 
 turned round in its own plane. It is then observed that there 
 are two positions of the plate in which the reflected light totally 
 disappears, just as if no crystal had been interposed. These two 
 positions are those in which the principal and the perpendicular 
 sections of the crystal coincide with the plane of the first reflexion. 
 When the plate is turned round from either of these positions, 
 the light gradually increases ; and it becomes a maximum when 
 the principal section is inclined at an angle of 45 to the plane 
 of the first reflexion. These phenomena were observed by 
 Malus. 
 
 The reflected light in these experiments was in all cases white. 
 But M. Arago observed that when the interposed plate is suffi- 
 
 * Essay on Light, pp. Sol, &c. 
 K
 
 130 REPORT ON PHYSICAL OPTICS. 
 
 ciently thin such as the laminae into which mica or sulphate of 
 lime may be readily divided by cleavage, the most gorgeous 
 colours appear, which vary with every change of inclination of the 
 plate to the polarized beam. When the plate is perpendicular 
 to the transmitted pencil, and then turned round in its own 
 plane, the tint does not change, but only varies in intensity, 
 being a maximum when the principal section of the crystal is 
 inclined at an angle of 45 to the plane of primitive polariza- 
 tion, and vanishing altogether when it coincides with that plane, 
 or is perpendicular to it. On the other hand, when the crys- 
 tal is fixed, and the analyzing plate turned, so as to vary the 
 inclination of the plane of the second reflexion to that of the 
 first, the colours change in the most striking manner ; and it 
 is found that the colour reflected, in any one position of the 
 plane of the second reflexion, is always complementary to that 
 reflected in the perpendicular position. The colours disappear 
 altogether when the thickness of the crystalline plate is reduced 
 below a certain limit.* 
 
 The experimental laws of these phenomena were investigated 
 with unwearied zeal by M. Biot.f When the light was inci- 
 dent perpendicularly on plates of the same substance, of different 
 thicknesses, the tints were observed to follow the same law 
 as the colours of thin plates ; the thicknesses of the crystal at 
 which each tint was developed in perfection being proportional 
 to the thicknesses of the plate of air which gave the same tint in 
 Xewton's scale. These thicknesses vary with the nature of the 
 crystal, and are always much greater than the corresponding 
 thicknesses of the uncrystallized plate which exhibit the same 
 tint. Pursuing the same inquiry, afterwards, for oblique inci- 
 dences, M. Biot found that, in uniaxal crystals, the tint de- 
 veloped was determined by the length of the path traversed by 
 the light within the crystal, and by the square of the sine of the 
 angle which its direction made with the optic axis, jointly. 
 From this law it followed, that if a crystalline plate of moderate 
 thickness be cut perpendicularly to the axis, and a converging 
 or diverging pencil transmitted through it, the lines of equal 
 tint or the isochromatic lines, as they are sometimes called, 
 will be disposed in concentric circles similar to Newton's rings. 
 
 * Him. Int. 1811. t nid ^ I8i2 .
 
 COLOURS OF CRYSTALLINE PLATES. 131 
 
 This phenomenon was observed, under different circumstances, by 
 Sir David Brewster, Dr. Wollaston, M. Biot, and M. Seebeck. 
 
 The researches of M. Biot were followed by those of Sir David 
 Brewster. In investigating the law of the tints in biaxal crys- 
 tals, Sir David Brewster considers the optic axes as the re- 
 sultants of others which he denominates polarizing axes. The 
 tint developed by a single axis is taken as the measure of its 
 polarizing force, and is assumed to vary as the square of the sine 
 of the angle contained by the ray with it ; and when two such 
 axes cooperate, the tint resulting from their joint action is measured 
 by the diagonal of a parallelogram whose sides represent the tints 
 produced by each axis separately, and whose angle is double the 
 angle contained by the two planes passing through them and the 
 ray. This law Sir David Brewster has verified by comparison 
 with the observations of M. Biot on sulphate of lime, and its 
 agreement with phenomena was complete.* When analytically 
 developed by M. Biot, it was found to accord with the beautiful law 
 to which he was himself conducted by analogy namely, that the 
 tint is measured by the product of the sines of the angles which 
 the direction of the ray within the crystal makes with the optic 
 axes.f From this law it easily followed that the isochromatio 
 lines, in biaxal crystals, will be lemniscates, whose poles are in the 
 apparent direction of the optic axes.J This phenomenon was first 
 discovered by Sir David Brewster in topaz. The law has been 
 established in the most complete manner by Sir John Herschel ; 
 and he has found that the constant parameter, or the product of 
 
 * " On the Laws of Polarization and Double Refraction in regularly crystallized 
 Bodies," Phil. Trans., 1818. 
 
 t From the researches of M. Biot it appeared that the measure of the tint, in 
 uniaxal crystals, observed the same law as that attributed to the difference of the 
 squares of the velocities of the two rays in the theory of emission. The same relation 
 was assumed to hold generally ; and thus from the law of the tints in biaxal crystals 
 the relation of the velocities of the two pencils, noticed in the preceding section, waa 
 inferred. 
 
 I M. Biot has observed an apparent exception to this law in the dioptiilr <>f the 
 Tyrol, in which the rings are in general unsymmetrical with respect to the two axes. 
 One of the axes presents the ordinary phenomena ; but in the neighbourhood of the 
 other there is a remarkable distortion of the rings near their centre, when the crystal- 
 line plate is turned in its own plane. These distortions seemed to observe a regular 
 law, and were the same in all the specimens examined. It may be remarked that the 
 optic axes of this crystal are unsymmetrically placed with respect to the crystalline 
 form, Mem. Inst., torn. x. 
 
 K2
 
 132 REPORT ON PHYSICAL OPTICS. 
 
 the radii-vectores drawn from any point to the two poles, varies 
 inversely as the thickness of the plate for different plates of the 
 same substance, and increases from one curve to another in the 
 same plate in the ratio of the numbers of the natural series. 
 
 To account for these varied phenomena in the hypothesis of 
 emission, M. Biot has imagined his ingenious and beautiful theory 
 of mo'veable polarization. When a polarized ray of any simple 
 colour enters a crystalline plate, the component molecules are 
 supposed, in this theory, to penetrate at first to a certain depth 
 without losing their primitive polarization ; and then to commence 
 a series of regular oscillations round their centres of gravity, the 
 axes of polarization being carried alternately to one side or other 
 of the axis of the crystal, or of the perpendicular line. These 
 oscillations being isochronous, the thickness transversed by the 
 molecule in its motion of translation during each of them is 
 constant, and is assumed to be equal to double the depth to which 
 it has penetrated before commencing its vibrations. The oscillatory 
 movement is supposed to stop, when the molecules repass into air 
 through the second face of the crystal ; and the emergent ray has 
 a fixed polarization, the same as if the last oscillation of the mole- 
 cules had been actually completed at the instant of emergence. 
 Thus a polarized ray which has traversed a thin crystalline plate 
 is ultimately polarized either in the primitive plane, or in a plane 
 inclined to it at an angle equal to double the angle which it forms 
 with the principal section, according as the thickness of the crystal 
 is an odd or an even multiple of a certain length.* The formulso 
 deduced from these postulates are found to represent all the more 
 obvious laws of the tints with much fidelity. 
 
 This assumed difference between the effects produced by thick 
 and thin crystals has however been completely disproved by the 
 decisive experiments of Fresnel. When two mirrors, slightly in- 
 clined, are placed so as to receive the incident light at the polar- 
 izing angle, and two laminae of sulphate of lime of the same 
 thickness are interposed one in the path of each of the reflected 
 pencils, and so that their principal sections are inclined at angles 
 of 45 on either side of the plane of primitive polarization, the 
 phenomena of the interference bands prove in the clearest manner 
 that the light emergent from each consists of two pencils polarized 
 respectively in the principal section, and in the perpendicular 
 
 * " Sur un nouveau genre d'Oscillation," &c., J/,/:.
 
 COLOURS OF CRYSTALLINE PLATES. 133 
 
 section of the crystals ; and that the results differ from those pro- 
 duced by thick crystals only in this, that the two pencils are 
 superposed.* The light resulting from the union of these oppositely 
 polarized pencils has, in certain cases, the properties ascribed to it 
 in the theory of M. Biot ; but these properties are immediate and 
 necessary consequences of the laws of interference of polarized 
 light, and of the theory of transversal vibrations. 
 
 Let us now inquire what account the wave-theory furnishes 
 of the same phenomena. A ray of light on entering a crystalline 
 plate is divided into two, or, in the language of the wave-theory, 
 a series of waves incident upon the crystal is resolved into two 
 within it, which traverse it in different directions and with different 
 velocities. One of these sets of waves, therefore, will lag behind 
 the other, and they will be in different phases of vibration at 
 emergence. When the plate is thin, the emergent waves are 
 superposed ; and as the retardation will then amount only to a few 
 undulations and parts of an undulation, it would appear that we 
 have here all the conditions necessary for their interference, and 
 the consequent production of colour. Such was the sagacious 
 conjecture of Young. And indeed, shortly after the publication 
 of the first researches of M. Biot on the laws of the tints for 
 different thicknesses, it was observed by Young that these tints 
 corresponded accurately to the interval of retardation of the two 
 pencils ; so that they were manifestly due to interference, f This 
 correspondence is now made out in the fullest manner. It is an 
 easy consequence of Fresnel's theory of double refraction, that the 
 interval of retardation of the two pencils, in traversing a crystal- 
 line plate, is nearly proportional to the length of their path within 
 the crystal multiplied by the product of the sines of the angles 
 which their directions make with the two optic axes ; and as this has 
 been found to be the general measure of the tint, it follows that 
 the forms of the isochromatic curves the lemniscates and the 
 circles, are all necessary consequences of the wave-theory. 
 
 * See Report made to the Academy of Sciences, in 1821, on the memoir of Freanel 
 relative to the colours of crystallized plates, Annalea de Chimie, torn. xvii. Indeed, a 
 more obvious objection to M. Biot's theory may be drawn from the fact which he has 
 himself observed ; namely, that the phenomena of colour may be produced by crottmg 
 two thick plates of nearly the same thickness, although the thickness in each was 
 sufficient to furnish two images sensibly separated, and therefore having a Jljctd 
 polarization. 
 
 f Quarterly Rn'icic, vol. xi.
 
 134 REPORT OX PHYSICAL OPTICS. 
 
 But in the first application of the principle of interference to 
 the colours of crystalline plates there arose a difficulty to which 
 the known laws afforded no answer. So far as this explanation 
 went, the phenomena of interference and of colour should be 
 produced by the crystal alone, and in common light, without either 
 polarizing plate or analyzing plate. Such, however, is not the 
 fact ; and the real difficulty seemed to be, not to explain how the 
 phenomena are produced, but to show why they are not always- 
 produced. It occurred to MM. Arago and Fresnel to inquire how 
 far the state of polarization of the two pencils might modify the 
 known laws of interference ; and the results of this inquiry* have 
 happily furnished an account of the difficulty, and completed the 
 solution of the problem. It was found that two rays of light 
 polarized in the same plane interfere, and produce fringes, under 
 the same circumstances as two rays of common light ; that, when 
 the planes of polarization are inclined, the interference is diminished 
 and the fringes decrease in intensity ; and that, finally, when the 
 angle between these planes is a right angle, the rays no longer 
 interfere at all. Hence the two rays which emerge from a crystal- 
 line plate, being oppositely polarized, cannot interfere ; and, to 
 produce the phenomena of colour in perfection, their planes of 
 polarization must be brought to coincidence by the analyzer. 
 
 The non-interference of rays oppositely polarized is a necessary 
 result of the mechanical theory of transversal vibrations. Fresnel 
 has shown, on the principles of that theory, that the intensity of 
 the light resulting from the union of two such rays is constant,. 
 and equal to the sum of the intensities of the components, what- 
 ever be the phases of vibration in which they meet. But though 
 the intensity of the light does not vary with the phase of the 
 component vibrations, the character of the resulting vibration will. 
 It appears from theory that two rectilinear and rectangular vibra- 
 tions compound a single vibration, which will be also rectilinear 
 when the phases of the component vibrations differ by an exact 
 number of semiundulations ; that, in all other cases, the resulting 
 vibration will be elliptic ; and that the ellipse will become a circk, 
 when the component vibrations have equal amplitudes, and the 
 difference of their phases is an odd multiple of a quarter of a 
 wave. These results of theory have been completely confirmed 
 
 " Mcmoire s.ir 1' Action qu 5 b s Rayons de la Lumicre polarisee exercent les uns 
 
 sur lea autref," ^nnales c'e C/n'mic, ton-, x.
 
 COLOURS OF CRYSTALLINE PLATES. llj-3 
 
 by experiment. When a polarized beam diverging from a lumi- 
 nous origin is transmitted through two rhomboids of Iceland spar 
 of equal thickness, having their principal sections inclined 45 on 
 either side of the plane of primitive polarization, the emergent 
 light will diverge as if from two near points, and the two portions 
 will be oppositely polarized. It was found by Fresnel and Arago 
 that the light resulting from the union of these pencils was plane- 
 polarized, circularly polarized, or e lliptically polarized, according to 
 the difference of the paths traversed when they met. 
 
 Here, then, we have an account of the facts which seem to 
 have suggested the theory of moveable polarization ; and we learu 
 moreover that they are but particular cases of the general result. 
 The light arising from the union of the ordinary and extraordinary 
 pencils, which emerge from the crystalline plate, will be polarized 
 in tl^e primitive plane, or in a plane inclined to it at an angle 
 equal to double the angle which it makes with the principal section, 
 according as the interval of retardation of the two pencils is an 
 even or an odd multiple of half a wave. In all other cases the 
 thickness of the crystal having any other value than those which 
 exactly answer to these intervals the resulting light will be ellip- 
 tically polarized. The ellipse will become a circle, and the .light 
 will appear to be completely depolarized, when the two pencils are 
 of equal intensity, and the interval of retardation is an odd 
 multiple of a quarter of a wave. Here, then, is suggested an easy 
 method of putting the theory of moveable polarization to the test. 
 If a plate of sulphate of lime, whose thickness corresponds to such 
 an interval, be placed in a beam of polarized light of some simple 
 colour, so that its principal section is inclined at an angle of 45 
 to the plane of primitive polarization, the emergent light should, 
 according to the theory of waves, be circularly polarized ; and the 
 two pencils into which it is divided by the analyzing rhomb should 
 not vary in intensity during its revolution. According to tho 
 theory of moveable polarization, on the other hand, the light 
 should be plane-polarized; and one of the images should vanish 
 when the principal section of the rhomb coincided either with the 
 primitive plane, or with the plane perpendicular to it. This experi- 
 tnentum crucis was tried by MM. Fresnel and Arago, and the 
 result was just as had been predicted by the wave-theory.* 
 
 * Anr.ales dc Chimie, torn. \vii.
 
 136 KEPOET ON PHYSICAL OPTICS. 
 
 In the prosecution of their researches on the laws of interference 
 of polarized light, MM. Fresnel and Arago discovered further that 
 two oppositely polarized rajs will not interfere, even when their 
 planes of polarization are brought to coincidence, unless they belong 
 to a pencil the whole of which was originally polarized in one 
 plane ; and that, in the interference of rays which have under- 
 gone double refraction, half an undulation must be supposed to be 
 lost or gained, in passing from the ordinary to the extraordinary 
 system. The latter principle is a beautiful and simple consequence 
 of the theory of transversal vibrations. When a vibration in any 
 given direction is resolved into two at right angles, and each of 
 these again into a second pair, in two fixed directions which are 
 also perpendicular, it will easily appear that, of the four com- 
 ponents into which the original vibration is thus resolved, the two 
 in one of the final directions conspire, while those in the other are 
 opposed. The tint produced by the interference of the former, 
 therefore, corresponds to the actual difference of routes of the two 
 polarized rays in the plate ; while that arising from the latter is 
 that due to the same difference augmented or diminished by half 
 an undulation. 
 
 The former of the two laws now mentioned explains the office of 
 the polarizing plate in these phenomena. To account mechanically 
 for the fact of the non-interference of the two pencils, when the 
 light incident upon the crystal is unpolarized, it is necessary to 
 consider such light as a rapid succession of systems of waves 
 polarized in all azimuths ; so that if any two planes be assumed 
 at right angles, there will be an equal quantity of light actually 
 polarized in each. Each of these portions, when resolved into two 
 within the crystal, and these afterwards reduced to the same plane 
 of polarization by the analyzing plate, wiU exhibit the phenomena 
 of interference. But the interval of retardation differs by half a 
 wave in the two cases ; the tints produced therefore will be com- 
 plementary, and the light resulting from their union will be of a 
 uniform whiteness. 
 
 We are obliged to admit, therefore, that common light consists 
 of a rapid succession of systems of waves, in each of which the 
 vibrations are different. But the phenomena of interference 
 (which are exhibited by common light) compel us also to admit, 
 as Professor Airy has observed,* that the vibrations do not change 
 
 * Mathematical Tracts, p. 407.
 
 COLOURS OF CRYSTALLINE PLATES. 137 
 
 continuously ; and that in each system of waves there are probably 
 several hundred successive vibrations, which are all similar, 
 although the vibrations of one system bear no relation to those of 
 another, and the different systems succeed one another with such 
 rapidity as to obliterate all trace of polarization. This per sattum 
 transition from one system of waves, to another in which the 
 vibrations are wholly different, seems a complication in the 
 machinery of light, for which the elegant simplicity of the parts 
 better known has not prepared us ; and I cannot but indulge the 
 hope that the hypothesis, which now stands as the representative 
 of experimental laws, may be found to merge in some simpler 
 physical principle. 
 
 The laws of interference of polarized light have thus supplied 
 the defective link in the explanation of the colours of crystalline 
 plates first suggested by Young. The magnitudes of the resolved 
 vibrations are known, when the planes of polarization of the two 
 pencils are given with respect to the plane of primitive polari- 
 zation, and the plane of analyzation ; and as the laws of double 
 refraction enable us to find the interval of retardation of these 
 pencils, we have all the data necessary for the computation of the 
 intensity and colour of the light resulting from their interference. 
 This computation has been given by Fresnel, not only for a single 
 plate, but likewise for two plates superposed ;* and the theory has 
 been since more fully developed by Professor Airy.f The results 
 are found to be, in all cases, in exact accordance with the observed 
 facts ; and all the circumstances of the coloured rings in uniaxal 
 and biaxal crystals are completely explained. 
 
 The form of the rings, or isochromatic curves, depends upon 
 the interval of retardation alone ; and the value of this interval 
 had been deduced but approximately. Mr. M'Cullagh has recently 
 given a general and exact method for its calculation, and for the 
 determination of the forms of the rings for any plate of a double- 
 refracting crystal bounded by parallel planes. This method is 
 made to depend upon the properties of the surface of wave-slowness, 
 of which I have spoken in another place ; and it is found that if 
 the incident ray be produced to meet the sphere (which is the 
 surface of wave-slowness for air), and through the point of inter- 
 
 * Annales de Chimic, torn. xvii. 
 
 t Cambridge Tra>tsactions, 1831, and Math. Tracts.
 
 138 REPORT ON PHYSICAL OPTICS. 
 
 section a perpendicular be drawn to the refracting surface, meeting- 
 the two sheets of the surface of wave-slowness for the crystal, the 
 interval of retardation of the rays at emergence will be measured 
 by the thickness of the crystal multiplied by the difference of the 
 corresponding ordinates.* By the aid of an expressive notation 
 for the path of a ray, the author has extended his conclusions to 
 the case of a ray which has undergone any number of internal 
 reflexions. 
 
 If the double-refracting energy of the crystal were the same 
 for the light of every colour, the colours of the rings should follow 
 exactly the Newtonian scale of tints, and their magnitudes should 
 observe the same laws as those of the rings formed between two 
 object-glasses. This is the case in carbonate of lime, beryl, and 
 some other crystals ; and in these, therefore, the colours are similar 
 to those of thin plates. But many remarkable deviations from 
 this law have been observed by Sir John Herschel and Sir David 
 Brewster. Thus, in the common uniaxal apophyllite, it waa 
 observed by the former writer, the diameters of the rings are very 
 nearly the same for all the colours of the spectrum ; so that the 
 rings of different colours are superposed, and form a succession 
 alternately black and white, which may be traced through a great 
 number of orders, f In this remarkable case, then, the double- 
 refracting energy of the crystal varies, very nearly, in the sub- 
 duplicate ratio of the lengths of the waves for the rays of different 
 colours. A very remarkable case of the inversion of the New- 
 tonian scale of tints was observed by Sir John Herschel in some 
 rare varieties of the same mineral. The diameters of the rings, 
 instead of contracting as the refrangibility increases, enlarge, and 
 actually become infinite for rays of mean refrangibility. Having 
 passed through infinity, they again acquire a finite value; and 
 diminish as the refrangibility increases up to the extremity of the 
 spectrum. Here, then, for rays of a certain mean refrangibility 
 the crystal is singly refractive ; and as the double refraction changes 
 its character in passing through zero, the crystal is positive for the 
 
 If yi , y , y. represent the corresponding ordinates of the sphere, and of the two 
 sheets of the surface of wave-slowness for the medium, and the thickness of the 
 
 stal, (y. - y,.), (y. _ y ,.) ^11 be the retardations of the two refracted waves at 
 emergence, and (y. - yj will be the interval between them.-" Geometrical Propo- 
 sitions applied to the Wave-theory of Light," Tram. Royal Irish Academy, vol. xviL 
 
 t Phil. Tram., 1820.
 
 COLOURS OF CRYSTALLINE PLATES. 139 
 
 rays of one end of the spectrum, and negative for those of the 
 other.* This singular phenomenon is accounted for on the prin- 
 ciples of Fresnel's theory by supposing that the elasticity increases, 
 with the length of the wave, faster in the direction of the axis of 
 the crystal than in the perpendicular direction ; so that the difference 
 of these elasticities is positive for the rays of one end of the spec- 
 trum, negative for those of the other, and vanishes at some inter- 
 mediate point. 
 
 In biaxal crystals similar deviations take place in the magni- 
 tude of the lemniscates corresponding to the different simple 
 colours. But there is here another source of irregularity which 
 is not found in uniaxal crystals. The optic axes vary, in general, 
 with the colour ; so that the lemniscates differ also in the position 
 of their poles, and the colours are not the same in different parts 
 of the same ring. Where the optic axes belonging to different 
 colours are in different planes, as Sir John Herschel has observed 
 to be the case in borax, the irregularity produced in the coloured 
 curves is yet more striking. 
 
 In all the preceding cases, the laws of double refraction are 
 dependent only on the direction, and are the same all throughout 
 the mass. It is otherwise, however, in many crystals, such as 
 analcime and some varieties of apophyllite. The complicated 
 arrangement of the coloured bands which these substances display 
 in polarized light proves them to consist of several distinct por- 
 tions, possessing different optical properties ; and the phenomena 
 indicate relations among the molecular forces, and principles of 
 aggregation, of which it is difficult in some cases even to form a 
 conception. These remarkable phenomena, and their laws, were 
 discovered by Sir David Brewster.f 
 
 When a polarized ray traverses a plate of Iceland spar, beryl, 
 or almost any other uniaxal crystal, in the direction of its axis, 
 it suffers no change of any kind ; so that when the emergent ray 
 is analyzed by a double-refracting prism, the two pencils into 
 which it is divided are colourless, and one of them vanishes when 
 the principal section of the prism is parallel or perpendicular to 
 
 * Cambridge Trans. 1821. Similar properties have boon observed by the same 
 author in other crystals, as hyposulphate O f limo and vesuvian. From th 
 tints exhibited by the latter substance it appears that the most refra 
 images is the least dispersed. 
 
 t Edin. Trans., vols. ix. & x.
 
 140 KEPORT ON PHYSICAL OPTICS. 
 
 the plane of primitive polarization. But when a ray passes in the 
 same manner through a plate of rock-crystal, the phenomena are 
 very different. Two images are given in every position of the 
 prism ; and these images are of complementary colours, while the 
 colours change in the most beautiful manner as the prism is turned 
 round in its cell. These phenomena indicate that the plane of 
 polarization has been changed, and differently for the different 
 rays of the spectrum. They were first observed by M. Arago ; 
 and he has given an account of his observations in his memoir on 
 the colours of crystalline plates, read to the Institute in the year 
 1811. 
 
 The subject was then taken up by M. Biot, in a paper published 
 in the Memoires de Vlnstitut in the year 1812 ; and the analysis 
 of the phenomenon was completed in a second memoir read in the 
 year 1818*. When a polarized ray of any simple colour passes 
 through a plate of rock-crystal in the direction of the optic axis, 
 it is still polarized after emergence ; but its plane of polarization 
 is changed. The angle through which the plane is made to re- 
 volve varies with the colour of the light, and with the thickness 
 of the plate, being proportional to that thickness divided by the 
 square of the length of the fit or wave. In some crystals the 
 plane of polarization revolves from left to right, while in others it 
 is turned in an opposite direction ; and the crystals themselves are 
 denominated right-handed or left-handed, according as they produce 
 one or other of these effects. When two plates are superposed, 
 the effect produced is, very nearly, the same as that due to a single 
 plate whose thickness is the sum or difference of the thicknesses of 
 the two plates, according as they are of the same or of opposite 
 denominations. 
 
 This curious distinction between plates cut from different 
 crystals has been connected by Sir John Herschel with a corre- 
 sponding diversity in the crystalline form. The ordinary form of 
 the crystal of quartz is the six-sided prism terminated by the six- 
 sided pyramid. The solid angles formed at the junction of the 
 pyramid and the prism are sometimes replaced by small secondary 
 planes, which in the same crystal lean all in the same direction ; 
 and it is found that when that direction is to the right (the apex of 
 
 " Memoire sur les rotations que certaines substances impriment aux axes de 
 polarisation des rayons iumineux."
 
 COLOUES OF CRYSTALLINE PLATES. 141 
 
 the pyramid "being uppermost), the crystal is right-handed, and 
 that, on the contrary, it is left-handed when the planes lean in the 
 opposite way.* Sir David Brewster has shown that the amethyst, 
 or violet quartz, is actually composed of alternate layers of right- 
 handed and left-handed quartz. It is to the cropping out of the 
 edges of these layers that the undulating appearance peculiar to 
 the fracture of this mineral is owing. The structure itself is dis- 
 played in the most beautiful manner in polarized light, f 
 
 Some liquids, and even gases, have been found by MM. Biot 
 and Seebeck to possess the same property as quartz, though in a 
 much feebler degree, and to impress a rotation on the plane of 
 polarization of the intromitted ray, which is proportional to the 
 thickness of the substance traversed. These liquids do not lose 
 their rotatory power by dilution with other liquids not possessing 
 the property. They retain it even when raised to the state of 
 vapour ; and, in general, the rotatory power is independent of the 
 mode of aggregation, provided the molecular constitution is un- 
 changed. Lastly, when two or more liquids possessing this pro- 
 perty are mixed together, the rotation produced by the mixture is 
 the sum of the rotations produced by the ingredients, in thicknesses 
 proportional to the volumes in which they are combined. From 
 these and other facts, M. Biot concludes that the property of rota- 
 tory polarization is inherent in the ultimate particles of bodies, 
 and does not depend on their mutual distance or arrangement.* 
 On the other hand, quartz is found to lose the property when 
 deprived of its crystalline structure. Thus, Sir John Herschel 
 observed that quartz held in solution by potash did not possess the 
 property : and the same thing has been remarked by Sir David 
 Brewster with respect to fused quartz. 
 
 The phenomena of rotatory polarization in rock-crystal M. 
 Biot ascribed to a continued rotation of the molecules of light 
 round their centres of gravity, produced by the operation of some 
 unknown forces. Fresnel has proved that they arise from the 
 
 * Cambridge Trans., vol. i. t &* Trans., vol. ix. 
 
 | M. Biot has recently extended his researches on this subject to a great variety of 
 substances, Annales du Museum d 'Histoire Naturelle, om. ii. In a memoir read to tho 
 French Academy last year he has applied the laws of circular polarization to tho ana- 
 lysis of the process of vegetation in the grasses : and he has shown, in general, the 
 importance of the indications drawn from these phenomena in the researches of organic 
 chemistry. Inttitut, Nos. 1 & 9.
 
 142 REPORT ON PHYSICAL OPTICS. 
 
 interference of two circularly polarized pencils which are propagated 
 along the axis with unequal velocities, one revolving from left to 
 right, and the other in the opposite direction. A plane-polarized 
 ray, in fact, is equivalent to two circularly polarized rays of half 
 the' intensity, in one of which the vibrations are from left to right, 
 and in the other in the opposite direction. When a plane-polar- 
 ized ray, therefore, is incident perpendicularly upon a plate of 
 rock-crystal, cut perpendicularly to the axis, it may be resolved 
 into two such circularly polarized rays. These are supposed to be 
 transmitted with different velocities ; so that when they assume a 
 common velocity at emergence, one of them is in advance of the 
 other. They then compound a single ray polarized in a single 
 plane ; and this plane, it can be shown, is removed from the plane 
 of primitive polarization through an angle proportional to the 
 interval of retardation of the two pencils, and therefore measured 
 by the thickness of the crystal. But this interval varies also with 
 the colour of the light ; and we are obliged to suppose that it is 
 the same for a given number of waves, whatever be their length, 
 so that, for a given thickness of the crystal, it varies inversely as 
 the length of the wave. From this supposition it will follow that 
 the deviation of the plane of polarization of the emergent ray is 
 inversely as the square of that length, agreeably to the experi- 
 mental results of M. Biot.* 
 
 The laws of rotatory polarization were thus completely ex- 
 plained ; and it only remained to prove the truth of the hypo- 
 thesis, that two circularly polarized pencils, whose vibrations are 
 in opposite directions, will actually be transmitted along the axis 
 of quartz with different velocities. This supposition is easily put 
 to the test -of experiment, since such a difference of velocities must 
 give rise to a difference of refraction, when the surface of emer- 
 gence is oblique to the direction of the ray. According to the 
 hypothesis, therefore, a plane-polarized ray, transmitted through a 
 prism of rock-crystal in the direction of the optic axis, should 
 undergo double refraction at emergence ; and the two pencils into 
 which it is divided should be circularly polarized. This has been 
 completely verified by Fresnel, by an achromatic combination of 
 right-handed and left-handed prisms arranged so as to double the 
 separation ; and he has shown that the two pencils are neither com- 
 
 * Annale* de Chimie, torn, xxviii. p. 147.
 
 COLOURS OF CRYSTALLINE PLATES. 143 
 
 mon nor plane-polarized light, but possess all the characters which 
 are impressed upon a polarized ray by two total reflexions from 
 glass at an angle of about 50. 
 
 The refraction of quartz, then, in the direction of its optic axis, is 
 wholly different from that of every other known crystal. In other 
 directions, the two pencils into which a single ray is divided were 
 supposed to obey the ordinary laws, and to be plane-polarized in 
 opposite planes. This supposition has been overturned by Pro- 
 fessor Airy ;* and it has been shown that the two pencils in quartz 
 are, each of them, elliptically polarized, the elliptical vibrations of 
 the two rays being in opposite directions, and the greater axes of 
 the ellipses being in the principal plane, and perpendicular to it, 
 respectively. The ratio of the axes, in these ellipses, is the same 
 in the two rays, f but varies with their inclination to the optic 
 axis, being a ratio of equality when the direction of the ray 
 coincides with the axis, and increasing indefinitely with their incli- 
 nation to that line according to some unknown law. As to the course 
 of the refracted rays, Professor Airy finds that it is still determined 
 by the Huygenian law ; but that the sphere and spheroid, which 
 determine the velocity and direction of the two rays, do not touch, as 
 in all other known uniaxal crystals, the latter surface being contained 
 entirely within the former. This position is certainly a startling 
 one. The two sheets of the wave-surface being thus absolutely 
 separated, there is a complete interruption of continuity in passing 
 from the velocity of one ray to that of the other ; a result which 
 does not hold in any other case with which we are acquainted. It 
 is however necessary to the explanation of the phenomena ; for 
 the interval of retardation does not vanish with the inclination of 
 the ray to the axis. Professor Airy has given an elaborate calcu- 
 lation, founded on these hypotheses, of the forms of the rings, &c., 
 displayed by quartz in plane-polarized and circularly polarized 
 
 * "On the Nature of the Light in the two rays produced by the double refraction 
 of Quartz." Cambridge Transactions, 1831. 
 
 t In the Supplement to this paper Professor Airy has explained a highly ingenious 
 method of determining experimentally the relation between the ellipticity and the dirvc- 
 tion of either of the rays. This method depends upon a remarkable effect which he 
 had been led to expect from theory : namely, a sudden change of half an undulation 
 in the interval of retardation, and therefore a change of half an ordrr in the rings 
 when the im-idftit light is elliptically polarized. From the results of some experiments 
 conducted in this method, Professor Airy seems to think that the ratio of the axes in 
 the ordinary ray approaches more nearly to one of equality than in the extraordinary 
 ray.
 
 144 REPORT ON PHYSICAL OPTICS. 
 
 light and in any position of the analyzing plate; and he has 
 found the most striking agreement between the results of calcu- 
 lation and those of observation. 
 
 We yet want a mechanical theory which will account for the 
 peculiar form of the wave-surface just alluded to. Fresnel seems 
 to have thought that the difference of the velocities of the two 
 rays in the direction of the axis might be physically explained 
 by an helicoidal arrangement of the molecules of the vibrating 
 medium, which will have different properties according as the 
 helices are right-handed or left-handed. But this hypothesis 
 can hardly be supposed to apply to the case of fluids, in which 
 the property of circular polarization is independent of direction ; 
 and we are driven to confess that, with respect to these import- 
 ant laws, physical theory is as yet wholly at fault. The singular 
 relation betweent he interval of retardation and the length of 
 the wave seems to afford the only clue to the unravelling of this- 
 difficulty. 
 
 The phenomena of depolarization, and of colour, impressed 
 by double-refracting substances upon the transmitted light, are, 
 we have seen, the necessary results of the interference of the 
 two pencils into which the light is divided within them. These 
 properties, then, enable us to discover the existence, and to- 
 trace the laws, of double refraction, even in substances in which 
 the separation of the two pencils is too minute to be directly 
 observed. By such means the important discovery has been made, 
 that a double-refracting structure may be communicated to bodies 
 which do not naturally possess it, by mechanical compression and 
 dilatation. Sir David Brewster observed that when pressure was 
 applied to the opposite faces of a parallelepiped of glass, it deve- 
 loped a tint in polarized light, like a plate of a double-refracting 
 crystal ; and the tint descended in the scale as the pressure was 
 augmented. Singly-refracting crystals, such as muriate of soda and 
 fluor-spar, acquired the properties of double refraction by the same 
 means.* All this is in perfect accordance with the wave-theory. 
 Owing to the connexion of the vibrating medium with the solid 
 in which it is contained, its elasticity is rendered unequal in differ- 
 ent directions by the effect of compression, the maximum and 
 minimum corresponding to the directions of greatest and least 
 
 * Phil Trrms. 1815 and 1816.
 
 COLOUES OF CRYSTALLINE PLATES. 145 
 
 pressure. Accordingly, the vibrations of the ray on entering the 
 plate are resolved into two in these rectangular directions, and 
 these are propagated with unequal velocities ; the colour developed is 
 determined by the interval of retardation. These results of theory 
 were experimentally confirmed by Fresnel, by the method of inter- 
 ferences ; and it was found that the velocity with which a ray traversed 
 the glass was greater or less, according as it was polarized parallel 
 or perpendicular to the axis of compression. The bifurcation of the 
 ray at oblique incidences is a necessary consequence of this difference 
 of velocities ; but this was also shown by Fresnel by direct experi- 
 ment. A series of glass prisms were placed together with their 
 refracting angles alternately in opposite directions, and the ends of 
 the alternate prisms powerfully pressed by screws. A ray trans- 
 mitted through the combination was found to be divided into two 
 oppositely polarized.* 
 
 The opposite effects of compression and dilatation may be seen 
 in a thick plate of glass which is bent by an external force. 
 When this body is interposed between the polarizing and analyz- 
 ing plates, so as to form an angle of 45 with the plane of 
 primitive polarization, two sets of coloured bands are seen sepa- 
 rated by a neutral line ; and these vanish altogether when the com- 
 pressing force is withdrawn. By crossing the glass with a plate 
 of mica or sulphate of lime, Sir David Brewster found that the 
 parts towards the convex, or dilated side of the neutral line, had 
 acquired a positive double-refracting structure, and those at the 
 concave, or compressed side, a negative one.f The intimate con- 
 nexion between the double-refracting property, and the internal 
 state of the body as to condensation or rarefaction, is likewise 
 proved by the curious observation of M. Biot, that glass, when 
 in a state of sonorous vibration, possesses the power of depolarizing 
 the light. 
 
 In these cases of induced double refraction, the phenomena are 
 related to the form of the entire mass ; and are essentially different 
 from those produced by regular crystals, in which the law of elas- 
 ticity and of double refraction depends solely on the direction, and 
 is the same in all parts of the substance. Sir David Brewster has 
 lately succeeded in communicating a regular double-refracting 
 structure to a mixture of resin and white wax, by pressing it into 
 
 Annalcs dc Chimit, torn. xx. 1 rhil. Tnms. 1310.
 
 146 REPORT ON PHYSICAL OPTICS. 
 
 a thin film between two plates of glass. This film had a single 
 axis of double refraction at every point in the direction of the axis 
 of pressure ; and the tint developed depended solely on the in- 
 clination of the ray to this line. Sir David Brewster has drawn 
 from this phenomenon some highly interesting conclusions respect- 
 ing the origin of double refraction in regular crystals. He men- 
 tions several facts which seem to prove that this property is not 
 inherent in the molecules themselves ; and he conceives that it is 
 developed by the unequal pressure caused by the forces of aggre- 
 gation, which are in general different in the direction of three 
 rectangular axes. Thus the double-refracting properties and the 
 crystalline form are referred to the same agency.* 
 
 Sir David Brewster and Dr. Seebeck had before observed the 
 phenomena arising from unequal condensation and rare faction in 
 the case of uncrystallized bodies unequally heated. These pheno- 
 mena may be studied by applying a bar of hot iron to the edge 
 of a rectangular plate of glass, and placing it in the polarizing ap- 
 paratus, so that the heated edge may form an angle of 45 with 
 the plane of primitive polarization. At the end of some time the 
 whole surface of the plate is observed to be covered with coloured 
 bands, the parts near the opposite edges having acquired a positive 
 double-refracting structure, and those near the centre a negative 
 one. The effects are reversed when a plate of glass uniformly 
 heated is rapidly cooled at one of its edges ; and all the appear- 
 ances vanish when the glass acquires the same temperature 
 throughout.! These phenomena maybe endlessly varied by vary- 
 ing the form of the glass to which the heat is applied. If now, by 
 any means, the glass be arrested in one of these transient states, 
 it will have acquired a permanent double-refracting structure. 
 This has been accomplished by M. Seebeck by raising the glass to 
 a red heat, and then cooling it rapidly at the edges. As the outer 
 parts, which are thus more condensed, assume a fixed form in cool- 
 ing, the interior parts must accommodate themselves to that form, 
 and therefore retain a state of unequal density. The law of the 
 change of density, and therefore the double-refracting structure, 
 will depend on the external form ; and M. Seebeck found, accord- 
 ingly, that the coloured bands and patches which such bodies 
 display in polarized light, assume a regular arrangement which 
 
 PA*ZVi..l880. t PAH. ZVM. 1816.
 
 COLOURS OF CRYSTALLINE PLATES. 147 
 
 yaries with the shape of the mass.* The laws of these pheno- 
 mena have been completely analyzed by Sir David Brewster ; and 
 he has shown that the colours are those of crystallized plates, the 
 direction of the axes, however, being different in different parts of 
 the substance. 
 
 As the double-refracting structure is communicated to bodies 
 which do not possess it naturally, by mechanical compression or 
 unequal temperature, so, by the use of the same means, that 
 structure may be altered in the bodies in which it already resides. 
 Thus Sir David Brewster and M. Biot have found that the double 
 refraction of regular crystals may be altered, and the tints they 
 display made to rise or descend in the scale, by simple pressure. 
 But the changes induced by heat are yet more remarkable. Pro- 
 fessor Mitscherlich discovered the important fact that, in general, 
 heat dilates crystals differently in different directions, and so alters 
 their form ; and their double-refracting properties have been found 
 to undergo a corresponding change. Thus Iceland spar is dilated 
 by heat in the direction of its axis ; while it actually contracts by 
 a small amount in directions perpendicular to it. The angles of 
 the primitive form thus vary, the rhomboid becoming less obtuse,f 
 and approaching the form of the cube. M. Mitscherlich, accord- 
 ingly, conjectured that its double-refracting energy must in these 
 circumstances be diminished ; and the conjecture was fully verified 
 by experiment. This inquiry has been followed up by M. Eud- 
 berg ; and the effects of heat on the refractive indices of double- 
 refracting crystals examined by the direct method of prismatic 
 refraction. In conformity with the observations of M. Mitscher- 
 lich, it was found that the extraordinary index in Iceland spar 
 increased considerably with the temperature, while the ordinary 
 index underwent little or no change. In rock crystal, on the 
 other hand, both indices diminished as the temperature augmented, 
 and nearly by the same amount. In arragonite a similar effect 
 was produced on the three principal refractive indices, the least 
 
 * The experiments of M. Seebeck are recorded in Sehweigger't Journal, 1814. 
 The depolarizing property of unannealed glass seems to have been first noticed by 
 M. Arago ; and was afterwards studied by Sir David Brewster in glass which had 
 been melted and cooled in water. Phil. Trans. 1814. 
 
 t A change of temperature, from the freezing to the boiling-point, produced a 
 <-hange of 8' in the dihedral angles at the extremity of the axis.-2?wtf. Soc. 
 March, 1824. 
 
 L2
 
 148 EEPOET ON PHYSICAL OPTICS. 
 
 index, however, undergoing the smallest proportionate diminu- 
 tion.* 
 
 The inclination of the optic axes, in biaxal crystals, is a simple 
 function of the elasticities of the vibrating medium in the direc- 
 tion of three rectangular axes ; and the plane of the optic axes is 
 that of the greatest and least elasticities. If, then, these three 
 principal elasticities be altered by heat in different proportions, the 
 inclination of the axes will likewise vary ; and if, in the course of 
 this change, the difference between the greatest elasticity and the 
 mean, or between the mean and the least, should vanish and after- 
 wards change sign, the two axes will collapse into one, and finally 
 open out in a plane perpendicular to their former plane. All 
 these variations have been actually observed. Professor Mitscherlich 
 found that, in sulphate of lime, the angle between the axes (which 
 is about 60 at the ordinary temperature) diminishes on the applica- 
 tion of heat ; that, as the temperature increases, these axes approach 
 until they unite ; and that, on a still further augmentation of 
 heat, they again separate and open out in a perpendicular plane. 
 The primitive form of the crystal undergoes a corresponding 
 change, the dilatation being greater in one direction than in another 
 at right angles to it. Sir David Brewster has observed an analo- 
 gous, and even yet more remarkable property, in glauberite. At 
 the freezing temperature this crystal has two axes for all the rays 
 of the spectrum, the inclination of the axes being greatest in red 
 light, and least in violet. As the temperature rises, the two axes 
 approach, and those of different colours unite in succession ; and at 
 the ordinary temperature of the atmosphere, the crystal possesses 
 the singular property of being unlaxal for violet light and biaxal 
 for red. When the heat is further increased, the axes which have 
 united open out in order, and in a plane at right angles to that in 
 which they formerly lay ; and at a temperature much below that 
 of boiling water, the planes of the axes for all colours are perpen- 
 dicular to their first position, f The inclination of the optic axes 
 in topaz, on the other hand, augments with the increase of tem- 
 perature ; and the variation, M. Marx has observed, is much 
 greater in the coloured than in the colourless varieties of this 
 mineral. + 
 
 * Phil. Mag., Third Series, vol. i. 409. 
 
 t Edin. Trans., vol. xi. ; and Phil. Mag., Third Series, vol. i. 417. 
 
 J Jahrb. do- Chanic, vol. ix.
 
 III. OK A NEW CASE OF INTERFERENCE OF THE RAYS 
 OF LIGHT. 
 
 Transactions of the Royal Irish Academy, Vol. XVII. 
 
 THE experiment of Fresnel, on the interference of the lights pro- 
 ceeding from the same origin, and reflected by two mirrors inclined 
 at a very obtuse angle, has been justly regarded as one of the 
 most important in the whole range of physical optics. The 
 principle of interference itself had, indeed, been stated broadly by 
 Young, and supported by the evidence of phenomena, which, to 
 the unbiassed inquirer, left little to desire. All these phenomena, 
 however, admitted of other possible explanations ; and the advo- 
 cates of the corpuscular theory of light had recourse to these, 
 rather than admit the truth of a law which afforded such strong 
 support to the undulatory theory. In most of these phenomena, 
 the light was in part intercepted by an obstacle, and it was con- 
 ceived that, in passing by the edge, the molecular action, which 
 might be supposed to exist between the particles of the body and 
 those of light, was sufficient to account for the facts observed. 
 But, in Fresnel's experiment, the two lights which interfere are 
 regularly reflected by the surfaces of the mirrors, according to 
 the ordinary laws, and are divested of every extraneous circum- 
 stance which could, by possibility, be supposed to influence the 
 result. This experiment, accordingly, has materially changed the 
 character of the controversy respecting the nature of light ; and 
 the advocates of the Newtonian theory, of the present day, are 
 forced to admit the principle thus rigidly established, and labour 
 only to show how the theory and that principle may be recon- 
 ciled.
 
 150 ON A NEW CASE OF INTEKFEEENCE 
 
 While examining this important experiment the adjustment 
 of which is a matter of some delicacy it occurred to me that the 
 fact of direct interference might be shown in a yet simpler man- 
 ner, by the mutual action of direct and reflected light. An inter- 
 ference of this kind was assumed by Young to account for some 
 of the phenomena of diffraction ; but Fresnel showed that the 
 explanation was incomplete, and that the phenomena in question 
 were caused merely by the interference of the secondary waves, 
 reflexion playing no part in their production. Under these cir- 
 cumstances it is somewhat strange that the fact of the interference 
 of direct and reflected lights should not have been itself submitted to 
 the test of experiment ; especially as the character of this interfer- 
 ence, if it were found to exist, might be expected to throw some 
 light upon the laws of reflexion itself. 
 
 The theory of such interference is easily deduced from the 
 general principles. Let light proceeding from a single luminous 
 origin fall upon a reflecting surface, at an incidence of nearly 90 : 
 a screen placed at the other side of the reflector will be illumi- 
 nated, throughout a certain extent, by both direct and reflected 
 lights ; and, if the difference of the paths traversed by these lights 
 amounts only to a small multiple of the length of an undulation, 
 the two lights will form fringes by their interference. 
 
 Let the intensities of the direct and reflected lights be 
 denoted by 2 and a' 2 , and that of the resulting light by A~ ; 
 then, by the theory of the composition of coexisting vibrations, 
 we have 
 
 A* = a~ + 2 oof cos 2ir 
 
 and V denoting the lengths of the paths traversed by the two 
 waves, from their origin to any given point, and X the length of an 
 undulation. 
 
 The intensity of the resulting light will be a maximum, and 
 equal to (a + a') 2 , at these points for which 
 
 cos 2 TT = + l , or y _ g = 2n 
 
 It will be a minimum, and equal to (a - a') 2 , when 
 
 r
 
 OF THE RAYS OF LIGHT. 151 
 
 n being any number of the natural series 0, 1, 2, 3, &c. Bright 
 fringes, therefore, will be formed at all the points included in the 
 former equation, and dark ones at the points corresponding to the 
 latter. 
 
 A 
 
 B 
 
 A. 
 
 M 
 
 
 
 Let OP be the reflector; OM the screen placed in contact with it, 
 and perpendicular to its plane ; and let A be the luminous origin, 
 and A its reflected image at an equal distance below the line OB. 
 Then, if M be any point whose illumination is required, 8 = AM, 
 X = AM. 
 
 Now if AB be denoted by p, BO by d, and OM by v, it is 
 obvious that 
 
 & = ffl + ( p _ ^ %* = d 2 +(p + z) 2 . 
 
 Hence, approximately, 
 
 and therefore 
 
 the angle AOB being denoted by a. Hence the general expres- 
 sion of the intensity of the light, at any point M, is 
 
 / #\ 
 
 A* = a 2 + 2aa cos UTT tan a v + a*. 
 
 Again, substituting for S' - S its value just found, we see that 
 the successive fringes will be formed at the distances given by the 
 
 formula 
 
 x = \ m X cotan a ; 
 
 in which m is any number of the natural series, its even values 
 giving the places of the bright fringes, and its odd values those of 
 the dark ones. Accordingly, the bright fringes are formed at t 
 distances 0, 21, 4/, &o., and the dark ones at the distances inter- 
 mediate, /, 3/, 5/, &c., / being equal to A cotan a : the successive 
 fringes, therefore, are equidistant. It is obvious that the angle
 
 152 ON A NEW CASE OF INTERFERENCE 
 
 a must be very small, or the incidence very oblique, in order that 
 the fringes should have any sensible breadth. 
 
 We have hitherto assumed that the light has undergone no 
 change by reflexion, excepting the change of direction. Let us 
 now suppose that the phase of the vibration is accelerated, and let 
 us examine the effect produced in the position of the fringes. 
 
 Let the amount of this acceleration be denoted by the angle 
 fnr ; then the differences of the phases will be 
 
 So that the successive fringes will be formed at the points for 
 which 
 
 m being any number of the natural series. But we have already 
 found that X - S = 2 tan ax; so that the points in question are 
 given by the formula, 
 
 x = | (m + /x) A cotan a ; 
 
 the even values of m corresponding to the bright fringes, and the 
 odd values to the dark ones. It is evident from this that the 
 magnitude of the fringes will be unaltered ; and that the only 
 effect of the acceleration is to push the entire system from the 
 edge, the amount of the shifting being equal to juA cotan a. 
 
 In order to submit these results to the test of trial, I employed 
 the apparatus consisting of two moveable metallic plates, which is 
 of so much use in experiments of interference. The plates being 
 closed, so as to form a narrow horizontal aperture, the flame of a 
 lamp was placed behind ; and the light thus diverging from the 
 aperture was received, at the distance of about three feet, on a 
 piece of black glass truly polished, and also horizontal. This 
 reflector was then adjusted, so that its plane might pass a little 
 below the aperture ; or, in other words, that the light might be 
 incident upon it at an angle of nearly 90. It is evident, then, 
 that the light thus obliquely reflected will meet the direct light 
 diverging from the aperture under a very small angle, and with a 
 difference in the lengths of their paths which is capable of indefi- 
 nite diminution. The two lights, therefore, are in a condition to 
 interfere ; and I found, accordingly, that when they were received 
 upon an eyepiece, placed at a short distance from the reflector, a very
 
 OF THE RAYS OF LIGHT. 153 
 
 beautiful system of bands was visible, in every respect similar to one- 
 half of the system formed by the two mirrors in Fresnel's experiment. 
 
 The first band was a bright one, and colourless. This was 
 succeeded by a very sharply defined black band ; then followed a 
 coloured bright band, and so on alternately. Under favourable 
 circumstances I could easily count seven alternations ; the breadth 
 of the bands being, as far as the eye could judge, the same 
 throughout the series, and increasing with the obliquity of the 
 reflected beam. The first dark band was of intense blackness. 
 The darkness of the succeeding bands was less intense, as they 
 were of higher orders ; and after three or four orders, they were 
 completely obliterated by the closing in of the bright bands. At 
 the same time the colouration of the bright bands increased with 
 the order of the band; until, after six or seven alternations, the 
 colours of different orders became superimposed, and the bands 
 were thus lost in a diffused light of nearly uniform intensity. 
 All these circumstances are similar to those observed in Fresnel's 
 experiment, and correspond exactly with the results of theory. 
 
 These bands are most perfectly defined when the eyepiece is 
 close to the reflector. Their breadth and colouration increased with 
 the distance of the eyepiece, but remained of a finite and very 
 sensible magnitude, when the latter was brought into actual 
 contact with the edge a circumstance which distinguishes them 
 altogether from the diffracted fringes formed on the boundary of 
 the shadow. 
 
 These fringes appear to me to possess some interest in a theo- 
 retical point of view, independently of that which attaches to 
 them as illustrations of an important general law. Depending on 
 the interference of two lights, one of which proceeds directly 
 from the luminous origin, while the other has undergone re- 
 flexion, they would seem to afford the means of detecting any 
 difference which might exist in their condition when they meet, 
 and therefore of tracing the modifications produced by reflexion. 
 
 There are two circumstances which chiefly demand our atten- 
 tion in the case of reflected light namely : 1st, tlic amplitude of 
 the vibration, on which the intensity of the light depends ; and 
 2ndly, the phase. The facts before us seem, to a certain extent, to 
 bear on both these points. 
 
 The reasonings of Fresnel, with respect to the intensity of 
 reflected light, are partly of an analogical nature, and very far
 
 154: ON A NEW CASE OF INTERFERENCE 
 
 indeed from being strictly demonstrative. Still, however, they 
 have led to conclusions fully borne out by experience, and of the 
 most interesting kind ; and we can hardly refuse our assent to 
 doctrines which bear with them such characters of truth. The 
 formula which Fresnel has obtained for the intensity of reflected 
 light has not received any direct confirmation from experiment, 
 except in the case of a few observations made by M. Arago. It 
 results from this formula that the intensity of the reflected light 
 must be equal to that of the incident, or the ichole of the light 
 reflected, at the limiting incidence of 90. Fresnel himself notices 
 this consequence, and adds that we should doubtless find it to 
 be experimentally true, if we could reach this limit. Now the 
 present experiment affords the means of examining this conclusion, 
 and seems fully to establish it. We have already alluded to the 
 intense blackness of the first dark bar, in the phenomena now 
 described. As far as the eye can judge, the intensity of the light 
 is absolutely nothing at the points corresponding to this bar ; and . 
 as the intensity of the light in the dark bands is generally ex- 
 pressed by the formula (a - a') 2 , we are forced to admit that a = d y 
 or that the intensities of the direct and reflected lights are equal 
 at this extreme incidence. 
 
 With respect to the effect of reflexion upon the phase of vibra- 
 tion, there seems to be some uncertainty in the theory. The 
 phenomena of thin plates compel us to admit that half an undula- 
 tion is either lost or gained, by the wave reflected from the first or 
 second surface ; so that half an undulation must be added to, or 
 subtracted from, the difference in the lengths of the paths traversed 
 by the two waves. That such an effect should take place is in the 
 highest degree probable from theoretical considerations. The 
 light in the one case is reflected from the surface of a denser, in 
 the other from that of a rarer medium ; and the mechanical laws, 
 on which Fresnel has founded the doctrine of reflexion, lead us to 
 the conclusion that the displacements of the ethereal particles, in 
 the moment after reflexion, must be of opposite signs in the 
 two cases. This difference in the phase of the vibration is equi- 
 valent to a difference of half an undulation in the length of the 
 path. 
 
 But it does not seem to be clearly understood to which surface 
 we are to attribute this physical change in the condition of the 
 ray. Dr. Young, indeed, who was the first to state this law, says.
 
 OF THE RAYS OF LIGHT. 155 
 
 expressly that where " light has been reflected at the surface of 
 the rarer medium, it must be supposed to be retarded one-half of 
 the appropriate interval." I cannot avoid thinking that the 
 very analogy by which he himself illustrates this point, and 
 still more the reasonings of Fresnel on the subject, lead to an 
 opposite conclusion, and tend to ascribe the effect which is found 
 to take place to reflexion at the surface of the denser medium. In 
 fact, it would appear from Fresnel's conclusions, that the sign of 
 the vibratory movement is in all cases changed by reflexion at the 
 surface of the denser medium, the angle of incidence exceeding the 
 polarizing angle ; and it can readily be shown that this change 
 of sign is equivalent to the addition of TT to the phase. 
 
 The present case of interference seems to support this view. 
 It follows, as we have seen, from theory, that if the light under- 
 goes no change of phase by reflexion, the distances of the succes- 
 sive dark fringes from the edge of the shadow will be as the odd 
 numbers, 1, 3, 5, &c. ; so that the distance of the first dark band 
 from the edge will be half the interval between each succeeding 
 pair of dark bands. But it appears, on the contrary, from the 
 phenomena, that the distance is as far as the eye can judge 
 exactly equal to the succeeding intervals ; or that the bands are 
 all shifted from the edge by the amount of half an interval The 
 phenomena, therefore, require us to suppose that the phase of the 
 reflected wave is accelerated, and that the amount of this accele- 
 ration is exactly half a phase, or TT. For the general expression for 
 the shifting of the bands is ^X cotan a ; and as this is found to 
 be equal to A cotan a, it follows that /x = 1, or the acceleration 
 equal to TT. It appears then that when light is reflected at the 
 surface of a denser medium, the wave at the limiting incidence 
 at least gains half an undulation at the instant of reflexion. 
 
 In order to satisfy myself more fully of the effects of reflexion 
 upon the phase, I repeated the experiment with polarized light. 
 The light was polarized, before it reached the aperture in the 
 screen, by transmission through a good tourmaline; and the 
 fringes were observed in various positions of the plane of polariza- 
 tion with respect to the plane of reflexion. I could detect 
 no sensible difference in the position of the fringes under all 
 these changes of circumstance ; and, in particular, the distance 
 of the first dark band from the edge of the shadow seemed, as 
 before, to be precisely equal to the intervals of the succeeding
 
 156 ON A NEW CASE OF INTERFERENCE. 
 
 bands, whether the light was polarized in the plane of incidence, 
 or in the plane perpendicular to it. 
 
 This result seems to be just what might be expected from 
 Fresnel's theory of reflexion. From this theory it appears that if 
 + a be the coefficient of the displacement of the incident ray, or 
 the amplitude of the vibration, and t and f the angles of incidence 
 and refraction, the coefficients of displacement of the reflected ray 
 
 will be 
 
 sin (t - tan (i - ?} 
 
 -a-^r. =, or +a 
 
 _ x . , tan ( + i'} 
 
 according as the plane of polarization coincides with the plane of 
 reflexion, or is perpendicular to it. Now the former quantity is 
 always negative, so long as i is greater than *', or the ray incident 
 on the surface of the denser medium. Under the same circum- 
 stances, the latter quantity is positive or negative, according as 
 i + i' is less or greater than 90, or the angle of incidence below or 
 above the polarizing angle. For very oblique reflexion, then, both 
 displacements are negative ; and, therefore, whether the plane of 
 polarization coincides with, or is perpendicular to the plane of 
 reflexion, the wave will undergo a change of half a phase at the 
 instant of reflexion. 
 
 From Sir David Brewster's important researches on the nature 
 of metallic reflexion, it appears that a plane-polarized ray, which 
 is incident upon a metallic reflector, becomes elliptically-polarized 
 after reflexion ; a result which indicates a difference in the phases 
 of the two resolved vibrations. But it appears further, from the 
 same researches, that this difference of phase varies with the inci- 
 dence, and vanishes altogether at the extreme incidences ; so that 
 at the limiting incidence of 90, there is either no alteration in the 
 phase of vibration, whether parallel or perpendicular to the plane 
 of reflexion, or that alteration is the same for the two vibrations. 
 From some observation of the fringes produced by the interference 
 of direct light with that reflected from speculum metal, I conclude 
 that the former is the case.
 
 IY. ON THE LIGHT REFLECTED AND TRANSMITTED BY 
 THIN PLATES. 
 
 Transactions of the Royal Irish Academy, Vol. XXIV. 
 
 THE problem of thin plates lias been completely solved for the 
 cases in which the incident light is polarized in either of the two 
 principal planes, and therefore also for the case of unpolarized 
 light, which, it is well known, may be regarded as composed of 
 two equal pencils, polarized respectively in these two planes. 
 
 There is no difficulty in perceiving in what manner the theory 
 may be extended to light polarized in any plane ; but the results 
 become more complicated, from the necessity of including the con- 
 sideration of phase. When the incident light is polarized in the 
 plane of incidence, or in the perpendicular plane, we have only to 
 seek the magnitude of the resultant vibration, after the successive 
 divisions which it undergoes by reflexion and refraction at the two 
 surfaces of the plate. But when the light is polarized in any 
 other plane, the incident vibration must be resolved into two, in 
 the two principal planes ; and for each of these components we 
 must know the phases, as well as the magnitudes of the resultant 
 vibrations, before we can estimate their joint effect. These phases 
 are in general different, and therefore the resulting light is ellipti- 
 caHy-polarized. 
 
 The preceding, and some other results of theory, were pointed 
 out by the author many years ago ; and the general formulir, 
 in which they are included, were at the time laid before tho 
 Academy.* In the present communication it is proposed to 
 develop these consequences ; and in particular, to deduce the law 
 
 * fromiliiiffs of the Koi/nl Irish Academy, June 13, 1842.
 
 158 ON THE LIGHT REFLECTED 
 
 -according to which the elliptic polarization varies, both with the 
 thickness of the plate and with the incidence. 
 
 It is assumed in this investigation, that in the reflexion and 
 refraction of light at the surface of a transparent medium, the 
 phases of the incident, reflected, and refracted vibrations coincide 
 at the refracting surface. This assumption is that made by 
 Fresnel. Its theoretical truth is indeed now disproved by the 
 more complete analysis of Cauchy, and by the experimental labours 
 of M. Jamin; but its deviation from the phenomena is exceedingly 
 small, except within a small range of incidence in the neighbour- 
 hood of the angle of polarization, and the conclusions based upon 
 it are therefore sensibly in accordance with fact, except for the 
 same incidences. 
 
 It is unnecessary to add, after what has been just stated, that 
 the elliptic polarization here considered is altogether dictinct, both 
 in its origin and in its laws, from that produced by reflexion at a 
 single surface. 
 
 Let us suppose that the incident light is polarized either in 
 the plane of incidence, or in the perpendicular plane. Let u and 
 u denote the ratios of the reflected and refracted vibrations to the 
 incident vibration at the first surface of the plate, and for light 
 falling upon it from without; (u) and (u'} the corresponding 
 ratios for light proceeding in the opposite direction ; and u 2 the 
 'ratio of the reflected to the incident vibration at the second 
 surface. Then, the amplitude of the incident vibration being 
 unity, the amplitudes of the vibrations which emerge at the first 
 surface, after one reflexion at the second, = u f u 2 (u) ; after three 
 internal reflexions, = ' 2 (u} 2 (u'} = 1st portion x (u) i^ ; after 
 five internal reflexions, = 2nd portion x (u) w 2 , &c. But 
 
 (u} = -u, u' (11} = 1 - u 2 * 
 
 These amplitudes, accordingly, form a series in geometric pro- 
 gression, whose first term is u' u z (u') = w 2 (1 - w 2 ), and whose 
 common ratio is (u) u 2 = - u u z . 
 
 But the interval of retardation, after one internal reflexion, 
 
 * The truth of these relations is evident from the known formulae of Fresnel. It 
 has heen deduced independently, from very simple general principles, by Professor 
 Stokes, and has been shown by him to hold even in the case of change of phase. 
 See an interesting paper " On the perfect blackness of the central spot in Newton's 
 Hinge." Cambridge and Lublin Mathematical Journal, 1849.
 
 AND TRANSMITTED BY THIN PLATES. 159 
 
 = 2 r cos 6', T being the thickness of the plate, and & the angle of 
 refraction ; and the corresponding difference of phase is 
 
 4"" n, 
 
 a = -r- T cos a ; 
 A 
 
 A being the length of an undulation. The difference of phase, 
 after three internal reflexions, is 2a ; after five internal reflexions, 
 3a ; and so on. Hence, if ^ denote the phase of the vibration 
 reflected at the first surface, at the instant of reflexion, - a will 
 be the phase of the portion which emerges there after one internal 
 reflexion ; $ - 2a, after three, &c. And the sum of all the inter- 
 nally-reflected vibrations will be 
 
 u-i (1 - u~) [sin (< - a) - uu 2 sin ($ - 2a) + u % u sin (0 - 3a) - &c.] . 
 in which, it can be easily shown, the quantity within the brackets 
 is equal to 
 
 sin (0 - a) + uu z sin <j> 
 
 1 + 2ww 2 cos a + w 2 M 2 2 * 
 
 Adding u sin $, the vibration reflected externally at the first 
 surface of the plate, the sum of all the reflected vibrations is 
 
 ,. sin (0 - a) + uu-i sin 6 
 
 u sin d> + 2 (1 - w 2 ) ^ - ,-V 
 
 ' 1 + 2uu 2 cos a + wW 
 
 Let this quantity be put under the form 
 
 P sin + Q cos ^. 
 Then we find 
 
 cos o + uu t 
 
 . 
 
 P = U + U 2 (1 - U) 
 
 ; 1 + 2uui COS a + W 
 
 - w 2 (1 - w 2 ) sin o 
 1 + 2miz cos a + ifu*' 
 
 IVherefore, the intensity of the resulting light is* 
 
 t/ 2 + 2m/ 2 cos a +t/^ t 
 * "l+2tt,COSa + V 
 
 ,nd its phase, ;//, will be given by the formula, 
 -_Q = M 2 (1 - M 2 ) sin a 
 
 n ^ ~ P ~ u (1 + w./j + ih (1 + ") cos a' 
 
 * This expression for the intensity has been alieady obtained by Mr. Airy "On 
 the Phenomena of Newton's Rings, when formed between two transparent substances 
 of different refractive powers." Camb. Tram., 1832.
 
 150 ON THE LIGHT REFLECTED 
 
 Substituting 1 - sin 2 ^ for cos a, the expression for the intensity 
 
 becomes 
 
 (u + # 2 ) 2 - 4ww 2 sin 2 ~ 
 
 (1 + ww 2 ) 2 - 4w* 2 sin 2 
 
 When the media are the same on the two sides of the plate, 
 2 = - u, and the foregoing formula is reduced to the known 
 
 one, 
 
 4w 2 sin 2 I 
 1 = 
 
 - w 2 ) 2 + 4w 2 sin 2 ^ 
 
 The greatest and least values of I, in the general formula, cor- 
 respond to sin a = 0, or a = mir. When a = 2mir, the expression is 
 
 reduced to 
 
 \1 + uuz 
 When a = (2m + 1) TT, it becomes 
 
 / 
 
 / u - u 2 V 
 
 \i - wJ * 
 
 When u and t* 2 have the same sign, the former value is a maximum,. 
 and the latter a minimum ; the rings consequently begin from a 
 bright centre. On the other hand, when u and 2 have opposite 
 signs, the former value is a minimum, and the latter a maximum ; 
 and the rings begin from a dark centre. 
 
 When the incident light is polarized in the plane of incidence? 
 the signs of u and w 2 are determined solely by the relative refrac- 
 tive densities of the plate, and of the two media which border it 
 on either side. When the refractive density of the plate is greater 
 or less than those of both media, M and u z are of opposite signs, and 
 the rings are dark-centred. On the other hand, when the refractive 
 density of the plate is intermediate to those of the two media on 
 either side, u and u z have the same sign, and the rings ar& 
 bright-centred. This inversion of the phenomenon was observed by 
 Young.
 
 AND TRANSMITTED BY THIN PLATES. 1G1 
 
 When the incident light is polarized perpendicularly to the plane 
 of incidence, the signs of u and w 2 depend on the incidence, as well 
 as on the relative refractive densities of the media. When the 
 angle of incidence is less than the polarizing angle at either .sur- 
 face, the sign of u, or of 2 , is the same as in the case of light 
 polarized in the plane of incidence ; when it is greater, the sign is 
 opposite. Accordingly, when the incidences at both surfaces are 
 less than their respective polarizing angles, the character of the 
 rings will be the same as for light polarized in the plane of inci- 
 dence. And the same thing is true when the incidences at both 
 surfaces are greater than their respective polarizing angles ; for 
 in this case the signs of u and w 2 are changed simultaneously. But 
 when the incidence at one surface is less, and at the other greater, 
 than their respective polarizing angles, one of the quantities, u and 
 w 2 , changes sign, and the other does not ; and the character of the 
 rings will be the opposite to that presented when the light is 
 polarized in the plane of incidence. 
 
 It follows, then, that when the refractive density of the plate 
 is greater or less than those of the two media, the rings will be 
 dark -centred at the lower and higher incidences, and bright-centred 
 at the intermediate incidences. This phenomenon was observed 
 by Arago, and explained by Mr. Airy. On the other hand, when 
 the refractive density of the plate is intermediate to those of the 
 two media (the light being still polarized in the perpendicular 
 plane), the rings will be bright-centred at the lower and higher 
 incidences, and dark-centred at the intermediate incidences. This 
 latter case has not been hitherto noticed. 
 
 At the polarizing angles of either surface, u = 0, or u = 0, and 
 the rings vanish. 
 
 7. Now let the incident light be polarized in any plane, inclined 
 at the angle y to the plane of incidence ; and let the amplitude of 
 the incident vibration (= 1) be resolved into two, cos y and sin 7, 
 in the plane of incidence and in the perpendicular plane, respec- 
 tively. Let v and i\ denote the values of u and v, in the case of 
 light polarized in the plane of incidence ; w and r 2 the correspond- 
 ing values for light polarized perpendicularly ; then the intensities 
 of the light in the two reflected pencils are 
 
 E* + 2cf, cos Q + t ./ ., r u? + 2M-tf> cos a + f^ h)2 
 
 ~ l + - + rY CCS ~ 7 ' " 1 + Stfw, cos a 4 tftf
 
 126 ON THE LIGHT REFLECTED 
 
 And the intensity of the reflected light will be the sum of the in- 
 tensities of the two component portions. 
 
 When the obliquity of the incident pencil is so small, that 
 the squares and products of v, v w, iff*, may be neglected in com- 
 parison with unity, the intensity of the reflected light will be, 
 nearly, 
 
 (p 2 + 2m, cos a + 2 2 ) cos 2 7 + (tf + 2ww, cos y + w?} sin 2 7. 
 
 This expression is independent of the phase, and therefore the 
 intensity is constant for a given incidence, when 
 
 W Z 
 
 w, cos 2 7 + vcw-i sin 2 7 = 0, or tan 2 7 = --- . 
 
 It will be easily seen, on substituting for v, v z , w, iff z , their well- 
 known values, that the value of tan 7 will be real, and therefore 
 the disappearance of the rings possible, only when the angles of 
 incidence at the two surfaces of the plate are, in the one case 
 greater, and in the other less, than the respective polarizing 
 angles.* This is the explanation of the phenomenon observed by 
 Sir David Brewster. 
 
 Again, since the values of v and v z are, in general, different 
 from those of w and w z , it follows that the phases of the two com- 
 ponent vibrations are unequal, and consequently that the result- 
 ing reflected light is elliptically-polarized. This consequence of 
 the wave-theory does not appear to have been noticed by observers. 
 
 8. We may now proceed to consider more particularly the 
 case in which the media are the same on the two sides of the 
 plate. 
 
 In this case, v z , = - v, w z = - w, and the general expressions for 
 the phases of the two polarized pencils are reduced to 
 
 The difference of phase is given by the formula 
 
 tan (,/, - v) = ^ ~ sin 
 
 1 - 
 
 p* + w 2 ) cos a + vW 
 It follows from this, that i// - x varies with a, and therefore with 
 
 * See the paper above referred to, Proceedings, vol. ii., p. 268.
 
 AND TRANSMITTED BY THIN PLATES. 16^3 
 
 the thickness of the plate ; and that, in the phenomena of the 
 rings, it will go through all its values within the limits of a single 
 ring. 
 
 9. The difference, ^ - \> generally vanishes, when sin o = 0,* 
 
 Accordingly, the difference of phase is nothing both at the bright 
 and at the dark rings ; and the light at the former is plane-polar' 
 izt'd. 
 
 The difference of phase is a maximum, when 
 
 tf + w z 
 
 cos a = ^ - ; 
 1 + 2 M? 2 
 
 and denoting by A the maximum value of i// - \, we have 
 
 i* - v? __ 
 
 V/KI-^HI-V)}' 
 
 10. In order to express a and A in terms of the angle of incidence, 
 let us make -- g- = p; and substituting in Fresnel's formulas, we 
 
 find 
 
 sin (9 - &} up - 1 tan(0-y) = /a-p. 
 
 ~ sin (0 + 9) ~ W + 1' " tan (0 + tf) ~ /i + p'' 
 
 H being the refractive index for light entering the plate from the 
 surrounding medium. Making these substitutions, the thickness 
 of the plate corresponding to the maximum difference of phase is 
 determined by the formula, 
 
 COS a 
 
 , 
 
 + fj.- i y 
 
 Or, since p 2 = 1 + (1 - ^} tan 2 0, 
 
 Accordingly, the value of cot ^ increases, from (p + p"*) at a 
 perpendicular incidence, to infinity when the incidence is most 
 
 * When 6 = 90, we have v* = !,; = !; and the expression for ten ty - X ) 
 becomes -, when a = Zmir. It appears from the following, that the difference of 
 
 phase is a maximum in this case. 
 
 M 2
 
 164 ON THE LIGHT REFLECTED 
 
 oblique ; and, in a plate of varying thickness, the points of maxi- 
 mum difference of phase commence near the middle of an interval, 
 and approach indefinitely to the dark rings as the incidence 
 approaches to 90. 
 
 The tangent of the maximum difference of phase is 
 
 ( - 1) (p 2 - 1) 
 
 tan A = 
 or, putting for p 2 its value, 
 
 When n is greater than unity, or the plate denser than the 
 surrounding medium, A = 0, when = 0. As 6 increases, A in- 
 creases continuously; until, when approaches to 90, A approaches 
 indefinitely to the value, 
 
 This is its greatest value. For ordinary flint glass, and for the 
 extreme red ray, ju = 1'60, and A = 26. 
 
 When fi is less than unity, or the plate rarer than the sur- 
 rounding medium, A = 0, when = 0, as before. And A increases 
 as increases, up to the limiting incidence, for which 8 = sin~>> 
 
 and cot A = 2 ^ . The greatest difference of phase, therefore, 
 
 is the same in hoth cases, and in both corresponds to the extreme 
 incidence at which light is admitted into the plate.* 
 
 11. Again, the media being the same on the two sides of the 
 plate, the expressions for the intensities of the two portions of the 
 reflected light, polarized respectively in the plane of incidence and 
 in the perpendicular plane, become 
 
 * It is evident that cot A = 0, and therefore A = 90", when the incidence has 
 either of the values given by the formulas 
 
 tan 1 = , and tan 2 = u 2 * ** 
 
 l-M 2 l-/i*' 
 
 hoth of which are real when the plate is rarer than the surrounding medium. Theee 
 values, however, are both greater than the limiting incidence, and the light dc.es net 
 enter the plate. When the incidence is inteimediate to the two preceding values, A is 
 imaginary.
 
 AND TRANSMITTED BY THIN PLATES. 105 
 
 sin 2 - cos 2 y u? sin 2 | sin 2 y 
 
 
 1 - "2v~ cos a + 1 <4> ~ 1 - 2iv- cos a + ic 1 ' 
 
 Let the ratio of the corresponding amplitudes be denoted by 
 tan y' ; then 
 
 w Ifl - 2c 2 
 
 - / -- 
 
 *v\i - 1 
 
 - c 2 cos a + 
 tan y = tan y - 
 
 ' 
 
 The angle 7' will be the azimuth of the plane of polarization, when 
 the reflected light is plane-polarized. 
 
 When the thickness of the plate is that corresponding to the 
 
 maximum difference of phase, or cos a = ^ - - , the ratio of the 
 
 1 + V 
 amplitudes becomes 
 
 tc 
 
 tan 7 = tan T,- 
 
 The angles A and 7' being known, the character of the elliptic 
 polarization is completely determined. 
 
 12. We may now proceed to examine the intensity and phase 
 of the transmitted light. 
 
 It will be easily seen, by following the same reasoning as 
 before, that the transmitted light consists of an indefinite number 
 of portions, which emerge at the second surface of the plate after 
 0, 2, 4, &c., internal reflexions ; and that the amplitudes of their 
 vibrations form a series in geometric progression, whose first term 
 is wV 2 , and whose common ratio is - w 2 , in which u and u 2 denote, 
 as before, the ratios of the amplitudes of the reflected to the 
 incident vibrations, at the first and second surfaces of the plate 
 respectively, and u' and w' 2 the corresponding ratios for the re- 
 fracted vibrations. It is likewise evident that, if $ denote the 
 phase of the first portion, $ - a will be that of the second, <J> - 2u 
 that of the third, &e., in which 
 
 4;r 
 
 a = - T cos u , 
 A 
 
 as before. Consequently the resulting vibration, which is the 
 sum of all these, is 
 
 liu't !sin <p - mtn sin (/> - a) + u'u-i sin (^ - 2a) - &c.j 
 sin d> + HH-, sin (^ + a) 
 
 " 
 
 M X 2 
 
 1 + Ktftfc cos a
 
 166 ON THE LIGHT KEFLECTED 
 
 Revolving this, we find 
 
 1 + uu z cos a 
 
 = W " 
 
 a _ , , 
 
 + W' * 1 
 
 1 + 2MW, COS a + W + 2WM 2 COS a + tt'tt, 
 
 Hence the intensity of the transmitted light is 
 
 r 
 
 and the phase is given by the formula 
 
 ., Q - wwa sin o 
 
 tan ;// = - -g = -= --- . 
 P 1 + UU Z COS a 
 
 13. When u and u, have the same sign, the greatest and least 
 intensities correspond to a = (2m + 1) TT, and a = 2imr. They are, 
 respectively, 
 
 , 
 
 and 
 
 1 - 
 
 When u and M 2 have opposite signs, the greatest and least values of 
 /' correspond to a = 2mtr, and a = (2m + I)TT. Hence the bright 
 rings of the transmitted system occur at thicknesses which produce 
 the dark rings of the reflected system, and vice versa. 
 
 These values never vanish, since u' and M' Z are never evanes- 
 cent ; and there are no Hack rings in the transmitted light. 
 
 14. When the incident light is polarized perpendicularly to the 
 plane of incidence, and when the coefficients u and u 2 are both 
 positive, or both negative, the preceding values of the greatest and 
 least intensities remain unaltered. In other words, the rings 
 exhibit the same character, whether the angle of incidence is less 
 than the polarizing angle at both surfaces, or greater. But when 
 one of these quantities is positive, and the other negative, i.e. 
 when the incidence at one surface is less than its polarizing angle, 
 and at the other greater, the preceding formulas are transposed, 
 and the bright rings are changed into dark ones, and nee versa. 
 When u = 0, or u z = 0, i.e. when the light is incident on either 
 surface at its polarizing angle, the preceding values are both re- 
 duced to (wV 2 ) 2 , and there is no variation of intensity caused by 
 interference. 
 
 15. It may be easily shown from Fresnel's formulas, that
 
 AND TRANSMITTED BY THIN PLATES. 167 
 
 When the media are the same on the two sides of the plate, 2 ' = 0, 
 and u z = - u. In this case, therefore, u'tt 2 ' = 1 - 2 , and the gene- 
 ral expression for the intensity becomes 
 
 (1 - ')' 
 
 I' 
 
 I - 2'U? COS a + U* ' 
 
 Comparing this with the expression for the intensity of the reflected 
 light (5), we learn that 
 
 /+/' = !; 
 
 or that the intensities of the reflected and transmitted lights are 
 complementary, the maximum of the former corresponding to the 
 minimum of the latter, and vice versa. This law explains the rela- 
 tions of the reflected and transmitted rings observed by Newton 
 and Arago. 
 
 The greatest and least intensities are 
 
 1 - tt'V 
 1 + U-) ' 
 
 1 and 
 
 Accordingly, the intensity of the light in the bright rings is equal 
 to that of the incident light. 
 
 16. When the incident light is polarized in any plane, inclined 
 at the angle y to the plane of incidence, the transmitted light is 
 composed of two portions, polarized in the plane of incidence, and 
 in the perpendicular plane, respectively. The phases of these two 
 portions are given by the formulas, 
 
 - W 2 sin a , ww-t sin a 
 
 tan w = - , tan v = -: - ; 
 l + ta*oea 1 + ww 2 cos a 
 
 and as these are in general unequal, the light will be elliptically- 
 polarized. The difference of phase is given by the formula 
 
 f 
 (r X. ) ~ j + ^p a 
 
 Hence the ellipticity varies with a, and therefore with the thick- 
 ness of the plate. 
 
 The difference, \J/ - x'> will be a maximum, when 
 
 cos a = 
 
 Substituting in the preceding formula, and denoting the greatest 
 difference of phase by A', we have
 
 ON THE LIGHT REFLECTED 
 
 tan A' = - 
 
 17. The intensities of the two component pencils are 
 
 (tV cos 7 ) 8 j, = (^V 2 sin T ) 2 _ ^ 
 
 " 1 + 2w , cos a + rV 1 + 2'Wa cos a + ftr a 8 ' 
 
 And denoting the ratio of the amplitudes by tan 7', as before, 
 
 llflDz V 1 + 2W 2 COS a + V^'V-i 
 
 tan 7 ' = tan 7 7^1 + 2tnc z cos a + w 
 
 When the thickness of the plate is that corresponding to the maxi- 
 mum difference of phase, this expression is reduced to 
 
 18. When the media are the same on the two sides of the 
 plate, ih = - v, ? a = - w, and the preceding formulas for the maxi- 
 mum difference of phase are reduced to 
 
 r + w , 
 
 cos a = , tan A = 
 
 which are identical with those already obtained for the reflected 
 light. Accordingly, the difference of phase of the two portions of the 
 polarized beam is the same in the reflected and in the transmitted 
 pencils. 
 
 In the same case the ratio of the amplitudes is 
 
 tan 7 ' = tan 7 
 
 In resuming the theory of the rings in polarized light, I was 
 under the impression that the knowledge of the subject was still 
 confined to the general principles laid down by myself, many years 
 ago. Since the foregoing paper was read, however, I have learned 
 that the problem has been discussed by M. Jamin, in an interest- 
 ing memoir published in the Annales de Chimie in 1822. In this 
 memoir the author has confined himself to the case in which the 
 media are the same on the two sides of the plate. In another 
 respect, he has treated the problem more generally than it has 
 been considered in the foregoing paper, having based it upon the 
 theory of Cauchy, instead of that of Fresnel. lie has thus been
 
 AND TRANSMITTED BY THIN PLATES. 169 
 
 led to detect some curious phenomena of the rings, when the light 
 is polarized perpendicularly to the plane of incidence, which had 
 escaped the notice of preceding observers. 
 
 In applying his theory, however, to light polarized in any 
 plane, M. Jamin disregards, as insensible, the additional terms 
 which depend upon the Cauchian phase. His formulas, thus 
 simplified, should therefore accord with those obtained in the 
 present paper for a plate bordered on both sides by the same 
 medium. Such, however, is not the case : the results, in fact, are 
 entirely at variance, M. Jamin's formulas giving plane-polarized 
 light at the extreme incidence, where (according to the theory 
 above given) the departure from plane polarization is greatest. 
 I believe that this discrepancy is accounted for by an error, into 
 which M. Jamin seems to have fallen, in computing the maximum 
 difference of phase of the two components of the light, which are 
 polarized respectively in the two principal planes.
 
 V. OBSERVATIONS ON THE DIRECTION AND INTENSITY 
 OF THE TERRESTRIAL MAGNETIC FORCE IN IRE- 
 LAND, MADE BY THE REV. HUMPHREY LLOYD, M.A., 
 F.R.S., &c.; BY CAPTAIN EDWARD SABINE, R.A., F.R.S., 
 &c.; AND BY CAPTAIN JAMES CLARKE ROSS, R.N., 
 F.R.S., &c. 
 
 Fifth Report of the British Association for the Advancement of Science. 
 
 THE observations which form the subject of the present communi- 
 cation were made during the years 1834 and 1835, in compliance 
 with the recommendation of the British Association urged in the 
 first and second Reports of its proceedings. Their main object 
 has been to determine the direction of the lines of magnetic dip 
 and intensity in Ireland, and to make a small, but it was hoped 
 exact, addition to our knowledge of the laws of distribution of the 
 earth's magnetism. The observations are threefold : first, observa- 
 tions of the horizontal part of the earth's magnetic force, as de- 
 termined by the time of vibration of a needle suspended horizontally, 
 after the method of Professor Hansteen ; secondly, observations of 
 dip, made in the usual manner ; and thirdly, observations oi dip 
 and intensity at the same time, and with the same instrument, 
 according to the method adopted by Professor Lloyd, and already 
 submitted to the Association.* 
 
 I. HORIZONTAL INTENSITY. 
 
 The instruments employed in the first series of observations 
 were constructed after the model of that of Professor Hansteen. 
 The needles are cylinders 2| inches long, and -13 of an inch in 
 diameter, suspended by a few filaments of the silkworm's thread. 
 
 * Fourth Report, p. 557. Transactions of the Royal Irish Academy, fW. XJ'IL
 
 TERRESTRIAL MAGNETIC FORCE IN IRELAND. 171 
 
 They are inclosed in a small rectangular box, supported upon 
 levelling screws, and having a tubular pillar screwed on at top for 
 the silk suspension. At the bottom of the box is a divided circle, 
 for the purpose of noting the arc of vibration : the temperature is 
 observed by means of a small thermometer inclosed in such a 
 manner as to avoid contact with the bottom and sides of the box. 
 Before the commencement of the observations, the bottom of the 
 box is to be rendered truly horizontal by means of the levelling 
 screws on which it rests, and of a small spirit level with which it 
 is furnished. The needle being then suspended so as to hang 
 near the bottom, its deviation, if any, from the horizontal position 
 will be detected by its inclination to the surface. It is then to be 
 slightly moved to one side or other in the brass stirrup by which 
 it is supported, until it hangs truly parallel to the lower surface of 
 the box ; and when this adjustment is once accurately made, no 
 further alteration will be required, unless the change of dip be 
 considerable. 
 
 When an observation is to be made, the needle is raised or 
 lowered by a small roller to which the silk suspension is attached, 
 so that it may hang about midway between the upper and lower 
 surfaces of the box. It is then drawn aside from the magnetic 
 meridian through an arc of 25 or 30, by a piece of brass wire 
 inserted in the side of the box, and is allowed to oscillate. The 
 registry of the oscillations is commenced when the amplitude of 
 the vibration on either side of the meridian is reduced to 20, and 
 it is continued during 360 vibrations ; 'the moment of the comple- 
 tion of every 10th vibration during that interval being noted by a 
 chronometer. The amplitude of the final arc, or of the arc of the 
 360th vibration, is also observed ; and the temperature of the air 
 in the box, as indicated by the interior thermometer, is noted at 
 the beginning and end of the observation. 
 
 It is obvious that in this manner seven intervals of time are 
 obtained, each corresponding to 300 vibrations, viz. the interval 
 between the Oth and 300th vibration, between the 10th and 
 310th, &o., and between the 60th and 360th ; and the mean of 
 these is taken as the result. But to this result several corrections 
 must be applied. 
 
 1. The time as shown by the chronometer is to be corrected for 
 rate; and accordingly the chronometer's rate must be determined 
 from time to time by comparison with a good timekeeper, or by
 
 172 OBSERVATIONS OF THE TERRESTRIAL 
 
 astronomical observations. In the present series the rate was 
 observed at the commencement and end of each group of observa- 
 tions by the former and easier method. The amount of the 
 correction due to rate is in most cases very small, the correction in 
 the time of 100 vibrations corresponding to a daily rate of 2 s 
 being less than O s> 01 with the slowest of the needles employed. 
 
 2. Professor Hansteen has applied a correction for the arc of 
 vibration, so as to reduce the time to that corresponding to in- 
 finitely small arcs. The correction is investigated on the same 
 principles as that usually applied to pendulum observations. It is 
 however more complicated in its form ; for, instead of a single 
 series of vibrations (as in the case of the pendulum), we have here 
 seven distinct series, each commencing from a different arc. The 
 principle, however, seems hardly applicable in the present instance. 
 It is assumed that the successive arcs of vibration decrease in 
 geometric progression, as they must necessarily do if the resistance 
 of the air be proportional to the velocity. This is found to hold 
 good in the vibrations of the pendulum when the arcs are very 
 small ; but it is by no means true when they are so considerable 
 as those in which the horizontal magnetic pendulum is made to 
 vibrate. Where, however, the vibrations commence from the same 
 arc, and the terminal arc does not much vary, the correction itself 
 may perhaps be disregarded. In the following observations, in 
 which the initial arc was 20, the 360th or terminal arc was 
 generally 2, and was in all cases included between the limits 1 
 and 4. In such cases, then, the correction must be, nearly, a 
 constant quantity ; its application to the observed times is there- 
 fore nearly equivalent to their multiplication by a constant co- 
 efficient, and the ratio of the times (with which alone we are 
 concerned in this class of observations) remains unaltered. For 
 these reasons no attempt has been made to introduce a correction 
 for the arcs in the following results ; but the terminal arcs are 
 given, so as to put the reader in possession of all the circumstances 
 of the observation. 
 
 3. By far the most important correction is that due to tem- 
 perature. If T' be the observed time of 100 vibrations correspond- 
 ing to the actual temperature t', and T the corrected time cor- 
 responding to the standard temperature t, the correction is 
 
 T- T' = T' t-f;.
 
 MAGNETIC FORCE IN IRELAND. 
 
 173 
 
 a being a constant coefficient whose value is to be determined 
 experimentally for each needle. 
 
 The following observations were made with the cylinders L (r/), 
 L (b), in order to determine the value of the coefficient a for each. 
 The apparatus being inclosed in a large glass bell, the time of 100 
 vibrations of cylinder L (a), commencing with the arc of 10, was 
 observed at the mean temperature of the room, and when the air 
 of the bell was heated artificially from below, by means of a spirit 
 lamp. The final arc varied between 4 and 5. The observations 
 with cylinder L (b), were made in the bell without the apparatus. 
 In this case no means were taken to observe with any accuracy the 
 arc of vibration ; and in order to reduce as much as possible any 
 error arising from this source, the observations were continued in 
 each instance until the arcs were reduced to the smallest appreci- 
 able, and the mean of the last five intervals of 100 vibrations then 
 taken as the result. The chronometer's rate varied from + 8 '6 to 
 + l s> 4 per diem, and had therefore no appreciable influence on the 
 results. 
 
 Cylinder L (a). Cylinder L (b). 
 
 Date. 
 
 Hour. 
 
 Time. 
 
 Temp. 
 
 
 h. m. 
 
 s. 
 
 
 
 March 4, 
 
 1 42 
 
 242-64 
 
 54-5 
 
 
 1 55 
 
 242-82 
 
 54-5 
 
 8, 
 
 3 46 
 
 242-30 
 
 58-8 
 
 
 4 4 
 
 242-24 
 
 58-0 
 
 
 Mean 
 
 242-50 
 
 56-5 
 
 1, 
 
 3 44 
 
 243-96 
 
 82-5 
 
 
 4 10 
 
 243-96 
 
 83-1 
 
 [ 8, 
 
 2 6 
 
 243-94 
 
 74-5 
 
 
 Mean 
 
 243-95 
 
 80-0 
 
 Date. 
 
 Hour. 
 
 Time. 
 
 Temp. 
 
 
 h. m 
 
 s. 
 
 
 
 March 19.* 1 11 7 
 
 293-48 
 
 53-6 
 
 
 11 40 
 
 292-52 
 
 55-0 
 
 
 2 42 
 
 294-00 
 
 60-3 
 
 
 3 5 
 
 293-76 
 
 59-5 
 
 
 Mean 
 
 293-44 
 
 57-1 
 
 
 12 50 
 
 295-24 
 
 80-0 
 
 
 1 16 
 
 295-20 
 
 83-3 
 
 
 Mean 
 
 295-22 
 
 81-6 
 
 The constant coefficient sought is to be calculated from the 
 formula 
 
 * A series of observations had been made with this cylinder, in the same manner 
 and on the same days as those with cyl. L (a) ; but the results were unsatuf 
 some of them indicating an increase of force with increased temperature. 1 
 dictory results have been noticed by many observers, and are usually at! 
 disturbing effects of current* of air, determined by inequality of
 
 174 OBSERVATIONS OF THE TEERESTRIAL 
 
 in which t and t' are the two temperatures, and T and T' the 
 corresponding times of vibration. We find 
 
 Cyl. L (a). T = 242 8 -50, T - T' = 1 8 '45, t - t' = 23-5 
 
 a = -000254 
 Cyl. L (J). T' = 293 s -44, T - T' = 1"78, t-f= 24-5 
 
 a = -000248. 
 
 It is to be observed that these cylinders were made at the same 
 time, and were therefore probably tempered to the same degree ; 
 and to this circumstance we may, with much probability, ascribe 
 the close agreement in the values of the constant which determines 
 the effects of temperature upon the force of the needle. 
 
 No observations were made to determine directly the effects of 
 temperature upon the other needles employed in the course of 
 these observations; and, in correcting the results obtained with 
 them, the coefficient employed by M. Hansteen, viz., -00017, has 
 been that adopted. The standard temperature (t), to which all 
 the results contained in the following pages are reduced, is 60 Fahr. 
 
 4. All that we know of the diurnal variations of the intensity of 
 the horizontal force is due to M. Hansteen and Professor Christie. 
 These writers agree in fixing the hours of minimum intensity at 
 10^- A. M. The intensity then increases, and attains its maximum, 
 according to Professor Christie, at about 7| p. M. The amount of 
 this maximum is 1*0024 in summer, the minimum intensity being 
 unity; but this amount, as well as the hour of its occurrence, 
 changes with the season. Of the law according to which the force 
 varies between its two limiting values, we know nothing ; and it 
 is therefore impossible, in the present state of our knowledge, to 
 apply a correction for these variations. It was proposed to evade 
 this difficulty, in the ensuing observations, by observing at a fixed 
 hour. To this limitation, however, it was found impracticable to 
 adhere, and the results still remain uncertain by the amount of the 
 diurnal change. 
 
 5. The variations of the magnetic force give rise to another 
 and still graver class of errors. The least experience in obser- 
 vations of this nature is enough to prove that the horizontal in- 
 tensity is, from some cause or other, subject to irregular fluctuations ; 
 and these fluctuations, like those of the barometer in our climates, 
 are much more considerable than the regular horary changes. It 
 seems probable that these variations in the intensity of the hori-
 
 MAGNETIC FORCE IN IRELAND. 
 
 175 
 
 zontal force are, like those in its direction, not local phenomena, 
 but occur at the same time at places widely separated. To elimi- 
 nate them from our results, therefore, it would suffice to have a 
 regular series of observations made at some fixed station, con- 
 temporaneous with those made at the different stations ; and, if 
 these be not very remote, we may assume that the variation of the 
 observed force at each from its mean amount is the same as that 
 observed at the same time at the fixed station. Unhappily these 
 means of freeing the results from the admixture of what may be 
 called accidental phenomena have not been attended to in the 
 following, or indeed in any similar series of observations, and 
 there is reason to believe that the errors due to this cause are the 
 largest in amount of any by which the present series is affected. 
 
 The amount of these fluctuations, from day to day, may be 
 judged of from the following specimen of a series of observations 
 such as that alluded to, commenced by Captain Sabine in the 
 month of June, 1835. The apparatus in which the needle was 
 vibrated was unmoved during the continuation of the series, and 
 the needle remained permanently suspended. The height of the 
 barometer was noted, as well as the temperature ; the hour of 
 observation was, nearly, 10 A. M. 
 
 Time 0/200 Vibrations of a Standard Needle. 
 
 Date. 
 
 Barom. 
 
 Therm. 
 
 Time. 
 
 June 15, 
 
 Inch. 
 30-260 
 
 66-0 
 
 1139-60 
 
 16, 
 
 30-268 
 
 64-5 
 
 1138-20 
 
 17, 
 
 30-188 
 
 62-0 
 
 1138-27 
 
 18, 
 
 30-188 
 
 61-0 
 
 1135-87 
 
 19, 
 
 30-200 
 
 59-0 
 
 1136-67 
 
 20, 
 
 30-080 
 
 62-0 
 
 1135-93 
 
 21, 
 
 
 62-0 
 
 1137-67 
 
 22, 
 
 29-640 
 
 61-0 
 
 1138-53 
 
 23, 
 
 29-682 
 
 59-0 
 
 1138-40 
 
 24, 
 
 29-360 
 
 57-5 
 
 1137-80 
 
 25, 
 
 29-850 
 
 57-0 
 
 1136-87 
 
 26, 
 
 29-580 
 
 57-0 
 
 1136-70 
 
 27, 
 
 30-165 
 
 57-0 
 
 1137-13 
 
 29, 
 
 30-120 
 
 59-0 
 
 1137-80 
 
 30, 
 
 29-820 
 
 58-0 
 
 1137-73 
 
 July 2, 
 
 29-900 
 
 62-0 
 
 1137-30 
 
 4, 
 
 29-850 
 
 60-5 
 
 111*71 
 
 5, 
 
 29-650 
 
 60-0 
 
 1135K>;5 
 
 6, 
 
 30-000 
 
 58-5 
 
 1136-60 
 
 7, 
 
 29-850 
 
 59-0 
 
 1137-87
 
 176 OBSERVATIONS OF THE TERRESTRIAL 
 
 The mean time of 200 vibrations, deduced from these results, 
 is 1137"'66 at the temperature 60'6. But the time observed 
 on the 18th of June is 1135"'87 at 61-0 ; so that on this day 
 the rate of the needle was less than the mean by 1 s - 79, a difference 
 which corresponds to an increase of '003 in the horizontal force. 
 The observation of the 5th of July exhibits a difference somewhat 
 greater on the other side. 
 
 6. The last source of error which requires to be noticed under 
 this head is the change of the magnetic condition of the needles 
 employed. Independently of the derangements of magnetic 
 equilibrium induced by the presence of iron, or other disturbing 
 causes, it is well known that most needles lose something of their 
 original force. This loss is greatest at first; and the needle, if 
 originally well tempered and then magnetized to saturation, is 
 usually found to arrive at a nearly settled state in about a year. 
 Most of the cylinders employed in the following observations 
 seem to have reached that condition ; and the changes of mag- 
 netic state which they have exhibited are, except in the case of 
 Cyl. S (b), unimportant. In order to detect any such changes, 
 and to correct for them if they arise, it is necessary to observe at 
 the place chosen as the base of reference, at the termination of 
 each series of observations, as well as at their commencement. 
 If it is then found that the needle has lost any small portion of 
 its force, or if the time of vibration has augmented, the amount 
 of the correction due to each result may be found by assuming 
 the change to have been regular, or proportional to the time elapsed. 
 When the loss is very small, however (as was the case in the obser- 
 vations which form the subject of this paper), the correction may 
 be disregarded, provided we take as the time of vibration at the 
 base of reference the mean of the times observed at the commence- 
 ment and end of the series. 
 
 The needles used in the present series are the cylinders L (a], 
 L (ft), made by Dollond, and belonging to Mr. Lloyd ; cylinder 
 S (b) belonging to Captain Sabine, and cylinders E (e) and B, (d) 
 in the possession of Captain James Boss. All the circumstances 
 of the observations are given in the annexed Table. The first, 
 second, and third columns contain time place, day of the month, and 
 hour of the observation. In the fourth column is set down the 
 observed time of 100 vibrations, or the immediate result of obser- 
 vation divided by 3. The fifth column contains the terminal an;
 
 MAGNETIC FORCE IN IRELAND. 177 
 
 the initial arc being in all cases 20. In the sixth column is given 
 the chronometer's rate ; in the seventh the temperature ; and in the 
 eighth the deduced or corrected time. The hour, set down in the 
 third column as the hour of observation , is the mean of the com- 
 mencement and end ; and the recorded temperature is also the 
 mean of those observed at the beginning and end of the observation. 
 It will appear from the preceding that the corrections employed in 
 deducing the corrected from the observed times are those due to 
 temperature and to the rate of the chronometer. 
 
 In addition to the observations which follow there were others 
 of an earlier date, made for the purpose of comparing the hori- 
 zontal intensity at Dublin and Limerick, the two stations with 
 which all the other places in Ireland have been immediately com- 
 pared. In the observations alluded to, the rate of cylinder S (b] 
 was observed in the Philosophy School, Trinity College ; and the 
 local attraction of the building was determined by subsequent 
 comparisons of the force there with that in the garden of Trinity 
 College, the place which was afterwards selected for all the Dublin 
 observations. These earlier comparisons, as well as some other 
 imperfect ones obtained previously to the autumn of 1834 with 
 two other cylinders, have not been included in the annexed Tables ; 
 partly because the needles employed do not seem to be as trust- 
 worthy as the rest, but chiefly because of the uncertainties of the 
 double comparison which they involve.
 
 178 
 
 OBSERVATIONS OF THE TERRESTRIAL 
 
 TABLE I. 
 Time of Vibration of Cylinder S (b)*. 
 
 Place,! 
 
 Date. 
 
 Hour. 
 
 Time. 
 
 Arc. 
 
 Rate. 
 
 Temp. 
 
 Corr. 
 Time. 
 
 
 
 h. m. 
 
 8. 
 
 
 s. 
 
 
 s. 
 
 Limerick, . 
 
 July 23, 
 
 1 44 
 
 400-23 
 
 *=w 
 
 0-0 
 
 66-0 
 
 399-82 
 
 
 >) >> 
 
 2 14 
 
 400-33 
 
 P 8- 
 
 
 
 67-0 
 
 399-85 
 
 
 25, 
 
 12 20 
 
 401-19 
 
 EL<3 
 
 
 
 62-5 
 
 401-02 
 
 
 
 12 50 
 
 400-77 
 
 CO 
 
 
 
 61-5 
 
 400-67 
 
 
 "Mean, 
 
 
 
 400-63 
 
 __ 
 
 
 
 64-2 
 
 400-34 
 
 London, . . 
 
 Aug. 20, 
 
 11 22 
 
 390-14 
 
 3-0 
 
 -0-3 
 
 65-0 
 
 389-81 
 
 
 
 
 11 46 
 
 390-08 
 
 3-0 
 
 
 
 66-2 
 
 389-67 
 
 
 > 5> 
 
 12 44 
 
 390-34 
 
 2-5 
 
 
 
 66-0 
 
 389-94 
 
 
 , 21, 
 
 10 58 
 
 389-98 
 
 2-5 
 
 
 
 62-7 
 
 389-80 
 
 
 
 11 29 
 
 389-88 
 
 3-0 
 
 
 
 63-0 
 
 389-68 
 
 
 , 
 
 12 
 
 389-70 
 
 2-8 
 
 
 
 62-5 
 
 389-53 
 
 
 > 
 
 12 31 
 
 389-78 
 
 3-0 
 
 
 
 62-0 
 
 389-65 
 
 
 , 22, 
 
 10 47 
 
 390-18 
 
 2-5 
 
 
 
 63-0 
 
 389 '98 
 
 
 
 11 17 
 
 389-93 
 
 3-0 
 
 
 
 62-5 
 
 389-76 
 
 
 > 
 
 11 47 
 
 389-82 
 
 3-0 
 
 
 
 61-0 
 
 389-75 
 
 
 > >? 
 
 12 33 
 
 389-76 
 
 3-0 
 
 
 
 61-5 
 
 389-66 
 
 
 i 23, 
 
 10 57 
 
 389-76 
 
 2-5 
 
 
 
 60-5 
 
 389-73 
 
 
 > 
 
 11 37 
 
 389-78 
 
 3-0 
 
 
 
 60-5 
 
 389-75 
 
 
 > ,, 
 
 12 13 
 
 389-37 
 
 3-0 
 
 
 
 60-5 
 
 389-34 
 
 
 , ,, 
 
 12 45 
 
 389-32 
 
 3-0 
 
 
 
 61-0 
 
 389-25 
 
 
 27, 
 
 10 27 
 
 389-50 
 
 2-8 
 
 ' 
 
 57-0 
 
 389-70 
 
 
 , )? 
 
 11 2 
 
 389-33 
 
 2-5 
 
 
 
 57-5 
 
 389-50 
 
 
 , ,, 
 
 11 36 
 
 389-30 
 
 2-5 
 
 
 
 56.5 
 
 389-53 
 
 
 , 
 
 12 13 
 
 389-43 
 
 3-0 
 
 
 
 57-0 
 
 389-63 
 
 
 , 
 
 12 49 
 
 389-43 
 
 3-0 
 
 
 
 57-0 
 
 389-63 
 
 Limerick, 
 Ballybunan, . 
 Glengariff, . 
 Killarney, 
 LimericK, 
 Tulla, . . . 
 Templemore, 
 
 Mean, 
 Sept. 9, 
 16, 
 27, 
 Oct. 4, 
 9, 
 
 M 12, 
 
 >, 17, 
 
 12 17 
 5 20 
 11 20 
 11 40 
 12 43 
 8 50 
 8 36 
 
 389-74 
 403-70 
 404-29 
 402-55 
 403-93 
 404-56 
 404-16 
 395-82 
 
 I Between 
 2 and 3. 
 
 0-0 
 
 61-2 
 61-0 
 62-0 
 66-0 
 65-5 
 53-5 
 52-0 
 51-jQ 
 
 389-66 
 403-63 
 404-15 
 402-14 
 403-56 
 405-01 
 404-70 
 396-43 
 
 * The observations in London were made by Captain James Ross ; all the others 
 with this needle by Captain Sabine. 
 
 t Limerick, garden at Somerville, one mile from town. London, Regent's Park. 
 Ballybunan, field adjoining the innGlengarifl; Mr. E cles' 8 garden.-Killarney, 
 Mueros8 demesne.-Tulla, Kiltanon, Mr. Molony's garden.- Templemore, Sir B. 
 Gardens grounds; local attraction suspected. -Clonmel, Darling Hill, garden adjoin- 
 ing the house. Fermoy, field near the river.
 
 MAGNETIC FORCE IN IRELAND. 
 
 179 
 
 TABLE I. (Continued.) 
 
 Place. 
 
 Date. 
 
 Hour. Time. 
 
 Arc. 
 
 Rate. 
 
 Temp. 
 
 Corn 
 Time. 
 
 
 h. m. 
 
 s. 
 
 
 8. 
 
 
 g 
 
 Clomnel, . . 
 
 Oct. 19, ! 9 
 
 402-16 
 
 ^W 
 
 0-0 
 
 55-0 
 
 402 : 50 
 
 Limerick,. . ,, 29, 
 
 12 6 
 
 404-16 
 
 1 
 
 
 55-5 
 
 404-47 
 
 Fermoy, . . Dec. 2, 
 
 3 45 
 
 399-93 
 
 s-i 
 
 
 
 48-0 
 
 400-75 
 
 Limerick,. . ,, 10, ! 2 45 
 
 402-67 
 
 ?3 
 
 
 
 42-0 
 
 403-89 
 
 London, . . July 4,1 2 43 
 
 402-36 
 
 1-0 
 
 
 
 70-0 
 
 401-68 
 
 
 3 14 
 
 402-38 
 
 1-5 
 
 
 
 71-0 
 
 401-63 
 
 
 ,, 5, 9 54 
 
 401-84 
 
 1-0 
 
 
 
 62-0 
 
 401-70 
 
 
 10 21 
 
 401-73 
 
 1-5 
 
 
 
 64-0 
 
 401-46 
 
 
 | 11 13 
 
 401-02 
 
 2-0 
 
 
 
 60-0 
 
 401-02 
 
 
 55 55 
 
 11 46 
 
 401-50 
 
 1-5 
 
 
 
 62-0 
 
 401-36 
 
 
 55 55 
 
 4 48 
 
 401-74 
 
 1-5 
 
 
 
 64-0 
 
 401-47 
 
 
 6, 
 
 9 53 
 
 401-36 
 
 2-0 
 
 
 
 65-0 
 
 401-02 
 
 
 
 10 30 
 
 401-96 
 
 2-0 
 
 - 68-0 
 
 401-42 
 
 
 55 7, 
 
 9 32 
 
 400-96 
 
 2-0 
 
 
 
 60-0 
 
 400-96 
 
 
 5> 55 
 
 10 6 
 
 401-09 
 
 1-5 
 
 
 
 62-0 
 
 400-95 
 
 
 
 10 43 
 
 401-53 
 
 1-5 
 
 
 
 64-0 
 
 401-26 
 
 Mean. 
 
 
 
 401-62 
 
 
 
 
 
 64-3 
 
 401-33 
 
 Limerick, . . 
 
 July 27,- 
 
 4 
 
 413-54 
 
 
 
 -12- 
 
 76-2 
 
 412-41 
 
 
 ,5 28, 
 
 11 58 
 
 412-83 
 
 
 
 
 
 66-8 
 
 412-35 
 
 
 Mean, 
 
 
 
 413-18 
 
 
 
 
 
 71-5 
 
 412-38 
 
 Time of Vibration of Cylinder L (a)* 
 
 Place.t 
 
 Date. 
 
 Hour. 
 
 Time. 
 
 Arc. 
 
 Rate. 
 
 Temp. 
 
 Corr. 
 Time. 
 
 
 
 h. m. 
 
 s. 
 
 
 s. 
 
 
 8. 
 
 Limerick, . . 
 
 Sept. 9, 
 
 1 23 
 
 243-26 
 
 
 
 0-0 
 
 60-0 
 
 243-26 
 
 Ballybunan, . 
 
 17, 
 
 10 35 
 
 243-87 
 
 
 
 
 
 63-0 
 
 243-69 
 
 Glengariif, .[ ' 21, 
 
 12 
 
 242-29 
 
 
 
 
 
 68-0 
 
 241-80 
 
 Killarney, . \ Oct. 4, 
 
 12 15 
 
 242-46 
 
 
 
 
 
 66-0 
 
 242-09 
 
 Limerick,. . 8, 
 
 1 14 
 
 243-16 
 
 4-0 
 
 f!5- 
 
 62-0 
 
 243-00 
 
 Dublin, . . ,, 10, 
 
 2 31 
 
 243-71 
 
 3-0 
 
 f 1- 
 
 55-2 
 
 244-00 
 
 
 99 99 
 
 2 50 
 
 243-81 
 
 3-5 
 
 
 
 55-0 
 
 244-11 
 
 
 H, 
 
 2 4 
 
 243-52 
 
 3-5 
 
 
 
 59-0 
 
 243-ijS 
 
 
 Mean. 
 
 
 243-68 
 
 
 
 
 56-4 
 
 243-90 
 
 Armagh, , . : ,, 14^ 
 
 2 22 
 
 246-23 
 
 3-5 
 
 
 
 49-5 
 
 246-88 
 
 15. 
 
 2 16 
 
 246-30 
 
 4-0 
 
 
 
 ,-,0-7 
 
 246-87 
 
 
 Mean, 
 
 
 246-26 
 
 1 
 
 
 
 50-1 
 
 246-88 
 
 * The first five observations, and those of December 19, 21, 23, 1835, were made 
 by Captain Sabine. All the others with this needle by Mr. Lloyd. 
 
 t Dublin, Provost's garden, Trinity College. Armagh, grounds of the obser- 
 eld near the barracks. Strabcme, an open field adjoining the
 
 180 
 
 OBSERVATIONS OF THE TERRESTRIAL 
 
 TABLE I. (Continued.} 
 
 Place. 
 
 Date. 
 
 Hour. 
 
 Time. 
 
 Arc. 
 
 Rate. 
 
 Temp. 
 
 Corr. 
 Time. 
 
 Cam, . . . 
 
 Oct. 21, 
 
 h. m. 
 2 57 
 
 247-49 
 
 2-5 
 
 s. 
 + 2-0 
 
 50-2 
 
 a. 
 248-10 
 
 Strabane, . . 
 
 23, 
 
 1 22 
 
 248-00 
 
 2-5 
 
 
 
 51-8 
 
 248-51 
 
 Enniskillcn, . 
 
 ,, 24, 
 
 3 45 
 
 247-09 
 
 3-5 
 
 
 
 38-5 
 
 248-42 
 
 Dublin, . . 
 
 25, 
 
 3 24 
 
 243-14 
 
 4-0 
 
 
 
 45-7 
 
 244-01 
 
 
 >, 28, 
 
 3 
 
 243-39 
 
 3-5 
 
 
 
 53-0 
 
 243-82 
 
 
 > 
 
 3 26 
 
 243-49 
 
 4-5 
 
 
 
 53-0 
 
 243-92 
 
 
 Mean, 
 
 
 
 243-34 
 
 
 
 . 
 
 50-6 
 
 243-92 
 
 Dublin, 
 
 Aug. 19, 
 
 2 39 
 
 243-81 
 
 3-0 
 
 + 7-3 
 
 72-0 
 
 243-06 
 
 Markree, . . 
 
 . 21, 
 
 2 35 
 
 249-30 
 
 3-5 
 
 
 69-2 
 
 248-71 
 
 Ballina, . . 
 
 22, 
 
 3 2 
 
 249-90 
 
 2-0 
 
 . . 
 
 71-5 
 
 249-16 
 
 Belmullet, . 
 
 24, 
 
 1 50 
 
 250-40 
 
 1-5 
 
 
 
 69-5 
 
 249-79 
 
 Achill Ferry, 
 
 25, 
 
 12 
 
 249-35 
 
 2-0 
 
 
 
 69-2 
 
 248-76 
 
 Leenan, . " . 
 
 ,, 26, 
 
 3 58 
 
 248-19 
 
 2-0 
 
 . 
 
 59-8 
 
 248-18 
 
 Oughterard, . 
 
 27, 
 
 3 16 
 
 246-06 
 
 4-0 
 
 . 
 
 57-5 
 
 246-19 
 
 Ennis, . . . 
 
 28, 
 
 3 42 
 
 244-44 
 
 2-0 
 
 . 
 
 75-2 
 
 243-49 
 
 Limerick, . . 
 
 29, 
 
 2 52 
 
 243-45 
 
 3.-5 
 
 . 
 
 67-8 
 
 242-96 
 
 Cork, . . . 
 
 ,, 31, 
 
 1 46 
 
 241-50 
 
 2-5 
 
 . 
 
 69-5 
 
 240-90 
 
 Waterford, . 
 
 Sept. 1, 
 
 1 55 
 
 242-48 
 
 2-0 
 
 . 
 
 69-0 
 
 241-92 
 
 Broadway, . 
 
 2, 
 
 3 15 
 
 241-24 
 
 2-0 
 
 . 
 
 66-5 
 
 240-83 
 
 
 
 
 3 35 
 
 241-26 
 
 2-5 
 
 
 
 66-2 
 
 240-87 
 
 
 Mean, 
 
 
 
 241-25 
 
 
 
 
 66-4 
 
 240-85 
 
 Rathdrum, . 
 
 Sept. 3, 
 
 4 8 
 
 243-47 
 
 3-5 
 
 . 
 
 63-0 
 
 243-27 
 
 Dublin, . . 
 
 12, 
 
 5 5 
 
 243-70 
 
 4-0 
 
 ^6-0 
 
 57-8 
 
 243-81 
 
 
 14, 
 
 2 29 
 
 243-92 
 
 4-0 
 
 
 
 60-2 
 
 243-89 
 
 
 15, 
 
 2 36 
 
 243-14 
 
 2-5 
 
 
 
 63-8 
 
 242-89 
 
 
 >> 
 
 3 2 
 
 243-73 
 
 3-0 
 
 
 
 63-5 
 
 243-50 
 
 
 Mean, 
 
 
 
 243-62 
 
 
 
 
 61-3 
 
 243-52 
 
 London, . . 
 
 Sept. 19, 
 
 11 48 
 
 236-51 
 
 3-0 
 
 
 
 68-6 
 
 235-98 
 
 
 ,, ?) 
 
 2 44 
 
 236-65 
 
 2-0 
 
 
 
 69-4 
 
 236-07 
 
 
 i, 22, 
 
 12 43 
 
 236-63 
 
 3-5 
 
 . 
 
 72-2 
 
 235-89 
 
 
 Mean, 
 
 ~~ 
 
 236-60 
 
 i 
 
 
 
 70-1 
 
 235-98 
 
 town. Enniskillen, field near town. Markree, demesne of the castle, part surrounded 
 nib tall trees. Ballina, open field near town ; no shelter from sun. Belmullet, on 
 the beach, at extremity of Broadhaven. Achill Ferry, on the beach, near ferry. 
 Leenan, field at extremity of Killery harbour.-Oughterard, in a wood near the 
 menEmus, open field near town. Limerick, garden at Somerville. Cork, demesne 
 e banks of river, between Cork and Blackrock. Waterford, demesne adjoining 
 Denver, side opposite town.-Broadway, open field.-Rathdrum, demesne of Avon- 
 dale ; deep wood London, Westbourne Green, Harrow Road.
 
 MAGNETIC FORCE IN IRELAND. 
 
 181 
 
 TABLE I. (Continued.} 
 
 Place. 
 
 Date. 
 
 Hour. 
 
 Time. 
 
 Arc. 
 
 Rate. 
 
 Temp. 
 
 Corr. 
 
 Time. 
 
 
 
 h. in. 
 
 8. 
 
 
 s. 
 
 
 8. 
 
 London, . . 
 
 Oct. 23, 
 
 1 18 
 
 235-09 
 
 3-0 
 
 + 7-8 
 
 52-4 
 
 235-52 
 
 
 24, 
 
 11 45 
 
 235-05 
 
 3-0 
 
 
 54-5 
 
 235-35 
 
 
 ? J ?J 
 
 2 23 
 
 235-12 
 
 3-5 
 
 
 
 55-0 
 
 235-39 
 
 
 Mean, 
 
 
 
 235-09 
 
 
 
 
 54-0 
 
 235-42 
 
 Dublin, . . 
 
 Xov. o, 
 
 1 46 
 
 243-18 
 
 3-0 
 
 
 
 54-2 
 
 243-51 
 
 
 ,, 6, 
 
 12 21 
 
 243-35 
 
 3-0 
 
 
 
 48-0 
 
 244-06 
 
 
 5 j M 
 
 1 55 
 
 243-37 
 
 3-5 
 
 
 
 48-7 
 
 244-04 
 
 
 Mean, 
 
 
 
 243-30 
 
 
 
 
 50-3 
 
 243-87 
 
 Limerick, . 
 
 Dec. 19, 
 
 11 40 
 
 243-03 
 
 
 
 + 4-0 
 
 45-5 
 
 243-90 
 
 
 21, 
 
 12 19 
 
 242-36 
 
 
 
 
 
 36-0 
 
 243-81 
 
 
 ii 23, 
 
 11 17 
 
 242-68 
 
 
 
 
 
 33-0 
 
 244-32 
 
 
 Mean, 
 
 
 
 242-69 
 
 
 
 
 
 38-2 
 
 244-01 
 
 Dublin, . . 
 
 Dec. 29, 
 
 1 31 
 
 243-22 
 
 4-0 
 
 -f 5-5 
 
 47-6 
 
 243-96 
 
 
 
 
 1 52 
 
 243-18 
 
 4-0 
 
 
 
 47-0 
 
 243-95 
 
 
 Mean, 
 
 
 
 243-20 
 
 
 
 
 
 47-3 
 
 243-95 
 
 Dublin, . . 
 
 Jan. 11, 
 
 11 21 
 
 242-67 
 
 3-0 
 
 
 
 33-8 
 
 244-24 
 
 
 >> >i 
 
 11 44 
 
 242-48 
 
 4-0 
 
 
 
 34-0 
 
 244-03 
 
 
 ii 12 > 
 
 10 12 
 
 242-86 
 
 2-0 
 
 
 
 33-8 
 
 244-43 
 
 
 Mean, 
 
 
 
 242-67 
 
 
 
 
 
 33-9 
 
 244-23 
 
 Time of Vibration of Cylinder L (b)* 
 
 Place. t 
 
 Date. 
 
 Hour. 
 
 Time. 
 
 Arc. 
 
 Rate. 
 
 Temp. 
 
 Corr. 
 Time. 
 
 
 
 h. m. 
 
 8. 
 
 
 s. 
 
 
 8. 
 
 Limerick, . 
 
 Sept. 9, 
 
 2 14 
 
 292-55 
 
 _ 
 
 0-0 
 
 60-2 
 
 292-54 
 
 Ballybunan, . 
 
 >i l"t 
 
 10 3 
 
 292-25 
 
 
 
 
 
 62-0 
 
 292-10 
 
 Glengariff, . 
 K'ilhirney, . 
 Limerick, 
 
 ,, 27, 
 Oct. 4, 
 
 8. 
 
 12 24 
 12 38 
 1 38 
 
 293*16 
 
 292-15 
 292-51 
 
 4-0 
 
 + 15- 
 
 68-0 
 68-0 
 (52-0 
 
 292-57 
 291-57 
 292-31 
 
 ' 
 
 2 o 
 
 292-92 
 
 4-0 
 
 
 
 82*0 
 
 292-72 
 
 "Mean, 
 
 
 292*72 
 
 
 
 
 
 152-u 
 
 292-52 
 
 Dublin, . . Oct. 11, 
 
 1 34 
 
 292-H2 
 
 1-5 
 
 + 1-0 
 
 62-5 
 
 292-63 
 
 
 2 50 
 
 292-73 
 
 2-5 
 
 
 
 
 292-84 
 
 
 Mean, 
 
 
 292-78 
 
 
 
 
 MM 
 
 292*74 
 
 C:.i-l in-ford,. 
 Aniia-h, . . 
 
 Oct. 13, 
 
 ,: 14, 
 i, 13, 
 
 1 45 
 1 M 
 1 45 
 
 294*60 
 
 29-VN9 
 29.V70 
 
 3-0 
 2-5 
 3-0 
 
 
 
 .VK-, 
 51-0 
 52-fi 
 
 294-69 
 296*66 
 
 2! I'-'-'' 
 
 
 Mean, 
 
 
 296*80 
 
 
 
 
 51-8 
 
 296-40 
 
 * First six observations, and those of 21st and 23rd of D"ecember, 1835, were made 
 by Captain Sabine : all the others with this needle by Mr. Lloyd. 
 
 t Carlingford, open field east of town. Coleraine, demesne adjoining th 
 spot near river surrounded by tall trees ; local attraction apparently due to basalt.
 
 182 
 
 OBSERVATIONS OF THE TERRESTRIAL 
 
 TABLE I. (Continued.} 
 
 Place. 
 
 Date. 
 
 Hour. 
 
 Time. 
 
 Arc. 
 
 Rate. 
 
 Temp. 
 
 Corfl 
 Time. 
 
 
 
 h. m. 
 
 s. 
 
 
 8. 
 
 
 s. 
 
 Coleraine, . 
 
 Oct. 18, 
 
 4 3 
 
 293-64 
 
 3-0 
 
 + 2-0 
 
 47-5 
 
 294-55 
 
 
 >i 20, 
 
 12 44 
 
 294-61 
 
 3-0 
 
 . 
 
 57-6 
 
 294-78 
 
 
 Mean, 
 
 
 
 294-12 
 
 
 
 
 
 52-5 
 
 294-66 
 
 Cam, . . . 
 
 Oct. 21, 
 
 2 28 
 
 297-07 
 
 2-0 
 
 . 
 
 51-2 
 
 297-71 
 
 Strabane, 
 
 23, 
 
 12 57 
 
 297-60 
 
 2-5 
 
 
 
 51-5 
 
 298-22 
 
 Enniskillen, . 
 
 24, 
 
 3 14 
 
 296-50 
 
 3-0 
 
 
 
 42-0 
 
 297-83 
 
 Dublin, . . 
 
 25, 
 
 4 
 
 292-70 
 
 3-0 
 
 __ 
 
 46-8 
 
 293-66 
 
 
 i> 28, 
 
 2 36 
 
 293-14 
 
 3-5 
 
 
 
 54-0 
 
 293-57 
 
 
 Mean, 
 
 
 
 292-92 
 
 _ 
 
 
 
 50-4 
 
 293-62 
 
 Dublin, . . 
 
 Aug. 19, 
 
 3 3 
 
 293-70 
 
 2-0 
 
 + 7-3 
 
 72-0 
 
 292-80 
 
 Markree, . . 
 
 21, 
 
 12 45 
 
 300-14 
 
 2-0 
 
 
 66-8 
 
 299-60 
 
 
 ) J 5 j 
 
 1 57 
 
 300-84 
 
 2-0 
 
 . . 
 
 72-0 
 
 299-91 
 
 
 Mean, 
 
 
 
 300-49 
 
 
 
 
 
 69-4 
 
 299-75 
 
 Ballina, . . 
 
 Aug. 22, 
 
 2 29 
 
 301-75 
 
 ins. 
 
 
 
 75-7 
 
 300-53 
 
 Belmullet, . 
 
 24, 
 
 12 26 
 
 302-23 
 
 1-0 
 
 
 
 65*5 
 
 301-78 
 
 
 
 1 15 
 
 301-98 
 
 1-0 
 
 
 
 69-0 
 
 301-27 
 
 
 "Mean, 
 
 
 
 302-10 
 
 
 
 
 
 67-2 
 
 301-52 
 
 Achill Ferry, ! Aug. 25 j 
 
 1 35 
 
 300-61 
 
 1-5 
 
 
 
 68-0 
 
 299-98 
 
 Leenan, . 1 ,, 26, 
 
 3 32 
 
 298-65 
 
 1-5 
 
 
 
 59-5 
 
 298-66 
 
 Oughterarcl, 
 
 27, 
 
 2 53 
 
 296-34 
 
 3-0 
 
 
 
 58-2 
 
 296-44 
 
 Ennis, . . 
 
 28, 
 
 3 18 
 
 294-61 
 
 1-5 
 
 
 
 74-5 
 
 293-52 
 
 Limerick, . 
 
 i, 29, 
 
 2 26 
 
 292-97 
 
 2-5 
 
 
 
 67-8 
 
 292-38 
 
 j Cork, . . . 
 Waterford, . 
 
 ii 31, 
 Sept. 1, 
 
 1 11 
 
 1 29 
 
 289-58 
 292-13 
 
 l-o 
 1-5 
 
 
 
 68-2 
 68-2 
 
 288-97 
 291-51 
 
 Broadway, . 
 Rathdrum, . 
 
 2, 
 ,, 3, 
 
 2 46 
 3 42 
 
 290-21 
 292-95 
 
 1-5 
 3-0 
 
 
 
 67-5 
 63-5 
 
 289-64 
 292-67 
 
 Dublin, . . 
 
 ii 12, 
 
 4 41 
 
 293-16 
 
 3-0 
 
 + 6-0 
 
 58-2 
 
 293-27 
 
 
 ii 14, 
 
 2 3 
 
 293-47 
 
 3-5 
 
 
 
 61-0 
 
 293-38 
 
 
 15, 
 
 2 9 
 
 293-62 
 
 2-5 
 
 
 
 64-5 
 
 293-27 
 
 
 Mean, 
 
 
 
 293-42 
 
 
 
 
 61'2 
 
 293-31 
 
 London, . . 
 
 Sept. 19, 
 
 11 20 
 
 284-46 
 
 2-0 
 
 . 
 
 69-0 
 
 283-80 
 
 
 > 
 
 3 19 
 
 284-51 
 
 2-5 
 
 . 
 
 66-2 
 
 284-05 
 
 
 ,i 22, 
 
 12 17 
 
 285-03 
 
 3-0 
 
 
 
 71-8 
 
 284-17 
 
 London, . . 
 
 Mean, 
 Oct. 23, 
 
 12 53 
 
 284-67 
 282-65 
 
 2-5 
 
 + 7-8 
 
 69-0 
 52-2 
 
 284-01 
 283-17 
 
 
 24, 
 
 12 12 
 
 282-76 
 
 2-5 
 
 
 52-8 
 
 283-24 
 
 
 
 
 12 33 
 
 282-84 
 
 3-0 
 
 . 
 
 53-0 
 
 283-31 
 
 
 ,, ,, 
 
 1 57 
 
 282-34 
 
 3-0 
 
 
 
 54-2 
 
 282-72 
 
 Dublin, . . 
 
 Mean, 
 Nov. 5, 
 
 1 19 
 
 282-65 
 292-61 
 
 2-5 
 
 
 
 53-0 
 55-0 
 
 283-11 
 292-95 
 
 
 ,, 6, 
 
 11 55 
 
 292-59 
 
 2-0 
 
 . 
 
 48-8 
 
 293-38 
 
 
 "nf " 
 
 2 23 
 
 292-67 
 
 3-0 
 
 
 
 48-4 
 
 293-49 
 
 
 Mean, 
 
 
 292-62 
 
 
 
 
 
 50-7 
 
 293-27
 
 MAGNETIC FORCE IN IRELAND. 
 TABLE I. (Continued.} 
 
 183 
 
 Place. 
 
 Date. 
 
 Hour. 
 
 Time. 
 
 Arc. 
 
 Rate. 
 
 Temp. 
 
 Corr. 
 Time. 
 
 
 
 h. m. 
 
 8. 
 
 
 8. 
 
 
 8. 
 
 Limerick, . 
 
 Dec. 21, 
 
 1 6 
 
 291-10 
 
 
 
 + 4-0 
 
 36-0 
 
 292-84 
 
 
 i. 
 
 1 44 
 
 291-14 
 
 
 
 
 36-0 
 
 292-88 
 
 
 ,, 23, 
 
 11 53 
 
 291-49 
 
 
 
 
 33-2 
 
 293-44 
 
 
 Mean, 
 
 . 
 
 291-24 
 
 
 
 
 35-1 
 
 293-05 
 
 Dublin, . . 
 
 Dec. 29, 
 
 12 44 
 
 292-42 
 
 2-5 
 
 + 5-5 
 
 49-7 
 
 293-15 
 
 
 99 9) 
 
 1 8 
 
 292-19 
 
 2-5 
 
 
 
 47-8 
 
 293-06 
 
 
 Mean, 
 
 
 
 292-30 
 
 
 
 
 48-8 
 
 293-10 
 
 Dublin, . . 
 
 Jan. 11, 
 
 10 55 
 
 291-85 
 
 2-0 
 
 
 
 35-2 
 
 293-64 
 
 
 n 12, 
 
 10 37 
 
 291-81 
 
 2-0 
 
 
 
 32-5 
 
 293-80 
 
 
 Mean, 
 
 
 
 291-83 
 
 
 
 
 
 33-8 
 
 293-72 
 
 Time of Vibration of Cylinder E (c}* 
 
 Place, t 
 
 Date. 
 
 Hour. 
 
 Time. 
 
 Arc. 
 
 Rate. 
 
 Temp. 
 
 Corr. 
 Time. 
 
 London, . . 
 
 July 8, 
 
 h. m. 
 7 34 
 
 440-08 
 
 1-5 
 
 8. 
 
 + 1-4 
 
 58-0 
 
 8. 
 
 440-22 
 
 
 
 10 9 
 
 440-57 
 
 1-5 
 
 
 
 60-0 
 
 440-56 
 
 
 
 12 20 
 
 441-03 
 
 2-0 
 
 
 
 64-0 
 
 440-72 
 
 
 
 4 17 
 
 441-33 
 
 2-0 
 
 
 
 66-0 
 
 440-ss 
 
 
 n 9 ', 
 
 11 26 
 
 441-93 
 
 
 
 . 
 
 57-0 
 
 442-15 
 
 
 
 2 15 
 
 441-55 
 
 
 
 
 
 61-0 
 
 441-46 
 
 
 
 6 10 
 
 441-06 
 
 
 
 
 
 61-0 
 
 440-97 
 
 
 ' 10, 
 
 11 7 
 
 441-76 
 
 5 
 
 
 
 64-0 
 
 441-45 
 
 
 
 4 47 
 
 441-78 
 
 2 
 
 
 
 62-0 
 
 441-62 
 
 ! 14. 
 
 10 41 
 
 441-31 
 
 5 
 
 
 
 58-0 
 
 441-45 
 
 
 i 13, 
 
 6 51 
 
 440-97 
 
 5 
 
 
 
 64-0 441-42 
 
 
 
 11 11 
 
 443-26 
 
 
 
 
 
 66-0 
 
 442-81 
 
 
 ' " 
 
 2 31 
 
 443-40 
 
 5 
 
 
 
 70-0 
 
 442-64 
 
 
 
 8 24 
 
 440-86 
 
 5 
 
 
 
 55-0 
 
 441-J.i 
 
 
 r, is, 
 
 7 39 
 
 441-19 
 
 1-0 
 
 
 
 52-0 
 
 441-78 
 
 
 
 11 35 
 
 442-68 
 
 1-0 
 
 
 
 64-0 
 
 HJ-:;T 
 
 
 
 8 2 
 
 441-53 
 
 1-0 
 
 
 
 57-0 
 
 441-75 
 
 
 18, 
 
 10 14 
 
 443-32 
 
 1-0 
 
 
 
 65-0 
 
 442-93 
 
 
 II 19 > 
 
 7 35 
 
 441-00 
 
 1-5 
 
 
 
 48-0 
 
 441-89 
 
 
 Mean, 
 
 
 441-61 
 
 
 
 
 60-1 
 
 441-59 
 
 Limerick, 
 
 July 27, 
 
 3 57 
 
 453-31 
 
 1-5 
 
 + 1-2 
 
 r,s-.-, 
 
 452-65 
 
 
 28, 
 
 12 39 
 
 454-60 
 
 2-0 
 
 
 
 60-0 
 
 I.', I -.-,! 
 
 
 
 1 7 
 
 454-06 
 
 1-5 
 
 
 
 59-0 
 
 404*18 
 
 
 ,, ,, 
 i, 
 
 1 40 
 
 454-18 
 
 2-0 
 
 
 
 59-0 
 
 4.'. I -J.i 
 
 * Observed by Captain James Rosa. 
 
 t London, Westbourne Green, Harrow Road. Limerick, garden at Somerrille. 
 Dublin, Provost's Garden, Trinity College. Markree, demesne of Castle ; spot sur- 
 rounded by lofty trees.
 
 184 
 
 OBSERVATIONS OF THE TERRESTRIAL 
 
 TABLE I. (Continued.} 
 
 
 1 
 
 
 i 
 Prtw 
 
 Place. 
 
 Date. Hour. 
 
 Time. 
 
 Arc. 
 
 Rate. 
 
 Temp. 
 
 L-ori. 
 Time. 
 
 Limerick, . 
 
 July 28, 
 
 h. m. 
 2 19 
 2 49 
 
 s. 
 453-84 
 453-70 
 
 1-8 
 2-2 
 
 s. 
 + 1-2 
 
 60-0 
 59-0 
 
 453-83 
 453-77 
 
 
 " 
 
 3 22 
 
 453-82 
 
 2-0 
 
 
 
 60-0 
 
 453-81 
 
 
 !' 29 
 
 11 
 
 454-00 
 
 2-2 
 
 
 
 56-0 
 
 454-30 
 
 
 
 11 31 
 
 453-88 
 
 2-2 
 
 
 
 57-0 
 
 454-10 
 
 
 
 12 
 
 454-04 
 
 2-0 
 
 
 
 59-0 
 
 454-11 
 
 
 "Mean, 
 
 
 453-94 
 
 
 
 
 
 59-8 
 
 453-95 
 
 Dublin, . . 
 
 Aug. 16, 
 
 7 21 
 7 51 
 
 453-90 
 453-69 
 
 2-0 
 2-0 
 
 
 
 56-0 
 56-0 
 
 454-20 
 453-99 
 
 " 
 
 8 21 
 
 453-77 
 
 2-0 
 
 
 
 57-0 
 
 453-99 
 
 "Mean, 
 
 
 453-79 
 
 
 
 _ 
 
 56-3 
 
 454-06 
 
 Markree, . , Aug. 19, 
 
 8 3 
 10 
 
 464-39 
 465-17 
 
 1-8 
 2-0 
 
 
 
 54-0 
 58-0 
 
 464-85 
 465-32 
 
 
 
 10 30 
 
 465-02 
 
 2-0 
 
 
 
 58-0 
 
 465-17 
 
 
 "Mean, 
 
 
 
 464-86 
 
 
 
 
 
 56-7 
 
 465-11 
 
 London, . . 
 
 Aug. 30, 
 
 9 41 
 
 440-72 
 
 2-5 
 
 
 
 60-0 
 
 440-71 
 
 
 11 
 
 10 10 
 
 441-52 
 
 2-0 
 
 
 
 61-0 
 
 441-43 
 
 
 11 
 
 10 38 
 
 441-72 
 
 2-0 
 
 
 
 61-0 
 
 441-63 
 
 
 11 31, 
 
 9 33 
 
 440-86 
 
 2-0 
 
 
 
 55-0 
 
 441-23 
 
 
 
 11 9 
 
 441-41 
 
 2-0 
 
 
 
 58-0 
 
 441-55 
 
 
 99 99 
 
 12 37 
 
 442-04 
 
 2-0 
 
 
 
 58-0 
 
 442-18 
 
 
 Mean, 
 
 
 
 441-38 
 
 
 
 
 
 58-5 
 
 441-46 
 
 Time of Vibration of Cylinder E (d)* 
 
 Place. 
 
 Date. 
 
 Hour. 
 
 Time. 
 
 Arc. 
 
 Rate. 
 
 Temp. 
 
 Corr. 
 Time. 
 
 
 
 h. m. 
 
 8. 
 
 
 8. 
 
 
 s. 
 
 London, . . 
 
 July 19, 
 
 9 44 
 
 437-75 
 
 1-0 
 
 + 1-4 
 
 58-0 
 
 437-89 
 
 
 99 99 
 
 10 30 
 
 438-10 
 
 1-0 
 
 
 
 59-0 
 
 438-17 
 
 
 
 11 44 
 
 438-39 
 
 1-2 
 
 
 
 62-0 
 
 438-23 
 
 
 99 9J 
 
 1 31 
 
 438-30 
 
 1-0 
 
 
 
 64-0 
 
 438-00 
 
 
 
 3 6 
 
 439-18 
 
 1-0 
 
 
 
 66-0 
 
 438-72 
 
 
 ," 20, 
 
 7 19 
 
 438-55 
 
 1-0 
 
 
 
 60-0 
 
 438-54 
 
 
 
 9 54 
 
 439-26 
 
 1-0 
 
 
 
 61-0 
 
 439-18 
 
 
 9) M 
 
 10 39 
 
 440-06 
 
 1-0 
 
 . 
 
 63-0 
 
 439-82 
 
 Mean, 
 
 
 
 438-70 
 
 
 
 
 61-6 
 
 438-57 
 
 Limerick, . July 29, 
 
 1 18 
 
 449-17 
 
 2-0 
 
 + 1-2 
 
 60-0 
 
 449-16 
 
 ,, ,, 
 
 1 50 
 
 450-05 
 
 2-0 
 
 
 
 61-0 
 
 449-96 
 
 2 41 
 
 449-16 
 
 2-0 
 
 
 
 62-0 
 
 449-00 
 
 Observed by Captain James Ross.
 
 MAGNETIC FORCE IN IRELAND. 
 
 185 
 
 TABLE I. (Continued.} 
 
 Place. 
 
 Date. 
 
 Hour. 
 
 Time. 
 
 Arc. 
 
 Rate. 
 
 Temp. 
 
 Corr. 
 Time. 
 
 
 
 h. m. 
 
 8. 
 
 
 s. 
 
 
 S. 
 
 Limerick, 
 
 July 30, 
 
 10 41 
 
 449-89 
 
 2-0 
 
 -f 1-2 
 
 55-0 
 
 450-27 
 
 
 >> 
 
 11 10 
 
 449-89 
 
 2-0 
 
 
 
 56-0 
 
 450-19 
 
 
 )> 
 
 11 40 
 
 449-80 
 
 1-5 
 
 
 
 56-0 
 
 450-10 
 
 
 > 
 
 12 14 
 
 449-77 
 
 1-5 
 
 
 
 57-0 
 
 449-99 
 
 
 31, 
 
 11 29 
 
 449-70 
 
 2-0 
 
 
 
 54-0 
 
 450-15 
 
 
 > 
 
 11 58 
 
 449-76 
 
 2-0 
 
 
 
 56-0 
 
 450-06 
 
 
 ,, ,, 
 
 12 28 
 
 449-91 
 
 2-0 
 
 
 
 57-0 
 
 450-13 
 
 
 5> 
 
 12 58 
 
 449-92 
 
 2-0 
 
 58-0 
 
 450-06 
 
 
 Mean, 
 
 
 
 449-73 
 
 
 
 - 57-5 
 
 449-92 
 
 Dublin, . . 
 
 Aug. 14, 
 
 6 36 
 
 451-82 
 
 2-5 
 
 54-0 
 
 452-27 
 
 
 99 9> 
 
 7 5 
 
 451-62 
 
 3-0 
 
 . 54-0 
 
 452-07 
 
 
 ?) 99 
 
 7 35 
 
 451-61 
 
 3-0 
 
 
 55-0 
 
 451-99 
 
 
 Mean, 
 
 
 
 451-68 
 
 
 
 
 54-3 
 
 452-11 
 
 Markree, 
 
 Aug. 19, 
 
 11 40 
 
 462-19 
 
 2-5 
 
 _ 
 
 59-0 
 
 462-26 
 
 
 
 
 12 10 
 
 462-00 
 
 2-5 
 
 
 59-0 
 
 462-07 
 
 
 20 
 
 8 37 
 
 462-54 
 
 2-5 
 
 
 
 54-0 
 
 463-00 
 
 
 Mean, 
 
 
 
 462-24 
 
 
 
 
 
 57-3 
 
 462-44 
 
 London, . . 
 
 Aug. 28, 
 
 7 16 
 
 437-91 
 
 2-0 
 
 
 
 53-0 
 
 438-43 
 
 
 > 
 
 7 56 
 
 438-42 
 
 2-5 
 
 
 
 56-0 
 
 438-71 
 
 
 
 
 9 48 
 
 439-01 
 
 2-5 
 
 
 
 60-0 
 
 439-00 
 
 
 29, 
 
 9 31 
 
 439-43 
 
 2-0 
 
 
 
 60-0 
 
 439-42 
 
 
 99 99 
 
 10 13 
 
 439-52 
 
 2-0 
 
 
 
 60-0 
 
 439-51 
 
 
 99 99 
 
 10 42 
 
 439-60 
 
 2-5 
 
 
 
 63-0 
 
 439-36 
 
 
 Mean, 
 
 
 
 438-98 
 
 
 
 
 
 58-7 
 
 439-07 
 
 The computed results of the preceding observations are given in 
 Table II. The first and second columns contain the place and the 
 date of the observations ; the third the designation of the needle em- 
 ployed ; in the fourth column is given the mean time of 100 vibra- 
 tions, corrected for temperature and for the rate of the chronometer ; 
 and the fifth and sixth columns contain the computed values of the 
 horizontal intensity the numbers in the fifth column being the 
 ratios of the horizontal intensity at the place of observation to that 
 at the station of the observer, and those in the sixth being the 
 ratios of the same force to that at London, to which place all the 
 observations are ultimately referred. 
 
 If T denote the reduced time of 100 vibrations at any place, 
 and T' that at the station with which it is immediately compared,
 
 186 OBSERVATIONS OF THE TERRESTRIAL 
 
 and if h and h f be the horizontal intensities at the two places, the 
 numbers of the fifth column are computed from the formula 
 
 Again, if A, denote the horizontal intensity in London, the ratio 
 - will be determined in the same manner ; and, multiplying by 
 
 *' // 
 
 it the numbers in the fifth column, we obtain the values of , 
 
 or the ratios of the horizontal intensity at the places of observation 
 to that at London, as given in the sixth and last column. 
 
 The stations with which all the other places in Ireland are 
 immediately compared are Dublin and Limerick ; and it will at 
 once appear that, as the ratios of the horizontal force at these 
 stations to that at London enter as factors in all the final results, 
 much accuracy is required in their determination. For this pur- 
 pose we have three distinct series of observations. In the first and 
 second the intensities of the horizontal force in Dublin and Lime- 
 rick are directly compared with that in London ; and in the third 
 these intensities are compared together. The results of these com- 
 parisons, given in Table II., are here put together, so as to be 
 seen at one view. 
 
 I. Horizontal intensity in Dublin, the horizontal intensity in 
 London being unity. 
 
 July, Aug., 1835, . . Cyl. R (c). . . Int. = -9456 
 
 ii ,, . . R (d). . . -9421 
 
 September, 1835, . . L (a). . . -9390 
 
 , L (6). . . 9376 
 
 Oct., Nov., 1835, . . L (a). . . '9319 
 
 >i >i ii . . - L (6). . . -9319 
 
 Mean = -9380 
 
 II. Horizontal intensity in Limerick, the horizontal intensity 
 in London being unity. 
 
 July, Aug., Sept., 1834, Cyl. S (i). . . Int. = -9396 
 
 July, 1835, .... _ -9470 
 
 July, August, 1835, . _ R ( c ). . . _ .946! 
 
 >i ii - R (rf); . . -9513 
 
 Mean = -9460
 
 MAGNETIC FORCE IN IRELAND. 187 
 
 III' Horizontal intensity in Limerick, the horizontal intensity 
 in Dublin being unity. 
 
 Sept., Oct., 1834, . 
 
 . Cyl. L(a). 
 
 . . Int. = 
 
 1-0064 
 
 
 
 . - L (5). 
 
 . . 
 
 1-0044 
 
 July, Aug., 1835, 
 
 . . - E (c). 
 
 . . 
 
 1-0005 
 
 ?> 
 
 . - R (d). 
 
 . . 
 
 1-0098 
 
 Aug., Sept., 1835, 
 
 . ' . - L (a). 
 
 . . 
 
 1-0027 
 
 M 
 
 . - L (5). 
 
 . . 
 
 1-0047 
 
 Nov., Dec., 1835, . 
 
 . - L (a). 
 
 . . 
 
 1-0001 
 
 > 
 
 . - L (6). 
 
 . . 
 
 1-0021 
 
 
 
 Mean = 
 
 1-0038 
 
 If then x and y denote the horizontal intensities in Dublin and 
 Limerick, that in London being unity, observation gives 
 
 x = "9380, y = -9460, | = 1-0038, 
 
 and it is required to determine the most probable values of x and y. 
 To generalize this problem, let the mean results of observation be 
 a, b, c, and let their weights be A, B, C respectively ; so that we 
 have 
 
 x - a - 0, weight = A, 
 
 y - b = 0, J0, 
 
 a and b being approximate values of x and y, let their true values 
 be x = a -\- x, y = b + S y, 
 
 and let - = c . Then y - - *-^j- = c + a~ l (S y - c' Sar), the squares 
 
 a x a + Sx 
 
 and higher powers of the quantities S x and 8 y being neglected ; 
 so that the preceding equations may be written 
 
 I x = 0, 8 y = 0, rr 1 (8y - e,S*0 + ^ - c = 0. 
 
 These three equations are to be combined by the method of least 
 squares. "We find in this manner 
 
 A$x- Cc/r l (a~ l $y - e<ar l %x + c, - c) = 0, 
 
 -c =0;
 
 188 OBSERVATIONS OF THE TERRESTRIAL 
 
 from which we obtain, by elimination, 
 
 B 
 
 J ac ,( c ,- c ) a(c-c) 
 
 If the weights of the three results be regarded as equal, that 
 is, if A = B = (7, the preceding values become 
 
 To apply these results to the present case, we have 
 = -9380, b = -9460, e = 1-0038; 
 
 c=- =1-0085, c-c='Q047. 
 a 
 
 And introducing these values into the preceding expressions, we 
 find 
 
 so that the corrected values of x and y are 
 
 x = -9395, y = -9445.
 
 MAGNETIC FORCE IN IRELAND. 
 
 TABLE II. 
 Intensity of the Horizontal Force. 
 
 189 
 
 Place. 
 
 Date. 
 
 Cy 
 
 L 
 
 Time. 
 
 Intensity. 
 
 Intensity 
 Lond. = 1. 
 
 
 
 
 
 3. 
 
 
 
 Limerick, . 
 
 July 23, 25, 1834, 
 
 B( 
 
 >) 
 
 400-34 
 
 
 9396 
 
 
 Sept. 9, .... 
 
 
 
 403-63 
 
 
 
 London, . . 
 
 Aug. 20-27, . . 
 
 
 
 389-66 
 
 
 1-0000 
 
 Limerick, . 
 
 Sept. 9, Oct. 9, 29, 
 
 sT 
 
 n 
 
 404-37 
 
 1-0000 
 
 . -9445 
 
 
 Sept. 9, Oct. 8, 
 
 M 
 
 ii 
 
 243-13 
 
 1-0000 
 
 
 
 >i 
 
 M 
 
 M 
 
 292-53 
 
 1-0000 
 
 
 Ballvbunan, 
 
 Sept. 16, '. . . 
 
 8 
 
 ;) 
 
 404-15 
 
 1-0010 
 
 9443 
 
 
 ii 17, ... 
 
 M 
 
 o 
 
 243-69 
 
 9954 
 
 
 
 
 M 
 
 I) 
 
 292-10 
 
 1-0029 
 
 
 Glengariff, . 
 
 " 27, ... 
 
 s 
 
 
 
 402-14 
 
 1-0110 
 
 9513 
 
 
 99 9t 
 
 L 
 
 ') 
 
 241-80 
 
 1-0110 
 
 
 
 
 L 
 
 IV 
 
 292-57 
 
 9997 
 
 
 Killarney, . 
 
 Oct. 4, ... 
 
 S 
 
 rf 
 
 403-56 
 
 1-0039 
 
 9505 
 
 
 
 
 L 
 
 r O 
 
 242-09 
 
 1-0086 
 
 
 
 
 L( 
 
 n 
 
 291-57 
 
 1-0066 
 
 
 Tulla, . . 
 
 12, 
 
 S( 
 
 
 
 404-70 
 
 9983 
 
 9429 
 
 Templemore, 
 Clonmel, 
 
 17, ... 
 
 ii 19, 
 
 
 
 396-43 
 402-50 
 
 1-0404 
 1-0092 
 
 9827 
 9532 
 
 Fermoy, . . 
 
 Dec. 2, ... 
 
 
 
 400-75 
 
 1-0157 
 
 9593 
 
 Limerick, . 
 
 10, ... 
 
 
 
 403-89 
 
 1-0000 
 
 9445 
 
 Dublin, . . 
 
 Oct. 10, 11, .. 
 
 L 
 
 ") 
 
 243-90 
 
 1-0000 
 
 9395 
 
 
 ,, 25, 28, . . 
 
 
 
 243-92 
 
 
 
 
 ii Hi 
 
 L( 
 
 5) 
 
 292-74 
 
 1-0000 
 
 9395 
 
 
 ii 25, 28, . . 
 
 
 
 293-62 
 
 
 
 Limerick, . 
 
 Sept. 9, Oct. 8, 
 
 L ( 
 
 ") 
 
 243-13 
 
 1-0064 
 
 
 
 
 L 
 
 '0 
 
 292-53 
 
 1-0044 
 
 
 Carlingford, 
 
 Oet 13, "... 
 
 
 
 294-69 
 
 9898 
 
 9299 
 
 Armagh, 
 
 , 14,15, . . 
 
 L] 
 
 J] 
 
 246-88 
 296-40 
 
 9761 
 9784 
 
 9181 
 
 Coleraine, . 
 Cam, . . . 
 
 \ 18, 20, . . 
 , 21, ... 
 
 L 
 
 ") 
 
 294-66 
 248-10 
 
 9900 
 9665 
 
 9301 
 9096 
 
 
 
 L 
 
 /, 
 
 297-71 
 
 9698 
 
 
 Strabane, 
 
 ' 23, . . . 
 
 L 
 
 i 
 
 248-51 
 
 9633 
 
 9066 
 
 
 
 L 
 
 /, 
 
 298-22 
 
 9665 
 
 
 Enniskillen, 
 
 J 
 
 , 24, ... 
 
 L 
 
 i 
 
 248-42 
 
 9640 
 
 9081 
 
 
 
 L 
 
 i, 
 
 297-83 
 
 9690 
 
 
 London, . . 
 
 July 4^7, 1835, 
 July 8-19, . . 
 
 s 
 
 ( 
 
 >, 
 
 i 
 
 401-33 
 441-59 
 
 
 1-0000 
 1-0000 
 
 
 Aug. 30, 31, . . 
 July 19, 20, . . 
 
 R( 
 
 ') 
 
 441-46 
 438-57 
 
 
 1-0000 
 
 Limerick, . 
 
 Aug. 28, 29, . . 
 July 27, 28, . . 
 27, 29, . . 
 
 I 7 
 
 \ 
 
 439-07 
 112-.-JS 
 408*90 
 
 l-(MM).-, 
 
 9470 
 9461 
 
 Dublin, . . 
 
 \ 29-31, . 
 
 Aug. 10, . . . 
 14, ... 
 
 R 
 R 
 R 
 
 i] 
 :,' 
 
 449-92 
 454 -(Mi 
 452-11 
 
 1-0098 
 1-0000 
 1-0000 
 
 '.I.'; l:> 
 
 9456 
 
 !)1-J1
 
 190 
 
 OBSERVATIONS OF THE TERRESTRIAL 
 
 TABLE II. (Continued.} 
 
 Place. 
 
 Date. 
 
 Cyl. 
 
 Time. 
 
 Intensity. 
 
 Intensity. 
 Lond. = 1. 
 
 
 
 
 s. 
 
 
 
 Markree, . 
 
 Aug. 19, 1835, 
 
 R (c) 
 
 465-11 
 
 9531 
 
 9012 
 
 
 19,20, . . 
 
 R (d) 
 
 462-44 
 
 9558 
 
 9005 
 
 Dublin, . . 
 
 Aug. 19, . . . 
 
 L(c) 
 
 243-06 
 
 1-0000 
 
 9395 
 
 
 Sept. 12-15, . . 
 
 
 243-52 
 
 
 
 
 Aug. 19, ... 
 
 L (&) 
 
 292-80 
 
 1-0000 
 
 9395 
 
 
 Sept. 12-15, . . 
 
 
 
 293-31 
 
 
 
 Markree, 
 
 Aug. 21, . . . 
 
 L 
 
 "} 
 
 248-71 
 
 9569 
 
 8986 
 
 
 5) ) j 
 
 L 
 
 i,\ 
 
 299-75 
 
 9559 
 
 
 Ballina, . . 
 
 22, ... 
 
 L 
 
 /) 
 
 249-16 
 
 9534 
 
 8946 
 
 
 >? 3 J 
 
 L 
 
 V 
 
 300-53 
 
 9509 
 
 
 Belmullet, . 
 
 ,, 24, ... 
 
 L 
 
 i 
 
 249-79 
 
 9486 
 
 8894 
 
 
 
 L 
 
 '>) 
 
 301-52 
 
 9447 
 
 
 Acbill Ferry, 
 
 " 25, ... 
 
 L 
 
 
 
 248-76 
 
 9565 
 
 8977 
 
 Leenan, . . 
 
 26, ... 
 
 L b) 
 L (a) 
 
 299-98 
 248-18 
 
 9544 
 9610 
 
 9038 
 
 
 
 L(ft 
 
 298-66 
 
 9629 
 
 
 Oughterard, 
 
 27, ... 
 
 L( 
 
 / 
 
 246-19 
 
 9766 
 
 9179 
 
 
 
 L ( 
 
 
 296-44 
 
 9773 
 
 
 Ennis, . . 
 
 ,',' 28, ... 
 
 L 
 
 / 
 
 243-49 
 
 9984 
 
 9373 
 
 
 
 L 
 
 
 293-52 
 
 9969 
 
 
 Limerick, . 
 
 ,',' 29, ... 
 
 L 
 
 / 
 
 242-96 
 
 1-0027 
 
 9430 
 
 
 
 L 
 
 'i 
 
 292-38 
 
 1-0047 
 
 
 Cork, . . . 
 
 " 31, . . . 
 
 L 
 
 
 240-90 
 
 1-0199 
 
 9582 
 
 Waterford, . 
 
 Se'pt. 'l, . . -. 
 
 L 
 L 
 
 ( 
 
 288-97* 
 241-92 
 
 1-0285* 
 1-0114 
 
 9498 
 
 Broadway, . 
 
 " 2, . . . 
 
 L 
 L 
 
 / 
 
 291-51 
 240-85 
 
 1-0107 
 1-0204 
 
 9602 
 
 Rathdrum, . 
 
 ;; 3, ... 
 
 L 
 L 
 
 i 
 i 
 
 289-64 
 243-27 
 
 1-0238 
 1-0002 
 
 9409 
 
 Dublin, . . 
 
 11 12-15, 
 
 L 
 
 L 
 
 > 
 /' 
 
 292-67 
 243-52 
 
 1-0027 
 
 9390 
 
 London, . . 
 
 L( 
 19-22, . . L 
 
 > 
 
 i 
 
 293-31 
 235-98 
 
 
 9376 
 1-0000 
 
 London, . . 
 
 L 
 
 Oct. 23, 24, .. L 
 
 > 
 
 i 
 
 284-01 
 235-42 
 
 
 1-0000 
 1-0000 
 
 Dublin, . . 
 
 Nov. 5,' 6, . . 
 
 M 
 
 LJ ( 
 
 > 
 
 i 
 
 283-11 
 243-87 
 
 
 1-0000 
 9319 
 
 Dublin, . . 
 
 Nov., Dec., Jan., 
 
 L 
 L < 
 
 > 
 
 t 
 
 293-27 
 244-02 
 
 1-0000 
 
 9319 
 
 Limerick, . 
 
 Dec. 10,'ai, 23,' 
 
 L i 
 L < 
 
 > 
 i 
 
 293-36 
 244-01 
 
 1-0000 
 1-0001 
 
 
 
 " " 
 
 L I 
 
 ) 
 
 293-05 
 
 1-0021 
 
 
 e number in the last column. 
 
 ; the result has been therefore
 
 MAGNETIC FORCE IN IRELAND. 191 
 
 II. Dip and Intensity. 
 
 All the observations with dipping needles are comprised in the 
 two Tables which follow. The first (Tab. III.) contains the results 
 obtained with needles of the ordinary construction, and used ex- 
 clusively for the determination of the dip. In the first, second, and 
 third columns are given the place , day of the month, and hour of 
 observation. The fourth column contains the observed inclination 
 (the mean of the usual 8 readings) when the marked end of the 
 needle is a north pole ; the fifth contains the similar result of ob- 
 servation with the poles reversed ; and the sixth is the mean of these 
 angles, or the resulting dip. The needles employed are Needle L (1) 
 constructed by Robinson, and Needle S (1) made by Dollond ; the 
 latter of these is 11 J inches in length, the former 4^ inches. 
 
 Table IV. contains the observations made for the purpose of 
 determining the dip and intensity at the same time ; the latter ele- 
 ment being deduced from the direction in which the needle rests 
 under the combined influence of magnetism and gravity, while the 
 former is inferred from the position assumed under the influence 
 of the earth's magnetism alone. Each of these angles of direction 
 is deduced from the usual eight readings, all the reversals being 
 made just as in the ordinary mode of observing the dip, the re- 
 versal of the poles of the needle excepted. These angles are given 
 in the fifth and sixth columns of the table ; is the angle which 
 the needle makes with the horizon when unloaded, and the in- 
 clination when a small weight is attached to the southern arm at a 
 fixed distance from the centre. The temperature is noted at the 
 commencement and end of each observation, with the view of 
 correcting the value of the force ; and the mean temperature is set 
 down in the fourth column of the table. The needles employed in 
 these observations are of the same dimensions as those used for the 
 determinaiion of the dip alone, and are adapted to the same divided 
 circles. Three small holes are drilled close to each other on each 
 arm, at a distance from the centre about two thirds of its length ; 
 and much care has been bestowed to make them coincide accurately 
 with the axis of form of the needle. The weight is a small cylinder 
 of brass, which is inserted in one of the holes on the southern arm, 
 the diameter of the cylinder corresponding accurately to that of the 
 hole. This weight is so adjusted as to bring the needle into a 
 position neajrly at right angles to the line of the dip, that being 
 the position in which the resulting value of the force will be leasf 
 affected by the friction of the axle on its supports.
 
 192 OBSERVATIONS OF THE TERRESTRIAL 
 
 TABLE III. 
 Observations of Dip. Needle L (1).* 
 
 Place. 
 
 Date. 
 
 Hour. 
 
 N. Pole. 
 
 S. Pole. 
 
 Dip. 
 
 
 
 h. m. 
 
 
 
 
 Limerick, . 
 
 July, 1834, 
 
 
 70 59-4 
 
 71 l'-8 
 
 71 0-6 
 
 
 ?j j? 
 
 
 70 58-0 
 
 70 52-6 
 
 70 55-3 
 
 
 
 
 
 71 3-6 
 
 70 59-8 
 
 71 1-7 
 
 
 ' j> 
 
 
 71 1-6 
 
 71 3-2 
 
 1 71 2-4 
 
 
 
 
 70 56-0 
 
 70 58-4 
 
 70 57-2 
 
 
 Mean, '.' . . 
 
 
 70 59-7 
 
 70 59-2 
 
 70 59-5 
 
 Dublin, . . 
 
 Aug. 7, . . 
 
 
 70 48-2 
 
 70 55-0 
 
 70 51-6 
 
 
 8, . . 
 
 
 70 55-9 
 
 70 59-4 
 
 70 57-6 
 
 
 9, . . 
 
 
 70 55-5 
 
 70 53-1 
 
 70 54-3 
 
 
 19, . 
 
 
 70 47-7 
 
 70 51-3 
 
 70 49-5 
 
 
 Sept. 22, . . 
 
 
 70 47-4 
 
 71 4-5 
 
 70 56-0 
 
 
 23, . . 
 
 
 70 48-5 
 
 70 59-0 
 
 70 53-8 
 
 
 Mean, . . . 
 
 
 70 50-5 
 
 70 57-1 
 
 70 53-8 
 
 Carlingford, 
 
 Oct. 13, . . 
 
 12'20 
 
 71 2-0 
 
 71 30-6 
 
 71 16-3 
 
 Armagh, 
 
 14, . . 
 
 12 30 
 
 71 27-2 
 
 71 33-1 
 
 71 30-2 
 
 
 .* 15, . . 
 
 12 10 
 
 71 30-6 
 
 71 34-8 
 
 71 32-7 
 
 
 Mean, . . , 
 
 
 71 28-9 
 
 71 34-0 
 
 71 31-5 
 
 Coleraine,t . 
 
 Oct. 20, . . 
 
 11 25 
 
 71 11-8 
 
 71 19-4 
 
 71 15-6 
 
 Cam, . . . 
 
 21, . 
 
 12 45 
 
 71 48-2 
 
 71 47-5 
 
 71 47-8 
 
 Strabane, . 
 
 23, . . 
 
 11 40 
 
 71 47-2 
 
 71 56-0 
 
 71 51-6 
 
 Enniskillen, 
 
 24, . . 
 
 2 28 
 
 71 48-5 
 
 71 47-5 
 
 71 48-0 
 
 Fermoy, . . 
 
 Dec. 2, . . 
 
 
 70 28-1 
 
 70 44-5 
 
 70 36-3 
 
 Markree, 
 
 Aug. 21, 1835, 
 
 12 
 
 71 54-6 
 
 71 51-2 
 
 71 52-9 
 
 
 " M 
 
 4 45 
 
 71 55-6 
 
 71 53-1 
 
 71 54-4 
 
 
 Mean, . . . 
 
 
 71 55-1 
 
 71 52-2 
 
 71 53-6 
 
 Ballina, . . 
 Belmullet, . 
 
 Aug. 22, . . 
 24, . . 
 
 4'l5 
 10 45 
 
 71 58-8 
 71 59-7 
 
 72 5-0 
 72 5-7 
 
 72 1-9 
 
 72 2-7 
 
 Achill Ferry, 
 
 25, . . 
 
 10 
 
 71 52-2 
 
 71 56-6 
 
 71 54-4 
 
 Galway, . * . 
 
 23, . . 
 
 7 50 
 
 71 20-4 
 
 71 23-4 
 
 71 21-9 
 
 Ennis," . . 
 
 >> 
 
 4 20 
 
 70 55-6 
 
 71 7-4 
 
 71 1-5 
 
 Limerick, . 
 
 it 29, . . 
 
 1 10 
 
 70 54-0 
 
 70 49-8 
 
 70 51-9 
 
 Cork, . . . 
 Waterford, . 
 Broadway, . 
 Gorey,. . . 
 Rathdrum, . 
 Dublin, , 
 
 t 31, . . 
 Sept. 1, . . 
 2, . . 
 3, . . 
 
 
 M 4 
 
 12 
 12 8 
 1 30 
 8 5 
 2 30 
 1 30 
 
 70 26-5 
 70 40-5 
 70 14-8 
 70 45-0 
 70 39-9 
 
 *TA AAA 
 
 70 32-1 
 70 34-7 
 70 24-0 
 70 41-8 
 70 42-3 
 
 *7/\ /iQ.fi 
 
 70 29-3 
 70 37-6 
 70 19-4 
 70 43-4 
 70 41-1 
 
 Tfk AG..^ 
 
 
 ,, 5, . 
 
 1 50 
 
 |U ''4: 
 
 70 53-0 
 
 /(J 49'U 
 
 70 58-2 
 
 i(J 4o / 
 
 70 55-6 
 
 ( 
 
 7, . . 
 
 3 35 
 
 70 56-0 
 
 70 52-5 
 
 70 54-2 
 
 
 9, . . 
 
 2 45 
 
 70 55-7 
 
 70 53-1 
 
 70 54-4 
 
 
 14, . . 
 
 12 35 
 
 70 55-9 
 
 70 57-5 
 
 70 56-7 
 
 
 ,, 15, . . 
 
 11 55 
 
 70 55-8 
 
 70 50-8 
 
 70 53-3 
 
 
 Mean, . . . 
 
 
 70 53-5 
 
 70 53-5 
 
 70 53-5 
 
 * The observations in Limerick (July, 1834) and that in Fermoy (Dec. 2), were 
 made by Captain Sabine : all the other observations with this needle by Mr. Lloyd, 
 t Evident local disturbance at this place : Rock, basalt.
 
 MAGNETIC FORCE IN IRELAND. 
 
 193 
 
 TABLE III. (Continued] . 
 Observations of Dip Needle S (1).* 
 
 Place. 
 
 Date. 
 
 Hour. 
 
 N. Pole. 
 
 S. Pole. 
 
 Dip. 
 
 Limerick, . 
 
 Aug. 1, 1834, 
 
 
 71 38-8 
 
 70 24-3 
 
 71 1-6 
 
 
 16t, - 
 
 
 70 48-5 
 
 71 22-3 
 
 71 5-4 
 
 
 Mean, 
 
 
 71 13-6 
 
 70 53-3 
 
 71 3-5 
 
 Glengariff, . 
 
 Sept. 27, . 
 
 
 70 52-3 
 
 71 9-0 
 
 71 0-6 
 
 
 28, . 
 
 
 70 50-4 
 
 71 14-2 
 
 71 2-3 
 
 
 Mean, 
 
 
 70 51-4 
 
 71 11-6 
 
 71 1-5 
 
 Killarney, . 
 
 Oct. 4, . 
 
 
 71 5-6 
 
 71 3-4 
 
 71 4-5 
 
 Tulla, . . 
 
 ,., 12, . 
 
 
 71 16-2 
 
 71 15-4 
 
 71 15-8 
 
 TABLE IV. 
 
 Observations of Dip and Intensity. Needle L (4) J. 
 
 Place $. 
 
 Date. 
 
 Hour. 
 
 Temp. 
 
 (CO 
 
 (0 
 
 Limerick, . 
 
 June, 21, 1834 
 
 h. m. 
 
 el-o 
 
 
 - 6 55-0 
 
 
 July, 22, . 
 
 
 65-0 
 
 
 _ 7 10-6 
 
 
 28, . 
 
 
 65-0 
 
 
 _ 6 21-3 
 
 
 Mean 
 
 
 64-7 
 
 
 _ 6 49-0 
 
 London, . . 
 
 Aug. 28, . 
 
 2'35 
 
 70-0 
 
 69 8'-0 
 
 _ 11 53-2 
 
 
 29, . 
 
 12 42 
 
 68-5 
 
 69 8-5 
 
 - 12 7-4 
 
 
 
 1 18 
 
 67-7 
 
 69 5-6 
 
 _ 12 26-1 
 
 
 " " Mean 
 
 
 68-7 
 
 69 7-4 
 
 _ 12 8-9 
 
 Dublin, . . 
 
 Sept. 22, . 
 23, . 
 
 2 is 
 
 2 45 
 
 61-0 
 62-5 
 
 71 2-2 
 70 53 -8 
 
 _ 8 5-6 
 - 7 37-0 
 
 
 26, . 
 
 2 40 
 
 66-2 
 
 
 _ 7 59-6 
 
 
 29, . 
 
 2 40 
 
 62-5 
 
 70 44 -8 
 
 _ 8 9-5 
 
 
 Mean, 
 
 
 63-0 
 
 70 53 -6 
 
 - 7 57-9 
 
 Carlingford, 
 
 Oct. 13, . . 
 
 12 52 
 
 61-2 
 
 71 20-6 
 
 _ 5 29-4 
 
 All the observations with Needle S (1) were made by Captain Sabine. 
 
 t The needle was rubbed on a hone in the interval between the observations 
 (Aug. 1 and 16) ; the marked end most. 
 
 JThe observations in Limerick (June, July 1834) were made by Captain Subine: 
 all the other observations with this needle by Mr. Lloyd. 
 
 London, Sir James South's observatory, Kensington. Limerick, garden :tt 
 Somervillo. Ballybunan, in the field in front of Captain Raymond's Lodge. Valentin. 
 
 O
 
 194 
 
 OBSERVATIONS OF THE TERRESTRIAL 
 
 TABLE TV .(Continued.} 
 Observations of Dip and Intensity. Needle Hi (4). 
 
 Place. 
 
 Date. 
 
 Hour. 
 
 Temp. 
 
 
 
 e. 
 
 Armagh, 
 
 Oct. 14, . . 
 
 h. m. 
 1 5 
 
 48-8 
 
 71 19-4 
 
 - 7 7-4 
 
 
 15, . . 
 
 12 38 
 
 52-0 
 
 71 33-2 
 
 - 7 15-2 
 
 
 Mean, 
 
 
 50-4 
 
 71 26-3 
 
 - 7 11-3 
 
 Coleraine, 
 
 20, . . 
 
 12" 2 
 
 56-3 
 
 71 12-2 
 
 - 8 19-2 
 
 Cam, . 
 
 21, . . 
 
 1 28 
 
 49-5 
 
 71 49-6 
 
 - 5 4-8 
 
 Strabane, 
 
 23, . . 
 
 12 18 
 
 48-8 
 
 71 39-4 
 
 - 5 59-1 
 
 Dublin, . 
 
 25, . . 
 
 3 15 
 
 47-0 
 
 70 54-1 
 
 - 8 53-9 
 
 Dublin, . 
 
 Aug. 19, 1835, 
 
 1 13 
 
 71-5 
 
 70 51-6 
 
 - 13 4-9 
 
 Markree, 
 
 21, . . 
 
 3 50 
 
 67-0 
 
 71 55-6 
 
 - 11 2-6 
 
 Ballina, . 
 
 22, . . 
 
 3 50 
 
 66-5 
 
 71 51-8 
 
 - 11 15-2 
 
 Belmullet, 
 
 24, . . 
 
 11 15 
 
 65-5 
 
 71 57-5 
 
 - 10 56-2 
 
 Achill Ferry 
 
 25, . . 
 
 10 37 
 
 62-0 
 
 71 53-2 
 
 - 10 49-2 
 
 Galway, . 
 
 28, . . 
 
 8 18 
 
 59-0 
 
 71 17-4 
 
 - 11 9-1 
 
 Ennis 
 
 jj ' ' 
 
 4 45 
 
 67-2 
 
 70 59-1 
 
 - 12 1-6 
 
 Limerick, 
 
 29, . . 
 
 1 40 
 
 69-2 
 
 70 47-5 
 
 - 12 32-0 
 
 Cork, . . 
 
 31, . . 
 
 12 30 
 
 68-5 
 
 70 33-2 
 
 - 13 18-5 
 
 Waterford, 
 
 Sept. 1, . . 
 
 12 35 
 
 66-2 
 
 70 38-8 
 
 - 13 38-6 
 
 Broadway, 
 
 2, . . 
 
 2 
 
 66-8 
 
 70 31-6 
 
 - 13 33-5 
 
 Gorey, . 
 
 3, . . 
 
 8 30 
 
 60-0 
 
 70 43-1 
 
 - 14 1-1 
 
 Rathdrum, 
 
 
 3 
 
 64-7 
 
 70 40-8 
 
 - 13 58-0 
 
 Dublin, . 
 
 Sept. 4, '. '. 
 
 1 56 
 
 71-8 
 
 70 43-6 
 
 - 12 29-4 
 
 
 5, . . 
 
 2 19 
 
 65-5 
 
 70 52-8 
 
 - 13 15-4 
 
 
 7, . . 
 
 4 8 
 
 70-0 
 
 70 52-2 
 
 - 13 20-8 
 
 
 9, 
 
 3 5 
 
 
 70 46-2 
 
 
 
 14, . . 
 
 1 5 
 
 
 70 53-4 
 
 
 
 15, . . 
 
 12 25 
 
 62-0 
 
 70 55-0 
 
 - 13 10-5 
 
 London, 
 
 Mean, 
 Sept. 19, .. 
 
 1 
 
 67-3 
 
 70 50-5 
 69 5-8 
 
 - 13 4-0 
 
 
 
 1 10 
 
 68-0 
 
 69 7-4 
 
 - 16 54-2 
 
 
 22, . . 
 
 11 32 
 
 70-8 
 
 69 12-4 
 
 - 17 16-3 
 
 
 
 
 1 45 
 
 70-0 
 
 69 13-6 
 
 - 16 49-4 
 
 London, . . 
 
 Mean, 
 Oct. 23, . . 
 
 11 33 
 
 69-6 
 50-5 
 
 69 9-8 
 69 10-6 
 
 - 17 0-0 
 - 16 32-0 
 
 
 
 2 25 
 
 51-6 
 
 69 2-2 
 
 - 16 35-4 
 
 
 24, . . 
 
 1 16 
 
 53-8 
 
 69 6-0 
 
 - 16 44-4 
 
 Dublin, . . 
 
 Mean, 
 Nov. 5, . . 
 
 12 22 
 
 52-0 
 56-2 
 
 69 6-3 
 70 49-6 
 
 - 16 37-3 
 - 12 54-6 
 
 
 
 2 32 
 
 52-8 
 
 70 45-8 
 
 - 12 54-5 
 
 
 " 6 \,' ' 
 
 1 15 
 
 49-0 
 
 70 53-9 
 
 - 12 36-6 
 
 
 Mean, 
 
 
 52-7 
 
 70 49-8 
 
 - 12 48-6 
 
 em the sea beach at the Foot."-Dingl e , on the sea beach at Lord Ventry's.-Tulla, 
 Kiltanon, Mr. Molony's demesne.- Youghal, in the garden of the "Devonshire 
 Anns inn. N
 
 MAGNETIC FORCE IN IRELAND. 
 
 195 
 
 TABLE IV . (Continued.) 
 Observations of Dip and Intensity. Needle S (2) *. 
 
 Place. 
 
 Date. 
 
 Hour. 
 
 Temp. 
 
 < 
 
 e. 
 
 
 
 h. m. 
 
 
 
 
 Limerick,* . 
 
 JuJy, 1835 
 
 
 63-0 
 
 71 16-9 
 
 - 15 9-0 
 
 Ballybunan, 
 
 Nov. 8, 
 
 
 52-0 
 
 71 29-1 
 
 - 13 56-3 
 
 Valentia, . 
 
 12, 
 
 
 47-0 
 
 71 15-0 
 
 - 14 37-3 
 
 Dingle,. . 
 
 18, 
 
 
 43-0 
 
 71 17-7 
 
 - 13 45-8 
 
 Tulla, . 
 
 Dec. 10, 
 
 
 47-0 
 
 71 36-5 
 
 - 14 46-0 
 
 Limerick, 
 
 26, 27, 
 
 
 45-0 
 
 71 14-6 
 
 - 15 29-6 
 
 Youghal, 
 
 29, . 
 
 
 47-0 
 
 70 49-0 
 
 - 16 0-5 
 
 Limerick, 
 
 Jan. 4, 1836, 
 
 
 52-5 
 
 
 - 15 23-7 
 
 When the observations of dip made at the same station with 
 different needles are compared together, it will be found that they 
 are by no means in accordance. Thus the dip at Limerick in 
 November, 1833, deduced from four observations with a needle on 
 Meyer's principle, was 71 ll'-7, while the mean of five observations 
 with needle L (1) at the same place and in the following year was 
 only 70 59'-5, differing from the former by 12'. When from this 
 difference the amount of the annual change is deducted, the re- 
 mainder appears to be greater than can be fairly ascribed to the 
 errors of observation. But these discrepancies in the results given 
 by different needles have been placed in the strongest light by the 
 recent observations of Captain James Ross in London. In these 
 observations, which were undertaken with the view of determining 
 the amount of the annual decrease of dip at London, eight different 
 needles were employed, and from eight to ten observations were 
 made with each, the result of each separate observation being a 
 mean of eighty readings. 
 The results were as follow : 
 
 Needle B (1), Admiralty, ... (10 obs.) 
 
 Needle L (1), (9 obs.) 
 
 Needle S (1), (8 obs.) 
 
 dip 
 
 69 r-5 
 
 69 6-3 
 69 11-3 
 
 * The observations in Limerick, July, 1835, made by Captains Sabine and Ross ; 
 ill the remaining observations with this needle by Captain Sabine. 
 
 o2
 
 196 OBSERVATIONS OF THE TERRESTRIAL 
 
 Needle J, (10 obs.) . . .dip. = 6916'-1 
 
 Needle E, (10 obs.) ... 69 18 -9 
 
 Meyer's needle, (8 obs.) ... 59 19 -6 
 
 Needle B (2), Admiralty, ... (10 obs.) ... 69 21 -8 
 
 Needle P, (8 obs.) ... 69 42 '6 
 
 Mean dip = 69 17 '3 
 
 Thus it appears that there is a difference amounting to 41' in 
 the results of two of the needles used ; and that this difference is 
 very far beyond the limits of the errors of observation will appear 
 from the fact that the extreme difference in the partial results with 
 one of these needles B (1) does not amount to four minutes and a 
 half, while with the other (P) the extreme difference is only two 
 minutes. In fact, it so happens that these very needles which 
 differ most widely in their mean results, are those in which the 
 accordance of the partial results is most complete. Of the eight 
 results obtained with needle (P), there is one only which differs 
 from the mean of the eight by a single minute ; and yet the mean 
 of all the observations with this needle differs by more than 20' 
 from the mean of any of the others, while its excess above the 
 mean of the entire series amounts to 25'. 
 
 These differences cannot be ascribed to any partial magnetism 
 in the apparatus ; for three of the needles (J, P, and E) were of the 
 same dimensions, and were used with the same circle, and yet their 
 results, as we see, are widely discordant. "We must seek, then, in 
 the needles themselves the cause of these perplexing discrepancies, 
 and we are forced to conclude that there may exist, even in the 
 best needles, some source of constant error which remains uncor- 
 rected by the various reversals usually made; and that accordingly 
 no repetition of observations with a needle so circumstanced can 
 furnish even an approximation to the absolute dip. If this error 
 be due to the incomplete adjustment of the needle (such as devi- 
 ation of centre of gravity from the axle, &c.), its magnitude will be 
 a function of the dip, and of the force, which may be assumed to 
 be constant where the variations of these elements are not consider- 
 able. Hence, to determine its amount for any particular needle, 
 it is necessary to make a careful series of observations with it at 
 some station for which the dip has been accurately determined 
 (from the mean of several needles) ; and the difference will be
 
 MAGNETIC FORCE IN IRELAND. . 197 
 
 a constant correction, to be applied to all future results within certain 
 limits. 
 
 It fortunately happens that the two ordinary needles used in 
 the present series of observations in Ireland were among those 
 employed by Captain James Eoss in London ; so that their cor- 
 rections may be considered to be accurately known. The mean 
 difference of the values of the dip as given by needles L (1) and 
 L (4) having been well determined by observations elsewhere, the 
 results obtained with the latter needle in London may be grouped 
 with those of the former. Thus, the mean of seven observations 
 made with needle L (4), September and October, 1835, when 
 reduced to needle L (1), is 69 9'8. If then we combine this 
 with the direct result of the nine observations with needle L (1), 
 viz. 69 6'3 (allowing double weight to each of the latter observa- 
 tions on account of the double number of readings), we find 
 69 7''3 as the mean value of the dip deduced from sixteen ob- 
 servations with the two needles, and reduced to needle L (1) as 
 the standard. Comparing this with the mean result of the eight 
 needles, the correction of needle L (1) is found to be + 10'*0. 
 
 For the other needles employed in Ireland, we have 
 
 Needle S (1), . . . . correction = + 6'-0. 
 Meyer's needle, ........ 2''3. 
 
 With respect to Meyer's needle, however, it is to be observed that 
 as the angles from which the dip is deduced differ in general very 
 widely, and as these angles are usually varied in different obser- 
 vations with the same needle, there is a presumption, at least, that 
 every constant error will be removed by repetition, and that the 
 differences of the separate results from the absolute dip will be 
 equal on the positive and on the negative side. This seems to be 
 confirmed by the amount of the final difference in the present in- 
 stance, which does not appear to be larger than may be fairly 
 ascribed to the errors of observation. It seems bettor therefore to 
 regard this needle as subject to no constant error. 
 
 The degree of confidence to which these determinations are 
 entitled may now be estimated, by applying the corrections so 
 obtained to the observations made with these needles at Limerick 
 in 1833 and 1834, the only other station at which they have been 
 all employed. The observations in the former year are reduced 
 to the latter, assuming the annual decrease of dip in Ireland to
 
 198 OBSERVATIONS OF THE TERRESTRIAL 
 
 be 3'. The very close agreement of the results must of course be 
 regarded as in a great measure accidental. 
 
 Observed Dip. Corrected Dip. 
 
 Needle L (1), July, 1834, .. 7059'-5 . . . 719'-5 
 Needle S (1), Aug., 1834, . . 71 3-5 ... 71 9 -5 
 Meyer's needle, Nov., 1833, . 7111-7 ...719-7 
 
 "We have hitherto spoken only of the needles whose poles are 
 changed in each observation, and which are used exclusively for 
 the determination of the dip. The necessity of a correction in the 
 results obtained with the other needles, whose poles are unaltered, 
 is obvious. By reason of the deviation of the centre of gravity of 
 the needle from the axle, the weight of the needle itself has in all 
 cases a certain moment acting with or against the directive force. 
 
 Let , as before, be the inclination of the needle to the horizon 
 when unloaded, and the corresponding angle when the weight 
 is attached, and let p denote the ratio of the moment of the needle 
 itself to that of the added weight ; then the dip, S, will be given 
 by the equations* 
 
 (1) 
 
 in which t is the correction sought. 
 
 The constant coefficient p in the expression for this correction 
 will be known when the corresponding values of the angles , , 
 and are known at some one station. Its value, in the case of 
 Needle IV., has been thus found to be 'O0205.t 
 
 It will easily appear, from the second of the preceding formulas, 
 that when the coefficient is so small as that just assigned, the 
 variations in the values of e, resulting from moderate changes in 
 the angles on which it depends, will be inconsiderable. In the 
 observations in Ireland, for example, the entire change in the 
 amount of the correction is a small fraction of a minute. In this 
 and other similar cases, therefore, the correction may be regarded 
 as constant; and its value maybe inferred from any series of simul- 
 taneous observations made with the needle to be corrected, and 
 
 * Transactions of the Royal Irish Academy, Vol. XVIL, p. 450. 
 . 451.
 
 MAGNETIC FORCE IN IRELAND. 199 
 
 with some other whose correction is already known. In this 
 manner it has been found that the mean difference of the results 
 of Needles L (1) and L (4) is & - 4 = + l'-5 ; being somewhat 
 smaller than that assigned above. But if 8 denote the absolute 
 dip, we have already found that 8 - Si = + 10'- ; and adding these 
 differences, the correction of Needle L (4) is 8 - S 4 = + ll'-S. 
 
 The correction of Needle S (2) is inferred from the observations 
 made with that needle in Limerick, as given in Table IV. 
 
 Limerick, July, 1835, . . dip = 71 16'-9 
 
 Dec., . . 71 14-6 
 
 Mean, . . 71 15 -8. 
 
 This mean corresponds, in time, to the middle of October, 1835. 
 But the true dip in Limerick (July, August, 1834) was found to 
 be 71 9'-5 ; and when reduced to October, 1835 (assuming the 
 annual decrease to be 3'), it is 71 6'*0. The correction of the 
 needle is therefore - 9' '8. 
 
 The corrections of the needles being determined, we may now 
 proceed to deduce the values of the absolute dip at the several 
 places at which observations have been made. These values are 
 given in the following table (Table V.). In the first and second 
 columns are written the place and date of the observation. The 
 third and fourth columns contain the corrected values of the dip, 
 deduced from the results of Tables III. and IV. by the application 
 of the corrections now explained ; and the last column contains 
 the mean dip inferred from the two preceding. In taking this mean, 
 double weight has been assigned to the results obtained with needles 
 of the ordinary construction, the number of readings with these 
 needles being double of that made with the needles whose poles 
 are unaltered.
 
 200 
 
 OBSEKVATIONS OF THE TERRESTRIAL 
 
 TABLE V. 
 Dip. Final Results. 
 
 Place. 
 
 Date. 
 
 Dip (1). 
 
 Dip (2). 
 
 Mean. 
 
 
 
 
 
 
 London, . . . 
 
 August, 1834, 
 
 . 
 
 69 18-9 
 
 69 18-9 
 
 Dublin, . . . 
 
 Aug., Sept. 
 
 71 3-8 
 
 71 5-1 
 
 71 4-1 
 
 Limerick, . 
 
 July, Aug. . 
 
 71 9-5 
 
 . 
 
 71 9-5 
 
 Glengariff, . 
 
 Sept., 27, 28, 
 
 71 7-5 
 
 . 
 
 71 7-5 
 
 Killarney, . 
 
 Oct., 4, . . 
 
 71 10-5 
 
 . . 
 
 71 10-5 
 
 TuUa, . . 
 
 12, . . 
 
 71 21-8 
 
 . 
 
 71 21-8 
 
 Carlingford, 
 Armagh, 
 
 13, . . 
 14, 15, . 
 
 71 26-3 
 71 41-5 
 
 71 32-1 
 71 37-8 
 
 71 28-2 
 71 40-3 
 
 Coleraine, . 
 
 20, . . 
 
 71 25-6 
 
 71 23-7 
 
 71 25-0 
 
 Cam, . . 
 
 21, . . 
 
 71 57-8 
 
 72 1-1 
 
 71 58-9 
 
 Strabane, . 
 
 23, . . 
 
 72 1-6 
 
 71 50-9 
 
 71 58-0 
 
 Enniskillen, 
 
 24^ , . 
 
 71 58-0 
 
 
 71 58-0 
 
 Fermoy, 
 London, . . 
 
 Dec., 2, . . 
 Sept., Oct., 1835, 
 
 70 46-3 
 69 16-3 
 
 69 19-8 
 
 70 46-3 
 69 17-3 
 
 Dublin, . . 
 
 Sept., 4-15, . 
 
 71 3-5 
 
 71 2-0 
 
 71 3-0 
 
 Markree, . 
 
 Aug., 21,. . 
 
 72 3-6 
 
 72 7-1 
 
 72 4-8 
 
 Ballina, 
 
 22, . . 
 
 72 11-9 
 
 72 3-3 
 
 72 9-0 
 
 BelmuUet, . 
 
 24, . . 
 
 72 12-7 
 
 72 9-0 
 
 72 11-5 
 
 Achill Ferry, 
 
 25, . . 
 
 72 4-4 
 
 72 4-7 
 
 72 4-5 
 
 Galway, . . 
 
 28, . . 
 
 71 31-9 
 
 71 28-9 
 
 71 30-9 
 
 Ennis, . . 
 
 
 71 11-5 
 
 71 10-6 
 
 71 11-2 
 
 Limerick, . 
 
 >, 29, . . 
 
 71 1-9 
 
 70 59-0 
 
 71 0-9 
 
 Cork, . . . 
 
 31, . . 
 
 70 39-3 
 
 70 44-7 
 
 70 41-1 
 
 Waterford, . 
 
 Sept., 1, . . 
 
 70 47-6 
 
 70 50-3 
 
 70 48-5 
 
 Broadway, . 
 
 2, . . 
 
 70 29-4 
 
 70 43-1 
 
 70 34-0 
 
 Gorey, . . 
 
 3, . . 
 
 70 53-4 
 
 70 54-6 
 
 70 53-8 
 
 Rathdrum, . 
 
 
 70 51-1 
 
 70 52-3 
 
 70 51-5 
 
 Dublin, . . 
 
 Nov., 5, 6, . 
 
 
 71 1-3 
 
 71 1-3 
 
 Limerick, . 
 
 July, Dec., . . 
 
 
 71 6-0 
 
 71 6'0 
 
 Ballybunan, 
 
 Nov., 8, ... 
 
 
 71 19-3 
 
 71 19-3 
 
 Valentia, . 
 
 12, ... 
 
 
 71 5-2 
 
 71 5-2 
 
 
 18, 
 
 
 71 7*9 
 
 71 7'9 
 
 Tulla, . . 
 Youghal, . 
 
 Dec., 10, . . . 
 29, ... 
 
 . . . 
 
 71 26-7 
 70 39-2 
 
 71 26-7 
 70 39-2 
 
 The dip being known, the intensity will be given by the formula 
 
 sin (S - 0) = cos 0, 
 
 (2) 
 
 in which /3 is constant, and $ the measure of the force exerted 
 by the earth on the needle. This force, however, varies with the 
 temperature to which the needle is exposed ; and it is necessary 
 to determine the amount of this variation before we can know the 
 relative values of the terrestrial magnetic force at different stations.
 
 MAGNETIC FORCE IN IRELAND. 201 
 
 Let t, then, be the observed, and t' the standard temperature, and 
 let #' be the value of corresponding to the latter ; then 
 
 ^ <j>' = a ({>' (t t'), (3) 
 
 in which a is a constant to be determined by observation. For 
 Needle L (4) it has been found thaf 
 
 a = -00016. 
 
 But we may proceed in another way, which will perhaps be 
 found convenient in practice. We may correct the observed value 
 of 9 by subtracting the change due to temperature ; or, in other 
 words, we may reduce the value of 9 to that corresponding to the 
 standard temperature, and to the standard condition of the needle. 
 For this purpose it is only necessary to find the relation between 
 the corresponding changes of and 9. Differentiating, therefore, 
 the equation (2) with respect to these variables, and dividing the 
 result by the equation itself, we find 
 
 d cos 8 sin 1' 
 
 d 9 ~ cos 9 sin (8 - 9)' 
 
 d 9 being expressed in minutes. Now it is easy to see that the 
 variations of the second member of this equation, arising from 
 changes in the angles 8 and 9 on which it depends, will be in- 
 considerable for the limited extent of those changes in Ireland. 
 Assuming it to be constant, therefore, its value will be given when 
 we know the corresponding values of 8 and 9 at some one station. 
 Thus, at Dublin, September, 1835, it was found that 
 
 3 = 71 3'-0, 9 = - 13 O'-O ; 
 
 from which we find the value of this constant to be -00010. But, 
 since d = ^ - q>' = - a $' (t - t'}, the first member of the equa- 
 tion is 
 
 -~ ---00016^; 
 
 (/ (/ U 17 
 
 so that the correction is finally 
 
 & - 9 = + 1-6 (t - *. 
 
 * It is obvious that the coefficient in this correction might hare been determined 
 directly, by observing the angles and 9' corresponding to very unequal tenipciuturr.- 
 It did not seem safe, however, to subject the apparatus to the action of high artificial 
 heat, and the thermo-electric currents induced by inequality of temperature would in 
 all probability havo sensibly affected the results.
 
 202 OBSERVATIONS OF THE TERRESTRIAL 
 
 Now if 0x, 8,, and 0j be the values of $, 8, and at the station 
 with which the rest are compared, we have 
 sin (8 - 0) = |3 cos 0, 
 0o sin (8 - ) = /3 cos ; 
 
 cos sin (8 - ) m 
 
 and dividing - = C08 Oo gin ( g _ 0) > 
 
 which expresses the ratio of the force at the two stations in a form 
 suited to logarithmic calculation. 
 
 The following table gives the results of this computation. It 
 contains the place and date of observation ; the angle corrected 
 for temperature ; and the total intensity at each station, compared 
 in the first instance with Dublin or Limerick, and in the second 
 with London. For the intensity of the magnetic force at Dublin 
 we have the three following determinations : * 
 
 * *' 
 Aug., Sept., 1834, . . Intensity = 1-0194 
 
 Sept., 1835, .... 1-0213 
 
 Oct., Nov., 1835, . . 1-0211 
 
 Mean, . . 1-0206. 
 
 The intensity at Limerick, compared with London, is observed 
 to be 1-0262 ; and the intensity at the same place, compared with 
 Dublin, is 1-0030. Accordingly, for the determination of the 
 values of the total force at Dublin and Limerick, observation 
 furnishes us with three results, in the two former of which the 
 intensities at these two stations are directly compared with that 
 at London, while in the third they are compared together. To 
 s infer from these data, therefore, the most probable values of the 
 force at the two stations, we must proceed precisely as in the ana- 
 logous problem respecting the horizontal intensities, and we have 
 only to substitute in the formulas already given,* for a, b, c, &c., 
 their particular values. We have then 
 
 a = 1-0206, b = 1-0262, e = 1'0030, 
 
 f, = - = 1-0055, c - c = -0025. 
 (t 
 
 And since the comparison of Dublin and London is the mean of 
 three distinct comparisons, while each of the other two results is 
 
 * Page 188.
 
 MAGNETIC FORCE IN IRELAND. 
 
 203 
 
 inferred from one only, the weights may be assumed as follow : 
 A = 3, 5 = 1, (7=1. 
 
 Substituting these values, therefore, in the formulas alluded to, we 
 find 
 
 x = a + B x = 1-0210, y = b + $y = 1-0251. 
 
 The numbers in the fifth column of the table are deduced from 
 those in the fourth, by multiplying by one or other of these 
 numbers, according as the force at the station in question has been 
 compared in the first instance with that at Dublin, or with that at 
 Limerick. 
 
 TABLE VI. 
 Intensity. Needle L (4). 
 
 Place. 
 
 Date. 
 
 Angle. 
 
 Intensity (1). 
 
 Intensity (2). 
 
 London, . . 
 
 Aug., 1834, . . 
 
 - 11 55-0 
 
 
 1-0000 
 
 Dublin, . . 
 
 Sept., .... 
 
 - 7 53-1 
 
 . 
 
 1-0194 
 
 Limerick, . 
 
 June, July, . . 
 
 - 6 41-5 
 
 . 
 
 1-0262 
 
 Dublin, . . 
 
 Sept., Oct., . . 
 
 - 8 33-9 
 
 1-0000 
 
 1-0210 
 
 Carlingford,* 
 Armagh, 
 
 Oct., 13, . . 
 14, 15 . . 
 
 - 5 27-5 
 - 7 26-7 
 
 1-0166 
 1-0044 
 
 1-0379 
 1-0255 
 
 Coleraine, . 
 
 20, . . 
 
 - 8 25-1 
 
 9997 
 
 1-0207 
 
 Cam, . . 
 
 21, . . 
 
 - 5 21-6 
 
 1-0151 
 
 1-0364 
 
 Strabane, . 
 
 23, . . 
 
 - 6 17-0 
 
 1-0100 
 
 1-0312 
 
 Dublin, . . 
 
 Aug., Sept., 1835, 
 
 - 12 49-4 
 
 1-0000 
 
 1-0210 
 
 Markree, . . 
 
 Aug., 21, . . 
 
 - 10 51-4 
 
 1-0091 
 
 1-0303 
 
 Ballina, . . 
 
 22, . . 
 
 - 11 4-8 
 
 1-0077 
 
 1-0289 
 
 Belmullet, . 
 
 24, . . 
 
 - 10 47-4 
 
 1-0093 
 
 1-0305 
 
 Achill Ferry, 
 Galway, . . 
 
 25, . . 
 
 28, . . 
 
 - 10 46-0 
 - 11 10-7 
 
 1-0096 
 1-0086 
 
 1-0308 
 1-0298 
 
 Ennis, . . 
 
 
 
 - 11 50-1 
 
 1-0055 
 
 1-0266 
 
 Limerick, . 
 
 29, . . 
 
 - 12 17-3 
 
 1-0030 
 
 1-0241 
 
 Cork, . . 
 
 31, . . 
 
 - 13 4-9 
 
 9992 
 
 1-0202 
 
 Waterford, . 
 
 Sept., 1, . . 
 
 - 13 28-7 
 
 9966 
 
 1-0175 
 
 Broadway, . 
 Gorey, . 
 
 2, . . 
 3, . . 
 
 - 13 22-6 
 - 14 1-1 
 
 9976 
 9933 
 
 1-0185 
 1-0142 
 
 Rathdrum, . 
 
 
 - 13 50-5 
 
 9944 
 
 1-0153 
 
 London, . . 
 
 Sept., 19-22, . . 
 
 - 16 44-6 
 
 . . . 
 
 1-0000 
 
 Dublin, . . 
 
 4-15, . . 
 
 - 12 52-3 
 
 . . . 
 
 1-0213 
 
 London, . . 
 
 Oct., 23, 24, . . 
 
 - \9 50-1 
 
 . . . 
 
 1-0000 
 
 Dublin, . . 
 
 Nov., 5, 6, . . 
 
 - 13 0* 
 
 ' ' 
 
 1-0211 
 
 Evident local distm-bance at these two stations. The district about Carlingford 
 is intersected with trap dykes; Coleraino lies within the basaltic field of the North 
 of Ireland.
 
 204 OBSERVATIONS OP THE TERRESTRIAL 
 
 TABLE VI. {Continued.} 
 Intensity. Needle S (2). 
 
 Place. 
 
 Date. 
 
 Angle. 
 
 Intensity (1). 
 
 Intensity (2). 
 
 Limerick, . 
 Ballybunan, 
 Valentia, 
 
 July, Dec., 1835, 
 Nov. 8, 
 ii 12 
 
 - 15 19-3 
 - 13 56-3 
 - 14 37-3 
 
 1-0000 
 1-0084 
 1-0047 
 
 1-0251 
 1-0337 
 1-0299 
 
 Dingle, . 
 
 i, 18, 
 
 - 13 45-8 
 
 1-0097 
 
 1-0350 
 
 Tulla, . 
 
 Dec. 10, 
 
 - 14 46-0 
 
 1-0035 
 
 1-0287 
 
 Limerick, 
 
 Dec., Jan., 
 
 - 15 26-6 
 
 1-0000 
 
 1-0251 
 
 Youghal, 
 
 Dec. 29, 
 
 - 16 0-5 
 
 9971 
 
 1-0221 
 
 HL.~Itodytutmic and Isoclinal Lines. 
 
 On a review of the preceding results of observation, it will be 
 seen that they exhibit much irregularity. The errors of observa- 
 tion in which we are to include the effects of the unsteadiness of 
 the magnetic state of the needles employed, as well as the various 
 other uncertainties arising from the imperfections of our methods 
 of observing have, of course, their share in these discrepancies ; 
 but they are by no means sufficient to explain the whole. The 
 action of the earth on the magnetic needle is itself subject to irre- 
 gularities, temporary as well as local ; and it is to these that the 
 observed anomalies must, in great part, be ascribed. 
 
 To the variations of the former kind we have already referred. 
 The direction and intensity of the terrestrial magnetic force, at 
 a given place, are subject to fluctuations, or irregular oscillations 
 round their mean state, the cause of which is as yet little under- 
 stood ; and it is only by means of simultaneous observations, made 
 at some fixed station within the limits of the district through 
 which these effects take place, that we can hope to ascertain their 
 amount, and to correct for them. 
 
 Of the local disturbing causes some are sufficiently obvious. 
 Thus the needle is in general affected by the vicinity of basaltic 
 rocks, owing to the quantity of iron they contain ; and instances 
 have been observed in which these rocks were even found to possess 
 magnetic polarity.* But there seem to be grounds for believing 
 
 * A remarkable case of this kind has been noticed at Fair Head, on the north coast 
 of Ireland. The magnetic polarity of one of the columns which compose this wonder- 
 ful facade is said to be so strong as to invert the position of the compass ncedje, when 
 the poles of the same name are made to approach.
 
 MAGNETIC FORCE IN IRELAND. 205 
 
 that disturbing actions of a local nature are exerted on a much 
 larger scale. Whether the earth's magnetic force be an inherent 
 property, and the resultant of the forces of all its parts, or whether 
 it be simply the effect of thermo-electric currents produced by 
 the heating action of the sun, the result must in either case be 
 greatly modified by the configuration of a country, and by the 
 nature of its superficial strata. If this view be just, the greatest 
 irregularities should prevail in those parts of the earth in which 
 the uniformity of surface is broken by hill and valley, and where 
 the strata have been rent and contorted by the uplifting of moun- 
 tain chains. In Ireland, accordingly, we should expect to find 
 much greater anomalies in the direction and intensity of the mag- 
 netic force than in the plains of central Europe ; and it must be, 
 consequently, in the same degree more difficult to arrive at general 
 results. 
 
 The only mode of escaping from these difficulties was to eeek 
 the general result of the entire series of observations, as to the po- 
 sition of the isodynamic and isoclinal lines ; and to combine the 
 partial results in such a manner that their deviations whether 
 local, temporary, or casual should have the least influence on the 
 final conclusion. Such is the object of the following computations. 
 
 Let A and fi denote the latitude and longitude 
 of any place at which an observation has been made, 
 Ao and fi the latitude and longitude of the station 
 which is chosen as the origin of the coordinates ; 
 then the position of the former place may be fixed 
 with reference to the latter in terms of these quan- 
 tities. For let P be the pole of the earth, M and 
 the two places, PM and PO their meridians, 
 and MQ a great circle passing through Jfand per- 
 pendicular to PO. It is obvious that the position 
 of M will be determined by the rectangular sphe- 
 rical coordinates, OQ and QJ/. Now in the right-angled triangle 
 MPQ, we have 
 
 tan PQ = tan PM cos P, sin MQ = sin PM sin P ; 
 or, denoting the co-ordinates OQ and QM by a and 0, 
 
 cot (A + a) = cot A cos (n - no] 
 
 (A) 
 sin /3 = cos A sin (ju - /*,).
 
 206 OBSERVATIONS OF THE TERRESTRIAL 
 
 When ju - juo is so small as it is within the limits of the present 
 district of observation, we may take 
 
 sin GU - /i ) = M - Mo> cos (ju - jtio) = 1, sin |3 = 0, 
 and the preceding equations become 
 
 |3 = (ft - jUo) COS X. 
 
 This simplification is obviously equivalent to the substitution of 
 the parallel of latitude for the perpendicular to the meridian. 
 
 Now let us conceive any line to pass through 0, making the 
 angle u with the meridian ; then, in the same order of approxima- 
 tion, the perpendicular from the point M upon that line will be 
 
 p = |3 cos u - a sin u ; 
 and, substituting for a and /3 their values just obtained, 
 
 p = (n - no) cos X cos u - (A - Ao) sin u. (C) 
 
 It is easy to see in what manner this result may be applied in 
 obtaining equations of condition from the data furnished by obser- 
 vation. The increase of the force, or of the dip, may (throughout 
 the limited area of the present district of observation) be assumed 
 to be proportional to the distance, measured in a direction perpen- 
 dicular to the line of equal force, or of equal dip. Accordingly, if 
 u be the angle which the line of equal horizontal intensity passing 
 through makes with the meridian of the place, the difference of 
 the intensities at the two stations will be proportional to p, or 
 
 h - h<> = rp ; 
 
 h and A being the horizontal intensities at the two stations, and r 
 a constant coefficient which determines the rate of increase. Sub- 
 stituting, then, for p its value (C), and making 
 
 r cos u = x, r sin u = ?/, (D) 
 
 we have 
 
 (ju - ju ) cos \ x - (\ - Ao) y = h - h Q . (E) 
 
 The equations of condition deduced from the observations of total 
 intensity, and of dip, will be of a similar form ; and the coefficients 
 of the unknown quantities, in the first member of the equations, 
 will be the same.
 
 MAGNETIC FORCE IN IRELAND. 
 
 207 
 
 The station chosen for the origin of the co-ordinates is Dublin, 
 and it is obvious that there will be as many equations of condition 
 a there are other places of observation. The coefficients of these 
 equations are given in the following table. The first, second, and 
 third columns contain the place of observation, its latitude and its 
 longitude*. The numbers in the fourth and fifth columns are the 
 differences of latitude and longitude (estimated in minutes #1 lati- 
 tude) of the place of observation and Dublin, or the values of 
 (A - Ao) and (/u - ju ) cos A ; and the numbers in the three remain- 
 ing columns are the corresponding differences of dip, of horizontal 
 intensity, and of total intensity, which form the second members of 
 the equations. The dip having been observed at Dublin in each of 
 the two years (1834 and 1835), the differences of dip are obtained 
 by subtracting that belonging to the year in which the observation 
 was made at the other station. 
 
 TABLE VII. 
 
 Place. 
 
 w 
 
 to 
 
 (A - Ao) 
 
 (M-/*O) 
 
 cos A 
 
 (8 - o) 
 
 (A -AC) 
 
 (/-/o) 
 
 Cam, . . 
 
 55 15 
 
 7 15 
 
 + 114 
 
 + 34 
 
 f 54-9 
 
 - -030 
 
 + 0154 
 
 Coleraine, . 
 
 55 8 
 
 6 40 
 
 + 107 
 
 + 14 
 
 + 21-0 
 
 - -009 
 
 -0003 
 
 Strabane, 
 
 54 49 
 
 7 28 
 
 + 88 
 
 + 42 
 
 + 54-0 
 
 - -033 
 
 + -0102 
 
 Enniskillen, 
 
 54 21 
 
 7 38 
 
 + 60 
 
 + 48 
 
 + 54-0 
 
 - -031 
 
 
 
 Armagh, 
 
 54 21 
 
 6 39 
 
 + 60 
 
 + 14 
 
 -1- 36-3 
 
 - -021 
 
 + 0045 
 
 Belmullet, . 
 
 54 20 
 
 9 50 
 
 + 59 
 
 + 125 
 
 -1- 68-5 
 
 - -050 
 
 + -0095 
 
 Markree, . 
 
 54 14 
 
 8 28 
 
 + 53 
 
 -1- 77 
 
 + 61-8 
 
 - -039 
 
 + 0093 
 
 Ballina, . . 
 
 54 10 
 
 9 3 
 
 + 49 
 
 + 98 
 
 + 66-0 
 
 - -045 
 
 + 0079 
 
 Carlingford, 
 
 54 2 
 
 6 11 
 
 + 41 
 
 - 3 
 
 + 24-2 
 
 - -010 
 
 + -0169 
 
 Achill Ferry, 
 
 54 
 
 9 51 
 
 + 39 
 
 + 127 
 
 + 61-5 
 
 - -042 
 
 + 0098 
 
 Leenane, . . 
 
 53 41 
 
 9 40 
 
 + 20 
 
 + 121 
 
 
 
 - -036 
 
 
 
 Oughterard, 
 Dublin, . . 
 
 53 27 
 53 21 
 
 9 18 
 6 15 
 
 + 6 
 - 
 
 + 109 
 + 
 
 + 0-0 
 
 - -022 
 + -000 
 
 - -oooo 
 
 Galway, . . 
 
 53 17 
 
 8 51 
 
 - 4 
 
 + 93 
 
 + 27-9 
 
 
 
 1 -(IONS 
 
 Rathdrum, . 
 
 52 55 
 
 6 12 
 
 - 26 
 
 - 2 
 
 - 11-5 
 
 + -001 
 
 -0057 
 
 Tulla.f . . 
 
 52 53 
 
 8 41 
 
 - 28 
 
 + 88 
 
 + 17-8 
 
 + -003 
 
 + 0077 
 
 Ennis, . . 
 
 52 52 
 
 8 54 
 
 - 29 
 
 + 96 
 
 + 8-2 
 
 - -002 
 
 + 0056 
 
 Limerick, t . 
 
 52 40 
 
 8 36 
 
 - 41 
 
 + 85 
 
 + 5-0 
 
 + -005 
 
 + -0041 
 
 * The latitudes and longitudes of some of the more important stations have been 
 kindly furnished by the officers of the Ordnance Survey. The remainder hare been 
 taken from Arrowsmith's map of Ireland. 
 
 t Observations made in the year 1835 give Tulla 5 - 5o = + 23'7 ; Limerick, 
 5 - 5 = - 2'-l.
 
 208 
 
 OBSERVATIONS OF THE TERRESTRIAL 
 
 TABLE VII. (Continued.) 
 
 Place. 
 
 w 
 
 w 
 
 (A-Xo) 
 
 (M-MO) 
 
 COS A 
 
 (8 - So) 
 
 (A-Ao) 
 
 (f-fo) 
 
 Goreyi* . 
 
 52 41 
 
 6 15 
 
 - 40 
 
 + 
 
 - 9-2 
 
 
 - -0068 
 
 Clonmel, 
 
 52 20 
 
 7 41 
 
 _ 61 
 
 + 53 
 
 
 
 4 '013 
 
 
 
 BaUybunan, 
 Broadway, 
 Waterford, 
 
 52 35 
 52 14 
 52 12 
 
 9 34 
 6 20 
 
 7 6 
 
 46 
 67 
 _ 69 
 
 4 121 
 + 3 
 + 31 
 
 + 16-3 
 - 29-0 
 - 14-5 
 
 + -004 
 + -021 
 + -010 
 
 4 -0127 
 - -0025 
 - -0035 
 
 Dingle, . 
 
 52 6 
 
 10 20 
 
 _ 75 
 
 + 150 
 
 4 4-9 
 
 
 
 4 '0140 
 
 Killarney, 
 
 52 3 
 
 9 31 
 
 - 78 
 
 4 121 
 
 4 6-5 
 
 + -Oil 
 
 
 
 Fennoy, . 
 
 52 1 
 
 8 34 
 
 - 80 
 
 + 86 
 
 - 17-7 
 
 + -019 
 
 
 
 Valentia, 
 
 51 56 
 
 10 12 
 
 - 85 
 
 4 146 
 
 4 2-2 
 
 
 
 4 -0089 
 
 Cork, . 
 
 51 54 
 
 8 28 
 
 - 87 
 
 + 83 
 
 _ 21-9 
 
 + -019 
 
 - -0008 
 
 Youghal, 
 
 51 53 
 
 7 51 
 
 - 88 
 
 4- 59 
 
 _ 23-8 
 
 
 
 4 -0011 
 
 Glengariff, 
 
 51 44 
 
 9 33 
 
 - 97 
 
 4 123 
 
 + 3-5 
 
 4 'Oil 
 
 
 
 The equations of condition (E) are of the first dimension with 
 respect to the two unknown quantities they contain, and may be 
 written 
 
 ax + by = c ; (F) 
 
 in which the values of a, b, and c (or of (p - /u ) cos A, A - A , and 
 h - h ), are given in the preceding table. In order to deduce the 
 most probable values of the two unknown quantities, these equa- 
 tions must be combined by the method of least squares. Accord- 
 ingly multiplying equation (F) by the coefficient of a? (a), and by 
 the weight (w) of the determination which it represents, and adding 
 the results, we have 
 
 and, performing the same operation with respect to the coefficient 
 of the other unknown quantity, 
 
 8 (icab) x 4 8 ( 
 
 8 (wbc) . 
 
 These are the two final equations which, by elimination, will fur- 
 nish the most probable values of the quantities sought. 
 
 Let the values of x and y, obtained from these equations, be A 
 and B ; then substituting in (D), 
 
 r cos u = A, r sin n - B ;
 
 MAGNETIC FORCE IN IRELAND. 209 
 
 and dividing, we have 
 
 tan u = -. ; (H) 
 
 .A. 
 
 by which the direction of the isodjnamic line is determined. Again, 
 squaring and adding, 
 
 B*', (I) 
 
 which gives the rate of increase of the force in the* normal direction. 
 The lines of absolute intensity, and of dip, will be obtained by a 
 similar process, the only difference being in the values of the 
 second members of the equation (F) . 
 
 Before we can apply these formulas to the investigation of the 
 lines of horizontal intensity, it is necessary to assign the weights 
 due to each equation of condition, or to the determination which it 
 involves. We shall assume, accordingly, that the weights of the 
 values of (h - /*), recorded in the preceding Table, are measured by 
 the number of separate comparisons from which they have been 
 deduced,* and we shall have, on this principle, 
 
 Limerick, . . . weight = 12, 
 Markree, ... 3, 
 
 Armagh, ... 2, 
 
 the weights of each of the other determinations being represented 
 by unity. 
 
 The values of a, b, and c being <:iven in Table VII., we may 
 now proceed to calculate the coefficients of the equations (Q-). "VVe 
 find, 
 
 (?ra 2 ) = 257431, S(wab) = + 49169, (#) = 116509, 
 
 S(tcac) = - 23-598, S(icbc) = + 35-644. 
 And the equations are 
 
 257431 x + 49169 y = - 23-598, 
 49169 x + 116509 y = 4- 35-644 ; 
 
 * For a more correct method of estimating the weights of observed results, th< 
 reader is referred to the Report on the Magnetic Isoclinal and iBodynamic lines in t!i- 
 British Islands, Eighth Report of the British Attociation for the Adfattcemt*tofSctrcr, 
 p. 95, &c. 
 
 P
 
 210 OBSERVATIONS OF THE TERRESTRIAL 
 
 from which we have, by elimination, 
 
 x = - -0001633 = A ; 
 y = + -0003748 = B. 
 Finally, substituting these values in equations (H, I) 
 
 tan u = - 2-2952, u = - 66 28', r = - -000409.* 
 
 The positive branches of the axes of co-ordinates having been 
 assumed to be those which stretch to the north and to the west, it 
 follows that the lines of equal horizontal intensity lie to the east of 
 north, making an angle of 66^ nearly with the meridian of Dub- 
 lin. The horizontal intensity decreases as we proceed northward, 
 the decrease being equal to the distance traversed in a direction 
 perpendicular to these lines (estimated in geographical miles, or 
 minutes of latitude) multiplied by the coefficient '000409. The 
 lines are laid down in the accompanying chart for differences of 
 O'Ol in the value of the intensity, the corresponding intervals of 
 distance being 24-4 geographical miles. 
 
 On a comparison of the separate determinations with the result- 
 ing lines, it will be observed that the intensities in the northern 
 group are greater than those due to their position, those of the 
 western group less, and those of the south-western again greater. 
 These deviations may, in part, arise from the inexactness of the 
 assumption with which we set out in the computation of the lines, 
 and from the sensible deviation of those lines from parallelism. 
 But they are probably owing in a much greater degree to the dis- 
 turbing causes to which we have already alluded. The separate 
 results composing each of these groups were for the most part ob- 
 tained about the same time, and they are therefore probably affected 
 in the same manner, and nearly in the same amount, by the irre- 
 gular fluctuations in the direction and intensity of the resultant 
 magnetic force. Of these, the changes in the direction of the force 
 are by far the most influential. The relation between the corre- 
 sponding changes in the dip and in the horizontal intensity is ex- 
 pressed by the formula 
 
 dh 
 
 y = - tang sin 1'rfg; 
 
 * The inclination of the lines of equal horizontal intensity, deduced with the 
 aid of additional observations, is = - 62 40', the rate of increase in the normal 
 direction remaining unaltered: Eighth Report, p. 174.
 
 MAGNETIC FORCE IN IRELAND. 211 
 
 (IS being expressed in minutes. Hence when 8 = 71 0', the change 
 of the horizontal intensity, , corresponding to a change of one 
 
 minute of dip, is - '00084 ; and for a variation of 12' in the dip, the 
 corresponding variation of the horizontal force is -01. 
 
 In deducing the lines of dip from observation, it seems advis- 
 able to separate the results of the two years. For the weights we 
 shall assume 
 
 Limerick (1834), .... weight = 5, 
 Armagh, .... = 2; 
 
 the weights of each of the other determinations being unity. 
 
 Making the computations for the year 1834, we obtain the fol- 
 lowing results : 
 
 S(urf) = 86660, S(icab) = + 36129, S(wb z ) = 64303, 
 
 S(wac) = + 11043, 8(wbc) = - 18633. 
 The final equations accordingly are 
 
 86660* + 36129y = + 11043; 
 36129* + 64303y = - 18633. 
 
 From which we deduce 
 
 a? = + -3228 = cos t>, 
 y = - '4705 = s sin v ; 
 
 in which v denotes the angle which the isoclinal line makes with 
 the meridian of Dublin, and s the coefficient which determines the 
 rate of increase of the dip in the perpendicular direction. Dividing, 
 squaring and adding, we find 
 
 tan v - - 1-458, t? = - 55 33', 
 
 - -571. 
 
 The following are the results of calculation for the year 1835 : 
 S (a 2 ) - 149922, 8(ab) = + 31821, S(V) - 
 S (ac) = + 32157, S (be) = - 18372 ;
 
 212 OBSERVATIONS OF THE TERRESTRIAL 
 
 so that the final equations are 
 
 149922o? + 31821 y = + 32157; 
 31821* + 55339y = - 18372. 
 From these we deduce 
 
 x = +'3250, y=- -5196, 
 tan v = - 1-599, v = - 57 59', 
 s = -613. 
 
 It would appear, then, that the angle which the isoclinal lines 
 in Ireland make with the meridian is on the increase a result 
 which is in conformity with the general progress of these lines, as 
 inferred from a comparison of recent observations with those of an 
 earlier date.* 
 
 For the mean of the two years, 
 
 x = + -3239, y=- -4950, 
 tan *? = - 1-528, = -5648', 
 s = -592. 
 
 The lines in the annexed chart are deduced from these last 
 results ; and it appears from them that the interval of the lines 
 corresponding to a difference of half a degree of dip is 50-7 geo- 
 graphical miles. 
 
 The lines of dip and of horizontal intensity being known, the 
 lines of total intensity may be deduced. For if / denote the total 
 intensity, h its horizontal component, and S the dip, as before, 
 
 and differentiating, and dividing by the equation itself, 
 
 /-' df=h~ l dh + tan S sin 1'dS. (I.) 
 
 Now, if the values of * and y for the lines of dip and of 
 horizontal intensity be denoted by ar (8) , ae w and y w , y (h] , and if x (f] 
 
 * This is further confirmed by the results obtained with the help of additional obser- 
 vations. See Eighth Report of the British Association for the Advancement of Science, 
 p. 118.
 
 MAGNETIC FORCE IN IRELAND. 213 
 
 and yy) be the corresponding quantities for the lines of total 
 intensity, 
 
 (II.) 
 
 df=ax (f) -by (f] , 
 
 in which a = (fjt - /K O ) cos A, b = A - A ; /* and A being the longitude 
 and latitude of any assumed station, and /i and A those of Dub- 
 lin. Substituting these values in (I.), it becomes 
 
 tan S sin 
 
 But as a and 6 are entirely independent, their coefficients must be 
 separately equal, and we have 
 
 - l x = k~ l xh + tan S sin 
 
 tan 5 sin l'y (6 ) ; 
 
 so that the values of #(/) and^(/) are found when those of #(*), &(&), 
 y (h }, ya) are known. 
 
 Let the second members of equations (IV.) be denoted, for 
 abridgment, by P and Q, then 
 
 X( f ] = tcOBW =/P, 
 
 2/(/) = ^ sin ; =/Q ; 
 
 in which w is the incKnation of the line of total intensity to the 
 meridian, and t the coefficient which determines the rate of increase. 
 Dividing the latter by the former, there is 
 
 tan w = -p . (V.) 
 
 And squaring and adding, 
 
 t=/SJ I Tw. (Vi.) 
 
 From the preceding formulas it appears that the direction of the 
 isodynamic line at any point is dependent on the values of /i and of c 
 at that point, so that these lines will not be parallel, even though tlie 
 lines of dip and of horizontal intensity should be so. The devia- 
 tions, however, will not be considerable within the limits of Ire-
 
 214 OBSERVATIONS OF THE TERRESTRIAL 
 
 land ; and for our present purpose it will be enough to seek the 
 mean direction of the lines, and the mean rate of increase in the 
 direction perpendicular to them. We must therefore employ in 
 the preceding formulas the values of /, h, and 8, corresponding to 
 the mean point of the island, or the point whose latitude and lon- 
 gitude are 53 25' and 7 55',* and for which therefore 
 
 Now it has been already found that 
 
 se w = - -0001633, a? (8) - + -3239, 
 y (k ) = + -0003748, y (8) = - -4950 ; 
 
 and substituting these values in the formulas 
 
 8 - 8 = (jU - fJLo) COS X(j) - (X - Xo)y(S), 
 
 h - h = (ju - juo) cos X#(A) - (X - X ) y(A), 
 we find 
 
 8 - 8 = 21'-4, h-h Q = - -0113. 
 Consequently, 
 
 8 = 7124'-4, A = -9282,/= 1-0295. 
 
 We have now the numerical values of all the quantities which 
 enter the formulas 
 
 P = Jr l x(h) + tan 8 sin l'a?( 8 ), 
 Q = h~ l y( h ) + tan 8 sin ry(s) ; 
 and we find on substitution, 
 
 P = + -0001042, Q = - -0000242. 
 Introducing these values in (V.) and (VI.), 
 
 tan w = - -2322, w = - 13 4', t = -0001102. 
 These results, however, are not entitled to much confidence. 
 An attentive consideration of the formulas (IV.) and (V.) will 
 show that the direction of the resultant isodynamic lines will vary 
 
 * This point corresponds, almost exactly, to the town of Athlonc.
 
 MAGNETIC FORCE IN IRELAND. 215 
 
 very widely with moderate variations in the values of X( h ^ xy w , (5 ), 
 i/(s), on which it depends ; or, in other words, that a small error in 
 the position of the lines of dip, or of horizontal intensity, will entail 
 a very great one in that of the lines of total force. Thus, if we 
 were to take for the lines of dip those inferred from the observa- 
 tions of the year 1835 alone, we should find 
 
 P = + -0001051. Q = - -0000455, 
 
 tan w = - -4329, w = - 23 25' ; 
 
 a result differing by more than 10 from the former. In these 
 latitudes, therefore, very great accuracy is necessary in the deter- 
 mination of the lines of dip and of horizontal force before we can 
 make, in this manner, even an approximation to the direction of 
 the lines of total force. For these reasons the results of the direct 
 method, to which we now proceed, seem to be deserving of more 
 confidence. 
 
 In the calculation of the isodynamic lines from the results of 
 observation by the statical method, we shall take the number of 
 observations at each station to represent the weight of the result ; 
 we have in this manner 
 
 Limerick, .... weight = 4, 
 Armagh, ..." =2, 
 
 Youghal, .... =2; 
 
 the weight of each of the other determinations being unity. 
 The following are the results of the computation : 
 
 S(wa*) = 178390, S(waV) = + 38216, 8(wb v ) = 96066, 
 
 8(wac) = + 13-3229, S(wbc) = - 2'2448. 
 The final equations therefore are 
 
 178390* + 38216^ = + 13-3229, 
 38216* + 96066y = - 2-2448 ; 
 from which we obtain, by elimination, 
 
 x = + -00008711, y = - -00005802.
 
 216 OBSERVATIONS OF THE MAGNETIC FORCE IN IRELAND. 
 
 Consequently, 
 
 tan w = - '6661, w = - 33 40', t = -0001047.* 
 
 The lines of total intensity thus deduced are laid down in the 
 annexed chart for differences of '005, these differences correspond- 
 ing to intervals of 47'6 geographical miles. It will be seen that 
 their direction diverges widely from that of the lines of dip ; 
 and although the position of the two classes of lines may need 
 further correction, it does not seem likely that such correction will 
 have the effect of diminishing, at least by any considerable amount, 
 the divergence. 
 
 * The mean inclination of the isodynamic lines deduced with the help of additional 
 observations is u = - 35 0', the rate of increase in the perpendicular direction remain- 
 ing unaltered. Eighth Rpeort of the British Association for the Advancement of Science, 
 p. 185.
 
 rERRESTRIAL MAGNETIC FORCE IN IRELAND. 
 
 +3.KrnjS!<
 
 VI. ON THE POSITION OF THE ISOGONAL LINES IN IRE- 
 LAND, DEDUCED PROM THE OBSERVATIONS OF 
 CAPTAIN SIR JAMES CLARK ROSS, R. N. 
 
 From the Proceedings of the Royal Irish Academy, 1850. 
 
 IN the year 1835 I laid before the British Association, then as- 
 sembled in Dublin, a Eeport on the Direction and Intensity of the 
 Terrestrial Magnetic Force in Ireland, based upon observations 
 made by Lieut.-Colonel Sabine, Sir. James C. Boss, and myself. 
 In these observations Mr. Eobert Were Fox and Professor Phillips 
 afterwards took part ; and the survey was subsequently extended 
 to the whole of the British Islands. The details of this extended 
 survey are given in a Memoir on the Magnetic Isoclinal and Iso- 
 dynamic lines in the British Islands, drawn up chiefly by Lieut.- 
 Colonel Sabine.* 
 
 The observations contained in these Reports are limited to the 
 Magnetic Inclination and Intensity. Observations of the Declina- 
 tion, as well as of the other two elements, were indeed made by 
 Sir James Boss ; but they have only lately been given to the public 
 in a Memoir by Lieut.-Colonel Sabine, on the lines of Magnetic 
 Decimation in the Atlantic, f In this Memoir, the observations 
 referred to are combined with a large mass of other materials, and 
 the position of the isogonal lines inferred from the whole by a 
 graphical process. The Irish portion of these observations is, how- 
 ever, so distinct, and so complete in itself, that it seemed to me 
 desirable that they should be discussed by the same method which 
 had already been applied to the observations of the other two ele- 
 
 * Eighth Report of the British Association for the Advancement ofScimet. 
 t Philosophical Transactions, 1849, Part ii.
 
 218 ON THE ISOGONAL LINES IN IRELAND. 
 
 ments, in the reports above referred to ; such a discussion serving 
 to complete the Magnetic Survey, so far as Ireland is concerned, 
 and to furnish a formula for the Magnetic Declination at any point 
 in the island whose position is known. 
 
 The following is the mode of doing this : 
 
 If S denote the magnetic declination at any place ; S that at 
 some near station which is taken as the origin of co-ordinates ; 
 and x and y the actual distances (in geographical miles) between 
 them, measured on the parallel of latitude and on the meridian, 
 respectively or the co-ordinates of position of the former station 
 referred to the latter as an origin ; the relation of these quantities 
 is expressed approximately by the equation 
 
 in which M and N represent the increase of declination correspond- 
 ing to each geographical mile of distance in the two directions. If 
 A and /j. denote the latitude and longitude of the former station, 
 A and [i those of the latter, 
 
 y = A-A , x = OU-M O ) cos A. 
 
 It is evident, that if X and y be treated as variable, S being 
 constant, the preceding equation is that of the locus of all the 
 points of given declination. It is that of a right line, making the 
 angle with the meridian, 
 
 and the increase of declination corresponding to each geographical 
 mile of distance, in a direction perpendicular to this line, is 
 
 It is evident then that, to obtain the values J/"and N, obser- 
 vation must give the values of the declination at three, or more, 
 stations. The observations of Sir James Boss were taken at 
 twelve stations, well distributed throughout the island ; and as they 
 were all made during the months of October and November, 1838, 
 no correction is required to reduce them to a common epoch. For 
 convenience of reference, they are here extracted from Colonel
 
 ON THE ISOGONAL LINES IN IRELAND. 
 
 219 
 
 Sabine's Memoir, together with the longitudes and latitudes of the 
 places of observation. 
 
 Station. 
 
 \ 
 
 M 
 
 S 
 
 Valentia, 
 
 51 56' 
 
 10 17' 
 
 28 42' 
 
 Killarney, 
 
 52 2 
 
 9 30 
 
 28 11 
 
 Westport, 
 
 53 48 
 
 9 29 
 
 29 9 
 
 Limerick, 
 
 52 40 
 
 8 36 
 
 28 3 
 
 Cork, . 
 
 51 54 
 
 8 28 
 
 27 44 
 
 Markree, 
 
 54 14 
 
 8 28 
 
 29 15 
 
 Shannon Harbour 
 
 53 14 
 
 7 53 
 
 28 3 
 
 Edgeworthstown, 
 
 53 42 
 
 7 33 
 
 28 8 
 
 Londonderry, . 
 Waterford, . . 
 
 54 59 
 52 15 
 
 7 19 
 
 7 8 
 
 28 47 
 26 44 
 
 Armagh, . . 
 
 54 21 
 
 6 39 
 
 28 8 
 
 Dublin, . . . 
 
 53 21 
 
 6 15 
 
 27 35 
 
 Taking Dublin as the origin of co-ordinates, and substituting 
 the values of A - A , /* - n , and S - S , given by this Table, in the 
 equation above given, we obtain eleven equations of condition, from 
 which the values of M and N are obtained by the method of least 
 squares. They are the following : 
 
 Jf=0'-690, ^ 
 
 We may now test the accuracy of these numbers, by employing 
 the formula to calculate the values of the declination at each of the 
 eleven stations. The result of this calculation gives, at Waterford, 
 a difference between the observed and calculated values amounting 
 to 34', an amount which far exceeds the probable error of obser- 
 vation. This difference is, therefore, probably due to some local 
 irregularity of the magnetic force. But, whatever be its cause, it 
 is obvious that it tends to vitiate the general result ; and that a 
 nearer approximation to the values of M and N will be obtained 
 by excluding that observation from the computation. We thus 
 obtain, from the remaining ten equations, 
 
 And substituting these values, we find 
 ang. (tang = - ~ ) = - 37 25' ; 
 
 0'-867.
 
 220 ON THE ISOGONAL LINES IN IRELAND. 
 
 Accordingly, the isogonal lines in Ireland lie to the east of north, 
 making an angle of 37 25' with the meridian of Dublin ; and the 
 declination increases as we proceed in the north-westerly direction, 
 the increase being 52" for each geographical mile, in a direction 
 perpendicular to these lines.* 
 
 Finally, the declination at any point of the island, whose longi- 
 tude and latitude are known, is given by the formula 
 
 S - S = 0'-527 (X - X ) + 0'-689 fc - ,,) cos X ; 
 
 the declination at Dublin, <5 , being supposed known. Or, if we 
 substitute for cos X the value corresponding to the mean latitude 
 (\-53ir), 
 
 S-S =0'-527 (X -X ) +0'-412 (^-^J. 
 
 The mean declination at Dublin, for the year 1850, is 26 29' 
 west ; and as the yearly value of the secular change of the declina- 
 tion is - 6' - 06, the mean declination, in any not very remote future 
 year, will be given by the formula 
 
 S = 2629'-6'-06x ; 
 
 n being the number of years, counted from the present. If greater 
 accuracy be desired, the diurnal and annual variations of the de- 
 clination, corresponding to the time of the day and of the year, 
 must be added. . 
 
 * This result agrees very closely with Colonel Sabine's map of the isogonal lines in 
 the Atlantic, as to the direction of the lines, but gives a more rapid rate of increase. '
 
 VII. ON A NEW MAGNETICAL INSTRUMENT, FOR THE 
 MEASUREMENT OF THE INCLINATION, AND ITS 
 CHANGES. 
 
 From the Proceedings of the Royal Irish Academy, 1842. 
 
 IF a soft iron bar, perfectly devoid of magnetic polarity, be held in 
 a vertical position, it immediately becomes a temporary magnet 
 under the inducing action of the earth's magnetic force, the lower 
 extremity becoming a north pole, and the upper a south pole. Ac- 
 cordingly, if a freely- suspended horizontal magnet, whose dimen- 
 sions are small in comparison with those[of the bar, be situated near, 
 in a plane passing through one of these 'poles, it will be deflected 
 from the magnetic meridian. The deflecting force is the induced 
 force of the bar, which may be regarded as proportional to the 
 energy of the inducing cause, i. e. to the vertical component of the 
 earth's force ; while the counteracting force is the horizontal com- 
 ponent of the same force, acting directly on the magnet itself, to 
 bring it back to the magnetic meridian. Thus the magnet will 
 take up a position of equilibrium, under the action of these oppos- 
 ing forces; and this position will serve to determine the ratio 
 which subsists between them. When the right line connecting 
 the centre of the horizontal magnet, and the acting pole of the 
 bar, is perpendicular to the magnetic meridian, the tangent of the 
 angle of deflection will measure the ratio of the two forces, and will 
 therefore be proportional to the tangent of the. magnetic inclination. 
 Accordingly, by observing the changes of position of the horizontal 
 magnet, so circumstanced, we can infer those of the inclination 
 itself. 
 
 But the iron bar may have (and generally will have) a certain 
 portion of permanent magnetism, which will concur with the in-
 
 222 ON A NEW MAGNETICAL -INSTRUMENT. 
 
 duced magnetism in producing the deflection ; and it becomes 
 necessary to institute the observations in such a manner as to be 
 able to eliminate the effects of this extraneous cause. For this 
 purpose we have only to invert the bar, so that the acting pole, 
 which was uppermost in one part of the observation, shall be lower- 
 most in the other. The induced polarity will, under these circum- 
 stances, be opposite in the two cases ; and the acting force will in 
 one case be the sum of the induced and permanent forces, and in the 
 other their difference. 
 
 Let X and T denote the horizontal and vertical components of 
 the earth's magnetic force, M the intensity of the permanent mag- 
 netism in the acting pole, and m the magnetic moment of the sus- 
 pended magnet. The intensity of the induced magnetism is, by 
 hypothesis, equal to 
 
 *T, 
 
 k being an unknown constant ; and when this is of the same name 
 as the permanent magnetism, the intensity of the acting force, at 
 the unit of distance, is 
 
 kY+ M. 
 
 Accordingly, the moment of this force to turn the suspended mag- 
 net is (kY+ M) mr cos u, u being the angle of deflection, and r a 
 constant depending on the distance ; or, making, for abridgment, 
 kr = p,Mr = q, 
 
 (p Y + q] m cos u. 
 
 But this deflecting force is resisted by the earth's horizontal force, 
 the moment of which to turn the magnet is 
 
 Xm sin u ; 
 
 and the magnet will rest when these moments are equal. Hence 
 the equation of equilibrium is 
 
 (1) 
 
 By the same reasoning it will appear, that when the induced and 
 permanent magnetisms are of contrary names, there is 
 
 pY- q = Xt&nu'; (2) 
 
 in which u' is the new angle of deflection when the bar is inverted. 
 Adding these equations together, and observing that Y = X tan 6,
 
 ON A NEW MAGNETICAL INSTRUMENT. 223 
 
 being the inclination, we have 
 
 2p tan = tan u + tan u '. (3) 
 
 This equation would furnish at once the inclination sought, 
 provided we knew the value of the constant k. In order to deter- 
 mine it, we have only to place the iron bar horizontally in the 
 magnetic meridian, its acting pole remaining in the same place as 
 before, but pointing alternately to the north and south. The in- 
 ducing force is, in this case, the horizontal component of the earth's 
 magnetic force ; and it will be readily seen that the equations of 
 equilibrium are similar to (1) and (2), substituting X for Y. If 
 therefore v and v denote the angles of deflection in these positions, 
 we have 
 
 2p = tan + tan if ; (4) 
 
 and dividing (3) by this, 
 
 tan u + tan u' /K \ 
 
 tan 9 = x - - -- r . (5) 
 
 tan v + tan v 
 
 Thus, from the deflections produced in these four positions of the 
 bar, we obtain the inclination. 
 
 In order to determine the changes of the inclination, it is not 
 necessary to observe the deflections in the horizontal position of the 
 bar. Let equation (1) be differentiated, X, Y, and u being all 
 variable, and let the resulting equation be divided by (3). We 
 thus obtain the following equation, from which p and q are both 
 eliminated : 
 
 A F 2Aw 2tanw AX 
 
 _ 
 Y ~ COS*M (tan u + tan u} tan u + tan u'' X ' 
 
 But from the relation Y = X tan 0, we have 
 AF AX A0 
 
 Y~~^~ + sin 0cos0 ; 
 
 and substituting 
 
 A0 cos?/ At/ + v BJn(i*-tQ AX ^ 
 
 snT20 " cos M sin (u + ') sin (w + n) X ' 
 
 The second term' of the right-hand member of this equation con- 
 tains a correction required for th- sii.iuli:inoous changes of the 
 horizontal intensity ; but this correction will be generally small,
 
 224 ON A NEW MAGNETICAL INSTRUMENT. 
 
 and, when the bar has no permanent magnetism, will vanish alto- 
 gether. In this latter case, in fact, it appears from (1) and (2) 
 that u' = u ; so that the preceding equation is reduced to 
 
 A-5L|A. (7) 
 
 We must remember that, since the angle u in the preceding for- 
 mulas is the deviation of the suspended magnet from the position 
 which it would assume under the action of the earth alone, its 
 changes are the differences between the observed changes of position 
 of the suspended magnet and the corresponding changes of decli- 
 nation. Let a denote the deviation of the suspended magnet, 
 measured from some fixed line, and a' the corresponding angle 
 when the iron bar is removed ; then 
 
 ., u = a - a', AM = Aa - Aa'. 
 
 But Aa = &w, Aa' = k'n' ; in which n denotes the number of divi- 
 sions of the scale of the instrument corresponding to the angle Aa, 
 n the number corresponding to the angle A a' as shown by the de- 
 clinometer, and k and k f the arc- values of a single division in each 
 instrument. Hence 
 
 Aw - 1m - k'n. (8) 
 
 I now proceed to the construction of the apparatus employed 
 in these measurements. 
 
 The magnet is cylindrical ; its length is three inches, and dia- 
 meter one-fourth of an inch. A mirror is attached to the stirrup 
 by which it is suspended, by means of which the varying position 
 of the magnet may be observed with a telescope at a distance, after 
 the method of Gauss. This mirror is of course vertical ; and it has 
 a motion round a vertical axis, by means of which it may be ad- 
 justed to any desired position of the observing telescope. The 
 mirror is circular, and is three-fourths of an inch in diameter. The 
 moveable part, the stirrup to which it is attached, has the form of a 
 cross ; and it is rendered vertical by means of three screws, near 
 the ^xtremities of three of the arms of the cross, the heads of which 
 project and hold it. The mirror is maintained in contact with 
 these heads by springs at the back. 
 
 The box is octagonal : the interval between the opposite sides is 
 four mches, and that between the top and bottom two inches. The
 
 ON A NEW MAGNETICAL INSTRUMENT. 225 
 
 top and bottom, and the connecting pillars, are formed of gun- 
 metal ; the eight sides are closed by moveable pieces, three of 
 which are of glass, and the rest of ebony. To the top of the box 
 is attached an upright tube of glass, eight inches in length, which 
 incloses the suspension thread. The suspension apparatus at the 
 top of the tube is of the usual construction ; the circular piece to 
 which it is attached has a movement of rotation, and its outer sur- 
 face is graduated to 5, for the purpose of determining the effect of 
 torsion of the suspension thread. 
 
 The base of the instrument is a circle of gun-metal, six inches 
 in diameter, graduated on the edge. The box is connected with 
 this circle by a short conical stem, forming the axis of a second 
 plate, which revolves upon the fixed one. This moveable plate 
 carries two verniers, by which the angle of rotation may be read 
 off to minutes. Two tubular arms, slightly inclined to one an- 
 other, are attached to this plate ; and their other extremities are 
 connected by a cross-piece, which carries a short scale at a distance 
 of eighteen inches from the mirror. This part of the apparatus is 
 employed in determining the total angles of deflection. 
 
 The soft iron bar is a cylinder, twelve inches long, and three- 
 fourths of an inch in diameter. One of its extremities is inclosed 
 in a hollow cylinder of brass, connected with a horizontal pivot 
 which revolves in a fixed socket. The axis of this pivot being in 
 the line passing through the centre of the suspended magnet, and 
 perpendicular to the magnetic meridian, it is obvious that the bar 
 has a movement of rotation in the plane of the magnetic meridian 
 itself. The distance of the axis of the bar from the centre of the 
 magnet is about five inches ; and it is so placed that the induced 
 pole is in the direction of the axis of the pivot, and thus remains 
 fixed during the movement of the bar. 
 
 The changes of position of the suspended magnet are observed 
 at a distance by means of a fixed telescope and scale. The scale, 
 whose divisions are reflected by the mirror, is attached above the 
 telescope to a support near the eye-end. 
 
 Having explained the principle of this instrument, and given 
 the details of its construction, it remains only that I should describe 
 the observations made for the purpose of testing its performance. 
 I shall pass over for the present those which relate to the absolute 
 inclination, because they have yielded results which can be regarded 
 only as approximations to the truth, and I have not succeeded as 
 
 Q
 
 226 ON A NEW MAGNETICAL INSTKUMENT. 
 
 yet in tracing the errors to their source. It is manifest, however, 
 that an instrument may be a good differential instrument, while it 
 is incapable of yielding absolute results; and there are special 
 reasons why this should be the case with the apparatus now under 
 consideration. Accordingly its failure in the latter respect, even 
 though established, would furnish no ground for despairing of its 
 success in the former. 
 
 It is obvious that the apparatus is wholly free from the errors 
 belonging to magnetical instruments moving on a fixed axle ; and 
 the only doubt of its performance must relate to the changes of 
 induced magnetism in the iron bar. Thus it might be questioned, 
 before trial, whether such a bar receives in all cases an amount of 
 free magnetism proportional to the inducing force ; whether, 
 again, the minutest changes in the latter are accompanied by 
 corresponding changes in the former; and whether, lastly, the 
 changes thus produced are instantaneous, or, at least, demand no 
 appreciable time for their development. 
 
 In the first experiments which I made, for the purpose of de- 
 termining these questions, the induced magnetism of the iron bar 
 was altered by means of a permanent magnet, placed in the same 
 right line with the bar, and at a known distance from it. The 
 effect produced upon the position of the suspended magnet being 
 observed, the distance was altered by a known amount, and a new 
 observation taken ; and so on, at many different distances. Then, 
 the law of action of the inducing magnet being known, we may 
 calculate the changes of deflection of the suspended magnet, on the 
 supposition that the changes of the induced force of the bar are 
 proportional to those of the inducing action, and then compare 
 them with the changes of deflection observed. The calculated and 
 observed results of many series of observations, taken in this 
 manner, were found to accord as nearly as the accuracy of the 
 observations themselves allowed. 
 
 In making this comparison, however, it is necessary to take 
 into account the effect of the direct action of the fixed magnet upon 
 the suspended one. The axis of the former magnet being not far 
 from the vertical passing through the centre of the latter, its action 
 upon it and upon the iron bar follow, nearly, the same law ; so that 
 its direct effects upon the position of the suspended magnet are, 
 very nearly, proportional to those which it produces through the 
 medium of the induced force of the bar. On this principle the
 
 ON A NEW MAGNETICAL INSTRUMENT. 227 
 
 observed results may be cleared, appf oximately, of those parts of 
 the changes which are foreign to the question. Still it must be 
 admitted that such a complication of the results tends to weaken 
 their evidence; and it was therefore desirable to obtain further 
 proof, in a manner less exceptionable. 
 
 The object being to alter the inducing action according to a 
 known law, and to observe the changes of the induced force, as 
 shown by the position of the suspended magnet, it is manifest that 
 it may be attained by simply varying the angle which the iron bar 
 makes with the direction of the earth's magnetic force, the distance 
 of its pole from the suspended magnet remaining unchanged. In 
 fact, it will be seen, by pursuing the same reasoning as before, that 
 if R denote the total force of the earth, and ^ the angle which the 
 bar makes with its direction, the equation of equilibrium of the 
 suspended magnet is 
 
 pit, cos i// + q = X tan u, 
 
 the line connecting the pole of the bar with the centre of the sus- 
 pended magnet being, as before, perpendicular to the magnetic 
 meridian. Hence, if the bar be devoid of permanent magnetism 
 (or q = 0), and if the forces R and X remain unchanged during 
 the experiments, we have 
 
 tan u = a cos ^, 
 being a constant. 
 
 In order to observe whether the deflections "of the suspended 
 magnet obeyed this law, a small divided circle was attached to the 
 piece upon which the iron bar moved, in such a manner that the 
 axis of the pivot passed through its centre. The circle being fixed, 
 and the bar connected with the moveable arm carrying the vernier, 
 we have the means of determining the angle through which it is 
 moved. The plane of the motion coinciding with the magnetic 
 meridian, the inclination of the bar to the vertical was altered by 
 5 between the successive observations of the position of the sus- 
 pended magnet. The following Tables contain the results of two 
 such series of observations. The first column of each gives the in- 
 clination of the bar to the vertical; the second, its inclination' (<A) to 
 the direction of the magnetic force, i.e., the former angle increased 
 by the complement of the magnetic inclination (19 10'). The third 
 column contains the observed readings of the scale, corresponding 
 to the positions of the suspended magnet ; the fourth, the differ- 
 
 Q2
 
 228 
 
 ON A NEW MAGNETICAL INSTRUMENT. 
 
 ences between each of these readings and the reading belonging to 
 the vertical position of the bar, converted into angular measure ; the 
 fifth, the actual deflections ; the sixth, the calculated deflections, as 
 deduced by the formula given above ; and the seventh, the differences. 
 In order to derive the numbers of the fifth column from those 
 of the fourth, it is necessary to know the deflection corresponding* 
 to the vertical position of the bar. This angle is determined by 
 placing the bar vertically, with its acting pole above and below 
 successively, and noting the readings of the horizontal circle, when 
 the same division of the moveable scale, reflected by the mirror, 
 was brought to coincide with the fixed wire of the telescope. 
 The differences between each of these readings, and the similar 
 reading when the bar is removed, are double the deflections 
 corresponding to the two positions of the bar ; and, when they 
 are nearly equal, the mean of these deflections may be taken as 
 that due to the induced force. 
 
 FIRST OBSERVATION. 
 
 Acting end of bar a south pole, reading = 14 8', deflection = 17 0' 
 north pole, ... 82 51, = 17 22 
 
 Bar removed, . . 48 7, mean =1711 
 
 Inclination 
 to Vertical. 
 
 * 
 
 Reading 
 of Scale. 
 
 Angular 
 Differences. 
 
 M 
 Observed. 
 
 n 
 Calculated. 
 
 Difference. 
 
 + 14 30 
 
 33 40' 
 
 2-2 
 
 -l56'-2 
 
 15 14'-8 
 
 15 14'-5 
 
 + 0'-3 
 
 + 10 
 
 29 10 
 
 13-2 
 
 - 1 12-4 
 
 15 58 -6 
 
 15 57 -2 
 
 + 1-4 
 
 + 50 
 
 24 10 
 
 23-1 
 
 - 33-0 
 
 16 38 -0 
 
 16 37 -8 
 
 + 0-2 
 
 
 
 19 10 
 
 31-4 
 
 0-0 
 
 17 11 -0 
 
 
 
 - 5 
 
 14 10 
 
 37-5 
 
 + 24-3 
 
 17 35 -3 
 
 17 36-7 
 
 -1-4 
 
 -10 
 
 9 10 
 
 42-8 
 
 + 45-4 
 
 17 56 -4 
 
 17 54-7 
 
 + 1 -7 
 
 -13 30 
 
 5 40 
 
 45-8 
 
 + 57-3 
 
 18 8-3 
 
 18 2-7 
 
 + 5-6 
 
 SECOND OBSERVATION. 
 
 , Acting end of bar a south pole, reading = 14 23', deflection = 16 36' 
 
 
 north pole, . . 
 
 . 82 15, = 17 20 
 
 
 j> Bar removed, . 
 
 . 47 35, mean = 16 58 
 
 Inclination 
 to Vertical. 
 
 * 
 
 Reading 
 of Scale. 
 
 Angular 
 Differences. 
 
 Observed. 
 
 u 
 Calculated. 
 
 Difference. 
 
 + 150' 
 + 10 
 + 50 
 
 
 34 10' 
 29 10 
 24 10 
 19 10 
 
 2-6 
 14-4 
 24-8 
 33-2 
 
 -2' l'-S 
 -1 14-8 
 - 33-4 
 -0 
 
 1456'-2 
 15 43 -2 
 16 24 -6 
 16 58 -0 
 
 1457'-8 
 15 45 -0 
 16 25 -2 
 
 -l'-6 
 -1 -8 
 -0-6 
 
 - 5 
 
 14 10 40-0 i + 27-1 
 
 17 25-1 
 
 17 23 -3 + 1 -8
 
 ON A NEW MAGNETICAL INSTRUMENT. 229 
 
 In the preceding observations a telescope of law power was 
 employed, and the arc-value of a single division of the scale 
 (which was at the distance of eighteen inches from the mirror) 
 was 3'-98. The differences of the observed and calculated results, 
 therefore, do not in general exceed the amount which may be 
 fairly ascribed to errors of observation ; and the accordance is 
 sufficient to establish the fact, that the changes of the induced 
 force of the bar are, within the observed limits, proportional to 
 those of the inducing action. It is important to note also that 
 the changes of the induced force, produced artificially in these 
 experiments, are much greater than any which are likely to arise 
 from the variations of the vertical component of the earth's 
 magnetic force, and therefore that the experiments may be 
 regarded as severe tests of the performance of the instrument. 
 
 The preceding observations further showed, that the changes 
 in the inducing force were imtantly followed by their effeets upon 
 the suspended magnet; so that the changes of induced force 
 required no appreciable time for their development. It remained 
 only to ascertain, in a somewhat fuller manner, how far the bar 
 was susceptible of minute magnetic changes, from very small 
 variations of the acting force. For this purpose, a series of 
 readings of the scale was taken, the inclination of the bar to the 
 vertical being altered by half a degree between the consecutive 
 readings. The mean difference of the successive readings was 
 found to agree, very exactly, with the calculated difference ; 
 while the partial differences deviated from the mean by an amount 
 not exceeding the limits of error of observation. It may be 
 presumed, therefore, that the changes of the induced force in the 
 iron bar are continuous ; and, accordingly, that the sensibility of 
 the instrument is only limited by the optical power, which is 
 applied to observe the changes of position of the suspended 
 magnet.* In the experiments above described, the arc- value of the 
 divisions of the scale was nearly 4' : with the modifications since 
 introduced into the reading part of the apparatus, the scale 
 
 * Against this conclusion is the fact, that considerable changes in the induced force 
 of the bar seem to be attended with some permanent changes of polarity ; and it may be 
 presumed that the same thing will take place, in a proportionate degree, with tho 
 minute changes induced by tho variations of the earth's force. It remains for future 
 examination to determine how far such permanent changes, if they occur, may impair 
 the accuracy of the results.
 
 230 ON A NEW MAGNETICAL INSTRUMENT. 
 
 divisions have nearly the same value as in the instrument for the 
 measurement of the declination, so that the readings may be 
 made with certainty to less than the tenth of a minute. The 
 present value of the inclination in Dublin is about 70 50'; and 
 the mean deflection produced by the iron bar in its actual position 
 being about 19, it follows that the changes of inclination are 
 inferred with the same degree of precision, very nearly, as the 
 observed changes of angle. 
 
 The last test to which the instrument was subjected was, to 
 employ it for some time in the regular observation of inclination 
 changes, for which it is destined, and to ascertain how far the 
 mean results of the observations of successive weeks agreed in 
 exhibiting the law of the diurnal variation. The instrument was 
 accordingly observed for five successive weeks, every second hour 
 during the day and night, and the means calculated, omitting those 
 days in which the series was broken by changes of adjustment 
 during experiment. The curves now laid before the Academy 
 represent the projected results of the observations of each of these 
 weeks, together with that of the mean of the whole. An inspec- 
 tion of them is sufficient to show that the curves of the separate 
 weeks accord with one another, and with the mean, as nearly as 
 can be expected in the results of such limited series, the dis- 
 cordances being only such as are due to the known irregularities 
 in the direction of the earth's magnetic force.
 
 Till. REMAKES ON THE THEORY OF THE COMPOUND 
 MAGNETIC NEEDLE. 
 
 Proceedings of the Royal Irish Academy, 1848. 
 
 WHEN two magnetic needles are united by a fixed vertical axis 
 passing through their centres, and perpendicular to both, the 
 moment of the force exerted by the earth upon them is the sum 
 of the moments which it exerts upon each needle separately, and 
 is, therefore, 
 
 X (M sin u + M' sin M') ; 
 
 in which M and M' denote the magnetic moments of the two 
 needles, u and u the angles which their magnetic axes make with 
 the magnetic meridian, and X the horizontal component of the 
 earth's magnetic force. In the state of equilibrium this moment 
 is nothing ; so that if u and U Q ' denote the corresponding values 
 of u and u' t there is 
 
 M sintfo + -3/'sinw'o = 0. (1) 
 
 Consequently, if two lines be taken from any point of the vertical 
 axis, parallel to the magnetic axes of the two needles, and pro- 
 portional to their magnetic moments, M and M', the diagonal of 
 the parallelogram constructed upon them must lie in the magnetic 
 meridian, when the compound needle is at rest. 
 
 Again, if we substitute u = t( + *', ' = '< + ''> i Q * ue general 
 expression of the statical moment, it becomes, in virtue of (1), 
 
 X(M cos + JT cos ') sin /. 
 Hence the compound needle is acted upon as a single needle,
 
 332 ON THE THEORY OF COMPOUND MAGNETIC NEEDLE. 
 
 whose magnetic axis lies in the direction of the diagonal of the 
 parallelogram above mentioned, and whose magnetic moment is 
 
 fj. = M cos MO + M' GOSU'O. (2) 
 
 Accordingly, the diagonal of the parallelogram already referred 
 to will represent in magnitude the magnetic moment of the 
 compound needle. For, if the equations (1) and (2) be squared, 
 and added together, and the angle contained by the magnetic 
 axes of the two needles, u' - u , be denoted by a, we have 
 
 t? = M 2 + 2MM' cos a + M '\ (3) 
 
 In the case of the astatic needle, a = 180 - S, being a very 
 small angle, and cos a = - cos 8 = - 1 + \ S 2 , q .p. whence 
 
 V = (H-M f y + MM'&. (4) 
 
 Accordingly, when M - M ' is not a very small quantity, the 
 second term may be neglected in comparison with the first, and 
 /u = H-M', nearly. On the other hand, when M - M' = 0, we 
 have n = MS. 
 
 Eeturning to (1), and substituting for u' its value U Q + a, we 
 have 
 
 to*- g-*" ; (5) 
 
 - + COSa 
 
 by which the position of the needle with respect to the magnetic 
 meridian, when at rest, is determined. In the case of the astatic 
 needle, the preceding equation becomes 
 
 tan w - -^fySsinl'. (6) 
 
 From this we learn, 
 
 1. That the tangent of the angle of deviation of the astatic 
 needle from the magnetic meridian varies, cceteris paribus, as the 
 angle, S, contained by the magnetic axes of the two component 
 needles. 
 
 2. That however small that angle be, provided it be of finite 
 magnitude, the tangent of the deviation may be rendered as great 
 as we please, and therefore the deviation be made to approach to 
 90 as nearly as we please, by diminishing the difference of the 
 moments of the two needles.
 
 IX. ON THE MEAN RESULTS OF OBSERVATIONS. 
 
 Transactions of the Royal Irish Academy. Vol. XXII. 
 
 1. THE problem in which it is sought to determine the daily mean 
 values of the atmospheric temperature or pressure, from a limited 
 number of observed values, is one of fundamental importance in 
 meteorology ; and, accordingly, many solutions of it have been 
 proposed by meteorologists. These solutions are derived, for the 
 most part, from the known laws of the diurnal variation of these 
 elements. Many of them are accordingly applicable only to the 
 particular cases considered ; while for others, which are really 
 general in their nature, that generality is not established. It is 
 the object of the following investigation to supply this deficiency, 
 and to show in what manner the daily and yearly means may 
 be obtained in all the periodical functions with which we are 
 concerned in magnetism and meteorology. 
 
 2. It is known that the mean value of any magnetical or 
 meteorological element, for any day, may be obtained, approxi- 
 mately, by taking the arithmetical mean of any number of 
 equidistant observed values ; the degree of approximation, of 
 course, increasing with the number. A somewhat more exact 
 mean may be deduced, as has been shown by Cotes and Kramp, 
 by combining the equidistant observed values in a different 
 manner ; and Gauss has given a method, whereby the values of 
 
 the integral, [*" Udx, may be obtained with still greater accuracy 
 
 J- 
 
 from the observed values of the ordinate, U, corresponding to 
 certain definite abscissae.* But in the case of periodical functions, 
 
 * Commentationes Socutatis Reyia Scicntiaruin Goltinyensis, torn. iii.
 
 234 ON THE MEAN RESULTS OF OBSERVATIONS. 
 
 it will appear from what follows that the refinement of Cotes is 
 unnecessary; and, in the case under consideration, there are 
 practical reasons of another kind for adhering to the method of 
 equidistant observations, and which, therefore, deprive us of the 
 advantages of Gauss's method. 
 
 3. Any periodical function U, of the variable x, may be 
 represented by the series 
 
 U = A n + Ai sin (x + ai) + A 2 sin (2x + a 2 ) + A 3 sin (3a? + o s ) + &c., 
 
 in which the first term, A , is the mean value of the ordinate 7", 
 and is expressed by the equation 
 
 ^o = 
 
 This is the quantity whose value is sought in the present inves- 
 tigation. 
 
 It is obvious that the values of U return again in the same 
 order and magnitude when * becomes x + 2ir ; so that if x = at, 
 
 the period is represented by -^. If then 2* be divided into n 
 equal parts, so that the abscissae of the points of division are x f 
 
 X + ~n' # + , &c., x + -, the sum of the corresponding 
 
 ordinates will be 
 
 -4 2 2 sin 
 
 + -4 3 S sin jsf x + ~\ + a 3 J + &c., 
 
 in which denotes any one of the series of integer numbers, 
 from to n - 1 inclusive. The multiplier of A m , in the general 
 term of this series, is 
 
 , K* 
 
 - sin (mx 4 a m ] S cos + cos (mx + a m ) S sin ?^ 
 
 But, when m is not a multiple of n,
 
 ON THE MEAN RESULTS OF OBSERVATIONS. 235 
 
 and, therefore, the preceding term vanishes. When m is a 
 multiple of , 
 
 2/W7T . 
 
 S cos - = n, S sin -- = ;* 
 n n 
 
 and accordingly the term is reduced to 
 
 Hence, all the terms of the series vanish, excepting those in which 
 m = kn, k being any number of the natural series, and 
 
 - S ( U] = Ao + A n sin (nx + a) + A 2n sin (2nx + a 3 ,) + &c. 
 
 That is, the arithmetical mean of the n equidistant ordinates is 
 equal to the sum of the terms of the original series of the order k)i> 
 whatever be the value of x. 
 
 The original series for V being always convergent, the derived 
 
 series, which expresses the value of - 2 ( U) t will be much more so ; 
 
 and, when the number n is sufficiently great, we may neglect all 
 the terms after the first. Hence, approximately, 
 
 The error of this result will be expressed by the second term 
 
 * These results are easily established. The roots of the equation y" - 1 = 0, being 
 
 comprised in the formula cos + V(- 1) sin, the m'* power of any one of these 
 n w 
 
 roots is cos 1- V ( 1) sin ; and the sum of the m lh powers of the roots is 
 
 limit ,. . 2imir 
 2 cos + v(-l) 2 sin . 
 
 Now, when m is not a multiple of , this sum = 0, and therefore 
 
 2tmir . limtr 
 
 2 cos =0, 2 sin = 0, 
 
 n n 
 
 as above. When m is a multiple of n, the sum of the m"' powers of the roots = n, 
 and therefore 
 
 2i;ir . 2wir 
 2 cos = ii, 2 sin = 0.
 
 236 ON THE MEAN RESULTS OF OBSERVATIONS. 
 
 of the series, -4 w sin (nz + a n ), the succeeding terms being, for the 
 same reason, disregarded in comparison ; and accordingly the 
 limit of error will be A n . Thus, when the period in question is a 
 day, we learn that the daily mean value of the observed element 
 will be given by the mean of two equidistant observed values, 
 nearly, when A* and the higher coefficients are negligible ; by the 
 mean of three, when A 3 and the higher coefficients are negligible ; 
 and so on. 
 
 4. The coefficient A 2 is small in the series which expresses the 
 diurnal variation of temperature ; and, consequently, the curve 
 which represents the course of this variation is, nearly, the curve 
 of sines. In this case, then, the mean of the temperatures at 
 any tico equidistant or homonymous hours is, nearly, the mean 
 temperature of the day. The same thing holds with respect to 
 the annual variation of temperature ; and the mean of the 
 temperatures of any two equidistant months is, nearly, the mean 
 temperature of the year. These facts have been long known to 
 meteorologists. 
 
 5. The coefficient A 3 is small in all the periodical functions 
 with which we are concerned in magnetism and meteorology; 
 and, therefore, the daily and yearly mean values of these functions 
 will be given, approximately, by the mean of any three equidistant 
 observed values. 
 
 In order to establish this, as regards the daily means, I have 
 calculated the coefficients of the equations which express the laws 
 of the mean diurnal variation of the temperature, the atmospheric 
 pressure, and the magnetic declination, as deduced from the 
 observations made at the Magnetical Observatory of Dublin 
 during the year 1843. The observations were taken every 
 alternate hour during both day and night; and the numbers 
 employed in the calculation are the yearly mean results corre- 
 sponding to the several hours. The origin of the abscissse is taken 
 at midnight. 
 
 6. The following is the equation of the diurnal variation of 
 temperature : 
 
 U- A, = + 3-60 sin ( * + 239-0) + 0-70 sin (2x + 67-2) 
 + -26 sin (3a? + 73 -5) + -03 sin (4x + 102 -7) 
 + -14 sin (5* + 258 -6) + -09 sin (6* + 180 -0). 
 Hence, the error committed in taking the mean of the temperatures
 
 ON THE MEAN RESULTS OF OBSERVATIONS. 237 
 
 at any two equidistant hours as the mean temperature of the da}% 
 is expressed nearly by the term 
 
 0'70sin(2#+67-2); 
 
 and, consequently, cannot exceed 0'70. To obtain the pairs of 
 honionymous hours, whose mean temperature corresponds most 
 nearly with that of the day, we have only to make sin (2* + 67 -2) = 0, 
 which gives for x the values 
 
 x = 56-4, x = 146-4, 
 corresponding to the times 
 
 t = 3 A 46"', t = 9* 46"'. 
 
 Accordingly, the best pairs of homonymous hours, so far as 
 this problem is concerned, are 3* 46'" A. M. and 3 7 ' 46"' p. M., or 
 9*46 M A.M. and 9* 46 m P.M. 
 
 The error committed, in taking the mean of the temperatures 
 at any three equidistant hours as the mean temperature .of the 
 day, is, very nearly, 
 
 andean not, therefore, exceed 0> 26. The best hours are those in 
 which the angle, in the preceding expression, is equal to 180 or 
 360. The corresponding values of x are 
 
 x = 35-5, x = 95-5 ; 
 whence 
 
 t = 2 h 22'", t = 6 A 22'". 
 
 Accordingly, the best hours of observation are 
 
 2 h 22"' A. M., 10 A 22'" A. M., 6* 22'" P. M. ; 
 and 
 
 Q k 22'" A.M., 2 h 22'" P.M., 10'' 22'" P.M. 
 
 By taking the mean of any four equidistant observed values, 
 the limit of error will, of course, be less. Its amount, which is 
 the coefficient of the fourth term of the preceding formula, is 
 only 0-03 ; and, accordingly, the mean temperature of the day is 
 inferred from the temperatures observed at any four equidistant 
 hours with as much precision as can be desired.
 
 238 ON THE MEAN RESULTS OF OBSERVATIONS. 
 
 7. The law of the diurnal variation of the atmospheric 
 pressure is contained in the following equation : 
 
 U-A, = + -0024 sin ( # + 244-3) + -0089 sin (2x + 144-4) 
 + -0008 sin (3a? + 27 -9) + -0006 sin (4as + 78 -5) 
 + -0001 sin (5x + 228 7) + -0002 sin (fa + 180 -0). 
 
 The second term in this formula being the principal one, the 
 mean of the pressures observed at any two equidistant hours, so 
 far from approaching the mean daily pressure, may recede from it 
 by the greatest possible amount within the limits of the diurnal 
 variation. The error committed, in taking the mean of the 
 pressures observed at three equidistant hours as the mean daily 
 pressure, is, very nearly, 
 
 + 0008 sin (3tf + 27'9), 
 
 and cannot therefore exceed '0008. It is needless to inquire into 
 the least value of this quantity, which is in all cases less than the 
 probable error. 
 
 8. The law of the diurnal variation of the magnetic declination 
 is expressed by the equation 
 
 U- A, = + 3'-29 sin ( * + 657) + 2'-08 sin (2* + 224-5) 
 + 0'-63 sin (3s + 71 7) + 0'-30 sin (40 + 237 -5) 
 + 0'-13 sin (5* +114 7), 
 
 the coefficient of the last term being evanescent. Hence the error 
 to which we are liable, in taking the mean of the decimations 
 observed at any three equidistant hours as the mean of the day, 
 is, very nearly, 
 
 + 0'-63sin(3tf + 717), 
 
 and cannot exceed 0'63. This term vanishes, and the mean of the 
 three observed values will deviate from the true daily mean by an 
 amount less than the errors of observation, when 
 
 * = 36-l, or x = 96-l ; 
 that is, when 
 
 t = W 25*, or t = Q h 25. 
 
 Accordingly, the best three hours of observation, for the elimination 
 of the diurnal variation of the declination, are 
 
 2* 25* A.M., 10* 25* A. M., 6* 25* P.M.; 
 
 625*A.M., 2*25* P.M., 10* 25* P.M.;
 
 ON THE MEAN EESULTS OF OBSERVATIONS. 239 
 
 which coincide, almost exactly, with the best hours for the deter- 
 mination of the mean temperature. 
 
 By taking the mean of the declinations observed at any four 
 equidistant hours, as the mean of the day, the limit of error is 
 reduced to 0'-30. 
 
 9. It appears from the preceding, that any three equidistant 
 observations are sufficient to give the daily mean values (and, 
 therefore, also the monthly and yearly mean values) for each of 
 these elements, with nearly the requisite precision ; and that, by 
 a suitable choice of the hours, the degree of accuracy may be 
 augmented as much as we please. But, in determining the par- 
 ticular hours for a continuous system of observations, this should 
 not be made the primary ground of selection. The error of the 
 daily means being in all cases reduced within narrow limits by 
 the method already explained, we should choose the particular 
 hours which correspond nearly to the maxima and minima of the 
 observed elements, so as to obtain also the daily ranges. This con- 
 dition will be fulfilled in the case of the magnetic decimation, very 
 nearly, by the hours 
 
 6 A.M., 2 P.M., 10 P.M. ; 
 
 which will, moreover, give nearly the maximum and minimum of 
 temperature, and of the tension of vapour, together with the maxi- 
 mum pressure of the gaseous atmosphere* And, if we add the 
 intermediate hours, 10 A. M. and 6 p. M., we shall have, nearly, 
 the principal maxima and minima of the two other magnetic 
 elements. Accordingly, for a limited system of magnetical and 
 meteorological observations, at places for which the epochs of 
 maxima and minima do not differ much from those at Dublin, 
 the best hours of observation appear to be 
 
 6 A.M., 10 A.M., 2 P.M., 6 P.M., 10 P.M. 
 
 The conditions of the problem are altered, if at any place the 
 laws of the diurnal variation have been already obtained from a 
 more extended system of observations. In this case the mean of the 
 day may be inferred from observations taken at any hours whatever, 
 
 * The ternary combination above proposed possesses the further advantage of coin- 
 ciding, nearly, with one of those deduced above, aa the most favourable for the deter- 
 mination of the mean temperature and mean declination. The errors of the resulting 
 means are found by making x = 90 in the third terms of the general formulas ; and we 
 thus find the error of temperature = - 0-07, while that of the declination = - 0'-20.
 
 240 ON THE MEAN EESULTS OF OBSERVATIONS. 
 
 by the addition of a known correction ; and the hours of observa- 
 tion should therefore be chosen chiefly, if not exclusively, with 
 reference to the diurnal range of the observed elements. 
 
 10. The next question which presents itself for consideration, 
 with respect to the daily means, is one which affects more nearly 
 the reduction of the observations hitherto made at Dublin. In the 
 extended system prescribed by the Council of the Royal Society in 
 1839, and followed at the Magnetical Observatory of Dublin 
 during the four years commencing with 1840, observations were 
 directed to be taken twelve times, at equal intervals, throughout 
 the day namely, at the even hours of Gottingen mean time. In 
 a system of observations so frequent, and extending over so con- 
 siderable a time, blanks must unavoidably occur ; and the question 
 which presents itself here is in what way are the daily means ta 
 be deduced in such a case ? 
 
 It has been shown that the effect of the regular diurnal variation 
 may be nearly eliminated, and the mean of the day obtained, by 
 taking the mean of three equidistant observed values. For the 
 elimination of the irregular changes, however, the number of ob- 
 servations combined should be as great as possible; and in the 
 case of the magnetic elements, in which these changes are often 
 very considerable, this condition is an important one. 
 
 Now it is obvious that the twelve results of any day may be 
 resolved into two groups of six equidistant results, or into three 
 groups of four, or into four groups of three. Hence, when one 
 result is wanting in the day, the mean may be inferred either 
 from one group of six results, from two groups of four, or from 
 three of three. The last of these combinations, containing nine 
 separate results, is, of course, to be preferred. When two results 
 are wanting, the mean may be inferred from one group of four re- 
 sults, or from two groups of three ; of which the latter combination, 
 containing six results, is to be preferred. When three results are 
 wanting, the mean of the day can be inferred (in general) only 
 from one group of three ; and when more than three are wanting, 
 that mean cannot be generally obtained. 
 
 11. What has been said above applies to the irregular changes 
 of short period such, especially, as those to which the magnetic 
 elements are subject. But there are also irregular changes of 
 longer duration (as, for example, those produced in the atmo- 
 spheric pressure by the passage of the greater aerial waves), which
 
 ON THE MEAN KESULTS OF OBSERVATIONS. 241 
 
 complicate the problem, inasmuch as a different process is required 
 for their elimination. 
 
 In the reduction of the magnetical and meteorological obser- 
 vations made at the Observatory of Dublin, the civil day is adopted ; 
 and the observations being made at the odd hours of Dublin mean 
 time, very nearly, the epoch of the mean of all the twelve results is 
 mean noon. But in the case of deficient observations, the epoch of 
 the mean, inferred from the remaining observations, may deviate 
 one or more hours from noon ; and its amount, therefore (as com- 
 pared with the mean reduced to noon), is affected by an error equal 
 to the change which the observed element undergoes in that time. 
 In the case of the atmospheric pressure, this error is often very 
 considerable, and much exceeds that due to the changes of whose 
 elimination we have hitherto spoken. 
 
 The law of the changes here referred to being unknown, we 
 can only deal with them on the assumption that their course is 
 uniform throughout the space of a day ; and this assumption will, 
 probably, seldom err much from the truth. Upon this principle, 
 the effect of the irregular change will be eliminated by taking the 
 mean of two or more results equidistant from noon (that is, the mean 
 of a forenoon and afternoon result corresponding to the hours x and 
 12 - x y or any combination of such means) ; and we have only to 
 consider in what manner this process can be combined with the 
 elimination of the regular diurnal change. 
 
 Let the mean of the four equidistant observed values commenc- 
 ing with the n th hour be denoted, for brevity, by IV ; then the 
 epochs of the means IVi, IV 3 , IV 5 , are 10 A.M., noon, and 2 P.M., 
 respectively ; so that the two conditions are satisfied by the com- 
 binations 
 
 | (TV, + IV.), and IV 3 . 
 
 In like manner, the means of any three equidistant observed values 
 being denoted by III,,, the epochs of the means IIIi, Ills, Ills* 
 III 7 , are 9 A. M., 11 A.M., 1 P. M., and 3 P.M. respectively ; so that 
 both conditions are satisfied by the combinations 
 
 i (III, + III 7 ), and | (III 3 + IH 5 ). 
 
 12. When, from the number and disposition of the blanks, none 
 of these combinations can be had, and therefore both changes (regu- 
 lar and irregular) cannot be eliminated, we must attend chiefly to
 
 242 ON THE MEAN RESULTS OF OBSERVATIONS, 
 
 that which is greater in amount. For the purpose of comparing 
 their magnitude, I have taken the differences of the successive 
 daily means, for the decimation, the atmospheric pressure, and 
 the temperature, as deduced from the observations of the year 
 1843; and have calculated the square-root of the mean of the 
 squares of these differences. The results, which may be taken as 
 the measures of the irregular changes from day to day, are the 
 following : 
 
 Mean Fluctuation from Day to Day. 
 
 Magnetic decimation, . . . Fluctuation = 1/-04. 
 
 Atmospheric pressure, ... =0 -214. 
 
 Atmospheric temperature, . . = 3'07. 
 
 Similarly, if we take the differences of the yearly means corre- 
 sponding to the successive hours of observation, and combine them 
 in the same way, we obtain the mean two-hourly fluctuations, 
 arising from the regular diurnal change. These numbers are the 
 following : 
 
 Mean Fluctuation in two Hours. 
 
 Magnetic declination, . . . Fluctuation = 2' f 04. 
 Atmospheric pressure, ... =0 -0065. 
 
 Atmospheric temperature, . . 1'46. 
 
 These numbers, compared with the twelfth part of the former, 
 serve to measure the relative magnitude of the regular and irregu- 
 lar changes to which the elements are subject in the same time. 
 We thus find that, in the case of the magnetic declination, the 
 irregular change (which is less than -^th part of the regular) may 
 be safely neglected ; and we have only to attend to the diurnal 
 changes, and to the irregular changes of short period. The daily 
 means are, therefore, to be deduced from one of the combinations 
 of Art. 10, giving the preference to that which contains the great- 
 est number of individual results. 
 
 In the case of the atmospheric temperature, the irregular change 
 (which is less than one-fifth part of the regular) is small ; and we 
 must attend chiefly to the latter. The mean of the day is, there- 
 fore, to be inferred from one of the combinations of Art. 10, giving 
 the preference to those of Art. 11, whoe epoch is noon. 
 
 In the case of the atmospheric pressure, on the contrary, the 
 irregular change (which is triple the regular) is the more import- 
 ant. The mean of the day is, therefore, to be deduced from any
 
 ON THE MEAN RESULTS OF OBSERVATIONS. 243 
 
 combination whose epoch is noon, giving, however, the preference 
 to one of those of Art. 11, in which the diurnal change is also 
 eliminated. 
 
 13. I now proceed to consider the reduction of the monthly 
 means, in the case of deficient observations. 
 
 For the purpose of determining the regular diurnal variation 
 of any magnetical or meteorological element, it is necessary to take 
 the mean of an adequate number of separate results corresponding 
 to each hour of observation, so as to eliminate the irregular and 
 accidental changes. The results usually so combined are those 
 of each month. Their number is, in general, sufficient for the 
 purpose above mentioned ; while, on the other hand, the course 
 of the diurnal change is sufficiently different from one month to 
 the next, to demand a separate determination. 
 
 But in the case of deficient observations, the monthly means of 
 the results corresponding to each hour will not exhibit, in general, 
 the true course of the diurnal change without a correction. If a 
 result be wanting at one hour of a day, in which all the results 
 are much above the mean, it is obvious that the monthly mean 
 corresponding to that hour will be too small, as compared with the 
 means of the other hours ; while, on the other hand, it will be too 
 great when all the results of the day in question are beloic the 
 mean. The error will be greater, the greater the variation of the 
 element observed from day to day. In the case of the atmospheric 
 pressure, it is so considerable, that the uncorrected monthly means 
 afford no approximation to the law of the diurnal change, in the 
 case of deficient observations. 
 
 The remedy which first suggests itself, in such a case, is to 
 omit all the results of a day in which one or more are wanting. 
 This process is inartificial and unsatisfactory. The weight of the 
 mean is diminished in the proportion of the number of observa- 
 tions combined ; and it is therefore important to employ all the 
 observed results in its deduction, provided we can obtain a 
 correction. Such a correction is easily found. 
 
 14. Let x denote the observed value of any element, at any 
 hour on any day ; and let a denote its mean value for that day ; 
 then 
 
 x = a + K, 
 
 in which is the magnitude of the diurnal variation corresponding 
 to the hour in question. Let there be n days of observation to be 
 
 R2
 
 244 ON THE MEAN RESULTS OF OBSERVATIONS. 
 
 combined ; then, summing the n results, dividing by , and denoting 
 the mean values by x, , and f , 
 
 Now, at any particular hour of any day, let one of the results 
 be wanting ; and let a' denote the mean for that day ; summing 
 the n - 1 ^results, 
 
 Sn-i* = S n a-a + Sn-it. 
 
 And dividing by n - 1, 
 
 8a -a f a- a' 
 
 a + 
 
 r- = - , 
 n-1 n-1 
 
 whence 
 
 a'-a 
 
 x + = - a 
 
 n-1 
 
 The correction, therefore, is + j. 
 
 Similarly, if ^> results be wanting, we find 
 
 Set -pa . 
 
 x + = a + c, 
 
 -|i 
 
 in which Sa' denotes the sum of the means of the days on which 
 the deficiencies occur. Hence, the correction to be applied to the 
 
 observed mean, x, deduced from the n -p values, is + =". 
 
 n-p 
 
 15. The preceding correction depends, as might have been 
 anticipated, on the difference of the daily means, for the days of 
 deficient observations, and the mean daily mean. "With the view 
 of determining its probable amount, I have taken the differences 
 between the mean of each day, and the mean of the month, for the 
 declination, the atmospheric pressure, and temperature, as deduced 
 from the observations of the year 1843 ; and have calculated the 
 square root of the mean of the squares of these differences, or 
 
 the values of the expression li L =Ll. The values of this 
 
 quantity, which may be denominated the mean daily error, are 
 the following :
 
 ON THE MEAN RESULTS OF OBSERVATIONS. 245 
 
 Mean Daily Error. 
 
 Magnetic declination, . . Daily error = 0'-95. 
 Atmospheric pressure, . . =0 '301. 
 
 Atmospheric temperature, . = 4'25. 
 
 Now, the mean value of n in each month (Sundays being 
 omitted) is 26. Hence the mean correction, in the case of a single 
 deficient observation, is, for the magnetic declination, 0' - 04 ; for 
 the atmospheric pressure, 0'012 ; and for the temperature, 0-17. 
 In the case of the two meteorological elements, and especially in 
 that of the atmospheric pressure, the correction is too considerable 
 to be overlooked ; in the case of the magnetic declination, and 
 probably also in that of the other magnetic elements, it may be 
 disregarded.
 
 X. ON THE DETERMINATION OF THE HORIZONTAL 
 INTENSITY OF THE EARTH'S MAGNETIC FORCE 
 IN ABSOLUTE MEASURE. 
 
 Transactions of the Royal Irish Academy. Vol. XXL 
 
 THE attention of mathematicians and experimentalists has been, 
 for some time past, directed to the means of determining the 
 intensity of the earth's magnetic force in absolute measure. 
 These means consist, it is well known, in observing the time of 
 vibration of a freely-suspended horizontal magnet, under the 
 influence of the earth alone, and then employing the same magnet 
 to act upon another, which is also freely suspended, and noting 
 the effects of its action combined with that of the earth. From 
 the former of these observations we deduce the product of the 
 horizontal component of the earth's magnetic force into the 
 moment of free magnetism of the first magnet, and from the latter, 
 the ratio of the same quantities ; and, the product and the ratio 
 being thus known, the two factors are absolutely determined. 
 The former part of this process involving no difficulty which may 
 not be overcome by due care in observing, we shall confine our 
 attention, in the present communication, to the latter. 
 
 Two methods have been proposed for this second observation, 
 one by Poisson, and the other by Gauss. The method of Poisson 
 consisted in observing the time of vibration of the second magnet, 
 under the combined action of the first and of the earth, the acting 
 magnet having its axis in the magnetic meridian passing through 
 the centre of the suspended magnet. In the method of Gauss, 
 which is now universally adopted, we observe the position of 
 equilibrium of the second magnet, resulting from the action of the 
 same forces. The acting magnet being placed transversely with
 
 INTENSITY OF THE EAETH's MAGNETIC FORCE. 247 
 
 respect to the suspended one, the latter is deflected from the 
 meridian, and the amount of this deflection serves to determine 
 the ratio of the deflecting force to the earth's force. The position 
 chosen by Gauss for the deflecting magnet is that in which its 
 axis is in the right line passing through the centre of the 
 suspended magnet, and perpendicular to the magnetic meridian, 
 in which case the tangent of the angle of deflection is equal to the 
 ratio of the two forces. From this ratio it remains to deduce that 
 of the magnetic moment of the deflecting bar to the earth's force. 
 
 The difficulty of this process arises from the form of the 
 expression of the force of the deflecting bar. This force being 
 expressed by a series descending according to the negative odd 
 powers of the distance, with unknown coefficients, it is evident 
 that observation must furnish as many equations of condition, 
 corresponding to different distances, as there are terms of sensible 
 magnitude in the series ; and from these equations the unknown 
 quantities are to be deduced by elimination. Now, the greater 
 the number of unknown quantities thus eliminated, the greater 
 will be the influence of the errors of observation on the final 
 result ; and if, on the other hand, the distance between the 
 magnets be taken so great, that all the terms of the series after 
 the first may be insensible, the angle of deflection becomes very 
 small, and the errors in its observed value bear a large proportion 
 to the whole. 
 
 It fortunately happens, that at moderate distances (distances 
 not less than four times the length of the magnets) all the terms 
 beyond the second may be neglected. The expression for the 
 tangent of the angle of deflection is thus reduced to two terms, 
 one of which contains the inverse cube of the distance, and the 
 other the inverse fifth power ; that is, if u denote the angle of 
 deflection, and D the distance, 
 
 in which Q and # are unknown coefficients, the former of which 
 is double of the ratio sought. Accordingly, the method recom- 
 mended by Gauss consists in observing the angles of deflection, 
 u and u', at two different distances, D and IX, and inferring the 
 coeflicient Q by elimination between the two resulting equations 
 of condition.
 
 248 ON THE DETERMINATION OF THE HORIZONTAL 
 
 The object of the present Paper is to point out the means by 
 which the quantity sought may be obtained, without elimination, 
 from the results of observation at one distance only ; and thus not 
 only the labour of observation be diminished, but (which is of 
 more importance) the accuracy of the result increased. Before 
 entering on this, however, it will be expedient to ascertain the 
 amount of the probable error in the received method. 
 
 The coefficient of the first term, obtained by elimination 
 between the two equations of condition above alluded to, is 
 
 The distances being greater than four times the length of the 
 magnets, the angles of deflection are small, and there is, approxi- 
 mately, t&mi = ^(tan^, tan*/ = w'tanl', u and u' being expressed 
 in minutes; and making If = qD, the preceding expression 
 becomes 
 
 The probable errors of u and a' are equal ; and, by a well-known 
 theorem of the calculus of probabilities, the probable error of Q is 
 
 ^TT AM ' 
 
 In determining the ratio of this error to the quantity itself, we 
 may observe that there is, approximately, <fu' = u, and 
 
 Q = 3 tanl'.; 
 and dividing the formula last found by this, 
 
 It appears, from the preceding theorems, that the value of AQ, 
 corresponding to a given value of Aw, varies with the assumed 
 ratio of the distances, q; and that, in order to apply the method 
 most advantageously, this ratio must be taken in such a manner 
 that the probable error, AQ, shall be the smallest possible. This 
 condition gives 
 
 d /VY+T
 
 INTENSITY OF THE EARTH'S MAGNETIC FORCE. 249 
 
 whence we obtain the following equation for the determination 
 of q : 
 
 3^0 _ 5 ? 8 _ 2 = o. 
 
 In order to solve this equation, we may observe that, q being 
 greater than unity, the last term of the equation may, in a first 
 approximation, be neglected in comparison with the others; so 
 that we have, approximately, 
 
 And setting out from this value, we find, by any of the known 
 methods of approximation, 
 
 q = 1-32 ; 
 
 or 1|, very nearly. Accordingly, the smaller distance, r, being 
 determined by the condition that the third term of the series shall 
 be insensible, the greater distance should be T32r. 
 
 If we substitute this value of q, in the expression for -^- above 
 obtained, we find 
 
 from which we can calculate the least probable error corresponding 
 to any given angle of deflection, the probable error of reading 
 being known.* 
 
 Now let us suppose the term containing the fifth power of the 
 distance to vanish, in the expression for the deflecting force. The 
 value of Q will then be reduced to 
 
 Q = D 3 tan u ; 
 
 * In the Dublin Magnetical Observatory tbe deflecting bar hitherto employed is 
 12 inches in length, and the least deflecting distance therefore 4 feet. The deflection 
 produced by it at this distance is about 3 56' ; and the probable error of observation 
 does not exceed 5". Hence, in this case, 
 
 AQ 5-563 
 
 Q ~ 236 x 12 
 The absolute intensity, X, varies inversely as the square root of Q ; so that 
 
 Consequently, the resulting probable error in the determination of the absolute 
 intensity, made according to the usual method, is, at this Observatory, about the 
 TuVoth part of the entire quantity.
 
 250 ON THE DETERMINATION OF THE HORIZONTAL 
 
 in which we may take tan u = u tan 1', as before. Hence there is 
 
 AQ Aw 
 -Q- '^' 
 
 and the probable error is less than in the usual method in the 
 ratio of 1 to 5*563, even when the latter is employed in the 
 manner most conducive to accuracy. Accordingly, if by any 
 means the coefficient of the inverse fifth power of the distance can 
 be annihilated, or rendered so small that the term shall have no 
 sensible influence, the accuracy of the results will be increased 
 more than five-fold, and, at the same time, the observations being 
 taken at one distance only, the labour of observation will be 
 halved. 
 
 The same advantages will be gained if, the coefficient of the 
 inverse fifth power of the distance retaining a sensible value, the 
 ratio of the two coefficients may be known d priori. Let 
 
 h being a known quantity. In this case the expression for the 
 tangent of the angle of deflection becomes 
 
 and the coefficient sought is obtained, from the result of obser- 
 vation at a single distance, by the formula 
 
 _ J 3 tan u 
 ^ ~ 1 + hD~* * 
 
 It is evident that the probable error of Q thus obtained, arising 
 from an error in the observed deflection, is the same as in the case 
 last considered, and therefore between five and six times less than 
 in the ordinary method. 
 
 The object of the following investigation is to point out the 
 means of attaining these advantages. 
 
 Let the axis of the deflecting magnet be supposed to lie in the 
 right line joining the centres of the two magnets, and let the axis 
 of the suspended magnet make the angle $ with that line. Then, 
 if X and Y denote the forces exerted by the deflecting magnet 
 upon any element of free magnetism, m, of the suspended magnet, 
 in the direction of the line connecting it with the centre of the
 
 INTENSITY OF THE EARTH'S MAGNETIC FORCE. 251 
 
 deflecting magnet, and in the line perpendicular to it, respectively, 
 their moment to turn the magnet round its point of suspension 
 will be 
 
 r denoting the distance of the particle m of the suspended magnet 
 from its centre, and the angle which the line connecting this 
 particle and the centre of the deflecting magnet makes with the 
 axis of the latter. Now, I have elsewhere shown* that, if we 
 include the terms involving the fifth power of the distance, the 
 values of X and T are 
 
 T = ~sin 9 Jf+f=^(5cos 2 9-l) ; 
 
 a being the distance of the particle m of the suspended magnet 
 from the centre of the deflecting magnet, and M and 1T 3 denoting, 
 respectively, the integrals corresponding to \mrdr,\mr*dr, for the 
 deflecting magnet, taken between the limits r = \ length. Now 
 
 sin 9 = - sin 
 
 so that, extending the approximation to the term involving the 
 fifth power of the distance only, we must make sin 9 = 0, cos 9 = 1, 
 in the coefficient of that term. The preceding expressions are 
 thus reduced to 
 
 and, substituting, the moment of these forces to turn the magnet is 
 
 ^ilff* sin * cos 9 cos i/, + (2 - 3 8in 2 9) sin^ + ^~ sin^J ; 
 or, eliminating by the relation between it and i//, 
 
 * Transactions of the Royal Irish Academy, vol. xix. p. 163.
 
 252 ON THE DETERMINATION OF THE HORIZONTAL 
 
 Now, if D denote the distance between the centres of the two 
 
 magnets, 
 
 a? = D* + r z 2x/r cos i. 
 
 Wherefore, developing the inverse powers of a in series ascending 
 according to the powers of ^, stopping at the inverse fifth power 
 of the distance, and substituting in the expression for the moment 
 above given, it becomes 
 
 This being the moment of the force exerted by the deflecting 
 magnet upon a single particle, m, of the suspended magnet, the 
 moment of the force exerted upon the entire magnet is obtained 
 by multiplying by dr, and integrating between the limits r = l, 
 I being half the length of the suspended bar.* The magnetism 
 being supposed to be distributed symmetrically on either side of 
 the centre of the suspended magnet, and the axis of suspension to 
 pass through that centre, we have- 
 
 f *i 
 -l 
 
 mr z dr = 0. 
 
 ( + l r+l 
 
 mrdr, m^dr, by M.' and 
 
 Jf s ', the expression for the moment of the whole force is 
 
 When there is equilibrium, this moment must be equal to that 
 of the force exerted by the earth upon the suspended magnet. 
 Let X be now taken to denote the horizontal component of the 
 earth's magnetic force. The moment of the force exerted by that 
 component upon the particle m of the suspended magnet is 
 
 mXr sin u ; 
 
 * "We have here assumed that the effect of a magnet is the same, with respect to 
 any point at a moderate distance, as if the magnetic elements in each section perpen- 
 dicular to its axis were all concentred in the axis ; or, in other words, that the 
 integration with respect to the other dimensions of the bar introduces no new term 
 into the integral. There is no difficulty in proving that such is the case, the magnetic 
 elements being supposed to be distributed symmetrically with respect to the axis.
 
 INTENSITY OF THE EARTH' S MAGNETIC FORCE. 253 
 
 M denoting the deviation of the axis of the magnet from the 
 direction of the force. Multiplying by clr, therefore, and in- 
 tegrating, the total moment is 
 
 XM'smu. 
 
 Hence the equation of equilibrium is 
 
 There are two cases of this solution which demand our con- 
 sideration. 
 
 In the method of Grauss, the deflecting magnet is perpendicular 
 to the magnetic meridian, and therefore i// = 90 - u. In this case, 
 then, the preceding equation becomes 
 
 Accordingly, the term containing the fifth power of the distance is 
 composed of two parts, one of which is constant, while the other 
 varies with the angle of deflection; so that, if there were no 
 
 11 f- li /"' 
 
 means of determining d priori the values of the ratios -ri -=^-, 
 
 JU. Ju. 
 
 three equations of condition would be, in strictness, required for 
 the determination of the three unknown quantities ; namely, the 
 coefficient of the inverse cube of the distance, and the two parts of 
 the coefficient of the inverse fifth power. However, the distance 
 being greater than four times the length of the magnet, the angle 
 of deflection, it, is always small, and the term involving the square 
 of its sine may be neglected in comparison with the others. 
 Accordingly, if we make, for abridgment, 
 
 2Jf M 3 Jf,' 
 
 the expression for the tangent of the angle of deflection is reduced 
 to the form 
 
 In the method of deflection employed by Professor Lamont, 
 the deflecting bar is always perpendicular to the suspended bar.
 
 254 ON THE DETERMINATION OF THE HORIZONTAL 
 
 In this case, therefore, ^ = 90, and the equation of equilibrium is 
 
 reducedt ajf (l /.* ,'\ij 
 
 Xsme, -l + -a-, 
 
 and the equation is the same as that to which it is reduced in the 
 former case, the sine of the angle of deflection being substituted 
 for the tangent. It appears from the result, that this method is to 
 be preferred to the former, not only because the angle of deflection 
 is greater, ccet. par., but also because the variable part in the 
 coefficient of the inverse fifth power of the distance is strictly 
 evanescent. 
 
 It remains now to inquire in what manner the quantity h, which 
 expresses the ratio of the two coefficients, may be known d priori ; 
 and whether that quantity can be made to vanish, by any simple 
 relation between the acting magnets. 
 
 For this purpose we must know, at least approximately, the law 
 of magnetic distribution, or the function of r by which m is repre- 
 sented. Almost the only knowledge which we possess on this sub- 
 ject is that derived from the researches of Coulomb. From these 
 researches M. Biot has inferred that the quantity of free magnet- 
 ism, in each point of a bar magnetized by the method of double 
 touch, may be represented by the formula 
 
 /u being a quantity independent of the length of the magnet, and 
 A a function of ju and /. M. Biot has further shown, that when 
 the length of the magnet is small, the relation between m and r is 
 approximately expressed by the simple formula 
 
 = 
 
 the curve of intensities becoming, in that case, very nearly a right 
 line passing through the centre of the magnet. 
 
 Employing, then, this approximate formula, we have 
 
 r+l r r-+i 
 
 M = J ^ mrdr = | r z dr = f w'/ 2 ; 
 
 r+f m ' r+i 
 
 M 3 = I mt*dr - j- r'dr = f m' I*.
 
 INTENSITY OP THE EARTH'S MAGNETIC FORCE. 255 
 
 The ratio of these quantities is independent of m', and we have 
 simply 
 
 *'-,,. 
 
 TT 
 
 Finally, substituting in the value of h above given, and designat- 
 ing the half lengths of the deflecting and the suspended magnets 
 "by / and /', respectively, 
 
 h = f (2l 2 - 3r 2 ) ; 
 
 a quantity whose value may be exactly known, independently of 
 experiment. This quantity vanishes, when P = f I' 2 , or 
 J- 1-224 /'; 
 
 a result which is independent of the magnetic state of the bars.* 
 
 As the preceding results depend, in part, upon an empirical law 
 of magnetic distribution, which is only approximately true in the 
 case of small magnets, it seemed desirable to obtain a confirmation 
 of their accuracy by direct experiment. The nature of such con- 
 firmation will be immediately understood from the form of the 
 relation between the angle of deflection and the distance. For 
 since, in the method of deflection employed by Gauss, DHanw 
 = Q (1 + /2D~ 2 ), the function D 3 tan u will be constant for all values 
 of D, when h = ; while, if the coefficient of the fifth power of the 
 distance has a sensible value, it will vary with D, its values form- 
 ing a decreasing or increasing series, as D increases, according as h 
 is positive or negative. Hence we have only to observe the deflec- 
 tions produced at different distances, when the two magnets have 
 the relative lengths pointed out above, and to compare the results 
 with those obtained under other circumstances. 
 
 Several series of experiments were accordingly made in the be- 
 ginning of the present month, in some of which the lengths of the 
 two magnets were the same, while in others they were in the 
 
 * If the centre of the deflecting magnet be in the magnetic meridian passing through 
 the centre of the suspended magnet, and its axis perpendicular to th same line, we find, 
 by a process similar to that above given, that the condition to be fulfilled, in oider that 
 the term involving the fifth power of the distance may vanish, is 
 
 *!_ 4 *L. 
 
 M M' ' 
 
 and, accordingly, that the corresponding relation between the lengths of the two magnets 
 
 is, in that case. 
 
 /= 2f.
 
 256 ON THE DETERMINATION OF THE HORIZONTAL 
 
 deduced ratio of the number 1'224 to 1. The form of the magnets 
 was cylindrical, their lengths being 3 inches, and 3f inches, and 
 their diameter -fV of inch. The suspended bar was hung by two 
 fibres of untwisted silk, and inclosed in a small wooden box with 
 glazed front. The deflections were observed by means of a mirror 
 attached below the magnet, which reflected the divisions of a scale 
 placed at a distance of nearly six feet from it. As the utmost 
 precaution was required in the experiments, the use of a copper 
 ring or metallic box was dispensed with, and the arc of vibration 
 reduced by means of a magnet, which was always replaced care- 
 fully in the same position after use. The deflecting magnet was 
 placed on the east and west sides of the suspended one, at distances 
 varying from 15 to 30 inches. The distances were observed by the 
 help of a standard scale, a line at the middle of the magnet being 
 made to coincide with the image of the division of the scale, re- 
 flected from its polished side. The observations were made begin- 
 ning with the longest, and proceeding to the shortest distance at 
 one side, and back again in the reverse order at the other, so that 
 the two observations at the same distance were taken at times 
 equally remote from the middle epoch. 
 
 The angles of deflection were calculated by the formula 
 
 tan 2u = I (n e - n w ) k ; 
 
 where n e and n w denote the observed readings of the scale, with the 
 marked end of the deflecting bar to the east and to the west 
 respectively. The value of the constant k is given by the formula 
 
 a denoting the length of one division of the scale, d its distance 
 
 TT 
 
 from the mirror, and the ratio of the torsion force to the 
 
 Jc 
 
 magnetic force. In the present instance, a = '038935 of an inch ; 
 
 JT 
 
 d = 68-52 inches ; and - -000345. Hence log k = 6-75467; and 
 
 the angle corresponding to one division of the scale was conse- 
 quently 
 
 I tan- 1 k = 58"-623. 
 
 The following Tables exhibit the results of the observations. 
 The first column of each contains the distances of the magnets, in
 
 INTENSITY OF THE EARTH'S MAGNETIC FORCE. 
 
 257 
 
 feet ; the second, the values of | (n e - w ), these values being the 
 means of those obtained with the deflecting magnet on the east and 
 on the west side of the suspended magnet ; the third column con- 
 tains the calculated values of u ; and the fourth those of D 3 tan u. 
 In the observations of I., II., and III., the lengths of the deflect- 
 ing and suspended magnets were in the ratio of the numbers 1'224 
 to 1 ; in those of IV. and V., the lengths of the two magnets were 
 equal. 
 
 I. Magnet away, Scale reading = 496-5 . . . 494-5. 
 
 D 
 
 !(*-*,) 
 
 u 
 
 D* tan u 
 
 1-5 
 2-0 
 2-5 
 
 351-05 
 146-92 
 75-12 
 
 5^ 38' 32"-5 
 2 23 13 
 1 13 21 
 
 33344 
 33347 
 33343 
 
 II. Magnet away, Scale reading = 495-9 . . . 495-0. 
 
 D 
 
 *(*.-**) 
 
 u 
 
 D 3 tan u 
 
 D 
 
 (*.-*) 
 
 I 
 
 D 3 tan u 
 
 1-5 350-61 
 
 5 38' 7"-5 
 
 33302 
 
 2-0 146-71 
 
 2 23 1 
 
 33300 
 
 2-5 
 
 75-06 
 
 1 13 17-5 
 
 33317 
 
 III. Magnet away, Scale reading = 496-4 . . . 494-3. 
 
 D 
 
 \ (n e - <*} 
 
 M 
 
 J) 3 tantt* 
 
 1-4167 
 
 417-24 
 
 6 40' 16" 
 
 33254 
 
 1-8750 
 
 177-89 
 
 2 53 13 
 
 33242 
 
 2-5000 
 
 74-96 
 
 1 13 12 
 
 33275 
 
 IV. Magnet away, Scale reading - 494-4 . . . 494-6. 
 
 D 
 
 J (. - *) 
 
 tt 
 
 IPt&nu 
 
 1-25 
 
 389-70 
 
 6 14' 42"-5 
 
 21373 
 
 1-50 
 
 223-95 
 
 3 37 38 
 
 21393 
 
 2-00 
 
 94-38 1 32 7-5 
 
 21444 
 
 2-50 
 
 48-45 47 1!) "> 
 
 21510
 
 258 ON THE DETERMINATION OF THE HORIZONTAL 
 
 V. Magnet away, Scale reading = 495-1 
 
 498-3. 
 
 !(.-*,) 
 
 u 
 
 D 3 tan n 
 
 368-46 
 
 5 54,' 52" -5 
 
 20233 
 
 
 
 
 211-99 
 
 3 26 8 
 
 20261 
 
 133-41 
 
 2 10 6 
 
 20292 
 
 89-39 
 
 1 27 16 
 
 20313 
 
 63-00 
 
 1 1 32 
 
 20390 
 
 45-99 
 
 44 55 -5 
 
 20420 
 
 1-25 
 1-50 
 1-75 
 2-00 
 2-25 
 2-50 
 
 These results verify the conclusions to which we have arrived 
 above. The values of the function D 3 tan u are constant for all 
 distances in the first three series, the differences in the resulting 
 values being less than the probable errors of observation ; and, 
 consequently, the coefficient of the inverse fifth power of the 
 distance is insensible. In the fourth and fifth series, on the other 
 hand, in which the lengths of the magnets are equal, the values 
 of this function form an increasing series, as D increases; and 
 therefore, in this case, the coefficient of the inverse fifth power of 
 the distance has a sensible negative value. 
 
 We may further employ these results to test the accuracy of 
 our conclusions, by deducing from them the values of the two 
 coefficients, in the expression for the tangent of the angle of 
 deflection, and comparing their ratio with that furnished by 
 theory. It is needless to make this computation for the numbers 
 of the first three series ; for it is manifest from the results, that 
 the second coefficient is insensible, as theoretically it should be. 
 From the results of IV. we deduce, by the method of least squares, 
 
 Q = -2148, hQ = - -0017, h = - -0078. 
 We obtain, in like manner, from the results of V., 
 
 Q = -2037, hQ = - -0022, h = - -0110. 
 
 And the mean of the resulting values is - '0094. Now, in these 
 two series, the length of each of the magnets was three inches ; 
 that is, I = I' = -125, the half lengths being expressed in feet. 
 Substituting these values in the expression for h, it becomes 
 
 h = - -0094, 
 agreeing exactly with the mean of the experimental values.
 
 INTENSITY OF THE EARTH'S MAGNETIC FORCE. 259 
 
 We are therefore justified in concluding that, in the case of 
 small magnets, the ratio of the two coefficients may be inferred 
 <l priori, by the formula 
 
 and, consequently, that the coefficient Q, or 2^-. may be obtained, 
 from the result of observation at a single distance, by the formula 
 Q m P'tanu^ 
 
 It follows from this, as we have seen, that when t = 1-224 /, // = 0, 
 iiud the value of Q is reduced to 
 
 Q = JD 3 tan u. 
 
 POSTSCRIPT. While the preceding pages were passing through 
 the press, I received a memoir from Professor Lament, on the 
 determination of the earth's magnetic force in absolute measure, 
 in which the author has proposed various modifications in the 
 existing method, and has considered, with great minuteness of 
 -detail, the many corrections which are required in the immediate 
 results of observation. Some of the conclusions cf the present 
 Paper are, I find, thus anticipated ; in particular, the form of 
 the equation of equilibrium of the suspended magnet, for the case 
 in which the axes of the two magnets are at right angles; and 
 the ratio of the coefficients of the terms in that formula, which 
 Professor Lamont has deduced in the case of what he calls a 
 ximple magnet, that is, the imaginary magnet in which the 
 attractive and repulsive forces are supposed to emanate solely 
 from two points or poles. The value, so inferred, he naturally 
 regarded as a mere approximation.; and he has accordingly not 
 thought of employing it, as is proposed in the present Paper, to 
 supersede experiment, and thus evade the errors resulting from 
 the process of elimination.
 
 XI. ON THE DETERMINATION OF THE TOTAL INTENSITY 
 OF THE EARTH'S MAGNETIC FORCE IN ABSOLUTE 
 MEASURE, BY MEANS OF THE DIP-CIRCLE. 
 
 Transactions of the Royal Irish Academy. Vol. XXIII. 
 
 THE force exerted by the earth upon a magnet is usually found 
 by suspending the bar horizontally, and observing its time of 
 vibration. The result thence obtained is the product of the 
 horizontal component of the earth's magnetic force by the 
 magnetic moment of the magnet ; and before we can know the 
 value of either of the factors which compose it, observation must 
 furnish another result in which they are combined differently. 
 This is effected, in the method of (rauss, by using the same 
 magnet to deflect another, similarly suspended, and by observing 
 the angles of deflection at known distances : this observation gives 
 the ratio of the magnetic moment of the deflecting magnet to the 
 horizontal component of the earth's force, and the two factors are 
 therefore absolutely known. 
 
 This method, although much improved by the labours of 
 Lament and others, has one insurmountable imperfection. The 
 total force must be inferred from its horizontal component, by 
 multiplying by the secant of the inclination. The relative error 
 of the deduced force, arising from a given error of inclination, 
 varies therefore as the tangent of that angle, and when the 
 inclination approaches to 90, it becomes very considerable. The 
 method is, accordingly, unsuited to the high magnetic latitudes. 
 
 I was induced to consider the means of supplying this defect 
 some years ago, upon the occasion of the Arctic Expeditions of 
 1845 and 1848 ; and I then suggested another process, by which
 
 INTENSITY OF THE EARTH'S MAGNETIC FORCE. 261 
 
 the total intensity might be found directly, without the inter- 
 vention of its horizontal component. In the Paper in which it 
 was explained,* it was shown that the ordinary dip-circle may be 
 employed in' both parts of the observation. Subsequent consider- 
 ations, however, derived from the probable errors of observation, 
 led me to propose that the dip-circle should be employed only in 
 one part of this process, and that the observation should be com- 
 pleted by the known methods. 
 
 The present communication is intended to show in what 
 manner this complication may be avoided, and the original 
 proposal carried out. It is of great importance to the scientific 
 traveller that the instruments which he has to carry should be 
 reduced, as far as possible, in number and in weight, and that 
 their adjustments should be few and simple ; and it is believed 
 that these objects are attainable by the method explained in this 
 Paper. Before entering into details, it will be convenient to revert 
 to the theoretical principles on which the method is founded. 
 
 If X and Y denote the horizontal and vertical components of 
 the Earth's magnetic force, m the magnetic moment of the needle 
 acted on, and a the azimuth of the plane in which it moves, 
 measured from the magnetic meridian, the effective forces exerted 
 upon it are 
 
 mXcosa, mY; 
 
 and their moment to turn the needle is 
 
 m ( Y cos ?/ - X cos a sin >j), 
 
 jj denoting the actual inclination of the needle to the horizon. 
 This moment is opposed by that of the added weight, or by Wr, 
 W being the weight, and r the radius of the pulley by which it 
 acts ;f and the equation of equilibrium is therefore 
 
 m ( Y cos ri - X cos a sin >j) = irr. 
 When the needle is removed, in the second part of the process, 
 
 * froecedinffs of the Royal Iruh Academy, January 24, 1848. 
 
 t It is here supposed that the weight is attached to a fine thread pasiii 
 light pulley, whose centre is on the axis of the cylindrical axle of the needle, in 
 manner proposed by Mr. Fox. If the weight he attached to the s< 
 needle, at a fixed point, its moment is icr COST;.
 
 262 OX THE DETEKMINATION OF THE TOTAL 
 
 and applied to deflect another substituted in its place, the moment 
 of its force to turn the latter is 
 
 mm 17', 
 
 in which m' is the moment of free magnetism of the second needle, 
 and U a function of the distance of the centres of the two needles, 
 and of certain integrals depending on the distribution of free 
 magnetism in them. The moment of the earth's magnetic force, 
 opposed to this, is of the form already assigned, in which we have- 
 only to substitute ', r/, and a', for m, 11, and a. Hence the equa- 
 tion of equilibrium is 
 
 Y cos i)' - X cos of sin r{ = m U ; (2) 
 
 the quantity m' disappearing from the result. The magnetic 
 moment of the deflecting needle, m, is eliminated from equations 
 (1) and (2) by multiplication ; and we thus obtain a single re- 
 lation between the intensity of the earth's magnetic force, the 
 observed angles a, TJ, a', rj', and the quantities ', r, and TJ. Hence 
 the magnetic intensity will be determined when these are known. 
 
 There are three obvious cases of these formulas, each of which 
 suggests a different method for the determination of the terrestrial 
 magnetic intensity. 
 
 1. When the planes in which the needles move coincide with 
 the magnetic meridian, or a = 0, and a = 0, the left-hand members 
 of (1) and (2) are reduced to mR sin (0 - ij), R sin (0 - r{) ; R 
 denoting the total force, and the inclination. "Wherefore, by 
 multiplication, we have 
 
 R 2 sin (0 - n) sin (0 - ,,') = Uwr. (3) 
 
 2. When the planes in which the needles move are per- 
 pendicular to the magnetic meridian, or a - 90, and a = 90, the 
 left-hand members of (1) and (2) become, respectively, w*Fcosj, 
 FCOSTJ' ; whence 
 
 Y- cos j cos i{ = Uicr. (4) 
 
 3. Finally, the equilibrium may be produced, in both cases, by 
 turning the instrument in azimuth until the free needle stands ver- 
 tically. In this case >, = 90, r,' = 90, and the left-hand members 
 become - mX cos a, - X cos a ; whence 
 
 X- cos a cos a = Vur. (5) 
 
 Thus we may apply this principle to the determination of the 
 total intensity, or to that of either of its two components.
 
 INTENSITY OF THE EARTH'S MAGNETIC FORCE. 263 
 
 In comparing the foregoing methods, it is to be observed that 
 the third fails when the inclination approaches to 90, on account 
 of the magnitude of the error of R resulting from a given error of 
 0, when the total force is deduced from its horizontal component. 
 In like manner, and for the same reason, the second method fails 
 in the vicinity of the magnetic equator, or line of no inclination. 
 The first alone is applicable at all parts of the earth's surface, and 
 I proceed to consider it more in detail. 
 
 The observed angles, rj and ?/, are liable to error, the friction 
 of the needles on their supports causing them to rest in positions 
 slightly different .from those due to the acting forces. The pro- 
 bable errors of TJ and /, due to this cause, vary with the angles 
 themselves. To determine their magnitude in any case, we have 
 
 mR sin (0 - TJ) = F, 
 
 F being the moment of the deflecting force ; and when friction is 
 taken into account, 
 
 mR sin (0 - rj + Arj) = F + f; 
 
 f denoting the moment of friction, and rj - Arj the new angle of 
 equilibrium. Developing the latter equation, and subtracting the 
 former, 
 
 mR cos (0 - rj) AJ/ = ./' ; 
 
 the angle A) being expressed in parts of radius. Hence, cos (0 - ri) A j 
 is constant with a given instrument, and at a given point of the 
 Earth's surface. 
 
 To find the probable error of the force corresponding to the 
 error of the observed angle, we must differentiate the equation 
 of equilibrium, mR sin u = F, with respect to R and w, where 
 u = - r j ; and we have 
 
 A R sin u + R cos u A = 0. 
 
 But 
 
 i / \ 
 
 u 5 I 1 ? 1 ~ 1v 
 
 tj, and rj, being the observed angles of inclination under ill 
 opposite actions of the deflecting force. Hence the probable error 
 
 of u is 
 
 - 1 
 
 Au = i -y/Arj'i + ATJ".. = , ' ' 
 
 v/x,
 
 264 ON THE DETERMINATION OF THE TOTAL 
 
 since Ar/ 3 = Arn. Accordingly, the second term of the preceding 
 
 equation becomes R cos u Aj = - ; and we have 
 
 &R = 
 
 We learn, then, that the probable error of the force varies 
 inversely as the sine of the angle of deflection ; and that it is 
 therefore requisite for accuracy that this angle should be con- 
 siderable. There is no difficulty in augmenting the angle of 
 deflection as much as we please in the first part of the process, in 
 which the magnet is deflected by a weight ; but in the second the 
 case is different, and with the slender needles to be employed as 
 deflectors, a large deflection can only be obtained by placing the 
 deflecting needle at a very short distance from the moveable one. 
 The most convenient arrangement appears to be to attach the 
 deflecting needle to the moveable arm of the divided circle which 
 carries the verniers, and at right angles to the wires of the 
 microscopes.* So attached, it must always be rendered perpen- 
 dicular to the deflected needle in the course of the observation, 
 although in a different plane. 
 
 The form of the function denoted by 77, in this position, is 
 easily found. 
 
 Let the distances of any points of the axes of the deflecting 
 and deflected magnets from their respective centres be denoted 
 by r and r', and let /u and // denote the quantities of free 
 magnetism at these points, contained in the slices perpendicular 
 
 * To obtain the value of AS by observation, we must substitute for / its value 
 given above. But when ij = 6, or when the needle is undeflected, / = mltAO ; 
 wherefore 
 
 V 2 sin u ' 
 
 In the instrument with which I made trial of this method, the length of the needles 
 was 3J inches, and the angle of deflection produced, in the position of the deflecting 
 needle here described, was 24 10'. But the probable error of a single reading of the 
 inclination, obtained by repetition the needle being lifted off the agate planes between 
 the successive readings-was l'-6 ; and if four readings (which is a very usual number) 
 e taken, the probable error of their mem will be one-half of this. In this case, 
 therefore, A0 = 0'-8 ; and the probable error of the deduced force, computed by the 
 preceding formula, is AS - -0004 Jt.
 
 to the axes whose thicknesses are dr and dr. Then the force 
 exerted by the former upon the latter is 
 
 MI drdr 
 ~* ' 
 
 s denoting their mutual distance. The portion of this force 
 contained in the plane of the deflected magnet, and perpendicular 
 to its axis, is 
 
 and the moment of this force to turn the magnet is obtained by 
 multiplying by r. But 
 
 s 2 = D 2 + r 2 + r\ 
 
 T) being the distances of the centres of the two magnets; and 
 accordingly the total moment of the acting forces is 
 
 fir dr . f/r'dr 
 
 nurdr.f, 
 (D 2 + r 
 
 Expanding the denominator, and making, for abridgment, 
 
 = i)h, &c., 
 = ' a , &c., 
 
 in which the integrals are to be taken between the limits = + /, 
 r =T 9 I and I' being half the lengths of the two magnets, this 
 becomes 
 
 -i/r -j o K JJ 
 
 - " 3 mm' - (m 3 m r + mm' 3}-- + -^-7 (rn^ti + 2m 3 m\+mm f ,}^ + &c. j , 
 
 or mm'U, in which 
 
 15 
 
 Now it is to be observed, that the variations of the ratios 
 
 ^ ^ & c arising from the variations of v, are of a lower order 
 m m 
 
 of magnitude than that of m, and may be disregarded in then- 
 effect upon the value of U* On the supposition that the quantity 
 
 * This circumstance was first pointed out by Dr. Lament.
 
 266 ON THE DETERMINATION OF THE TOTAL 
 
 of free magnetism, at any point of a magnet, is proportional to 
 the distance from the centre, or that /u = AT, we have 
 
 * = A-/ 3 , z 3 = | A-/ 3 , w 5 - 1 M\ 
 
 and when & becomes k + SA-, these values will all be altered 
 proportionally, and consequently the ratios '-, , &c., will be 
 
 absolutely unchanged ; and the same thing is manifestly true, if 
 the quantity of free magnetism be supposed to vary as any simple 
 power of the distance, whether integer or fractional. 
 
 This is a point of considerable importance in reference to the 
 method now proposed. For it follows that, at a given distance 
 between the two needles, the function V may be regarded as 
 constant; and therefore that, even when U is unknown, the value 
 of R will be relatively determined, by a process which is inde- 
 pendent of the changes induced by time in the magnetic moments 
 of the needles employed. Accordingly, if the value of the force 
 be found at any one place, by any independent means, it will be 
 absolutely known at all ; and it is only necessary that the observer 
 should include in his series an observation at some base-station, at 
 which the absolute value of the force is determined simultaneously 
 by the ordinary method. 
 
 I now proceed to show, however, that the value of the constant 
 V may be found by deflection, by the instrument itself, and 
 without any subsidiary apparatus ; and that the method may 
 therefore be rendered rigorously absolute. It is obvious that the 
 ordinary process is inapplicable in this case, owing to the large 
 number of terms which acquire a sensible value, in the value of 
 the function U, and the consequent difficulty and uncertainty of 
 the elimination : moreover, the position which has been adopted 
 for the deflecting needle will not admit of the required alteration 
 of distance. 
 
 Now here I premise, that it is not necessary that the usual 
 deflection distance should be one of the series employed in 
 deducing the coefficients of the inverse powers of the distance in 
 the value of U: it is not even requisite that the relative positions 
 of the two magnets should be the same in the two cases. For if 
 the value of the corresponding function be found, for any other 
 position, and at any distance, that of U will be known by a 
 comparison of the deflections produced. Accordingly, 1 propose
 
 INTENSITY OF THE EARTH'S MAGNETIC FORCE. 267 
 
 to determine, in the first place, the value of the corresponding 
 function in a different relative position of the two magnets, and 
 by means of deflections at the usual distances; and thence to 
 conclude that of U in the position of the magnets here employed. 
 
 In using the dip-circle for this purpose, it will be found most 
 convenient to adopt the third of the methods above described, in 
 which the equilibrium is produced by turning the instrument in 
 azimuth until the deflected magnet becomes vertical ; for in this 
 case the deflecting magnet is always horizontal, and can be placed 
 in the usual position with respect to the deflected magnet without 
 difficulty. For this purpose the apparatus is provided with a gun- 
 metal bar, the middle of which is broad, and has a rectangular 
 aperture which enables it to pass over the box containing the 
 deflected magnet : this bar rests horizontally on two supports 
 fixed outside the box, on the level of the agate planes. The 
 deflecting magnet is to be placed on this support at different 
 known distances, and on each side of the deflected magnet, its 
 axis being in the plane in which the latter moves ; and the 
 apparatus is to be turned in azimuth until the deflected needle is 
 vertical. In this case equation (2) becomes 
 
 - X cos a = m V ; 
 in which V is of the form 
 
 where 
 
 n = --- - - , q = -- ----- / - 6 --- 
 
 ,,i m m m m 8 m 
 
 /., -HI r, ,. flaw's 45 ;;/.-, 
 
 - 3- , q = 3 -- 15 ----- / + - 6 --- 7> 
 
 Let F,, F-, F 3 , &c., denote the values of V corresponding to the 
 distances D,, A, -D 3 , &o. ; and a,, a 2 , a ;i , &c., the corresponding 
 
 azimuths observed ; then it is obvious that 
 
 V-. cos ! - Fi cos a, = 0, F 3 cos ai - F, cos a a = 0, & 
 
 from which equations the values of the coefficients j>, J . 
 obtained by elimination in the usual manner. IIen- / is com- 
 pletely determined. 
 
 Now let the deflecting magnet be removed from the horizontal 
 bar, and placed in its ordinary position between the microscopes ; 
 and let the observation be it-peat ed, tin- tnrfniment being turned
 
 268 ON THE DETERMINATION OF THE TOTAL 
 
 in azimuth until the deflected needle is vertical. Then, if a,, 
 denote the corresponding azimuth, we have 
 
 - X cos a y = m U ; 
 whence there is 
 
 U = F cosa . 
 cos a 
 
 Thus the uncertainty of the result, arising from the smallness of 
 the angle of deflection at the usual distances, is removed from the 
 regular series of observations, and is thrown upon the determina- 
 tion of the constant, which may be made at leisure, whenever 
 convenient, and may be repeated as often as is required for 
 accuracy. 
 
 In speaking of U as constant, and independent of the changes 
 of the magnetic moments of the needles, I have expressly limited 
 the statement to those small and regular losses of magnetism 
 which occur in time. It would not be safe to extend the assump- 
 tion to the case of the larger changes brought about abruptly by 
 concussion, or by any other accidental cause; and still less to 
 those in which the magnetic distribution of the needles is altered 
 by contact with, or proximity to, magnetic bodies. In such cases 
 (the occurrence of which is easily detected), the value of the 
 constant U should be re-determined. 
 
 It may be useful to add a few words respecting the order of 
 the observations. 
 
 The apparatus should be furnished with three needles, all of 
 the same size, viz., 3^ inches in length. One of these (which we 
 shall denote by the letter A) is to be employed in observations 
 of inclination : the other two, B and 0, are to be used in the 
 observations of intensity, B being the loaded needle, which is 
 also used as a deflector, and C the deflected needle. The two 
 latter needles should not have their poles reversed, nor be touched 
 with a magnet. 
 
 The observations may be conveniently taken in the following 
 order : 
 
 1. Needle A is to be placed on the agate planes, the other two 
 needles being removed, and a complete observation of inclination 
 taken in the four usual positions of the needle and limb, and with 
 the poles of the needle direct and inverted.
 
 INTENSITY OF THE EARTH'S MAGNETIC FORCE. 260 
 
 2. Needle A is then to be removed, and the loaded needle, B, 
 substituted ; and its inclination to the horizon, TJ, is to be observed 
 in the four positions of the needle and limb. The deviation of 
 this needle from the position due to the earth's magnetic force 
 alone is u = 9 - j, the angle 7j being positive when measured at 
 the same side of the horizontal line with 0, and negative in the 
 contrary case. 
 
 3. Needle B is now to be removed from the agate planes to its 
 supports between the microscopes, and needle C substituted ; and 
 the inclination of the latter to the horizon is then to be observed 
 in one position of the needle and limb. The observation is to be 
 repeated with the north end of needle B turned in the opposite 
 direction, by the revolution of the moveable arms which cany 
 the microscopes ; half the difference of the readings in the two- 
 positions is the angle of deflection, u'. 
 
 The total intensity is given by the formula 
 
 sm u sin u 
 
 which is fitted, without any artifice, for logarithmic computation.* 
 In strictness a correction is required for the effect of the 
 change of temperature of needle B, in the two observations in 
 which it is employed ; but as one of these observations may be 
 made to follow the other quickly, and as the needle may be placed 
 in both in nearly the same circumstances, the correction may 
 generally be disregarded. It will be necessary, however, that this 
 needle, when employed as a deflector, should be protected from 
 the heat of the observer's body by a small case of glass or 
 of metal. 
 
 The method here proposed appears to offer the following 
 advantages to the travelling observer : 
 
 1. It is applicable, with equal accuracy, at all parts of the 
 globe. 
 
 2. It dispenses with the employment of a separate instrument 
 
 * If the weight be attached to the loaded needle at a fixed point, the formula 
 becomes
 
 270 ON THE DETERMINATION OF THE TOTAL INTENSITY. 
 
 for the determination of the magnetic intensity, and with the 
 separate adjustments required in erecting it. 
 
 3. The constants to be determined the magnitude of the 
 added weight, and the radius of the pulley by which it acts, can 
 be ascertained with more ease and certainty than those which 
 are required in the method of vibrations, and are less liable to 
 subsequent change. 
 
 4. The observations themselves are less varied in character 
 than the usual ones, and may be completed in a shorter time.
 
 XII. OX EARTH CURRENTS, AND THEIR CONNEXION WITH 
 THE DIURNAL CHANGES OF THE HORIZONTAL 
 MAGNETIC NEEDLE. 
 
 Transactions of the Royal Irish Academy. Vol. XXIV. 
 
 1. WHEN the discovery of Oersted had made known the con- 
 nexion which subsists between magnetism and current electricity, 
 the idea occurred to many that the magnetism of the earth or, 
 at least, its diurnal fluctuation, was the result of electric currents 
 traversing its crust. This idea gained much force from the fact, 
 soon after discovered by Seebeck, that electric currents are 
 generated when heat is applied to a circuit composed of different 
 metals ; and it was supposed that the phenomena were thus 
 traceable to the thermal agency of the sun, operating in succes- 
 sion upon the conducting substances of which the earth's crust 
 is composed. 
 
 The most explicit statement, and chief support of this hypo- 
 thesis, is contained in a memoir by Professor Christie, published in 
 the Philosophical Transactions for 1827. In this memoir it is 
 maintained that the phenomena of the diurnal variation of the 
 horizonal magnetic needle correspond with those which are pro- 
 duced experimentally, by the application of heat to a globe 
 composed of two metals ; and the author was even led by his 
 experiments to anticipate the fact, at that time unknown, that at 
 opposite sides of the equator the poles of the needle, having the 
 same name as the latitude, are always deflected in the same 
 direction. 
 
 I propose, in the present memoir, to examine this theory apart 
 from the hypothesis as to the origin of the currents ; and to show,
 
 272 ON EARTH CURRENTS, AND THEIR CONNEXION 
 
 that the diurnal variation of the horizontal magnetic needle is due 
 to electric currents traversing the earth's crust. 
 
 2. The first and most important step towards the result above 
 referred to has been made by Mr. Barlow. In a Paper* com- 
 municated by him to the Royal Society in the year 1848, he 
 established the important fact, that a wire, whose extremities are 
 connected with the earth at two distant points, is unceasingly 
 traversed by electric currents, the intensity of which varies with 
 the azimuth of the line joining the points of contact with the 
 ground. The direction of these currents was proved to be the 
 same at both extremities of the same wire, and was shown to 
 depend on the relative positions of the Earth-connexions, while 
 it was wholly independent of the course followed by the wire 
 itself. The currents cease altogether when either of the contacts 
 with the earth is interrupted. From these facts Mr. Barlow 
 concluded that " the currents are terrestrial, of which a portion is 
 conveyed along the wire, and rendered visible by the multiplying 
 action of the coil of the galvanometer." 
 
 Mr. Barlow further observed that, apart from sudden and 
 occasional changes, the general direction of the needle of the 
 galvanometer appeared to exhibit some regularity. He was thus 
 led to institute a series of observations for fourteen days and nights 
 simultaneously on two telegraphic wires, one connecting Derby 
 and Eugby, and the other connecting Derby and Birmingham, 
 the positions of the needles in both circuits being recorded every 
 five minutes, day and night. From these observations he con- 
 cluded 
 
 " 1. That the path described by the needle consisted of a 
 regular diurnal motion, subject to disturbances of greater or less 
 magnitude. 
 
 " 2. That this motion is due to electric currents passing from 
 the northern to the southern extremities of the telegraph wires, 
 and returning in the opposite direction. 
 
 " 3. That, exclusive of the irregular disturbances, the currents 
 flowed in a southerly direction from about 8 or 9 A.M. until the 
 evening, and in a northerly direction during the remainder of the 
 twenty- four hours." 
 
 * " On the spontaneons Electrical Currents observed in the wires of the Electric 
 Telegraph." Phil. Trans., 1848.
 
 VARIATIONS OF THE MAGNETIC NEEDLE. 273 
 
 Mr. Barlow was thus led to examine whether any relation 
 subsisted between these movements and the daily changes of the 
 horizontal magnetic needle. And having made, for this purpose, 
 a series of simultaneous observations with a delicate declinometer, 
 he came to the conclusion that, although generally the currents 
 flow southwards during that part of the day in which the variation 
 of the horizontal needle is tcesterly, and northwards when the vari- 
 ation is easterly, " yet simultaneous observations showed no simi- 
 larity in the paths described by the magnetic needle and the 
 galvanometer." 
 
 An examination of the galvanometrio observations above re- 
 ferred to led me, some time since, to an opposite conclusion ; and 
 at the last meeting of the British Association I stated my convic- 
 tion, founded on these observations, that the earth-currents, whose 
 continuous flow Mr. Barlow has the merit of establishing, would 
 eventually explain the variations of terrestrial magnetism, both 
 periodic and irregular. I now proceed to state some of the grounds 
 of this conviction ; and in the present paper I hope to show that 
 the diurnal changes of the earth-currents correspond with those of 
 the horizontal component of the earth's magnetic force. 
 
 4. Before proceeding to the detailed examination of this .corre- 
 spondence, it is necessary to advert to a difference between the things 
 compared, which will account for the method employed in the com- 
 parison. The cause of this difference will be adverted to hereafter. 
 
 When we examine the curves,* in which Mr. Barlow has re- 
 presented the course of the galvanometric deflections caused by the 
 earth-currents, we observe that the regularity of that course is con- 
 tinually interrupted by rapid reciprocating movements, in which 
 the needle oscillates from one side to the other of the zero, alter- 
 nately. These movements are very different in magnitude at 
 different times: thus, May 29 was a day of considerable movement ; 
 May 25, one of comparative rest. These movements are similar 
 to those of the magnetometers, with which we are familiar ; but 
 they are much more rapid, and bear a larger proportion to the 
 regular changes. Among the days of observation whose results 
 are given in this diagram, it fortunately happens that one, viz., 
 the day commencing May 28, 10 p. M. (Gdttingen time), was a 
 " term-day " of the magnetic system, during which the magneto- 
 meters were observed every five minutes at the Greenwich Obser- 
 
 * Philowphical Transaction*, 1848, Diagram, No. 1. 
 T
 
 274 ON EARTH-CURRENTS, AND THE DIURNAL 
 
 vatory, and consequently at the same intervals of time as the 
 needles of the galvanometers in Mr. Barlow's observations. I find, 
 upon an examination of the two records, that there were on that 
 day, on the average, 5-1 alternations of the galvanometer needles in 
 the hour, the corresponding number of alternations of the magneto- 
 meters being only 3-1. The numbers are very nearly the same for 
 the two galvanometers of the two lines of telegraph, as well as for 
 the two magnetometers of the Greenwich Observatory. And the 
 disproportion in the magnitude of the deflections, as compared with 
 the amount of the regular daily changes, appears to be even more 
 considerable. 
 
 The frequency and the magnitude of the deflections may both be 
 taken into account, by adding together the alternate changes, with- 
 out regard to sign, and dividing the sum by the regular daily 
 changes. I have selected for this calculation the observations 
 made during the six hours commencing at 3 A. M. on May 29, that 
 being a period of comparative disturbance. The sum of the changes 
 of the galvanometer needle during that period, on the Derby and 
 Rugby line, was equivalent to 571 divisions of the instrument, the 
 mean daily range for the entire week being 11 "4 divisions: and the 
 ratio = 50. The corresponding ratio, for the galvanometer of the 
 Derby and Birmingham line, is somewhat smaller. The sum of the 
 changes of the Greenwich declinometer during the same period was 
 only 57 minutes, the mean daily range being 12*4 minutes. In 
 like manner, the sum of the changes of the horizontal force (in 
 parts of the whole) was -0158, the mean daily range being -0034. 
 The ratio is accordingly the same for the two magnetic elements, 
 and its amount is 4'6, or less than one-tenth of the corresponding 
 ratio in the case of the galvanometric changes. We learn there- 
 fore that the rapid changes of the earth- currents are much greater, 
 in proportion to the regular daily changes, than the corresponding 
 movements of the magnetometers. 
 
 The physical interpretation of the foregoing facts will be con- 
 sidered in the sequel. For the present, I shall merely notice the 
 consequence which appears to flow immediately from them namely, 
 that little or no accordance is to be expected, in comparing the 
 individual remits of the two classes of measures. I have verified 
 this conclusion by a comparison of Mr. Barlow's diagram, for 
 the period above referred to, with the corresponding Greenwich 
 observations.
 
 VARIATIONS OF THE MAGNETIC NEEDLE. 
 
 275 
 
 5. For the foregoing reasons, the magnetometric observations 
 are here compared, not with the single corresponding deflections of 
 the galvanometer needles, but with the means of several. The 
 observations instituted by Mr. Barlow on the two lines of telegraph 
 were taken at intervals of five minutes, and were continued for 
 fourteen consecutive days, commencing May 17, 1847. In the 
 Tables given in his Paper, the individual results are grouped into 
 means corresponding to the beginning of each hour ; so that each 
 number of the Table is the result of twelve distinct readings. 
 The means so obtained are, notwithstanding, more affected by 
 irregularities than the single readings of the magnetometers cor- 
 responding to the same epochs ; and I have found it advisable to 
 group the results still further, by taking the mean of each pair of 
 succeeding hourly means. The following Tables, accordingly, 
 contain the means of the results belonging to the hours, 1 A.M. 
 and 2 A.M., 3 A.M. and 4 A.M., &c. ; they therefore correspond to 
 the epochs, P 30 m , 3 h 30 m , &c., each number being the mean 
 of twenty-four single readings. The positive numbers indicate 
 currents proceeding towards Derby ; and the negative, currents in 
 the contrary direction. It is only necessary to observe further, 
 that of the fourteen days of observation, four, viz., May 17, 23, 
 24, 30, are very incomplete, and are therefore omitted altogether 
 in this place : 
 
 TABLE I. 
 
 Intensity of the Currents traversing the Wire connecting Derby and Rugby. 
 
 
 A.M. 
 
 MAY. 
 
 I'- :jo m 
 
 3 1 ' 30 m 
 
 5 h 30 m 
 
 7 h 30 m 
 
 9 h 30 m 
 
 J.l h 30 
 
 18 
 
 + 1-9 
 
 -3-5 
 
 -1-7 
 
 4- 1-8 
 
 4-4-9 
 
 - 1-4 
 
 1!) 
 
 + 4-6 
 
 + 1-4 
 
 -0-8 
 
 4- 4-5 
 
 -0-5 
 
 - 3-S 
 
 *>() 
 
 
 
 m 
 
 
 - 1 ,-, 
 
 - 2-< 
 
 21 
 
 + 0-6 
 
 + 0-3 
 
 + 1-2 
 
 4 0-2 
 
 41-1 
 
 - 2-4 
 
 I'l 
 
 + 3-2 
 
 + 2-5 
 
 41-0 
 
 + 2-8 
 
 -2-3 
 
 - 5-2 
 
 25 
 
 -1-3 
 
 43-6 
 
 46-5 
 
 + 1-8 
 
 -0-6 
 
 - 3-2 
 
 26 
 
 + l-s 
 
 + 5-0 
 
 + 3-1 
 
 + 2-2 
 
 -1-7 
 
 - M 
 
 27 
 
 -0-2 
 
 + 0-6 
 
 45-0 
 
 + 4-7 
 
 + 1-9 
 
 - 2-5 
 
 28 
 
 -2-1 
 
 -1- 1-4 
 
 + 2-4 
 
 + 10-3 
 
 .V! 
 
 - -1-1 
 
 29 
 
 -2-9 
 
 4 0-1 
 
 -0-4 
 
 + 2-8 
 
 -2-1 
 
 - 12-2 
 
 Means 
 
 4 0-9 
 
 4 1-3 
 
 4 1-7 
 
 4 3-.J 
 
 40-5 
 
 - !_'
 
 276 
 
 ON EAETH-CUERENTS, AND THE DIUENAL 
 
 TABLF, I. continued. 
 
 \ 
 
 P.M. 
 
 
 li>30> 
 
 3 h 30 m 5 h 30 m 
 
 7 h 30 
 
 9 h 30 
 
 ll'> 30 m 
 
 18 
 
 - 7-5 
 
 -8-3 
 
 -8-8 
 
 - 1-5 
 
 + 3-5 
 
 + 6-1 
 
 19 
 
 - 0-1 
 
 -0-4 
 
 . , 
 
 
 . . 
 
 . . 
 
 20 
 
 - 2-7 
 
 - 1-9 
 
 -2-1 
 
 -8-6 
 
 + 1-3 
 
 + 5'5 
 
 21 
 
 - 2-2 
 
 -2-4 
 
 -2-0 
 
 -5-2 
 
 -3-4 
 
 + 2-6 
 
 22 
 
 - 1-8 
 
 -1-2 
 
 -1-7 
 
 -2-2 
 
 -2-3 
 
 -1-1 
 
 25 
 
 - 2-7 
 
 + 0-8 
 
 + 0-6 
 
 o-o 
 
 -1-0 
 
 + 1-4 
 
 26 
 
 - 3-9 
 
 + 0-7 
 
 + 4-4 
 
 + 3-1 
 
 + 1-8 
 
 -0-1 
 
 27 
 
 - 4-3 
 
 -0-5 
 
 + 0-6 
 
 -4-7 
 
 + 6-5 
 
 + 4-7 
 
 28 
 
 - 7-8 
 
 -0-9 
 
 -2-9 
 
 + 4-2 
 
 + 3-5 
 
 + 1-9 
 
 29 
 
 - 10-6 
 
 -6-6 
 
 -6-9 
 
 -1-0 
 
 -0-5 
 
 -3-5 
 
 Means 
 
 - 4-4 
 
 - 2-1 
 
 -2-1 | -1-7 
 
 + 1-0 
 
 + 1-9 
 
 TABLE II. 
 
 Intensity of the Currents traversing the Wire connecting Derby and Birminylunn* 
 
 
 lh 30* 
 
 3>>30 m 5 h 30 ra 
 
 71, 30 m 
 
 9 h 30 m 
 
 ll''30' 
 
 18 
 
 + 0-3 
 
 -9-7 
 
 -5-7 
 
 + 5-7 
 
 + 6-6 
 
 - 10-0 
 
 19 
 
 + 3-6 
 
 + 6-0 
 
 -7-0 
 
 + 9-7 
 
 -0-6 
 
 - 10-3 
 
 20 
 
 + 8-7 
 
 -2-6 
 
 -1-1 
 
 + 7-2 
 
 + 1-1 
 
 - 8-5 
 
 21 
 
 + 2-1 
 
 + 1-7 
 
 + 5-0 
 
 + 1-5 
 
 + 7-6 
 
 - 9-0 
 
 22 
 
 + 9-7 
 
 + 8-5 
 
 + 5-2 
 
 + 9-9 
 
 -6-0 
 
 -17-5 
 
 25 
 
 + 1-0 
 
 + 2-4 
 
 + 3-0 
 
 + 0-4 
 
 -0-6 - 3-1 
 
 26 
 
 + 1-8 
 
 + 3-4 
 
 + 1-2 
 
 + 0-8 
 
 -1-6 
 
 - 4-7 
 
 27 
 
 -0-8 
 
 + 0-3 
 
 + 2-3 
 
 + 2-4 
 
 + 0-5 i - 2-5 
 
 28 
 
 -1-7 
 
 + 0-4 
 
 + 1-4 
 
 + 8-4 
 
 + 5-1 
 
 - 3-7 
 
 29 
 
 -2-4 
 
 -1-1 
 
 + 1-4 
 
 + 7-8 
 
 + 1-4 
 
 - 5-7 
 
 Means 
 
 + 2-2 
 
 -t-0-9 
 
 + 0-6 
 
 + 5-4 
 
 + 1-4 
 
 - 7-5 
 
 
 i 
 
 P. M. 
 
 MAT. 
 
 
 
 Ih 30 m 311 30 m 
 
 5 h 30 
 
 7 h 30 
 
 9 h 30 m 
 
 II 1 ' 30 
 
 18 
 
 -17-4 -21-1 
 
 -10-6 
 
 - 4-2 
 
 + 3-7 
 
 + 5-6 
 
 19 - 9-2 - 10-8 
 
 -18-2 
 
 -13-0 
 
 + 2-4 
 
 + 9-0 
 
 20 
 
 - 11-6 
 
 - 9-9 
 
 - 6-1 
 
 -10-0 
 
 + 2-9 
 
 + 11-6 
 
 21 -11-3 
 
 -12-8 
 
 - 7-0 
 
 -16-7 
 
 -5-2 
 
 + 6-4 
 
 22 - 9-3 
 
 - 7-3 
 
 - 8-9 
 
 - 9-3 
 
 -8-6 
 
 - 2-2 
 
 25 - 3-2 
 
 - 0-6 
 
 -- 1-1 
 
 - 1-5 
 
 - 1-7 
 
 + 1-0 
 
 26 - 5-5 - 3-6 
 
 + 2-3 
 
 + 0-3 
 
 + 0-1 
 
 - 2-1 
 
 27 - o-() 
 
 - 1-8 
 
 - 2-1 
 
 - 7-7 
 
 + 4-4 
 
 + 4-2 
 
 28 ; - 8-0 
 
 - 2-9 
 
 - 6-1 
 
 -i- 1-4 
 
 + 0-7 
 
 + 1-6 
 
 29 - 4-2 j - 2-6 
 
 - 3-0 
 
 + 2-5 
 
 + 2-2 
 
 + 0-8 
 
 Means - 8-5 - "-3 
 
 -6-1 
 
 -5-8 +0-1 
 
 + 3-6
 
 VARIATIONS OF THE MAGNETIC NEEDLE. 277 
 
 The means corresponding to each epoch are given in the 
 lowest lines of the preceding Tables. On examining them, it 
 will be seen that the law of the diurnal changes in the force and 
 direction of the currents is very systematic. In both lines the 
 current flows southwards from ll b 30 m A.M. to 7 h 30 m P.M. inclusive; 
 and northwards at the remaining epochs. The maximum of the 
 southerly current occurs at l h 30 m P.M., and that of the northerly 
 current at 7 h 30 m A.M. 
 
 6. Let us now compare these results with those deducible from 
 the diurnal changes of the magnetic declination and horizontal 
 force, on the assumption that the forces which produce the latter 
 are due to electric currents traversing the upper strata of the 
 earth in a horizontal direction. 
 
 Let rj denote the disturbing force by which the north pole of 
 the magnet is urged to the eastward of its mean position ; , that 
 by which it is impelled northward. Then, on the assumption 
 above* referred to, the force of the current in the magnetic 
 meridian, flowing northward, = aij, a being an unknown constant ; 
 and that of the current perpendicular to the magnetic meridian, 
 flowing eastward, = - . Hence, the force of the current in any 
 direction, making the angle e with the magnetic meridian measured 
 to the east of north, is 
 
 / = a (n cose -K sins). 
 
 The quantities r? and % are given, in terms of the horizontal 
 component of the earth's magnetic force, by the readings of the 
 two horizontal magnetometers. For it is evident that 
 
 X being the horizontal component of the earth's magnetic force, 
 uiid \ft the magnetic declination ; and 
 
 = X - X = $X. 
 
 7. Now, to reduce the preceding formula into numbers, we 
 have e = a - 1//, in which a is the azimuth of the line connecting 
 the two stations, measured from the true meridian eastward. The 
 observations of Sir James Boss, at Derby, give 
 
 = - 22 25' ;
 
 278 ON EARTH-CURRENTS, AND THE DIURNAL 
 
 and for the line connecting Derby with Bugby, 
 = - 13 7', = + 9 18'. 
 Introducing these values in the expression for /, 
 
 (85T\ 
 000287^-0-16-^-). 
 A / 
 
 The following Table gives the values of the quantity within 
 the brackets in this formula, for the days on which the force of 
 the currents was observed, and for the even hours of Gottingeu 
 
 $X 
 mean time, the unit being 10 ^ 00 . The values of <ty, and -=- are 
 
 obtained from the Greenwich observations.* 
 
 * In my first calculation of the Intensity of the Currents, communicated to the- 
 Academy on the llth November, I employed the mean values of Sif and for the 
 
 month of May, as deduced from observations made at the Dublin Magnetical Obser- 
 vatory in the years 1840-1843. My reason for this was, that in the year 1848, which 
 was stated in Mr. Barlow's Paper to have been the year of his galvanometric observa- 
 tions, the daily observations at the Dublin Observatory were not sufficiently numerous 
 for the required comparison ; while the Greenwich published observations were then 
 limited to term-days, and days of unusual disturbance. But I soon after learned from 
 Mr. Barlow himself, that his observations were made in 1847, and that the date in the 
 heading of his Tables had been misprinted by oversight. And as the Greenwich 
 observations were taken twelve times in the day in 1847, 1 have recalculated the forces 
 from the simultaneous elements thus furnished. The comparison is, of course, in 
 every way more satisfactory than the former.
 
 VARIATIONS OF THE MAGNETIC NEEDLE. 
 
 279 
 
 TABLE III. 
 
 Calculated Values of the Intensity of the Earth- Currents, in the Line connecting 
 Derby and Rugby. 
 
 
 A.M. 
 
 MAY. 
 
 
 
 I h 20 m 
 
 3>>20 ra | 5 h 20 m 
 
 7 h 20 m 
 
 9 h 20 m 
 
 Il h 20 m 
 
 18 
 
 + 13-8 
 
 + 10-7 
 
 + 12-0 
 
 + 9-4 
 
 + 2-6 -14-2 
 
 19 
 
 - 2-9 
 
 + 0-5 
 
 + 4-3 
 
 + 9-5 
 
 - 0-3 -21-6 
 
 20 
 
 + 12-6 
 
 + 9-1 
 
 + 21-7 
 
 + 16-5 
 
 + 7-0 - 17-7 
 
 21 
 
 - 0-8 
 
 + 6-8 
 
 + 7-9 
 
 + 14-7 
 
 4- 9-5 , - 12-8 
 
 22 
 
 + 7-2 
 
 + 14-1 
 
 + 7-8 
 
 + 14-9 
 
 + 11-8 -13-1 
 
 25 
 
 + 4-7 
 
 + 7-9 
 
 + 19-2 
 
 + 20-8 
 
 4- 10-6 - 5-1 
 
 26 
 
 + 14-7 
 
 + 16-5 
 
 + 16-5 
 
 + 17-2 
 
 + 0-5 
 
 -19-7 
 
 27 
 
 - 0-1 
 
 + 2-8 
 
 + 13-7 
 
 + 19-0 
 
 + 11-3 
 
 -10-9 
 
 . 28 
 
 - 2-6 
 
 + 12-0 
 
 + 9-8 
 
 + 23-1 
 
 + 8-1 
 
 - 7-7 
 
 ' 29 
 
 + 4-0 
 
 + 7-1 
 
 + 28-3 
 
 - 3-8 
 
 -f 2-9 
 
 -17-8 
 
 Means 
 
 + 5-1 
 
 + 8-8 
 
 + 14-1 
 
 + 14-1 
 
 4-6-4 
 
 -14-1 
 
 
 P. M. 
 
 MAY. 
 
 
 
 l>>20 m 
 
 3 h 20 m i 5 h 20 ra j 7 h 20 m 
 
 9 h 20 m 
 
 Il h 20 ra 
 
 18 
 
 -27-4 
 
 -20-5 - 2-9 
 
 -5-9 
 
 -4-2 
 
 - 3-5 
 
 19 
 
 - 24-2 
 
 - 9-0 - 1-5 
 
 -3-9 
 
 -0-3 
 
 + 5-5 
 
 20 
 
 -17-7 
 
 - 4-8 - 2-7 
 
 + 1-5 
 
 + 1-3 
 
 4- 1-7 
 
 21 
 
 -19-8 
 
 - 8-6 + 0-9 
 
 + 7-9 
 
 + 1-6 
 
 + 3-8 
 
 22 
 
 -22-6 
 
 - 6-0 - 3-0 
 
 -1-5 
 
 + 1-2 
 
 + 1M 
 
 25 - 16-2 
 
 - 8-4 - 3-8 
 
 -0-8 
 
 -0-5 
 
 + 8-1 
 
 26 - 29-4 
 
 - 19-3 | - 11-0 
 
 -1-9 
 
 -0-9 
 
 + 3-6 
 
 27 
 
 -19-6 
 
 - 9-6 - 1-2 
 
 -5-7 
 
 -1-9 
 
 + 12-9 
 
 28 
 
 -20-1 
 
 -10-3 
 
 - 5-0 
 
 -0-7 
 
 + 2-6 
 
 + 3-1 
 
 29 
 
 -23-0 
 
 -13-2 
 
 - 8-6 
 
 -7-1 
 
 -1-4 
 
 + 2-7 
 
 Means 
 
 -22-0 
 
 -11-0 
 
 -3-9 
 
 -1-8 
 
 -0-3 
 
 4 4-n 
 
 8. For the line connecting Derby and Birmingham, we have 
 
 = 4- 33 27', = 4- 55 52' ; 
 and, introducing these values, the formula becomes 
 
 g Y 
 0001C3 fy - 0-83 ~
 
 280 
 
 ON EARTH-CURRENTS, AND THE DIURNAL 
 
 The values of the quantity within the brackets, for the same days 
 and hours, are given in the following Table : 
 
 TABLE IV. 
 
 Calculated Values of the Intensity of the Earth- Currents, in the Line connecting 
 Derby and Birmingham. 
 
 
 
 
 A. 
 
 M. 
 
 
 
 MAT. 
 
 
 
 
 
 
 
 
 l>>20 m 
 
 3 h 20 m 
 
 5 h 20 
 
 7 h 20-0 
 
 9 h 20 m 
 
 ll h 20 
 
 18 
 
 + 13-8 
 
 + 11-1 
 
 + 13-4 
 
 + 25-4 
 
 + 24-2 
 
 + 8-9 
 
 19 
 
 - 7-5 
 
 - 6-3 
 
 - 3-4 
 
 + 8-2 
 
 + 17-7 
 
 - 1-3 
 
 20 
 
 + 11-7 
 
 - 0-3 
 
 + 12-4 
 
 + 10-4 
 
 + 25-2 
 
 + 2-5 
 
 21 
 
 + 1-6 
 
 + 4-5 
 
 + 10-0 
 
 + 18-5 
 
 + 24-5 
 
 + 4-7 
 
 22 
 
 + 0-5 
 
 + 6-3 
 
 + 3-7 
 
 + 5-1 
 
 + 23-4 
 
 - 3-9 
 
 25 
 
 + 1-3 
 
 + 4-2 
 
 + 11-8 
 
 + 14-4 
 
 + 12-1 
 
 + 4-2 
 
 26 
 
 + 3-8 
 
 + 10-5 
 
 + 10-4 
 
 + 12-9 
 
 + 3-0 
 
 - 9-1 
 
 27 
 
 + 2-4 
 
 + 1-8 
 
 + 8-1 
 
 + 17-2 
 
 + 12-7 
 
 4 1-3 
 
 28 
 
 - 9-0 
 
 + 8-7 
 
 + 3-7 
 
 + 23-5 
 
 + 27-8 
 
 + 16-1 
 
 29 
 
 + 3-8 
 
 + 8-2 
 
 + 8-1 
 
 + 25-8 
 
 + 23-5 
 
 -10-0 
 
 Means 
 
 + 2-2 
 
 + 4-9 
 
 + 7-8 
 
 + 16-1 
 
 + 19-4 
 
 + 1-3 
 
 
 
 
 p. 
 
 M. 
 
 
 
 MAT. 
 
 
 
 
 
 
 
 
 li>20 m 
 
 3 h 20 m 
 
 5 h 20 m 
 
 7 h 20 m 
 
 9 h 20 m 
 
 Il h 20 m 
 
 18 
 
 -14-5 
 
 -18-0 
 
 -17-1 
 
 -11-4 
 
 - 10-9 
 
 - 9-3 
 
 19 
 
 -19-0 
 
 - 7-8 
 
 - 6-3 
 
 - 8-0 
 
 - 2-4 
 
 + 1-1 
 
 20 
 
 - 7-9 
 
 - 4-3 
 
 -17-6 
 
 -13-9 
 
 - 4-7 
 
 + 5-5 
 
 21 
 
 -16-0 
 
 - 16-3 
 
 - 8-0 
 
 - 6-4 
 
 - 2-9 
 
 - 3-3 
 
 22 
 
 -18-7 
 
 -11-9 
 
 - 5-3 
 
 - 3-2 
 
 - 1-4 
 
 - 0-5 
 
 25 
 
 -12-1 
 
 -11-3 
 
 -ll-l 
 
 -10-2 
 
 - 6-2 
 
 - 2-3 
 
 26 
 
 -23-3 
 
 -19-7 
 
 -15-8 
 
 - 8-3 
 
 + 2-5 
 
 + 2-0 
 
 27 
 
 -14-8 
 
 - 9-1 
 
 - 5-8 
 
 -23-9 
 
 - 14-4 
 
 + 10-6 
 
 28 
 
 - 6-8 
 
 - 9-2 
 
 -12-2 
 
 - 4-0 
 
 + 2-5 
 
 + 3-7 
 
 29 
 
 -17-6 
 
 - 10-8 
 
 -16-1 
 
 -15-2 
 
 - 1-6 
 
 - 2-6 
 
 Means 
 
 - 15-1 
 
 -11-8 
 
 -11-5 
 
 -10-5 
 
 -4-0 
 
 + 0-5 
 
 9. The mean results corresponding to the several hours, in these 
 four Tables, are projected in curves in Plate I., figs. 1 and 2. 
 As we are concerned only with relative values in both cases, the 
 ranges of the observed and computed results have been previously
 
 VAKIATIONS OF THE MAGNETIC NEEDLE. 281 
 
 equalized, by multiplying the former by constant coefficients. The 
 curves of both lines exhibit a general resemblance to the course of 
 the diurnal variation of the declination ; but the influence of the 
 horizontal force is also very evident, especially in the afternoon 
 branch of the curve, where its effect is to retard the return from 
 the minimum at 1 P. M. This effect is much greater in the Derby 
 and Birmingham line than in that of Derby and Eugby, the 
 azimuth of the former line, measured from the magnetic meridian, 
 being much greater than that of the latter. The agreement of 
 the calculated with the observed curves is probably as close as 
 could be expected in the results of so short a series ; and we seem 
 entitled to conclude that the diurnal movements of the two mag- 
 netometers are justly accounted for by electric currents traversing 
 the upper strata of the earth. 
 
 10. Upon a closer examination of the two sets of curves, how- 
 ever, there are found some differences to which it is necessary to 
 advert. In the first place, the turning points of the calculated 
 curves are generally later than those of the observed, by about one 
 hour. Thus, in the Derby and Birmingham line, the maximum 
 of the observed force occurs about 8 h O m A.M., and the minimum 
 about 12 h 40 m r. M. The corresponding times for the calculated 
 force are 9 h O m A. M., and l h 40 m P. M., nearly. We shall presently 
 find grounds for believing that time may possibly be required, in 
 order that the current may produce its full magnetic effect. 
 
 11. Another discrepancy is, that the calculated curve is, for 
 the most part, above the observed, especially in the Derby and 
 Birmingham line. This will be evident if the two curves be 
 referred to the same axis of abscissae. It is probably to be accounted 
 for by the fact, that the zero from which the magnetic deflections 
 are measured is not the true one, corresponding to the absence 
 of deflecting force. As we have no means of determining the 
 latter, we are accustomed to take the mean position for the entire 
 day, or the mean of the readings taken at equal intervals, as the 
 point from which the deflections are measured. But there is 
 reason to believe that this is not the true position of rest, corre- 
 sponding to the absence of all disturbing force. The comparative 
 quiescence of the magnets, during the early hours of the morning, 
 seems to indicate that they are then near their true positions of 
 equilibrium ; and this indication is confirmed by the galvanometric 
 curves, the zero-line, which corresponds to the absence of all current,
 
 282 ON EARTH-CURRENTS, AND THE DIURNAL 
 
 dividing the area of the diurnal curve unequally, and being nearer 
 to the night observations than to those of the day. From the last 
 line in Tables I. and III., we find that the mean of all the daily 
 observations of the galvanometers is neyatire on both lines, or 
 below the true zero. On the other hand, the mean of the niyhi 
 observations is positive, or above the zero ; and the same thing is 
 true of that portion of the night (from 1 A. M. to 5 A. M.) during 
 which the magnetic changes are smallest. From these facts it 
 would seem to follow that the true zero of the magnetometric 
 observations lies between the mean of the day and the mean of 
 the hours of magnetic repose. This conclusion, however, it must 
 be remembered, is derived from the observations of a single fort- 
 night only; and, in the absence of fuller knowledge, we should 
 not be justified in changing the origin usually employed. 
 
 Thus magnetometric observations furnish merely differential 
 results; and we are ignorant even of the relative values of the 
 effects, and therefore unable to compare them accurately with their 
 physical causes, whether real or supposed. It is true that, if the 
 galvanometricandthe magnetometric results were completely iden- 
 tified, the zero of the latter could readily be obtained by their com- 
 parison. For if rj and be the values of rj and ,* corresponding 
 to the true zero, measured from the mean of the day, it is plain 
 that, for the hours at which the current changes sign on any line, 
 
 ijo cos i - sin E = rj cos e - % sin t. 
 
 If therefore these hours be known for two lines, which differ con- 
 siderably in azimuth, and also the corresponding values of j and , 
 we should have two equations for the determination of the two 
 unknown quantities, i and . It is obvious, however, that this 
 process cannot be legitimately employed in the comparison and 
 identification itself. 
 
 12. In order to see how far the correspondence, which we 
 have found in the mean results, is traceable in separate days, I 
 projected in curves the observed and calculated values of the 
 intensity of the currents on the Derby and Birmingham line, as 
 given in Tables II. and IV., for the five days commencing May 25. 
 The accordance of the two curves is very remarkable, every alter- 
 nation in direction in one of them having its counterpart in the 
 other. 
 
 13. It remains to say a few words of the manner in which the
 
 VARIATIONS OF THE MAGNETIC NEEDLE. 283 
 
 electric currents may be supposed to operate in producing the 
 magnetic effects. 
 
 An electric current, traversing the earth's crust in a horizontal 
 direction, may affect a horizontal magnetic needle above its 
 surface in two ways. For the current may either act directly 
 upon the needle, according to the known laws of electro-magnetic 
 action ; or it may induce temporary magnetism in the earth itself, 
 which will thus affect the needle differently from before. I believe, 
 with Dr. Lament, that the former hypothesis is inadmissible, at 
 least as regards the principal part of the observed effect. In 
 addition to the reason assigned for this by Dr. Lamont, I may 
 adduce the known similarity in the course of the magnetic changes 
 over considerable portions of the earth's surface, a similarity incom- 
 patible with the supposition that the magnet is directly acted on, 
 to any great extent, by the subjacent current. We must suppose, 
 therefore, that the earth is acted on, to a considerable depth, by 
 the wave of currents which sweep over its surface, and which alter 
 by induction the magnetism of the subjacent mass, and that the 
 effect produced upon the freely suspended magnet at its surface is 
 the result of this induced change. On this supposition, the mag- 
 netic phenomena, whose laws we are considering, are the indirect 
 effects (not of the subjacent current merely, but) of the entire 
 wave traversing an extended portion of the earth's surface. We 
 can thus understand the cause of the similarity in the more rapid 
 magnetic changes to which we have adverted ; and we may even 
 frame some idea of the depth acted on by the superficial current, 
 from the geographical limits of the phenomena. 
 
 Upon this supposition, also, we are prepared to expect differences 
 in the laws of the observed and computed currents, such as have 
 been above noticed. For the galvanometric measures belong only 
 to currents at the place of observation ; while the magnetic changes 
 are, by hypothesis, the mean results of currents occupying a con- 
 siderable portion of the earth's surface. Hence, also, it follows 
 that the complete identification of the two classes of phenomena 
 can only be made by the help of simultaneous observations of 
 earth-currents at numerous points in an extended district. 
 
 14. Before concluding this part of the subject, I must refer 
 briefly to the previous investigations of Dr. Lamont connected 
 vvith it, so far as they have been yet made public. 
 
 In a letter, dated July 29, 1SG1, which was read by the
 
 284 ON EARTH-CURRENTS, AND THE DIURNAL 
 
 Astronomer Boyal at the last meeting of the British Association, 
 Dr. Lament stated that he had found " that electric currents, or 
 (as they may be more properly termed) electric wares, varying in 
 direction and intensity, are constantly passing at the surface of 
 the earth, and that these waves correspond perfectly with the 
 variations of terrestrial magnetism." The correspondence here 
 referred to seems to relate to the epochs of the two classes of 
 changes, and not to their amount. For in the latest account of 
 Dr. Lament's researches, of which I am aware, and which is con- 
 tained in a letter to Professor De la Eive, dated October 30, 1861, the 
 writer states that the galvanometer indicates, not the earth-current 
 itself, but its momentary changes. In fact the needle of the galva- 
 nometer, in his observations, appears to have been affected only 
 during a rapid increase or decrease of the earth-current, and to 
 return to zero when the current became equable. It is obvious 
 that, if such were the case generally, there could be no corre- 
 spondence, such as has been pointed out in the preceding pages, 
 between the magnitude of the magnetic changes and the deflections 
 of the galvanometer. It is stated, in fact, by Dr. Lamont, that in 
 such circumstances the galvanometer does not vary much from its 
 mean position, even when the magnetometers have changed con- 
 siderably; and he expresses his doubt whether the constant part 
 of the action of the earth-current can be observed at all with our 
 present means. 
 
 Dr. Lamont ascribes the singular effect above described to the 
 double conductor, the current moving (as he believes) at first in 
 the wires, and afterwards diffusing itself in the earth below. I 
 venture to suggest that it may be due to some disturbing cause, 
 which operates more powerfully (in relation to the principal effect) 
 in short than in long wires. No effect of a similar kind appears 
 to have occurred in the observations of Mr. Barlow, which were 
 made upon telegraphic wires of great length. And, on the other 
 hand, it is a fact well known to telegraphists, that the currents, 
 produced by chemical action upon the terminal plates, interfere 
 with the primary current much more in short, than in long wires. 
 In confirmation of the same view, I may mention the fact observed 
 at many points of the earth during the remarkable aurora of 
 August and September, 1859, namely, that the proper earth- 
 current was strongest, caten's paribus, in the longest lines of 
 telegraph.
 
 VARIATIONS OF THE MAGNETIC NEEDLE. 285 
 
 15. The connexion of the diurnal changes of the horizontal 
 needle with earth-currents being assumed, we may reason from 
 the former to the latter, and infer the laws which govern the 
 diurnal changes of the earth-currents from the known laws of the 
 related phenomena. 
 
 We have already seen that the intensity of the current in the 
 magnetic meridian (flowing northward) = ai\ ; and that of the 
 current perpendicular to the magnetic meridian (flowing east- 
 ward] = - . Hence, if p denote the intensity of the resultant 
 current, and the angle which it makes with the magnetic 
 meridian, measured to the east of north 
 
 in which r\ = Xty sin 1', and = $X, X being the horizontal 
 component of the earth's magnetic force, and ip the magnetic 
 declination*. The azimuth of the direction of the current, 
 measured from the true meridian in the same direction, is 
 
 Substituting in these formulas the mean values of cty and 
 $X at Dublin, for summer, winter, and for the entire year, we 
 obtain the daily changes of p and o>, given in the following Table. 
 The values of Si/ and $X were observed at Dublin during the four 
 years 1840-43, twelve times in the day, namely, at the alternate 
 hours. The values corresponding to the intermediate hours are 
 obtained from them by the usual formulas of interpolation. 
 
 * The preceding combination of the daily changes of the declination and horizontal 
 intensity, as well as the graphical representation of the results, seems to have been first 
 employed by Professor Hansteen, to represent the laws of the disturbing force, to which 
 these changes are due. The only difference between the two representations is, that 
 the azimuth of the disturbing force at any hour is 90 greater than that of the earth- 
 current. Hence, if the diagrams of Plate II. be turned 90 forward in azimuth, th. y 
 represent the daily changes of the horizontal disturbing force.
 
 286 ON EARTH-CURRENTS, AND THE DIURNAL 
 
 TABLE Y. 
 
 HOUR. 
 
 AZIMUTH. 
 
 
 Summer. 
 
 Winter. 
 
 Year. 
 
 Summer. 
 
 1 A.M. 
 
 2 
 
 324 
 338 
 
 353 
 360 
 
 336 
 346 
 
 20-9 
 21-2 
 
 3 
 
 342 
 
 353 
 
 345 
 
 24-7 
 
 4 
 
 342 
 
 327 
 
 338 
 
 29-6 
 
 5 
 
 344 
 
 301 
 
 332 
 
 35-5 
 
 6 
 
 350 
 
 288 
 
 336 
 
 42-1 
 
 7 
 
 3 
 
 303 
 
 352 
 
 49-4 
 
 8 
 
 22 
 
 351 
 
 16 
 
 56-0 
 
 9 
 
 45 
 
 37 
 
 43 
 
 61-6 
 
 10 
 
 72 
 
 81 
 
 75 
 
 66-5 
 
 11 
 
 100 
 
 115 
 
 104 
 
 71-7 
 
 Noon 
 
 124 
 
 134 
 
 128 
 
 77-3 
 
 1 P.M. 
 
 143 
 
 149 
 
 145 
 
 78-0 
 
 2 
 
 158 
 
 162 
 
 160 
 
 70-6 
 
 3 
 
 174 
 
 174 
 
 174 
 
 57-1 
 
 4 
 
 196 
 
 191 
 
 194 
 
 46-6 
 
 5 
 
 223 
 
 218 
 
 221 
 
 45-9 
 
 6 
 
 241 
 
 247 
 
 243 
 
 50-8 
 
 7 
 
 252 
 
 279 
 
 258 
 
 50-5 
 
 8 
 
 261 
 
 311 
 
 277 
 
 43-8 
 
 9 
 
 273 
 
 327 
 
 297 
 
 35-8 
 
 10 
 
 285 
 
 333 
 
 309 
 
 31-0 
 
 11 
 
 296 
 
 336 
 
 315 
 
 27-8 
 
 12 
 
 308 
 
 342 
 
 324 
 
 24-0 
 
 INTENSITY. 
 
 "Winter. 
 
 Year. 
 
 16-0 
 
 18-1 
 
 13-6 
 
 17-1 
 
 12-2 
 
 18-4 
 
 12-5 
 
 20-9 
 
 13-9 
 
 23-3 
 
 14-3 
 
 25-1 
 
 12-5 
 
 27-8 
 
 13-6 
 
 34-1 
 
 19-1 
 
 39-3 
 
 26-4 
 
 46-6 
 
 39-7 
 
 54-6 
 
 49-8 
 
 63-3 
 
 51-5 
 
 64-4 
 
 46-3 
 
 58-1 
 
 35-5 
 
 46-6 
 
 23-3 
 
 34-8 
 
 15-7 
 
 30-3 
 
 14-3 
 
 32-4 
 
 15-3 
 
 34-5 
 
 21-6 
 
 29-9 
 
 28-9 
 
 29-9 
 
 31-0 
 
 28-2 
 
 26-4 
 
 25-8 
 
 20-2 
 
 21-2 
 
 16. The numbers in the fourth and seventh columns of the 
 foregoing Table are graphically represented in the annexed 
 diagram (Plate II., fig. 1), which accordingly exhibits the law 
 of the changes for the entire year, the radius- vector of the curve 
 measuring the intensity of the current, and the angle which it 
 makes with the meridian, its azimuth. The corresponding hours 
 are indicated on the perimeter of the curve, the afternoon hours 
 being distinguished by brackets. It will be seen that in the early 
 hours of the morning, namely, from 1 A. M. to 6 A. M., inclusive, 
 the direction of the current changes little ; its mean azimuth for 
 that period is N. 21 W. At 7 A. M. the current begins to move 
 eastward, and its direction is due north at about 7 h 15 m . At 
 10 h 25 m A.M., the azimuth of the resultant current is 90, or its 
 direction is to the cast; at 3 h 15 m P.M., it becomes south; and at
 
 VARIATIONS OF THE MAGNETIC NEEDLE. 287 
 
 7 h 35 m P. M., it is west. Finally, after midnight it reaches its 
 stationary position to the west of north. 
 
 The order of the changes is similar in summer and in winter. 
 The principal differences lie in the times of reaching the azimuths 
 and 270, the direction of the current being in the former 
 azimuth about 1^ hours earlier in summer than in winter, and in 
 the latter about two hours later. The time of the afternoon meri- 
 dian passage is nearly the same at the two seasons. 
 
 The intensity of the current is greatest in the south and east. 
 The maximum intensity occurs at 1 P.M., the azimuth of the current 
 being then S. 35 E. There is a secondary maximum about 7 P.M., 
 preceded by p, secondary minimum about 5 P.M. 
 
 A curious inversion, or fold of the curve, takes place during the 
 night, between 10 P.M. and 6 A.M. The nocturnal minimum occurs 
 between 1 A.M. and 2 A.M. ; and the direction of the current is then 
 nearly opposite to that of the maximum at 1 p. M. 
 
 17. In the foregoing deductions, it is to be borne in mind, in 
 conformity with the remarks of Art. 13, that the current referred 
 to is not that actually subjacent to the place of observation, but the 
 resultant, for that place, of all the currents occupying a consider- 
 able portion of the earth's surface. The reasoning, in fact, relates 
 to the magnetic effects of the currents, rather than to the currents 
 themselves, and the immediate subject of calculation is the intensity 
 of the magnetic disturbing force, and the normal to its direction. 
 
 It is further to be remembered, that the conclusions are affected 
 by the uncertainty to which we have before adverted (Art. 11), re- 
 specting the zero, or origin, from which the magnetic deflections 
 are to be measured. It is probable, however, that this uncer- 
 tainty does not materially affect the results, except at those hours 
 at which the magnetic variations are small, and when, of course, 
 any given change in the amount of the deflections bears a much 
 larger proportion to the whole. 
 
 18. Although the laws of the diurnal changes of the magnetic 
 elements at different points of the globe have much in common, 
 they present nevertheless marked differences. Corresponding dif- 
 ferences must, therefore, be expected in the diurnal changes of the 
 earth-currents at different places ; and, consequently, the general 
 laws to which they are subject can only be known by a comparison 
 of the results at many places widely distributed over the globe. I 
 have accordingly thought that it would reward the labour to make
 
 288 ON EAETH CURRENTS, AND THE DIURNAL 
 
 a calculation, similar to the foregoing, for places at which hourly, 
 or two-hourly, observations of the two magnetic elements have 
 been made for any considerable period. The results of these- 
 calculations are given in the following Tables. 
 
 Table YI. contains the names of the places, together with their 
 geographical co-ordinates, and magnetic elements, the positive sign 
 denoting north latitude, east longitude, and easterly declination. 
 The years in the sixth column of the Table are those of the hourly 
 observations which have been employed in the calculation. The 
 absolute values of the magnetic declination and intensity, in the 
 fourth and fifth columns, correspond to the mean time of the period. 
 The observations were taken, in all cases, at the full hours of 
 Gottingen mean time ; but the corresponding local time is indicated 
 in the last column of the Table, the numbers being the minutes to 
 be added to, or subtracted from, the Tabular hours. 
 
 Tables VII. and VIII. contain the calculated values of the 
 azimuth and intensity of the current, at the several hours of obser- 
 vation, for each of the foregoing stations.* 
 
 * The diurnal changes of declination and horizontal intensity, employed in the cal- 
 culation, are contained in the following works : 
 
 1. " Magnetical and Meteorological Observations made at the Royal Observatory, 
 Greenwich (1844-47)." 
 
 2. " General Results of the Makerstoun Observations." Edin. Trans., vol. ix. 
 
 3. "Resultate des Magnetischen Observatoriums in 'M.vnchen."Abhandh<ycH 
 der K. Akademie der Wissenschaften, Miinchen, band v. 
 
 4. "Resultate aus den Magnetischen Beobachtungen zu ~Pro.s"Denkschriften 
 der Eaiserlichen Akademie, Wien, band viii. 
 
 5. " Annales de 1'Observatoire Physique Centrale de Russie (1850-55)." 
 
 6. " Observations made at the Magnetical and Meteorological Observatories at 
 Toronto, Hobarton, St. Helena, and the Cape of Good Hope." 
 
 7. " Magnetic and Meteorological Observations made at the Girard College, Phi- 
 ladelphia."
 
 VARIATIONS OF THE MAGNETIC NEEDLE. 289 
 
 1 
 
 l2^2?3S5 2 
 
 CO O O CM * 
 
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 ^^<Tt<^>O3>O3 
 
 QOoooooooooooooD 
 
 tr- ~ t- t O 
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 OSOOi-IOOOOSkOO 
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 eo o oo -" 
 
 I 
 
 o 
 
 ooi-ii-HTfii-ieooo-* 
 1 II 1 1 + -t- 1 
 
 eo co i- t- 
 
 CM >O CM 
 
 ^ - s g 
 
 1 + 1 1 
 
 Longitude. 
 
 ^.(Mt-HT^OOCOOS 
 O >-H rH CO <O 00 >-< 
 
 1 + + + + + + 
 
 1 1 + 1 + 
 
 o 
 
 ^kOGOOOiCOCO^H 
 
 koio-^io^oo^'O 
 
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 1 I 1 '1 1 1 1 1 
 
 iS ,'si H . .. IB PI . o . ; - * 
 
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 290 ON EAETH-CUERENTS, AND THE DIUENAL 
 
 
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 i-ii-ii-<^<MC<ic^< 
 
 OO'-<CO-<t< 
 
 C<icococo 
 
 O5C5<N'-ICOCOC<Ii-lr-li-l 
 TH !M Tt< >0 >0 1-1 CO t- 
 
 i-< rt< CO CD r- Ci (M -O 1 GC 
 
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 COOOlMTt<OCOCOCDkOC5 
 
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 TH rlr-l ,-KN
 
 VARIATIONS OF THE MAGNETIC NEEDLE. 
 
 291 
 
 >0 00 W >0 C5 fO CO CM 
 
 ^-t ip CO ^ 
 
 n m oi o 
 
 > i o o ca OD >o H c i- (?i <N > cs c H < o s T- 
 
 CM <M <M r-l r-l .-< ,-1 SO -^ CO >0 CO CM .-H .-H CM CM <M CO CM CM 
 
 
 -^ -W O 'OS -O 
 
 ificJb-t'Ooo 
 
 -CP -CO -^ "CM -C^
 
 292 
 
 ON EAKTH-CURRENTS, AND THE DIUKNAL 
 
 19. From a review of the preceding, we are enabled to see what 
 are the laws of the earth-currents common to all, or to the greater 
 number of the places of observation ; and to ascertain in what 
 manner, and to what extent, these laws are departed from in par- 
 ticular instances. And from a consideration of the physical cir- 
 cumstances of the localities in which these deviations occur, we 
 may, in some cases at least, be enabled to trace them to their 
 probable origin. 
 
 I. In the first place, then, it will be seen that at most of the 
 stations in the northern hemisphere the direction of the current 
 changes, throughout the day, according to the same general law. 
 This will be evident from the annexed Table, which contains the 
 hours at which the direction of the current passes through the car- 
 dinal points at the undermentioned stations. 
 
 TABLE IX. 
 
 Direction of the Currents. 
 
 Station. 
 
 X. 
 
 E. 
 
 S. 
 
 w. 
 
 Greenwich, . 
 
 
 
 7 h O m AJT. 
 
 10 h 30 m A.M. 
 
 3 h O m p.M. 
 
 7 h 25 m p.M. 
 
 Dublin, . . 
 
 
 
 7 15 
 
 
 10 25 
 
 
 3 15 
 
 7 35 
 
 
 Petersburg, 
 
 
 
 3 20 
 
 
 10 30 
 
 
 2 30 
 
 7 
 
 
 Catherinburg, 
 Bamaoul, . 
 
 
 
 3 20 
 2 50 
 
 
 10 50 
 10 35 
 
 
 2 
 1 25 
 
 7 
 
 6 45 
 
 
 Nertchinsk, 
 
 
 
 7 5 
 
 
 10 45 
 
 
 3 30 
 
 7 15 
 
 
 Toronto, . . 
 
 
 
 7 25 
 
 
 10 30 
 
 
 1 50 ,, 
 
 7 20 
 
 
 From this Table we learn that the times of passage of the cur- 
 rent through the east, south, and west points, vary within narrow 
 limits. The means are : 
 
 Mean time of easterly current, . . . 10 h 36 m A.M. 
 southerly current, . . 2 30 P.M. 
 
 westerly current, . . . 7 10 p. M. 
 
 The mean time of the south meridian passage is earliest at Bar- 
 naoul, and latest at Nertchinsk. The times of the north meridian 
 passage differ much more widely, the mean epoch being 3 u 10 m A. M. 
 for the east of Europe, and for the west of Asia, and 7 h 10 m A. M. 
 for the west of Europe, the east of Asia, and America.
 
 VARIATIONS OF THE MAGNETIC NEEDLE. 
 
 293 
 
 II. In the southern hemisphere, so far, at least, as may be 
 inferred from the phenomena at Hobarton, the rotation of the 
 currents is in the opposite direction to that in the northern. This 
 will be best seen by a comparison of the annexed diagrams (Figs. 
 1 and 2) , which represent the directions of the currents at the several 
 hours at Toronto, and at Hobarton, places which have equal lati- 
 tudes north and south. 
 
 It appears, therefore, that the point to which the earth-current 
 is directed in all cases follows the sun, although at unequal intervals 
 at the different periods of the day. 
 
 III. The hour at which the force of the current is greatest, in 
 the northern hemisphere, ranges between noon and 2 p. M., being 
 earliest in the British Islands, and latest in Western Siberia. Its 
 change with longitude will be understood from the following : 
 
 Western Europe, hour of maximum = 12 h 30 m r. M. 
 
 Central Europe, 
 Eastern Europe, 
 Western Siberia, 
 Central Siberia, 
 Eastern Siberia, 
 Canada, 
 
 
 35 
 
 
 
 55 
 40 
 15 
 
 The men n tim<' of the maximum is l h 25 m r. M. 
 
 IV. The minimum, of current intensity during the night takes 
 } 'lace at an interval of about twelve hours from the epoch of the 
 maximum; and the directions of the yn-nli f an-l /< tui currents are, 
 in nearly all cases, exactly
 
 294 ON EARTH-CURRENTS. 
 
 20. The foregoing are the general features of the diurnal varia- 
 tion of the earth-currents, as inferred from the changes of direction 
 and intensity of the horizontal magnetic force. But while the 
 phenomena have much in common, there is at the same time great 
 diversity in the details. This will be evident upon inspection of 
 the diagrams of Plate II., which represent the diurnal changes 
 of the currents at the different stations. The most remarkable 
 peculiarities are those presented at Munich and Prague in Europe, 
 at Catherinburg in Siberia, at Philadelphia in the United States, 
 and at St. Helena and the Cape of Good Hope in the southern 
 hemisphere.* 
 
 21. The great diversity which, in the midst of order, we have 
 thus seen to prevail in the diurnal changes of the earth-currents,, 
 cannot be wondered at, when we consider the endless variety which 
 exists in the distribution of land and water on the earth's surface, 
 as well as in the configuration of the land itself, and in the 
 materials of which it is composed; for all these circumstances 
 affect, in a material degree, the conductibility of the superficial 
 strata. In some of the instances above referred to, we have found 
 a probable connexion between these physical circumstances and 
 the observed facts. We are thus encouraged to hope, that the 
 complex phenomena of the diurnal change may at some future 
 time be completely unravelled, and the peculiar features which it 
 presents at each place traced to their causes. Meanwhile, it would 
 be of great importance to determine more precisely the influence of 
 lines of coast, of mountain chains, and of other geographical and 
 physical conditions, by short series of observations of the diurnal 
 changes of the two magnetic elements at well-selected stations. 
 Such observations would add little to the labour or expense of our 
 numerous exploring expeditions, while they would further in an 
 important degree the knowledge of Terrestrial Magnetism. 
 
 * The remarks in the original Paper upon these diversities, and upon their prohable 
 causes, have been here omitted.
 
 by 
 
 U.M. 3 5 7 9 II 
 
 7k .' K.IU.ttL *OOTuy. S- <
 
 EARTH CURRENTS.
 
 XIII. ON EARTH-CURRENTS IN CONNEXION WITH MAG- 
 NETIC DISTUBBANCES. 
 
 Proceedings of the Royal Irish Academy, 1862. 
 
 IN a Paper recently communicated to the Academy, the author 
 showed that the regular diurnal changes of the horizontal com- 
 ponent of the earth's magnetic force were probably due to electric 
 currents traversing the earth's crust, these currents operating as 
 disturbing forces, which cause the magnets to deviate from their 
 mean positions according to known laws. This relation being 
 established, the diurnal laws of the earth-currents may be inferred 
 from their effects. It was thus concluded that the azimuth and 
 the intensity of the currents varied throughout the day, according 
 to fixed laws depending upon the hour-angle of the sun. At 
 different parts of the globe these laws were found to exhibit certain 
 well-marked features in common; while their differences were 
 probably accounted for by the geographical and physical characters 
 of the region in which they occur. The author now proceeds 
 to extend the same inquiry to the currents which produce the 
 magnetic disturbances. 
 
 It has been shown, by the labours of Kreil, Sabine, and others, 
 that the disturbances of the magnetic elements are subject to 
 periodical laws, depending upon the hour, which are constant for 
 a given place, and for a given season of the year. The sums of 
 the changes produced by these disturbances, at each hour of 
 observation, have been calculated by General Sabine for three of 
 the British Colonial Observatories. The corresponding quantities 
 have been deduced by Dr. Lamont, for Munich ; by Mr. Broun, 
 for Makerstoun, in Scotland ; and by the author, for Dublin. We 
 possess, in addition to the foregoing, similar results nt Lako 
 Athabasca, in British North America, deduced by Colonel Lrfroy
 
 296 ON EARTH-CUERENTS IN CONNEXION WITH 
 
 from observations made by himself, which, although derived 
 from a shorter series of observations, are of the highest scientific 
 value. For these places, therefore, it only remains to combine 
 the results of the declination and horizontal intensity, by the 
 method which has been already applied to the regular changes 
 of the same elements. 
 
 The result of this calculation, applied to the Dublin observa- 
 tions, shows that the direction of the disturbance-current at that 
 place observes a mean law, not very dissimilar to that which 
 governs the regular diurnal current. Its azimuth rotates, during 
 the day, in the same direction as the sun, its direction pointing 
 almost exactly to the luminary. The direction is east about 5 A. M. ; 
 south, about noon ; and west, at 6 p. M. The current is easterly 
 from 9 p. M. to 9 A. M., inclusive, and westerly during the remainder 
 of the 24 hours. The mean azimuth of the easterly current, 
 measured from the north eastward, is 40 15' ; that of the westerly 
 is 230 18'. If the mean directions of the easterly and westerly 
 currents be assumed to be in the same right line, the mean 
 azimuths will be N. 45 E., and S. 45 W. This result agrees, 
 in a very remarkable manner, with those obtained by Mr. Barlow 
 and Mr. Walker from the direct measures of the intensity of the 
 earth-currents, as observed on days of disturbance in several of 
 the telegraphic lines of England; and the agreement must be 
 regarded as an additional proof of the dependence of the magnetic 
 changes upon earth-currents. 
 
 The phenomena at Makerstoun are very similar to those at 
 Dublin ; and the epochs of the passage of the current through the 
 cardinal points are nearly the same. 
 
 At Toronto, in Canada, the current is wholly easterly, the mean 
 azimuth being 81 25'. On the other hand, at Athabasca, the 
 current is easterly from 12 p. M. to 6 A. M., inclusive, and westerly 
 during the remainder of the 24 hours. The sums of the easterly 
 and westerly changes for the entire day balance one another, the 
 easterly currents being as much greater in magnitude as they are 
 less in duration. Their mean azimuths are 110 18' and 290 56'. 
 
 At St. Helena the direction of the current is easterly throughout 
 the day, the mean azimuth being 70 53'. The direction is singu- 
 larly constant, the greatest deviation from the mean being only 
 10. The phenomena at the Cape of Good Hope closely resemble 
 those at St. Helena. The direction of the current is easterly at
 
 MAGNETIC DISTURBANCES. 
 
 297 
 
 every hour, excepting 5 A.M. when there is a slight westerly 
 movement. The mean azimuth is 77 54'. 
 
 It thus appears that at some places as in the British Islands 
 the mean direction of the disturbance current rotates through the 
 entire compass in the course of the day; while at others as 
 Munich, Toronto, St. Helena, and the Cape of Good Hope it is 
 easterly throughout the day. While, therefore, there is a periodicity 
 in the easterly and westerly currents depending on the hour, we 
 are obliged to infer that there is, at the same time, some cause 
 constantly operating which tends to produce an easterly current. 
 
 The mean azimuth of this current appears to be connected with 
 the magnetic meridian of the place, to which it is nearly perpen- 
 dicular. This will appear from the following Table of the mean 
 azimuths of the disturbance-currents at the northern stations, 
 measured from the astronomical and from the magnetical meridians, 
 respectively : 
 
 Places. 
 
 Az. (Astron.) 
 
 Az. (Magn.) 
 
 Dublin, .... 
 
 45 
 
 72 
 
 Makerstoun, . . . 
 
 51 
 
 76 
 
 Munich, .... 
 
 52-5 
 
 69 
 
 Toronto, .... 
 
 81-5 
 
 83 
 
 Athabasca, . . . 
 
 110 
 
 81 
 
 The mean azimuth (magnetic) for the five stations is E. 14 N. 
 
 The mean azimuth at the two stations in the southern hemi- 
 sphere is E. 11 S., deviating nearly as much to the south, as that 
 of the northern stations deviates in the opposite direction. It 
 thus appears that while the principal current is eastward in both 
 hemispheres, there is also a meridional current tending northward 
 in the northern hemisphere, and southward in the southern. Its 
 intensity is between one-fourth and one-fifth of that of the other 
 component. 
 
 These results are wholly at variance with the hypothesis imagined 
 by H. de la Rive in explanation of the phenomena of magnetic 
 disturbances, according to which the disturbance-current flows 
 from north to south only.* 
 
 * The discrepancy of M. de la Rive's hypothesis with the phenomena of the earth- 
 currents, as observed in the British Islands, has been already pointed out by .Mr. 
 Walker. It is even more marked at other parts of the globo.
 
 298 ON EARTH-CURRENTS. 
 
 The diurnal changes of the intensity of the disturbance-currents 
 present features equally marked. In order to perceive them 
 clearly, it may be convenient to examine separately the meridional 
 currents, and those at right angles to the magnetic meridian. 
 
 The meridional currents are developed chiefly at the European 
 stations, and at Toronto, in Canada: at Athabasca, and at the 
 southern stations, they are comparatively small. The northerly 
 maximum occurs at Toronto, at 9 p. M., at Munich at 10 p. M., and 
 at Dublin at 11 P. M. Its epoch at Makerstoun is between 9 p. M. 
 and 11 P. M. The southerly maximum occurs at 8 A. M., very nearly, 
 at the four stations. Thus the epochs are nearly at the same hours 
 of local time, notwithstanding the differences of longitude. 
 
 A similar result appears from an examination of the currents 
 at right angles to the magnetic meridian. Thus, in the northern 
 hemisphere, the easterly maximum occurs between 2 A. M. and 
 4 A. M., and the westerly maximum (or easterly minimum) between 
 3 P. M. and 5 p. M. The two epochs are precisely the same at 
 Makerstoun and at Toronto, places which differ more than five 
 hours in longitude. 
 
 The corresponding epochs for the two stations in the southern 
 hemisphere in like manner agree with one another. The easterly 
 maximum occurs between 6 p. M. and 7 P. M. at St. Helena and at 
 the Cape of Good Hope, and the easterly minimum between 5 A. M. 
 and 6 A. M. It is deserving of remark that these epochs do not 
 differ considerably from those of the opposite movements in the 
 northern hemisphere, the easterly extreme in the one corresponding 
 nearly with the westerly extreme in the other. A similar opposition 
 in the phenomena of the regular diurnal change in the two hemi- 
 spheres was pointed out by the author on a former occasion, and 
 there seems good reason to suppose that the two facts are physically 
 related. 
 
 It appears, then, that the principal epochs of the disturbance- 
 currents are connected with the sun's hour-angle, and are inde- 
 pendent of the longitude of the place at which they occur. 
 
 The foregoing relations appear to be of a very general nature, 
 and such as to afford a distinct basis for physical theory.
 
 XIV. ON TfiE PROBABLE CAUSES OF THE EARTH- 
 CURRENTS. 
 
 Proceedings of the Royal Irish Academy, 1862. 
 
 IN a former communication to the Academy, I endeavoured to 
 prove that the diurnal changes of the horizontal needle were the 
 results of electric currents traversing the earth's crust. The ex- 
 istence and continuous flow of such currents had been established, 
 as I believe, by the observations of Mr. Barlow made on two of 
 the telegraphic lines of England ; and it only remained to show 
 that their laws corresponded with those of the magnetic changes. 
 
 In that communication I refrained from offering any conjec- 
 ture as to the origin of the currents themselves. Every speculation 
 of this kind must remain a pure hypothesis, until it can be con- 
 fronted and compared with facts; and the magnetic phenomena 
 presented at different points of the earth's surf ace are so diversified, 
 that a wide collection of the facts is necessary in order to form the 
 basis of any sound physical theory. For these reasons, I have 
 deemed it the more proper course to ascertain the laics of the 
 diurnal changes of the earth-currents at many places, so far as they 
 may be inferred from the magnetic phenomena, before proceeding 
 to the consideration of their causes. 
 
 It has been shown, in the Paper referred to, that the earth- 
 currents, as inferred from the changes in the two horizontal com- 
 ponents of the magnetic force, observe certain general laws, which 
 are common to all the stations at which these changes have been 
 observed ; while, on the other hand, their departures from a com- 
 mon type are various and considerable. We thus learn that tin- 
 phenomena are produced by a common cause, the effects of which 
 are greatly modified by the physical peculiarities of the parts of the
 
 300 ON THE PKOBABLE CAUSES 
 
 earth where they are observed. The following are the principal 
 features of the phenomena common to all, or to most of the places 
 of observation. 
 
 I. The point to which the resultant earth-current is directed 
 follows the sun, although not at a uniform rate, throughout the day. 
 In the northern hemisphere its direction is eastward, on the average, 
 at 10 h 30 m A. M. ; southward, at 2 h 30 m P. M. ; and westward, at 
 7 P.M. 
 
 II. The intensity of the current is greatest between noon and 
 2 P.M., the mean time of the maximum in the northern hemisphere 
 being about l h 30 m p. M. The intensity of the current is least at an 
 interval of about twelve hours from the epoch of the maximum ; 
 and the direction of the current of least intensity is, in nearly all 
 cases, opposite to that of the greatest. 
 
 III. There are two subordinate maxima, separated from the 
 principal maximum by intervening minima. The morning maxi- 
 mum occurs, on the average, at 8 h 30 ra A. M. It may be traced in 
 the diurnal curves of the American and Siberian stations, and in 
 those of the Cape of Good Hope and Hobarton. The current is 
 then northerly in the northern hemisphere, and southerly in the 
 southern. The evening maximum occurs at about 10 P.M., and is 
 observed at almost all the stations. 
 
 The foregoing facts leave no doubt that the sun is the primary 
 cause of the currents ; and the only question is as to the mode of 
 its agency. Upon this point I concur with Dr. Lament in believ- 
 ing the electrical currents (or waves) on the earth's surface to be 
 due to disturbances of equilibrium of statical electricity; but I 
 regard these derangements of equilibrium to be simply the effects 
 of solar heat, and not (as Dr. Lament believes) the results of an 
 electrical force emanating directly from the sun. 
 
 It is well known that the earth and the atmosphere are, in 
 ordinary circumstances, in opposite electrical states the electricity 
 of the earth being negative, and that of the atmosphere positive. 
 It is also known that the electricity of the air increases rapidly 
 with the height, a few feet and in some cases even a few inches 
 being sufficient to manifest a difference of electrical tension. The 
 rate of this increase is very different at different periods of the 
 day, the difference appearing to be due to the greater or less 
 conductibility of the lower strata of the atmosphere, causing a 
 greater or or less interchange of the opposite electricities.
 
 OF THE EARTH-CURRENTS. 301 
 
 Now, we have in this machinery, as it appears to me, means 
 fully adequate to the production of the observed effects. If it be 
 assumed that the sun produces these changes by its calorific action, 
 the effects at any given place will depend upon the relative tempe- 
 ratures of the neighbouring portions of the earth's surface. The 
 earth being, in its normal state, negatively electrical, the negative 
 electricity will be greatest or the positive electricity least, at 
 the parts most heated ; and there will, consequently, be a flow of 
 electricity to those parts from the place of observation. Thus the 
 varying azimuth of the current, which is directed towards the most 
 heated parts of the earth's surface, is explained. The maximum 
 intensity of the current, at l h 30 m P.M. is also accounted for, that 
 being the period of the day when the solar calorific action is 
 most intense. It should be noted, however, that the magnitude 
 of the effect will depend, not on the absolute temperature, but on 
 its relative increase. It is, accordingly, greatest at those parts of 
 the earth at which the increment of temperature corresponding to 
 a given distance is greatest. 
 
 The secondary maxima are probably due to the recombination 
 of the atmospheric and terrestrial electricities, through the medium 
 of vapour in the lower regions of the atmosphere. The effects of 
 this recombination in producing horizontal currents in the earth's 
 crust will, of course, be differential only, and will depend on the 
 excess of the positive electricity thus transported at the places 
 on the same meridian which are nearer to the equator. In confir- 
 mation of this view it may be observed, that the epochs correspond 
 with those of the maxima of atmospheric electricity, as deduced 
 by Quetelet from the observations made under his direction at 
 Brussels, the morning maximum of atmospheric electricity in 
 summer occurring at 8 A.M., and the evening maximum at 9 P.M. 
 
 The phenomena hitherto described are such as would take place 
 if all the parts of the earth's crust were similarly constituted, and 
 therefore similarly acted on by the solar rays. In order to be able 
 to explain the diversity which exists in the magnetic phenomena 
 at different places, we must know something more of the nature 
 of the solar action, and of the mode in which electricity is developed 
 by it. 
 
 The speculations respecting the origin of atmospheric and ter- 
 restrial electricity are various. Thus De Saussure believed that 
 this electricity was developed by evaporation, the vapour taking
 
 302 ON THE PROBABLE CAUSES 
 
 the positive electricity, and the water the negative ; and this hypo- 
 thesis, with some limitations, has been very generally admitted by 
 physicists. On the other hand, M. de la E-ive is of opinion that 
 the origin of this electricity is to be sought in the chemical actions 
 which he supposes to be going on in the interior of the solidified 
 crust of the earth ; and he thinks that evaporation acts merely by 
 transporting one of the separated electricities, and carrying it into 
 the higher regions of the atmosphere. But whatever be the correct 
 view as to the force which develops the electricity, it seems to be 
 granted that the separation of the two electricities (in the earth 
 and the atmosphere) is the consequence of evaporation, the vapour 
 carrying with it the positive electricity, and the vaporizing body 
 retaining the negative. It follows from this, that the effect pro- 
 duced will vary greatly with the distribution of land and water, 
 and will be greatest, cceteris paribus, where they come into juxta- 
 position along the coasts .of the great continents, especially where 
 the coast-lines are in, or near, the meridian. The evaporation 
 from the surface of the sea being much greater than from the 
 land, the electricity will be most deficient at the former. Hence 
 there will be a flow of electricity from land to sea, which will 
 combine with, and often mask, that due to the sun's position alone. 
 
 Now this seems to be what happens. The most marked instance 
 of the phenomenon which we possess is that afforded by the diurnal 
 changes of the currents at St. Helena. There the currents (as I 
 have already shown) flow /row the coast of Africa during the hottest 
 portion of the day, and towards it during the night. The influence 
 of the form of the coast seems to be shown in the diurnal curve of 
 the Cape of Good Hope, by the existence of three maxima) of which 
 the principal is directed from the land, and the two subordinate 
 along the lines of coast. At Hobarton, in Van Diemen's Land, 
 the same influence appears in the extension of the southern lobe 
 of the curve, which is there nearly equal to the northern. 
 
 I have since calculated the direction and intensity of the cur- 
 rents at the Indian stations, and I find that the curves follow 
 nearly the type of the St. Helena curve. Thus, at Singapore, for 
 which place we possess the results of observation during the three 
 years 1843-1845, the maximum of current intensity takes place 
 between 10 A.M. and 11 A.M., and its direction is S. 80 W. At 
 Madras, so far as may be inferred from the observations of a 
 single month, the maximum takes place at noon ; and the direction
 
 OP THE EARTH-CURRENTS. 303 
 
 of the current is then nearly the same as at Singapore. At 
 Simla, in the Himalaya, the maximum occurs also at noon ; 
 but the direction of the current of greatest intensity is more 
 southerly, its mean yearly direction being S. 47 W. This is 
 precisely what should happen according to the hypothesis, this 
 being nearly the direction of the line drawn to the nearest point of 
 the coast.* 
 
 The variation in the epoch of the maximum intensity of the 
 current, at different places, is also in accordance with the same 
 principles ; that epoch being earliest in islands, or places nearly en- 
 compassed by sea, and latest in the interior of the great continents. 
 Thus it occurs at noon at St. Helena, and in the southern parts of 
 the peninsulas of Hindostan and the Malaya ; while it takes place 
 at 2 P. M. at Catherinburg and Barnaoul, in the interior of Siberia. 
 This accords with the laws of the sun's calorific action. 
 
 It will be seen, upon an inspection of the diurnal curves 
 of the earth-currents,t that at most of the northern stations, as 
 well as at Hobarton in the southern, the easterly currents are 
 greater than the westerly. I believe this effect to be due to 
 the disturbance-currents, which (as I have already shown) have an 
 easterly tendency. This preponderance of the easterly currents, 
 however, is found to be greater at places such as Greenwich, 
 Dublin, Makerstoun, and Toronto which are near an eastern 
 coast, than at those places such as Petersburg, Catherinburg, 
 and Barnaoul which are in the interior of the continent. The 
 results, therefore, so far confirm the supposition above made. 
 
 There are, unfortunately, very few places situated near the 
 western shore of a great continent, at which continued observations 
 of the two magnetic elements have been made. At Sitka, on the 
 western coast of North America, the results confirm the view above 
 stated, the westerly currents being there greater than the easterly. 
 
 There are probably other circumstances in the configuration 
 
 * These additional results oblige me to abandon the conclusion formerly derived 
 from a more limited induction, that the direction of the current of greatest intensity 
 is connected with the magnetic meridian of the place. From the facts which \v,- 
 now possess, it would appear that the currents affect a meridional direction in the 
 higher latitudes, while they are nearly parallel to the equator within the tropics. Tlii* 
 will be seen in a striking manner by comparing the directions of the maximum current 
 in India, above given, with those of the Russian stations in the northern part of the 
 Asiatic Continent. 
 
 f Transactions of the Royal Irish Acafcmy, Vol. XXIV.
 
 304 ON THE PROBABLE CAUSES 
 
 and structure of the earth's surface which influence the direction 
 and magnitude of the currents ; but I incline to think that the 
 principal one is that ahove stated, viz. the distribution of land and 
 water in the vicinity of the place of observation. It may be, also, 
 that this cause is sufficient to account for some of the peculiarities 
 in the form of the diurnal curve noticed in my former communica- 
 tion, and there referred to other causes. Thus, it is not improbable 
 that the persistent direction of the current at Munich, there referred 
 to the influence of a mountain range, may be, in fact, the result of 
 the proximity of the Adriatic Gulf, which lies nearly in the direc- 
 tion of the persistent current. 
 
 In the preceding remarks I have referred only to the regular 
 diurnal changes. I believe that the irregular are produced by the 
 same forces, but operating in a somewhat different manner. The 
 regular currents are produced, as I conceive, chiefly by the separa- 
 tion of the two electricities by evaporation, under the action of the 
 sun ; while the disturbance-currents are caused by their rapid re- 
 combination, through the medium of moisture, in the lower strata 
 of the atmosphere.* In connexion with this view, I may refer to 
 the fact which has been established by an examination of the mean 
 effects of the magnetic disturbances,! namely, that the epochs of the 
 maxima of the disturbance-currents depend, in their mean values, 
 upon the sun's hour-angle, and are independent of the longitude 
 of the place. This result is in accordance with the hypothesis 
 which ascribes these currents to changes in the sun's calorific 
 agency, and to the meteorological effects which these engender. 
 
 In the limits within which it is necessary to confine this 
 abstract, I have been able only to refer to some of the leading 
 facts in confirmation of the hypothesis which I have ventured to 
 propose ; and I am obliged to omit altogether all reference to the 
 objections which will probably be raised against it. There is, how- 
 ever, one fact which appears at first sight to offer a formidable 
 difficulty to its reception, and which it seems necessary to notice 
 here. The regular magnetic changes are greater in summer than 
 
 * This hypothesis as to the cause of magnetic disturbances is due to M. de la Rive ; 
 but his views ^ respecting the laws of the resulting currents are, as I have elsewhere 
 shown, mconsistent with the phenomena. The regular diurnal changes of terrestrial 
 magnetism are ascribed by M. de la Rive to a direct electrical action emanating from 
 the sun. 
 
 t Prceeedings of the Royal Irish Academy, April 28, 1862.
 
 OF THE EARTH-CURRENTS. 305 
 
 in winter ; while with the electrical tension, and its changes, it is 
 the reverse. This objection, however, disappears when it is viewed 
 more closely. The physical quantity measured by our electro- 
 meters is not the absolute electric tension, but its variation with the 
 It eight ; while the electric changes which engender terrestrial cur- 
 rents are the variations as depending on horizontal distance. It is 
 easily conceivably that these should not correspond. In fact, it 
 is natural to suppose that in summer the zero-plane, which sepa- 
 rates the two electricities, should rise considerably ; and thus that 
 the variations for a given increase of altitude (which probably 
 diminish with the distance from that plane) should lessen, although 
 the absolute tensions, as well as the changes in horizontal distance, 
 may be greater. 
 
 It would be of importance, in reference to this inquiry, to insti- 
 tute electrical observations of a totally different kind from any 
 which we now possess, and to measure the differences of tension 
 as depending on horizontal distance. There seems to be no diffi- 
 culty in the way of such observations, at least none greater than 
 those which present themselves in the ordinary observations of 
 atmospheric electricity ; and the results would probably do more 
 to clear up the physical aspect of these complex and interwoven 
 phenomena than any other observational means.
 
 XV. ON THE DIEECT MAGNETIC INFLUENCE OF A DIS- 
 TANT LUMINARY UPON THE DIURNAL VARIATIONS 
 OF THE MAGNETIC FORCE AT THE EARTH'S SUR- 
 FACE. 
 
 Philosophical Magazine, March, 1858. 
 
 IT has been usual to ascribe the ordinary diurnal variations of the 
 terrestrial magnetic force to solar heat, whether operating directly 
 upon the magnetism of the earth, or generating thermo-electric 
 currents in its crust. The credit of these hypotheses has been 
 somewhat weakened by the discovery of a variation which is cer- 
 tainly independent of any such cause, namely, the lunar varia- 
 tion of the magnetic elements ; while at the same time new laws 
 of the solar diurnal change have been established, which are 
 deemed to be incompatible with the supposition of a thermic agency. 
 There has been, accordingly, a tendency of late to recur to the 
 hypothesis, that the sun and moon are themselves endued with 
 magnetism, whether inherent or induced ; and it is therefore of 
 some importance to determine the effects which such bodies would 
 produce at the earth's surface, and to compare them with those 
 actually observed. 
 
 I have endeavoured, in what follows, to solve this question, on 
 the assumption that the supposed magnetism of these luminaries 
 is inherent. The result will show the insufficiency of the hypo- 
 thesis to explain the phenomena ; and will therefore bring us one 
 step nearer to their explanation, by the removal of 'one of their 
 
 Let x, y, z be the coordinates of any point of a fixed magnet, 
 referred to three rectangular axes passing through its middle 
 point ; cr, b, c those of a distant magnetic element, m ; and e their
 
 ON THE MAGNETIC INFLUENCE OF THE SUN OR MOON. 307 
 
 mutual distance. Then, if p denote the quantity of free magnet- 
 ism contained in the element ds of the magnet at the point (z,y, r), 
 the force exerted by n on m is 
 
 and its resolved portions in the directions of the three axes of coor- 
 dinates are 
 
 m (a - x) fids m (b - y) pds m (c - s) fads 
 -# ' # 
 
 Let the magnitudes of the lines connecting the points (a, b, c) 
 and (a-, y, c) with the origin be denoted by u and s, and let the 
 angle contained by their directions be o>. Then 
 
 e* = u- - 2us cos a + s 2 ; 
 
 and if s be so small in comparison with u that the squares and 
 higher powers of - may be neglected, 
 
 T 3 = M~ 3 ( 1 + COS (i) ). 
 
 V w / 
 
 Again, if a, j3, 7 denote the angles contained by the axis of the 
 magnet with the three axes of coordinates, 
 
 x - s cos a, y = s cos /3, s = s cos 7. 
 
 Substituting these values in the expressions for the components of 
 the force above given, integrating, and observing that J /ucfe = 0, 
 we have, for the components of the total force exerted by the mag- 
 net on the magnetic element, 
 
 Mmf 
 u 3 \ 
 
 Mmf n o 
 
 -3- cosw - co"s/3 
 
 in which we have put, for abridgement, M = J /i&. The angle w is 
 connected with a, |3, 7 by the relation 
 
 u cos <i> = a cos a f b cos /3 + c cos 7. 
 
 Now let the point (a, b, c) be on the earth's surface, and let us 
 x2
 
 308 ON THE DIRECT MAGNETIC INFLUENCE OF THE SUN 
 
 suppose, for simplicity, that the acting magnet is in the plane of 
 the equator. Let that plane be taken as the plane of (#, y\ and 
 the line connecting the centre of the magnet and that of the earth 
 as the axis of x. Then, if the distance of the acting magnet be 
 considerable, relatively to the earth's radius, b and c are small in 
 comparison with a, and we may neglect the small quantities of the 
 
 b z <? be 
 
 second order, ,, . Wherefore, substituting for cos w its 
 a a a' 
 
 value, the components of the acting force become 
 36 
 
 n 
 H 2 cos a + 
 
 36 3c \ 
 
 cos p + cos y J, 
 
 mf , 36 
 
 -COS/3 + - 
 
 Mmf_ 
 3 V 
 
 cos 7 + cos a J. 
 
 Now, if D denote the distance of the centre of the magnet from 
 the centre of the earth, r the earth's radius, A the latitude of the 
 point (a, b, c) on its surface, and the angle contained by the 
 meridian passing through it with that containing the acting 
 magnet, 
 
 a = D - r cos A cos B, b = r cos A sin B, c = r sin A. 
 
 Hence the maximum values of - and - are equal to - ; and if we 
 a a a 
 
 disregard the terms containing them in comparison with the rest, 
 the preceding values are reduced to 
 
 Mm Mm Mm 
 
 .5-^-cosa, - cos0, - cosy. 
 
 Now, in place of a single magnet, let there be an indefinite 
 number distributed in any manner throughout the entire magnetic 
 body ; and let us make, for abridgement, 
 
 S ( M cos a) = P, s (M cos /3) = Q, S (M cos 7) = R. 
 Then, if the radius of this body be small in comparison with its 
 distance, we may neglect the variations of D y and we shall have, 
 for the three components of the acting forces, 
 
 -^ - mQ ~ mR
 
 OR MOON AT THE EARTH'S SURFACE. 309 
 
 In order to determine the effect of these forces upon a freely 
 suspended horizontal magnet at the earth's surface, we must resolve 
 X and T in the direction of the tangent, and of the radius, of the 
 parallel of latitude. The resolved forces are, respectively, 
 
 X sin + T cos 0, X cos 6 - Y sin 0. 
 
 Again, resolving|the forces Z and X cos - T sin in the direction 
 of the tangent to the meridian, and in that of the radius of the 
 earth, we have finally the three components, viz. : 
 
 X sin + Y cos 0, directed eastward ; 
 Z cos A + (X cos - Y sin 0} sin X, directed northward; 
 - Z sin A + (X cos - Y sin 0) cos X, vertical, towards centre. 
 
 Of these, the latter has no effect upon the horizontal magnet. The 
 moment of the two former to turn it is 
 
 {X sin + Fcos 0) cos 3 - (^cos X + (X cos & - Fsin 0) sin X| sin 8, 
 
 8 denoting the magnetic declination ; or, substituting for X, F, Z 
 their values, 
 
 |UcosS(2P sin0- Q cos 0} - sin 8 (2P cos + Q sin 0)' sin A 
 
 But the moment of the earth's magnetism, opposed to this, is 
 
 JTA8 sin 1', 
 
 in which H denotes the horizontal component of the earth's mag- 
 netic force. Wherefore 
 
 A8= ,,*. , Jsin0(2PcoB8- QsinXsinS) 
 D H. sin 1 ( 
 
 -cos0(2PsinAsin8 + QcosS) + R cos A sin8 j. 
 At the equator, this is reduced to 
 
 AS - - cos 82P sin - Q cos0) + ^si 
 
 To determine the effect of the magnetic body upon the hori- 
 zontal component of the earth's magnetic force, we must resolve
 
 310 ON THE DIRECT MAGNETIC INFLUENCE OF THE SUN 
 
 the horizontal parts of the disturbing forces, viz., X sin + Fcos 0, 
 acting eastward, and Z cos X + (X cos - F sin 0) sin X, acting 
 northward, in the direction of the magnetic meridian. We have 
 thus 
 
 ZcosX + (XcosO - Fsin0)sinX 
 
 ) 
 
 =i jsin0 (2P sinS + Q siaX cosS) + cos0 (2P sin X cos 8 - Q sing) 
 
 - R cosX cosS ; 
 and at the equator, 
 
 Ajff= jp jsing(2P sin0 - Q cos0) - R cosSJ. 
 
 Lastly, if V denote the vertical component of the earth's mag- 
 netic force, we have 
 
 Fsin0)cosX 
 
 = \(2P cos0 + Q sin0) cosX + R sinX ; 
 
 a result which, as might have been anticipated, is independent 
 of the magnetic declination. At the equator 
 
 A V = jR- 3 (2P cos0 + Q sin0). 
 
 From the foregoing we learn : 
 
 1. That the effect of a distant magnetic body on each of the 
 three elements of the earth's magnetic force consists of two parts, 
 one of which is constant throughout the day, while the other varies 
 with the hour-angle of the luminary. 
 
 2. Each of these parts varies inversely as the cube of the dis- 
 tance of the magnetic body. 
 
 3. The variable part will give rise to a diurnal inequality, hav- 
 ing one maximum and one minimum in the day, and subject to the 
 condition 
 
 A 9 + A^ = 0. 
 
 The third of these laws does not hold, with respect either to the 
 solar-diurnal or to the lunar-diurnal variation. Thus, in the solar- 
 diurnal variation of the declination, the changes of position of the
 
 OR MOON AT THE EARTH'S SURFACE. .'ill 
 
 magnet throughout the night are comparatively small, and do not 
 correspond, with change of sign only (as required by the foregoing 
 law), to those which take place at the homonymous hours of the day. 
 The phenomena of the lunar-diurnal variation are even more op- 
 posed to the foregoing law, the variation having two maxima and 
 two minima of nearly equal magnitude in the twenty-four lunar 
 hours, and its values at homonymous hours having for the most part 
 the same sign. Hence the phenomena of the diurnal variation are 
 not caused by the direct magnetic action of the sun and moon. 
 
 It is true that if we proceed another step in the approximation, 
 nnd include in the values of the disturbing forces the terms con- 
 
 b c 
 
 turning the first powers of -, -, the former will produce in the re- 
 sulting values of AS, AJ7, and AF, terms containing sin 20, cos 20, 
 and giving rise therefore to a semidiurnal inequality. But the co- 
 efficient , by which these terms are multiplied, amounts in the 
 
 case of the sun to -g-gVjr on ly> while in that of the moon it is about 
 yV ; and the magnitude of the semidiurnal inequality should bear 
 to that of the diurnal the ratios designated by these small fractions. 
 The facts are altogether opposed to this result. The coefficient of 
 the solar-diurnal inequality of the declination at Dublin, in the 
 mean of the entire year, is 3'- 52, while that of the semidiurnal is 
 2'-13, nearly two-thirds of the former. In the case of the lunar- 
 diurnal variation, the semidiurnal inequality exceeds the diurnal.
 
 XVI. ON THE STORM OF THE 18m OF APRIL, 1850. 
 
 Proceedings of the Royal Irish Academy, 1850. 
 
 HAVING watched attentively the progress of the late storm, from 
 a favourable position, and collected some facts relative to it from 
 the records of the Observatory, and from other sources, I avail 
 myself of the present opportunity to lay them before the Academy. 
 The phenomena were of a nature so unusual (I may say unex- 
 ampled) in these climates, that it is desirable that some notice of 
 them, however imperfect, should be placed on record; and the 
 present summary of facts is offered, chiefly in the hope that it 
 may serve as a nucleus to a more complete one. I shall limit 
 myself, mainly, to those which have an immediate scientific bearing. 
 The morning of the 18th was fine in Dublin, with bright sun- 
 shine, light cirrous clouds being scattered loosely over the sky ; at 
 ten o'clock these became diffused, and the sky was evenly, but 
 lightly overcast. 
 
 From the tracings of the self -registering anemometer, erected 
 in Trinity College, it appears that on the 17th, and during the 
 morning of the 18th, the wind blew gently from the south-west. 
 Towards noon, on the latter day, it gradually veered to the south, 
 and continued at that point until the arrival of the storm. This 
 veering of the wind, however, appears to have been confined to 
 the lower current ; the direction of the upper current, as estimated 
 by the motion of the clouds, appeared to be nearly south-west. 
 
 The first indications of the approach of the storm were observed 
 soon after three o'clock. Massive cumuli were seen in the western 
 and south-western portions of the horizon. These became denser 
 as they approached, until they formed a mass of an ash-grey
 
 ON THE STORM OF THE 18TH OF APRIL, 1850. 313 
 
 colour, projected on a sky of a paler tint, while the rugged outliers 
 from the mass, of the peculiar form which indicates a high degree 
 of electrical tension, showed plainly that a storm was approaching. 
 About half-past three o'clock it burst forth. The flashes of light- 
 ning (generally forked) succeeded one another with rapidity, and 
 at length the roar of the thunder seemed continuous. Some persons 
 who observed the 'phenomena from a distance were able to dis- 
 tinguish the two strata of oppositely electrical clouds, and to see 
 the electrical discharges passing between them. 
 
 Hitherto the wind was light, and there was that peculiar close- 
 ness in the air which is the result of high temperature and excessive 
 humidity. Shortly before four o'clock the rain commenced; this 
 was followed almost immediately by discharges of hail, and at 
 four, P. M., the terrific tornado, which was the grand and peculiar 
 feature of this storm, reached us. 
 
 This gale, which appears to have been a true whirlwind, first 
 sprung up from the south-east, driving the hail before it impetu- 
 ously. It then suddenly, and apparently in an instant, shifted to 
 the point of the compass diametrically opposite, and blew with 
 increased violence from the north-west. The noise about this time 
 of the shifting of the wind was terrific, and arose (as is conjectured 
 respecting similar tropical phenomena) from the confused conflict 
 of hail in the air. The size of the hailstones, as well as the 
 vehemence of the gale, appeared to be greater during the second 
 phase of the storm than the first. These masses, many of which 
 were as large as a pigeon's egg, were formed of a nucleus of snow 
 or sleet, surrounded by transparent ice, and this again was suc- 
 ceeded by an opaque white layer, followed by a second coating of 
 ice. In some of them I counted five alternations. 
 
 In less than ten minutes the tornado had passed. The wind 
 returned to a gentle breeze from the south-west, the clouds dis- 
 persed, and the weather became beautiful. All the phenomena, 
 the direction of the gale perpendicular to that in which the storm- 
 cloud was advancing, and the sudden reversal of that direction, 
 seem to prove that it was a tornado, whose centre passed directly 
 over the place of observation. It is evident, on comparing the 
 direction of the wind when the whirl first reached this part of the 
 town, with that of the progressive motion of the vortex itself, that 
 its rotatory motion was retrograde, or in an opposite direction to 
 that of the hands of a watch with its face upward. It is deserving
 
 314 ON THE STORM OF THE 18TH OF APRIL, 1850. 
 
 of notice also, that in the northern hemisphere this is the invariable 
 direction of the cyclones, or great revolving storms, to which the 
 attention of meteorologists has been directed by Colonel Eeid and 
 Mr. Eedfleld. The late storm was, however, different from a 
 cyclone, both in the dimensions of the vortex and in the causes 
 from which it originated. The horizontal section of the cyclone 
 where it meets the earth is often 500 miles in diameter ; and the 
 vortex is supposed to be the effect of two crossing currents of air, 
 which generate a movement of rotation. In the tornado (to which 
 species the late storm belonged) the vortex is of much smaller 
 dimensions, and is produced by rapidly ascending currents of air, 
 caused by the heating of a limited portion of the earth's surface 
 under the action of the sun's rays. In the temperate zones, 
 accordingly, it is never produced in winter. 
 
 The evidence relating to the direction of the gale, and its 
 changes, as it passed over the College Park, is very complete and 
 satisfactory. In the park, and garden adjoining, nineteen trees 
 were rooted up and prostrated, eleven of them being trees of large 
 size. Of these ten have fallen from the south-east, or under the 
 action of the first half of the gale, and nine from the north-west. 
 Their bearings have been accurately taken ; and the general result 
 is, that the mean direction of the south-east gale, as indicated by 
 that of the trees, is S. 56 E., and that of the north-west gale 
 N. 53 W. I believe that these results are even more accurate than 
 those furnished by the anemometer ; and they prove that in this 
 locality the direction of the wind was exactly reversed, and, there- 
 fore, that the centre of the vortex passed over the College. 
 
 A remarkable circumstance connected with the direction of the 
 fallen trees is their great uniformity, the individual directions 
 seldom differing more than 10 from the mean. This is an indi- 
 rect evidence of the great violence of the gale; and it proves, 
 moreover, that the transition from the south-east to the north-west 
 wind was immediate. There is greater regularity in the direction 
 of the trees fallen from the north-west than in those which have 
 been blown down from the opposite quarter. This may have 
 arisen partly from the greater violence of the gale in the former 
 direction ; but it is partly also due to the circumstance that the 
 trees which fell from the north-west are generally larger, and in a 
 less inclosed portion of the ground. It may be mentioned also, 
 that the trees which fell from the north-west generally lie to the
 
 ON THE STORM OF THE 18TH OF APRIL, 1850. 315 
 
 southward of the others ; there are, however, two large trees in the 
 garden lying side by side, but in directions diametrically opposed. 
 
 It has been stated that in the College Park the shifting of the 
 wind amounted to 180 ; and it has been inferred that the centre 
 of the vortex passed over that spot. From what has been said as 
 to the nature of % the phenomenon, it will follow that in other 
 localities, over which the vortex did not pass centrally, the wind 
 must have shifted through different points of the compass, and 
 through angles smaller in proportion to their distances from the 
 centre. Thus, on the southern side of the line described by the 
 centre of the vortex, the change of the wind should be from south 
 to west, and on the northern side of the same line from east to north. 
 We are not yet in possession of facts which bear upon this point ; 
 but from the limited dimensions of the vortex, and the consequent 
 smallness of the distance necessary to produce such a variation, it 
 is probable that evidence bearing upon it may be obtained. I 
 shall only observe that, in seeking and comparing such evidence, 
 care must be taken not to confound eddies arising from local 
 obstructions with the general direction of the current. 
 
 The hours of observation at the Magnetical Observatory are 
 7 A. M., 10, 1 P. M., 4, 7, 10. The observations of the barometer, 
 and of the dry and wet thermometers, made at these hours on the 
 day of the storm, are the following : 
 
 Hour. 
 
 Barometer. 
 
 Dry Therm. 
 
 Wet Therm. 
 
 7A.M. 
 
 29-944 
 
 49-5 
 
 47-4 
 
 10 
 
 29-952 
 
 54-7 
 
 50-5 
 
 IP.M. 
 
 29-964 
 
 58-6 
 
 52-0 
 
 4 
 
 29-930 
 
 56-0 
 
 52-3 
 
 7 
 
 29-944 
 
 52-6 
 
 52-0 
 
 10 
 
 29-936 
 
 51-0 
 
 49-6 
 
 The fall of rain, and melted hail, in Trinity College during the 
 storm amounted to 0'596 of an inch ; but it is probable that much of 
 the hail was driven out of the receiver of the gauge by the wind. 
 
 It will be seen that the barometric fluctuation is small. It is 
 stated, however, that a sudden and considerable fall of the 
 barometer took place shortly before the storm. From the obser-
 
 316 ON THE STORM OF THE 18TH OF APRIL, 1850. 
 
 vations above given, at 1 P. M. and 4 P. M., it will be seen that the 
 barometric equilibrium, if so disturbed, was soon restored. 
 
 I have collected, from the newspapers and other sources, sucli 
 information as I could obtain respecting the area of the city visited 
 by the gale, but it is as yet incomplete. It appears, however, that 
 the diameter of the vortex was not very different from the length 
 of the city from north to south ; the gale having been limited by 
 the Circular-road in these two directions. Hail fell, however, 
 abundantly beyond the limits of the gale. Thus, at the gardens 
 of the Eoyal Dublin Society, at Grlasnevin, the damage done by the 
 hail was very great ; but it was limited to the roofs of the houses, 
 the hail having fallen perpendicularly. The amount of the rain 
 and melted hail registered there was 1'7 inches in 35 minutes. 
 
 Further information is wanting to enable us to determine 
 exactly the progressive movement of the centre of the vortex. We 
 are informed by the newspapers that a storm similar to that which 
 visited Dublin, although not so severe, took place at Mullingar, 
 about an hour and a half previously. If this be the same storm, 
 the direction of the progressive movement must have been nearly 
 from west to east, and its velocity about thirty miles an hour. 
 This direction accords with that given by the observed limits of 
 the storm on the northern and southern sides of the city; but it 
 seems to have been modified, at the surface of the earth, by the 
 lower current. The velocity of the rotatory movement was, of 
 course, vastly greater than that of the progressive ; but we have no 
 direct measure of its amount. 
 
 The damage done in Dublin has been principally in the destruc- 
 tion of glass caused by the hail; but many chimneys have been 
 thrown down, and many roofs dismantled, by the gale. The 
 estimated amount of the loss sustained, as ascertained by the 
 Metropolitan Police, is 27,800. Many houses were struck by 
 the lightning; but, happily, there was no loss of life from that 
 cause. 
 
 There seemed to have been a disturbance of electrical equi- 
 librium, accompanied by rain, in many remote parts of Ireland on
 
 XVII. NOTES ON THE METEOROLOGY OF IRELAND, DE- 
 DUCED FROM THE OBSERVATIONS MADE IN THE 
 YEAR 1851, UNDER THE DIRECTION OF THE ROYAL 
 IRISH ACADEMY. 
 
 Transactions of the Itoyal Irish Academy, Vol. XXII. 
 
 THE science of meteorology is, perhaps more than any other, 
 dependent upon co-operation and upon method. Individual ob- 
 servers may investigate successfully certain detached meteorolo- 
 gical problems, such as the laws of the diurnal and annual changes 
 of temperature, pressure, and humidity, at a given place ; but little 
 progress can be made in climatology, or in the knowledge of the 
 greater movements of the atmosphere, and their relation to the 
 non-periodic variations of temperature and pressure, without the 
 co-operation of many observers distributed over a large area, and 
 acting upon a common plan. 
 
 For this task the voluntary association of individuals is insuffi- 
 cient. However zealous such persons may be, it is not possible to 
 bind them to that uniformity of system without which little can be 
 effectively done. Observations taken at different hours, or by dif- 
 ferent methods, can never be compared satisfactorily; and any 
 comparison will involve an amount of labour in the processes of 
 reduction which may render them impracticable. In addition to 
 this, certain rules of observation are imposed by the conditions of 
 some of the great problems of meteorology ; and no co-operation 
 in which these. rules are deviated from can contribute to their 
 solution. 
 
 For these and other reasons it is desirable that, in every country, 
 such observations should be provided for by the Government, and 
 placed under the direction of one of its official departments. And
 
 318 ON THE METEOROLOGY OF IRELAND. 
 
 there can be no doubt of the services which meteorology, properly 
 studied, may be made to contribute to those interests which it is 
 the duty of every Government to promote. The health of man, 
 the operations of agriculture by which he procures his food, and 
 many other of his material interests, are dependent upon climat- 
 ological relations, which must be known and studied before they 
 can be applied. Every one acknowledges the fact, that the salu- 
 brity of a district, and its adaptation (or the reverse) to particular 
 human constitutions, is intimately connected with its meteorological 
 conditions. And the same thing is true of all organized beings, and 
 especially of those which are subservient to the uses of man. Thus, 
 the question of the naturalization of exotic plants is, mainly, a me- 
 teorological problem, dependent upon the climatological relations of 
 the region to which the plant is indigenous, and of that to which 
 it is to be transferred ; and the importance of obtaining accurate 
 data for its solution will be recognised, when it is borne in mind 
 that, in Europe, most of the plants useful to man belong to this 
 class, and that those hitherto acclimatized probably bear a very 
 small proportion to the whole. Lastly, the processes of cultivation, 
 to which these vegetables are to be subjected, are also connected 
 in an intimate manner with meteorological knowledge. We may 
 instance this connexion in the operations of irrigation, and of 
 drainage, both of which are dependent upon the knowledge of 
 the amount of rain-fall in the district to be operated on. 
 
 It is true that meteorological science has been hitherto compa- 
 ratively barren in such applications ; and the fact itself, with many 
 persons, would be accepted as evidence that abstract and practical 
 knowledge are wholly separate and unconnected. But, when pro- 
 perly understood, it leads to a different conclusion. Superficial 
 knowledge in this science can indeed yield but few practical 
 results ; and those by whom such results have been hitherto sought 
 have expected to find them at the surface. There are indeed 
 cases such, for example, as the one last referred to in which 
 the connexion between meteorological science and its applications 
 is obvious and simple, and in which, accordingly, that connexion 
 has been traced and made use of. But in general it is otherwise. 
 In a subject so complex as the laws which govern the aerial enve- 
 lope of the earth, and where so many causes are in operation, prac- 
 tical applications can be obtained only from mature theoretical 
 knowledge. Thus, it may be shown that the knowledge of the
 
 ON THE METEOROLOGY OF IRELAND. 319 
 
 phenomena of temperature, requisite for the determination of the 
 possible geographical limits of a single species of plants, is by no 
 means inconsiderable ;* and when to this we add the consideration 
 of the various other agencies which are at work in the atmosphere, all 
 influencing vegetable life, it is plain that we are not in a condition to 
 deduce any useful result connected with the distribution of species, 
 until we have mastered a much larger amount of theoretical know- 
 ledge than is usually brought to bear in such deductions. 
 
 It would seem, therefore, to be the duty of the Government of 
 every civilized state to provide the statistical data which have so 
 many important bearings upon the material welfare of the people, 
 and in the form best fitted for their discussion and examination. 
 And to the lover of truth itself, for its own sake, the fulfilment of 
 this duty would, fortunately, supply the wants of science in the 
 most complete and satisfactory manner. 
 
 In many countries, accordingly, provision has been made by 
 their respective Governments for the collection and discussion of 
 meteorological data upon a uniform and well-digested plan. The 
 Government of Prussia appears to have taken the lead in this im- 
 portant labour. Its example has been followed by those of Russia, 
 Austria, Bavaria, and Belgium ; and the names of Dove, Kupffer, 
 Kreil, Lamont, and Quetelet, to whom the superintendence of these 
 observations has been intrusted, afford the surest warrant of their 
 successful prosecution. f But perhaps the most important under- 
 taking of this nature is the recent organization of a system of 
 meteorological observations at sea by the Government of the 
 United States. There are, at the present time, nearly 1000 
 masters of ships, belonging to the navy and merchant services of 
 
 * For each plant there is a lower limit of temperature, helow which it will cease to 
 vegetate; while, in order that it may blossom and bear fruit, it must receive, botwtvn 
 the two seasons of this minimum temperature, a certain amount of heat beyond this 
 limit which is constant for each species. It is upon this integral of effective heat, as has 
 been shown by De Candolle, that the existence of the species depends. For informa- 
 tion on this and other subjects connected with the applications of meteorology, see tin- 
 interesting introduction, by M. Martins, to the Annuaire Meteorologiqtie de la Frann: 
 
 t The results of many of these series have been already published. Professor Dove 
 has published the results of the observations made in Prussia in the years 1848 ami 
 1849. The observations made at the Hn-<ian }>-> Tviitorirs h;iv- b.M-n pultlishrd from 
 time to time by M. Kupffer, in the Recuril <l> -K (t/wn-Hfinimfnit,;* il<, - 
 The results of the Bavarian observations have hrcu j, p ivm by Mr. L-miniit. in t!, 
 tnitt-n <t,'r Metcorofagir ; and those cf the IScl-ian s\ Mnn, in tlu- adiniial.lc .-rricsof papery 
 drawn up by M. Quctelct, Stir le Climat de Jicfy
 
 320 ON THE METEOROLOGY OF IRELAND. 
 
 the United States, engaged in such observations ; and the dis- 
 cussion of the results, by Lieutenant Maury, has led to many 
 consequences of great value to the sciences of meteorology and 
 hydrography, and rich in practical applications to navigation. 
 The Government of the United States has earnestly sought the 
 co-operation of the Governments of the several maritime nations 
 of Europe in this enterprise, and the demand has led to a Con- 
 ference at Brussels, for devising a uniform system of meteoro- 
 logical observations at sea. This Conference, held in August 
 and September last, was attended by individuals representing the 
 respective Governments of Belgium, Denmark, France, Great 
 Britain, the Netherlands, Norway, Portugal, Russia, Sweden, and 
 the United States. 
 
 Impressed with the conviction that it was the duty of each 
 country to take its part in these labours, and especially in the 
 investigation of its own climatology, the Council of the Royal 
 Irish Academy directed their attention, early in the year 1850, 
 to the object of organizing a uniform system of meteorological 
 observations in Ireland. And the peculiarity of the climate of 
 this island perhaps more than balances the smallness of its extent, 
 in giving an interest to the investigation. Situated as it is at the 
 north-western extremity of Europe, and exposed to the full influ- 
 ence of the northern branch of the gulf stream which sweeps its 
 western shores, its winter temperature is as high as that of the 
 southern shores of the Euxine ; while, on the other hand, the 
 great precipitation of vapour, due to the same cause, gives it a 
 summer heat as low as in parts of Finland. 
 
 The questions whose solution was aimed at by this measure, are 
 thus stated by the Council in their second Eeport : 
 
 1. The distribution of temperature, humidity, and rain, as 
 affected by geographical position and by local circumstances ; and 
 the other phenomena of climate. 
 
 2. The effect of season (combined with the influences already 
 referred to) upon the distribution of temperature, and the varying 
 position of the isothermal lines from month to month. 
 
 3. The non-periodic variations of pressure, temperature, and 
 humidity, and their connexion with the course and direction of the 
 aerial currents. 
 
 4. The phenomena and laws of storms, whether revolving or 
 otherwise.
 
 ON THE METEOROLOGY OF IRELAND. 321 
 
 5. The periodical winds prevailing during certain seasons, and 
 their modifications, from geographical position or local causes. 
 
 6. The course and rate of progress of atmospheric waves. 
 
 Concurrently with the meteorological observations, it was de- 
 termined to institute an extended series of observations on the 
 phenomena and laws of the tides around the coasts of Ireland, the 
 results of which will be laid before the Academy by Mr. Haughton. 
 The observations of the former class having been intrusted by the 
 Council to my care, for reduction and discussion, I now proceed 
 to lay before the Academy their principal results. It will be 
 necessary, however, in the first instance to describe the plan of 
 observation itself. 
 
 Stations. The meteorological stations are : 
 
 1. The Coast-guard stations at Portrush, Buncrana, Donaghadee, 
 Courtown, Dunmore East, Castletownsend, Cahirciveen, and Kil- 
 rush ; and, for observations of sea temperature only, those of 
 Cushendall and Bunown. At all of these the observations were 
 taken, with the permission of the Lords of the Treasury and of the 
 Comptroller-General, by the boatmen belonging to the Coast-guard 
 Service, the individuals having been specially selected for the duty 
 by the inspecting officers, and having been instructed in the mode 
 of observing by members of the Council of the Academy. 
 
 2. The Light-houses at Killough, Inishgort, and Killybegs, 
 where, with permission of the Ballast Board, the observations were 
 made by the light-keepers, instructed as before. 
 
 3. The Astronomical Observatories of Armagh and Markree, 
 where the observations were taken by the Observatory assistants, 
 with the permission of Dr. Robinson and Mr. Cooper ; the Magne- 
 tical Observatory of Dublin, where they were made with the per- 
 mission of the Board of Trinity College ; and the stations at 
 Portarlington and Athy, at which they were undertaken by Dr. 
 Hanlon and Alfred Haughton, Esq. 
 
 In addition to these, the Academy has received observations, 
 made upon the prescribed plan, from the Eoyal Observatory of 
 Dublin, and from the Queen's Colleges at Belfast and Galway, 
 which could not conveniently be included in the following discus- 
 sions, not having extended over the whole of the period discussed. 
 The observations at the Royal Observatory, and at the Queen's 
 College, Belfast, commenced in April 1851, and have been
 
 322 
 
 ON THE METEOROLOGY OF IEELAND. 
 
 nued to the present time ; the necessity for their omission is the 
 more to be regretted, as they appear to have been made with every 
 possible care. 
 
 The positions of the several stations, together with the heights 
 (in feet) of the cisterns of the barometers above the mean sea level,* 
 are given in the annexed Table. They are shown in Plate i. 
 
 POSITIONS OF THE METEOROLOGICAL STATIONS. 
 
 Station. 
 
 Lat. 
 
 Long. 
 
 Height 
 above 
 Sea. 
 
 Locality. 
 
 Portrush, . . 
 
 55 13' 
 
 6 41' 
 
 29 
 
 Coast-guard Station. 
 
 Buncrana, . . 
 
 55 8 
 
 7 27 
 
 48 
 
 Do. 
 
 Donaghadee, 
 
 54 38 
 
 5 33 
 
 16 
 
 Do. 
 
 Killybegs, . . 
 
 54 34 
 
 8 27 
 
 20 
 
 Light-house. 
 
 Armagh, . . . 
 
 54 21 
 
 6 39 
 
 211 
 
 Observatory. 
 
 Killough, . . 
 
 54 13 
 
 5 40 
 
 23 
 
 Light-house. 
 
 Markree, . . . 
 
 54 14 
 
 8 28 
 
 132 
 
 Observatory. 
 
 Westport, . . 
 
 53 50 
 
 9 37 
 
 17 
 
 Light-house. 
 
 Dublin, . . . 
 
 53 21 
 
 6 15 
 
 19 
 
 Magnetical Observatory. 
 
 Portarlington, . 
 
 53 9 
 
 7 12 
 
 230 
 
 Dr. Hanlon's residence. 
 
 Athy,. . . . 
 
 53 
 
 6 58 
 
 200 
 
 Mr. Haughton's residence. 
 
 Courtown, . . 
 
 52 39 
 
 6 13 
 
 34 
 
 Coast-guard station. 
 
 Kilrush, . . . 
 
 52 38 
 
 9 30 
 
 19 
 
 Do. 
 
 Dunmore, . . 
 
 52 8 
 
 6 59 
 
 66 
 
 Do. 
 
 Cahirciveen, 
 
 51 56 
 
 10 13 
 
 52 
 
 Do. 
 
 Castletownsend, 
 
 51 33 
 
 9 9 
 
 18 
 
 Do. 
 
 * At Portarlington and Athy these heights have been taken from the Contour Maps 
 of the Ordnance Survey, and must, therefore, be considered as only approximate : at 
 all the other places they have been obtained by actual levelling from the nearest Ord- 
 nance bench-marks.
 
 ON THE METEOROLOGY OF IRELAND. 323 
 
 The instruments were furnished by the Academy to the Coast- 
 guard and Light-house stations, and were constructed under the 
 direction of the Council, and upon a common plan. They consist of 
 a barometer ; a pair of ordinary thermometers (dry and wet bulb) ; 
 a pair of self-registering thermometers; a wind- vane; Lind's 
 anemometer; a rain-gauge; and (at the Coast-guard stations) 
 a thermometer adapted to the observation of sea temperature. 
 The thermometers were previously compared in Dublin with the 
 standards belonging to the Magnetical Observatory, and their 
 errors exactly determined. The barometers were compared with 
 the Dublin standard, after they were placed at the several stations, 
 by means of good portable barometers ; and the heights of the 
 cisterns above the sea were ascertained by levelling. All this was 
 done by members of the Council, under whose superintendence the 
 instruments were erected. 
 
 The four thermometers at every station were inclosed in a 
 shallow box with a sloping roof, and wire-gauze front. A vertical 
 gnomon was fixed at most of the stations in the window-sill of the 
 guard-house, for the purpose of determining the time of noon ; and 
 the observers were furnished with a Table of the equation of time, 
 computed for the year 1851, and for the mean longitude of Ireland. 
 The barometers were put up, generally, in the guard-house of the 
 station. 
 
 Plan of Observation. It is probable that over a tract of country 
 so limited as this island, the distribution of temperature, humidity, 
 and rain, does not vary materially from one year to another ; and 
 that, consequently, a tolerable approximation to the laws of this 
 distribution may be obtained from the results of a single year, if 
 every precaution be adopted to insure the perfect comparability of 
 the results. It was arranged, accordingly, that the observations 
 should be coijtinued at the Coast-guard stations until the end of the 
 year 1851, so as to embrace a period of at least one year, reckon. -.1 
 from the time when the observers had acquired the power of ob- 
 serving with accuracy. The monthly means for this year may be 
 reduced to their absolute mean values, by the help of the more 
 extended series of observations made in Dublin, by which the 
 deviations of any monthly result from its absolute mean value 
 is sufficiently known. 
 
 The Committee, upon whom the duty of superintending these
 
 324 ON THE METEOROLOGY OF IRELAND. 
 
 arrangements devolved, were desirous that the plan of observation 
 should be the least onerous that could lead satisfactorily to the 
 results aimed at. One of the principal of these the determination 
 of the movements of masses of air, whether in storms, or in the 
 displacement of atmospheric waves, demands, as has been said, 
 that the observations should be taken at equal intervals of time ; and 
 the only condition imposed by the other meteorological problems 
 is, that these times should be so chosen as to furnish the daily 
 means of the elements sought. Now any three observations, taken 
 at equal intervals throughout the day, are sufficient to eliminate the 
 diurnal variation, and therefore to give the daily means of all the 
 meteorological elements ; and undoubtedly, where such a system is 
 practicable, the observations should be taken at 6 A.M., 2 P.M., and 
 10 P.M., which has been shown to be preferable to any other eight- 
 hourly group, for meteorological purposes. 
 
 At the Coast-guard stations, however, such a plan of observation 
 would have been incompatible with the regular duties of the men ; 
 and it was advisable to adopt a less complete system, which might 
 be followed at all the stations, and in which interruptions were not 
 likely to occur. Fortunately, two observations in the day, taken at 
 equal intervals, are sufficient to give the daily means of all the mete- 
 orological elements, excepting the atmospheric pressure ; and, as the 
 diurnal variation of the pressure is very small much smaller than 
 its irregular fluctuations in these latitudes, it may be disregarded, 
 and the objects for which the present system was instituted may be 
 attained by taking two observations in the day, at homonymous hours. 
 
 The best pair of homonymous hours, for the determination of 
 the mean temperature, and nearly also for that of the mean humidity, 
 are 9 h 46 m A.M., and 9 h 46 m P.M. Limiting themselves to the exact 
 hours, the Committee might accordingly have chosen either 9 A. M. 
 and 9 P.M., or 10 A.M. and 10 P.M. ; the former pair was adopted, 
 its superior convenience seeming to outweigh the advantage of the 
 latter in accuracy. 
 
 For the fuller elucidation of some of the questions proposed, it 
 was further arranged that hourly observations should be taken at all 
 the stations for twenty-four hours, at the equinoxes and solstices, 
 according to the plan laid down by Sir John Herschel. It was 
 likewise provided, that hourly observations should be taken occa- 
 sionally, under special circumstances, such as storms, unusual dis- 
 turbances of barometric equilibrium, &c.
 
 ON THE METEOROLOGY OF IRELAND. 325 
 
 For further details of the plan of observation, the reader is 
 referred to the " Instructions" prepared by the Council of the 
 Academy. I now proceed to the results of the observations. 
 
 TEMPERATURE OF THE AIR. 
 
 Corrections. It has been already stated, that the thermometers 
 employed in measuring the temperature and humidity of the air 
 were carefully compared with a standard thermometer, and their 
 errors noted. When the errors differed by more than 0'2 in diffe- 
 rent parts of the scale, the instrument was rejected ; when they did 
 not, the mean of the observed errors was adopted as a constant 
 error for the whole scale of the instrument. 
 
 It has been stated that the mean of the temperatures observed 
 at 9 A. M. and 9 P.M. is, very nearly, the mean of the entire day. 
 The small corrections required, in order to reduce the former to the 
 latter, are obtained from the bi-hourly observations of temperature 
 made at Dublin in the years 1840-1843. The following Table 
 contains the results of that series, and gives the mean differences 
 between the temperature at each hour of observation, and that of 
 the entire day :
 
 326 
 
 ON THE METEOROLOGY OF IRELAND. 
 
 a 
 
 CO 
 
 b 
 
 9 
 
 
 
 1 
 
 "* 9 
 
 CM CO 
 I I 
 
 1 1 
 
 Cl 
 
 1 
 
 eo 
 1 
 
 CM 9 
 
 CO rH 
 1 1 
 
 9 
 1 
 
 o 
 l 
 
 f 9 
 
 CM 
 
 OS 
 
 >o 
 
 
 
 1 
 
 ir- 
 es 
 1 
 
 1 1 
 
 9 op 
 
 CM CM 
 
 1 1 
 
 H- 
 CM 
 
 9 
 
 CM 
 
 1 
 
 t-H CO 
 
 1 1 
 
 00 
 
 
 
 1 
 
 
 
 1 
 
 00 CD 
 
 rH CM 
 
 1 1 
 
 O 
 
 
 CM 
 
 * 
 
 ^ ^ 
 
 CO O 
 
 co 
 
 CM 
 
 CD rH 
 
 rH 
 
 CM 
 
 o co 
 
 CM 
 
 *" 
 
 b 
 
 
 
 I 
 
 O 
 
 1 I 
 
 O rH 
 
 O 
 
 O 
 + 
 
 O 
 
 1 1 
 
 O 
 I 
 
 O 
 
 1 
 
 b 
 
 -h + 
 
 O 
 1 
 
 >0 
 
 
 
 o 
 
 9 ,-1 
 
 CM * 
 
 -H CM 
 
 eo 
 
 9 
 eo 
 
 9 9 
 
 CM rH 
 
 CD 
 
 O 
 
 
 
 cp op 
 
 CM CO 
 
 cp 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 o 
 
 eo 
 
 O ^ 
 
 rH CM 
 
 _, 
 
 
 
 CD 
 
 e 
 
 
 
 IO CD 
 
 ^ 
 
 CO 
 
 co 
 
 eo 
 
 >O CD 
 
 CO >O 
 
 o 
 
 
 
 <* 
 
 CM 
 
 ~ 
 
 Tfl O 
 
 co 
 
 
 
 
 
 
 
 
 
 
 
 
 
 PH 
 
 9 
 
 M 
 
 9 
 * 
 
 9 9 
 
 CO CO 
 
 op -* 
 
 
 
 9 
 
 O *O 
 
 CD *0 
 
 eo 
 
 9 
 
 CO 
 o o 
 
 * 
 
 *" 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 CM 
 
 TH 
 
 ^ 
 
 05 r- 
 
 CO 
 
 rH 
 
 00 CO 
 
 
 
 9 
 
 9 9 
 
 op 
 
 "- 1 
 
 
 ! 
 
 -f~ ~f~ 
 
 
 + 
 
 * 
 
 
 5 
 
 J 
 
 eo ^ 
 
 CM 
 
 O5 
 
 I 
 
 
 
 O CM 
 
 00 rH 
 
 c-i eo 
 
 s 
 
 9 
 
 CM 
 
 i-H O 
 
 9 
 
 
 
 op 
 o 
 
 rH 3 
 rH CM 
 
 co 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 9 
 
 ,_, 
 
 rH CO 
 
 
 
 CC 
 
 OS 
 
 ^ 
 
 00 
 
 CM 
 
 CM CM 
 
 CO 
 
 *~ 
 
 
 CM 
 1 
 
 eo rH 
 1 1 
 
 O CM 
 
 o 
 
 
 
 1 
 
 CM 
 
 1 I 
 
 1-1 
 
 ** 
 
 rH 
 1 1 
 
 CM 
 1 
 
 
 ~ 
 
 ? 
 
 t*. CD 
 
 CM O5 
 
 05 
 
 r^ 
 
 CM 05 
 
 ^ 
 
 eo 
 
 CO rH 
 
 9 
 
 5 
 
 ' 
 
 CM 
 
 1 1 
 
 1 1 
 
 ' 
 
 I 
 
 1 1 
 
 ! 
 
 1 
 
 I | 
 
 ' 
 
 
 oo- 
 
 CO 
 
 I- T* 
 
 3 
 
 ^ 
 
 TH 
 
 CM CM 
 
 
 
 ^ 
 
 05 t- 
 
 ,_, 
 
 eo 
 
 1-1 
 
 1 
 
 1 1 
 
 co t- 
 
 1 
 
 O 
 1 
 
 1 1 
 
 1 
 
 ^ 
 
 & 
 
 1 1 
 
 CM 
 
 * 
 
 ep 
 
 2 
 
 1 1 
 
 i- CM 
 
 3 CO 
 1 I 
 
 9 
 1 
 
 
 5 
 
 T 9 
 
 CO CM 
 1 I 
 
 CM 
 
 I 
 
 op 
 
 
 
 * rH 
 
 
 
 CO >O 
 
 1 1 
 
 2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 J"! 
 
 J 
 
 
 
 
 s- 
 1 
 
 
 n 
 
 1! 
 
 t 
 
 < 
 
 J tT 
 
 
 Decembe 
 
 ,1 
 
 s a 
 
 H ^ 
 
 Winter, .
 
 ON THE METEOROLOGY OF IRELAND. 327 
 
 From the preceding Table we obtain the following corrections, 
 which are to be applied to the means of the observed temperatures 
 at 9 A.M. and 9 P.M., in order to reduce them to the mean of 
 the day : 
 
 April, . . corr. = + 0'l 
 May, . * : +0-1 
 June, . . -0-1 
 July, . . +0-1 
 August, . 0-0 
 
 + 0-2 
 
 October, . . corr. = + 0'5 
 
 November, . + '7 
 
 December, . + '6 
 
 January, . . + '7 
 
 February, . +0'6 
 
 March, . . + -5 
 
 It hence appears that the correction is nearly constant through- 
 out the summer, and throughout the winter months, respectively. 
 The mean summer correction is + 0'l ; the mean winter correction 
 + 0-6. 
 
 Mean Monthly Temperatures. The mean temperatures have been 
 obtained, at all but three of the stations, from the observations at 
 9 A.M. and 9 P.M., by the application of the preceding corrections. 
 At Markree the observations were taken at 10 A.M. and 10 P.M. ; 
 and the reducing numbers are therefore somewhat different, and 
 smaller in amount. At Portarlington and Athy the observations 
 were taken but once in the day, namely, at 9 A. M. ; and at these 
 stations, accordingly, the mean temperatures are inferred from the 
 maximum and minimum temperatures, as given by the self-regis- 
 tering thermometers. The formula employed is that of Kromtz, 
 viz. : 
 
 mean temp. = min + a (max. - mi>i.) 
 
 The mean value of the coefficient,* as deduced from the observa- 
 tions at the observatories of Armagh, Markree, and Dublin, is 
 a = 0-41. 
 
 The following Table contains the resulting values of the mean 
 temperature for the several months of the year 1851 : 
 
 The coefficient in Ksemtz's formula appears to vary considerably at different 
 places, both in its -mean amount, and in the law of its variation from month to month. 
 At Armagh and Markree its greatest value is in December, and ite least in July ; at 
 Dublin, it is the reverse. I have taken above the mean of the yearly values for the 
 
 three stations.
 
 328 
 
 ON THE METEOROLOGY OP IRELAND. 
 
 
 rH 
 
 co oo 
 
 CO CM 
 
 CN 
 
 t CO 
 
 co 
 
 T* 
 
 eo 
 
 05 
 
 CD CO 
 
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 ON THE METEOROLOGY OF IRELAND. 329 
 
 Before we proceed to discuss the mean temperatures in the 
 several months of the year 1851, it is important that we should 
 know the absolute mean temperatures at some one station, and 
 thereby the deviations from the means in the several months of the 
 year in question. Over a tract of country so limited as Ireland, 
 these deviations, will not differ much in different localities ; and 
 therefore, knowing them for one station, we are enabled to reduce 
 the results of the single year, with probably sufficient exactness, to 
 their absolute mean values at all the rest. 
 
 The absolute mean temperatures of the several months are 
 known, at Dublin, by means of the series of observations made 
 during twelve years at the Magnetical Observatory. The monthly 
 mean temperatures, deduced from that series, are given in the fol- 
 lowing Table. From the year 1840 to 1843, inclusive, the daily 
 means are those of twelve equidistant hours ; from 1844 to 1850, 
 inclusive, they are inferred from the temperatures observed at 
 10 A.M. and 10 P.M. ; and in 1851, from those at 9 A.M. and 
 9 p. M. In the last line of the Table are given the deviations of 
 the monthly means in 1851, from the mean monthly means, as 
 deduced from the twelve years. 
 
 It will be seen from the Table, that the temperature in the 
 months of January, February, and October, 1851, was higher than 
 the average temperature, while, in November, it was considerably 
 lower. The mean temperature of the entire year was only 0-3 
 above the average. 
 
 The depression of temperature in the month of November is a 
 remarkable case of those non-periodic fluctuations to which the at- 
 tention of meteorologists has been drawn by Professor Dove. This 
 fluctuation appears to have proceeded from north-east to south- 
 west, and to have been nearly obliterated when it reached the 
 western coast of the island. At the northern and eastern stations the 
 unusual cold began on the 24th day of the month ; at the southern 
 and western it commenced on the 26th and 27th. It reached its 
 maximum about the 30th, and ceased about the 3rd of December. 
 When we compare the mean temperatures of November and De- 
 cember at Killough, Dublin, Courtown, and Dunmore, on the 
 eastern coast, with those at Killybegs, Westport, Kilrush, and 
 Cahirciveen, on the western, we observe that the temperature of 
 November is less than that of December by 3"'3 at the former 
 stations, while the defect is only 0"-6 at the latter.
 
 330 
 
 ON THE METEOROLOGY OF IRELAND. 
 
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 ON THE METEOROLOGY OF IRELAND. 331 
 
 Upon a comparison of the mean yearly temperatures of the 
 several stations, we observe that those of the inland stations are in 
 defect, as compared with the corresponding coast stations. ThQs 
 the mean temperature of Armagh (48'6) is less than that of 
 Donaghadee by 1, and less than that of Killough by 1'6. The 
 mean temperature of Markree (48'2) is less than that of Killybegs 
 by 2'6, and than that of Westport by 3'5. The mean temperatures 
 of Portarlington and Athy (47'3 and 48 0< 4) are in like manner in 
 defect, when compared with those of Dublin and Courtown, and 
 by an intermediate amount. I shall return to this subject hereafter, 
 and merely notice it at present for the purpose of observing that 
 no satisfactory conclusion can be drawn as to the dependence of 
 temperature upon geographical position, unless the inland and 
 coast stations be compared separately. 
 
 Confining ourselves for the present to the coast stations, which 
 are the most numerous and the most widely distributed, we observe 
 that there is an increase of mean annual temperature in proceeding 
 from north to south of the island, the mean temperature of Portrush 
 and Buncrana being 49*0, and that of Dunmore, which is nearly 
 on the intermediate meridian. 51'6. Similarly there is an increase 
 of temperature in proceeding from east to west, the mean tempera- 
 ture of Killough and Dublin being 50'2, and that of Westport, 
 which is nearly on the intermediate parallel, 51 0< 7. 
 
 But for an accurate determination of the rate of increase of 
 temperature in the two directions, it is necessary to combine the 
 results by the method of least squares. For this purpose let t 
 denote the observed mean temperature of any month, at any given 
 station ; T the probable temperature of the same month at an 
 assumed central station; and let the distances (in geographical 
 miles) of the former from the latter, measured on the meridian 
 and parallel of latitude to the north and west, respectively, be 
 denoted by y and x ; then, if V and U be the increase of tempe- 
 rature corresponding to a single mile in each direction, 
 
 t=T+Ux+ Vy. 
 
 There will be a similar equation for each station ; and combining 
 them by the method of least squares, we shall obtain the most 
 probable values of the unknown quantities T, U, and V. 
 
 The simplest mode of employing this method in the present 
 instance is to take, as the arbitrary central station, that whose
 
 332 ON THE METEOROLOGY OF IRELAND. 
 
 latitude and longitude are the arithmetical means of the latitudes 
 and longitudes of the stations of observation. The resulting equa- 
 tions are thus reduced to the following : 
 
 (a?) 4 FS (xy] = S (a*), 
 S (yf). 
 
 For the reason already stated, I shall employ in this calculation 
 only the results obtained at the coast stations. These are, in the 
 order of latitude, Portrush, Buncrana, Donaghadee, Killybegs, 
 Killough, "Westport, Dublin, Courtown, Kilrush, Dunmore, Cahir- 
 civeen, Castletownsend. The mean latitude and longitude of these 
 stations are 53-29', and 7'39' respectively. And we find 
 
 S (ar 2 ) = 39094, S (xy) = - 22569, Z (f) = 65811. 
 
 Substituting and eliminating between the second and third equa- 
 tions, we obtain 
 
 J7= -0000319 S (arf) + -0000109 S (yf) ; 
 F= -0000109 S (xt) + -0000189 S (yt). 
 
 By these formulas the values of T, U, and F, for each month are 
 calculated. They are given in the following Table. 
 
 The values of U and F being known, the positions of the iso- 
 thermal lines are determined. The inclination of the isothermal 
 lines to the meridian, measured from north to west, w, and the rate 
 of increase of temperature in the direction perpendicular to them, 
 W, are known by the formulas 
 
 tan = -^, W=J(U*+ F) 2 . 
 
 The values of u and W for the several months are given in the 
 Table.
 
 ON THE METEOROLOGY OF IRELAND. 
 
 333 
 
 ELEMEMTS OF MONTHLY ISOTHERMAL LINES. 
 
 tf 
 
 T 
 
 U 
 
 V 
 
 W 
 
 u 
 
 1851. 
 
 Mean. 
 
 January, . . . 
 
 M 
 
 41-7 
 
 + -0080 
 
 - -0102 
 
 0130 
 
 52 
 
 February, . . 
 
 44-2 
 
 42-3 
 
 + -0093 
 
 -0119 
 
 0151 
 
 52 
 
 March, . . . 
 
 44-6 
 
 44-1 
 
 + -0131 
 
 -0064 
 
 0146 
 
 26 
 
 AprU, . . . . 
 
 46-9 
 
 47-1 
 
 + 0043 
 
 -0070 
 
 0082 
 
 59 
 
 May, .... 
 
 52-0 
 
 52-9 
 
 + -0012 
 
 - -0139 
 
 0140 
 
 85 
 
 June, .... 
 
 56-8 
 
 56-7 
 
 - -0031 
 
 - -0109 
 
 0114 
 
 106 
 
 July, . . . . j 58-9 
 
 58-8 
 
 -0049 
 
 - -0202 
 
 0208 
 
 104 
 
 August, . . .1 60-6 
 
 58-3 
 
 + -0029 
 
 - -0121 
 
 0124 
 
 77 
 
 September, . . i 57-4 
 October, . . . 52-7 
 November, . . I 44-1 
 
 57-8 
 50-2 
 48-4 
 
 + -0101 
 + 0059 
 + 0304 
 
 -0090 
 -0070 
 + -0077 
 
 0135 
 0092 
 0313 
 
 42 
 50 
 -14 
 
 December, . . 1 45-7 
 
 45-4 
 
 + -0103 
 
 -0017 
 
 0104 
 
 9 
 
 Year, . . . . 50-7 
 
 50-3 
 
 + 0073 
 
 -0085 
 
 0112 
 
 49' 
 
 We see then that, on the mean of the whole year, the isothermal 
 lines are inclined to the meridian by the angle N. 49 W. ; and 
 that the temperature increases in a direction perpendicular to these 
 lines, by -0112 of a degree for each geographical mile, or at the 
 rate of 1 degree for 89 miles. The increase of temperature, in 
 proceeding from north to south, is V= '0085, or 1 in 118 geogra- 
 phical miles ; the corresponding increase, in proceeding from east 
 to west, is U = -0073, or 1 in 137 geographical miles. 
 
 We learn further, that the mean annual isothermal lines furnish 
 a very inadequate representation of the progression of temperature ; 
 and that when we follow the course of these lines from month to 
 month, we find them to vary within very wide limits. The extreme 
 positions of -these lines, as given in the preceding Table, are those 
 for the months of June and November. But the result obtained 
 for the latter month must, I think, be regarded as anomalous, on 
 account of the irregularity in the distribution of temperature already
 
 334 
 
 ON THE METEOROLOGY OF IRELAND. 
 
 noticed ; and, rejecting it, the extreme positions correspond to the 
 two solstitial months. They are the following : 
 
 June, . . 
 December, . 
 
 = N. 106 W., 
 = N. 9 W., 
 
 w= 
 
 0114, 
 0104; 
 
 so that the direction of the isothermal lines varies through an angle 
 of 97 in the course of the year, being nearly parallel to the meri- 
 dian in December, and nearly perpendicular to it in June. (See 
 Plate i.) 
 
 We may now employ the formula 
 
 = T+ 
 
 Vy, 
 
 to deduce the probable temperature at any place, and compare it 
 with that actually observed ; we shall thus find the effect [due to 
 local causes. Making this calculation for the four inland stations, 
 we obtain the results given in the following Table : 
 
 EXCESS OF CALCULATED TEMPERATURES AT INLAND STATIONS. 
 
 Month. 
 
 Armagh. 
 
 Markree. 
 
 Portarlington. 
 
 Athy. 
 
 January, . . 
 
 r-8 
 
 4-4 
 
 3-6 
 
 3'5 
 
 February, . . 
 
 1 -5 
 
 2-7 
 
 3-7 
 
 3-4 
 
 March, . . . 
 
 1-3 
 
 2-4 
 
 4-1 
 
 2-7 
 
 April, ... 
 
 1-0 
 
 1-4 
 
 3-9 
 
 1 -6 
 
 May, . . . 
 
 0-9 
 
 1 -3 
 
 3-1 
 
 1 -8 
 
 June, . . . 
 
 0-1 
 
 0-5 
 
 2-2 
 
 0-3 
 
 July, . . . 
 
 0-9 
 
 1 -2 
 
 2-0 
 
 1-4 
 
 August, . . 
 
 1-3 
 
 1-4 
 
 3-1 
 
 0-1 
 
 September, . . 
 
 1-3 
 
 2-2 
 
 3-7 
 
 3-8 
 
 October, . . 
 
 1-7 
 
 2-7 
 
 2-6 
 
 1 -8 
 
 November, . . 
 
 2-4 
 
 3-5 
 
 4-1 
 
 3-4 
 
 December, . . 
 
 2-1 
 
 3-7 
 
 3-3 
 
 4-2 
 
 
 
 
 
 Year, . . . 
 
 1-4 
 
 2-3 
 
 3-4 
 
 2-3
 
 ON THE METEOROLOGY OF IRELAND. 
 
 335 
 
 We learn that the defect of temperature due to inland position 
 is, as might have been expected, least in summer and greatest in 
 winter. A small part of this defect is due to elevation ; but it is 
 easily eliminated. The mean height of the instruments at the coast 
 stations above the level of the sea is 30 feet. We have, therefore, 
 only to subduct' this from the known heights at the inland stations, 
 and to correct for the difference of level at the rate of 1 Fahr. for 
 276 feet, which is the mean of the determinations made by Mr. 
 Welsh in his balloon ascents, for the lower portion of the atmo- 
 sphere lying beneath the great vapour plane. The mean yearly 
 results at the four inland stations, thus corrected, are as follows : 
 
 
 Observed 
 Defect. 
 
 Height 
 above Sea. 
 
 Correction. 
 
 Reduced 
 Defect. 
 
 Armagh, . . . 
 
 1M 
 
 211 
 
 -0^-7 
 
 0-7 
 
 Markree, . . . 
 
 2 -3 
 
 132 
 
 -0-4 
 
 1-9 
 
 Portarlington, . 
 
 3 -4 
 
 230 
 
 -0-7 
 
 2-7 
 
 Athy,. . . . 
 
 2 -3 
 
 200 
 
 -0-6 
 
 1-7 
 
 
 
 
 Mean = 1-S 
 
 DIURNAL EANGES OF TEMPERATURE. 
 
 Climatology depends upon the ranges of temperature (whether 
 diurnal, monthly, or annual), no less than upon mean values; and 
 their investigation is accordingly a necessary part of the present 
 inquiry. In the present series of observations, the diurnal ranges of 
 temperature are given by means of the results obtained with self- 
 registering thermometers. These results are the least satisfactory 
 portion of the whole series. It is well known that the ordinary 
 self -registering thermometers are extremely apt to get out of order, 
 the maximum, by the index becoming entangled in the mercury, 
 and the minimum, by the distillation of the spirit into the upper 
 part of the tube ; and although the observers were carefully in- 
 structed in the mode of remedying these derangements, no one (I 
 believe) who has handled such instruments will wonder that men 
 previously unaccustomed to them should have sometimes failed, in 
 what is in all cases a somewhat delicate operation.
 
 336 
 
 OF THE METEOROLOGY OF IRELAND. 
 
 But there is another source of error affecting the maximum 
 thermometer, which it is still more difficult to avoid. If the in- 
 strument be exposed to the influence of radiation for any portion 
 of the day, however short, it will, from its construction, retain the 
 impression made upon it ; and, consequently, if the abnormal tem- 
 perature to which it has been thus subjected exceeds the greatest 
 temperature of the air in the day, an erroneous result will be re- 
 corded. The difficulty of guarding thermometers completely from 
 such influences is well known; and although some trouble was 
 taken to insure this protection, the observations themselves show 
 that it was not effective at all the stations. I have, accordingly, 
 been compelled to reject a portion of the results obtained with the 
 maximum thermometer, as defective from this cause. 
 
 In the following Table are given the diurnal ranges deduced 
 from the maximum and minimum temperatures, combined in 
 yearly and half-yearly periods, retaining only those stations at 
 which one or other of the two half-years is complete : 
 
 DIURNAL BANGES (HALF-YEARLY AND YEARLY MEANS). 
 
 Station. 
 
 Summer. 
 
 Winter. 
 
 Year. 
 
 Portrush, . . 
 
 12'2 
 
 lQ^-3 
 
 no.o 
 
 Donaghadee, .... 
 
 10-9 
 
 8-3 
 
 9-6 
 
 Armagh, .... 
 
 13 -3 
 
 10 -4 
 
 11 - 8 
 
 KillmipV . 
 
 
 9 *9 
 
 
 Markree, 
 
 14-3 
 
 11 -0 
 
 12-6 
 
 Dublin, . . . 
 
 11 '5 
 
 8*K 
 
 1ft .1 
 
 Portarlington, . . , . 
 
 17-1 
 
 12-6 
 
 14-9 
 
 Athy, 
 
 15-0 
 
 11-0 
 
 13-0 
 
 Kilrush, . . 
 
 
 9.7 
 
 
 Cahirciveen, .... 
 
 
 
 7-4 
 
 
 Castletownsend, . . . 
 
 11-8 
 
 8-2 
 
 10-0 
 
 Coast Stations, . . . 
 
 ll-6 
 
 8-9 
 
 10-3 
 
 Inland do., ... 
 
 14-9 
 
 11-3 
 
 13-1 
 
 Differences, . . . 
 
 3-3 
 
 2-4 
 
 2-8
 
 ON THE METEOROLOGY OP IRELAND. 337 
 
 From the mean results of the preceding Table, we learn that 
 the diurnal range is greater at the inland than at the coast stations, 
 the mean excess being 2-8 degrees. The excess is greater in 
 summer than in winter, being 3'3 in the former, and 2'4 in the 
 
 latter season. 
 
 "We are now in a position to refer to one, at least, of the 
 practical inferences which may be deduced from the preceding 
 results. 
 
 The climatological conditions connected with temperature, 
 which favour the prevention or cure of pulmonary diseases, are, 
 firstly, a high winter temperature ; and secondly, a small amount 
 of diurnal range. It has been already stated that Ireland is well 
 circumstanced as to these conditions ; let us now inquire which is 
 its most favourable region as respects them. 
 
 The months of lowest temperature in Ireland, and which are 
 on that account the most trying to the sufferers from the diseases 
 referred to, are those of December, January, February, and March. 
 During these months the mean temperature varies very little in 
 Ireland, the mean range at Dublin varying from 41'7 in January, 
 to 45 0< 4 in March, or only 3'7 degrees. Now the mean direction of 
 the isothermal lines for these four months is N. 37 W. ; so that 
 the highest mean temperature for these months is to be found on 
 the south-western coast, not far from Valentia. 
 
 The second condition above mentioned, although not frequently 
 taken into account, is, perhaps, still more important. In proof of 
 this it may be mentioned that in Norway, which is remarkable for 
 the small amount of the diurnal range of temperature, consump- 
 tion is uncommon, even in the highest latitudes ; while in parts 
 of Sweden, where this condition does not hold, it is prevalent. 
 Now, we learn from the preceding Table that, among the stations 
 at which observations were made in 1851, the winter diurnal range 
 of temperature is least at Cahirciveen. Both conditions, therefore, 
 point to the sputh- western coast of Kerry as the region in Ireland 
 most favourable to patients affected with these formidable maladies. 
 
 I am not in possession of any statistical data bearing upon this 
 question, and am therefore unable to say how far the conclusion 
 thus drawn is borne out by facts.
 
 338 0& THE METEOROLOGY OF IRELAND. 
 
 TEMPERATURE OF THE SEA. 
 
 Provision was made that the temperature of the sea should 
 be observed at all the places at which tidal observations were 
 taken. For this purpose each station was furnished with a 
 thermometer, having its bulb inclosed within a small reservoir of 
 copper, for the double purpose of guarding it from accident, and 
 of protecting it (by means of the contained water) from rapid 
 changes of temperature, when it was lifted into the 'air for obser- 
 vation. The observer was instructed to note its indications twice 
 in the day, at intervals of about twelve hours, the thermometer 
 being attached to a pole, and plunged to the depth of about one 
 foot in deep water. The diurnal change of the temperature of 
 the sea being very small, it is completely eliminated by two such 
 observations. At many of the stations the instrument was lost, or 
 broken, in the attempt to use it during boisterous weather. We 
 are, therefore, only in possession of the results from six stations, 
 which are contained in the following Table. 
 
 In the last two lines of the Table are given the mean results 
 of the six stations, and the differences between them and the mean 
 of the entire year. These numbers accordingly exhibit the law 
 of the annual variation of sea temperature, around the coasts of 
 Ireland ; and the remarkable regularity in their progression shows 
 that, even from the results of a single year, we obtain a close 
 approximation to the actual law.
 
 ON THE METEOROLOGY OF IRELAND. 
 
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 co 9 
 
 1 
 
 g. 
 
 9 9 ? T 9 T 1 
 
 cb co eo oo co i- 
 
 o 
 
 
 
 
 Station. 
 
 s 1 1 g 6 | 
 6 S 3 1 i ^ 
 
 ii 
 
 II 
 
 1 
 
 z2
 
 340 ON THE METEOROLOGY OF IRELAND. 
 
 We learn from these numbers that the annual variation of the 
 sea-temperature, at the surface, differs considerably from that of 
 the air above it, the difference consisting chiefly in a retardation 
 of the epochs of maximum and minimum. Thus the minimum 
 temperature occurs in the middle of February, and the maximum 
 in the middle of August, or about a month after the corre- 
 sponding epochs of the temperature of the air. The annual range 
 is also, as might have been expected, considerably less than that 
 of the air. These results accord sufficiently well with the conclu- 
 sions drawn by Ksenitz, from a comparison of the results of many 
 voyagers. 
 
 But the most interesting result is that concerning the relation 
 between the temperature of the sea at the surface, and that of the 
 superincumbent air. Upon this subject the greatest discordance 
 exists in the statements of different observers. According to 
 Humboldt, the mean temperature of the Atlantic Ocean, at the 
 surface, is in all cases higher than that of the atmosphere above it. 
 This conclusion is confirmed by the observations of Peron and 
 Fitzroy, and is contradicted by those of Irving, Forster, and 
 Kotzebue. From an elaborate discussion of the observations of 
 many voyagers, Ksemtz infers that the temperature of the sea is less 
 than that of the air over the land in the lower latitudes, while in the 
 higher latitudes it is greater. The original conclusion of Humboldt, 
 however, seems to be placed beyond all doubt by the recent obser- 
 vations of Captain Duperrey, which appear to be more numerous, 
 and taken with more precautions to insure accuracy, than any 
 preceding. It seems now to be generally admitted that, in the 
 temperate and polar regions, the temperature of the sea is higher 
 than that of the air ; and the only question that remained was as 
 to the tropics. Now the observations of Duperrey were made all 
 round the globe, between 10 N. and 10 S. latitude ; and they 
 were taken at intervals of four hours, so as completely to eliminate 
 the effects of the diurnal change. From these observations it 
 appears that the temperature of the sea is higher than that of the 
 air within the zone already mentioned, the mean excess in the 
 Atlantic being 0'83 Fahr., and in the Great Ocean about half 
 that amount. 
 
 The present observations possess much interest in connexion 
 with these questions. In order to perceive their bearing, I have, 
 in the Table which follows, given the half-yearly and yearly
 
 ON THE METEOROLOGY or IKEEAND. 341 
 
 means of the sea-temperature at the several stations, together with 
 the differences between them and the corresponding means of the 
 temperature of the air. At Cushendall and Bunown no observa- 
 tions of the temperature of the air were actually made ; and for 
 these stations^, consequently, the latter means are calculated from 
 the isothermaf lines. 
 
 TEMPERATURE or THE SEA (YEARLY AND HALF-YEARLY MEANS). 
 
 Station. 
 
 Summer. 
 
 Winter. 
 
 Year. 
 
 Temp. 
 
 Excess. 
 
 Temp. 
 
 Excess. 
 
 Temp. 
 
 Excess. 
 
 Portrush, . . 
 
 54-6 
 
 + r-o 
 
 48M 
 
 + 3-8 
 
 51-5 
 
 + 2M 
 
 Cuahendall, 
 
 53-2 
 
 - 1-0 
 
 49-1 
 
 + 4-4 
 
 51-1 
 
 + 1 -7 
 
 Donaghadee, . 
 
 53-6 
 
 -0-6 
 
 48-6 
 
 + 3-6 
 
 51 -1 
 
 + 1 -5 
 
 Bunown, . . 
 
 58-0 
 
 + 2-4 
 
 50-2 
 
 + 3-2 
 
 54-1 
 
 42-8 
 
 Courtown, . . 
 
 57-7 
 
 + 2-2 
 
 47-9 
 
 + 3-0 
 
 52-8 
 
 + 2-6 
 
 Castle to wnsend, 
 
 56-9 
 
 + 0-1 
 
 48-9 
 
 + 1 -5 
 
 52-9 
 
 + 0-8 
 
 
 
 
 ! 
 
 
 
 Meandiff., . 
 
 
 40-7 
 
 
 + 3-3 
 
 
 + 2-0 
 
 It appears from the last line of this Table, that the temperature 
 of the sea is, upon the mean of the entire year, 2'0 higher than 
 that of the air above the coast. The excess is 3'3 in winter, and 
 0-7 in summer. There appears also to be considerable diversity 
 in the amount of the excess at the different stations; it is 
 greatest, on the mean of the entire year, at Bunown, and least at 
 Castletownsend. 
 
 This excess of the temperature of the sea above that of the air 
 furnishes the explanation of the fact already noticed, namely, 
 the diminution of the temperature of the air in proceeding from 
 the coasts inland ; for it is obvious that the air in the vicinity 
 of the sea must have its temperature raised by contact with 
 the water. 
 
 It follows also, that the absolute excess of sea-temperature 
 considerably exceeds that above stated. Thus, w Imv M6O, th.
 
 342 ON THE METEOROLOGY OF IRELAND. 
 
 temperature of the sea, on the average of the entire year, exceeds 
 that of the air over the coasts by2'0 ; while the latter temperature 
 exceeds that of the air inland (for the same latitude and longitude) 
 by l-8. The total excess of the sea-temperature above that of 
 the air amounts, therefore, to 3'8 Fahrenheit. 
 
 This excess, which appears to be much greater than has been 
 observed elsewhere, is to be ascribed, mainly, to the influence of 
 the gulf-stream upon the temperature of that part of the ocean 
 which bathes our shores. But there is likewise another cause 
 which undoubtedly contributes to the effect. It has been shown 
 by Mayer and Joule, that heat is generated by the friction of 
 fluids in motion, and the latter experimentalist has established 
 the important physical law, that there is a definite relation 
 between the heat so produced, and the mechanical power ex- 
 pended by the moving mass. Mr. Eankine has applied this 
 principle to explain the fact, observed by M. Eenou, namely, that 
 the temperature of the river Loire at Vendome is higher than that 
 of the air above it ; and it is obvious that a similar explanation 
 is applicable to the phenomenon under consideration. There is 
 no doubt as to the reality of the cause ; the only question is as 
 to the magnitude of the effect to be ascribed to it. That such 
 effect is, at all events, sensible, I infer from two circumstances. 
 The first of these is, that the phenomenon of the excess of sea- 
 temperature appears to be general, and must, therefore, be the 
 effect of some general cause ; the second is, that on the coasts of 
 Ireland there is no sensible difference between the amount of the 
 excess on the eastern and on the ivestern shores. 
 
 Should the effect of this cause be found to be sensible, and its 
 amount be determined, our views of the cycle of meteorological 
 phenomena would be much enlarged. The elevation of tempera- 
 ture rarefies the air ; the denser air flows in to supply the partial 
 vacuum, and wind is produced ; and finally, this wind, both by its 
 own motion, and by that of the ocean which is so subject to its 
 power, restores again the heat which had been converted. Thus the 
 normal condition of temperature is preserved, not only throughout 
 the changes which render it latent and sensible, in the generation 
 and condensation of vapour, but also in its conversion into 
 mechanical power, and its reproduction, in the phenomena of the 
 tempest and of the billowy sea.
 
 ON THE METEOROLOGY OF IRELAND. 343 
 
 BAROMETRIC PRESSURE. 
 
 An attempt* was made to correct the barometric results, by a 
 careful comparison of the several instruments with the Dublin 
 standard, by means of portable barometers, and by the reduction 
 of the results to the sea-level, calculated at the rate of '0011 of an 
 inch for each foot of altitude. These results are, however, incom- 
 plete, no comparisons having been made of the barometers at the 
 four inland stations. For this reason, and also because of the 
 uncertainty attending the comparison of barometers by means of 
 portable instruments, I have thought it necessary to seek th 
 corrections by a comparison of the observed results themselves. I 
 comparisons of this kind, where the stations are widely separate; 
 it seems necessary to employ the means of a somewhat extendt 
 series of observed results, during which the fluctuations of bare 
 metric pressure are small. I have accordingly selected for the 
 purpose the monthly means of May, July, and September, in which 
 months there was but little variation of barometric equilibrium. 
 The defects of the means at each station, compared with those at 
 Dublin, for these months, are given in the following Table, and 
 the last column contains the inferred corrections, which are equal 
 to the mean differences + *021, the added number being the reduc- 
 tion of the Dublin results to the sea-level.
 
 ON THE METEOROLOGY OF IRELAND. 
 
 BAROMETRIC CORRECTIONS. 
 
 Station. 
 
 Defect from Dublin. 
 
 Correction 
 by 
 Comparison. 
 
 May. 
 
 July. 
 
 Sept. 
 
 Portrush, .... 
 
 058 
 
 070 
 
 056 
 
 + 082 
 
 Buncrana, . . . 
 
 120 
 
 100 
 
 088 
 
 + 124 
 
 Donaghadee, . . 
 
 052 
 
 062 
 
 054 
 
 + -077 
 
 Killybegs, . . . -056 
 
 032 
 
 080 
 
 + 077 
 
 Armagh, .... 
 
 252 
 
 257 
 
 248 
 
 + 273 
 
 Killough,. . . . 
 
 058 
 
 054 
 
 068 
 
 + -081 
 
 Markree, .... 
 
 134 
 
 130 
 
 155 
 
 + 161 
 
 Westport, . . . 
 
 046 
 
 058 
 
 114 
 
 + -094 
 
 Dublin, .... 
 
 000 
 
 000 
 
 000 
 
 + 021 
 
 Portarlington, . . 
 Athv, . 
 
 254 
 325 
 022 
 
 268 
 304 
 008 
 
 309 
 317 
 014 
 
 + -298 
 + 336 
 + -036 
 
 Courtown, . . . 
 
 Kilrush, .... 
 
 090 
 
 062 
 
 089 
 
 + 101 
 
 Dunmore, . . . '078 
 
 056 
 
 076 
 
 + -091 
 
 Cahirciveen, . , . 
 
 062 
 
 034 
 
 085 
 
 + 081 
 
 Castletownsend, 
 
 016 
 
 006 
 
 054 
 
 + 046 
 
 Applying the foregoing corrections, we obtain the numbers 
 of the following Table. In order to perceive more clearly the 
 simultaneous variations in the distribution of pressure, I have, in 
 the last four lines of the Table, combined the stations, and their 
 results, into four groups, as hereafter described in treating of the 
 observations of wind-force :
 
 ON THE METEOROLOGY OF IRELAND. 
 
 345 
 
 - ^ " _r
 
 346 ON THE METEOEOLOGY OF IRELAND. 
 
 The phenomena of the distribution of pressure are very clearly 
 shown in the foregoing Table. It will be seen from it that, on the 
 average of the entire year, there is an excess of pressure in the south 
 of the island, and a defect in the north, the minimum being at the 
 north-western extremity. This excess of pressure in the south is 
 shown in the means for the several seasons of summer, autumn, 
 and winter, respectively ; and the cause of it will, I think, here- 
 after appear upon the discussion of the phenomena of storms. In 
 the separate months, the points of greatest and least pressure vary 
 somewhat irregularly ; but they are, in nearly every month, at 
 opposite extremities of the island. Thus, in January, the maxi- 
 mum pressure is in the south-east, and the minimum in the north- 
 west ; and so for the others. This circumstance is what should 
 have been expected d priori ; and it affords satisfactory evidence of 
 the general accuracy of the results themselves. 
 
 DIRECTION AND FORCE OF THE WIND. 
 
 Direction of Wind. The direction of the wind was observed, 
 at most of the stations, by means of the ordinary wind-vane. 
 Much care was taken, not only in placing these instruments 
 truly in azimuth, but also in selecting positions for them which 
 seemed least exposed to eddies or other local irregularities. At 
 Armagh and Dublin the direction of the wind was recorded 
 continuously, by means of self-registering anemometers. 
 
 The following Tables give the number of times, out of 100, in 
 which the wind blew from each of the eight points at the several 
 stations, for the summer and winter half-years respectively, and 
 for the entire year. The winds from the intermediate points, when 
 observed, were divided equally between the two adjacent jmncipal 
 points :
 
 ON THE METEOROLOGY OF IRELAND. 347 
 FREQUENCY OF THE SEVERAL WINDS (SUMMER). 
 
 Station. - * 
 
 N. 
 
 N.E. 
 
 E. 
 
 S.E. 
 
 S. 
 
 S.W. 
 
 w. 
 
 N.W. 
 
 Portrush, . . 
 
 20 
 
 5 
 
 6 
 
 6 
 
 24 
 
 15 
 
 11 
 
 13 
 
 Buncrana, . . 
 
 13 
 
 8 
 
 6 
 
 12 
 
 11 
 
 19 
 
 12 
 
 19 
 
 Donaghad.ee, . 
 
 23 
 
 6 
 
 5 
 
 13 
 
 11 
 
 14 
 
 16 
 
 11 
 
 Killybegs, . . 
 
 15 
 
 9 
 
 14 
 
 7 
 
 8 
 
 13 
 
 21 
 
 14 
 
 Armagh, . . 
 
 12 
 
 9 
 
 7 
 
 6 
 
 16 
 
 19 
 
 18 
 
 15 
 
 Killough, . . 
 
 11 
 
 7 
 
 14 
 
 12 
 
 16 
 
 18 
 
 8 
 
 14 
 
 Markree, . . 
 
 14 
 
 5 
 
 4 
 
 17 
 
 14 
 
 15 
 
 10 
 
 21 
 
 Westport, . . 
 
 10 
 
 10 
 
 14 
 
 10 
 
 3 
 
 3 
 
 32 
 
 19 
 
 Dublin, . . . 
 
 2 
 
 10 
 
 12 
 
 13 
 
 8 
 
 23 
 
 11 
 
 19 
 
 Portarlington, 
 
 5 
 
 28 
 
 2 
 
 11 
 
 7 
 
 14 
 
 13 
 
 21 
 
 Athy, . . . 
 
 13 
 
 1 
 
 2 
 
 12 
 
 16 
 
 12 
 
 25 
 
 19 
 
 Courtown, . . 
 
 13 
 
 17 
 
 5 
 
 7 
 
 8 
 
 23 
 
 15 
 
 13 
 
 Kilrush . . 
 
 12 
 
 10 
 
 14 
 
 8 
 
 8 
 
 13 
 
 19 
 
 17 
 
 Dunmore, . . 
 
 15 
 
 8 
 
 14 
 
 5 
 
 7 
 
 18 
 
 8 
 
 16 
 
 Cahirciveen, . 
 
 11 
 
 9 
 
 12 
 
 9 
 
 12 
 
 18 
 
 16 
 
 14 
 
 Castletownsend, 
 
 8 
 
 9 
 
 11 
 
 12 
 
 2 
 
 37 
 
 15 
 
 6 
 
 FREQUENCY OF THE SEVERAL WINDS (WINTER). 
 
 Station. 
 
 N. 
 
 N.E. 
 
 E. 
 
 S.E. 
 
 S. 
 
 S.W. 
 
 W. 
 
 N.W. 
 
 Portrush, . . 
 
 15 
 
 3 
 
 4 
 
 7 
 
 35 
 
 23 
 
 9 
 
 4 
 
 Buncrana, . . 
 
 10 
 
 5 
 
 5 
 
 10 
 
 15 
 
 27 
 
 15 
 
 13 
 
 Donaghadee, . 
 
 9 
 
 7 
 
 4 
 
 7 
 
 14 
 
 25 
 
 26 
 
 9 
 
 Killybegs, . . 
 
 11 
 
 6 
 
 8 
 
 9 
 
 13 
 
 19 
 
 18 
 
 15 
 
 Armagh, . . 
 
 6 
 
 5 
 
 2 
 
 5 
 
 26 
 
 35 
 
 12 
 
 10 
 
 Killough, .' . 
 
 9 
 
 4 
 
 4 
 
 5 
 
 18 
 
 25 
 
 12 
 
 24 
 
 Markree, . . 
 
 12 
 
 4 
 
 4 
 
 19 
 
 19 
 
 23 
 
 9 
 
 10 
 
 Westport, . . 
 
 13 
 
 4 
 
 12 
 
 10 
 
 6 
 
 8 
 
 26 
 
 21 
 
 Dublin, . . . 
 
 2 
 
 1 
 
 2 
 
 14 
 
 14 
 
 38 
 
 14 
 
 13 
 
 Portarlington, 
 
 5 
 
 11 
 
 1 
 
 4 
 
 10 
 
 19 
 
 20 
 
 30 
 
 Athy, . . . 
 
 7 
 
 2 
 
 1 
 
 15 
 
 28 
 
 11 
 
 23 
 
 13 
 
 Courtown, . . 
 
 7 
 
 5 
 
 4 
 
 4 
 
 18 
 
 23 -'! 
 
 in 
 
 Kilrush, . . 
 
 10 
 
 9 
 
 10 
 
 6 
 
 16 
 
 23 
 
 13 
 
 11 
 
 Dunmore, . . 
 
 16 
 
 4 
 
 3 
 
 5 
 
 1 1 'Jo 
 
 22 
 
 16 
 
 Cahirciveen, . 
 
 8 8 13 
 
 12 
 
 1-J 20 
 
 17 
 
 10 
 
 Castlrtownsoml, 
 
 i:j 5 :$ 
 
 6 
 
 :;.-, 
 
 11 
 
 13
 
 348 
 
 ON THE METEOROLOGY OF IRELAND. 
 
 FREQUENCY OF THE SEVERAL WINDS (YEAR). 
 
 Station. 
 
 N. 
 
 N.E. 
 
 E. 
 
 S.E. 
 
 S. 
 
 S.W. 
 
 W. 
 
 N.W. 
 
 Portrush, . . 
 
 17 
 
 4 
 
 1 
 5 
 
 6 
 
 30 
 
 19 
 
 10 
 
 8 
 
 Buncrana, . . 
 
 12 
 
 7 
 
 6 
 
 11 
 
 13 
 
 23 
 
 14 
 
 16 
 
 Donaghadee, . 
 
 16 
 
 7 
 
 4 
 
 10 
 
 13 
 
 19 
 
 21 
 
 10 
 
 Killybegs, . . 
 
 13 
 
 8 
 
 11 
 
 8 
 
 10 
 
 16 
 
 20 
 
 15 
 
 Armagh, . . 
 
 9 
 
 7 
 
 4 
 
 5 
 
 21 
 
 27 
 
 15 
 
 12 
 
 Killough, . . 
 
 10 
 
 5 
 
 9 
 
 8 
 
 17 
 
 21 
 
 10 
 
 19 
 
 Markree, . . 
 
 13 
 
 4 
 
 4 
 
 18 
 
 17 
 
 19 
 
 10 
 
 16 
 
 "Westport, . . 
 
 11 
 
 7 
 
 13 
 
 10 
 
 4 
 
 5 
 
 29 
 
 20 
 
 Dublin, . . . 
 
 2 
 
 6 
 
 7 
 
 14 
 
 11 
 
 31 
 
 13 
 
 16 
 
 Portarlington, 
 
 5 
 
 19 
 
 1 
 
 7 
 
 9 
 
 16 
 
 16 
 
 25 
 
 Athy, . . . 
 
 10 
 
 2 j 1 
 
 13 
 
 22 
 
 12 
 
 24 
 
 16 
 
 Courtown, . . 
 
 10 
 
 11 1 4 
 
 6 
 
 13 
 
 23 
 
 19 
 
 14 
 
 Kilrush, . . 
 
 11 
 
 9 
 
 12 
 
 7 
 
 12 
 
 18 
 
 16 
 
 16 
 
 Dunmore, . . 
 
 15 
 
 6 
 
 9 
 
 5 
 
 11 
 
 19 
 
 20 
 
 16 
 
 Cahirciveen, . 
 
 9 
 
 8 
 
 13 
 
 10 
 
 12 
 
 19 
 
 17 
 
 12 
 
 Castletownsend 
 
 10 
 
 7 
 
 7 
 
 9 
 
 3 
 
 36 
 
 18 
 
 9 
 
 The following are the mean results for the whole island : 
 
 
 N. 
 
 N. E. 
 
 E. 
 
 S. E. 
 
 s. 
 
 s. w. 
 
 W. 
 
 N. W. 
 
 Summer, 
 
 . 12 
 
 9 
 
 9 
 
 10 
 
 11 
 
 17 
 
 16 
 
 16. 
 
 Winter, 
 
 . 10 
 
 5 
 
 5 
 
 9 
 
 16 
 
 23 
 
 18 
 
 14. 
 
 Year, 
 
 . 11 
 
 7 
 
 7 
 
 9 
 
 14 
 
 20 
 
 17 
 
 15. 
 
 We learn from them that, in the year 1851, the wind blew, on the 
 average of the entire year, most frequently from between S. W. 
 and W., and least frequently from between N. E. and E. The 
 same thing holds also for the summer half-year, the point of maxi- 
 mum frequency being, very nearly, W. 8. W., and that of mininmm 
 frequency E. N. E. In the winter half-year the point of maximum 
 frequency is more nearly S.W., that of the minimum being as 
 before. The ratio of the numbers representing the greatest and 
 least frequency is greater in winter than in summer.
 
 ON THE METEOROLOGY OF IRELAND. 349 
 
 It is not necessary to enter more minutely into the discussion 
 of the numbers of the preceding Tables, as it is probable that the 
 results of a single year, as to the frequency of the several winds, 
 will deviate considerably from the means of several. I may 
 observe, however, that they afford some indications of a law of 
 distribution, depending upon the aspect of the coast. Thus, on 
 comparing the numbers denoting the frequency of any particular 
 wind at the several stations, with their mean for the whole island, 
 it would seem that easterly winds are slightly in excess on the 
 western coast, and westerly winds on the eastern. In other words, 
 there appears to be a preponderating tendency of the wind to blow 
 front the tand, at each place, as compared with the mean of all. It 
 will remain for future inquiry to ascertain whether this holds good 
 in other years, and is, therefore, to be referred to a general law. 
 If so, it is probably the effect of the land and sea breezes, the 
 former preponderating in the average of the winds at 9 A. M. 
 and 9 p. M. 
 
 Pressure of the Wind. For the measurement of the pressure of 
 the wind, a Lind's anemometer was furnished to each station. The 
 difficulty of obtaining accurate results with this little instrument 
 arises, partly, from the smallness of its indications, and, partly, 
 from the oscillations of the fluid in the tube ; the latter are so 
 considerable as to render the instrument of little value, except 
 in the hands of a patient and somewhat practised observer. After 
 some trial, accordingly, it was deemed advisable that the force of 
 the wind should be in all cases estimated, and that the use of Lind's 
 anemometer should be limited to that of furnishing a check upon 
 this estimation in the case of the stronger winds. 
 
 The first thing to be determined, then, was the choice of a 
 scale of force. The scales in use are various : in one of them 
 there are four degrees of wind- force ; in another six ; and in a 
 third (the Admiralty scale) there are ticeke. The last of these 
 appears to be too minute for the ordinary powers of unaided esti- 
 mation, and the first not sufficiently so. The intermediate scale 
 (from to 6) was accordingly adopted ; and it appears to be 
 further recommended by the circumstances, 1, that it is the 
 subdivision most generally used on the Continent; and 2, that, 
 as its numbers represent the same degrees of wind-force with 
 the alternate numbers of the Admiralty scale, the latter are readily
 
 350 ON THE METEOROLOGY OF IRELAND. 
 
 convertible into the former. The six degrees of wind-force were de- 
 signated as follow : 1. Light breeze; 2. Moderate breeze; 3. Strong 
 breeze ; 4. Moderate gale ; 5. Strong gale; 6. Storm. 
 
 In order to know the amount of confidence which may be 
 placed in such observations, it is necessary to determine how far, 
 in respect of accuracy, six degrees of wind- force can be estimated, 
 the observations being supposed to be made by practised observers. 
 And to be able to apply the observations, we must further know 
 what are the pressures and velocities of the wind corresponding 
 to the several terms of the scale. For these purposes I made a 
 somewhat extended series of observations, estimating the force 
 of the wind according to the prescribed scale, and, at the same 
 time, measuring its velocity by means of Robinson's anemometer. 
 The following Table gives the mean results of these observations. 
 The numbers in the first column are the terms of the scale ; those 
 in the second are the corresponding times of 100 revolutions of 
 the instrument, expressed in seconds ;* the third column contains 
 the corresponding velocities of the wind, in feet per second; 
 and the fourth the calculated velocities, deduced as hereafter 
 described. 
 
 * Dr. Robinson has shown (Trans. S. I. A., vol. xxii., p. 167) that the velocity of 
 the wind is to that of the centres of the hemispherical cups, as 3 to 1. But r being 
 the length of the horizontal arms of the instrument, measured to these centres, the 
 circumference of the circle described by them is 2irr ; and if r be expressed in feet, and 
 n be the number of revolutions performed in a second, their velocity is 2*r x n. The 
 corresponding velocity of the wind therefore is V= 6- x . In the instrument in 
 
 my possession the radius is 5-5 inches. Hence 2r = , and substituting for IT its nu- 
 merical value, V= 8-64 x n. 
 
 Instead of noting the number of revolutions, and parts of a revolution, performed 
 in a given time, I have found it convenient to observe the time of performing 100 revo- 
 lutions. I have had the instrument accordingly provided with a little hammer, which 
 is pressed against the registering wheel by a spring, and which, being raised by a pro- 
 jecting pin at one point of its circumference, falls again with a sharp noise when this 
 has passed. The interval between two such strokes of the hammer, therefore, is the 
 time of one whole revolution of the registering wheel, or of 100 revolutions of the 
 arms. Accordingly, a chronometer being held close to the ear, the whole observation 
 effected by the help of that organ. The velocity of the wind in this case is given 
 by the formula V = ~, T being the observed time of 100 revolutions.
 
 ON THE METEOROLOGY OF IRELAND. 
 
 351 
 
 VELOCITIES OF THE WIND CORRESPONDING TO THE TERMS OF THE 
 f SCALE (0-6). 
 
 n 
 
 T 
 
 V (observed). 
 
 F (calculated). 
 
 I. 
 
 71 s 
 
 12 
 
 12 
 
 II. 
 
 35 
 
 25 
 
 23 
 
 III. 
 
 25 
 
 35 
 
 35 
 
 IV. 
 
 20 
 
 43 
 
 46 
 
 V. 
 
 16-8 
 
 51 
 
 58 
 
 YI. 
 
 11-6 
 
 75 
 
 70 
 
 We see that the terms of the estimated scale correspond, nearly, 
 to an arithmetical progression of velocities, and not of pressures. 
 This fact has been already noticed by Dr. Eobinson. 
 
 The common difference in this series, which is equal to its first 
 term, is obtained from the numbers of the third column by means 
 of the formula V = n Fi. The following are the deduced values : 
 I. V, = 12-0. IY. V, = 10-8. 
 
 II. 12-5. Y. 10-2. 
 
 III. 117. VI. 12-5. 
 
 The mean of these values is Fi = 11*6. The calculated values of 
 F, contained in the last column of the foregoing Table, are, accord- 
 ingly, obtained from the formula 
 
 r- 11*6x11; 
 
 their agreement with the observed values is sufficient to establish 
 the assumed law. 
 
 As a verification of the preceding result, I took also a tolerably 
 extended series of measurements of the pressures of the wind, corre- 
 sponding to the highest term of the scale, with Lind's anemometer. 
 Their mean gave 2'06 inches for the reading of the instrument 
 corresponding to that term ; and the corresponding pressure on one 
 square foot of surface, computed in the proportion of 5 -20 pounds 
 to the inch, is 10*7 pounds. Hence, the pressure belonging to the 
 unit of the scale is Pi = 0'30. The corresponding velocity is in- 
 ferred from the formula F 2 = 437 P. Its value is F, = 11 '5; a 
 result which agrees very closely with that already deduced from 
 Robinson's anemometer. 
 
 The results hitherto given rest only on my own estimations ; it 
 remains to POP bow far tlvv accord with those <>f otln-r obsr-r.
 
 352 
 
 ON THE METEOROLOGY OF IRELAND. 
 
 I have selected for this purpose the results of the observations with 
 Lind's anemometer, made at Portrush and Donaghadee by two of 
 the best of the Coast-guard observers, and have placed my own 
 beside them, for comparison. The results, converted into pressures 
 (expressed in pounds on the square foot) are contained in the fol- 
 lowing Table. The numbers in the last column are the calculated 
 pressures, deduced from the formula 
 
 P = Ptf, 
 
 n being the number of the term of the scale, and P 1 ( = 0'30) the 
 pressure corresponding to the first term. 
 
 PRESSURES or THE WIND CORRESPONDING TO THE TERMS or THE 
 
 SCALE (0-6). 
 
 Term. 
 
 Dublin. 
 
 Portrush. 
 
 Donaghadee. 
 
 Calculated. 
 
 I. 
 
 0-5 
 
 0-4 
 
 0-5 
 
 0-3 
 
 11. 
 
 1-3 
 
 1-3 
 
 1-1 
 
 1-2 
 
 III. 
 
 3-0 
 
 2-9 
 
 2-9 
 
 2-7 
 
 IV. 
 
 4-2 
 
 5-3 
 
 5-3 
 
 4-8 
 
 V. 
 
 7-0 
 
 7-3 
 
 7-9 
 
 7-5 
 
 VI. 
 
 10-7 
 
 
 
 
 
 10-8 
 
 It will be seen, that the differences of the corresponding num- 
 bers at the three stations are small, and that their means agree 
 very well with the calculated pressures. It seems, therefore, to be 
 fully proved that the velocity of the wind may be estimated to six 
 degrees, by practised observers, with sufficient accuracy. 
 
 In the following Table are given the results of the observed 
 wind-force for the entire year, and for its two principal divisions. 
 The excess of the force in winter appears at all the stations, ex- 
 cepting Dublin, Portarlington, andAthy.* At these three stations, 
 also, the force of the wind is below the average. 
 
 The mean force for the entire year is 1'76, corresponding to a 
 velocity of 20'4 feet per second. The force is, of course, greater in 
 winter than in summer, the mean force for the winter half-year 
 being 1*87, and that for the summer half-year 1'65. 
 
 * Buncrana is likewise an exceptional case ; hut the exception is there probably due 
 to inaccuracy of observation.
 
 ON THE METEOROLOGY OF IRELAND. 
 
 MEAN FORCE OF THE WIND FOR THE SUMMER AND WINTER 
 HALF-YEARS, AND FOR THE WHOLE YEAR. 
 
 Station. 
 
 Summer. 
 
 "Winter. 
 
 Year. 
 
 Portrush .... 
 
 1'68 
 
 1'85 
 
 1 *77 
 
 Buncrana, 
 Donaghadee, .... 
 Killybegs, 
 Armagh, 
 Killough, 
 
 2-15 
 1-50 
 1-40 
 1-23 
 1-60 
 
 2-15 
 1-82 
 1-75 
 1-78 
 1-92 
 
 2-15 
 1-66 
 1-58 
 1-51 
 1-76 
 
 Markree, 
 Westport, 
 Dublin 
 
 1-68 
 2-20 
 1-33 
 
 1-82 
 2-78 
 1-32 
 
 1-75 
 2-49 
 1*33 
 
 Portarlington, .... 
 Athy 
 
 1-42 
 1-42 
 
 1-27 
 1-20 
 
 1-34 
 1*31 
 
 Courtown, 
 
 1-40 
 
 1-70 
 
 1-55 
 
 Kilrush, 
 
 1-72 
 
 2-02 
 
 1-87 
 
 Dunmore, 
 
 1-88 
 
 2-03 
 
 1-96 
 
 Cahirciveen, .... 
 Castletownsend, . . . 
 
 1-80 
 1-93 
 
 2-17 
 2-38 
 
 1-98 
 2-16 
 
 If, to eliminate local irregularities, we combine the preceding 
 results in groups, according to the arrangement hereafter described, 
 we find the following values for the mean forces of the entire 
 year: 
 
 North-east, . . 1'64. North-west, . . 1-94. 
 
 South-east, . . 1-61. South-west, . . 2-00. 
 
 From this it appears that the mean force of the wind is consider- 
 ably greater in the icest of the island than in the east, the ratio 
 being somewhat greater than that of 1 '2 to 1. There is but little 
 difference between the forces in the northern and southern portions 
 of the island. 
 
 CYCLONIC MOVEMENTS. 
 
 In analyzing the phenomena of rotation, the first step was to 
 note those cases in which the mean directions of the wind, in any 
 two districts, differed by 90, or upwards. It was soon perceived, 
 that no conclusion could be drawn as to a general movement of the 
 atmosphere, when the wind was very moderate, the direction being 
 
 2 A
 
 354 ON THE METEOROLOGY OF IRELAND. 
 
 then greatly influenced by local causes. Accordingly, excluding 
 those cases in which the wind did not exceed a light breeze at most 
 of the stations, the remainder were examined in detail, by laying 
 down the simultaneous directions of the wind upon a series of 
 skeleton charts prepared for the purpose ; and there was no diffi- 
 culty in ascertaining, by the inspection of these charts, the exist- 
 ence or non-existence of rotatory movement. The Fame means 
 sufficed to determine, very nearly, the position of the centre of the 
 vortex at each epoch ; and the places of the centre being thus 
 found, for epochs distant by intervals of twelve hours, the direction 
 and velocity of its progressive movement are ascertained. 
 
 The position of the centre of the vortex at any instant may be 
 determined, more accurately, by calculation. Thus, if y and x 
 denote the distances (in geographical miles) of the place of obser- 
 vation from any assumed central point, measured on the meridian, 
 and on the perpendicular to the meridian, respectively ; ?/ and ^ 
 the corresponding co-ordinates of the centre of the vortex ; and 
 the angle which the direction of the wind at the point (y, x) makes 
 with the meridian, measuring from north to east : 
 
 y - y + (x - a*,) tan = 0, 
 
 the direction of the wind being perpendicular to the line connect- 
 ing the points (y, x) and (y , x ). Now, all the quantities in this 
 equation are given, excepting y n and as a ; so that, if the direction 
 of the wind be accurately known at two stations, the co-ordinates 
 of the centre of the vortex may be completely determined. The 
 irregularities due to local causes, and the errors of observation 
 themselves, forbid this ; and, in order to lessen their influence, it is 
 necessary to know the direction of the wind at several stations. 
 There will then be as many equations of the preceding form as 
 there are places of observation ; and the unknown quantities, ?/ 
 and ar , are to be determined by combining these equations by the 
 method of least squares. 
 
 It is found, that the centre of the vortex is also the point of 
 least barometric pressure, and that the pressure increases regularly 
 with the distance from it. Hence the position of the centre may 
 be inferred from the barometric observations alone. The positions 
 thus determined have been found to coincide in all cases, very 
 nearly, with those deduced from the observed directions of the 
 wind.
 
 ON THE METEOROLOGY OF IRELAND. 3;V> 
 
 The following are the well-marked instances of aerial rotation 
 whichhave -occurred in Ireland in the course of these observations. 
 No case has been included in the enumeration, in which the simul- 
 taneous directions of the wind did not differ, at two points, by at 
 least 90 ; and thus, probably, many cases of cyclonic movement 
 are passed over, in which the centre of the vortex was remote. 
 
 1850. Oct. 6, 7. Cyclone and storm, moving from S.W. to 
 N. E., with a velocity of about 290 geographical miles per diem. 
 (Plate II., figs. 1, 2, 3.) 
 
 Oct. 6, 9 A.M. Centre of the vortex on the south-western 
 coast of Ireland, west of Kilrush. Least pressure at Cahirciveen. 
 Mean velocity of the wind = 25 feet per second ; greatest do. (on 
 the west coast) = 45 feet. The atmosphere at the northern stations 
 unaffected by the vortex at this epoch. 
 
 Oct. 6, 9 P.M. Centre of the vortex over the north of Ireland, 
 a few miles north of Killybegs. Absolute barometric minimum 
 (= 28-836) at Killybegs ; increase of pressure in 100 miles = 0'30 
 inch. Mean velocity of wind = 35 feet per second ; greatest do. 
 (Markree) = 70. Southern stations unaffected by the vortex. 
 
 Oct. 7, 9 A.M. Centre on south-western coast of Scotland. 
 Least pressure at Donaghadee. Mean velocity of wind = 45 feet 
 per second ; greatest do. (north coast) = 60 feet. Hail fell at 
 Markree ; wind amounting to a gale in the north, in the evening 
 of the same day. 
 
 The diameter of the vortex may be estimated with tolerable 
 precision in this case, by measuring from the centre to the limits 
 of the region affected by the movement ; it was about 280 geogra- 
 phical miles. 
 
 Oct. 22, 23. An interesting and instructive case of conflicting 
 currents generating a rotatory movement. The velocity of the 
 wind was uniform throughout the island, and was from 30 to 35 
 feet per second. (Plate II., figs. 4, 5, 6.) 
 
 Oct. 22, 9 P. M. Wind from N. W. in the north of Ireland, 
 and from S. W. in the south-east. The central point of junction 
 of these currents was over the channel, to the north-east of Dublin. 
 Least pressure at Donaghadee. 
 
 Oct. 23, 9 A.M. A distinct rotatory movement, whose centre 
 was a little to the north-east of the point of junction above referred 
 2A2
 
 356 ON THE METEOROLOGY OF IRELAND. 
 
 to, not far from Donaghadee. Least pressure at Donaghadee, as 
 before. 
 
 Oct. 23, 9 P. M. Rotatory movement continued. Centre of 
 vortex had moved from S.W. to N.E., at the rate of about 100 
 miles per diem. Absolute minimum of pressure (=29 -3 60) at Donagh- 
 adee; increase of pressure in 100 miles = O'lO inch. 
 
 Nov. 18, 19. A cyclone, with violent storm, crossing the island 
 from W. S.W. to E.N.E. (Plate III., figs. 1,2,3.) The movement 
 of the centre of the vortex appears to have been curvilinear, and to 
 have varied considerably in velocity. Between 9 p. M. of the 18th, 
 and 9 A.M. of the following day, its path was from S. W. to N. E., 
 and its velocity about 320 miles per diem ; in the succeeding twelve 
 hours its course was nearly from W. to E., with a greatly diminished 
 velocity. The mean velocity of the wind, throughout the storm, 
 was from 45 to 50 feet per second. 
 
 Nov. 18, 9 P. M. Centre of the vortex on the south-western 
 coast, about 30 miles to the north of Cahirciveen. Least pressure 
 at Kilrush. Maximum velocity of wind (in south of island) = 60 
 feet per second. 
 
 Nov. 19, 9 A.M. At this epoch the wind was blowing from N. 
 at Killybegs, and from S. at Donaghadee ; it was blowing from 
 S. E. at Portrush, and from N. W. at Castletownsend ; from 
 S. S. E. at Armagh, and from N. N. W. at Markree. The centre 
 of the vortex was therefore over Ireland at that time, and between 
 the stations above mentioned, its exact position being about 15 
 miles to the west of Armagh. Absolute minimum of pressure 
 (= 28*248) at Armagh ; increase of pressure = 0'31 inch. Maximum 
 velocity of wind (in south) = 65 feet per second. 
 
 Nov. 19, 9 p. M. Centre over the Channel, to the south-east of 
 Donaghadee. Absolute minimum of pressure (= 28*410) at Donagh- 
 adee ; increase of pressure = 0-28 inch. Maximum velocity of wind 
 (in south) = 55 feet per second. 
 
 We have seen that the centre of the vortex was between Armagh 
 and Markree at 9 A.M. of the 19th ; and, as the direction of its 
 progressive movement was not far from the line connecting these 
 places, it must have passed nearly centrally over both. Hence we 
 should expect there the peculiar phenomena the Ml of the wind, 
 and the sudden reversal of its direction which are observed to 
 occur at places in the path of the centre of a cyclone. I shall,
 
 ON THE METEOROLOGY OF IRELAND. 
 
 857 
 
 therefore, briefly describe the series of changes at these two stations. 
 The observations at Armagh are taken from the records of the self- 
 registering anemometer, which were, of course, continuous; those at 
 Markree were made at short intervals. 
 
 At Armagh the wind began to blow at 7 p. M. of the 18th, with 
 a velocity of 32 feet per second. The maximum velocity, with the 
 exception of a short squall* at 5 A. M., occurred at 7 A. M. of the 
 19th, and amounted to 43 feet per second. From this time the 
 wind abated rapidly almost to a calm, its velocity at noon amount- 
 ing only to 6 feet per second ; but at 3 p. M. it rose again, with a 
 velocity of 22 feet. The initial direction of the gale was from the 
 E. S. E. From 9 p. M. on the 18th, to 1 A. M. on the 19th, it veered 
 to S., at which point it continued for several hours, including the 
 period of greatest force of the gale. At 11 A.M. its direction had 
 returned to S. E., and it then suddenly shifted to W. N. W., alter- 
 ing through 160 in 24 minutes. The minimum of pressure took 
 place at ll h 30 m , at the close of this movement; its amount was 
 27-930 inches.f 
 
 At Markree the gale commenced at 4 h 30 m P.M. of the 18th, 
 with a rapidly falling barometer. At 7 P. M. the wind abated to a 
 breeze, the barometer still falling. It recommenced at 10 p. M. 
 
 During the squall, which lasted only three minutes, the velocity reached 90 feet 
 per second. 
 
 t The following are the anemometric observations above referred to. The direction 
 is measured from S. through W. to N. ; the velocity is expressed in miles per hour. 
 On the 19th, from 4 A. M. to 8 A. M., the direction-registering pencil was thrown out of 
 gear, but there appears to have been no change of any magnitude in the interval: 
 
 
 Nov. 18, A.M. 
 
 Nov. 18, P.M. 
 
 Nov. 19, A.M. 
 
 Nov. 19, P.M. 
 
 Hour. 
 
 Vel. 
 
 Dir. 
 
 Vel. 
 
 Dir. 
 
 Vel. 
 
 Dir. 
 
 Vel. 
 
 Dir. 
 
 
 
 12-2 
 
 28-8 
 
 4-8 
 
 212-3 
 
 23-4 
 
 335-2 
 
 4-1 
 
 124-0 
 
 1 
 
 8-3 
 
 28 -2 
 
 5-3 
 
 243 -6 
 
 24-4 
 
 354 -3 
 
 10-5 
 
 104 4 
 
 2 
 
 5-9 
 
 47 '8 
 
 8-7 
 
 276 -2 
 
 22-2 
 
 353 -4 
 
 12-0 
 
 93 9 
 
 3 
 
 7-2 
 
 49 -8 
 
 7-8 
 
 274 -5 
 
 23-6 
 
 345 -6 
 
 15-4 
 
 00 2 
 
 4 
 
 8-1 
 
 48 -1 
 
 14-7 
 
 278 -8 
 
 23-2 
 
 
 
 16-9 
 
 108 8 
 
 5 
 
 3-8 
 
 41 -3 
 
 Hf-1 
 
 281 -7 
 
 25-3 
 
 
 
 13-8 
 
 136 7 
 
 6 
 
 2-9 
 
 76 -0 
 
 16-6 
 
 281 -9 
 
 27-4 
 
 
 
 16-1 
 
 i:;s 3 
 
 7 
 8 
 9 
 
 19 
 11 
 
 3-7 
 1-5 
 2-3 
 4-9 
 5- 
 
 162 -3 
 162 -0 
 212 -4 
 206 -4 
 209 -2 
 
 22-0 
 19-2 
 19-3 
 17-6 
 20-1 
 
 283 -5 
 285 -5 
 282 -1 
 321 -3 
 330 -6 
 
 29-4 
 29-0 
 17-6 
 14-6 
 7-6 
 
 339 -8 
 320 -6 
 324 -5 
 
 16-2 
 16-6 
 15-8 
 9-2 
 11-8 
 
 161 1 
 163 6 
 161 -2 
 147 '6 
 159 -5
 
 358 
 
 ON THE METEOKOLOGY OF IRELAND. 
 
 from the S. E. ; and at 3 A. M. on the 19th it appears to have 
 attained its maximum. At 6 A. M. the wind again abated ; and at 
 7 A. M. there was a calm. The minimum pressure took place at this 
 time, and amounted to 28170 inches. At 9 A. M. the wind rose 
 again from the N. N. W., but not with such force as before ; and 
 in the afternoon there was a strong gale again.* 
 
 From these facts it is evident, that the centre of the vortex 
 passed nearly over Markree at 7 A. M., and over Armagh at ll h 30 m 
 A. M. At Donaghadee, which is nearly in the prolongation of the 
 line connecting the two former places, the wind ceased at 1 P. M., 
 and recommenced at 5 p. M. ; so that the vortex passed nearly cen- 
 trally over this station at about 3 p. M. From these data we learn 
 that the cyclone moved from W. S. W. to E. N. E. ; and that the 
 velocity of the progressive movement was then about 12 miles per 
 hour. 
 
 The dimensions of the vortex may likewise be collected from 
 the same data. The interval between the commencement of the 
 storm, and the passage of the centre, at Armagh, was 16| hours ; 
 and, the velocity being 12 miles an hour, the radius of the vortex 
 
 * The following are the extra observations at Markree above referred to. The 
 numbers in the column headed " Barometer," are the excesses above 28 inches : 
 
 Date. 
 
 Nov. 18. 
 
 Nov. 20, 
 
 Hour. 
 
 Bar. 
 
 Ther. 
 
 Remarks. 
 
 4" 30" 
 6 
 
 1-124 
 1-002 
 
 46 -8 
 48 -8 
 
 Blowing a gale ; storm and rain began about noon. 
 Ditto; rain. 
 
 7 
 8 
 
 0-926 
 0-835 
 
 49 -5 
 50 -5 
 
 Strong breeze ; heavy rain. 
 Ditto ; ditto. 
 
 10 
 
 0-652 
 
 53 -7 
 
 Gale. 
 
 11 
 12 
 
 0-577 
 0-538 
 
 54 -0 
 52 -5 
 
 Wind rising to gale ; mizzling rain. 
 Strong breeze ; ditto. 
 
 3A.M. 
 
 5 
 6 
 
 0-315 
 0-120 
 0-027 
 
 50 -5 
 46 -5 
 45 -5 
 
 Wind higher than at any previous time. 
 Gale ; mizzling rain. 
 Strong breeze. 
 
 7 
 
 0-009 
 
 47 -3 
 
 Calm. 
 
 8 
 
 0-023 
 
 48 -2 
 
 Light breeze ; mizzling rain. 
 
 9 
 
 0-067 
 
 45 -8 
 
 Gale. 
 
 10 
 
 0-124 
 
 46 -0 
 
 Strong breeze ; wind N. N. W. 
 
 3 P.M. 
 
 0-303 
 
 48 -8 
 
 Strong breeze. 
 
 7 
 
 0-483 
 
 49 -5 
 
 Strong gale. 
 
 10 
 11 30 
 
 0-533 
 0-578 
 
 48 -0 
 49 -0 
 
 Gale from N. W. ; light showers. 
 Strong gale. 
 
 10 A.M. 
 
 1-084 
 
 48 -4 
 
 Ditto ; showers. 
 
 11 
 
 1-128 
 
 48 -3 
 
 Ditto. 
 
 1 30 
 
 1-227 
 
 47 -5 
 
 Ditto. 
 
 3 
 
 1-282 
 
 46 -5 
 
 Ditto ; heavy rain. 
 
 5 
 
 1-376 
 
 44 -8 
 
 Moderate gale.
 
 ON THE METEOROLOGY OF IRELAND. 359 
 
 was about 200 miles. The magnitude of the nearly quiescent por- 
 tion of air in the centre of the vortex is better defined. At Armagh 
 the lull lasted from three to four hours ; at Markree three hours ; 
 and at Donaghadee four hours. The diameter of the quiescent 
 central portion was, therefore, about 40 miles. 
 
 We may now refer to some particulars connected with this gale, 
 which appear to merit attention although probably, in the present 
 state of our knowledge on this subject, we should not be justified 
 in offering any suggestions in explanation. 
 
 Among the first of these are the abnormal variations in the 
 rotatory movement, especially along the track of the centre. The 
 most curious of these irregularities is that of the direction. At 
 Armagh this began to change rapidly at 9 p. M. of the 18th. At 
 9 p. M. it was E. S. E. ; at 10 p. M., 8. E. ; at midnight, S. S. E. ; 
 and at 1 A. M. on the 19th, 8. At this latter point it remained for 
 several hours ; and the direction then retrograded through an arc 
 of about 45. At 9 A. M. on the 19th it was S. S. E. ; and at 1 1 A. M. 
 it came back to S. E., after which the sudden shift to W.N.W., 
 already noticed, took place. 
 
 The next point which seems to merit notice is the fact, that the 
 force of the gale was considerably greater to the south of the line 
 of passage of its centre, than on that line itself, or to the north of 
 it. Thus, at Killiney, where I made frequent observations during 
 the gale, I found the maximum velocity to be 80 feet per second ; 
 at Armagh it was little more than half that amount. 
 
 It has been already mentioned that the greatest force of the 
 storm occurred at Armagh and Markree, before the epoch of mini- 
 mum pressure, the interval at both places being about four hours 
 and a half. A similar interval took place at Killiney, but in the 
 opposite direction, the epoch of greatest intensity following that of 
 least pressure by four hours and a half. 
 
 The last point which appears to demand notice is the fact, thai 
 there was a considerable interval between the epochs of the ^-i 
 intensity of the storm at Dublin and at Killiney, places only ten 
 miles apart. The greatest force of the gale, at Dublin, took place 
 between 1 p. M. and 2 p. M. ; at Killiney it occurred between 5 p. M. 
 and 6 p. M. There is a similar interval between the times of mini- 
 mum pressure at the two places, the least height of the barometer 
 occurring later at Killiuey than at Dublin by two or three hours.
 
 360 
 
 ON THE METEOKOLOGY OF IRELAND. 
 
 These differences are probably connected with the difference of 
 altitude of the places of observation. 
 
 1851. Jan. 15, 16. A remarkable case of a double cyclone 
 with storm, and a double minimum of pressure. (Plate III., figs. 
 4, 5, 6.) The first of the two vortices crossed the island from S. 
 to N. on the 15th, and the second traversed the north-western 
 portion of it, from S. W. to N. E., on the following day. The 
 velocity of the former is not well determined ; that of the latter was 
 about 270 miles per diem. The mean velocity of the wind was 
 from 30 to 35 feet per second on the former day, and from 55 to 
 60 on the latter.* 
 
 Jan. 15, A. M. Centre of vortex about 20 or 30 miles south of 
 Dunmore. Absolute minimum of pressure (= 28'718) at Dunmore ; 
 increase of pressure = 0-15 inch. Maximum velocity of wind (west 
 coast) = 60 feet per second. 
 
 Jan. 15, 9 p. M. Centre of vortex appears to have been at this 
 time a few miles north of Buncrana ; the cyclonic movement was, 
 
 * The following extra observations were taken at Markree : 
 
 Date. 
 
 Hour. 
 
 Bar. 
 
 Ther. 
 
 Wind. 
 
 Remarks. 
 
 Jan. 15, 
 
 2 30 
 
 0-786 
 0-832 
 
 42-l 
 41 -5 
 
 N. W. 4 
 
 N. W. 4 
 
 Mizzling rain. 
 Mizzling rain. 
 
 
 4 
 
 0-921 
 
 40 -8 
 
 W.N.W. 4 
 
 Rain. 
 
 
 5 
 
 0-986 
 
 41 -5 
 
 W.N.W. 
 
 Rain. 
 
 
 6 
 10 
 12 5 
 12 17 
 
 1-040 
 1-204 
 1-242 
 1-240 
 
 42 -5 
 37-9 
 34 -4 
 34 -1 
 
 W.N.W. 
 S.W. 
 S.W. 
 S.W. 
 
 Clouds breaking all round- 
 Began to clear at 6 h 30 m . 
 Clouds rising from south-west. 
 
 -Jan. 16, 
 
 1 A.M. 
 
 1-225 
 
 34 -3 
 
 S.W. 
 
 A large halo round moon. 
 
 
 8 30 
 9 
 
 0-776 
 0-751 
 
 42 -0 
 43-7 
 
 S.E. 5 
 S. E. 5 
 
 Mizzling rain. 
 
 
 9 30 
 
 0-726 
 
 45 -5 
 
 S.S.E. 5 
 
 
 
 10 
 
 0-718 
 
 47-2 
 
 S. S. E. 5 
 
 Lind's anemometer = 0*85 inch. 
 
 
 11 
 
 0-668 
 
 49-7 
 
 S. 5 
 
 Wind not as strong as at 10 A.M. 
 
 
 12 
 
 1 P.M. 
 
 0-614 
 0-566 
 
 50 -0 
 51 -5 
 
 S. 4 
 S. 4 
 
 Rain ; rough, with heavy rain. 
 
 
 2 
 9 
 
 0-534 
 0-620 
 
 50 -5 
 46 -8 
 
 S. 4 
 S.W. 5 
 
 Clouds began to break at 1 A.M. 
 
 
 9 30 
 10 
 
 0-661 
 0-715 
 
 46 -7 
 46 -1 
 
 S.W. 5 
 S.W. 5 
 
 Gusts very high occasionally* 
 Lind's anemometer = 0-80 inch. 
 
 
 11 
 
 0-794 
 
 45 -2 
 
 S.W. 4 
 
 
 
 11 30 
 
 0-824 
 
 44 -8 
 
 S.W. 5 
 
 Rain. 
 
 
 12 
 
 0-835 
 
 43 -0 
 
 S.W. 4 
 
 
 Jan. 17, 
 
 1 A.M. 
 
 0-890 
 
 43 -5 
 
 S.W. 4 
 
 
 
 2 
 
 0-920 
 
 42 -7 
 
 S.W. 

 
 ON THE METEOROLOGY OF IRELAND. 361 
 
 however, not distinctly marked, probably owing to the influence of 
 the second cyclone. Least pressure at Buncrana. Velocity of wind 
 uniform throughout the island. 
 
 Jan. 16, 9 A. M. Centre of second vortex to the south-west of 
 Westport. Least pressure at Westport. 
 
 Jan. 16, 9 P.M. Centre about 20 miles west of Buncrana. 
 Absolute minimum of pressure (= 28'671) at Buncrana ; increase of 
 pressure = 0'20 inch. 
 
 Jan. 30, 31. A very interesting cyclone traversing the western 
 portion of the island, in direction from N. to S. nearly, at the rate 
 of about 150 miles per diem. The wind light, the mean velocity 
 being about 20 feet per second. 
 
 Jan. 30, 9 p. M. Centre of vortex over north-western portion 
 of the island, a little to the north of Killybegs. Least pressure at 
 Killybegs. Maximum velocity of wind (in south-west) = 40 feet 
 per second. 
 
 Jan. 31, 9 A. M. Centre a little to the eastward of Westport. 
 Absolute minimum of pressure (=29*032) at Westport ; increase of 
 pressure = 0*10 inch. Maximum velocity of wind (in south-west) 
 = 25 feet per second. Lightning observed in north in evening of 
 this day and day preceding. 
 
 March 18. A cyclone, with storm, traversing the island from 
 S. to N., at the rate of about 200 miles per diem. 
 
 March 18, 9 A. M. Centre of vortex near Markree. Absolute 
 minimum of pressure (= 29 '328) at Armagh ; increase of pressure 
 = 0-10. Mean velocity of the wind = 45 feet per second ; greatest 
 do. (west coast) = 50 feet. 
 
 March 18, 9 p. M. Centre of vortex north of the island. Ab- 
 solute minimum of pressure (= 29-371) at Portrush ; increase of 
 pressure = 0'13 inch. Mean velocity of the wind = 35 feet per 
 second ; greatest do. (north-west) = 50 feet. 
 
 March 19, 9 A. M. Rotatory movement broken up, and wind 
 lessened. Barometer fell, and wind rose again to a gale in the 
 evening ; greatest velocity (north-west) = 65 feet per second. 
 
 March 25. A distinct rotatory movement at 9 A. M. of this 
 dav, the centre of which was ;i liHl<> 1<> tin- north "f
 
 362 ON THE METEOROLOGY OF IRELAND. 
 
 Absolute minimum of pressure (= 29*408) at Westport; increase of 
 pressure = 0'13 inch. The velocity of wind uniform, and about 
 30 feet per second. The wind was very light at the preceding and 
 subsequent observations, so that the progressive movement of the 
 vortex cannot be traced. 
 
 June 11, 12. Cyclone crossing the island from S. W. to N. E., 
 with a velocity of about 260 miles per diem. 
 
 June 11, 9 p. M. Centre of the vortex a little to the west of 
 Cahirciveen. Least pressure at Cahirciveen. Mean velocity of 
 wind = 40 feet per second. 
 
 June 12, 9 A. M. Centre over the island, between Kilrush and 
 Westport. Absolute minimum of pressure (= 29 - 347) at Kilrush ; 
 increase of pressure = 0'04 inch. Mean velocity of wind = 25 feet 
 per second. 
 
 June 12, 9 p. M. Centre over the channel, to the east of Kil- 
 lough. Least pressure at Dublin. Mean velocity of wind = 20 
 feet per second. 
 
 July 27, 28. Cyclone traversing the western coast, in direc- 
 tion from S. S. W. to N. N. E. Velocity of wind = 30 feet per 
 second. 
 
 July 27, 9 A. M. Centre of vortex west of Cahirciveen. Least 
 pressure at Cahirciveen. Greatest velocity of wind in south-west. 
 The wind at the north-eastern stations uninfluenced by the vortex. 
 
 July 27, 9 P. M. Centre south of Westport. Absolute mini- 
 mum of pressure (=29'559) atMarkree ; increase of pressure = (HO 
 inch. Velocity of wind uniform. 
 
 July 28, 9 A. M. General current from S. W. ; mean velocity 
 = 30 feet per second. 
 
 August 23, 24. Well-defined cyclone advancing in a curvili- 
 near path, the movement of the centre being at first from N. W. 
 to S.E., and afterwards from S. W. to N.E. 
 
 Aug. 23, 9 p. M. Centre of the vortex north-west of the island. 
 Least pressure at Buncrana. Mean velocity of wind = 25 feet 
 per second. Lightning along the whole of the eastern coast during 
 the day. 
 
 Aug. 24, 9 A. M. Centre near Armagh. Absolute minimum 
 of pressure (= 29 -439) at Armagh ; increase of pressure = 0-13 inch.
 
 ON THE METEOROLOGY OF IRELAND. 
 
 363 
 
 Mean velocity of wind = 35 feet per second ; greatest do. (south) 
 = 55 feet. The centre of the vortex appears to have passed over 
 Donaghadee about noon. At 9 A. M. the direction of the wind 
 at that place was E. S. E. ; at 12 (noon) W. S. W. ; and at 
 l h 30 m p. M. W. N. W., the shift being accompanied by strong gales 
 and heavy rain. 
 
 Aug. 24, 9 P. M. Centre north-east of the island. Least 
 pressure at Donaghadee. Mean velocity of wind = 25 feet per 
 second. 
 
 September 29, 30. Interesting cyclone and storm, crossing the 
 island from S. S. W. to N. N. E., with a velocity of about 270 
 miles per diem. (Plate IV., figs. 1, 2, 3.) Mean velocity of wind 
 on the 29th = 45 feet per second.* 
 
 Sept. 29, 9 A. M. Centre of vortex off the south-western coast, 
 to the west of Cahirciveen. Force of wind greatest at the same 
 station at 3 A. M. ; but the barometer continued to fall until noon, 
 when the pressure was 28'970. Increase of pressure = 0*22 inch. 
 Greatest velocity of wind (north-west) = 60 feet per second. 
 
 Sept. 29, 9 P. M. Centre over the island, about midway between 
 Kilrush and Dublin. Absolute minimum of pressure (= 29' 030) 
 at Markree ; increase of pressure = 0'12 inch. Least pressure in 
 
 * The following extra observations were taken at Markree : 
 
 Date. 
 
 Hour. 
 
 Bar. 
 
 Ther. 
 
 Wind. 
 
 Remarks. 
 
 Sept. 29, 
 
 7A.M. 
 
 197 
 
 50 -3 
 
 S.E. 5 
 
 Rain; 100 rev. anem. in 29". 
 
 
 8 
 
 169 
 
 51 -1 
 
 S. E. 5 
 
 Ditto. 
 
 
 9 
 
 145 
 
 51 -1 
 
 S.E. 6 
 
 Ditto. 
 
 
 10 
 
 125 
 
 51 -4 
 
 S.E. 5 
 
 Ditto ; 100 rev. anem. in 29 1 . 
 
 
 11 
 
 '111 
 
 52-7 
 
 S.E. 6 
 
 Ditto. 
 
 
 12 
 
 070 
 
 64 -2 
 
 S.E. 5 
 
 Ditto. 
 
 
 IP.M. 
 
 059 
 
 55 -0 
 
 S.E. 5 
 
 Ditto. 
 
 
 3 
 
 0-998 
 
 66-2 
 
 S.E. 
 
 Ditto. 
 
 
 5 
 
 0-955 
 
 55 -3 
 
 E. 
 
 Ditto. 
 
 
 7 
 
 0-932 
 
 55 -0 
 
 E. 
 
 Ditto. 
 
 
 10 
 
 0-869 
 
 55 -0 
 
 N.E. 
 
 100 rev. anem. in 164' ; aurora. 
 
 Sept. 30, 
 
 7 A.M. 
 
 0-952 
 
 55 -0 
 
 W. 
 
 A little rain. 
 
 
 8 
 
 0-979 
 
 54 -4 
 
 W.N.W. 
 
 Mizzling rain. 
 
 
 10 
 
 0-948 
 
 64 -0 
 
 W. 4 
 
 
 
 11 
 
 1-062 
 
 54 -2 
 
 W.S.W. 4 
 
 
 
 11 P.M. 
 
 0-833 
 
 50 -2 
 
 S.E. 5 
 
 
 
 12 
 
 0-801 
 
 50 -2 
 
 S.E. 5 
 
 
 Oct. 1, 
 
 1 A.M. 
 
 0-752 
 
 51 -0 
 
 S.E. 5 
 
 
 
 i 
 
 0-700 
 
 61 -0 
 
 S.E. 4 

 
 364 ON THE METEOROLOGY OF IRELAND. 
 
 south-east at 6 p. M. Greatest velocity of wind (north-east) = 55 
 feet per second. 
 
 Sept. 30, 9 A. M. Centre near Malin Head, at northern ex- 
 tremity of the island. Absolute minimum of pressure (= 29*020) 
 at Portrush ; increase of pressure = 015 inch. Mean velocity of 
 wind = 35 feet per second ; greatest do. (north-west) = 55 feet. 
 
 Sept. 30, Oct. 1. Cyclone moving apparently in curvilinear 
 path, its course being at first from W. to B., until it reached the 
 centre of the island, and afterwards from S. S. W. to N. N. E. 
 Mean velocity of wind between 25 and 30 feet per second. 
 
 Sept. 30, 9 p. M. General southerly current. Centre of vortex 
 to the west of the island ; least pressure on west coast. Greatest 
 velocity of wind (on west coast) = 45 feet per second. 
 
 Oct. 1, 9 A. M. Centre of vortex over the island, between Kil- 
 rush and Courtown. Absolute minimum of pressure (= 28'838) 
 equally distant from Dublin, Courtown, and Dunmore. Northern 
 stations beginning to be affected by vortex. Greatest velocity of 
 wind (north-east) = 50 feet per second. 
 
 Oct. 1, 9 p. M. Centre north of Portrush. Absolute minimum 
 of pressure (= 28'853) at Portrush ; increase of pressure = 0'09 inch. 
 At Donaghadee a sudden shift of the wind from S. S. E. to "W.took 
 place at 4 h 30 m P.M. 
 
 Oct. 4, 5. Distinct cyclone moving fromW.S.W. to E.N.E., 
 and passing over (or near) the northern extremity of the island. 
 (Plate IV., figs. 4, 5, 6.) Mean velocity of wind = 35 feet per second. 
 General electrical disturbance. 
 
 Oct. 4, 9 A. M. General current from S. W. ; centre of vortex 
 north-west of the island. Greatest velocity of wind (on west coast) 
 = 45 feet per second. 
 
 Oct 4, 9 p. M. Centre close to northern extremity of the island. 
 Absolute minimum of pressure (= 29-182) at Portrush ; increase of 
 pressure = Oil inch. Greatest velocity of wind (north-west) = 55 
 feet per second. 
 
 Oct. 5, 9 A. M. Centre north of the island ; least pressure at 
 Portrush. Greatest velocity of wind (in the north) = 60 feet per 
 second.
 
 ON THE METEOROLOGY OF IRELAND. 365 
 
 From the facts above stated, we may draw the following general 
 conclusions : 
 
 1. The occurrence of cyclonic movements in the atmosphere is 
 not infrequent in Ireland, and may be traced even in the case of 
 moderate winds. 
 
 2. The rotatory movement is invariably in the same direction, 
 namely, that opposite to the diurnal movement of the sun in 
 azimuth. 
 
 3. This rotation is always accompanied by a considerable dis- 
 turbance of barometric equilibrium, which is greater in proportion 
 to the velocity of the rotatory movement, the pressure being a mi- 
 nimum at the centre of the vortex, and increasing regularly with 
 the distance from that point. 
 
 4. The place of greatest velocity appears to have no very defi- 
 nite relation to that of the centre of the vortex, sometimes nearly 
 coinciding with it, and at others being situated in front, or in the 
 rear, on the right hand, or on the left, of the centre.* 
 
 5. The vortex itself has a progressive movement, at the rate of 
 from 100 to 300 miles per diem, the average velocity of those 
 observed being 220 miles per diem. The direction of this movement 
 in Ireland is generally from S. W. to N. E. 
 
 6. If a line be drawn through the centre of Ireland, in the 
 direction from S. W. to N. E., the track of the centres of by far 
 the greater number of the cyclones, passing over or near Ireland, 
 lies to the north of that line. 
 
 7. There is reason to conclude, that these rotatory movements 
 are caused by the conflict of two rectilinear currents moving in dif- 
 ferent directions. 
 
 STORMS. 
 
 For the purpose of eliminating local irregularities, and (to a 
 certain extent also) inequalities of estimation, I have, in examining 
 the distribution of the higher winds, combined the stations into 
 four groups, omitting Portrush and Buncrana, which lie somewhat 
 apart. These groups are as follow : 
 
 I. NORTH-EASTERN. Donaghadee, Killough, Armagh. Mean 
 latitude = 54 24'; mean longitude = 5 57'. 
 
 In the remarkable cyclone of November 18, 19, 1850, the wind raged with 
 greatest violence on the right hand of the centre (looking in the direction of the pro- 
 gressive movement) ; and this appears to be the case of most frequent occurrence.
 
 366 ON THE METEOROLOGY OF IRELAND. 
 
 II. NORTH-WESTERN. Killybegs, Markree, Westport. Mean 
 latitude = 54 13'; mean longitude = 8 51'. 
 
 III. SOUTH-EASTERN. Dublin, Courtown, Dunmore. Mean 
 latitude = 52 43' ; mean longitude = 6 29'. 
 
 IV. SOUTH-WESTERN. Kilrush, Cahirciveen, Castletownsend. 
 Mean latitude = 52 2', mean longitude = 9 37'. 
 
 The line joining groups I. and IV. lies, almost exactly, N. E. 
 and S. W. ; and that joining groups II. and III., N. W. and S. E. 
 
 The following are the numbers of times in which the average 
 force of the wind, in each of these groups, amounted to a strong 
 breeze : or the average velocity to 35 feet per second, and upwards : 
 
 NUMBER OF TIMES IN WHICH THE VELOCITY OF THE WIND WAS 
 35 FEET PER SECOND AND UPWARDS. 
 
 Month. 
 
 North-East 
 
 North-West, South-East 
 
 South- West 
 
 
 
 ! 
 
 
 January, .... 
 
 18 
 
 19 
 
 13 
 
 29 
 
 February, . . . 
 
 7 
 
 15 
 
 10 
 
 13 
 
 March, .... 
 
 5 
 
 15 4 
 
 14 
 
 April 
 
 3 
 
 11 3 
 
 12 
 
 May 
 
 2 
 
 10 
 
 j 
 
 
 June, 
 
 2 
 
 15 
 
 5 
 
 10 
 
 July 
 
 3 
 
 9 
 
 4 
 
 
 August, .... 
 
 
 
 9 
 
 3 
 
 7 
 
 September, . . . 
 
 2 
 
 11 
 
 3 
 
 6 
 
 October, .... 
 
 3 
 
 21 
 
 4 
 
 17 
 
 November, . . . 
 
 
 
 14 
 
 1 
 
 6 
 
 December, . . . 
 
 3 
 
 9 
 
 9 
 
 14 
 
 Spring, .... 
 
 10 
 
 36 
 
 8 
 
 30 
 
 Summer, .... 
 
 5 
 
 33 
 
 12 
 
 26 
 
 Autumn, .... 
 
 -. 5 
 
 46 
 
 8 
 
 29 
 
 Winter, .... 
 
 28 
 
 43 
 
 32 
 
 56 
 
 Year, 
 
 48 
 
 Io8 
 
 60 
 
 141
 
 ON THE METEOROLOGY OF IRELAM). f 'J07 
 
 From the foregoing numbers it appears, that high winds are 
 much more frequent on the western than on the eastern coast, the 
 numbers denoting the relative frequency, on the average of the 
 entire year, being nearly as 3 to 1. This preponderance of high 
 winds on the western coast holds at all seasons of the year, the 
 maximum occurring at the north-western extremity in autumn, and 
 at the south-western in winter. The greatest frequency is in the 
 north-west, on the average of the entire year. 
 
 The following are the cases in which the mean force of the 
 wind, over the whole island, amounted to a gale ; or in which the 
 mean velocity was 45 feet per second and upwards : 
 
 Nov. 23, 24, 1850. Storm along the western coast, blowing at 
 first from S. S. W., and veering through S.W. to W. Least pressure 
 in north-west throughout. 
 
 Nov. 23, 9 p. M. Storm began at south-western extremity of the 
 island ; velocity = 45 feet per second. 
 
 Nov. 24, 9 A. M. Wind continued to blow in same district ; 
 velocity increased to 60 feet per second. Absolute barometric mi- 
 nimum (north-west) = 28*644. 
 
 Nov. 24, 9 P. M. Storm extended over whole of western coast ; 
 velocity of wind = 55 feet per second. 
 
 Dec. 14. Storm affecting the whole island, but chiefly the 
 western coast. Wind at first from S. S. W., but veering to W. S.W. 
 at 9 p. M. Least pressure in north-west throughout. Electrical 
 disturbance over the whole island. 
 
 Dec. 14, 9 A. M. Velocity on western coast = 65 feet per 
 second. Absolute barometric minimum (north-west) = 28*952. 
 
 Dec. 14, 9 P. M. Velocity on western coast = 50 feet per 
 second. 
 
 Dec. 31, Jan. 1, 1851. Storm from S. W. and S., beginning 
 on western coast, and extending over the whole island. 
 
 Dec. 31, 9 A.M. Velocity on western coast = 50 feet per 
 second. Direction S. S. W. and S. W. 
 
 Dec. 31, 9 P.M. Gale affecting the whole island, except north- 
 eastern extremity. Greatest in south-west ; velocity = 60 feet per 
 second. Direction as before. Absolute barometric minimum 
 (north) = 29177.
 
 308 ON THE METEOROLOGY OF IRELAND. 
 
 Jan. 1, 9 A. M. Wind abated. 
 
 Jan. 1, 9 P.M. Gale from S. W. and S. over the whole island, 
 except north-western extremity. Velocity (south-east) = 55 feet per 
 second. Absolute barometric minimum (north) = 28*975. 
 
 In this case, therefore, there were two storms succeeding each 
 other on consecutive days, with a double fall of the barometer. 
 The direction of the wind on Jan. 1, 9 P.M. was remarkable. The 
 prevailing current was from S. W., and extended over the central 
 parts of the island ; while there appears to have been an indraught 
 towards it, from the north-western and south-eastern quarters. 
 
 Jan. 12, 13. Storm from S. andS. W., beginning in the north* 
 west, and advancing in the direction from N. W. to S. E. Velocity 
 of wind = 60 feet per second. Least pressure in north-west 
 throughout. 
 
 Jan. 12, 9 P.M. Gale in north-west. 
 
 Jan. 13, 9 A.M. Storm advanced to line joining north-east and 
 south-west centres. Absolute barometric minimum (north-west) 
 = 29' 174 ; pressure least at Markree at noon. 
 
 Jan. 27. Storm from S. and S. W. in the afternoon of this 
 day, chiefly along the western coast. Velocity of wind = 55 feet 
 per second. Absolute barometric minimum (north-west) = 29'309. 
 
 June 15, 16. Gale from S. W. and W., on the western coast. 
 
 June 15, 9 A. M. Wind from S. W. Velocity on western coast 
 = 50 feet per second. Least pressure in north-west. 
 
 June 15, 9 P.M. Velocity = 45 feet per second. Absolute 
 barometric minimum (north) = 29'575. 
 
 June 16, 9 A. M. Wind from W. Velocity = 50 feet per 
 second. 
 
 July 13, 14. Storm chiefly in north-west, blowing at first 
 from S. S.W. and veering through S. W. to W. This appears 
 to have been a cyclonic gale, the centre of the cyclone passing to 
 the north of the island ; it is not included in the former series on 
 account of this circumstance. The velocity of the wind was greatest 
 in the north-west throughout ; the barometric pressure was least
 
 ON THE METEOROLOGY OF IRELAND. 869 
 
 in the north-.west on the 13th, and in the north-east on the fol- 
 lowing day. 
 
 July 13, 9 A. M. Storm from S. S. W., in the north-west of the 
 island. Velocity = 60 feet per second. 
 
 July 13, 9 p. M. Gale veered to S. W., and affected a large 
 portion of the island. Velocity of wind = 60 feet per second, as 
 before. Absolute barometric minimum = 29-052. 
 
 July 14, 9 A. M. Wind veered to W. Velocity in north-west 
 increased to 65 feet per second. 
 
 Dec. 7. Storm began in south-western extremity of the island, 
 and extended thence over the whole. Direction of wind between 
 S. and S. W. 
 
 Dec. 7, 9 A. M. Gale from S. S. W. in the south-west. 
 
 Dec. 7, 9 p. M. Storm over the whole island. Greatest velocity 
 and least pressure in north-west. Velocity = 70 feet per second. 
 Absolute barometric minimum = 29*267. At Cahirciveen the baro- 
 meter fell until 7 p. M. ; and the wind shifted from S. to W. at the 
 same time. 
 
 Dec. 9. Storm from S. W. along the western coast. Least 
 pressure in north-west throughout. 
 
 Dec. 9, 9 A. M. Velocity of wind in west = 50 feet per se- 
 cond. 
 
 Dec. 9, 9 P. M. Velocity = 60 feet per second. Absolute baro- 
 metric minimum = 29-632. 
 
 Dec. 20. Gale blowing from S. S. "W., beginning on western 
 coast, and advancing to eastern. Least pressure in north and 
 north- west. 
 
 Dec. 20, 9 A. M. Gale on west coast. Velocity = 55 feet per 
 second. 
 
 Dec. 20, 9 P.M. Gale transferred to east-coast. Velocity = 50 
 feet per second. Absolute barometric minimum (north) = 29--l~>7. 
 At Markree there was a sudden shift of the wind from S. S. W. 
 to N. W. at 7 h 35 m p. M. 
 
 From the foregoing facts we may draw the following general 
 conclusions : 
 
 1. The greater gales are much more frequent on the western,
 
 370 ON THE METEOROLOGY OF IRELAND. 
 
 than on the eastern coast, the numbers denoting the relative fre- 
 quency being nearly as 5 to 1. The frequency of storms is nearly 
 the same in the northern and southern portions of the island. 
 
 2. The direction of the wind, in all the cases enumerated, was 
 between S. and W. In about half of these cases the wind blew, 
 throughout, from the same point ; in half it veered from 4 to G 
 points of the compass, the veering being in the direction produced 
 by a cyclone moving from S. W. to N. E., and having the path of 
 its centre to the north of the island. 
 
 3. The axis of the gale is in some cases transferred parallel to 
 itself, to the eastward. Remarkable instances of this movement 
 occur in the gales of January 12, 13, and December 20. 
 
 4. The least barometric pressure occurs, in almost every instance, 
 in the north-western quarter of the island.* 
 
 5. The locality of the highest wind sometimes coincides with that 
 of least pressure, and sometimes does not. In the latter case, the 
 axis of least pressure is generally to the westward of the axis of the 
 storm. 
 
 6. On either side of the axis of a storm, the wind appears to 
 blow towards that line. A remarkable instance of this phenomenon 
 occurred in the storm of January l.f 
 
 We are now in a position to consider the question, whether all 
 storms are cyclonic ? and if not, what proportion do rotatory storms 
 bear to the whole ? Of the greater storms which have occurred 
 since the commencement of these observations, the rotatory charac- 
 ter of five those of October 6, 1850, November 18, January 15, 
 1851, March 18, and September 29 has been completely established. 
 We have seen in this section, that the same character may be pre- 
 dicated, with great probability, of five more ; while there remain five 
 in which the wind has blown, throughout, in the same direction. 
 In fifteen months, accordingly, there have occurred fifteen storms, 
 of which two-thirds were cyclonic. As respects the remaining one- 
 third, the phenomena are characterized, not only by the absence of 
 any veering of the wind, but also by the fact, that the pressures 
 
 * In one case only, the locality of least pressure shifted from the north-western to 
 the north-eastern extremity of the island. This is consistent with the supposition, that, 
 the storm in question was a cyclone, whose centre had a progressive motion eastward. 
 
 t The conclusions numbered 3, 5, 6, have already been drawn by Mr. Espy, from 
 an examination of the storms in the United States in the early months of the votr 
 18-13. Fir at Report on Metioro'.ogy.
 
 ON THE METEOROLOGY OF IRELAND. ,371 
 
 appear to increase with the distance from a line or axis of minimum 
 pressure, rather than from a point ; or, in other words, that the 
 iwbaric lines are parallel right lines, instead of concentric circles. 
 It is true that these facts are by no means decisive in disproving 
 rotatory movement ; for they are consistent with a rotation of the 
 wind in a plane perpendicular, or highly inclined, to the horizon. 
 Still we are perhaps not justified in assuming the existence of a 
 rotation of this kind, without further evidence ; and it seems more 
 reasonable, in the present state of our knowledge, to admit two dif- 
 ferent kinds of winds, than to endeavour to reduce all to one by 
 the help of a gratuitous hypothesis. 
 
 Hourly Observations. It has been already stated, that hourly 
 observations were appointed to be made during twenty- four conse- 
 cutive hours, at the equinoxes and solstices, in the hope that their 
 results might throw light upon the simultaneous atmospheric 
 changes occurring over the island, and especially upon the direc- 
 tion and rate of progress of atmospheric waves. The results of the 
 observations on the first two of these term-days March 21, and 
 June 21 are here given. During the two latter September 22 
 jmd December 22 no atmospheric change of a marked kind 
 occurred. 
 
 March 21. A gale occurred on this day, accompanied by a 
 marked barometric depression. The minimum of pressure took 
 place during the observations, the time of its occurrence varying 
 considerably at the different stations. At Cahirciveen, there was 
 a sudden fall of the barometer between 9 A. M. and 10 A. M., fol- 
 lowed by a sudden rise between 12 and 1 P. M., the mercury being 
 nearly stationary from 10 A. M. to 12. A similar change took 
 place at Dunmore East, and at the same hours. For these two 
 stations, accordingly, the epoch of minimum pressure may be taken 
 to be 11 A.M. ; the subsequent changes were small and irregular. 
 At Courtown, the barometer descended very slowly and gradually 
 until 5 p. M. ; it then ascended until 10 p. M., after which it de- 
 scended again. All the changes were, however, very small. 
 
 At the northern stations the fall of the barometer was more 
 considerable, and more regular. At Markree, where it was most 
 rapid, it amounted to 0*210 in 6 hours. The minimum at Markree 
 occurred between 3 P. M. and 4 P. M. ; at Armagh, the minimum 
 took place at 6 p. M. ; and at Portrush, at 8 p. M. 
 
 2 B2
 
 372 ON THE METEOROLOGY OF IRELAND. 
 
 From these results it would appear that the trough of the wave 
 travelled from south to north, nearly, with a velocity of about 22 
 miles per hour. The barometric depression was greatest at Markree, 
 where the barometer stood at 28'689, when lowest. The lowest 
 pressure increased from that point in the south-easterly direction, 
 being 28-972 at Dunmore. 
 
 At Markree the wind shifted from S. S. E. to S. S. "W. at the 
 time of greatest depression. The same phenomenon took place at 
 Armagh and Portrush, although not with such precision; the 
 change of direction at the former station being from S. S. E. to S., 
 and at the latter from S. E. to S. No similar change occurred at 
 the southern stations. 
 
 The foregoing phenomena are not necessarily to be ascribed to 
 the transit of a rectilinear wave. They are all consistent with the 
 effects of a cyclone, coming from the S. or S. W., the track of its 
 centre lying to the west of the island. 
 
 June 21, 22. The changes of the direction and of the pressure 
 of the wind, on these days, are manifestly the effects of a cyclonic 
 movement, the centre of the vortex sweeping round the north coast 
 of Ireland, in a somewhat curvilinear path, from west to east. It 
 has not been included in the former series, the force of the wind 
 having been below the limit there adopted. At 9 A. M. of the 21st, 
 the centre of the vortex was off the north-west coast, to the west 
 of Killybegs. At 9 p. M. of the same day it had arrived to the 
 north of Portrush ; and at 9 A. M. of the 22nd it was to the north- 
 east of Donaghadee. 
 
 The veering of the wind was, on the average, about 90; its 
 duration was very different at the different stations, being shortest 
 for those near the path of the centre of the vortex, and longest for- 
 t-hose remote. The wind, which was very light throughout, fell 
 about the time of veering at most of the stations. 
 
 The descent and subsequent rise of the barometer were regular, 
 and the minimum well-defined. The time of least pressure coin- 
 cided at all the stations, very nearly, with the middle of the time 
 of veering of the wind ; it was earliest on the western coast, and 
 latest on the eastern, the epoch of its occurrence being between 12 
 and 1 P. M. at Markree and Cahirciveen, and between 5 p. M. and 
 6 p. M. at Dublin and Courtown. The barometric depression was 
 small, the mean pressure at the epoch of minimum being 29 '74.
 
 ON THE METEOROLOGY OF IRELAND. 373 
 
 HUMIDITY OF THE AIR. 
 
 The first two of the Tables which follow give the results of 
 the psychrometrical observations. The first contains the monthly 
 means of the tension of vapour at the several stations, calculated by 
 iiegnault's Table ; and the second the corresponding values of the 
 relative humidity, the state of saturation being represented by 100. 
 
 Very few results of a general nature can be drawn from these 
 observations, the distribution of vapour being governed by the 
 proximity of the station to the sea, or by other local circumstances. 
 It will be seen, from the last column of the first Table, that the 
 yearly mean tension of vapour increases, although not in any 
 regular progression, in proceeding from the north to the south of 
 the island. Its mean value for the entire island is 0*326 of an 
 inch ; its greatest value (at Westport) is 0'374. 
 
 The distribution of humidity is still more under the influence of 
 local circumstances, and therefore still less regular. Thus, Portrush 
 and Castletownsend the one at the northern, the other at the 
 southern extremity of the island have nearly the same mean 
 humidity ; while Portarlington and Athy places near each other, 
 and both inland are almost at the opposite extremities of the 
 .scale. The driest station is Portarlington; the most humid. 
 Westport. At the latter place, in fact, the air is nearly saturated 
 with moisture, the place of observation being entirely surrounded 
 by water, and but a few feet above the sea. The mean humidity 
 for the entire island, for the year 1851, is 87. 
 
 EAIN. 
 
 Before proceeding to the observations of rain-fall throughout 
 Ireland in the year 1851, it is important that we should know its 
 normal amount at one or more stations, as deduced from the mean 
 of several years. We have, for this purpose, two series of obser- 
 vations, one at Dublin, and the other at Armagh, extending 
 uninterruptedly over eleven and twelve years respectively. The 
 results of these two series are contained in the third and fourth of 
 the following Tables. 
 
 The lowest line in each gives the mean monthly fall of rain. 
 It will be seen, from an inspection of the numbers, that there is
 
 ;J74 ON THE METEOROLOGY OF IRELAND. 
 
 110 regular progression in the amount of rain-fall throughout the 
 year, such as is observed in the phenomena of temperature or 
 humidity. In Dublin the greatest rain-fall, in the mean of the 
 eleven years, occurs in October, and the least in February ; their 
 amounts are 3 '34 and 1'74 inches respectively. At Armagh the 
 maximum is in January, and the minimum in May; and they 
 amount to 375 and 215 inches. 
 
 The fifth and last Table gives the monthly fall of rain in the 
 year 1851, at all the meteorological stations. 
 
 It will be seen that the greatest diversity exists in the amount 
 of rain-fall in different localities. To render this more apparent, 
 ;md to facilitate the examination of the causes which influence the 
 distribution, I have, in the following Table, given the yearly rain- 
 fall at the several stations arranged in the order of magnitude, 
 beginning with the smallest : 
 
 TOTAL RAIN-FALL IN THE YEAR 1851, AT THE SEVERAL 
 METEOROLOGICAL STATIONS. 
 
 20-25 inches ( Portarlington, .... 21-23 inches. 
 
 (KiUough, ..... 23-19 
 /Dublin, ...... 26-40 
 
 25-30 
 
 j Donaghadee, .... 27-93 ,, 
 
 \ Courtown, ..... 29-64 
 
 /Kilrush, ...... 32-58 
 
 30-35 \ Armagh, ...... 33-05 
 
 j Killybegs, ..... 33-20 
 
 \Dumnore, ..... 33-54 
 
 35-^0 . j Por tsh, ..... 37-24 
 
 ( Buncrana, ..... 39-28 ,, 
 
 40-45 jMarkree, ...... 40-31 ,.. 
 
 ( Castletownsend, . . . 42-53 
 
 4550 ,, .... Westport, ..... 45-86 
 
 50 60 .... Cahirciveeu, .... 59-37 
 
 Thus, the greatest rain (at Cahirciveen) is nearly treble of the 
 least (at Portarlington). The mean rain-fall throughout Ireland, 
 in the year 1851, was 34'50 inches. 
 
 If we assume the proportion of rain at the different stations to 
 be constant, or nearly so, the numbers of the preceding Table may
 
 ON THE METEOROLOGY OF IRELAND. 375 
 
 all be reduced to their mean values, by multiplying by the factor 
 which expresses the relation of the rain of 1851 to the mean at 
 any one station. We already possess two such mean values : viz., 
 at Armagh and Dublin. They are 29'14 and 34'68 inches re- 
 spectively ; and the factors thence deduced are T10 and 1'05. 
 
 When we examine the results of the preceding Table, taken in 
 connexion with the geographical position and physical circum- 
 stances of the stations, we arrive at the following conclusions : 
 
 1. The places of least rain are either inland, or on the eastern 
 coast ; while those of greatest rain are at, or near, the western 
 coast. Thus the stations at which the yearly fall of rain exceeds 
 40 inches are all on the western and south-western coasts ; while 
 those at which it is below 30 inches are either inland or on the 
 eastern. 
 
 2. The amount of rain is greatly dependent on the proximity 
 of a mountain chain or group, being always considerable in such 
 neighbourhood, unless the station be to the east or north-east of 
 the same. Thus, of the places of least rain, Portarlington lies to 
 the north-east of Slieve-bloom ; Killough, to the north-east of the 
 Mourne range ; Dublin, to the north-east of the Dublin and 
 Wicklow range ; while, on the other hand, the places of greatest 
 rain Cahirciveen, Westport, and Castletownsend are in the 
 vicinity of high mountains, but on a different side. 
 
 These facts are easily explained. The prevailing wind blows 
 from the S. W., and reaches this island loaded with the vapour of 
 the Grulf-Stream. This vapour is condensed and precipitated in 
 rain, when it first meets the colder air over the land, namely, on 
 the western and south-western shores. But the principal con- 
 densing centres are the mountains, in the neighbourhood of which, 
 consequently, the precipitation is more abundant, especially on 
 their western and south-western sides. And the same circumstance 
 which causes the greater precipitation at these points must al> 
 protect the region over which the wind next passes (the north-east), 
 the air being thus deprived of a large portion of its vapour before 
 arriving there. 
 
 NOTE A few of the latter Tables of this Paper, aa originally printed, hare been 
 omitted here as unnecessary.
 
 376 
 
 ON THE METEOROLOGY OF IRELAND. 
 
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 ON THE METEOROLOGY OF IRELAND. 
 
 1 
 
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 THE METEOROLOGY OF IRELAND.
 
 THE METEOROLOGY OF IRELAND. 
 
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 THE METEOROLOGY OF IRELAND. 

 
 THE METEOROLOGY OF IRELAND. 
 
 
 .nt.Gu-.im
 
 XVIII. THE CLIMATE OF IRELAND, AND THE CURRENTS 
 OF THE ATLANTIC. 
 
 Lecture delivered before the Dublin Young Men's Christian Association, Oct. 25th, 1865. 
 
 IT is an old remark of Dr. Johnson, that " when two Englishmen 
 meet, their first talk is of the weather ; they are in haste to tell 
 each other, what each must already know, that it is hot or cold, 
 bright or cloudy, windy or calm." And he ascribes this to the 
 variability of our climate, and to the hopes and apprehensions 
 Avhich constant change is sure to engender ; for we naturally 
 congratulate or condole with one another, according as the. one 
 or the other is realized. 
 
 Now although in this climate the state of the weather from 
 day to day is so changeable as almost to baffle the power of 
 anticipation, there are yet mean laws, and average results, which 
 we obtain from systematic observation, followed throughout long 
 periods, and which teach us what, in the long run, we may expect. 
 To some of the more important of these laws, especially in their 
 bearing on our own climate, I propose to invite your attention 
 this evening ; and I trust you will bear with me if, in a subject 
 adapted to instruction rather than amusement, I am obliged to 
 enter occasionally into what some may consider dry details. 
 
 I need not tell you, that the existence, and the continued 
 support, of animal and vegetable life, are dependent upon solar 
 heat. If the sun were extinguished, a few hours would suffice to 
 voduce our globe to a frozen and unchanging mass, and to destroy 
 ji.ll living beings on its surface. It has been calculated that the 
 amount of heat received by the earth from the sun in the course
 
 382 THE CLIMATE OF IRELAND, AND 
 
 of a year is such as would suffice to melt a coating of ice, covering 
 the whole glohe, and 101 feet in thickness. This great amount is, 
 however, very unequally distributed. The heating power of the 
 sim's rays depends, according to a very simple law, on their 
 ohliquity; but an elaborate analysis is required to calculate 
 the total quantity of heat received, during any given time, at a 
 given place. This much, however, it is easy to see namely, that 
 so far as solar heat alone is concerned, the mean temperature will 
 be greatest at the Equator, and diminish regularly as the latitude 
 of the place increases. 
 
 But there are causes on the earth itself which interfere with 
 this regularity of distribution. If the surface of the globe were 
 all dry land, composed of the same kind of rock or soil, and 
 unchequered with vegetation, the law above referred to would 
 accurately hold, and the lines of equal mean temperature the 
 isothermal lines, as they are called would be all parallel to the 
 Equator. This, however, is far from being the fact. The land, 
 you know, is in part covered with the waters of the ocean, and in 
 part dry ; while the surface of the latter is endlessly varied in its 
 own nature, and in that of its vegetable covering. These causes 
 produce an inequality in the action of the sun's rays in places 
 having the same latitude, which will be readily understood. The 
 same amount of heat which would raise the temperature of the 
 rock, or soil, through any given number of degrees, will raise the 
 temperature of an equal weight of water through a much smaller 
 amount, on account of what is called its greater capacity for heat. 
 And, in addition to this, a very large portion of the heat which is 
 absorbed by the water is employed, not in raising its temperature, 
 but in changing its state into that of vapour. It becomes thus 
 what is called latent, and does not affect the thermometer or the 
 sense. Every pound of water converted into vapour takes in, in a 
 latent form, as much heat as would raise the temperature of 960 
 pounds through one degree. And all this heat is carried away by 
 the vapour, to reappear at some remote place, where the vapour is 
 converted into rain. 
 
 Owing to these and other causes, the surface of the ocean is 
 never raised to so high a temperature as that of the dry land. It 
 rarely exceeds 85 Fahrenheit, even within the Tropics, while the 
 surface of the soil in the same region is sometimes heated to 140, 
 and upwards. Captain Sturt relates that, in parts of Australia, a
 
 THE CURRENTS OF THE ATLANTIC. 383 
 
 lucifer match will take fire, if it chance to fall on the arid and 
 heated soil. 
 
 You see then that, owing to the diversity in the physical 
 characters of the earth's crust, the heat developed is hy no means 
 proportionate to the intensity of the solar action. But there is 
 another, and a powerful cause, which tends to distribute the heat 
 actually imparted, and to render it more uniform. The air ahove 
 the Equatorial regions of the earth ascends, and flows over towards 
 the Poles ; while the colder air of the Polar regions flows beneath 
 in the opposite direction to take its place. In this manner a 
 double system of aerial currents is established, which tends to 
 mitigate the extremes of heat and cold on the earth's surface, and 
 to reduce the differences which would otherwise exist. 
 
 And a similar interchange 'of temperatures is effected by means 
 of the waters which cover so large a portion of the earth's surface. 
 The Oceanic currents, like great arteries, distribute to the more 
 remote portions of the globe the vast store of heat which it 
 receives from the sun in the intertropical regions. To one of 
 these I wish to invite your attention more particularly, because it 
 is to it, mainly, that the peculiarities of our own climate are owing. 
 Let us trace it from its source. 
 
 In the Atlantic Ocean, within the Tropics, the waters flow 
 from east to west in a majestic stream, whose breadth occupies 
 30 of latitude. It is known under the name of the " Equatorial 
 current." This current breaks into two, or bifurcates, when it 
 encounters the projecting shoulder of the South American Continent 
 at the Cape St. Eoque ; the main portion sweeping along the 
 northern shore of the Continent, while another portion is deflected 
 to the southward, and follows the eastern shore. The former of 
 these is the parent of the " Gulf-Stream." Continuing its westerly 
 course, along the north coast of South America, it enters the 
 Caribbean Sea, and passes into the Gulf of Mexico through the 
 channel of Yucatan. It then makes the entire circuit of the gulf, 
 clinging to the shore of the North American Continent, until its 
 direction is changed from westerly to easterly ; and it passes out 
 of the gulf through the Straits of Florida, and issues into the 
 Atlantic. 
 
 It is at this point that the current takes the name of the 
 4t Gulf-Stream." Its breadth is here upwards of 30 miles, and 
 its depth more than 2000 feet ; and it has a velocity of four miles
 
 384 THE CLIMATE OF IRELAND, AND 
 
 an hour. Following the line of the coast from the Straits, it 
 trends in a north-easterly direction as far as the great hank of 
 Nantucket, off Newfoundland, where its direction is changed to 
 easterly ; and it leaves the land near Cape Fear, and crosses the 
 Atlantic. Here reaching the colder water, it rises to the surface 
 "by its relative lightness, while, at the same time, it spreads super- 
 ficially. When it reaches the meridian of 38 W. longitude, it 
 subdivides, the main portion of the current proceeding in a north- 
 Avesterly direction to the North Sea, hathing the western coasts of 
 Ireland and Scotland on its way while another portion bends 
 round to the southward, and forms a great eddy not far from the 
 Azores, in the midst of which is found that vast floating mass of 
 .sea-weed known as the sargasso, which lies between the Azores 
 and the Cape de Verd Islands. It thus at length rejoins the 
 waters of the Equatorial sea, and completes the circuit of the 
 Atlantic. 
 
 Confining our attention, for the present, to that portion of the 
 circuit which is more especially designated as the Grulf-Stream, 
 and whose limits are the Straits of Florida and the Azores, we 
 find that it runs its entire course of 3000 miles in 78 days ; so 
 that its average rate of progress is 38 miles per diem. Its speed is, 
 however, very different in different parts of its course. In the 
 Straits of Florida it has a velocity of 100, and sometimes 120 
 miles in the day ; but by the expansion of its waters this is soon 
 lessened. Its average velocity in the first portion of its course 
 /. e., from its origin to the point at which it leaves the American 
 shore is 63 miles a day ; in mid- Atlantic it is 55 miles ; and in 
 longitude 42|, where it begins to bend southward, it is 35 miles. 
 
 And the temperature of the waters decreases with their speed, 
 although much less rapidly. When they issue from the Gulf of 
 Mexico, they have a temperature of 86 Fahr. ; and near the 
 termination of their course at the Azores, in 40 W. longitude, 
 they have a temperature of 74, having lost only 12 in traversing 
 a space of 3000 miles. It is to this great mass of heated water, 
 and to the westerly and south-westerly winds which carry to us 
 the heated air above it, that we owe the genial climate of the 
 British islands. 
 
 A circuit of waters, similar in its principal features, is per- 
 formed in the South Atlantic also. I have already mentioned 
 that the great Equatorial current breaks into two at the Cape
 
 < THE CURRENTS C-F THE ATLANTIC. 385 
 
 St. Eoque, where it first encounters the American shore. The 
 smaller portion descends along the eastern shore of South America, 
 under the name of the "Brazil current," until it arrives at the 
 latitude of 30 south. It then turns eastward, and, under the 
 name of the " southern connecting current," it crosses the South 
 Atlantic much like the Gulf-Stream in the North Atlantic 
 until it reaches the western coast of Africa. It finally returns 
 along that coast to the northward, under the name of the 
 " Southern Atlantic current," and rejoins the Equatorial current 
 from which it originally broke off. 
 
 And the same phenomena are repeated in the Pacific Ocean. 
 In it, also, there is an Equatorial current, which travels in a 
 westerly direction between the Tropics, until it meets the land at 
 Australia, and the barrier of islands which lies to the eastward of 
 the Continent of Asia. A portion is then deflected northward, 
 and recrosses the Pacific from west to east at a higher latitude, 
 to bathe the shores of California and Oregon. Finally, another 
 current detaches itself from the Equatorial current, on the western 
 side of the great basin of the Pacific, and, after travelling for 
 some distance southward, returns eastward to meet the western 
 shore of South America, and finally rejoins its source. 
 
 The generally received explanation of these phenomena is that 
 given by Franklin. The Trade-winds, acting on the waters of 
 the ocean on both sides of the Equator, produce a drift of the 
 surface water between the Tropics, the waters north of the 
 Equator being impelled in a south-westerly direction, and those 
 south of it in a north-westerly. At the Equator, or near it, these 
 two drifts combine, and form one great westerly stream, which is 
 the Equatorial current. This current is deflected when it meets 
 with a barrier of land ; and the effect is magnified, when that 
 barrier takes the form of a gulf, and so prevents the lateral escape 
 of the waters. These conditions are satisfied in the Mexican 
 gulf. The waters of the Equatorial current, which enter it along 
 its southern shore, are pent up into narrower limits within it, and 
 increase in depth and speed, until they finally escape along the 
 northern shore through the Straits of Florida. And a similar 
 explanation will apply to the other great oceanic currents which 
 I have briefly described, bearing in mind, of course, the differences 
 due to the different configuration of the land. 
 
 I have spoken of these ocean streams generally, in order that 
 2c
 
 886 THE CLIMATE OF IRELAND, AND 
 
 you might see that they have all certain features in common. 
 But in considering the climate of Ireland, and the influences to 
 which it is subject, we may confine our attention to that branch 
 of the circuit of waters which bathes its shores. 
 
 I have said that the Gulf-Stream divides when it reaches the 
 meridian of 38 W., a portion there turning off to the southward, 
 while the greater part bends to the north-east, sweeping along the 
 western shores of Ireland and Scotland on its way to the North 
 Sea. That these warm waters reach the shores of Ireland is 
 proved, not only indirectly, by their effect on the climate but 
 also, directly, by the drift-wood and the fruits of the Tropics, 
 which they often carry thither. Even the living inhabitants of 
 the Tropical seas are thus sometimes transported to our waters. 
 It is only a few years since the bonita, and other tropical fishes, 
 entered the English Channel in vast numbers, and destroyed 
 the pilchard, which is the chief support of the fishermen of the 
 southern coast. 
 
 But although there can be no doubt of the presence of these 
 warm waters on our shores, it was desirable to obtain some 
 measure of their influence ; and accordingly, in the year 1851, 
 when a general system of meteorological observations was carried 
 out in Ireland, the attention of the observers was specially directed 
 to this subject, and measures of the temperature of the sea were 
 taken at several of the coast-stations. When the results were 
 compared with those of the temperature of the air, it was found 
 that the sea was sensibly warmer than the air over the land, the 
 difference amounting, in the mean of the year, to 3'8. The 
 excess is, as might be expected, much greater in winter than in 
 summer : in the latter season it is l-8 only ; in the former, it 
 amounts to 5*7. 
 
 But this difference is by no means a measure of the whole 
 heating effect of the Gulf-Stream ; for the temperature of the air 
 over the land is elevated by the influence of the heated waters 
 which encompass it. We obtain a juster notion of the magnitude 
 of the effect, by noting the course of the lines of equal temperature 
 in the Atlantic. Looking at the map of the isothermal lines 
 which is before us, we observe that, in the Atlantic, these lines all 
 deviate greatly from the parallels of latitude, as they recede from 
 the Equator, their convex summits falling near the western shore of 
 the Atlantic, while their concave summits are on the eastern. It
 
 THE CURRENTS OF THE ATLANTIC. 
 
 will be noted, also, that the most sudden bending of these curves 
 takes place in the neighbourhood of the British Islands, the 
 greatest deviation from the parallels of latitude being in, or near, 
 the meridian of London. And, in accordance with this, London 
 has the same mean temperature as Philadelphia, although it is 
 11^ nearer to the Pole ; while Trondjhem, in Norway, has the 
 same mean temperature as Halifax, notwithstanding the difference 
 of 19 in latitude. 
 
 What has been just said relates to the mean temperature of the. 
 >/ear ; but the influence of the Gulf-Stream is much greater upon 
 the temperature of winter. Thus the winter temperature of Dublin 
 is considerably higher than that of Milan ; and Stromness, in 
 the Orkneys, has a winter temperature greater than that of 
 Paris. In fact, the isothermal line for January, which passes 
 through the Shetland Islands, runs almost exactly from north to 
 xouth ; and thus the winter temperature is nearly the same along 
 the whole eastern coast of Great Britain, while it increases as we 
 proceed from that coast to the westward. In Norway the effect is 
 even more remarkable. Owing to the interposition of the British 
 Islands, the Gulf-Stream is intercepted from the southern portion 
 of the Norwegian coast, while it reaches the northern. The 
 southern limit of the stream thus falls on the town of Bergen ; 
 and accordingly, in winter, the temperature actually increases in 
 proceeding northicard from that point. 
 
 But the disturbing effect of local causes on the temperature is 
 measured exactly by the method employed by Professor Dove. 
 In this method the mean temperature, corresponding to any 
 parallel of latitude, is deduced from the observed temperatures 
 at 36 equidistant points on the parallel, and is regarded as th 
 normal temperature of all places on that parallel ; and the difference 
 between this, and the actual temperature of the place, is obviously 
 u measure of the local influence. This difference is called by 
 Professor Dove the thermic anomaly. We thus find that the 
 measure of the influence of the Gulf-Stream, or the thermic 
 anomaly, at the Orkneys is, on the mean of the entire year, 15 ; 
 while, in the month of January, it amounts to 34. The excess 
 of the actual above the normal temperature is greatest between 
 Jan Meyen and the Lofoden Islands, a little above the Arctic 
 Circle. The mean thermic anomaly is there 22'5 ; while, in the 
 month of January, it amounts to 45.
 
 388 THE CLIMATE OF IRELAND, AND 
 
 The mean thermic anomaly for Ireland, or the excess of the 
 mean temperature of the year (50'3) above that due to the 
 latitude (37'7), is 12 J. The corresponding excess for the month 
 of January is 27. Our winter temperature is thus raised, by the 
 Gulf-Stream, as much as if our place on the globe had been 15 
 nearer to the Equator ! 
 
 The Gulf-Stream changes its boundaries from time to time ; 
 and these changes are sometimes indicated in a singular manner. 
 The Medusa?, or " sea-nettles," as they are commonly called, are 
 often found in vast numbers in the stream ; and it seems to be 
 owing to the attraction which these creatures have for the whale, 
 who feeds upon them, that the leviathan is so often found hovering 
 on its skirts for its temperature is too high to permit him to 
 enter it. Now this fact furnishes some curious evidence respecting 
 the boundary of the stream, and its changes. Thus M. Babinet 
 tells us, that in the autumn of 1846 he learned that the whalers 
 had been obliged to run up to a higher latitude in search of their 
 prey. From this fact he concluded that the stream had advanced 
 further northward than usual ; and he predicted, in consequence, 
 that the following winter would be one of unusual mildness in 
 Europe. The prediction was fulfilled. 
 
 I now proceed to consider, somewhat more particularly, the 
 influence of these and other causes on the climate of Ireland. 
 
 I have already adverted to the system of meteorological obser- 
 vations adopted in 1851, under the direction of the Boyal Irish 
 Academy. In addition to the observatories of Armagh, Markree, 
 and Dublin, where such observations are made continuously, the 
 observations were taken at eight coast-guard stations, by boatmen 
 belonging to the service, and at three of the lighthouses, by the 
 light-keepers. The instruments were furnished by the Academy. 
 They were constructed on a common plan, and carefully compared 
 with standard instruments by members of the Council of that 
 body, by whom also the men were instructed in their use. The 
 instruments were recorded daily at 9 A. M. and 9 p. M. ; and obser- 
 vations were also taken, on the same system, at two stations in the 
 interior of Ireland, where the task was voluntarily undertaken by 
 private individuals. 
 
 The mean temperatures of the several months having been 
 calculated, and reduced to their normal values by means of the 
 Dublin observations, it was found that the temperatures of the
 
 THE CURRENTS OF THE ATLANTIC. 380 
 
 inland stations were in defect, as compared with the coast stations. 
 The cause of this is obviously their greater distance from the 
 warm waters of the surrounding sea; and it follows evidently 
 from the fact, that the actual isothermal lines in Ireland are 
 inflected in passing from the sea to the land, and must even, in 
 part of the island as Mr. Hennessy has pointed out take the 
 form of closed curves, dependent on the position of the places 
 traversed with respect to the coast-line, as well as upon their 
 longitude and latitude. To determine such curves with exactness 
 would require a far greater number of stations than those em- 
 ployed, and would not seem likely to yield results of corresponding 
 value. The most feasible course seems to be to determine, in the 
 first instance, the law of distribution of temperature depending on 
 geographical position alone ; the disturbing influence of the land 
 can afterwards be computed approximately, and allowed for. 
 
 Dealt with in this manner, the observations show that, on the 
 mean of the whole year, the isothermal lines are inclined to the 
 meridian by the angle N. 49 W., and that the temperature 
 increases, in a direction perpendicular to these lines, at the rate of 
 1 Fahr. for 89 miles. 
 
 "We learn further, that the mean isothermal lines for the entire 
 year furnish a very inadequate representation of the progression of 
 temperature, and that, when the course of these lines is traced 
 from month to month, they vary within very wide limits. The 
 extreme positions correspond to the months of June and December. 
 In the former, the inclination of the isothermal lines to the 
 meridian is N. 106 W. ; in the latter, it is N. 9 W. Thus 
 these lines vary in direction through an angle of 97 in the course 
 of the year, being nearly parallel to the meridian in December, 
 and nearly perpendicular to it in June. The rate of increase of 
 temperature changes little. 
 
 The mean yearly temperature for the central station, whoso 
 latitude and longitude are the arithmetical means of those of the 
 stations of observation, is 50-3. It is thus distributed throughout 
 the year :
 
 390 
 
 THE CLIMATE OF IRELAND, AND 
 
 Month. 
 
 Mean 
 Temperature. 
 
 Month. 
 
 Mean 
 Temperature. 
 
 January, . . 
 
 41"-7 
 
 July, . . . 
 
 58-8 
 
 February, . . 
 
 42 -3 
 
 August, . . 
 
 58-3 
 
 March, . . . 
 
 44 -1 
 
 September, . . ! 57-8 
 
 April, . . . 
 
 47 -1 
 
 October, . . j 50-2 
 
 May, . . . 
 
 52 -9 
 
 November, . . 
 
 48 -4 
 
 June, . . . 
 
 56-7 
 
 December, . . 
 
 45-4 
 
 These facts are in entire accordance with the general course of 
 the isothermal lines, as laid down by Dove. After what has been 
 said, they are readily accounted for. The heating effect of the 
 Gulf-Stream is greatest about the time of the winter solstice, or 
 soon after. It then overpowers altogether the effect of solar 
 radiation, which is then weakest ; and the temperature increases 
 as we approach the waters of the stream i. e., as we proceed to 
 the westward. On the contrary, the effect of the stream is least, 
 and that of the sun greatest, about the time of the summer solstice; 
 and the heat increases as we proceed southward. The maxima of 
 the curves in Europe, at this period of the year, show that the 
 burning soil of the African Continent then influences most the 
 distribution of temperature to the north of it.* 
 
 * The following are the mean temperatures of the several places of observation in 
 Ireland, reduced to their normal values, for the four seasons of the year, and for the 
 entire year : 
 
 Place. 
 
 Spring. 
 
 Summer. 
 
 Autumn. 
 
 Winter. 
 
 Year. 
 
 Portrush,. . . . 
 
 4G"-5 
 
 56'0 
 
 5l'l 
 
 41'5 
 
 48-8 
 
 Buncrana, . . . 
 
 46 -6 
 
 56 -5 
 
 oO -6 
 
 41 -0 
 
 48 -7 
 
 Donaghadee, . . 
 
 47 -1 
 
 56 -4 
 
 51 '4 
 
 42 -2 
 
 49 -3 
 
 Killybegs, . . . 
 
 48 -1 
 
 57 -6 
 
 52 -8 
 
 4:$ -1 
 
 50 -4 
 
 Armagh, . . . 
 Killough, . . . 
 
 46-3 
 47 -4 
 
 56 -5 
 56 -6 
 
 49 -6 
 
 01 '9 
 
 40 -6 
 43 -5 
 
 48 -3 
 
 49 -8 
 
 Markree, .... 
 Westport, . . 
 
 46 -1 
 48-7 
 
 56 -2 
 57 '7 
 
 49 '6 
 53 -8 
 
 39 '4 
 44 -9 
 
 47 "8 
 51 -3 
 
 Dublin, .... 
 
 48 -0 
 
 59 -5 
 
 50 -4 
 
 42 -0 
 
 50 -0 
 
 Portarlingtoii. . . 
 
 44 -4 
 
 55 -8 
 
 48 -5 
 
 39 -0 
 
 46 -9 
 
 Athy, ... 
 
 46 -1 
 
 57 -8 
 
 48 -8 
 
 39 -4 
 
 48 -0 
 
 Courtown, . 
 
 48 -0 
 
 58 -3 
 
 50 -7 
 
 42 -5 
 
 49 -9 
 
 Kilrush, . . 
 
 48 -2 
 
 57 "9 
 
 52 -o 
 
 43 -4 
 
 50 -5 
 
 Dunmore, 
 Cahircivcen, . 
 Castletownscn il , 
 
 48-7 
 49 -8 
 49 -4 
 
 59 -9 
 59 -3 
 59 -0 
 
 52 -6 
 
 o:; -8 
 r>:5 -9 
 
 43 -9 
 44 -7 
 44 -6 
 
 51 -3 
 51 -9 
 
 51 -7
 
 * THE CURRENTS OF THE ATLANTIC. 391 
 
 But the climate of a place depends upon the ranges of tempera- 
 ture, whether diurnal or annual, no less than upon the mean 
 rallies. It is a well known meteorological fact, that the ranges of 
 temperature on the globe vary within very wide limits, being 
 least of all at sea, and increasing with the distance of the place 
 from the ocean, until in the interior of the continents they become 
 very great. Thus, the difference between the mean temperatures 
 of summer and winter, or the annual range, is, on the average, 
 19 in Great Britain ; 27 in France ; 36 in the eastern parts of 
 Germany ; 40 in European Russia ; 60 in Siberia until at 
 Jakoutsk, in that inhospital clime, it reaches the enormous amount 
 of 101 ! And these differences exist even among places having the 
 same mean temperatures. Thus Dublin, Prague, and Astrakhan 
 on the shores of the Caspian, have all nearly the same mean 
 annual temperature. But the difference between their summer 
 and winter temperatures are respectively, 17'5 for Dublin, 37 
 for Prague, and 57 for Astrakhan. These differences are due to 
 the different effects of solar radiation on water and on dry so/7, 
 already explained ; and climates have been distinguished into 
 marine and continental, according to the amount of this variation. 
 The annual range in Ireland is the smallest in Europe ; on the 
 coasts it falls as low as 14. 
 
 The difference between the mean temperature of day and 
 night, or the diurnal range, follows the same law, being least on 
 the coasts, and greatest in the interior of the continents. I have 
 already adverted to the principal cause of this. A great portion 
 of the solar heat which falls on the water during the day is 
 employed in changing its state into that of vapour, and does not 
 affect its temperature ; and, on the other hand, the heat so 
 employed is, in part, restored and rendered sensible, when the 
 vapours are condensed during the night. Thus the two extremes 
 approach one another. But another reason is, that the vapour 
 itself stops, or absorbs, a large portion of the sun's heat ; and the 
 effect, of course, is greatest when the air is most humid. Dr. 
 Livingstone found a difference of temperature, amounting to 48, 
 between sun-rise and mid-day, on the eastern side of South Africa ; 
 while in the valley of the Zambesi, on the opposite side of the 
 Continent, where the air is loaded with moisture, the difference 
 amounted only to 12. 
 
 In accordance with this, the diurnal rmigo of temperature
 
 392 
 
 THE CLIMATE OF IRELAND, AND 
 
 in Ireland is small, the mean difference between the greatest 
 temperature of the day, and the least temperature of the night, 
 being only 117. The range is greater inland than on the coast, 
 the mean range of the inland stations being 13'l, and that of 
 the coast stations 10'3. Among the places of observation, it is 
 greatest at Portarlington, and least at Cahirciveen at the south- 
 western extremity of Ireland. 
 
 Having spoken of the temperature of the air, I must now say 
 a few words of its movement and, first, of the direction of that 
 movement. 
 
 During the period of the simultaneous observations already 
 referred to, the wind blew, on the average of the entire year, most 
 frequently from S.W. and W., and least frequently from N.E. 
 and E. Thus, taking the mean of all the stations, the number of 
 times in which the wind blew from the N.E. is only 7 per cent, of 
 the whole, while the number of S.W. winds is 20 per cent. The 
 ratio of the numbers is greater in winter than in summer. The 
 following Table gives the number of times out of 1000, in which 
 the wind blew from each of the eight principal points of the 
 compass, for the whole island. 
 
 Direction of Wind. 
 
 Summer. 
 
 Winter. 
 
 Year. 
 
 N. 
 
 122 
 
 96 
 
 108 
 
 N.E. 
 
 94 
 
 52 
 
 73 
 
 E. 
 
 89 
 
 50 
 
 69 
 
 S.E. 
 
 100 
 
 86 
 
 92 
 
 8. 
 
 107 
 
 164 
 
 136 
 
 S.W. 
 
 170 
 
 234 
 
 202 
 
 w. 
 
 163 
 
 176 
 
 170 
 
 N.W. 
 
 156 
 
 144 
 
 150 
 
 The velocity of the wind varies from to 70 feet per second, 
 and upwards this last being the speed corresponding to a storm. 
 If we confine our attention for the present to winds whose average 
 velocity is not less than 35 feet per second, which is the velocity 
 of a strong breeze, we find that the high winds are much more 
 frequent on the western than on the eastern coast, the numbers 
 denoting their relative frequency being, on the average of the
 
 "THE CUERENTS OF THE ATLANTIC. 393 
 
 entire year, nearly as 3 to 1. This preponderance of high winds 
 on the western coast holds at all seasons, the maximum occurring 
 at the north-western extremity in autumn, and at the south- 
 western in winter. 
 
 But of these winds, there are two distinct kinds. In one of 
 these, the wind blows steadily in the same direction for a con- 
 siderable time, and the axis of the gale is a straight line, or a line 
 but slightly curved. In the other, the wind rotates round a centre, 
 while the centre itself has a progressive motion just as we see, on 
 a miniature scale, in the vortices of dust which sweep along the 
 road in gusty and unsettled weather. These rotating winds are 
 called cyclones. They are from 200 to 300 miles, and upwards, in 
 diameter, and their centres move with a speed of from 100 to 300 
 miles per diem. The direction of the rotation is invariably the 
 same. In the northern hemisphere the wind revolves in the 
 direction opposite to that of the sun in its daily course, i.e., in the 
 direction N. W. S. E. In the southern hemisphere, the direction of 
 rotation is with the sun, or N. E. S. W. When a cyclone passes 
 over any point on the earth's surface, the wind must veer. If the 
 centre of the cyclone passes directly over the place of observation, 
 the veering is through 180 degrees, or the wind changes to the 
 opposite. The amount of veering is less, the smaller the chord of 
 the circle which passes over the place; until, for places at the 
 circumference, there is no veering whatever. 
 
 But there is another remarkable distinction between these two 
 classes of winds. In the case of the cyclone, the barometric 
 pressure diminishes to a point, which is the centre of the vortex. 
 In the non-rotatory gales, the pressures diminish to a line, which 
 is the axis of the storm. 
 
 The most remarkable of the cyclonic movements traced in the 
 course of the simultaneous observations was that which occurred 
 on the 18th and 19th of November, 1851. The centre of the 
 vortex passed over two of the principal stations, Markree and 
 Armagh, at both of which all the changes were accurately ob- 
 served ; and the velocity of the wind reached a maximum of Go 
 feet per second. The lull oi the wind during the passage of the 
 central portion of the vortex, and the reversal of its direction, were 
 observed at Markree, Armagh, and Donaghadee. The diameter 
 of the vortex was about 400 miles ; that of the quiescent central 
 portion 40 miles.
 
 394 THE CLIMATE OF IRELAND, AND 
 
 The facts collected relating to these winds lead to the following 
 conclusions : 
 
 1. The occurrence of cyclonic movements in the atmosphere is 
 not infrequent in Ireland, and may be traced even in the case of 
 moderate winds. 
 
 2. The rotatory movement is invariably in the same direction 
 namely, that opposite to the diurnal movement of the sun in azimuth. 
 
 3. This rotation is always accompanied by a considerable 
 disturbance of barometric equilibrium, which is greater in pro- 
 portion to the velocity of the movement, the pressure being a 
 minimum at the centre of the vortex, and increasing regularly 
 with the distance from that point. 
 
 4. The vortex itself has a progressive movement, at the rate 
 of from 100 to 300 miles per diem, the average velocity of those 
 observed being 220 miles per diem. The direction of this move- 
 ment is generally from S. W. to N. E. 
 
 5. If a line be drawn through the centre of Ireland, in the 
 direction from S. W. to N. E., the track of the centres of the 
 greater number of the cyclones, passing over or near Ireland, lies 
 to the north of that line. 
 
 With reference to the first of these conclusions viz., the pre- 
 valence of cyclonic movements in the atmosphere over, or near, 
 this island I may here state, that of all the greater storms which 
 occurred during the period of observation, no fewer than two-thirds 
 were cyclonic ; while several cyclonic movements of smaller velo- 
 city were distinctly traced. The area of observation may be 
 thought, perhaps, to be too small to furnish conclusive evidence 
 relating to these great aerial movements. But I have the satis- 
 faction of knowing, that of the cases recorded in the Memoir on 
 the subject published in the Transactions of the Royal Irish Aca- 
 demy, the cyclonic character of most (if not all) has been since 
 confirmed by the late Admiral Fitzroy, from the records of the 
 logs of ships. 
 
 The prevalence of such movements is just what we should 
 be led, a priori, to expect, from the vicinity of the GruH'-Stream. 
 The waters of the stream in mid-Atlantic have a temperature 
 of 80 Fahr., while the air on either side of it is, in winter, 
 at the freezing temperature. We have here all the conditions 
 required for the production of cyclonic storms. Aqueous vapour 
 is much lighter than air at the same temperature, and conse-
 
 THE CURRENTS OF THE ATLANTIC. 395 
 
 quently ascends in it ; and, in its ascent, it drags the heated air 
 along with it, and produces an upward current. There is thus an 
 upward rush of heated air and vapour above the heated waters, 
 and an inward rush of cold air from either side to supply its place ; 
 and such a combination of movements will produce a great rotat- 
 ing eddy, much in the same manner as the downward flow of 
 water through a hole in the bottom of a vessel will give rise to a 
 vorticose movement of the whole liquid mass. 
 
 Accordingly, the most terrific hurricanes of which we have any 
 record have been generated on the borders of the Gulf-Stream. 
 In the hurricane of 1780, in the Bermudas, houses were levelled 
 by the gale ; forts were washed away by the waves ; heavy pieces 
 of ordnance were lifted into the air ; and the bodies of animals 
 were carried aloft, and dashed to pieces in the fall. The loss of 
 human life was terrible. It is computed that not fewer than 
 20,000 lives were lost on shore; and on the water no vessel 
 could stand the gale. 
 
 And the Gulf-Stream appears also to exert a marked influence 
 on the course of storms which are engendered in other parts of the 
 Atlantic. Erom the examination of the logs of ships, Captain 
 Maury has ascertained that the gales, which are produced in the 
 Atlantic to the south-east of the current, usually travel to the 
 north-west until they meet it, after which they turn along with 
 it, and follow its course. And, according to Mr. Espy, a similar 
 effect is produced in the case of storms which have their birth- 
 place in the valley of the Mississippi. 
 
 There are two facts which have been brought to light by the 
 Irish meteorological observations, which confirm in a remarkable 
 manner this explanation. The main branch of the Gulf-Stream 
 approaches the coasts of Ireland most nearly at the north-western 
 extremity of the island ; and it is, accordingly, there, if this ac- 
 count be the true one, that the evidences of cyclonic movement 
 .should be most marked. And such is the fact : the track of the 
 centres of most of the cyclones whose course has been investigated 
 lies to the north-west of the island. And in exact accordance with 
 this fact is another of a different kind. I have said that, in the 
 area covered by a cyclone at any moment, the minimum of baro- 
 metric prcaaure is at the centre of the vortex. Hence the frequent 
 passage of cyclones in any particular direction must affect the 
 mean distribution of atmospheric pressure, the prepsuro being most
 
 ;}96 THE CLIMATE OF IRELAND, AND 
 
 diminished at those places which are nearest to the track of their 
 centres. It has been found, accordingly, that there is an ine- 
 quality in the distribution of the atmospheric pressure in Ireland, 
 and that the minimum occurs in the north-western quarter of 
 the island. 
 
 I now proceed, lastly, to the effects of the Grulf-Stream on the 
 humidity, and on the rain-fall, in this island. 
 
 The amount of evaporation from the surface of water increases 
 rapidly with its temperature. Consequently the air above the 
 Gulf-Stream is loaded with vapour to a much greater degree than 
 that which rests on other portions of the Atlantic. This vapour 
 is borne to the British Islands by the south-west winds, which are 
 the predominating winds in this portion of the globe ; and, in 
 consequence, these islands have more than their average share of 
 humidity. The effect is, of course, greatest at those places which 
 the wind first reaches. It is, accordingly, greatest in Ireland, less 
 in England, and still less on the Continent of Europe, diminish- 
 ing with the distance of the place from the Atlantic. Thus, in 
 Paris (and probably in France generally) the mean amount of 
 vapour in the air is about 77 per cent, of the maximum which 
 it is capable of- holding. In London, it is 84 per cent. ; and in 
 Dublin it amounts to 88 per cent., which is about the average 
 for Ireland. 
 
 The humidity is greatest, as we should expect a priori, on the 
 western coast of Ireland, and least on the eastern the former 
 being about 90 per cent., and the latter 85. The following Table 
 gives the mean humidity of the several months of the year at 
 Dublin. It is greatest in December, and least in June : 
 
 Month. 
 
 Humidity. 
 
 Month. 
 
 Humidity. 
 
 January, . . 
 
 92 
 
 il July, . . . 
 
 84 
 
 February, . . 
 
 88 
 
 : August,. . . 
 
 86 
 
 March, . . 
 
 88 
 
 ! September, . . 
 
 90 
 
 April, . . . 
 
 87 
 
 October, . . 
 
 91 
 
 May. . . . 
 
 85 
 
 Xovember, . . 
 
 92 
 
 June, . . 
 
 83 
 
 !{ December, . . 
 
 92
 
 THE CURRENTS OF THE ATLANTIC. 397 
 
 The distribution of rain is very unequal. In the east of Eng- 
 land, the annual rain-fall is between 20 and 25 inches only ; in 
 the west of Ireland, it is between 40 and 50 inches. In Ireland, 
 in the year 1851, the greatest amount of rain fell at Cahirciveen, 
 and the least at Portarlington, the amounts being 59*4 inches, 
 and 21*2 inches, respectively. The mean rain-fall for the whole 
 island, in that year, was 34'5 inches. 
 
 The causes already adverted to explain, in part, the distribu- 
 tion of rain. The vapour which is borne to us by the south- 
 westerly winds is partly condensed into rain when the air is 
 cooled by contact with the land. The chief condensers are the 
 mountains, because they interpose the greatest obstacle to the 
 movement of the vapour-laden air. Accordingly the high moun- 
 tains of Kerry, which offer the first barrier to the progress of these 
 winds, bring down on their flanks the largest amount of rain ; 
 and, generally, the rain-fall is greatest on the western and south- 
 western coasts, while the places of least rain are either inland or on 
 the eastern coast. The disparity is greatest in winter, when the 
 clouds are low ; in summer, when they are high, they escape the 
 condensing effect of the land over which they pass, and the rain is 
 more evenly distributed. 
 
 The amount of rain is always considerable in the neighbour- 
 hood of a mountain chain or group, except at places to the east- 
 ward of it, where it is small. Thus, the places of least rain in 
 Ireland Portarlington, Killough, and Dublin all lie to the 
 north-east of a mountain range ; while the places of greatest rain. 
 Cahirciveen, Westport, and Castletownsend are all in the 
 vicinity of high mountains, but on a different side. All this is 
 readily understood from what has been stated. The prevailing 
 wind is the south-west, which comes to us laden with the vapour 
 of the Gulf-Stream, and this vapour is precipitated chiefly on the 
 flanks of the mountains. And the same cause protects the region 
 over which the same wind next passes the east and north-east 
 the air having been deprived of its excess of vapour before arriv- 
 ing there. 
 
 The distribution of rain throughout the year in Ireland will be 
 understood from the following numbers, which give the mean rain- 
 fall in each month at Dublin, as deduced from the observations of 
 the eleven years (1841-1851). The mean yearly rain-fall is 29'1 
 inches.
 
 398 
 
 THE CLIMATE OF IRELAND, AND 
 
 Month. 
 
 Rain-fall. 
 
 Month. 
 
 Rain-fall. 
 
 January, . . 
 
 2-9 inches. 
 
 July, . . . 
 
 2-4 inches. 
 
 February, . . 
 
 1-7 
 
 August, . . . 
 
 2-7 
 
 March, . . . 
 
 1-9 
 
 September, . . 
 
 2-3 
 
 April, . . . 
 
 2-5 
 
 October, . . | 3-3 
 
 May, . . . 
 
 2-0 
 
 November, . . j 2-9 ,, 
 
 June, . . . 
 
 2-2 
 
 December, . . 2-2 ,, 
 
 In dealing with the subject of Climate, even in the cursory 
 manner which alone is suited to a discourse such as this, it is 
 impossible to overlook its effects upon animal and vegetable life ; 
 and therefore, although no physiologist myself, I will offer no 
 apology for laying before you some broad facts connected with 
 the sciences of life, in relation to Meteorology. 
 
 To begin with the vegetable kingdom it is well known that 
 plants are dependent, in a remarkable degree, upon every change 
 of heat and moisture ; and that, accordingly, the genera and species 
 of plants are distributed on the earth's surface so that each shall 
 receive its proper supply. The distribution of temperature being 
 much more regular than that of moisture, the general features of 
 the geography of plants are determined by the former ; and thus 
 the several divisions of the vegetable kingdom are found disposed 
 in broad bands on the earth's surface, which are closely connected 
 with the isothermal lines. And the succession of these bands is 
 similar but of course more rapid, and therefore more readily 
 seen on the flanks of high mountains. Thus we meet, near the 
 base of the Andes, first the palms ; and then the tree-ferns. At 
 greater altitudes there, or at lower heights in the temperate re- 
 gions, we come to the deciduous trees among which the oak, the 
 beech, and the birch, are the principal. Then, as we ascend, we 
 reach the pines ; next the rhododendrons, and other dwarf shrubs ; 
 after these, at still higher elevations, the creeping herbaceous 
 plants ; and, lastly, at the very limit of vegetation, the lichens. 
 
 But in studying the effects of temperature upon vegetable life, 
 it is important to observe, there are two pairs of limiting tempera- 
 tures to be considered, one wider, and the other narrower. The 
 former are the limits beyond which the existence and continued
 
 THE CURRENTS OF THE ATLANTIC. 399 
 
 life of the plant is impossible ; the latter are the limits which de- 
 termine its flowering, and the ripening of its seed or fruit. 
 
 It is hardly needful to remind you, that the very existence of 
 plants is dependent upon two extremes of temperature, one higher 
 and the other lower. In the temperate regions of the earth, in 
 which we ourselves have the happiness to live, the effect of the 
 higher extreme is seldom felt ; for there are few plants which will' 
 not bear our highest summer heat. Accordingly, with us it is the 
 winter temperature, or rather the lowest temperature of the year, 
 which determines the existence of most perennials. We are all fami- 
 liar with this fact in the case of our ornamental greenhouse plants, 
 which are for the most part natives of warmer climates, and will 
 not bear the rigours of our own without protection ; and the same 
 thing is true of many native and acclimatized plants in seasons of 
 unusual severity. On the other hand, in the south-west of Ireland, 
 which has the highest winter temperature of any in the British 
 islands, there are twelve species of wild plants which are natives of 
 Spain. 
 
 But within the limits beyond which the plant cannot live, there 
 are two other limits which determine its fruitfulness. It is now 
 well established that, in order to blossom, and to ripen its seed or 
 fruit, each species of plant requires a certain definite amount of 
 summer heat, above that which is necessary to the continuance of 
 its existence as a vegetable ; and that, provided it receives this 
 fixed amount, the time in which it is imparted is not essential. 
 This determines the lower limit to the successful culture of the 
 fruit-bearing plants. 
 
 But there is also a higher limit, which is less obvious. Thus in 
 the case of the annuals, which include the plants most useful to 
 man, there is a certain temperature at which the plant becomes 
 perennial, and is propagated by lateral shoots, and not by seed. 
 When the temperature reaches this limit for any plant, its culti- 
 vation for seed becomes impossible, and we can use it only for its 
 leaves or root. On the other hand, tuberous plants become seed- 
 bearing, by the lowering of the temperature. We have a familiar 
 instance of the latter transformation in our fields. Most of our 
 green crops, such as turnips and mangolds, are cultivated for their 
 roots, and under ordinary circumstances produce neither flower nor 
 seed. But it sometimes happens that certain plants in a field have 
 received a smaller amount of heat than is required for this mode
 
 400 THE CLIMATE OF IRELAND, AND 
 
 of growth ; and these plants throw tip a lofty stem, and flower, 
 while the tuberous growth ceases altogether. This is one of those 
 many beautiful adaptations which compel us to look up from 
 nature to nature's Grod. When the plant is under such conditions 
 that it must perish, it sends up its spikelet of flowers as it were 
 by an instinct and matures the seed, which is destined to continue 
 the life of the species, while the individual fades and dies ! 
 
 And here I cannot refrain from throwing out a suggestion 
 which, if found to be true, may be of some practical importance. 
 The plant which we chiefly cultivate for its root, and whose life 
 and health is of such importance to this part of the kingdom, pro- 
 duces (as you know) flower and seed, as well as tuberous root. I 
 venture to suggest to physiologists the inquiry, whether this cir- 
 cumstance may not be closely connected with the uncertainty of 
 the crop ? and whether, if means could be found to repress the 
 flower, the root might not acquire vigour and strength to resist 
 disease ? But however this may be, the transition from the con- 
 dition of perennial to that of annual is a subject of much import- 
 ance in connexion with the question of the acclimatization of plants. 
 It is probable that there are many tropical plants, unknown to this 
 climate, which are perennial in their native place, but which would 
 become annuals, with seed and fruit, when transferred to a colder 
 clime. When we consider the acquisitions which have been already 
 made by such transfers, we can hardly over-estimate the import- 
 ance of future gains, or the benefits which may be thus acquired 
 for the human family. 
 
 But the lower limit of summer temperature is by much the most 
 important to us ; for it is that which in our climates determines 
 the question of success in the culture of the cereals. I will there- 
 fore refer to it a little more particularly. 
 
 There is no doubt that the integral of solar heat, taken between 
 the limits of time when the vegetation becomes active in Spring, 
 and when the seed is ripened in Autumn, is the element which 
 determines one of the geographical limits which Nature has im- 
 posed to the culture of the plant. To find this, for each important 
 species of plant, would require an amount of observation which 
 has not yet been bestowed. In the meantime, however, a tolerable 
 approximation to its value may be made, by taking simply the 
 mean summer temperature i.e., the average temperature of the
 
 THE CUREENTS OF THE ATLANTIC. 401 
 
 months of June, July, and August. Now, if we look to the dis- 
 tribution of the cereals in Europe, as given by Berghaus or John- 
 stone in their physical Atlases, we observe that they are arranged 
 in belts, or zones, whose limits correspond nearly with the lines of 
 equal summer temperature. Thus we have, first, a belt of barley 
 alone, which extends from the North Cape, in latitude 70 N. to 
 about midway in Norway and Sweden. This is followed, as we 
 proceed southward, by a belt containing oats and rye, as well as 
 barley. Then comes a belt of rye and wheat, in the south of Scan- 
 dinavia, and in the north of central Europe. In the southern 
 half of Europe, we have wheat alone ; and, beyond this, wheat and 
 maize on the coasts of the Mediterranean. And the boundary lines 
 of these several districts are all related, more or less closely, to the 
 isothermal lines of mean summer temperature. 
 
 It is of the first importance to the agriculturist to know these 
 limits in his own district ; for on their position will depend the 
 chances of successful cultivation of the particular crop. I shall 
 therefore ask your attention for a few moments longer, while I 
 endeavour to ascertain the limit of wheat, the most important of 
 the cereals, in these islands. The result of the inquiry is some- 
 what startling, and it deserves to be more fully known. 
 
 There is some doubt still as to the native place of the cereal 
 grasses. Most of them have been found growing wild in Persia, 
 on the banks of the Euphrates, and in Tartary. Whatever their 
 original habitat may have been, it was a warmer clime than ours. 
 The mean summer temperature of the British Islands is under 60, 
 while that of the plains of Lombardy, where wheat is grown in 
 perfection, is 73 ; and that of Sicily " the granary of ancient 
 Rome " is 77. "We are, therefore, in these countries, probably 
 near the lower limit of the wheat crop, beyond which its successful 
 culture is impossible. It is important that we should know how 
 near. 
 
 We have some of the data requisite for the determination of 
 this question, in the long series of observations of temperature 
 made at the apartments of the Eoyal Society, in London, as com- 
 pared with the prices of wheat, given for an equally long series of 
 years in " Tooke's History of Prices." From the former we learn 
 how far the summer temperature of each year deviated from the 
 mean ; while the latter furnish us with a measure of the abundance 
 
 2 D
 
 402 THE CLIMATE OF IRELAND, AND 
 
 or scarcity of the years in question.* The comparison has been 
 made by Mr. Whitley, of Truro, in Cornwall, and the result 
 which he has obtained from it is interesting and important. 
 
 The observations of temperature to which I refer were begun 
 in the year 1774, and were continued (with only an interruption 
 of five years) to the year 1842, inclusive ; they thus extend through 
 sixty-four years. They have been carefully reduced by Mr. 
 Grlaisher, and the means of each month and season computed. 
 One of the results which may be inferred from them and it is 
 a result of some interest in connexion with the effects of season 
 is that, for the most part, the spring and summer of the same 
 year are of the same character, either both above, or both below 
 the mean. In the course of the sixty-four years, the character of 
 the two seasons was the same forty-six times, and opposite only 
 eighteen times ; so that the chances that a warm summer will 
 follow a warm spring, or vice versa, are as two and a-half to one. 
 
 A like fact appears also from Dr. Butty's observations of the 
 weather in Dublin, which extended through forty-one years in 
 the last century (1725-1765). In these observations the character 
 of each season is defined, with reference to the rain-fall, as dry, 
 wet, or variable. The observations have been discussed by Kirwan ; 
 and it appears from that discussion, that wet springs are followed 
 by wet summers five times out of six. 
 
 But to return to the London observations the greatest devia- 
 tion of any particular year, from the mean of all, was 4'8 in defect ; 
 it occurred in the year 1816, which was a year of famine. In 
 the course of the sixty-four years, a deviation of 2, and upwards, 
 occurred twenty-three times, the summer temperature being thirteen 
 times above the mean to that amount, and ten times below it. IS ow it 
 is deserving of notice, that there is no appearance of a regular cycle 
 in these good or bad years, such as Luke Howard and many other 
 meteorologists have imagined. On the contrary, both the warm 
 nnd the cold seasons usually occur in groups, comprising three or 
 four years in succession ; and the groups themselves do not recur 
 
 * It is not, of course, meant that prices furnish an accurate measure of the abund- 
 ance or scarcity of the crop ; for they are dependent, we know, on other causes also, 
 ;imong which legislative enactments regulating the import of foreign grain are the 
 principal. It is enough for the argument in the text, that prices varied with abundant 
 or scanty harvests, as with their principal cause ; and this we know to have been the 
 fact, as long as any restriction on the import of com remained.
 
 N THE CURRENTS OF THE ATLANTIC. 403 
 
 in any order or regularity. The most remarkable of these 
 groups is that of the years 1809-1817, comprising no fewer than 
 nine years in which the temperature was below the mean. The 
 average price of wheat in these years was 95.$. the quarter, the 
 ordinary average being 70s. ; while in the years 1811 and 1812, 
 it reached 122s. The total deficiency of summer temperature in 
 these nine years amounted to twenty-three degrees. 
 
 I need not remind you of the incidental confirmation of this 
 law of groups, in the account which we have in Grenesis of the 
 seven years of famine, following seven years of abundance, in Egypt 
 and Syria. Our own recent experience at home has instructed us, 
 that years of deficient harvest come in succession. But I wish 
 particularly to point out, that this recurrence of bad years by no 
 means justifies the conclusion which some have drawn from it 
 namely, that our climate has changed, or was changing, for the 
 worse. On the contrary, we learn from observation that such 
 unpropitious years are not likely to occur more frequently than 
 three or four in succession ; and that they will probably be suc- 
 ceeded, at some future time, by three or four years of an opposite 
 character. 
 
 Now when these years of low summer temperature are ex- 
 amined, with reference to the price of wheat, it is found that they 
 are, with few exceptions, years of scarcity and high prices. A de- 
 ficiency of temperature, amounting only to 2, is most injurious to 
 the wheat harvest in England ; while a deficiency of 3 is almost 
 destructive. The reverse is the case when the summer tempera- 
 ture exceeds the average by the same amounts. 
 
 This result is of considerable importance. The lowest summer 
 temperature at which wheat can be successfully cultivated in Eng- 
 land, is only 2 below the mean ; and, as the mean summer tem- 
 perature of England is 60, it follows that the minimum for wheat 
 is 58. This minimum, however, is not absolute. It varies a 
 little with the soil, and other circumstances ; and thus it is, that 
 we find the culture of wheat in Scotland extended as far as Inver- 
 ness, where the mean summer temperature is only 57. 
 
 Now taking this lower limit as the most favourable, let us see 
 what we are to learn from it in Ireland. In this island, the mean 
 temperature of the three Bummer months is 58 ; and, accordingly, 
 for places about the centre of Ireland, a deficiency of a */;///' tl^ir,-.- 
 of summer temperature brings us to the very limit of wheat culti-
 
 40-1: THE CLIMATE OF IRELAND, AND 
 
 vation ; while a greater deficiency is fatal to the crop. The case 
 is somewhat better in the southern half of the island, and some- 
 what worse in the northern ; and we are therefore justified in 
 concluding, that it is contrary to the rules of all sound experience 
 to attempt the culture of this cereal in Ireland, except in the most 
 favoured localities. 
 
 In the preceding discussion I have considered only the relation 
 of temperature to the culture of wheat. I have not adverted to the 
 frequently destructive en 3 ect of the autumn rains, which set in with 
 the fall of temperature, and often before the harvest is gathered. 
 Time will not permit me to discuss the corresponding questions 
 for the other cereals ; nor to advert to the fact, which is now be- 
 ginning to gain general acceptance, that the climate of this island, 
 while it is unfavourable to the higher cereals, is adapted in a pecu- 
 liar manner to the cultivation of root-crops, and of fodder.* I 
 hasten to say a few words, before I conclude, of the effects of 
 climate in general, and especially of our own climate, upon the 
 health of man. 
 
 We are all familiar with the command of the physician to the 
 patient, " to change the air ;" and most of us know something, 
 although probably less than the importance of the subject demands, 
 of the salubrity or insalubrity of different districts. 
 
 Of all the meteorological elements, that which exerts the most 
 direct effect upon human health is the temperature of the air ; and 
 in this respect the two forms of organized life are subject to one 
 law. We all know the effects upon the bodily frame of an ex- 
 treme cold in winter, and of harsh winds in spring ; and some of 
 us are obliged to leave our homes and daily occupations, and to 
 take refuge from these dangers in the more genial climates of the 
 south, f 
 
 M. Quetelet, in his important work " On Man," has brought 
 together many curious facts connected with the influence of climate 
 upon human life. Dividing Europe into three zones which we 
 
 * The turnip depends chiefly on a proper supply of moisture during the summer 
 months ; and it is injured by much heat. Accordingly, moist and cool summers such 
 as are frequent in Ireland are the fittest for this vegetable. The same rule applies 
 to grass. 
 
 t The connexion of the mortality with the cold of winter is very distinctly marked 
 in the weekly returns of the Registrar-general. In the severe frost of Christmas, 1860, 
 the increase in the number of deaths in London was forty daily, being greater than 
 the increase caused by cholera.
 
 ^ THE CURRENTS OF THE ATLANTIC. 405 
 
 may call northern, central, and southern Europe, respectively he 
 finds that the mortality in the last is by much the greatest, while 
 it is nearly equal in the two other divisions. In this comparison 
 M. Quetelet has considered merely the effect of latitude upon 
 mortality. But as we have already shown that places in the 
 same parallel of latitude often have widely different temperatures, 
 it seems plain that the comparison should be made differently, and 
 that we should group together for the purpose places under the 
 same, or nearly the same, isothermal line. When we compare in 
 this manner the death-rates of the several countries of Europe 
 with their mean temperatures, we find that the mortality is greatest 
 in Italy and Greece, where the temperature is highest ; and that 
 it decreases as the temperature decreases, down to a certain limit, 
 after which it appears to increase again. 
 
 But this is obviously an inadequate mode of considering the 
 problem. It seems plain that, for animals as well as for plants, 
 the salubrity of a climate will depend on the extremes of tempera- 
 ture, much more than on the mean ; and that, of these extremes, 
 the most influential on life will be that most removed from the 
 normal temperature which is best adapted to the species. Accord- 
 ingly, we should expect the mortality to be influenced chiefly by 
 the summer temperature in hot climates, and by the uinter tempera- 
 ture in cold ones. Arid this I find to be the case in Europe, where 
 alone we have the data requisite for the comparison. 
 
 The following are the principal conclusions which we seem to 
 be warranted in drawing : 
 
 1. In the southern half of Europe the mortality depends upon 
 the temperature of summer, being greatest where that temperature 
 is greatest, and diminishing with it down to a certain limit. 
 
 2. In the northern half of Europe, on the contrary, the mor- 
 tality depends on the temperature of winter, being greatest when 
 that is least. 
 
 3. The boundary line between these two regions is not far from 
 the mean yearly isothermal of 50, which is accordingly the line 
 of least relative mortality. 
 
 4. The mortality attains an absolute minimum in the British 
 islands, at the western extremity of this line, the annual range of 
 temperature being there least. 
 
 These conclusions will be evident on the inspection of the fol- 
 lowing Table, in which the mortality is compared with the
 
 406 
 
 THE CLIMATE OF IRELAND, AND 
 
 of the temperature of the hottest month above 50 Fahr., or with 
 the defect of temperature of the coldest "below the same.* 
 
 Countries. 
 
 Excess of 
 Summer 
 Temperature. 
 
 Defect of 
 Winter 
 Temperature. 
 
 Death rate i 
 per 1000. 
 
 Italy; Turkey, . . . 
 
 + 25 
 
 
 
 33 
 
 France; Austria, . . 
 
 + 18 
 
 
 
 25 
 
 Central Germany, . . 
 
 + 15 
 
 
 
 22 
 
 British Islands, . . . 
 
 + 12 
 
 -13 
 
 21 
 
 Belgium, 
 
 
 
 -16 
 
 23 
 
 Holland . . 
 
 
 -18 
 
 26 
 
 Prussia 
 
 
 -22 
 
 28 
 
 
 
 -36 
 
 37 
 
 
 
 
 
 I believe that this decrease of the mortality, in proceeding 
 from the hotter to the colder parts of Europe, and its subsequent 
 increase, result from fas joint operation of different diseases having 
 opposite relations to temperature. Epidemic and endemic diseases 
 appear to diminish indefinitely, as the temperature diminishes ; 
 while consumption, and other diseases of the respiratory organs, 
 increase. These are the maladies most destructive of human life ; 
 and it will be readily understood in what manner their contrary 
 tendencies may produce a minimum mortality at some temperature 
 far removed from either of the two extremes.! 
 
 I have already stated that the absolute minimum of mortality 
 is to be sought for at the western extremity of the yearly isother- 
 mal of 50 i. e., in our own island ; and the facts bear out this 
 conclusion. The average mortality of Ireland, so far as it can be 
 
 * There is, of course, some uncertainty in comparing numbers, one set of which are 
 dependent on political boundaries, and the other upon physical features. In Russia, 
 the mean winter temperature adopted is that of the January isothermal passing nearly 
 through three of the great centres of population Petersburgh, Moscow, and Astrakhan. 
 No attempt has been made to include Sweden and Norway in the comparison, the 
 extraordinary flexures of the January isothermals in these countries rendering the 
 deduction of a mean winter temperature uncertain. 
 
 t This law appears to be exhibited, even within the narrow limits of our own 
 island. It appears from the valuable statistics of disease collected during the Census, 
 and discussed by Sir W. Wilde, that deaths by consumption are least numerous in the 
 south-west of Ireland, while deaths from epidemic and contagious diseases are most 
 numerous in the same district.
 
 THE CURRENTS OF THE ATLANTIC. 
 
 407 
 
 determined by the imperfect method of a decennial census, is 21 
 per 1000, that of England being 22. And here I cannot avoid 
 remarking, that the connexion of these facts with temperature has 
 been strangely mis-stated by the eminent French statist, M. Moreau 
 de Jonnes, by whom these vital statistics were first collected. After 
 observing that, of all the states of Europe, the British Islands are 
 the most favoured by a low mortality, he adds with evident sur- 
 prise " It is on the frozen rocks of Ireland (les rochers glaoes de 
 1'Irlande) and in the midst of the eternal mists of Scotland, that 
 man reaches the most advanced age !" 
 
 But the season of the year, and probably even the hour of the 
 day, exert their influence upon mortality. The following numbers 
 give the relative mortality of the several months of the year in Bel- 
 gium, that of the whole year being taken as unity : 
 
 Month. 
 
 Mortality. 
 
 Month. 
 
 Mortality. 
 
 January, . . 
 
 1-21 
 
 July, . . . 
 
 0-81 
 
 February, . . 
 
 1-20 
 
 August, . . 
 
 0-82 
 
 March, . . . 
 
 1-19 
 
 September, . . 
 
 0-89 
 
 April, . . . 
 
 1-12 
 
 October, . . 
 
 0-93 
 
 May, . . . 
 
 0-98 
 
 November, . . 
 
 0-94 . 
 
 June, . . . 
 
 0-88 
 
 December, . . 
 
 1-03 
 
 The regularity of these numbers is very remarkable. The mortality 
 is greatest in January, the coldest month of the year, and least in 
 July, which is the warmest ; and the proportion of the former to 
 the latter is that of three to two. 
 
 These facts are in accordance with the laws of mortality stated 
 above ; for Belgium is to the north of the neutral line, and in it, 
 therefore, the mortality should depend chiefly upon the cold of 
 winter. To the south of that line we should expect an opposite 
 result namely, that the mortality should be greatest in the hottest 
 months of the year. We do not possess the data necessary to verify, 
 or to disprove, this conjecture. It is worthy of remark, however, 
 that in Ireland, which 'is traversed by the mean isothermal of 50, 
 the periods of greatest and least mortality are neither the coldest 
 nor the hottest months, but the intermediate periods of spring and 
 autumn. It appears from the Census of 1851, that the number of
 
 408 
 
 THE CLIMATE OF IRELAND, AND 
 
 burials in Dublin was greatest in March, and least in October and 
 November; and in Ireland generally the mortality is greatest in 
 spring, and least in autumn. The following numbers represent 
 the relative mortality at each of the four seasons, that of the entire 
 year being taken, as before, as unity : 
 
 Season. 
 
 Relative Mortality. 
 
 Spring, , 
 
 1-31 
 1-11 
 
 Autumn, 
 Winter 
 
 0-57 
 1-01 
 
 
 
 Even for places under the same isothermal line, and at the same 
 season of the year, the difference between the temperatures of day 
 and night, or the diurnal range, exerts an effect upon health. When 
 it is great, the extremes are, of course, more divergent. But, in- 
 dependently of this circumstance, the suddenness of the change of 
 temperature very probably adds to its influence, especially in the 
 case of individuals predisposed to lung-disease. I have already 
 pointed out the fact that, in islands this variation is small, com- 
 pared with the interior of continents. Throughout Ireland, the 
 diurnal range of temperature is small. It is less on the coast than 
 in the interior of the island ; and it is least of all on the coast of 
 Kerry, in the neighbourhood of Valentia, Now it is remarkable 
 that this region is also that most favoured by a high winter tem- 
 perature. The mean direction of the isothermal lines in Ireland, 
 in the winter months, is N. 40 W. ; so that the highest winter 
 temperature is at the south-western extremity of the island, and 
 the lowest at the north-eastern. The former, therefore, seems to 
 be the region most favourable to the patients I have referred to, 
 as well on account of its high winter temperature, as because of 
 its small daily range ; while the latter is the least so. 
 
 This conclusion (which I ventured to advance some years ago, 
 before the facts were known) has since been fully verified by Sir 
 William Wilde, in his analysis of the Census of 1851. Neglecting 
 the inland districts, for which the meteorological data are insuffi- 
 cient, he finds that the deaths from consumption, at the several
 
 THE CURRENTS OF THE ATLANTIC. 
 
 409 
 
 parts of the coast-line of Ireland, are as follow, the deaths from all 
 causes being 1000 : 
 
 North-east, from Glenarm to Dublin, . . 
 South-east, from Dublin to Youghal, . . 
 South, from Youghal to Bantry Bay, . . 
 South-west, from Bantry Bay to Galway, 
 North-west, from Galway to Donegal Bay, 
 North, from Donegal Bay to Glenarm, . 
 
 172 
 
 161 
 
 106 
 
 76 
 
 83 
 
 127 
 
 The proportion of the highest of these numbers to the lowest is 
 nearly that of 2 to 1. 
 
 I have hitherto spoken only of the relation of the temperature 
 of the air to health : it remains to say a few words of its moisture. 
 
 We all know that the outer covering of the human body is 
 porous, and that these pores are incessantly engaged in the per- 
 formance of an office, upon the due discharge of which the health 
 is closely dependent ; but we are perhaps not all aware of the 
 magnitude of the operation. The experiments of Lavoisier and 
 Seguin show that the quantity of water, which transudes through 
 the skin of an average-sized man, in 24 hours, is 30 ounces ; and 
 this, in the ordinary state of things, is carried off by evaporation 
 as fast as it is secreted. Now, it is a well-known meteorological 
 law, that evaporation is less, the greater the amount of moisture 
 actually present in the air ; and that it ceases altogether when the 
 air is saturated with moisture. It follows, therefore, that the due 
 performance of one of the most important functions of the animal 
 system is dependent on the dryness of the air. It is not to be in- 
 ferred from this, however, that the transpiration, as Blumenbach 
 denominates the process, ever wholly ceases, even when the air is 
 saturated with moisture. For the air in contact with the body 
 rises in temperature, and is thus enabled to take up a fresh supply 
 of moisture from the skin. 
 
 But besides the effect of humidity in checking the process of 
 the insensible perspiration, it also operates in reducing the animal 
 heat, when the temperature of the air is low. This seems to re- 
 quire some explanation. One of the immediate consequences of 
 evaporation is, we know, the abstraction of heat ; and as the eva- 
 poration from the surface of the body is less in moist air than in
 
 410 
 
 THE CLIMATE OF IRELAND, AND 
 
 dry, it would seem at first sight that the chilling effect should be 
 less also. But this is more than compensated by the increased con- 
 ducting power of air when charged with moisture. When such air 
 is much below the temperature of the body itself, the heat of the 
 latter will escape through it, much more rapidly than through air 
 that is dry. The chilling effect of the damp fogs of winter, with 
 all their train of attendant evils, is due to this cause. 
 
 On the other hand, extreme dryness of the air produces an in- 
 jurious effect of a different kind. When the air in contact with 
 the lungs is excessively dry, inflammation of the organ is apt to 
 ensue ; and thus, to those who have a constitutional tendency to 
 such disease, a very dry air is often fatal. To this cause are to 
 be ascribed the painful, and even fatal effects of the simoom, the 
 dry wind of the African desert. And it is on this account also 
 that, in rooms heated by iron stoves, which are so common in 
 Germany, a vessel containing water is usually placed at the top 
 of the stove, to give the suitable degree of moisture to the air. 
 
 The mortality in towns is much greater than in the rural 
 districts adjoining. Thus in Belgium, where vital statistics have 
 been collected with much care, the death-rate in the towns is 27 
 per 1000, while in the country it is only 21. This is in part 
 accounted for by the deficiency of pure air produced by over-crowd- 
 ing. Every adult inhales about 13 cubic feet of air in an hour, 
 from which his lungs extract the vital element, and replace it by a 
 noxious gas ; and in populous cities and especially in the dwell- 
 ings of the poor this waste is not adequately supplied.* The 
 effects of overcrowding have been clearly shown by Dr. Farr, in 
 his useful analysis of the Eeports of the Eegistrar-general on the 
 mortality of London. The following are the results of his com- 
 parison of the mortality with the density of the population, in the 
 three principal districts : 
 
 
 
 Square yards 
 to each 
 person. 
 
 Death-rate 
 per 1000. 
 
 I. 
 
 Whitecnapel district, . 
 
 57 
 
 33 
 
 II. 
 
 St. Saviour do. 
 
 78 
 
 28 
 
 III. 
 
 Kensington do. 
 
 217 
 
 22 
 
 It has only lately been brought to light, by the philanthropic exertions of the
 
 THE CURRENTS OF THE ATLANTIC. 411 
 
 But the supply of air in towns is not merely deficient in quan- 
 tity it is also greatly deteriorated in quality. This is mainly 
 owing to the impurity caused by decaying animal matter. The 
 fluids of the body have a tendency to decompose, which is resisted 
 by the vital power ; and when that power is finally withdrawn, 
 we all know how soon the work of destruction is completed. Life 
 is thus a continued struggle between the chemical and the vital 
 powers ; and the effect of decaying animal matter is to stimulate 
 the chemical forces, and to a degree which the vital power may be 
 unable to resist. The actual contact of such matter with the blood 
 will destroy life speedily ; and every surgeon knows the danger of 
 a wound from the dissecting-knife. But the poison is usually 
 administered more slowly. The effluvium pollutes the air we breathe, 
 and reaches the blood through the lungs ; and thus the process of 
 destruction goes on more slowly, indeed, but as surely. 
 
 These agents of disease and death may be, and have been, suc- 
 cessfully controlled by means within our own power. The death- 
 rate of London was formerly 57 per 1000 as great as it is in 
 Constantinople now. At present it is only 23 ; while, in some of 
 the London districts, the death-rate has been reduced to 17, a 
 proportion as small as that of the healthiest of the rural districts. 
 This is very encouraging to the sanitary reformer. 
 
 The first attempt to legislate for the sanitary improvement of 
 towns was made as recently as the year 1848. Since the passing 
 of the " Public Health Act " of that year, the death-rate in the 
 towns to which it has been applied has diminished by 6 per 1000 ; 
 and, in Liverpool, the death-rate is said to have been reduced from 
 '38, which was its amount in 1846, to 24. Much useful work has 
 also been effected by voluntary associations, and especially by the 
 " Metropolitan Association for Improving the Dwellings of the 
 Industrial Classes." In one of the great lodging-houses of that 
 Society the " Metropolitan Buildings," in Pancras-road the 
 death-rate has been reduced to 13| per 1000, which is little more, 
 than one half the average death-rate of London. The effects of 
 these improvements are even more marked in the case of children, 
 who are far more susceptible than adults to the deleterious effects 
 of impure air.* The death-rate of children under five years of 
 
 Lite lamented Lord Herbert, that one half of the barracks of the United Kingdom 
 furnished little more than 400 cubic feet of space to each soldier. 
 
 * It appears from the Census of Ireland, that the number of deaths of children, in
 
 412 THE CLIMATE OF IRELAND, AND 
 
 age, in the buildings of the Association, is said to be only 5 per 
 1000, the corresponding death-rate for the whole Metropolis 
 being 46 ! 
 
 The annual death-rate in Dublin, as deduced from the returns 
 of the Census of 1851, was 29 per 1000. The Act for the registra- 
 tion of births and deaths in Ireland came into operation only at 
 the beginning of last year ; and the death-rate in Dublin, deduced 
 from the returns made under that Act, was 27 per 1000. Thus 
 there has been some amelioration in our sanitary state, although 
 much still remains to be done. We have every reason to hope 
 that the sanitary measures now in progress in this city, under the 
 direction of a gentleman so competent to the task as the present 
 Medical Officer of Health, will before long effect the desired im- 
 provements. 
 
 I have ventured to touch upon these painful topics, on account 
 of their urgent importance at the present time. A fearful epidemic 
 has, in its stern undeviating march, revisited Great Britain, and, 
 if the arm of the Almighty be not stretched forth to arrest its 
 progress, will shortly reach our homes. Whatever be the original 
 source of this formidable disease, it seems to be now generally 
 believed that its proximate cause is the poisoning of the blood ; and 
 we cannot doubt that this poison is communicated to others, whose 
 vital powers are unable to resist it, through the air for we can in 
 no other way explain the fact, that the disease in its progress fol- 
 lows the great highways of human intercourse, while at the same 
 time it is little, if at all, contagious. It is thus refemBle to the 
 general cause already adverted to namely, the power of disorgan- 
 ized matter to generate decay although the effect bears in this, 
 as in other familiar cases, the impress of the original type. It is 
 true, we have not yet succeeded in tracing the organic element in 
 the air, to which it owes its destructive power. But there are 
 many facts which prove that the air does contain elements which 
 evade all the resources of chemistry, while, nevertheless, their 
 presence is proved by their physiological effects. No chemist has 
 detected the substance which imparts the perfume of the rose to 
 the air ; and yet there are individuals so sensitive to the odour of 
 flowers, as to be rendered ill by inhabiting the room in which they 
 lie. It is even stated I quote from a high French authority 
 
 the first year of their age, is 9 per cent, of the total number in the rural districts, while 
 it is 16 per cent, in towns.
 
 THE CURRENTS OF THE ATLANTIC. 413 
 
 that the air taken in the great sewer of Montmartre, and that 
 collected in the Place de la Concorde (one of the most open spaces 
 in Paris), have been carefully compared, and found to be undistin- 
 guishable by the most delicate chemical tests. But, whatever be the 
 source of the virus, its action is, at all events, powerfully stimulated 
 by the co-operation of decaying organic matter in its ordinary 
 forms ; and as this ally of disease is within our power, we shall be 
 without excuse if we neglect the known precautions for defence.* 
 
 I regret to have to close this brief sketch of our atmospheric 
 relations with a disagreeable topic. I have endeavoured to bring 
 before you the more salient features of our climate, so far as they 
 can be exhibited in a popular form ; and, on a review of all, we 
 have, I think, no reason to repine. If the humidity of the air by 
 which we are enveloped is at times depressing to our energies of 
 body, or of mind, we must remember that we are indebted to it 
 for the luxuriant crops, which furnish food to our cattle, and 
 through them to ourselves. Our summer temperature may be too 
 low to bring some of our seeds and fruits to perfection ; but, on 
 the other hand, it is to its moderated heat that we owe our exemp- 
 tion from some of the maladies which afflict the inhabitants of 
 more southerly climes ; while our mild winters press gently on the 
 springs of life, and suffer man to reach an advanced age. 
 
 Let us be thankful to-ihe Giver of all good gifts for these His 
 blessings ! and if as all earthly blessings are they are at times 
 checquered by afflictions, let us remember that these too come from 
 a Father's hand. Let them serve to remind us how far we may 
 have strayed from Him, and bring us back, as sorrowing and re- 
 pentant children, to His outstretched arms ! 
 
 * This seems to be conclusively shown by the effect of elevation on the number of 
 deaths by cholera in London, in the year 1849. The Table contained in the Reports 
 of the Registrar-general gives the heights above the Thames, and the corresponding 
 number of deaths by cholera, out of a population of 10,000. The numbers decrease at 
 first rapidly, and afterwards slowly, until, at heights above 100 feet, the variation in 
 the number of deaths is very small. The facts are justly ascribed to the imperfect 
 drainage of places situated at low levels.
 
 XIX. ON THE RISE AND PROGRESS OF MECHANICAL 
 PHILOSOPHY. 
 
 Introductory Lecture delivered in the Philosophy School of Trinity Colkge, in Hilary 
 Term, 1834. 
 
 GENTLEMEN, I have lately endeavoured to lay before you an 
 outline of the methods which have been pursued in the culti- 
 vation of Physical Science; and I dwelt in particular on the 
 principles of the inductive philosophy as laid down by Bacon. 
 At present I propose that we should confine our attention to that 
 branch of natural philosophy which is to form the subject of our 
 consideration during the ensuing Term ; and review briefly the 
 rise and subsequent advances of Mechanical Science. 
 
 The fallacious methods adopted by the ancients in physical 
 science, generally, did not exclude a certain progress in the science 
 of force. The doctrine of equilibrium, as you will soon learn, is 
 altogether independent of experience ; and the laws which deter- 
 mine the relations of balancing forces may be deduced wholly by 
 a priori reasoning. In this department, accordingly, some steps 
 were early made. From the metaphysical principle of sufficient, 
 reason, Archimedes derived the properties of the lever; and showed 
 that two weights attached to it are in equilibria, when they are to 
 one another inversely as their distances from the fulcrum. This 
 important and fundamental principle contained the germ of Statical 
 Science : Archimedes himself was able to deduce from it the rules 
 for the composition of parallel forces ; and to show that there 
 existed in every body, or system of bodies, a point now known 
 by the name of the Centre of Gravity in which its weight might 
 be supposed to be concentred.
 
 KISE AND PEOGKESS OF MECHANICAL PHILOSOPHY. 415 
 
 The foundations of Hydrostatical Science were also laid by the 
 same great geometer. His work de humido imidentibiis is derived 
 from the principle of the equality of fluid pressure a principle 
 still adopted as the basis of this science. In this work he has 
 shown that a heavy body, when immersed in a liquid, loses a 
 portion of its weight equal to that of the liquid displaced. It is 
 by the aid of this theorem a theorem on which the present mode 
 of determining the specific gravities of bodies is made to depend 
 that the philosopher of Syracuse is supposed to have solved the 
 famous problem of the crown, proposed by King Hiero, and to 
 have detected the fraud of his workman. 
 
 A long period of darkness followed the discoveries of Archi- 
 medes. The philosophers of Alexandria, Ctesibius, and Hero, 
 Pappus Alexandrinus and others, pursued the inquiries which he 
 had begun, and by their inventions added much to practical 
 mechanics. To the two first of these authors we owe the analysis 
 of the various classes of machines, and their reduction to five 
 simple ones ; and the name of $vvajj.ttc, or powers, which they 
 affixed to these elementary machines, is still retained. But yet 
 the theory remained nearly as it had been left by Archimedes, 
 and the doctrine of equilibrium was destined to receive no addition 
 until the close of the 16th century. 
 
 Hitherto the theory of the Mechanic Powers was understood 
 only so far as it could be derived from the principle of the lever ; 
 and no method was known of determining the conditions of equili- 
 brium of forces whose directions were inclined. It was at this 
 point that the progress of the ancients in Mechanical Philosophy 
 was arrested, and it is here that we are to look for the first im- 
 portant extension of this science. The problem was attempted, 
 but unsuccessfully, by Ghiido "Ubaldi, a mathematician of Italy, 
 in the 16th century ; and was finally solved by Stevinus, a cele- 
 brated engineer of the Low Countries, who demonstrated the 
 principle of equilibrium on the Inclined Plane. In this remarkable 
 demonstration, he supposes a chain of uniform thickness to encom- 
 pass the plane entirely round : part of this will rest on the plane, 
 along its hypothenusal side, part will hang vertically beside its 
 altitude, and the remainder will form a loop below the base. 
 Now the whole is in equilibria, for if not, a perpetual motion must 
 ensue in the direction of the greater force ; and as the part which 
 hangs below the plane draws equally in both directions, its effect
 
 416 RISE AND PEOGEESS OF 
 
 may be disregarded. There is equilibrium, therefore, between the 
 other two portions that which is equal to the length of the plane, 
 and that which is equal to its altitude ; and it follows that two 
 weights, which balance by means of the inclined plane, one hanging 
 freely, and the other resting on the plane, must be to one another 
 in the ratio of the height of the plane to its length. This singular 
 solution of the problem was given in the year 1585 ; and from 
 it the author has derived the general conditions of equilibrium 
 among any three forces meeting at a point. Thus, though he 
 does not seem to have been aware of the full value of the prin- 
 ciple, he touched the very corner-stone of statical science. 
 
 The theory of the Equilibrium of Fluids is also largely indebted 
 to Stevinus ; and he was the first to determine the pressure which 
 the bottom of a vessel sustains from the contained liquid. 
 
 The second grand division of mechanical philosophy the 
 Doctrine of Motion is of much later birth. We are here beyond 
 the circle of abstract truth, and experience alone can furnish the 
 principles of our reasonings. We are not to wonder, therefore, 
 that no progress was made in this department of science, when the 
 true principles of experimental inquiry were themselves unknown. 
 The school of Aristotle taught that motions are either natural or 
 unnatural The natural tendency of all terrestrial bodies was said 
 to be, either to fall directly to the ground, or to ascend from it 
 until they reached their place ; while bodies that were impelled 
 obliquely were believed to pursue a violent or unnatural course, 
 and the motions thus generated were supposed to tend continually 
 to decay. In the heavens all this was different : the natural 
 motions of the heavenly bodies were pronounced to be circular ; 
 and, as their matter was incorruptible, so their motions were 
 eternal and immutable. Amid these reveries, we can still trace 
 throughout the workings of genius ; and in some parts of the 
 mechanical speculations of Aristotle, we find very just views 
 respecting the nature of gravity, and of force in general. The 
 principle of the Composition of Motion that fertile principle which 
 served as the basis of the reasonings of Gralileo, and was more 
 fully developed by Newton is to be found distinctly stated, and 
 reasoned on in Aristotle's writings. 
 
 For more than two thousand years the dogmas of Aristotle 
 continued to extort the assent of mankind, and though here and 
 there a bold inquirer might be found, who ventured to doubt the
 
 MECHANICAL PHILOSOPHY. 417 
 
 authority of the " great master," and, to appeal to nature herself, 
 yet the science of motion was not destined to profit by these 
 glimmering lights, and its very foundations remained unlaid until 
 the close of the 16th century. 
 
 Galileo was born at Pisa, in the year 1564, and at an early 
 age devoted the energies of an ardent and powerful mind to the 
 mathematical and physical sciences ; and here was first formed 
 that union of abstract and experimental reasoning, whose force and 
 value in explaining the phenomena of nature is now so well under- 
 stood. While yet pursuing his studies at the university, Galileo 
 had begun to make experiments on the laws of falling bodies; 
 and he then discovered the fact, that all bodies, whether light or 
 heavy (the effect of the air's resistance being abstracted), fall to 
 the ground from the same height in the same time. This im- 
 portant law of gravity was in direct contradiction to the principles 
 of the Aristotelian philosophy, then in full repute ; and, unac- 
 countable as it now seems, it was believed that two unequal 
 weights, if let fall at the same instant, and from the same height, 
 would reach the ground in times inversely proportional to the 
 weights that a weight of 100 Ibs. (for example) would descend 
 in the y^oth part of the time occupied by a weight of 1 Ib. 
 Galileo tried this very case before many witnesses, from the 
 summit of the famous leaning tower of Pisa. The two weights 
 were found to reach the ground in precisely the same time ; and 
 the decisive result of the experiment did more, perhaps, to shake 
 the empire of the Aristotelian philosophy, than any single effort 
 of opposition hitherto made. 
 
 Setting out from the principle that bodies, in their free 
 descent towards the earth, receive equal increments of velocity in 
 equal times, Galileo deduced, by the application of mathematical 
 reasoning, the known laws of falling bodies; and having proved 
 that these laws must hold good also in the case of bodies de- 
 scending on inclined planes, where a portion of the weight is 
 sustained, and where consequently the acceleration is not so rapid, 
 he was enabled to bring the whole theory to the test of experi- 
 ment. He applied himself, in the next place, to the consideration 
 of the motion of a heavy body projected obliquely ; and by the aid 
 of the principle of the composition of motion a principle tacitly 
 assumed in his reasoning he proved that the path traced by a 
 projectile was the well known curve of Appolonius the parabola, 
 
 2K
 
 418 RISE AND PROGRESS OF 
 
 All these results were confirmed by observation, and thus the 
 nature and laws of terrestrial gravity were fully established. 
 
 Galileo seems to have turned his attention at an early period 
 to the motions of pendulous bodies ; and he is said to have been 
 conducted to the knowledge of the fact that all the vibrations 
 of the same pendulum, whether great or small, are performed in 
 the same time by observing the swinging of the lamps in the 
 Cathedral of Pisa. The tautochronism of the pendulum, however, 
 seems to have been noticed, and even applied, at a much earlier 
 period. The astronomers of Arabia employed the instrument in 
 some of their observations, patiently counting the number of its 
 oscillations during the period of an eclipse, and renewing the 
 motion with a slight push of the finger, when the arcs of vibration 
 became too small. The same mode of observation was practised 
 in more recent times by Gassendi, Biccioli, and other astronomers 
 of Europe, when the attention of the scientific world was again 
 drawn to the principle of tautochronism. 
 
 By these important discoveries, Galileo has justly earned the 
 title of " father of dynamical science." But to estimate duly the 
 merits of this great man, we must consider the age in which he 
 lived, and the darkness with which he was encompassed. Alone 
 and unsupported, he assailed the Aristotelian philosophy with all 
 the weapons of sound argument and caustic ridicule ; and the 
 inveterate spirit of hostility which he thus excited, the rancour 
 of rivals, and the intolerant persecution of the Church, ended 
 only with his life. Notwithstanding all this opposition, however, 
 truth was progressive. The proofs which the astronomical dis- 
 coveries of Galileo brought in support of the Copernican system 
 roused the attention of philosophers; and it may be fairly ques- 
 tioned whether the discoveries of the Florentine philosopher have 
 not had as great an influence on the progress of physical science, 
 as the works of his immortal contemporary Lord Bacon. 
 
 While to Galileo we owe the foundation of the doctrine of 
 motion, to his pupil Torricelli we are indebted for the first step 
 which was made in that branch of the doctrine which relates to 
 fluids. The fundamental problem of hydraulics that which de- 
 termines the velocity of efflux of a fluid through an aperture in 
 the bottom or side of a vessel was first solved by this writer, in 
 his work de motu gravium. 
 
 As the terrestrial mechanics of Aristotle were overthrown by
 
 MECHANICAL PHILOSOPHY. 419 
 
 Galileo, so, about the same time, his theory of the heavenly 
 motions was shown to be baseless. According to Aristotle, it 
 has been already mentioned, the motions of the celestial bodies 
 are circular and uniform because the circle is a perfect figure. 
 Many of his followers, however, attempted to support the doctrine 
 on physical grounds, and asserted with Eudoxus, that the planetary 
 bodies are confined by crystalline spheres, the movements of which 
 gave rise to the motions we perceive. It is somewhat remarkable 
 that the very same bodies, whose motions now tend to establish 
 the existence of a resisting medium in the heavens, should be the 
 first to give evidence against the theory of the crystalline spheres. 
 It was ascertained by Tycho Brahe, from astronomical observations, 
 that the comets were not, as Aristotle supposed, meteors in our 
 atmosphere, but moved throughout the planetary spaces ; and it 
 was plain that, as they crossed the orbits of the planets in every 
 direction, they could have encountered no obstacles such as the 
 spheres of Eudoxus. Yet the doctrine of circular motion remained 
 still undisputed, until Kepler, the successor of Tycho Brahe, 
 announced to the world his great discoveries the elliptic motion of 
 the planets, the equable description of areas, and the harmonic law. 
 It is impossible to read the account given by Kepler of these 
 discoveries, without feeling animated with a portion of his en- 
 thusiasm. " I have stolen," says he, " the golden vases of the 
 Egyptians, to build up a tabernacle for my God, far from the 
 confines of Egypt." But when from these laws of observation he 
 attempts to ascend to their physical causes, his reasonings are 
 deeply tinged with the mysticism which seems to have gained so 
 powerful an ascendancy over his great mind. Of the existence 
 of gravitation, as the ruling principle of the universe, he enter- 
 tained very strong and clear views ; but the attraction itself he 
 conceived to be of the nature of animal force. "If the moon 
 and the earth," he wrote, " were not retained in their orbits by 
 their animal force, or some other equivalent, the earth would 
 mount to the moon by a fifty-fourth part of their distance, and 
 the moon fall towards the earth by the other fifty-three parts, 
 and they would thus meet, the substance of both being assumed 
 to be of the same density. If the earth should cease to attract 
 its waters to itself, all the waters of the sea would be raised, 
 and would flow to the body of the moon." The earth itself he 
 supposed to be an enormous living animal, of which the tides
 
 420 RISE AND PROGRESS OF 
 
 constituted the act of respiration ; and as this vital function was 
 supposed to be produced by the influence of the moon, so its other 
 living energies were dependant on the configurations of the planets. 
 In the Harmonies of the celestial motions, he assigns to Jupiter 
 and Saturn the bass, to Mars the tenor, the counter-tenor to the 
 Earth and Venus, and the treble to Mercury. 
 
 The cosmical system of Des Cartes is too important in the 
 history of science to be passed over without notice, although it 
 seems to have been but a refinement on the doctrine of Eudoxus, 
 and was as remote from real existence. Kepler, we have seen, 
 had endowed the great bodies of the universe with vital powers, 
 and chained them together, in their wanderings through space, by 
 the ties of animal sympathy. The astrologers of the day borrowed 
 from the region of spirit itself, and, by a beautiful fiction, assigned 
 to each planet its guardian angel, whose office it was to guide its 
 career through the trackless void. Des Cartes was the first who, 
 with any show of plausibility, attempted to reduce the whole to 
 physical principles, and to derive the phenomena of the material 
 world from the fundamental properties of body. Matter, accord- 
 ing to this ingenious philosopher, fills all space ; and its parts are 
 endued with motion in every possible direction. By the combina- 
 tion of these infinitely varied motions, matter is supposed to be 
 continually deflected from its rectilinear course ; and thus at length 
 to form itself into vortices, in which the denser bodies of the 
 universe floated, and of whose motion they partook. In this 
 manner the earth and planets were supposed to be borne round the 
 sun, in the vortex of the solar system : and each planet itself was 
 the centre of a lesser vortex, which carried its secondaries. Such 
 was the system which preceded the theory of universal gravitation. 
 Mankind looked up with wonder on the symmetrical fabric 
 which the enchanter's wand had raised, and they examined not 
 too narrowly into its foundations ; but a mightier wizard soon 
 after came upon the scene, and the rod of Aaron swallowed the 
 rod of the Egyptian. 
 
 The actual contributions of Des Cartes to mechanical science 
 are inconsiderable. He was an a priori philosopher, in the strictest 
 sense of the word; and in the barrenness of that philosophy 
 aided as it was by powerful talents, and by the force of these 
 talents gaining an ascendancy, which for a time closed men's eyes 
 to the truth we have, perhaps, as striking a proof as could be
 
 MECHANICAL PHILOSOPHY. 421 
 
 given of the soundness of Bacon's views. " We wish," says 
 Des Cartes, "to deduce effects from their causes, and not, con- 
 versely, causes from their effects. We appeal to experience only, 
 that out of innumerable effects which may he produced from the 
 same cause, we may direct our attention to one rather than to 
 another." The axioms, to which he endeavoured to reduce all his 
 theories, were grounded on metaphysical notions of the attributes 
 of the Deity ; and we have a remarkable instance of the presump- 
 tion and error, which characterized most of his reasonings, in the 
 dogma, that the quantity of motion in the universe must remain 
 always the same, because the Divine nature is immutable. 
 
 To Des Cartes, however, we are indebted for the first distinct 
 enunciation of the laics of motion; although his own conception 
 of these laws was far from accurate, and he seems, in particular, to 
 have regarded the inertia of matter as a kind of active force. 
 
 The first actual contributions of importance which dynamical 
 science received subsequently to the discoveries of Galileo are due 
 to Huygens. By the aid of the most refined geometry, of which 
 he was so perfect a master, this mathematician discovered the 
 relation which subsists between the length of a pendulum and the 
 time of its vibration ; and having developed the theory of the 
 instrument, he realized the conception of Galileo, and applied it to 
 the regulation of the clock. On pursuing his inquiries, however, 
 Huygens ascertained that the property of tautochronism belonged 
 to the circular pendulum only when the arcs of vibration are 
 indefinitely small; and he was thus led to inquire what curve 
 possessed the property universally. Finding this curve to be the 
 cycloid, he conceived the idea of making a pendulous body move 
 in it'; and his mathematical skill soon after enabled him to point 
 out the means of accomplishing this object. His account of this 
 construction, and of the principles on which it depends, was pub- 
 lished in the year 1670, in a work entitled Horologimn Oscillatorinm, 
 many years after the date of the discovery. But interesting as the 
 cycloidal pendulum is in theory, it has been long since abandoned, 
 as useless, in practice ; and the clocks to which the circular 
 pendulum was adapted were found far to excel the cycloidal 
 clocks of Huygens. 
 
 To Huygens we are indebted also for the next great step 
 which was made in dynamical science the theory of enrufur 
 )uoti<i ; and the laws of centrifugal force were developed by him
 
 422 RISE AND PROGRESS OF 
 
 with much clearness and simplicity. Thus was laid the foundation 
 of the doctrine of central forces a doctrine which, in the hands of 
 Newton, served as the basis of the theory of universal gravitation. 
 I must pass over the names of Leibnitz and Varignon, Wallis, 
 Wren, Hooke, and Halley, all of whom have made valuable 
 contributions to mechanical science. We have now reached a 
 period, in which the achievements of a single individual outweigh 
 the collected labours of all his predecessors in discovery; and 
 before the lustre of whose genius the lesser lights of science 
 " pale their ineffectual fires." The time had indeed arrived in 
 which one great mind was wanting, to concentrate the rays of 
 knowledge, which were now beginning to dawn in various quarters ; 
 and the state of physical science was prepared for a vast revolution. 
 The cumbrous apparatus of cycles and epicycles, with which 
 Ptolemy had deformed the heavens, had disappeared ; and the 
 true system of the universe was established by Copernicus. The 
 planetary motions were reduced by Kepler to three general laws ; 
 and one of these laws was found by Cassini to hold in the 
 miniature system of Jupiter and his satellites, showing thereby 
 that it was not the result of any accidental congruity, but had its 
 origin in the nature of things. Again, the barrier which the 
 ancient physics had raised between celestial and terrestrial motions 
 had crumbled away, and the dogmas of Aristotle were no longer 
 articles of belief. Lastly, the true road to philosophical discovery 
 was pointed out by Bacon: to precept, Gralileo added the more 
 powerful influence of example, and laid the foundations of 
 dynamical science in the laws which regulate the motions of 
 bodies at the surface of our globe. In such a time Newton 
 
 There is not a single department of knowledge approached by 
 Newton, that did not receive the impress of his mighty genius. 
 Some branches of science were his exclusive creation ; and when 
 the difficulties of the investigations, into which his physical 
 speculations led him, surpassed the power of the geometry of his 
 day, he at once created an instrument which enabled him to 
 grapple with, and overcome them. But I must confine myself 
 here to those discoveries of Newton which are connected with 
 the subject of mechanical philosophy : to some of his other 
 discoveries I shall have occasion to draw your attention hereafter. 
 
 The theory of equilibrium, in the different simple machines,
 
 MECHANICAL PHILOSOPHY. 423 
 
 had been hitherto established by separate and independent 
 methods ; and the principles of the solution were in many cases 
 obscure and unsatisfactory. Newton traced the whole theory to 
 one fundamental principle, and thus raised Statics to the un- 
 doubted rank of a science. The principle of the composition of 
 motions had, it has been said, been assumed by Galileo, though no- 
 where formally stated in his writings. Newton felt the full force 
 and value of the principle, and combining it with the second law 
 of motion, which states . the proportionality of the force to the 
 motion generated, he gave the first formal proof of the celebrated 
 principle of the composition of forces. I shall not dwell upon the 
 objections which have been urged against this mode of establishing 
 the important theorem of the parallelogram of forces, nor upon 
 the attempts which have since been successfully made to assert 
 for this principle the dignity of an abstract truth. It is sufficient 
 at present to observe that the conditions of equilibrium, in the 
 different classes of simple machines, were shown by Newton to 
 flow easily and simply from this fertile principle ; and that it has 
 been since generally taken as the basis of statical science. 
 
 But much as the doctrine of equilibrium is indebted to 
 Newton, the science of motion has received yet greater accessions 
 from his hand. We have already seen that some great steps 
 were made in this branch of mechanical science by Galileo and 
 Huygens ; and many important problems were solved by other 
 writers. Yet these were but so many detached spots in the wide 
 field of truth, reached by independent paths, and cultivated by 
 different processes. No highway had as yet been opened into its 
 fertile territory ; and its unexplored recesses were still as difficult 
 of approach, as if no part whatever had been subjugated to 
 human reason. This great want was supplied by Newton ; and, 
 in the first book of the Principia, he has developed, by general 
 and uniform methods, the laws of rectilinear and curvilinear 
 movement under the influence of a central force ; the theory of 
 the motion of bodies confined to given curves or surfaces, &c. 
 
 But great and valuable as were these additions to dynamical 
 science, they seem to have been regarded by Newton but as steps 
 to that system of the universe, the key of which he had early 
 mastered. The principle of universal gravitation his grand dis- 
 covery is indeed the highest and most comprehensive physical 
 truth ever reached by man ; and we shall not mis-spend our time
 
 424 RISE AND PROGRESS OF 
 
 in reviewing briefly the principal steps which led to its complete 
 discovery. 
 
 In the year 1666, the visitation of the plague compelled the 
 young philosopher, then about the age of twenty-four, to leave 
 Cambridge and retire into the country : and we are told that as 
 he sat one day in a garden, meditating on the wonders of nature, 
 his attention was arrested by the falling of the apples from the 
 trees ; and it at once occured to him that, as the force of gravity 
 appeared to extend from the earth's surface to the tops of trees 
 and of houses, and even to the summits of the highest hills, 
 without any apparent diminution, might it not reach even to the 
 moon itself ? And may not our satellite be retained in its orbit 
 by this very force, combined with an original impulse just as a 
 projectile at the earth's surface is forced to describe a curve under 
 the same influences ? 
 
 But another question here arose. Although the force of 
 gravity does not appear to vary sensibly in the limited distance 
 from the earth's surface at which we can make observations, yet, 
 at the distance of the moon from the earth, this force (supposing 
 it to extend so far) may be greatly diminished ; and if so, it 
 would be necessary to ascertain the law of the diminution, before 
 we could submit the question to calculation. Here the mind of 
 Newton made another vast stretch. If the moon be retained in 
 her orbit round the earth, by the attraction of the latter body, 
 may not the earth, also, and the other planets, be held in their 
 paths round the sun by the action of a similar force tending to 
 that luminary? Now, it was not difficult to prove that the 
 centripetal forces of bodies, revolving in circles round a common 
 centre, must be inversely as the squares of their distances from that 
 point, provided that (as is the case with the earth and planets) 
 the squares of their periodic times varied as the cubes of their 
 distances from the centre. If this law, therefore, be extended by 
 analogy to terrestrial gravity, at the distance of the moon (which 
 is about sixty semi-diameters of the earth), that force must be less 
 than at the earth's surface, in the duplicate ratio of sixty to one. 
 Is then the space through which the moon is bent in a second, 
 from the rectilinear direction towards the earth, the 3600th part 
 of that through which a body will fall, in the same time, at the 
 earth's surface ? 
 
 Here was a question that could at once be submitted to
 
 MECHANICAL PHILOSOPHY. 425 
 
 calculation. Unfortunately, one of the data necessary to the 
 calculation the magnitude of the earth's circumference was 
 hitherto very erroneously determined ; and the result, in conse- 
 quence, appeared to be inconsistent with the assumed law. In 
 the true spirit of philosophy, Newton at once abandoned his 
 hypothesis, the moment that it appeared at variance with facts ; 
 and it was not until some years afterwards that his thoughts 
 seemed to have been recalled to the subject by the remarkable 
 speculations of Hooke. The measurement of a meridional arc, 
 undertaken by Picard, was soon after completed, and the new 
 determination of the earth's radius happening to be the subject 
 of discussion at the Royal Society, one day that Newton was 
 present, he instantly perceived its bearing upon his own in- 
 quiries, and noting down the result, he hurried home to resume 
 his calculations. He had scarcely substituted the new value in 
 his formula, when the greatness of the anticipated conclusion 
 overpowered him, and he was unable to proceed : a friend who 
 happened to come in at the moment completed the calculation, 
 and the theory of Newton was verified. 
 
 Such was the first step to the theory of universal gravitation. 
 The law was now ascertained, and the analogy which Newton had 
 already remarked, between the moon and earth and the planetary 
 system, led him at once to apply the same great principle to the 
 latter. Accordingly he next inquired what must be the paths, 
 velocities, and periodic times of the planets, on the hypothesis that 
 each of them had received an original impulse in any direction, 
 and was at the same time urged towards the sun with a force 
 varying inversely as the square of the distance. The result of 
 this inquiry was the complete confirmation of the principle. The 
 known motions of the planets, and even of the comets, were shown 
 to flow immediately from the law of gravitation ; and the famous 
 laws of Kepler were among its first consequences. 
 
 It remained to prove that the forces by which these vast 
 bodies are actuated, and which they exerted in turn, arose from 
 the combined attraction of all their parts ; and that the law 
 which was thus manifested among the great bodies of the solar 
 system was, in fact, a universal property of matter. Many 
 strong arguments induced Newton to take this for granted ; and 
 assuming that every particle of matter attracts with a force 
 directly proportional to its mass, and inversely as the square of
 
 426 RISE AND PROGRESS OF 
 
 its distance from the attracted body, he showed that spheres thus 
 composed must attract according to the same law. Thus the 
 hypothesis had all the certainty that could arise from the ^agree- 
 ment of its results with established facts : its full confirmation 
 from direct experiment was reserved for a later period. 
 
 That every particle of matter attracts every other, and is itself 
 attracted in turn, is a proposition to which, at first, we find some 
 difficulty in giving credence. We do not see the effects of such 
 attractions, among the smaller masses of matter with which we 
 are surrounded, and therefore cannot easily admit their existence. 
 But the slightest consideration must convince us that these 
 attractions, under ordinary circumstances, cannot be sensible. 
 The force is proportional to the mass of the attracting body ; 
 and as the largest mountain on the earth's surface is but as a 
 grain of sand on an ordinary globe, the attraction of the earth 
 cannot, to any considerable extent, be modified by the effects of 
 the irregular masses on its surface. Delicate observations, how- 
 ever, have rendered these comparatively minute forces perceptible. 
 In Peru, La Condamine noticed the effect of the attraction of a 
 mountain, in causing the plumb-line to deviate from the vertical. 
 Maskelyne observed a similar effect produced by the attraction of 
 Schehallien in Scotland ; and from the amount of this deviation 
 he was enabled to compare the mass of the earth, and therefore 
 its mean density, with those of the mountain. 
 
 The effects of local attractions have been exhibited in another 
 form, in the interesting pendulum experiments of Captain Sabine. 
 This able observer found a difference in the rate of going of 
 his pendulums, amounting to ten seconds in twenty-four hours, 
 and due wholly to the effects of local attraction. The rate was 
 quickest when the soil over which the pendulum vibrated was 
 compact basalt, the heaviest of the known substances composing 
 the crust of our globe; and slowest, when it was alluvial soil, 
 which is among the lightest. From an extensive comparison 
 of these effects with the subjacent strata, he concludes that 
 the nature of the soil may in general be determined, within 
 tolerable limits, and thus the pendulum be rendered a useful 
 instrument of geological inquiry. These important conclusions 
 have, very lately, received the fullest confirmation from the 
 pendulum observations of Captain Foster. 
 
 Time will not permit me more than to allude to the decisive
 
 MECHANICAL PHILOSOPHY. 427 
 
 experiment of Cavendish. By an instrument called the balance 
 of torsion an instrument of the highest value in the measurement 
 of minute forces this philosopher was enabled to measure with 
 precision the attraction of large metallic globes, and to compare 
 their forces with that of the earth itself. From these investiga- 
 tions it appeared that the mean density of the earth is about 
 double of that of its superficial parts, and five and half times 
 that of water. 
 
 I cannot terminate this subject without noticing the inter- 
 esting experiment proposed by Mr. Whewell and Professor Airy, 
 in order to determine the law of terrestrial gravity by direct 
 observation. The experiment consisted in comparing the rate of 
 a pendulum clock with that of a chronometer, at the surface of the 
 earth, and at the bottom of one of the deepest mines in England. 
 The rate of the pendulum varying with the force of gravity, 
 while that of the chronometer is independent of it, it is obvious 
 that their comparison would afford the means of determining the 
 relative forces at the two stations. The experiment, I believe, 
 was not completed. But there can be no doubt of its sufficiency ; 
 and it is a remarkable fact that Bacon proposed one altogether 
 the same in principle, and having nearly the same objects in view. 
 He observes, that if the tendency of bodies downwards be the 
 result of the earth's attraction, it must vary with the distance 
 from the earth's centre, and he proposes to determine this by 
 comparing the effects of a weight and of a spring at different 
 heights and depths. 
 
 Such are a few of the leading facts by which the universal 
 gr a citation of matter was established. But numberless appli- 
 cations of the principle at once suggested themselves to its 
 discoverer. The inequalities in the lunar motions, some of which 
 had been detected by observation so far back as the time of 
 Hipparchus and Ptolemy, were shown to arise from the disturbing 
 attraction of the sun. The evection, the variation, and the annual 
 equation, were all traced to this cause ; and the same cause was 
 found sufficient to explain the principal of the inequalities affect- 
 ing the orbit itself, such as its change of inclination to the ecliptic 
 and the motion of its nodes. 
 
 It had been observed by Richer, Varin, and Des Hayes, that 
 a pendulum vibrated more slowly near the equator than in the 
 higher latitudes, and the result had been a subject of much
 
 428 RISE AND PROGRESS OF 
 
 wonder to the learned. Newton immediately perceived in it a 
 new effect of gravitation : he proved that the earth itself, sup- 
 posing it to be fluid and homogeneous, would assume the form of 
 an oblate spheroid, whose greatest and least diameters are in the 
 ratio of 230 to 229 ; and that the force of gravity must increase 
 from the equator to the poles, the increment being proportional to 
 the square of the sine of latitude. The attraction of the sun and 
 moon upon the redundant matter encompassing the equatorial 
 parts of the earth was shown to account for the precession of the 
 equinoxes. The phenomena of the tides were proved to arise from 
 the same actions, exerted upon the waters of our ocean ; and 
 from a comparison of the effects produced at spring and neap 
 tides (when these two forces conspire or are opposed) Newton 
 deduced the proportion of the forces, and thence determined 
 approximately the mass of the moon, and even its density, as 
 compared with the earth. 
 
 This last result is certainly one which cannot fail to strike the 
 uninstructed with wonder. That the mathematician should be 
 enabled to weigh the moon's mass, and even to compute its 
 density, from its effects upon the waters of our sea, is indeed 
 truly wonderful ; but it is only one of many results of the same 
 nature reached by Newton in following out the great principle of 
 universal gravitation. By comparison of the orbit of the moon 
 round the earth with that of the earth round the sun, the mass 
 of the earth (relatively to that of the sun) is at once determined ; 
 and the same principles are applicable to all the planets which 
 are attended by satellites. 
 
 Such are among the more prominent discoveries developed in 
 the Principia of Newton. Its concluding pages are dedicated to 
 the proofs, which the laws of the material world afford, of the 
 existence and attributes of the great First Cause. This is as it 
 should be : and while we admire the genius of the man who could 
 penetrate so far into nature's mysteries, and bind all these varied 
 and complicated phenomena by a single tie, our thoughts are 
 insensibly raised from the creature, to whom it was permitted to 
 gain so large an insight into this wondrous work, to the Infinite 
 Intelligence that planned the whole, and the Infinite Power that 
 called it into being. 
 
 )f the advances which mechanical science has made, since the 
 time of Newton, I must speak but briefly. The first great step
 
 MECHANICAL PHILOSOPHY. 429 
 
 was that which clothed the processes of dynamics in the symbolical 
 language of analysis. In order to accommodate his discoveries 
 to the actual state of mathematical knowledge, Newton chose to 
 exhibit them in a geometrical form, and by the aid of a new 
 doctrine which he had invented for the purpose. Thus his re- 
 sults are deprived of that elegance of form which is, in so eminent 
 a degree, characteristic of the conclusions of analysis ; and the 
 method of inquiry itself, in the higher and more difficult problems, 
 becomes elaborate and revolting. It must therefore be considered 
 an important era in mechanical science, when it received the aid of 
 the fluxional or differential calculus, the powerful instrument of 
 Newton's own invention, and when its principles were developed 
 by the fixed and uniform processes of analysis. This application 
 of the calculus to mechanical questions was made at an early 
 period, and by several hands ; but the systematic development 
 of the science in this new form is perhaps to be dated from the 
 publication of the mecanique of D'Alembert, in the year 1743. 
 
 In what relates to the discovery of important principles, much 
 was also done. So early as the year 1592, in a short treatise on 
 mechanical science, Galileo had reduced the equilibrium of the 
 simple machines to a single principle ; and showed that the power 
 and the equilibrating weight are to one another inversely as the 
 spaces which they tend to describe in the same time. This is a 
 limited case of the general principle which has since been assumed 
 by Lagrange, as the basis of the whole of statical science the 
 principle of virtual velocities. The principle itself was first stated, 
 in all its generality, by John Bernoulli, in the year 1717. 
 
 The science of motion was destined to receive a yet greater 
 extension by the accession of a general principle. The dynamical 
 problems, of which we have hitherto spoken, are those in which 
 the several parts of the body acted on are urged alike, and all 
 partake of a common movement. There are, it is true, many and 
 important problems in which this simplification is admissible : but 
 there are many cases, also, in which the parts of the body, in 
 virtue of their 'mutual connexion, are not free to obey the forces 
 which act externally upon each ; and to these the existing theories 
 did not apply. The first problem of this kind that engaged the 
 attention of mathematicians was the famous one proposed by 
 Mersenne the determination of the centre of oscillation of a 
 compound pendulum ; or, in other words, the investigation of
 
 430 RISE AND PROGRESS OF 
 
 the length of a simple pendulum which will perform its vibrations 
 in the same time. Huygens was the first to give a complete 
 solution of this important problem. James Bernoulli afterwards 
 treated the subject with great elegance ; and derived its solution 
 from the general and self-evident principle that the motions 
 lost by the different parts of the body, in virtue of their mutual 
 connexion, must be in equilibrio. This important and funda- 
 mental principle was afterwards adopted by D'Alembert, as the 
 basis of his treatise on dynamics, and it is now connected with 
 his name. The science of motion was thus reduced to that of 
 equilibrium, and was made to assume the perfect form in which 
 we find it at present. Its application to particular problems is 
 now made by regular and consistent methods, and the success 
 of such applications is limited only by the powers of the 
 analytical instrument which is employed in their development. 
 In the elegance and generality of its methods, the Mecanique 
 Analytique of Lagrange now leaves little to desire ; and we cannot 
 hesitate to rank this great work among the most perfect creations 
 of human genius. 
 
 But though the general methods of dynamical science may be 
 fixed, and its doctrines complete, yet, when we come to apply these 
 to particular problems, we find abundant room for ingenuity and 
 analytical skill. The cases are comparatively few, in which we can 
 proceed to the direct solution of a dynamical problem by a complete 
 integration of the equations on which it depends. The resources of 
 analysis are, in most cases, unequal to such an attempt, and we are 
 generally obliged to content ourselves with approximate determina- 
 tions. This is especially the case in celestial mechanics, when we 
 introduce the consideration of even a third body into the system 
 whose motions we seek to determine ; and in this department of 
 dynamical science, accordingly, there was abundant scope for the 
 highest exercise of the reasoning powers. We have already spoken 
 of the rise of this science in the mind of Newton, and of the vast 
 steps which he made towards its completion : it now remains to 
 say a few words of the additions which it has since received. 
 
 Clairaut was the first writer who made any important addition 
 to physical astronomy, as it had been left by Newton. Observa- 
 tions had shown that the apogee of the moon's orbit was not fixed 
 in space, but moved according to the order of the signs with a 
 motion of about 3 yearly. Newton proved that such a progres-
 
 MECHANICAL PHILOSOPHY. 431 
 
 sion of the apogee would necessarily arise from that part of the 
 sun's disturbing force which acts in the direction of the radius- 
 rector of the moon's orbit ; but on calculating the amount of the 
 progression due to this cause, it was found to be only the one-half 
 of that observed. Clairaut, Euler, and D'Alembert, attacked the 
 problem with all the resources of analysis, and their first investi- 
 gations led to a similar conclusion. This remarkable discrepancy 
 between observation and theory was so startling, as to induce 
 Clairaut for a time to doubt the accuracy of the Newtonian law 
 of gravity, and to propose a new and more complex one in its 
 stead ; but he soon after abandoned this idea, and found that the 
 apparent deviation arose from the incompleteness of his approxi- 
 mations. There are few things which tend so strongly to confirm 
 our belief in a law, as when a fact, which at first appears at 
 variance with it, turns out on fuller examination to be one of its 
 necessary consequences ; and accordingly we find that the explana- 
 tion of the progression of the lunar apogee, on the law of Newton, 
 dissipated all remaining doubts as to its truth. 
 
 The complete solution of the problem of the figure of the earth 
 was also reserved for Clairaut. In Newton's determination of this 
 question, the mass was assumed to be homogeneous ; and his method, 
 limited by this hypothesis, was followed up and perfected by 
 Maclaurin. But Clairaut considered the problem generally, and 
 upon any supposed law of change of density ; and the result at 
 which he arrived and which has been distinguished by the name 
 of Clairaut's theorem is as beautiful as it is comprehensive. 
 
 The general methods adopted by Clairaut (and after him by 
 other writers) in the lunar theory were soon found to be appli- 
 cable, with proper modifications, to the determination of the 
 planetary inequalities also. Since all the bodies of the system 
 attract one another, these attractions must cause each to deviate 
 from the elliptical path, in which it would move under the 
 influence of the sun alone ; and the determination of these devia- 
 tions was obviously of the utmost importance in the completion 
 of the theory of the system. The planetary theory, in this 
 enlarged sense, was the next great addition made to physical 
 astronomy, and is due to the united labours of Clairaut, D'Alem- 
 bert, and Euler. 
 
 Bnt among the perturbations of the bodies composing the 
 solar system, there was one wliich, on account of its magnitude,
 
 432 RISE AND PROGRESS OF 
 
 engaged the attention of mathematicians at an early period. 
 Astronomers had long observed that Saturn's mean motion was 
 subject to a slow retardation, and it was discovered by Halley 
 that the motion of Jupiter was in like manner accelerated. It 
 was natural, then, to look for the cause of these phenomena in the 
 mutual action of the two planets; and accordingly the French 
 Academy soon proposed the theory of Jupiter and Saturn, as the 
 subject of their prize-essay. Its difficulties, however, were such 
 as to baffle the genius of Euler, who engaged in the research. 
 Laplace and Lagrange afterwards entered on the investigation, 
 and advanced, almost side by side, to its complete solution. In 
 the course of these researches it was proved that the mean motions 
 of the planets were subject to no secular inequalities; and accord- 
 ingly the retardation of Saturn's motion, which was supposed to 
 be of that nature, appeared to be at variance with the law of 
 universal gravitation. It was finally shown, however, by Laplace, 
 that the mean motions of Jupiter and Saturn were subject to an 
 inequality of a very long period ; and that the retardation of the 
 one planet, and the acceleration of the other, would in time cease, 
 and the effects be reversed. This remarkable irregularity in the 
 motion of these two planets was found to depend upon the near 
 commensurability of their mean motions. A phenomenon of the 
 same kind, depending upon a similar cause, is found to take place 
 in the motion of the earth and of Yenus ; and these two bodies 
 also are subject to an inequality of a long period, lately brought 
 to light by Professor Airy. 
 
 The principle above referred to namely, that the mean 
 motions of the planets are subject to no secular inequalities was 
 discovered by Lagrange, who was the first writer to examine with 
 attention the variations of the elements of the planetary orbits. 
 The importance of the discovery is obvious : if the mean dis- 
 tances and mean motions were under the influence of secular 
 inequalities if Saturn should continue to be retarded, and Jupiter 
 to be accelerated the one would recede from the sun, until it 
 finally fell under the influence of some distant body of the starry 
 universe ; while the other would approach indefinitely, and at last 
 reach the central mass. This however is not the case : the inequa- 
 lities which exist are all periodical, and the changes which occur 
 are continually repaired. It is in this sense that the planetary 
 system is said to be stable.
 
 MECHANICAL PHILOSOPHY. 433 
 
 It was soon after found that the eccentricities of the orbits of 
 the planets, and their inclinations to a fixed plane, in like manner 
 oscillated within certain small limits which they could never trans- 
 gress. Thus, though the inclination and eccentricity of the orbit 
 of each planet is continually changed by the action of the rest, yet, 
 after certain periods, the same forces which have deranged it from 
 its mean state, will bring it back to that state "again, and repair 
 their work of disturbance. To use the words of a distinguished 
 French writer of the present day " La stabilite du systeme solaire 
 est done a jamais assuree: les orbites des planetes dans les ages 
 futurs ne pourront que s'aplatir legerement en conservant les memes 
 grandes axes, et les plans de ces orbites ne feront que de petites 
 oscillations autour d'une position moyenne : immenses pendules 
 de I'eternite, qui battent les siecles, comme les notres battent les 
 secondes." 
 
 Thus it appeared that the planetary system contained in itself 
 the principle of reparation and permanence. So far as depended 
 on the mutual action of the great bodies which compose it, the 
 system would endure for ever ; and would not (as Newton seems 
 to have supposed) ever require the repairing hand of its Divine 
 Author to check the progress of destruction. Late observations, 
 however, render it in the highest degree probable, that there exists 
 an external cause which, in the course of time, must bring all this 
 vast machinery to rest, and precipitate the gigantic masses which 
 compose it into the body of the sun. There are, in fact, strong 
 reasons for believing that a resisting medium is diffused throughout 
 the planetary spaces, the effect of which must be to diminish the 
 velocity and the distance of each revolving body from the sun, 
 until it at length reaches that centre. This medium is of such 
 tenuity, that it has, as yet, produced no perceptible effect upon 
 the motions of the denser bodies of the solar system. Our own 
 gross atmosphere, we know, offers a comparatively feeble resistance 
 to the bullet in its fall ; while the descent of the feather may be so 
 retarded, that it may seem almost suspended in the air. If then 
 the spaces which intervene between the great bodies of the solar 
 system be filled with a medium far rarer, as compared with the 
 lower regions of our atmosphere, than these are in relation to the 
 globe* they envelop, we are not to look for its effects upon the 
 motions of such bodies as the planets and their satellites. 
 
 But there are other mysterious bodies connected with our 
 
 2F
 
 434 RISE AND PKOGRESS OP 
 
 system, which, we have now reason to believe, are less dense than 
 the clouds which float above us ; and it is among these that we 
 must seek the effects of resistance. The singular body, now- 
 known by the name of Encke's comet, was first observed in the 
 year 1786; and has since that time been frequently seen, its 
 periodic time being only about three years and one-third. It was 
 not until after its return in 1819, however, that its identity was 
 established by Encke, and its subsequent returns calculated. This 
 comet reappeared in 1822, and on comparing the observed with the 
 calculated places, Encke found that there was a difference, which 
 seemed to be completely accounted for only on the supposition of 
 a resisting medium. He has been thus led to examine in detail 
 the effects of such a medium on the motion of the comet ; and 
 its subsequent appearances in 1825 and 1828 completely fall in 
 with the supposition. 
 
 The effect of this resistance is indeed very small : according to 
 the observations hitherto made, the diminution of velocity, in ten 
 revolutions of Encke's comet, has not amounted to the one- 
 thousandth part of the entire. And when we proceed from this 
 to speculate upon the probable amount of the effects produced 
 upon the motion of the earth and the other dense bodies of our 
 system, we are compelled to admit it to be so minute, that millions 
 of years must elapse before it becomes sensible. But, however 
 long the time required for the development of its effects, we have 
 here a cause which eventually must put a stop to all the great 
 movements which we observe in the heavens. The earth and the 
 planets must gradually be retarded by the resistance of the medium 
 in which they move : their gravity towards the sun must thus 
 preponderate over the centrifugal force ; and they will gyrate in 
 nearer and nearer orbits, and in continually diminished periods, 
 until at length they reach the central body, and then all motion 
 will be at an end. 
 
 This termination to our system cannot fail to suggest many 
 and grave reflections. Indeed there are few subjects which force 
 so strongly upon the mind the conviction of a ruling Power, as 
 those which indicate the finite nature of all created things which 
 mark the period when the now order of nature did not exist, and 
 predict the time when it shall cease which point, in short, to a 
 beginning and an end. But while our thoughts are thus arrested 
 by the probable termination of our system, the astronomer bids us
 
 MECHANICAL PHILOSOPHY. 435 
 
 look out upon the starry concave, and learn how insignificant a 
 part our sun and all his attendant worlds form of the boundless 
 universe. He tells us that in the deepest abysses of space, the 
 Creator has ordained suns, and assigned to them their appointed 
 courses, which will remain unmoved by our catastrophe. Among 
 these dazzling wonders he points to many that are united into 
 systems, endued with proper movements of revolution, and chained 
 together by some attracting tie : and we are prompted to ask, are 
 these attractions similar to that which binds together the parts of 
 our own system ? Is the law of gravitation obeyed in these re- 
 mote regions of the universe ? If this be the case, we know these 
 bodies should describe conic sections round their common centre 
 of gravity, and round each other : Are then the orbits of the 
 double stars ellipses, like the orbits of our planets, and are their 
 motions in these ellipses governed by the same laws ? This inquiry 
 appears at first to involve insurmountable difficulties. The distances 
 of these bodies from one another seldom exceed a few seconds ; 
 and the changes in these distances, from which we might hope to 
 compute the orbit, are far within the limits of the errors of observa- 
 tion. But these difficulties have been surmounted by Sir John 
 Herschel. By taking as his data the observed angles of position, 
 instead of the distances, and by the happy union of graphical 
 witli analytical methods, he has obtained the orbits of several of 
 the double stars, and deduced their elements. The result of these 
 investigations has been the complete verification of the assumed 
 law; and thus the grand principle of gravitation which Newton 
 showed to belong to the bodies composing our own system is exten- 
 ded to the remotest regions of the starry universe, and found to be 
 the universal principle of the material creation. 
 
 Before I conclude, suffer me to draw your attention for a few 
 moments to an objection often urged, and too easily credited, 
 against the value of the pursuit on which you are about to enter. 
 You will hear theory and practical knowledge contrasted together : 
 you will be taught to despise the former as vain and barren specu- 
 lation ; while the fruits of the latter its immediate application to 
 the uses of life, and the amelioration of the state of mankind, which 
 are its results will be paraded ostentatiously before you. 
 
 In reply to this it might be enough to ask has our nature's 
 noblest part no pleasures, no cravings of its own? Is there no 
 part of our complex being which seeks truth for itself ? Are the
 
 436 KISE AND PROGRESS OF MECHANICAL PHILOSOPHY. 
 
 pure and disinterested enjoyments which the philosophic mind 
 derives from its exalted speculations are these unreal ? or are 
 they inferior to those which minister to the animal part of our 
 being ? But I will quit this high vantage ground, and descend 
 into the field which the utilitarian has chosen for himself. I will 
 assume that the objects of his desire are, and should be, those of all 
 mankind ; and I will tell him that science true science alone 
 can point out the road to their full attainment. In fact, the 
 objection betrays an ignorance of the real character of inductive 
 philosophy, and of the spirit of its votaries. The true philosophy 
 of nature is founded upon facts, and it is its very essence to admit 
 of practical application : It takes its rise from particulars, and to 
 particulars it is in fine applied. But, unlike that with which it is 
 contrasted, it embraces phenomena not in their accidental charac- 
 ters but in their generic and essential ones. It rises from tho 
 maze of individual cases, with which alone the man of mere 
 practical detail is conversant, but it rises that it may enlarge its 
 view that it may trace (to use the expressive words of a favourite 
 writer) the spirit of the laws of nature from the letter; and then, 
 and then alone, is it in an attitude to descend, and with all its 
 acquired lights to advance the physical condition of man. 
 
 There are some, indeed, whose habits of generalization, and 
 love for the pure abstractions of science, lead them to fix the abode 
 of their thoughts wholly in its loftiest regions while others ascend 
 into its pure atmosphere, only that they may " steal the fire," and 
 apply it to their earthly uses. It is wisely ordered that it is so ; 
 for each of these has his proper part to fill, and both conspire for 
 the good of mankind. Each, too, has his own peculiar pleasures. 
 Those of the former, perhaps, are more remote from sense more 
 exalted more near to what we may conceive to be the enjoy- 
 ments of a purely intellectual being; while those of the latter, 
 on the other hand, are more adapted to our mixed and com- 
 pound nature. In both, the social and benevolent affections have 
 full room for exercise. But it is from a higher source that the 
 true philosopher to whichsoever class he belongs draws his 
 deepest and most exalted pleasures. In the events which pass 
 each moment before the uninstructed eye, and pass unheeded 
 or unseen, he discerns the hand of Infinite Power, guided by Infi- 
 nite Skill and surrounded by wonders here, he is brought into 
 close and multiplied contact with the wisdom of God.
 
 XX. THE APPLIED SCIENCES, AND) THE MODE OF 
 TEACHING THEM. 
 
 Frakction delivered on the occasion of the opening of the School of Engineering in t/it 
 University of Dublin, on the 15th of November, 1841. 
 
 ' ' Magnum certe discrimen inter res civiles et artes : non enim idem periculum a 
 novo motu et a nova luce. Verum in rebus civilibus mutatio etiam in melius suspecta 
 est ob perturbationem : cum civilia authoritate, consensu, famS et opinione, non demons- 
 tratione nituntur. In artibus autem et scientiis, tanquam in metalli fodinis, omnia 
 novis operibus ct ulterioribus progressibus circumstrepere debent." BACON, Novmn 
 Oryanum, lib. i. 
 
 GENTLEMEN, It has been said by one of the wisest of men, that 
 every thing in the institutions and customs of colleges was opposed 
 to the progress of science. "We are met this day to exhibit a prac- 
 tical refutation of this vaunted aphorism ; to prove that the 
 universities of the present day, so far from impeding the march 
 of truth, form themselves the vanguard of that intellectual army, 
 whose victories are in the region of the unknown ; and that, 
 while with one hand they are engaged in flinging back the fruits 
 of conquest, with the other they aid in propelling the triumphal 
 car of science into new and remoter regions. 
 
 We are met this day, under the auspices of the University, to 
 follow together some of the principal applications of science to the 
 wants and to the uses of man. But, in stating that such is the 
 object of the addition which has been recently made to the insti- 
 tutions of this college by its heads, let me guard you against tho 
 notion, that it is in anywise intended as a concession to that un- 
 philosophical, but unhappily too popular feeling, which decries as 
 worthless every intellectual pursuit, if unaccompanied by results
 
 438 THE APPLIED SCIENCES, 
 
 of a practical nature, which can discern no value in speculation, 
 unless it conducts us to conclusions bearing immediately upon the 
 uses and the necessities of daily life. I feel that there is some 
 degree of humiliation even in the task of defending the pursuit 
 of abstract truth. Yet, though many a voice has been loudly 
 raised in protest against this utilitarian spirit, the feeling, but 
 half smothered, breaks forth again and again. The mind unused 
 to science has a natural tendency to regard it simply as a mean, 
 a mean to an ulterior end ; and it is only just so far as this end is 
 attained, it is only by the direct advantages which science confers 
 upon the physical condition of man, that its value is wont to be 
 estimated. 
 
 Must it then again and again be repeated, that man has a two- 
 fold nature ? that the intellectual and the bodily have each its own 
 aliment, each its own gratifications ? and that truth speculative, 
 abstract truth is as properly the food of the one, as that which 
 ministers to the support of physical life is of the other ? And 
 shall we compare the intellectual, and its enjoyments, with the 
 inferior part of our being, and the things which minister to its 
 gratification ? Shall we degrade the high and disinterested plea- 
 sures that attend the discovery of the links in the chain of a priori 
 knowledge, or those which flow from the contemplation of har- 
 mony and order, which reign in the works of God, shall we demean 
 enjoyments such as these, by bringing them into comparison with 
 those of sense ? No ! I trust the day will never come, when a 
 spirit such as this shall take possession of the halls of our venerated 
 universities : I trust that those who occupy their chairs may never 
 be called upon to meet such an antagonist within their walls. 
 
 But while we advocate the claims of speculative knowledge, 
 considered apart from its applications, let it not be supposed that 
 we are insensible to the value of such applications, or that our 
 voices will not swell the shout of applause, whenever science 
 yields results bearing upon social well-being, or social progress. 
 Among the heathen nations of early antiquity, the inventors of 
 the sickle and the plough were deemed worthy of a place among 
 their gods: and shall we affect to disdain the richer fruits of 
 modern science, or to look down upon those who have contributed 
 to raise them from her prolific soil ? Reason forbids it : self- 
 interest forbids it. The useful arts are the results of such applica- 
 tions ; modern civilisation is mainly based upon them. And it is
 
 AND THE MODE OF TEACHING THEM. 439 
 
 remarkable that speculative knowledge itself is amply repaid for 
 the time thus lent to practical science ; and that man advances in 
 the scale of intellectual being, not only by the acquisition of new 
 materials for the exercise and development of his intellectual 
 powers, but still more by his release from the thraldom of those 
 corporeal occupations to which his bodily wants coerced him. 
 
 It is, in fact, one of the precious advantages of applied science, 
 that its results have delivered man from a great part of that toil 
 to which he was condemned in the infancy of society for the 
 supply of his animal wants ; from that abject condition, in 
 which the body is at once his taskmaster and his slave. This re- 
 volution has been accomplished by the knowledge which he has 
 acquired of the forces of nature, and the means which he has con- 
 trived to compel them to act on his behalf. The Romans, with 
 whom mechanical science was in its infancy, had recourse to human 
 labour in grinding their corn ; in crushing the seeds of plants, and 
 expressing their juices; in removing the earth and the water which 
 covered the treasures of the mine. Slaves, in immense numbers, 
 were condemned to these toils, toils so severe, as to constitute the 
 heaviest punishment, next to death itself. But man has since 
 learned the art of employing the forces of nature, the action of 
 the wind, and of the running stream, to accomplish his will. 
 He has even learned how to develope such forces when otherwise 
 latent ; to call into action the elastic forces of steam, and of the 
 gases ; and constrain them to execute his commands. 
 
 We shall better learn to estimate the benefits which applied 
 science has conferred upon man, if we reflect for a moment upon 
 the advances in social progress which the application of any of 
 these agents has effected, and the character of superiority that 
 has attached to the nation which has been the first to discover and 
 employ them. 
 
 Let us take, for example, the combination of the moving force 
 of air, and the resisting force of water, in propelling and guiding 
 the vessel on the waves. What advantages has not this appli- 
 cation of natural forces conferred upon the people of antiquity 
 which was the first to make it ? What advantages does it not 
 still bestow upon the nation, whose pre-eminence in nautical skill 
 has earned for her the proud title of " Mistress of.the Seas " ? Sho 
 carries the products of her industry across the ocean, to exchange 
 them for the riches of distant nations. She spreads the terror of
 
 440 THE APPLIED SCIENCES, 
 
 her arms to the remotest regions of the globe. She peoples the 
 most distant shores with her colonies ; and gives birth to nations 
 affiliated to her by the ties of a common blood, a common lan- 
 guage, and a common interest. She diffuses in every quarter her 
 science and her arts, the gifts of civilisation, and the blessings 
 of religion. 
 
 Let us take, as another example, the discovery and the appli- 
 cation of the power of steam. It was long known that water, in 
 passing into the state of vapour, acquired a great expansive force ; 
 yet it is little more than a century since this force has been applied, 
 as a moving power, in the mechanical arts. And yet what has 
 been the progress which civilisation has made, in that short inter- 
 val, by the aid of this agent ? " Survey the metropolis of England, 
 look through her towns ; visit her arsenals and her manufactories ; 
 explore the depths from which they are raising the riches of the 
 mine, and see the labours executed above the surface ; in fine, sail 
 along her rivers, her canals, and the seas which bathe her shores, 
 and you will discover on every side evidence of the benefits which 
 she owes to the inventor of the steam-engine." It is equally 
 available in operations requiring a great expenditure of power, 
 and in those where delicacy and perfection of workmanship are 
 the chief requisites. "The heaviest labours, such as the cutting 
 of wood and of stone, or the raising of water, are accomplished by 
 the same moving force which produces the most delicate pieces of 
 workmanship. The anchor is forged, and the counter stamped, 
 the metal is rolled out, and the bauble carved, by this all- 
 powerful and universal agent. And the same giant arms, which 
 twist the cable of the man-of-war, draw out the slender gold and 
 silver wire which form the lightest tissue."* 
 
 But we shall better appreciate the value of this agent, if we 
 confine our attention for the moment to what it has accomplished 
 in one or two branches of the arts. 
 
 In the year 1789, the first steam-engine was erected in Man- 
 chester. The manufacture of cotton goods, which before that 
 epoch depended, almost solely, on animal labour for its moving 
 power, received a new life. The various branches of the manu- 
 facture were brought together, to share the energy which the new 
 
 * Speech made by Sir Humphry Davy, at the meeting held in 1824, for the purpose 
 of paying a tribute to the memory of "Watt.
 
 AND THE MODE OP TEACHING THEM. 441 
 
 power conferred ; and all the operations necessary to convert, the- 
 raw material into the perfect web were conducted in the same 
 establishment. From that period and chiefly from that source- 
 riches have overspread the land. Manchester, Nottingham, Pres- 
 ton, and Glasgow, and many towns of less note, owe their wealth 
 and their prosperity to this single manufacture ; and millions of 
 inhabitants are indebted to it for their subsistence.* Such, in fact, 
 has been the progress of the cotton manufacture in England, in 
 these fifty years, that, notwithstanding the pressure of the national 
 debt, the heavy burden of the taxes, and the consequent dearness 
 of all the necessaries of life, notwithstanding these great dis- 
 advantages of England, as compared with other nations, she 
 purchases the raw cotton of another hemisphere, carries it 10,000 
 miles to her workshops, transforms it into a web, and sends it back 
 again the same distance, to China and to India, to surpass in 
 beauty, in perfection of workmanship, and in cheapness, the 
 products of the native art, fabricated with all the refinements of 
 manual labour, and with the traditionary experience of many 
 centuries, f 
 
 But let us look to actual numbers. At the accession of George 
 III., in 1760, the value of the cotton goods annually manufactured 
 in Great Britain was estimated at 200,000. In the year 1824, 
 according to the statement of Mr. Huskisson, it amounted to 
 thirty-three millions and a half ; and of this sum more than half 
 is returned to the country annually by foreign nations, in the shape 
 of profit and wages. During the war with France, 569 millions 
 sterling was added to the national debt. The sum returned by 
 foreign countries as the price of British manufactures, during the 
 same period a period, of course, o crippled commercial energy 
 amounted to 548 millions, 400 millions of which was the return 
 for British capital and British labour. And the large share which 
 the steam-engine has had in this manufacturing prosperity is 
 such as fully to justify the assertion often made, that it was the 
 invention of this instrument which enabled England to sustain a 
 
 * In the first and last of the above-named towns, the increase of tho population in 
 thirty years (from 1801 to 1831) amounted to upwards of 150 per cent. The total 
 number of individuals directly employed in the cotton manufacture in Great Britain is 
 estimated at 800,000. 
 
 t "At Calicut, in the East Indies," says Mr. Babbage, "whence tho cotton cloth 
 called calico derives its name, the price of labour is one-seventh of that in England, 
 yet the market is supplied from British looms."
 
 442 THE APPLIED SCIENCES, 
 
 struggle, the most menacing and the most dangerous of any in 
 which she has ever been engaged. 
 
 Let us take another example. At the time of the inventions 
 of Watt, the north of England, which supplied by far the greater 
 part of the coal for domestic consumption, and for the arts, had 
 seen all the upper beds of her great mineral treasure exhausted. 
 It was necessary to penetrate to greater depths, in order to supply 
 to Britain a fuel which its forests had long ceased to furnish. 
 But this circumstance greatly increased the cost. The metals, 
 which formed the wealth of whole counties, could no longer be 
 smelted at the same prices as before. The working of the mines 
 thus became more and more disadvantageous ; each year brought 
 a sensible diminution in their produce ; and all the secondary arts, 
 which depended on them for their material, were menaced with 
 decay and ruin. 
 
 The employment of the steam-engine put an end to this down- 
 ward movement, and the whole face of things was altered. A 
 power was obtained, which, with a comparatively small expendi- 
 ture of fuel, lifts an enormous weight from the greatest depths ; 
 and thus renders the expense of raising the coal a very small frac- 
 tion of its cost. The average performance, or (as it is technically 
 called) duty of the Cornish engines, is equivalent to the elevation of 
 fifty-five millions of pounds through a foot in height, by the con- 
 sumption of a single bushel of coal; while that of some of them 
 surpasses eighty millions. And thus it is computed that a weight 
 exceeding one thousand tons is lifted one foot, for the sum of one 
 farthing ! In fact, the economical value of the engine, in mining 
 operations, may be judged from the circumstance that, during 
 the continuance of the patent granted to Watt and Boulton, when 
 they received one-third of the price of the fuel saved, the propietors 
 of a single mine in Cornwall thought it worth while to purchase 
 the right of the inventors for 7500 per annum. 
 
 We have stated that the reduction of the metallic ores was en- 
 tirely dependent upon the supply of coal, and shared its fortune. 
 But the supply of metal was influenced in another, and more direct 
 way, by the steam-engine. The mining engineer was forced, by 
 the feebleness of his mechanical means, to stop at a comparatively 
 moderate depth in the search of mineral treasures. Independently 
 of the labour necessary to lift the ore to the surface, the power re- 
 quired to clear the mine of water soon exceeded any which, previ-
 
 AND THE MODE OF TEACHING THEM. 448 
 
 ously to the invention of the steam-engine, he could with profit 
 employ,* But, aided by the steam-engine, he has successively 
 doubled, trebled, and quadrupled the depths to which he can descend, 
 in order to return loaded with the riches of the mine. As he 
 penetrates deeper, he discovers richer and more widely-spread- 
 ing veins of treasure, to which he sends his " captains " and his 
 " companies," and which soon are forced to render up their store. 
 At the head of his well-disciplined army he forces his way through 
 the hardest rock, he removes the earth and the ore, and the 
 earth's bosom is furrowed even more diligently than its surface.f 
 
 And when these sources of national wealth are found com- 
 bined, when the metal and coal occur in juxta-position, in such 
 favoured localities the application of steam-power effects still 
 greater wonders. The arts spring up and multiply, upon this new 
 and rapid supply of their material, and of the means of fabricating 
 it. An immense population, gathered from all quarters, derives 
 its subsistence from them. Opulent cities arise, as if at the wand 
 of the enchanter ; and towns, such as Birmingham and Sheffield, 
 the former of which in the beginning of the last century numbered 
 scarcely thirty streets, are now among the largest, the most popu- 
 lous, and the most wealthy of the empire. 
 
 What a gain to our country are such possessions ! We' lavish 
 wealth, and life itself, upon distant conquests, which may be 
 wrested from our possession in a moment by invasion or revolt, 
 conquests which we are compelled to protect by costly fortifications, 
 and to defend with troops, who perish by thousands, the victims of 
 a pestilential climate, conquests, whose fruits reach our shores at 
 a vast expense, with great risk, and frequent loss. What service, 
 then, does not that power render, which, by a few mechanical 
 means, and at the cost of a little fuel, brings up upon the surface of 
 our own soil its hidden treasures, and enriches us with the produce 
 of a territory situated beneath our feet ! These are triumphs, in- 
 deed, bloodless victories won by the arm of science from unreluc- 
 tant nature, conquests that no rival can wrest from us, no caprice 
 detach. 
 
 I have already alluded, generally, to the moral revolution which 
 
 * The removal of the water which rises daily in the galleries of the Cornish mines 
 would require the labour of upwards of 44,000 horses, or of about 300,000 men. 
 
 t In a single mining establishment (the consolidated mines) in Cornwall, wliich I 
 visited last summer, the total length of the shafts and galleries now measures 68 miles-
 
 444 THE APPLIED SCIENCES, 
 
 applied science has effected, in delivering man from the thraldom 
 of brute toil, and leaving him more free to cultivate the intellectual 
 part of his nature. The share which the steam-engine has had in 
 producing this effect is pointedly exhibited in the well-chosen illus- 
 tration of M. Dupin. One of the most wonderful monuments of 
 antiquity, as well for the mass of its materials, as for the height to 
 which they are raised, is, doubtless, the great pyramid of Egypt. 
 Let us compare the labour, which history tells us was bestowed 
 upon this colossal structure, with the calculated steam-power of 
 England. Herodotus informs us that Cheops ordered all the 
 temples of Egypt to be closed, and forbade the sacrifices, in order 
 that the people might devote themselves exclusively to the heavy 
 task which he imposed upon them. Some were employed in work- 
 ing the quarries of the mountains of Arabia ; others in transporting 
 the elevated blocks of granite to the banks of the Nile, and in lad- 
 ing the boats to pass the stream ; others, lastly, received them there, 
 and bore them to their intended site. A hundred thousand men, 
 says the historian, were employed for twenty years, in the works of 
 quarrying and building alone. The steam-power of England, said 
 M. Dupin twenty years ago, would have effected the task, the 
 double task of lifting the stone from its bed in the quarry, and rais- 
 ing it to its place in the structure in eighteen hours ! In fact, the 
 steam-engines constructed in the establishment of Watt and Boulton 
 alone, in the year 1819, were equivalent to the work of 100,000 
 horses, or 700,000 men ; and the sum of money annually saved, by 
 their substitution for animal labour, amounted to more than three 
 millions sterling. The total number of engines, existing in Great 
 Britain at the same period, exceeded 10,000 : their work was equi- 
 valent to that of 500,000 horses ; and the yearly saving thence 
 arising was from twelve to sixteen millions sterling. 
 
 But, notwithstanding this transfer to which I have alluded, the 
 effect of the employment of machinery in the arts has not been, on 
 the whole, to set aside human labour. The severer kinds of toil 
 are, indeed, now transferred from the labourer to the engine ; but> 
 from the best calculations of the effects of machinery, it appears 
 that an increased demand for labour, although of a different 
 kind, has, in general, been the result. This remarkable consequence 
 is clearly exhibited in the history of the cotton manufacture. Be- 
 fore the inventions of Watt and Arkwright, the total number of 
 labourers employed in connexion with this manufacture in Great
 
 AND THE MODE OF TEACHING THEM. 445 
 
 Britain was under fifty thousand ; it now amounts to a million and 
 a half!* 
 
 The legitimate the direct effect of machinery is indeed to 
 diminish the amount of labour necessary to the production of a 
 given quantity of manufacture. But, in so doing, it lessens the 
 cost ; and the effect of this, again, is to augment the demand, and 
 of course also the production, to augment it to such an extent, as, 
 notwithstanding the reduction of price, to increase greatly the actual 
 value of the produce. The number of workmen, therefore, so far 
 from being lessened, is in general increased by the introduction of 
 machinery, and by the means which it supplies of rapid fabrica- 
 tion. We are to remember also, that, by lessening the cost of any 
 one article of manufacture, an increased stimulus is given to the 
 production of every other. The restless activity of man, disencum- 
 bered of the toil before necessary for the supply of his wants, or 
 enabled to satisfy them at a less expense, bestows the labour or the 
 money thus saved upon some new object. New wants arise, new 
 gratifications are indulged ; his physical condition is bettered at 
 very step, and he advances in the scale of civilisation. 
 
 Thus the result of the application of machinery, so far from 
 corresponding with the forebodings of unwise economists, and 
 misguided artisans, is, in fact, to increase the demand for labour. 
 And when we turn our view in the other direction, we find that 
 its effect its much most important effect is to extend the advan- 
 tages and the comforts of the products of labour, from the wealthy 
 classes downwards, to the lowest grade in society ; to elevate the 
 inferior, without prejudice to the interests of the higher ranks; 
 and thus to smooth down the inequalities of our artificial con- 
 dition. 
 
 In illustrating the benefits which the applications of science 
 have conferred upon the condition of man, and the social progress 
 which has resulted from them, I have dwelt chiefly upon the 
 discovery and employment of steam-power, both on account of 
 the universality of its application, and the gigantic magnitude of 
 its effects. In fact, a powerful and economical agent once obtained, 
 
 * In the town of Stockport alone, says Mr. Babbage, the number of hand-looms was 
 reduced to less than one-third, while that of the power-looms increased fivefold, in the 
 ten years ending in 1832 ; yet the number of workmen, so far from diminishing, in- 
 creased by one-third during the same period.
 
 446 THE APPLIED SCIENCES, 
 
 there is almost no one of the arts which it may not subserve. The 
 mechanical arts, the arts of construction, mining, and naviga- 
 tion, are all indebted to it. Every operation, in short, in which 
 motion is to be communicated according to fixed rules, and in a 
 settled order, must be capable of receiving that motion, which is its 
 life, from this universal agent. 
 
 But let us turn to those operations in which this condition 
 does not hold, in which the ever- varying circumstances almost 
 preclude the employment of any agent but one endowed with free- 
 will or, at all events, one whose effects may be made to vary with 
 the ever-changing conditions, and we shall still find abundant 
 evidence of the debt which civilisation owes to the applications of 
 science. Let us look to the public works of England, and we shall 
 learn how much the spirit of free enterprise, leaning on the arm 
 of science, can accomplish. We may take on this subject the 
 testimony of an impartial and enlightened foreigner. Until the 
 year 1756, says M. Dupin, England did not possess a single line 
 of artificial navigation ; while her land communications were limi- 
 ted to a small number of. ill-planned and ill- constructed roads. 
 Then, for the first time, a private individual ventured upon an 
 outlay, which his bold speculations told him must eventually bring 
 a large return ; and he constructed a canal, which was to carry to 
 the town of Manchester the produce of his mines. Soon after, 
 Liverpool, seeking a freer passage for her commerce, formed and 
 realized the project of opening a navigable way between the Irish 
 channel and the German ocean. Other canals, more extended 
 still, were by degrees constructed ; and, in the short space of half 
 a century, a double system of canals has ramified itself throughout 
 Great Britain, exceeding three thousand miles in length. 
 
 The roads of England, adds the same writer, are the subject of 
 yet vaster labours. The existing roads have been enlarged, and 
 constructed anew on better principles ; new roads have been opened 
 to commerce, and internal* intercourse ; and a network of lines of 
 land communication now exists in England alone, measuring 
 115,000 miles ! Meanwhile spacious harbours are formed to contain 
 her vessels ; piers, embankments and light-houses, augment the se- 
 curity of approach, and of shelter, over an extent of more than 1500 
 miles of coast ; and 22,000 merchant vessels, capable of carrying two 
 millions of tons of merchandize, and manned by 160,000 sailors, 
 are scarce sufficient for her commerce and her carrying trade.
 
 AND THE MODE OF TEACHING THEM. 447 
 
 Now I shall asume it as an admitted truth, that the mode of 
 carrying on these gigantic operations must be taught. The public 
 will guard itself against incompetency, and stand forward to protect 
 interests of such magnitude ; and emulation will play its part, and 
 force the engineer to qualify himself, in some way or other, for his 
 task. The only question is whether his education is to be allowed 
 to take the direction which chance, or circumstances, have given to 
 it, or whether, on the contrary, the public bodies (which have 
 been endowed for the professional education of the youth of the 
 country) should step forward, and offer the assistance, which it is 
 their bounden duty to give if required. I think there can be little 
 hesitation in replying to this question. There can hardly be a doubt, 
 that where the practical applications of science are concerned, the 
 sciences themselves must be systematically taught at least so far 
 as to insure a knowledge of the principles which are thus applied. 
 I am sure, above all, that it is in the universities the established 
 schools of science that such applications may be best unfolded; 
 because in them provision has already been abundantly made for 
 communicationg the knowledge of those principles of which these 
 applications are the results. 
 
 If it be said (as I know is sometimes said) that many of the 
 most important of the inventions to which I have referred some 
 of the successive improvements of the steam-engine, for example 
 are the results, not of science, but of a happy chance, I do not 
 hesitate to meet the objection by a direct denial. It is true, there 
 are happy moments in the history of every inventive mind, at 
 which new ideas seem to rise as it were by a kind of inspiration. 
 It is even true, that a fortuitous circumstance may have been the 
 means of awakening the train of thought which has ended in great 
 discovery. But it is nevertheless certain that all this is of no 
 avail, unless the mind be already prepared to combine the prolific 
 thought with its existing store, unless, in fact, the soil be pre- 
 pared for the seed which the capricious wind has borne to its bosom. 
 The apple might have fallen unheeded from the bough, had not 
 the master-mind of Newton been prepared to connect the fact with 
 the treasures of his existing knowledge. And (to return to the 
 example which I have already so often cited) the circumstances 
 which suggested some of the improvements of the steam-engine 
 might have occured in vain, had not the mind of "Watt been 
 prepared, by his acquirements in chemistry and mechanics, to
 
 448 THE APPLIED SCIENCES, 
 
 seize their bearing, and to embody the idea which they suggested 
 in his machine. These improvements were, in fact, the results of 
 the most assiduous labour, aided by the most extensive knowledge. 
 The amount of the dilatation of water, in passing into the state of 
 vapour, the quantity of coal requisite to vaporise a given quantity 
 of the liquid, the amount of steam expended in each stroke of 
 an engine of known dimensions, and the elastic force of the 
 vapour itself at different temperatures, were all the subjects of 
 experimental research, and of rigorous calculation. It was thus 
 that he succeeded, step by step, in diminishing the quantity of 
 fuel necessary to produce a given effect. It was thus that he dis- 
 covered the means of alternately disengaging and absorbing the 
 steam, and of transmitting, with the smallest loss, the moving 
 power which he had thus developed. Finally, it was by the same 
 knowledge, and the same mechanical resources, that he succeeded 
 in applying the powerful instrument which he had contrived, and 
 modifying it for the accomplishment of the most opposite pro- 
 cesses. " Practical mechanics," says Sir John Herschel, " is, in 
 the most preeminent sense, a scientific art; and it may be truly 
 asserted, that almost all the great combinations of modern mecha- 
 nism, and many of its refinements and nicer improvements, are 
 creations of pure intellect, grounding its exertion upon a moderate 
 number of very elementary propositions in theoretical mechanics 
 and geometry." And the same may be said (though, of course, 
 in ever-varying degrees) of the relative position of the arts, in 
 general, and the physical sciences. The arts, in their highest 
 development, are but the applications of the powers of nature to 
 some practical object; and these powers must be known, the 
 uncontrollable laws of nature must be understood, before they 
 can be directed to the uses of life, and to the improvement of our 
 physical condition. 
 
 But we have to deal with an objection of more weight. It 
 has been said, and it no doubt will be said, that skill in such opera- 
 tions as we have been speaking of is only to be acquired by practice ; 
 that the mechanical arts, and the arts of construction, are still arts, 
 a knowledge of whose processes must be learned by experience, and 
 by experience alone; and that it is only in the engine factory, or 
 in the field, that any solid information can be gained. 
 
 Now, we freely grant that there is much that is true in this 
 statement, but, at the same time, we assert that it oversteps the
 
 AND THE MODE OF TEACHING THEM. 449 
 
 truth. "We fully admit that no perfect knowledge, in any art, can 
 be communicated by oral teaching alone ; that the mechanical 
 engineer, the mining engineer, the civil engineer, and the archi- 
 tect, must not only see the processes of their respective arts, but 
 also exercise themselves in them, before they are competent to con- 
 duct them on their own responsibility. But is this any reason 
 why the principles of these several arts should not be taught sys- 
 tematically ? As well might the physician say " Away with 
 your schools of medicine! let the student accompany me to the 
 hospital ; he will see there the disease and the remedy in juxtaposi- 
 tion ; he will observe the malady and the cure ; and he may turn 
 his back for ever on the lecture-room." Would reasoning such as 
 this be listened to, in a profession already acquainted with better 
 modes of teaching, teaching in which the principles and the 
 practice are mingled in due proportion ? And yet, is not this the 
 very argument of those who ignorantly cry up practice, in opposi- 
 tion as if it were in opposition to theory ? No ! a wise teach- 
 ing will give practice practice, without which there can be no 
 skill : but it will not fail to base practical knowledge upon a know- 
 ledge of principles, without which all skill is but the blind per- 
 formance of a task, as senseless and soulless as that of the engine 
 in its routine of toil. 
 
 The extremes of opinion on this question are exemplified in 
 the widely different states of the engineer profession itself in 
 England and in France. Up to the present day, the education of 
 the engineer student in the latter country has been too merely 
 theoretical; while in the former, practice has been insisted on, 
 almost to the exclusion of theoretical knowledge. The Poly- 
 technic School of France, the school in which the young engineer 
 commences his education, though perhaps the first school of pure 
 science in the world, is decidedly too abstract in the character of 
 its studies, to satisfy the wants of the professional student. And 
 though, after two years of preparation there, he is transferred to 
 the School of Mines, the Naval School, or the School of Roads and 
 Bridges, notwithstanding this apparently excellent arrangement 
 for imparting special, as well as general information, it is found, 
 in the end, that his practical acquirements have not kept pace with 
 his theoretical knowledge. In England, on the other hand, the 
 student enters the office of the professional engineer, whom he 
 accompanies in the execution of his public duties. He thus 
 
 2o
 
 450 THE APPLIED SCIENCES 
 
 acqiures, in the most complete manner, that practical skill which 
 is only to be attained by seeing and handling; but is it not 
 evident that such a mode of teaching alone must be defective in 
 forming the counterpart of his knowledge ? His master is too 
 actively engaged in the duties of professional life to attend to the 
 task of oral instruction : the utmost that he can do is to direct his 
 reading, and to superintend his work ; and he is almost left to- 
 himself, to acquire, or not, the knowledge of those principles 
 which he is afterwards to apply. 
 
 The consequences of these widely different modes of instruc- 
 tion are very evident in the opposite character of the professions 
 in the two countries. The French engineer possesses a confidence- 
 in his own resources, which he often displays in meeting and mas- 
 tering a difficulty ; while perhaps he fails in the execution of an 
 ordinary task. The English engineer, on the other hand, guided 
 by rule in place of theory, is more successful in the daily walk of 
 his profession, while (unless a man of natural genius) he is often 
 unprepared to cope with new emergencies. The Englishman, 
 from the practical character of his education, and of his mind, 
 goes straightforward to the end proposed ; the Frenchman devi- 
 ates from the road to seek some opportunity of putting forth his 
 skill. The Englishman sometimes commits mistakes, in new and 
 untried cases ; the Frenchman is often in error, because he is as 
 likely to err in cases of daily occurrence, as in those which are 
 infrequent and uncommon. 
 
 But happily the men of science in both countries now see, 
 and have begun to remedy, the extremes into which this branch of 
 education has fallen, those of England, by the infusion of theo- 
 retical knowledge, the French, by the addition of practical ac- 
 quirement. It is strange, that in a country which has been long 
 forward in raising the intellectual character of the artisan, in a 
 country where schools and mechanics' institutes have sprung up 
 without number, for the benefit of the working classes, no regu- 
 lar education should have been provided (until within the last few 
 years) for the master artist, the engineer, or the manufacturer. 
 The University of Durham has been the first to wipe away this 
 reproach, and her example has been ably and successfully followed 
 in King's College, London. 
 
 In France, on the other hand, and about the same time, the 
 Central School of Arts was founded, with that profusion of scien-
 
 AND THE MODE OF TEACHING THEM. 451 
 
 tifio strength which the capital of France can wield ; and the in- 
 stitution has been followed by the establishment of preparatory 
 schools having the same objects. I would gladly, did time permit, 
 have dwelt upon the arrangements of this important school, which 
 I had the opportunity of visiting within the last few months. 
 There is one part, however, of the system pursued there, which I 
 cannot forbear noticing, not only on account of its intrinsic ex- 
 cellence, but because there is nothing in it of a local character, 
 nothing which will not bear transportation to another soil. In 
 the concluding examination, in which is tested the fitness of the 
 student to enter on his professional career, he is, furnished by his 
 examiners with a projet. An engine is to be constructed for some 
 special work ; a suspension-bridge is to be thrown across a certain 
 river ; an embankment, or a harbour, is to be constructed under 
 given conditions ; or a manufactory of some kind is to be esta- 
 blished on a given piece of ground, and with a given capital. Such 
 are the comprehensive queries put to the candidate, queries ad- 
 dressed, not to an insulated point, but to a large circle of his 
 acquired knowledge. He is called upon to put himself, for the 
 time, in the place of the professional engineer, to whom such an 
 inquiry is addressed by the capitalist; and he is expected, not 
 only to furnish complete working drawings of all the parts of his 
 design, but also to accompany them by an explanatory memoir, in 
 which the calculations of the dimensions and strength of every 
 part, of the quantity of materials requisite, and of the cost, are 
 all given in full. The best of these plans and memoirs are pre- 
 served in the archives of the school ; and, when corrected by the 
 professors, they furnish the materials for future teaching. 
 
 It remains now that I should say a few words of the arrange- 
 ments which the Heads of this University have made, bearing upon 
 the same objects. I have already stated what seem to be the faults 
 in the existing systems of engineer education ; and have shown, I 
 think, the importance of a systematic instruction, in which theory 
 and practice are attempered in just proportion. Such is the prin- 
 ciple which has been steadily kept in view, in the course of educa- 
 tion which the University now offers to the engineer student. It 
 is intended to communicate just so much of theoretical knowledge 
 as is indispensable, in on ICY to enable the student to understand 
 fully its applications. The applications themselves will next be
 
 452 THE APPLIED SCIENCES, 
 
 offered to his attention in detail ; and finally, means will be pro- 
 vided to familiarise him with them, by experience and actual 
 manipulation, as well as by oral teaching. 
 
 It has been accordingly arranged, that the first year of the 
 student's course is to be passed in those studies which are prescribed 
 by the University to Students in Arts of the same standing. This 
 course, you are aware, embraces the elements of geometry, trigo- 
 nometry, and algebra, all of which are necessary to the engineer 
 student as necessary as arithmetic is to the merchant ; and, in add- 
 ing to these the amount of classical knowledge required in the Junior 
 Freshman year, it is conceived that the indirect advantages of even 
 a partial classical education will more than outweigh those which 
 might be derived from the employment of the same time in purely 
 professional study. After the expiration of a year, so employed, 
 the engineer student will commence his professional course, under 
 the teaching of the professors connected with the school, and their 
 assistants. In the first year he is required to attend three courses 
 of lectures. The first of these comprises the branches of mathe- 
 matics which are specially required by the mechanical and con- 
 structive engineer, as logarithms, the applications of trigonometry, 
 and the elements of solid and descriptive geometry. The second 
 course comprehends the principles of mechanical science ; and the 
 third, the elements of chemistry and geology, and the application 
 of these sciences in the arts of construction. The courses prescribed 
 for the second year are more exclusively practical ; and are, first, a 
 course of practical mechanics, including the theory and construction 
 of the steam-engine ; and, secondly, a course on the practice of engi- 
 neering itself. Each of these years of study will close with an 
 examination, to be conducted by the professors connected witli 
 the school ; and at the end of the second, or concluding year, a 
 diploma will be conferred by the University upon those who shall 
 have attended all the prescribed courses, and acquitted themselves 
 with credit at the examinations. 
 
 I must pause here; for here terminate the arrangements, so 
 far as they are at present defined. These arrangements, however, 
 will certainly require and receive a further extension, as they are 
 brought into operation ; and means will doubtless be provided to 
 instruct the student in drawing, both mechanical and constructive, 
 and to render him familiar with the manipulations of the labora- 
 tory, the workshop, and the field.
 
 AND THE MODE OP TEACHING THEM. 453 
 
 Such, Gentlemen, are the provisions which the Heads of the 
 University have made for your instruction. The profession you 
 have adopted, whose duties were not long since limited to the 
 construction and care of engines, has now risen to take its rank 
 among the first of the liberal professions. In a country like ours, 
 where public works of such magnitude are ever in progress, the 
 interests committed to its keeping are numerous and weighty; 
 and the knowledge demanded of it proportionably varied and 
 extensive. It is your part, then, to try to profit by the oppor- 
 tunities thrown open to you. Attend with diligence to the 
 instruction which will be given to you in these halls ; take notes 
 of what you hear ; and endeavour to combine the knowledge thus 
 gained with the results of your private reading. You have every 
 inducement that can be offered to exertion. The path which is 
 to conduct you to the goal of your profession is interesting and 
 attractive ; and the career which afterwards expands before you 
 is one in which you may serve your country nobly, and earn for 
 yourselves an honourable independence, and an honourable fame.
 
 XXI. ADDRESS DELIVERED AT A MEETING OF THE ROYAL 
 IRISH ACADEMY, HELD APRIL 13TH, 1846, ON THE OCCA- 
 SION OF TAKING THE CHAIR. 
 
 Proceedings of the Royal Irish Academy, 1846. 
 
 GENTLEMEN, My first my most urgent duty on this, to me 
 most solemn occasion, is to thank you for the high distinction you 
 have conferred. It would be idle to attempt to express how highly 
 I esteem the honour. The thought that I had been deemed worthy 
 to occupy the chair which has been filled by Kirwan, by Brinkley, 
 and by Hamilton, might, indeed, well nigh overwhelm me, did I 
 not know that there were other merits, more humble than theirs, 
 upon which you set a value other qualities less dazzling, which 
 may find here their employment and their use. An institution 
 such as this has been compared to the House of Solomon, in 
 Bacon's philosophical fiction, the New Atlantis, in which the in- 
 vestigation of truth is carried on by labourers of various kinds, to 
 each of which he has assigned a separate task. We have had, in 
 this Academy, the representatives of each of these classes : we, too, 
 have had our " Miners," our " Lamps," and our " Interpreters of 
 Nature." I am content to enrol myself in the lowest class ; or if, 
 by reason of the high trust which you have now reposed in me, 
 other tasks should fall to my lot, I am proud to accept a new 
 station among the intellectual workmen, and to perform the part 
 of one whose office it is to harmonize and give effect to the labours 
 of all. 
 
 There is another personal consideration, to which I cannot 
 refrain from alluding; and yet it is one upon which I hardly
 
 ADDRESS DELIVERED AT THE ROYAL IRISH ACADEMY. 455 
 
 trust myself to speak. Among my predecessors in this high office 
 was one whom I am still more proud to follow : my nearest 
 relative filled this chair. I know how he was valued here ; and I 
 cannot but feel that much of the indulgent estimation which you 
 have formed of my fitness for the same station has come to me 
 reflected from his memory, and that you hope to find in the son 
 some of those qualities for which the father was loved and honoured. 
 But, Gentlemen, whatever qualifications I may want, there is 
 one to which I lay claim : I mean that of deep interest in the 
 welfare of this Body, and zeal for its service. Here I will yield 
 to none ; and I console myself with the hope that it may make 
 some amends in your estimation for the many wants which you 
 will hereafter have occasion to observe. 
 
 My predecessor in this chair, upon an occasion similar to the 
 present, laid before you some of his views respecting the constitu- 
 tion of the Academy, and the means by which its future interests 
 might be promoted. I am sure that you will permit me to follow 
 this precedent, and to offer a few remarks firstly, upon the mixed 
 nature of that constitution under which we are here ilnited for the 
 pursuit of truth, and, secondly, upon the progress that has been 
 made, or that may hereafter be made, in that high object of our 
 incorporation. It is of the future that it is important to speak : 
 the precept 
 
 Ta /J.fv oiriffu) firi\av0avo/jifvos, rois 8e f/j.irpoffQfi> 
 
 holds good in the pursuit of knowledge, no less than in the ad- 
 vance in piety. But still our hopes of the future, if they are to 
 be more than dreamy visions, must be based upon the history of 
 the past. 
 
 The first thing that must strike every one, in considering the 
 constitution of this Academy, is the comprehensiveness of its 
 scheme, and the wide scope of its labours ; and we are inclined 
 to ask, whether a constitution so large and so varied, so opposed 
 to modern precedent, can be sound and healthful ? When we 
 look into the recent history of Associations for the advancement 
 of knowledge, we see that each division of the wide domain of 
 truth, as it has arisen into prominent view by the labours of those 
 engaged in its cultivation, has claimed for itself the concentrated 
 energy, and the undivided resources, of an exclusive Society. In
 
 456 ADDRESS DELIVERED AT A MEETING 
 
 this manner the Boyal Society of London, which included origi- 
 nally, and still includes, representatives from every department of 
 philosophy, has seen Society after Society spring up, manned by 
 its own members, and claiming to perform, in a more complete 
 and effective manner, the separated portions of its work. 
 
 Such a state of things is the natural result of increased acti- 
 vity in any department, and of the consequent demand which 
 it makes for a larger portion of time, and the other appliances of 
 labour, than can be devoted to it in a body of mixed constitution, 
 and more comprehensive plan. Nor can it be doubted that such 
 a multiplication of the instruments, by which intellectual force is 
 concentrated and applied, is attended with the many advantages 
 which arise from the division of labour, nor that it has actually 
 tended, and in a very important degree, to push forward and to 
 extend the boundary which divides the known from the unknown. 
 
 But perhaps these advantages, great as they are, have not been 
 wholly unbalanced. Have we not reason to apprehend that philo- 
 sophy has suffered, while the portions of her mighty empire have 
 asserted their independence, and erected themselves into separate 
 kingdoms ? -So far as we insulate any portion of Truth from the 
 rest, by an exclusive devotion to its pursuit and there can be no 
 doubt that such exclusiveness tends to insulation, so far we muti- 
 late the fair proportions of Truth itself, and injure and impair the 
 philosophic spirit whose vital power should animate and pervade 
 the whole. And the injury, great as it is, does not end here. 
 There is an evil partaking of a moral nature obviously springing 
 from this exclusiveness, and which, unhappily, we see too often 
 realized, unless where some counteracting power is brought in to 
 check it. I mean its effect in narrowing our views, in rendering 
 us bigots in philosophy, and in causing us to undervalue that 
 which we do not understand. 
 
 Now, the mixed constitution of our Society has a manifest ten- 
 dency to overcome, or, at least, to mitigate, these evils. I do not 
 mean to say that these evils, and these means of combating them, 
 were distinctly perceived by the first founders of this Body. It is 
 an humbling lesson, that human institutions, in which we have 
 learned to find wisdom, have often had their origin in circum- 
 stances, and their, growth amid the adjustments of conflicting in- 
 terests. The plan of this Academy took its rise, I believe, in the 
 union of two small Societies, calling themselves the Pakeosophers
 
 OF THE ROYAL IRISH ACADEMY, 1846. 457 
 
 and the Neosophcrs, starting originally from opposite extremities 
 of the field of Truth. But, whatever may have been its origin, 
 we may now derive from it lessons not only of mutual forbear- 
 ance, but of mutual instruction. The mathematician may imbibe 
 from the antiquarian the taste which will lead him to explore, 
 with reverence, the early history of the efforts of those master- 
 minds in Science, whose very failures are fraught with philosophic 
 interest, and to trace the progress of discovery up to the first dawn 
 of thought ; and he will return from the investigation with clearer 
 views of the human mind itself, and of the means by which it 
 attains Truth. The antiquarian may learn from the man of 
 science those habits of precise thought, and exact reasoning, which, 
 in the mysterious twilight that surrounds the fascinating objects 
 of his pursuit, he is apt to think inapplicable ; and both may learn 
 from the cultivator of literature to value and to acquire that magio 
 power which language confers upon thought. 
 
 Having said thus much in vindication of the constitution of the 
 Academy, suffer me, in the next place, to consider how far it has 
 been effective in attaining the ends proposed. For this purpose, 
 it will be requisite to take a brief survey of the recent advance- 
 ment of knowledge in this country, so far as it has been influenced 
 by this Academy. And if, in the brevity with which the necessary 
 limits of this Address compel me to glance over the subject, I 
 should appear to have overlooked, or not to have assigned its due 
 weight to any portion of our labours, you will, I trust, attribute 
 this to its true cause. 
 
 The prominent place which the mathematical sciences have 
 occupied in our Transactions may be dated from the time when 
 Brinkley was enrolled amongst our members. But it is to the 
 labours of your late President, and your late Secretary, in this 
 department, that the Academy, in a great measure, owes the high 
 place which it holds among the Scientific Bodies of Europe. Of 
 these labours, it might, perhaps, be rash to single out any portion 
 as pre-eminent, had not the Academy itself, and the Royal Society 
 of London, by the awards of their highest honours, marked out the 
 researches of Sir William Hamilton and Professor Mac Cullagh, 
 in connexion with the wave-theory of light, as of especial value. 
 The theoretical discovery of conical refraction, by Sir William 
 Hamilton, the theory of crystalline reflexion and refraction, by
 
 458 ADDRESS DELIVERED AT A MEETING 
 
 Professor Mac Cullagh, and the general dynamical theory of Light 
 by the same author, mark an era in this branch of science not in- 
 ferior to that of Fresnel. 
 
 Time will not permit me to do more than allude to the new 
 branch of analysis, which has recently engaged so much of the 
 attention of mathematicians, and which originated in the Theory 
 of Quaternions of Sir William Hamilton, and has received an im- 
 portant modification and development in the Triplet theory of 
 Professor Graves. As a Member of the University, I rejoice to 
 be able to add, that worthy successors, even to such men as I have 
 named, are arising there ; and that the recent union of the mathe- 
 matical strength of Cambridge and of Dublin in the Mathematical 
 Journal, which was so long and so ably supported by the former 
 University, is likely to give a new impulse to this branch of science 
 amongst us. And long may these sciences continue to flourish in 
 the University, and in this Academy ! Independently of the 
 magnitude and sublimity of their own proper objects, indepen- 
 dently of their direct value in Physical Science, as instruments of 
 research, they confer a no less important, but indirect service, in 
 disciplining the mind, and correcting those tendencies of other 
 portions of our mental constitution, which, when unbalanced, are 
 sure to mislead. 
 
 Turning from the mathematical to the physical sciences, 
 and first of all to astronomy, which stands upon the confines of 
 both, we cannot fail to be struck by the fact, that in this one 
 Island, with all its disadvantages of climate, there are no fewer 
 than four Astronomical Observatories, each claiming a high place 
 in the history of European science; and that while, in other 
 countries, these costly institutions have been, with but few excep- 
 tions, founded and endowed by their respective Governments, in 
 Ireland (a country not certainly among the foremost in pecuniary 
 resources) they have been erected, equipped, and, with but one 
 partial exception, maintained by the munificence and public spirit 
 of individuals. The names of Mr. Cooper, and of the Earl of 
 llosse, will henceforward be added to those of Provost Andrews 
 and Primate Eobinson, as benefactors of science in this country ; 
 and Markree and Parsonstown be united to Armagh and Dublin 
 in the future history of Astronomy. 
 
 The Dublin Observatory is the eldest of this noble sisterhood. 
 As respects its connexion with this Academy, I need not remind
 
 OF THE ROYAL IRISH ACADEMY, 1846. 459 
 
 you that its chair has been filled by two of your Presidents. 
 With the labours of Brinkley the Dublin Observatory will always 
 stand connected in the history of science. I am sure that it is un- 
 necessary for me to remind you of his researches connected with 
 the problem of the " Stellar Parallax," of which your Transactions 
 contain the first results that great problem, whose final solution 
 has at length been placed beyond question by the observations 
 of Bessel. Of the other and better known inequalities, which 
 affect the apparent places of the stars, all have been illustrated by 
 the observations made with the meridional circle of the Dublin 
 Observatory. In this important class of astronomical investigations, 
 the able director of the Armagh Observatory has had a dis- 
 tinguished share ; and the labours of Dr. Robinson have conferred, 
 as might have been expected, increased accuracy upon the result- 
 ing values of the constants. 
 
 And here, Gentlemen, you will permit me to pause for a mo- 
 ment, and having named the name of Bessel, to offer a passing 
 tribute to his memory. He, who but a few months since occupied 
 the foremost place in the ranks of living Astronomers, is now no 
 more ! He died on the day which followed the last meeting and 
 anniversary of this Body ; and those among us who had the 
 happiness to form his acquaintance, during his short visit to 
 England, and to the British Association, four years ago, will be 
 able to sympathize with his personal friends, no less than with the 
 world of science, in deploring his loss. 
 
 Of the astronomical and optical labours of the Earl of E-osse, 
 and of his great reflector the marvel of astronomical science it 
 is needless for me to speak. No one who was present when the 
 account of its construction, and of its first achievements, was given 
 in this room by Dr. Robinson, can readily forget it ; and for others, 
 the printed notice of that account, in the last number of our Pro- 
 ceedings, will give the fullest information we yet possess respect- 
 ing it. Even from this statement of its earliest trials, it is 
 manifest that the astronomical history of the nebula: will, ere long, 
 be re-made ; and it must be satisfactory to us to know, that the 
 noble artist has arranged a plan of systematic observation, directed 
 to these remote and mysterious portions of the universe, which 
 promises to reveal all that can be known, until a still higher 
 optical power (if such be practically possible) shall be applied to 
 their examination. The imagination is bewildered when it seeks
 
 460 ADDRESS DELIVERED AT A MEETING 
 
 to grasp the possible Mure which may be opened to this and 
 other departments of Astronomical Science by the application of 
 such means : I will mention but one amongst the many anticipa- 
 tions which press for utterance. The observations of Bessel have 
 detected proper motions in the fixed stars, Sinus and Procyon, 
 which appear to establish the existence of invisible companions, of 
 vast magnitude, about which they revolve. Is the invisibility of 
 these great bodies relative only ? and if so, may it not be dispelled 
 before the optical power which Lord Rosse has brought to bear 
 upon the Heavens ? 
 
 " Astronomy, however," to use the words of one whose philoso- 
 phic mind, and varied and profound acquirements, well entitle him 
 to legislate for science, " is only one out of many sciences, which 
 can be advanced by a combined system of observation and calcula- 
 tion, carried on uninterruptedly. * in a utili- 
 tarian point of view, the globe which we inhabit is quite as 
 important a subject 'of scientific inquiry as the stars. We depend 
 for our bread of life, and every comfort, on its climates and seasons, 
 on the movements of its wind and waters. We guide ourselves 
 over the ocean, when astronomical observations fail, by our know- 
 ledge of the laws of its magnetism ; we learn the sublimest lessons 
 from the records of its geological history ; and the great facts 
 which its figure, magnitude, and attraction offer to mathematical 
 inquiry form the very basis of Astronomy itself. Terrestrial 
 Physics, therefore, form a subject every way worthy to be associa- 
 ted with Astronomy as a matter of universal interest and public 
 support, and one which cannot adequately be studied except in the 
 way in which Astronomy itself has been by permanent establish- 
 ments keeping up an unbroken series of observation." 
 
 Two of the leading branches of Terrestrial Physics the sciences 
 of Meteorology and Magnetism have now, as you know, for the 
 last six years, been investigated after one uniform and comprehen- 
 sive scheme, in more than thirty observing stations scattered over 
 the entire globe; and the very bounds of civilization itself have 
 been overleaped in order to give a wider development to the sys- 
 tem. In order to realize the view which Sir John Herschel has so 
 often and so ably advocated, it is only necessary to give permanence 
 to the more important of these Observatories, and to enlarge some- 
 what their sphere of labour. All the phenomena of which our 
 earth, its ocean, or its atmosphere, is the seat ; the tides and the
 
 1846. 461 
 
 oceanic currents, no less than the winds ; the temperature of the 
 earth and of the sea, as well as that of the air ; the movements of 
 the earth's crust, whether calm or convulsive, no less than the 
 changes of the mysterious power which animates and pervades its 
 mass ; all these, and more which might be easily added, are the 
 proper subjects for continued and systematic observation. We 
 have arrived at a period in the history of these branches of science, 
 when the more obvious phenomena have revealed themselves to our 
 desultory efforts, and when the precise laws, and the quantitative 
 measurements, which must form the basis of exact theory, can be 
 reached only by sustained and systematic exertion. 
 
 In these researches, no less than in those of Astronomy, this 
 country has taken its part. The Meteorological Observatory at the 
 Ordnance Survey office in the Phoenix Park, planned and directed 
 by Captain Larcom, has now been upwards of ten years in active 
 operation, and may be taken as a model for similar establishments. 
 Of the Magnetical and Meteorological Observatory of Dublin, 
 founded in the year 1838 by the University, I have already had 
 frequent occasion to speak at these meetings, and I hope before 
 long to communicate some of the ultimate results. 
 
 Of the geology of Ireland I have, perhaps, less right to speak, 
 as the subject has been appropriated by another and a younger So- 
 ciety. Yet there are two facts in its recent history, of such import- 
 ance, that it is impossible not to refer to them in noticing the 
 labours of the members of this Academy. I mean the completion 
 of the Geological Map of Ireland by Mr. Griffith, which, as the 
 work of one man, is certainly one of extraordinary merit ; and the 
 recent arrangements for the continuation of the Geological Survey 
 of this country, the first fruits of which are before the world in 
 Captain Portlock's able and elaborate report on the geology of 
 Londonderry. 
 
 Passing now from the sciences of Observation to those of Experi- 
 ment, we hero also meet with labourers of our own Body, and our 
 Transactions are enriched with the results of their successful toil. 
 Here are to be found the hygrometric researches of Dr. Apjohn, 
 which have solved one of the most intricate problems in Meteor- 
 ology ; and the still more refined researches of the same author 
 upon the Specific Heats of the Gases, to which you have awarded 
 your medal. Here too are to be found most of the chemical re- 
 searches of Sir Eobert Kane, upon the chief of which you have
 
 462 ADDRESS DELIVERED AT A MEETING 
 
 conferred a similar reward ; and to this body were communicated 
 the first investigations of Dr. Andrews, upon the heat developed 
 in chemical combination, which have recently been honoured with 
 the Eoyal Medal. 
 
 To remind you of the progress which Natural History has 
 made, and is yet likely to make in this country, I have only to 
 mention the names of Ball, of Thompson, of Mackay, and Harvey, 
 and Allman, whose contributions to the history of the Fauna and 
 the Flora of Ireland are too well known to need any comment here. 
 The researches of Dr. Harvey, indeed, have embraced a wider 
 range ; and his latest work, the Phycologia Brittanica, now in 
 course of publication, cannot fail to sustain his high character as a 
 descriptive botanist. As a member of the University, I rejoice to 
 be able to add that, of the distinguished Naturalists just mentioned, 
 four are now connected with her teaching ; and that a large portion 
 of the plan contemplated by her late head, with reference to the 
 advancement of those branches of science within her walls, has now 
 been realized. 
 
 The contributions to the department of Polite Literature, which 
 in the early volumes of our Transactions occupied a large and con- 
 spicuous place, have, I regret to say, been of late years less numer- 
 ous. To whatever cause this may be ascribed, we are the more 
 indebted to such men as Dr. Wall, Dr. Hincks, and Dr. Kennedy 
 Bailie, who have enriched our volumes with the results of their 
 learning and their research. But it would not be difficult to name 
 others, fellow-countrymen and fellow-members, who are qualified to 
 share with them the honour and the toil. The latest communica- 
 tion that we have received in this department the paper by Dr. 
 Hincks upon Egyptian Hieroglyphics, the first part of which was 
 recently read promises to throw much light upon the deciphering 
 of these ancient and mysterious records, and, if the author be right 
 in his theory, to add considerably to the discoveries of Young and 
 Champollion. 
 
 The study of Antiquities, on the other hand, and especially of 
 the Antiquities of Ireland, has never been, and, I hope, never 
 will be, out of fashion here. From the time of Molyneux, and of 
 the Dublin Philosophical Society, the earliest of the learned Socie- 
 ties in Ireland from which we can trace our descent, the pursuit of 
 Irish Antiquities has been a favourite one. Of the researches of 
 our living antiquaries, the most conspicuous, undoubtedly, is the
 
 OF THE ROYAL IRISH ACADEMY, 1846. 463 
 
 important work of Mr. Petrie, on the Ecclesiastical Architecture 
 of Ireland, which has been referred to in the recent Eeport of 
 your Council, and which forms, as you know, the last volume of 
 your Transactions. Of the value of that work we should judge in- 
 adequately, were we to confine our view to the light which it has 
 thrown upon the subject discussed ; it is, perhaps, still more valu- 
 able as an example of the mode of dealing with Antiquarian ques- 
 tions, and of the evidences which may be brought to bear in their 
 investigation. 
 
 The study of Irish Antiquities will, there can be no doubt, re- 
 ceive both aid and impulse from the institution of your Museum, a 
 collection well worthy of this Academy, and of this country. It 
 may be rash in one wholly unacquainted with the subject, as I am, 
 to offer any suggestion respecting it ; yet I cannot but think that 
 much more may be done, in advancing our knowledge of Antiqui- 
 ties generally, and especially of that higher department of it which 
 borders so closely upon History, the distribution of the early 
 races of mankind, by the comparison of our own Monuments, and 
 other relics of early civilisation, with those of other countries. The 
 information we gather from a cairn, a torque, or a spear-head, 
 will then no longer be limited to the light which they may throw 
 upon the arts and manners of our Celtic ancestors. We may 
 obtain from them a knowledge of the geographical distribution of 
 their various tribes, much in the same manner as the geologist 
 recognises the fragments of one of the great formations which com- 
 pose the earth's crust by the comparison of their imbedded fossils ; 
 we may approach the history of their families, and trace them up 
 to the parent stock. Studied with this reference, Antiquities may, 
 perhaps in an important degree, tend to advance the science of 
 Ethnology ; and be combined with the study of Language, and of 
 Physiological characters, as a new instrument in its research. 
 
 GENTLEMEN, I fear I have already trespassed too long upon 
 your time. But I desire, before I conclude, to offer a few remarks 
 upon the future advancement of the objects of the Academy, and 
 upon some of the modes by which it may be accelerated. 
 
 The first and chief of these, beyond all question, is rapid 
 publication. It is not to be expected that men, who find a reward 
 for their toils in the sympathy with which they are hailed by 
 those engaged elsewhere in the same pursuits it is not to be
 
 464 ADDRESS DELIVERED AT A MEETING 
 
 expected that they will communicate to us the fruits of those 
 toils, if they should he long withheld from puhlic view. Already 
 there are indications that researches, which should naturally find 
 their place in our Transactions, are about to reach the public 
 through other channels. I trust that this evil may be stayed. 
 The injury that it inflicts is not merely the loss of so much that 
 should add to our credit and our character as a public body, but 
 this very loss itself reacts upon, and augments the evil from which 
 it has sprung. Nor is it necessary for me to urge, that publica- 
 tion is the first, the main and essential duty of such a body as 
 ours. No matter what may be the interest of our meetings, no 
 matter how far the study of Science, Literature, or Antiquities, 
 may be aided by our library and our museum, it is by our 
 published works that we shall be judged, and by which we must 
 stand or fall. I have only to add, that your Council are duly 
 impressed with this feeling ; and that your Officers are at present 
 engaged in the consideration of some measures which promise 
 to give not only a speedy, but also an increased publicity to our 
 Proceedings. 
 
 Another instrument of progress, to whose efficacy I will advert, 
 and which this Academy may, I think, effectively wield, is the 
 directing power which it may reasonably assume, in pointing out 
 to its members problems of local interest remaining to be solved, 
 and encouraging them to the task by the proposal of Honorary 
 Rewards. The practice of proposing subjects for investigation, 
 and of honouring them by prizes, has existed, you must be aware, 
 from the very origin of the Academy ; and it has tended to elicit 
 researches of considerable interest and value. Some years since, 
 indeed, it was generally felt that the system had failed; and that 
 opinion (in which at the time I shared) led to an alteration in the 
 system of Honorary Rewards, with which you are of course ac- 
 quainted. It may be doubted, however, whether this failure was 
 the necessary result of the system itself, and not rather of the 
 nature of some of the topics selected and proposed. It must be 
 manifest, I think, that no encouragement which such a Society 
 as this can bestow will be likely to stimulate a man of genius 
 to the investigation of an abstruse question, to which he feels 
 no predisposing movement, that no reward can usurp the place 
 of inspiration itself. But there are problems of a different stamp, 
 whose solutions may be expected as the certain result of well-
 
 THE ROYAL IRISH ACADEMY, 1846. 465 
 
 directed labour ; to such problems as these, especially when their 
 local character invests them with additional interest, and in some 
 degree prepares men's minds for the research, to such problems 
 the recommendation of a learned Society may, with full assurance 
 of the result, direct the attention of its Members. We know how 
 much our knowledge of the Antiquities of this country has bene- 
 fited by the proposal of such questions. Allow me to suggest one 
 or two of a similar character connected with Physical Science, as 
 examples of what may be done in other departments. 
 
 In an interesting paper recently printed in the Philosophical 
 Magazine, Colonel Sabine has suggested that the almost unparal- 
 leled mildness of the late winter may possibly be explained by an 
 unusual extension of the Gulf-stream, bathing the shores of these 
 Islands, and carrying with it a portion of the high temperature of 
 the tropical region from which it flows. And the probability of 
 this explanation has been augmented by the fact, that in the 
 winter of 1821-2 (a winter in many respects resembling the last) , this 
 great oceanic current, whose force is usually spent when it reaches 
 the Azores, was actually observed in the neighbourhood of our 
 shores. I have long speculated upon the probable influence of the 
 Gulf-stream upon the Irish winters generally, which appear to be 
 much milder, in comparison with those of England, than can be 
 well accounted for upon the principles of insular climate alone ; 
 and I was glad to see, from Colonel Sabine' s paper, that my con- 
 jectures had some real foundation. Whether or not they will 
 account for the fact may, I think, be easily tested by a series of 
 observations of the temperature of the sea on the eastern and 
 western coasts of the Island, and under the same parallel ; and 
 I cannot but think that such a result, throwing so great a light 
 upon the Climatology of this country, would, if established, well 
 reward the labour bestowed in the investigation. 
 
 The Climate of Ireland, indeed, engaged a large share of the 
 attention of the Academy during the lifetime of Kirwan; and 
 several papers on the subject, by himself and others, are to be 
 found in the early volumes of our Transactions. Should the 
 Royal Irish Academy, as I think it ought, take that subject again 
 under its peculiar care, the knowledge of it might be extended and 
 improved, by the observation of the times of the leafing and flower- 
 ing of certain plants, after the plan suggested and carried out by 
 M. Quetelet of Brussels, and now extensively followed in many
 
 463 ADDRESS DELIVERED AT A MEETING OF 
 
 parts of Europe. Such observations furnish us with a simple but 
 admirable measure of the total e/ects of all the influential causes in 
 their combination and uoion. 
 
 Another subject of special inquiry, which might be fitly urged 
 by this Society, is the history of the Tides on the coasts of Ireland. 
 On this subject much has been already done ; but probably much 
 yet remains to be accomplished. Of the observations made in the 
 summer of 1842, by the non-commissioned officers of the Ordnance 
 Survey under the direction of Colonel Colby, Mr. Airy (by whom 
 they have been ably discussed in a paper recently printed in the 
 Philosophical Transactions) observes, that " extent of time alone 
 appears wanting to render them the most important series of tide- 
 observations that has ever been made." Among the results to 
 which Mr. Airy has arrived is the remarkable one, that in the 
 harbour of Courtown, on the coast of Wexford " the only place 
 on the earth in which such a result has been distinctly obtained," 
 the Solar Tide exceeds the Lunar. Such a result as this affords 
 not only encouragement to fresh exertion, but also direction as to 
 its application. 
 
 Another, and most interesting subject of research, which this Aca- 
 demy might direct, if not itself undertake, is that to which attention 
 has been recently drawn by Mr. Mallet, the movements of the 
 earth's crust, .whether convulsive and paroxysmal, or gentle and 
 regular. The phenomena of earthquake shocks in Scotland have 
 been systematically observed for the last five years, at the instance 
 of the British Association, and yearly reports of the results have 
 been made, and published in its Proceedings. Although there 
 appears to be nothing in this country analogous to the local move- 
 ments at Comrie, in Perthshire, still there is no doubt that earth- 
 quake shocks have been felt here ; and that more refined methods 
 of observation would detect numberless others, which wholly escape 
 the cognizance of the unaided senses. 
 
 These and many other investigations, connected with the phy- 
 sical, the physiological, and the monumental history of Ireland, 
 appear to be fitting subjects, if not for the direct labours of this 
 Academy, at least for its encouragement. Science has a right to 
 demand such histories of local phenomena from the representatives 
 of Science in each portion of the civilized globe, and shall this 
 Academy be deaf to the call ?
 
 THE ROYAL IRISH ACADEMY, 1846. 467 
 
 GENTLEMEN, I have, at the outset of these remarks, noticed 
 the moral, as well as the intellectual benefits which result from the 
 union of different mental powers, such as this Academy presents, 
 combined in the investigation of different portions of Truth. But 
 there is a yet higher principle, to which this union may lead us a 
 yet holier temper which it may inculcate ; I mean the contempla- 
 tion of Truth itself as essentially ONE, under its many and diversi- 
 fied forms, and the habit of tracing all its varied and refracted 
 rays to its One and Eternal Source. Strengthened by this high 
 thought, our feelings raised and spiritualized by this habit, 
 there: is no danger that we shall give place to the weak apprehen- 
 sion (which is but a subtle form of unbelief itself), that any portion 
 of Truth can ever prove inconsistent with any other. And the 
 same principle, while it saves us from slavish fear, will also guard 
 us from presumption. Standing in the presence of confessed and 
 established truth, we shall feel that we are treading upon holy 
 ground ; and we shall demean ourselves, not with the elation and 
 pride of conquest, but with the devotion of worship and of love. 
 
 2 ii 2
 
 XXII. ADDRESS DELIVERED AT A MEETING OF THE 
 ROYAL IRISH ACADEMY, HELD JUNE 26iH, 1848, ON THE 
 OCCASION OF THE PRESENTATION OF THE MEDALS 
 AWARDED BY THE COUNCIL. 
 
 Proceedings of the Royal Irish Academy, 1848. 
 
 GENTLEMEN, We have this night reached the close of a Ses- 
 sion of more than usual activity ; and I might, therefore, naturally 
 have desired, before leaving this chair and adjourning the Aca- 
 demy to another winter, to trespass for a short time upon your 
 attention, and to lay before you a brief summary of the results of 
 our toil.. On the present occasion, however, my duty is narrowed 
 and defined ; and the recent award of the Cunningham Medals by 
 the Council renders it imperative on me to submit to the Academy 
 the grounds of their decision. In doing this, it will be necessary 
 for me to present a brief analysis of the results of those labours 
 whose value your Council have thus honourably recognised ; and 
 in the execution of this task I must request the indulgence of the 
 Academy, and still more that of the gentlemen of whose discove- 
 ries I am to speak, if, in my imperfect acquaintance with them, I 
 should fail to do justice to their merits. 
 
 You are aware that, during the past Session, the laws respect- 
 ing the award of medals have occupied the attention of the Council ; 
 and that certain new regulations relating to it were, upon their 
 suggestion, adopted by the Academy. It is unnecessary for me 
 to recapitulate these regulations, or to state the grounds for the 
 changes therein made, as this has been fully done by the Council in 
 their last Annual Eeport. It will be sufficient for me on the pre-
 
 ADDRESS DELIVERED BEFORE THE ROYAL IRISH ACADEMY. 469 
 
 sent occasion to remind you, that the principal alteration in the 
 rules respecting the award of medals under the Cunningham be- 
 quest has been to extend the limit within which the Council are 
 enabled to bestow such rewards, and to confine them only to 
 memoirs or works printed and published in Ireland, or relating to 
 Irish subjects. 
 
 A considerable interval having elapsed since the last award of 
 these prizes, the Council for the present year, on coming into office, 
 referred the matter to the three Committees of which that body is 
 composed. Upon the recommendation of these Committees, in 
 their several departments, the Council have adjudicated Medals to 
 the following gentlemen : 
 
 1. To Sir William Eowan Hamilton, for his " Eesearches re- 
 specting Uuarternions," published in the twenty-first volume of 
 the Transactions of the Academy. 
 
 2. To the Eev. Samuel Haughton, Fellow of Trinity CoUege, 
 Dublin, for his Memoir " On the Equilibrium and Motion of 
 Solid and Fiuid Bodies," published in the same volume. 
 
 3. To the Rev. Edward Hincks, D. D., for his various papers 
 on Egyptian and Persepolitan Writing, also published in the same 
 volume. 
 
 4. To John O'Donovan, Esq., for his contributions to the 
 Transactions of the Irish Archaeological Society, for his Irish Gram- 
 mar, and for his edition of the Annals of the Four Masters.- 
 
 In attempting to lay before the Academy a concise account of 
 the origin of the new Calculus invented by Sir William Hamilton, 
 and of the principles upon which it is based, I shall avail myself of 
 the elucidations and applications of the theory which its gifted 
 author has, from time to time, communicated to the Academy, and 
 of which abstracts have appeared in our Proceedings as also of the 
 series of papers published by him in the Philosophical Magazine 
 upon the same subject. Of the latter, the author's letter to John 
 T. Graves, Esq., written immediately after the discovery, possesses 
 a high value, not only as a fragment of scientific history, but still 
 more, as laying bare in a new instance that most interesting and 
 instructive of all the mental phenomena, the actual train of 
 thought which takes place in the creative mind, from the first dawn 
 of truth within it to its full and noon-tide effulgence.
 
 470 ADDRESS DELIVERED AT A MEETING OF 
 
 It is now twenty years since the Rev. Mr. Warren of Cambridge* 
 showed that the ordinary imaginary symbol (v/ - 1) had a geome- 
 trical significancy, and denoted a right line whose length was equal 
 to unity, to be measured, not on the axis of the real units, but on an 
 axis at right angles to it. It followed from this, and from another 
 principle respecting the symbolical meaning of the sign +, as ap- 
 plied to lines, that the ordinary binomial imaginary, whose real 
 parts, or constituents, are multiplied by unity and v/ - 1, respec- 
 tively, may be taken to represent both the length and direction of 
 a right line in a given plane ; the square root of the sum of the 
 squares of the constituents being the length of the line, and their 
 quote, or ratio, the tangent of the angle which it forms with the 
 axis on which the first of them is measured. These quantities 
 have been denominated the modulus and the amplitude of the ima- 
 ginary binomial. 
 
 Now, if two such binomials, or couplets, be added together ,fthe 
 sum is a binomial of a similar form, or a couplet whose constituents 
 are the sums of the constituents of the original couplet. And if two 
 couplets be multiplied together, the product is likewise a couplet ; 
 and the relation of the product to the factors is such, that the 
 modulus of the product is the product of the moduli of the factors, 
 and the amplitude of the product is the sum of the amplitude of the 
 factors. From these algebraical properties of couplets, combined 
 with their geometrical significancy, it follows that right lines in a 
 plane, having direction as well as magnitude, may be operated 
 upon according to certain simple algebraical conditions, and the 
 direction and amplitude of the resultant lines obtained by certain 
 simple algebraical rules. 
 
 It was in the effort to generalize the theory of Couplets, and to 
 extend their properties to right lines in space, that Sir "William 
 Hamilton was led to the construction of his theory of Quaternions. 
 " Since," he says, " ^/ - 1 is, in a certain well- known sense, a line 
 
 * Since the delivery of this Address the attention of the writer has heen directed by 
 Sir William Hamilton to the earlier steps of the inquiry. The first appears to have 
 been made by M. Buec, in a Paper published in the Philosophical Transactions for 
 1806, in which he lays down the principle that the symbol V^i, as applied to lines, 
 denoted perpendicularity. A further step was made by M. Argand, in a memoir pub- 
 lished at Paris in the same year, in which he sho'ws that the sum of two lines, 
 estimated in direction as well as magnitude, is the diagonal of the parallelogram con- 
 structed upon them. The subject was resumed and more fully developed by M. 
 Francois, in a memoir published in the Annales des Mathematiques for 1813.
 
 THE ROYAL IRISH ACADEMY, 1848. 471 
 
 perpendicular to the line 1, it seemed natural that there should be 
 some other imaginary to express a line perpendicular to both the 
 former ; and because the rotation from 1 to this also, being doubled, 
 conducts to - 1, it also ought to be a square root of negative unity, 
 though not to be confounded with the former." 
 
 Starting thus with the conception of triplets involving two dis- 
 tinct square roots of negative unity, and endeavouring to frame 
 laws for their algebraical treatment, analogous to those which hold 
 in the case of couplets, he was soon led to perceive that the exist- 
 ence of the two imaginaries, just alluded to, necessarily involved 
 the existence of a third, which was also a square root of negative 
 unity distinct from either of the former. He was thus led to the 
 conception of quaternions, or quadrinomials whose real parts, or 
 constituents, are multiplied, the first by unity, and the other 
 three by the imaginary roots of negative unity just referred to ; 
 and he determined the conditions which must subsist amongst these 
 new imaginary coefficients, in order that the resulting quadrino- 
 mials should be subject to the same algebraical laws as the ordinary 
 imaginary binomials, or couplets. 
 
 I may here observe, in passing, that one of these laws, namely, 
 the law of the moduli, is equivalent to a celebrated theorem of 
 Euler, viz. : that the sum of four squares, multiplied by the sum 
 of four squares, is also a sum of four squares. An extension of 
 this theorem to sums of eight squares has been effected, inde- 
 pendently, by Mr. John Graves and Professor Young ; and the 
 latter writer (whose paper on the subject is published in the last 
 part of the Transactions of the Academy) has proved that the pro- 
 perty cannot be extended to higher numbers. 
 
 To return to the Quaternion we have seen that it is made up 
 of a real part, and an imaginary trinomial, using the terms real 
 and imaginary in their ordinary acceptation. The latter of these 
 represents a right line in space, drawn from the origin to the 
 point whose co-ordinates are the three constituents of the tri- 
 nomial ; and it is accordingly designated by Sir William Hamilton 
 by the term vector. The real part of the quaternion, on the other 
 hand, designates number alone, whether positive or negative, with- 
 out direction in space; and, accordingly, although real in the 
 algebraical sense of the term, it is in some sense imaginary, when 
 contemplated on the geometrical side. This part of the quaternion 
 is denominated by Sir William the scalar.
 
 472 ADDRESS DELIVERED AT A MEETING OF 
 
 Thus we see that a quaternion is reducible to a binomial, the 
 component parts of which the scalar and the vector designate, 
 the one a number, the other a line. The whole tendency of the 
 later speculations of the author has been to realize this reduction, 
 and having determined the laws of operation upon scalars and vec- 
 tors, to dismiss altogether the consideration of the constituents of 
 the vector, and to treat it as a single integral quantity. It is easy 
 to see what amount of simplicity is thus, at one step, introduced 
 into the whole of Geometry and Mechanics. In place of the three 
 co-ordinates (rectilinear or polar) by which the magnitude and 
 direction of a line, or of a force, are ordinarily determined, the 
 theory of Sir William Hamilton deals with the line itself, or with 
 the force, directly ; and thus not only is the number of necessary 
 equations reduced at once, in the proportion of three to one, but 
 also the interpretation of the equations themselves is rendered 
 simpler and more direct. 
 
 The scalar, or algebraically-real part of the quaternion, thus 
 appearing to have no direct geometrical significancy, geometers 
 seemed inclined to regard it as a sort of intruder in their domain ; 
 and I believe it was to the desire to exclude it, that we may, in 
 part, attribute the very elegant and ingenious theories of triplets 
 invented by Professor De Morgan and Professor Graves. The sca- 
 lar, however, is represented in mechanics by the time ; and even in 
 its application to pure geometry, Sir "William Hamilton has shown 
 that the introduction of this fourth quantity confers power and ge- 
 nerality upon the Calculus of Quaternions, inasmuch as no direction 
 in space is thus selected as eminent above another, but all are re- 
 garded as equally related to the extra-spatial, or scalar direction. 
 The calculus thus frequently admits of a simpler and more direct 
 application to geometrical problems than the Cartesian method of 
 co-ordinates, inasmuch as it demands no previous selection of arbi- 
 trary axes. 
 
 I may observe, also, that in the triplet theories of Professor 
 De Morgan and Professor Graves, the law of the moduli is not pre- 
 served, if the term modulus be taken in its ordinary signification, 
 it being not generally true that the sum of three squares, multiplied 
 by the sum of three squares, is a sum of three squares. 
 
 But whatever be thought of the principles of the Calculus of 
 Quaternions, its advantages as an instrument of mathematical 
 thought will undoubtedly be judged by the simplicity and ease
 
 THE ROYAL IRISH ACADEMY, 1848. 473 
 
 with which it may be applied. In this the author has already done 
 enough to establish its power. He has applied it with great success 
 to many problems of the geometry of Surfaces ; and he has given a 
 sketch of its application to the problem of the Three Bodies, and to 
 the Mechanics of the Heavens generally. These instances of its 
 application, whether we look to the elegance and simplicity of the 
 method, or to the beauty and symmetry of the results, are abun- 
 dantly sufficient to demonstrate the power and pliancy of the in- 
 strument. 
 
 Still, however, more will be required from its author, before the 
 weapon which he wields with a giant's grasp may be touched by 
 feebler hands. It will be necessary that the principles and funda- 
 mental rules of the calculus should be rendered familiar by elemen- 
 tary exposition, and their certainty tested by ordinary applications, 
 before the violation of known analogies which some of them present 
 will be universally acquiesced in ; and I am happy to be able to 
 say that the large debt, which Science already owes at his hands, is 
 likely to receive ere long this addition, and that, like a genuine 
 lover of Truth, he will not rest content until the difficult path 
 which he has cut for himself into her tangled and obscure recesses 
 shall become a highway for all. 
 
 I now proceed to the consideration of Mr. Haughton's memoir 
 *' On the Equilibrium and Motion of Solid and Fluid Bodies." 
 
 The object of this memoir, as stated by the author himself, is 
 " to deduce, by the method of the Mecanique Anatytique of La- 
 grange, the laws of equilibrium and motion of elastic solid and 
 fluid bodies from the same physical principles, and to discover by 
 the same method the conditions at the limits." The method of 
 Lagrange (which is so peculiarly adapted to the mechanics of a 
 system composed of an indefinite number of acting molecules, situ- 
 ated indefinitely near each other) seems to have been first applied 
 to the problem of elastic bodies by M. Navier, who determined by 
 that method the laws of equilibrium of a homogeneous uncrystallized 
 solid. The late Mr. Green, of Cambridge, applied the same me- 
 thod to the more difficult di/nnniical question of the movement of 
 the molecules of the Iiuninifcrous ether; in which application he 
 was followed by the distinguished mathematician whose name is 
 imperishably connected with the records of this Academy. 
 
 Mr. Haughton has judiciously adopted the same mathematical
 
 474 ADDEESS DELIVERED AT A MEETING OF 
 
 method ; and he has determined the form of the function which 
 enters the general equation of Lagrange (and which depends upon 
 t.he internal forces acting at any point of the medium), from the 
 assumed principle, that the molecules of solid and fluid bodies act 
 on each other only in the direction of the line joining them, and with 
 forces which depend on the magnitude and direction of that line. 
 This function is easily shown to consist of two parts, one of them 
 depending on the first power of the displacement, and the other 
 upon its square ; the former of these is assumed to relate to perfect 
 fluids, and the latter to solids, while both must be taken into account 
 in imperfect or viscous fluids. The form of this function, in the case 
 of solids, bears some analogy to (although it is quite different from) 
 that of the function employed by Professor M'Cullagh in his- 
 dynamical theory of light ; and the author deduces, from that dif- 
 ference, the important physical consequence that the molecules of 
 the luminiferous ether do not, according to that theory, act on one 
 another in the direction of the line joining them. 
 
 The differential equations of motion cannot be integrated gene- 
 rally ; but the values of the three component displacements which 
 correspond to the case of plane waves are manifestly particular in- 
 tegrals ; and the equations of condition, which result from the sub- 
 stitution of these values in the general equations of motion, lead to 
 a remarkable geometrical construction for the three possible direc- 
 tions of molecular vibration, and the corresponding velocities of the 
 plane waves, by means of six fixed ellipsoids. 
 
 The author then determines the equation of the surface of icave- 
 slowness (or the reciprocal polar of the wave-surface), the nature 
 and properties of which are analogous to those of the surface of the 
 same name in the theory of light. This surface is of the sixth de- 
 gree, and has three sheets, corresponding to the three velocities of 
 wave propagation ; and, like the corresponding surface in the theory 
 of light, it serves to determine the direction of the refracted waves, 
 in passing from one medium to another, as well as the laws of pro- 
 pagation in the same medium. In the most general case consi- 
 dered by the author, namely, when the molecules of the medium 
 are arranged symmetrically round three rectangular planes, it is 
 shown that this surface has four nodes, at which the tangent plane 
 is a cone of the second degree ; and thence arises a conical refrac- 
 tion in Sound, similar to that discovered theoretically by Sir Wil- 
 liam Hamilton in the case of Light.
 
 THE ROYAL IRISH ACADEMY, 1848. 47-> 
 
 That such analogies, and points of correspondence, should exist 
 between the theory of light, and any general theory of vibration in 
 crystalline solids, was, of course, to be expected from the common 
 foundation and the common postulates of the two theories. Not- 
 withstanding this, however, the two theories diverge at a very 
 early point. In both, indeed, the form of the characteristic func- 
 tion is deduced from the assumed molecular constitution of the 
 medium. But that constitution is essentially different in the two 
 cases, the fundamental molecular property of the luminiferous 
 ether, in the theory of Professor M'Cullagh, being the un- 
 changeableness of its density, while the corresponding basis of 
 the theory of Mr. Haughton is the property that the molecules of 
 the medium act on one another in the direction of the joining 
 line.* 
 
 In conclusion, I may observe that the value of Mr. Haughton's 
 theory considered on its physical side, and independently of its 
 mathematical elegance consists in its high degree of generality ; 
 which is such as necessarily to embrace all the fundamental condi- 
 tions of the problem, and thus to leave to future mathematicians 
 the task only of limiting and interpreting his results. 
 
 In speaking of Dr. Hincks' philological researches I must pass 
 over those which relate to Egyptian Hieroglyphics, and hasten to 
 his more recent, and (at the present time) more interesting labours 
 connected with Persepolitan writing. And in order to present an 
 intelligible statement of the nature of these labours, and of the 
 additions which have been thereby made to the existing amount of 
 knowledge upon this curious subject, it will be necessary to take a 
 hurried glance at the history of the investigation, and its principal 
 steps. 
 
 The cuneiform writing has been generally reduced to three 
 leading divisions, which have been denominated, respectively, 
 Persian, Median, and Babylonian. Many of the cuneiform inscrip- 
 tions contain all the three kinds of writing, the first being the 
 principal, and apparently the vernacular record, and the other two 
 
 * The theory of Mr. Haughton bears a much closer resemblance, in many of its re- 
 sults, to the wave-theory of M. Cauchy than to that of Professor M'Cullagh, although 
 it differs from it wholly in method. The theory of M. Cauchy is, in fact, a theory of 
 the laws of propagated vibration in solids, and is inapplicable (as was shown by Pro- 
 fessor M'Cullagh) to light.
 
 476 ADDRESS DELIVERED AT A MEETING OF 
 
 translations. They are found on rocks, slabs, and pillars, at Per- 
 sepolis, at Behistun, at Van, at Murghab, and at Hamadan. These 
 trilingual inscriptions are all, without exception, records of the 
 Achsemenian dynasty ; the earliest which has been discovered (the 
 inscription at Murghab, or Pasargadse) relating to Cyrus the Great, 
 and the latest to Artaxerxes Ochus. 
 
 Of the three kinds of writing found in these inscriptions, the 
 first, or Persian, is the simplest, containing the fewest and least com- 
 plicated characters. It is also distinguished from the other two by 
 the divisions between the words, which are separated by an oblique 
 wedge ; and this circumstance, of course, greatly facilitates the 
 task of the decipherer. The second Persepolitan writing appears 
 to have been co-eval with the first, and to have been employed only 
 in conjunction with it, in the trilingual monuments of the Achse- 
 menian princes ; it is accordingly ascribed by the concurrent voice 
 of philologers to the Medes, the people next in importance to the na- 
 tive Persians under the Achsemenian dynasty. The number of cha- 
 racters in this writing is far greater than in the Persian, its alpha- 
 bet (or syllabary) containing about 100 letters. The third Perse- 
 politan writing belongs to one of a group of languages (distinguished 
 by Major Eawlinson into the Babylonian, the Assyrian, and the 
 Elymcean] written in a similar character. It is ascribed, with every 
 probability, to the Babylonians, legends in a like character being 
 found on cylinders and bricks excavated from the foundations of 
 the primaeval cities of Shinar. It is unquestionably the most ancient 
 of the three kinds of cuneiform writing, and was probably the type 
 upon which the other two were constructed. The characters are 
 more numerous and more complicated than those of the first and 
 second kinds. 
 
 The process of resolving and interpreting an inscription in an 
 unknown and extinct language, and written in an unknown cha- 
 racter, appears to include three distinct and principal steps. The 
 first of these is that of deciphering (properly so called), or deter- 
 mining the phonetic powers of the letters. The next step is the 
 determination of the nature of the inflections, and the grammatical 
 structure of the language itself, and the discovery of its congeners 
 or representatives amongst the living languages. The third and last 
 step consists in tracing from these sources the meaning of its roots, 
 ^and thus translating the inscription. 
 
 The first of these steps wasJong since taken, with respect to the
 
 THE ROYAL IRISH ACADEMY, 1848. 477 
 
 first Persepolitan writing. In the year 1802, Professor Grotefend, 
 of Gottingen, examined two short trilingual inscriptions, which had 
 been copied at Persepolis by the traveller Niebuhr, and succeeded 
 in identifying the names of Cyrus, Darius, Xerxes, and Hystaspcs, 
 in all the three characters. The analysis of these names, in the 
 case of the Persian, enabled him to determine the values of eleven 
 out of the sixteen letters of which they were composed, or nearly 
 one-third of the entire alphabet. 
 
 The next step was made by Professor Bask, of Copenhagen, in 
 1826. He recognised the title Achcemenide in the inscription of 
 Niebuhr, and thus determined the values of two important letters, 
 m and n, which occur in it. But the most valuable contribution 
 made by Eask to this branch of palaeography, consisted in his dis- 
 covery of the resemblance of the extinct language to the Sanscrit 
 in some of its inflections, a discovery which has been justly re- 
 garded as the key to its interpretation. Ten years later the inquiry 
 received a fresh impulse by the simultaneous publication of two 
 works, one by M. Burnouf, of Paris, and the other by the distin- 
 guished orientalist, Professor Lassen, of Bonn. By the analysis 
 of a trilingual inscription, containing the names of the provinces of 
 the Persian empire, the values of many new characters were ascer- 
 tained, and the known alphabet was enlarged to twenty-six letters. 
 In the year 1838 the values of five new characters were added to 
 the list, two by Dr. Beer, of Leipsic, and three by M. Jacquet, 
 of Paris ; and the same writers discovered, independently, the fun- 
 damental principle which, strange to say, had hitherto escaped 
 notice, that the Persian alphabet contained but three vowels, a, /, 
 and u* 
 
 But the most important of the researches connected with the 
 first Persepolitan writing are those of Major Eawlinson. Hitherto 
 little had been accomplished beyond the first step of the process, 
 the determination of the values of the letter*. Eask, indeed, 
 had observed the similarity of the language to the Sanscrit, and 
 this was confirmed by Lassen and Beer, the former of whom 
 proposed to employ the Sanscrit as a key to its interpretation ; 
 but, as yet, little had been correctly done on this head. In 1835, 
 
 * This striking similarity of the Persian to the languages of the Slicmitir fypo, in 
 its vocalic structure, has been recently drawn still closer by Dr. AV.ill. in bis able 
 paper on the different kinds of cuneiform writing, published in the last volume of the 
 Transactions of the Academy.
 
 478 ADDEESS DELIVERED AT A MEETING OF 
 
 Major Eawlinson commenced his labours, in the country of the 
 inscriptions ; re-discovered for himself the greater part of what 
 had been already done by European scholars ; and determined 
 the values of, at least, four new characters. But his chief work 
 in which he has, by one great stride, surpassed all his predecessors 
 is the translation of the Persian portion of the great trilingual 
 inscription at Behistun, containing above 400 lines of cuneiform 
 writing. This inscription had been copied, in part, by Major 
 Eawlinson in 1837 ; and a large portion of the translation was 
 made by him, and communicated to the Royal Asiatic Society, in 
 1839. His philological labours were suddenly interrupted in the 
 following year, by active duty at Affghanistan ; but in the autumn 
 of 1845 he succeeded in making a correct copy of the whole of the 
 Persian inscription (together with a considerable portion of the Me- 
 dian and Babylonian), and soon after completed the translation in 
 the form in which it has been recently published. With the contents 
 of this singular record, written more than twenty-three centuries 
 since, and throwing an unexpected light upon one of the most 
 controverted questions of early history, the literary public are 
 now well acquainted. 
 
 Dr. Hincks' first paper on Persepolitan writing was communi- 
 cated to the Academy in June, 1846, before the publication of the 
 first part of Major Eawlinson's memoir. In this paper he pro- 
 poses three general principles respecting the orthography of the 
 Persian, in which he corrects Lassen's account of that language. 
 The most important of these consists in the distinction of the 
 consonants into two classes, which he calls primary and secondary, 
 the former being those which may be used before the vowel a, 
 expressed or supplied, the latter such as are only used before one 
 of the other vowels. Dr. Hincks maintains, in opposition to 
 Lassen, that these secondary consonants are phonetically equiva- 
 lent to their primaries ; and he lays it down, " as an invariable 
 rule, that if a primary consonant precedes i or u, when a secondary 
 consonant existed of the same value as the primary one, and 
 appropriate to that vowel, an a must be interposed, either as a dis- 
 tinct syllable, or as a guna to the vowel." The Persian alphabet 
 may now be considered to be completely established. Of the 
 thirty-nine letters which compose it, Major Eawlinson and Dr. 
 Hincks are now agreed as to the values of all but one; Dr. 
 Hincks having adopted three of Major Eawlinson's values, and
 
 THE ROYAL IRISH ACADEMY, 1848. 479 
 
 Major Kawlinson having taken, independently, nine of those as- 
 signed by Dr. Hincks. 
 
 The data for the investigation of the Median or second Perse- 
 politan writing are abundant, the trilingual inscriptions of Perse- 
 polis and Behistun furnishing more than ninety proper names, 
 together with their Persian equivalents. Notwithstanding this, 
 the progress made in the investigation has been comparatively 
 small. In fact, with the exception of Grotefend, who made the 
 first step, Westergaard is the only writer who has attempted the 
 task of deciphering it with success. Major Kawlinson indeed 
 informs us, in his memoir on the Persian character, that he has 
 made considerable progress in deciphering the two other kinds of 
 Persepolitan writing ; and he has given a sketch of his views on 
 the orthography, and the general structure and affinities of the 
 language of the second kind : but none of his results, as" to the 
 values of the characters, have been as yet published. 
 
 Westergaard held that the Median alphabet had six vowels 
 and sixteen consonants ; and that the characters represented first 
 these twenty-two letters, and then syllables composed of the conso- 
 nants followed by vowels. Dr. Hincks maintains, on the contrary, 
 that there are but four vowels and five consonants ; and that, besides 
 the characters representing these nine simple sounds, there are 
 also characters representing combinations of the five consonants 
 with preceding and following vowels, as also combinations of the 
 vowels with each other. Again, while according to Westergaard 
 the vowels are not all expressed, according to Dr. Hincks every 
 vowel is expressed at least once, and often more than once ; it 
 being customary to write vowels twice over, at the end of one 
 character and at the begining of the next. In accordance with 
 this principle, Dr. Hincks adds vowels, in many cases, to Wester- 
 gaard's values, thus making the characters to represent syllable* 
 instead of letters. Notwithstanding these important differences, 
 however, he confirms, in general, the values given by Westergaard, 
 although he differs from him altogether as to five of the characters, 
 and assigns values to five more, which that writer had not valued 
 at all. 
 
 But it is upon his labours connected with the third Perse- 
 politan writing that Dr. Hincks' chief claim as an original 
 discoverer must be founded. Grotefend discovered that the 
 characters, in this writing, were partly expressive of syllables, and
 
 480 ADDRESS DELIVERED AT A MEETING OF 
 
 partly of letters : to a few of them, also, he assigned phonetic 
 values; and he ascertained the fact of the correspondence of certain 
 lapidary with certain cursive characters. To this little has been 
 added by the many archaeologists who have written upon the 
 subject, beyond the mere classification of the characters. At an 
 early period of his inquiries, Dr. Hincks arrived at the conclusion 
 that the Babylonian and Assyrian writing agreed with the second 
 Persepolitan in many of the features of the latter already noticed. 
 The chief of the materials upon which he has since laboured are 
 the Achsemenian inscriptions published by Westergaard, and the 
 great inscription of the East India Company, containing 619 lines 
 of lapidary characters. His first step in the deciphering of these 
 documents was, of course, to analyze the proper names which 
 occur in the third columns of the trilingual inscriptions, and to 
 compare them with their equivalents in the other two. The 
 values of many characters were thus determined ; those of others 
 were ascertained by comparing different modes of writing the 
 same words in the inscriptions which commence with the same 
 formula ; and, finally, when the equivalence of two sets of charac- 
 ters, lapidary and cursive, was ascertained, more values were 
 determined by comparing the proper names in the great inscrip- 
 tion with their representatives in the other languages. By such 
 means Dr. Hincks has constructed an alphabet, or syllabary, of 
 the third Persepolitan writing, containing the values of ninety-five 
 characters, together with the corresponding lapidary characters; 
 and he has given a series of numbers from the rock inscription at 
 Yan, exhibiting the mode of expressing numerals in cuneatic 
 characters. 
 
 Before I take leave of this subject, one more remark is 
 necessary. It has been assumed by every writer who has hitherto 
 engaged in the investigation of the cuneiform inscriptions, that the 
 writing of the second and third kinds (as well as that of the first) 
 is alphabetical. This fundamental position, however, has been 
 recently assailed by Dr. Wall, in a very able critical paper read 
 before the Academy ; and arguments of much weight have been 
 adduced to distinguish the principle of these two kinds of cunei- 
 form writing from that of the first, and to prove them to be idea- 
 graphic. It is not my duty (even if I were competent to the task) 
 to offer any opinion upon the question thus raised. I have only 
 to observe that what has been said above, respecting the progress
 
 THE ROYAL IRISH ACADEMY, 1848. 481 
 
 recently made in deciphering these two kinds of writing, is 
 upon the ordinary assumption, and must be received with the 
 based reserve which necessarily attaches to a controverted posi- 
 tion. 
 
 With Mr. O'Donovan's archaeological labours I regret to say 
 that I possess no direct acquaintance ; and, accordingly, in the 
 present notice of them, I am compelled to lean upon the friendly 
 aid of the Secretary of the Academy, who is himself a large con- 
 tributor to the same department of literature. 
 
 Mr. O'Donovan's vast acquirements connected with Irish ar- 
 chseology may be traced, in a great measure, to his connexion 
 with the Ordnance Survey. In the course of the duties which this 
 connexion imposed upon him, he visited every part of Ireland for 
 the purpose of tracing the ancient names of places, and of collect- 
 ing the local traditions connected with them, all of which he 
 compared with the existing records in the historical manuscripts 
 preserved in the Libraries of the Academy and of the University. 
 The object of these inquiries was to collect materials for the His- 
 torical and Antiquarian memoirs, which it was the original inten- 
 tion of the enlightened officers at the head of the Irish Survey to 
 compile and publish, an intention which (as the Academy are 
 aware) was unhappily frustrated by the interference of Government. 
 In the researches in which Mr. O'Donovan was thus for many 
 years engaged, he acquired the vast amount of historical and topo- 
 graphical knowledge which his subsequent writings have displayed. 
 He availed himself of the same opportunities to perfect his acquaint- 
 ance with the dialects of the Irish language ; and he has thus been 
 enabled to throw a light on this department of philology, such as 
 probably no other could have done. 
 
 The works edited by Mr. O'Donovan for the Irish Archaeo- 
 logical Society are the first of his published labours which claim our 
 attention. They are the following : 
 
 1. " The Circuit of Ireland, by Maircheartach Mac Neill, Prince 
 of Aileach. A poem written in the year 942, by Cormacan Eigeas, 
 chief poet of the North of Ireland." 
 
 2. " The Battle of Magh Rath(Moira), from an ancient manu- 
 script in the Library of Trinity College, Dublin." 
 
 3. " An Account of the Tribes and Customs of the district of 
 Hy-Many, commonly called 'Kelly's Country, in the counties of 
 
 2i
 
 482 ADDRESS DELIVERED AT A MEETING OF 
 
 Galway and Boscommon. Edited from the Book of Lecan, in the 
 Library of the Eoyal Irish Academy." 
 
 4. " An Account of the Tribes and Customs of the district of 
 Hy-Fiachrach, in the counties of Sligo and Mayo. Edited from 
 the Book of Lecan, in the Library of the Eoyal Irish Academy, and 
 from a copy of the Mac Firbis manuscript in the possession of the 
 Earl of Eoden." 
 
 Mr. O'Donovan has also edited the following minor pieces in 
 the Miscellany of the Irish Archaeological Society, viz. : " An an- 
 cient poem attributed to St. Columbkille ; " " The Irish Charters in 
 the Book of Kells ;" " A covenant in Irish between Mageoghegan 
 and the Fox ; " and " The Annals of Ireland from A. D. 1453 to 
 1468. Translated from a lost Irish original, by Dudley Firbisse." 
 
 These historical tracts and bardic tales are edited, for the most 
 part, in the original Irish, with translations and notes. In the 
 latter Mr. O'Donovan has brought together a vast body of historical 
 and genealogical information connected with the ancient families 
 referred to ; and ho has illustrated the subjects with much curious 
 antiquarian lore, respecting the manners and customs of the times. 
 He has also, in many cases, annexed maps of the districts described, 
 and topographical indexes, in which the etymology of the ancient 
 names is given, together with the corresponding modern appel- 
 lations. 
 
 Among the works of Mr. O'Donovan enumerated by the Council 
 in awarding him the Cunningham Medal, [is his Irish grammar. 
 This work was undertaken for the use of the senior classes in the 
 College of St. Columba, and was published at the expense of the 
 trustees of that institution. The publication has supplied a want 
 long felt by the philologers of Europe ; and the Celtic student is 
 now in possession of a grammar compiled by a scholar who has 
 studied the ancient language as it exists in our manuscript litera- 
 ture, and whose judgment and learning have enabled him to discri- 
 minate between the original and characteristic grammatical forms, 
 and the accidental peculiarities belonging to particular districts or 
 periods. The vast body of examples which Mr. O'Donovan has 
 collected from Irish MSS., in illustration of this work, contributes 
 greatly to enhance its value. 
 
 But Mr. O'Donovan's principal work is his edition of the Annals 
 of the Four Masters, from the autograph manuscript in the Library 
 of the Eoyal Irish Academy. The publication of this curious and
 
 THE ROYAL IRISH ACADEMY, 1848. 483 
 
 important chronicle had been long and earnestly desired by Irish 
 scholars. The language in which it is written was fast becoming 
 obsolete, and another half century would probably have interposed 
 3, serious difficulty in its interpretation ; while the curious mass 
 of information which Mr. O'Donovan has brought together in 
 illustration of it, collected, as it has been, in a great part, from 
 oral traditions, would, in all likelihood, have been wholly lost. 
 This work will ever remain a monument of the learning and labour 
 of its author, and would suffice alone to place his name in a high 
 rank in the list of Archaeologists. The three large quarto volumes 
 which have already appeared [contain the Annals from A. D. 1172 
 to 1616 ; Mr. O'Donovan is now engaged in preparing for publi- 
 cation the earlier portion, which will be accompanied by a com- 
 plete index of the names of 'persons and places mentioned in the 
 Annals. 
 
 Upon the conclusion of his Address, the President presented 
 the Medals to Sir William Hamilton, Mr. Haughton, Dr. Hincks, 
 and Mr. O'Donovan, addressing them separately, as follows : 
 
 SIR WILLIAM HAMILTON, In awarding you this Medal, the 
 Council cannot have the gratification of feeling that they are con- 
 tributing to the reputation of a name which is already known 
 wherever Science is cultivated. But they trust that you will 
 value it as a mark of sympathy from the Society, whose scien- 
 tific character you have raised by your labours, and whose interests 
 you have done so much in other ways to promote. Suffer me, on 
 my own behalf, to add, that the duty which I now discharge, as 
 the organ of the Academy on the present occasion, is to myself, 
 personally, the most grateful of any which have devolved upon me 
 as your successor in this Chair. 
 
 MR. HAUGHTON. Accept this Medal as a testimony of the 
 high value which the Council of the Royal Irish Academy set 
 upon your researches, connected with a most difficult branch of 
 Applied Mathematics ; and as an expression of their hope that the 
 labours in the application of the higher branches of analysis to 
 physical problems, for which you have proved yourself so eminently 
 qualified, and which have been already crowned with such success, 
 may long continue to add to your own honour, and to that of tho 
 Academy of which you are a member. 
 
 2i2
 
 484 ADDRESS DELIVERED AT A MEETING, ETC. 
 
 DR.HINCKS, Accept this Medal as a proof of the high opinion 
 with which the Council of the Eoyal Irish Academy regard your 
 researches, connected with some of the most obscure and difficult 
 problems of Archaeology. Allow me to add, that the merit of those 
 researches, high as it is in itself, is enhanced in your case by the 
 circumstance, that they have been pursued in the seclusion of 
 retirement, and without any of those aids derived from the inter- 
 course with others engaged in similar pursuits, which are usually 
 so effective in impelling to and suggesting inquiry. 
 
 MR. O'DoKovAN, Accept this Medal as a testimony of the 
 high value which the Council of the Royal Irish Academy set upon 
 your labours connected with Irish philology, and Irish history and 
 antiquities. This is the first occasion on which the Council, act- 
 ing on the laws recently enacted by the Academy, have conferred the 
 honour of the Cunningham Medal for works not published in the 
 Transactions of the Academy. They therefore hope that you (and 
 through you the literary public) will receive this award, not only 
 as a just tribute to the value of your own researches, but also as a 
 token of their sympathy with all who are engaged in the common 
 pursuit of Truth.
 
 XXIII. ADDRESS DELIVERED AT THE OPENING MEETING 
 OF THE BRITISH ASSOCIATION FOR THE ADVANCEMENT 
 OF SCIENCE, HELD IN DUBLIN, AUGUST 26, 1857. 
 
 Report of the British Aisociation for the Advancement of Science, 1857. 
 
 GENTLEMEN OF THE BRITISH ASSOCIATION, Before I proceed to 
 the task which devolves upon me this evening, in virtue of the 
 position in which your kindness has placed me, suffer me first to 
 thank you for the high honour you have conferred. But, highly 
 as I esteem the distinction, it was not without hesitation fhat I 
 accepted it ; for no one can feel more strongly than I do myself 
 how unfit I am for some of the duties connected with it, or how 
 much more adequately they might have been performed by others. 
 But I knew, at the same time, that it has been the desire of your 
 Council, when practicable, to select your President from among 
 those local Members who had served in the ranks of the Associa- 
 tion, and had shared in its labours : and with such knowledge, 
 and the consciousness that I had, at least, that humble claim, I 
 felt that I had no right to dispute your choice. 
 
 I do not know whether I may venture to interpret further 
 your motives, and to assign another reason for your selection. 
 Two-and-twenty years have elapsed since you visited this City. 
 Upon that occasion my nearest relative presided, and I myself had 
 the honour of serving as one of your local Secretaries. Many 
 concurring circumstances contributed to make that Meeting an 
 agreeable one ; and if your Council lias thought fit, on this occa- 
 sion, to associate the present with the memories of the past, the 
 motive is, at least, a pardonable one.
 
 480 ADDRESS DELIVERED BEFORE THE BRITISH ASSOCIATION 
 
 Gentlemen, this is to me a solemn occasion. Two-and-twenty 
 years are no inconsiderable portion even of the longest life ; 
 and that man's moral nature is not to be envied, who can contem- 
 plate the distant past thus vividly recalled without emotion. These 
 two decades have brought with them their own large measure of 
 change. The Body in which we are associated has grown up 
 from youth to maturity ; and many of its honoured names are now 
 sought for only in the imperishable records of their toils. The in- 
 stitutions which welcomed It here, upon its former visit to this City, 
 have all received the impress of the changing times. And yet, 
 amid all this change, we meet once more in the same city, in 
 the same room, to enter again on the same labours ; our assem- 
 blage is now, as it was before, dignified by the presence of the 
 Eepresentative of Majesty ; and I see around me, associated for 
 this task, many of those who shared it before ; the men whose 
 sagacity first perceived the want of such a Society as this, whose 
 energy supplied it, and whose wisdom directed its steps while 
 it had need of guidance. 
 
 I trust I may be forgiven for dwelling thus far on the peculiar 
 circumstances under which we are here assembled ; and I now 
 hasten to discharge the task which the usages of this Chair impose 
 upon me, and proceed to lay before you, as well as I am able, 
 a brief sketch of the recent progress of some of those Sciences 
 to whose advancement we are pledged by our Institution. In 
 doing so, I gladly follow the practice which has of late become 
 the rule, namely, that your President for each year should bring 
 under your notice, chiefly, the recent additions to those departments 
 of Science with which he happens to be himself most familiar. It 
 is plainly fitting that he who addresses you should speak, as far as 
 he can, from his own acquired knowledge. Partial views are 
 better than inexact ones ; and provision is made for their comple- 
 tion in the annual change of your Officer. In the present in- 
 stance I derive the full advantage of this arrangement, inasmuch 
 as the subjects upon which I could not thus speak have been, most 
 of them, ably treated by my predecessor in this Chair. 
 
 To commence, then, with Astronomy : The career of planetary 
 discovery, which began in the first years of the present century, 
 and was resumed in 1845, has since continued with unabated 
 ardour. Since 1846 not a single year has passed without some one
 
 FOR THE ADVANCEMENT OF SCIENCE, 1857. 487 
 
 or more additions to the number of the planetoids; and in one 
 year alone (1852), no fewer than eight of these bodies were disco- 
 vered. The last year has furnished its quota oifve; and in the 
 present, three more have been found, one by Mr. Pogson, of Oxford, 
 and the other two by M. Groldschmidt, of Paris. Their known 
 number is now forty-five. Their total mass, however, is very 
 small; the diameter of the largest being less than forty miles, 
 while that of the smallest, Atalanta, is little more than four. 
 
 These discoveries have been facilitated by star-maps and star- 
 catalogues, the formation of which they have, on the other hand, 
 stimulated. Two very extensive works of this kind are now in 
 progress, the Star-catalogue of M. Chacornac, made at the Ob- 
 servatory of Marseilles, in course of publication by the French 
 Government ; and that of Mr. Cooper, made at his Observatory at 
 Markree, in Ireland, which is now being published by the help of 
 the parliamentary grant of the Eoyal Society. It is a remark- 
 able result of the latter labour, that no fewer than seventy-seven 
 stars, previously catalogued, are now missing. This, no doubt, is 
 to be ascribed, in part, to the errors of former observations ; but it 
 seems reasonable to suppose that, to some extent at least, it is the 
 result of changes actually in progress in the Sidereal Systems. 
 
 The sudden appearance of a new fixed star in the heavens, it* 
 subsequent change of lustre, and its final disappearance, are 
 phenomena which have at all times attracted the attention of 
 astronomers. About twenty such have been observed. Arago has 
 given the history of the most remarkable, and discussed the various 
 hypotheses which have been proposed for their explanation. Of 
 these, the most plausible is that which attributes the phenomenon 
 to unequal brightness of the faces of the star, which are presented 
 successively to the earth by the star's rotation round its axis. On 
 this hypothesis the appearances should be periodic. M. Goldschmidt 
 has recently given support to this explanation, by rendering it 
 probable that the new star of 1609 is the same whose appearance 
 was recorded in the years 393, 798, and 1203 ; its period, in such 
 case, is 405 years. 
 
 The greater part of the celestial phenomena are comprised in 
 movements of the heavenly bodies, and the configurations depend- 
 ing on them ; and they are for the most part reducible to the same 
 law of gravity which governs the planetary motions. But there 
 are appearances which indicate the operation of other forces, and
 
 488 ADDRESS DELIVERED BEFORE THE BRITISH ASSOCIATION 
 
 which therefore demand the attention of the physicist, although, 
 from their nature, they must probably long remain subjects of 
 speculation. Of these the spiriform nebulae, discovered by Lord 
 Rosse, have been already referred to from this Chair, as indicating 
 changes in the more distant regions of the universe, to which there 
 is nothing entirely analogous in our own system. These appear- 
 ances are accounted for, by an able anonymous writer, by the 
 action of gravitating forces combined with the effects of a resisting 
 medium, the resistance being supposed to bear a sensible propor- 
 tion to the gravitating action. 
 
 The constitution of the central body of our own System pre- 
 sents a nearer and more interesting subject of speculation. To- 
 wards the close of the last century many hypotheses were advanced 
 regarding the nature and constitution of the Sun, all of which 
 agreed in considering it to be an opaque body, surrounded at some 
 distance by a luminous envelope. But the only certain fact which 
 has been added to Science in this department is the proof given by 
 Arago, that the light of the Sun emanated not from an incandes- 
 cent solid but from a gaseous atmosphere; the light of incan- 
 descent solid bodies being polarized by refraction, while the light of 
 the Sun, and that emitted by gaseous bodies, is -unpolarized. 
 
 According to the observations of Schwabe, which have been 
 continued without intermission for more than thirty years, the 
 magnitude of the solar surface obscured by spots increases and 
 decreases periodically, the length of the period being 11 years and 
 40 days. This remarkable fact, and the relation which it appears 
 to bear to certain phenomena of terrestrial magnetism, have at- 
 tracted fresh interest to the study of the solar surface ; and upon 
 the suggestion of Sir John Herschel, a photo-heliographic appa- 
 ratus has lately been established at Kew, for the purpose of de- 
 picting the actual macular state of the Sun's surface from time 
 to time. 
 
 It is well known that Sir "William Herschel accounted for the 
 solar spots by currents of an elastic fluid, ascending from the body 
 of the Sun, and penetrating the exterior luminous envelope. A 
 somewhat different speculation of the same kind has been recently 
 advanced by Mosotti, who has endeavoured to connect the phe- 
 nomena of the solar spots with those of the red protuberances which 
 appear to issue from the body of the Sun in a total eclipse, and which 
 so much interested astronomers in the remarkable eclipse of 1842.
 
 FOR THE ADVANCEMENT OF SCIENCE, 1857. 489 
 
 Next to the Sun, our own satellite has always claimed the 
 attention of astronomers, while the comparative smallness of its 
 distance inspired the hope that some knowledge of its physical 
 structure could be attained with the large instrumental means now 
 available. Accordingly, at the Meeting of the Association held at 
 Belfast in 1852, it was proposed that the Earl of Rosse, Dr. 
 Eobinson, and Professor Phillips, be requested to draw up a Report 
 on the physical character of the Moon's surface, as compared with 
 that of the earth. That the attention of these eminent observers 
 has been directed to the subject, may be inferred from the commu- 
 nication since made by Professor Phillips to the Eoyal Society on 
 the lunar mountain, Grassendi, and the surrounding region ; but I 
 am not aware that the subject is yet ripe for a Report. 
 
 I need not remind you, that the Moon possesses neither sea, nor 
 atmosphere of appreciable extent. Still, as a negative, in such case, 
 is relative only to the capabilities of the instruments employed, the 
 search for the indications of a lunar atmosphere has been renewed 
 with every fresh augmentation of telescopic power. Of such indi- 
 cations the most delicate, perhaps, are those afforded by the occul- 
 tation of a planet by the Moon. The occultation of Jupiter, which 
 took place on the 2nd of January last, was observed with this refer- 
 ence, and it is said to have exhibited no hesitation, or change of 
 form or brightness, such as would be produced by the refraction or 
 absorption of an atmosphere. As respects the sea, the mode of 
 examination long since suggested by Sir David Brewster is proba- 
 bly the most effective.*; If water existed on the Moon's surface, the 
 Sun's light reflected from it should be completely polarized at a 
 certain elongation of the Moon from the Sun. No traces of such 
 light have been observed; but I am not aware that the obser- 
 vations have been repeated recently with any of the larger teles- 
 copes. 
 
 It is now well understood that the path of astronomical discovery 
 is obstructed much more by the earth's atmosphere, than by the 
 limitation of telescopic powers. Impressed with this conviction, the 
 Association has, for some time past, urged upon her Majesty's Go- 
 vernment the scientific importance of establishing a large reflector at 
 some elevated station in the Southern Hemisphere. In the mean- 
 time, and to gain (as it were) a sample of the results which might 
 be expected from a more systematic search, Professor Piazzi Smyth 
 undertook, last summer, the task of transporting a large collection of
 
 490 ADDRESS DELIVERED BEFORE THE BRITISH ASSOCIATION 
 
 instruments meteorological and magnetical, as well as astronomi- 
 cal to a high point on the Peak of Teneriffe. His stations were 
 two in number, at the altitudes above the sea of 8840 and 10,700 
 feet respectively ; and the astronomical advantages gained may be 
 inferred from the fact, that the heat radiated from the Moon, 
 which has been so often sought for in vain in a lower region, was 
 distinctly perceptible with the aid of the thermo-multiplier. 
 
 The researches relative to the Figure of the Earth, and the 
 Tides, are intimately connected with Astronomy, and next claim 
 our attention. 
 
 The results of the Ordnance Survey of Britain, so far as they 
 relate to the earth's figure and mean density, have been lately laid 
 before the Royal Society by Colonel James, the Superintendent of 
 the Survey. The ellipticity deduced is -^WW-TS- ^ ne mean spe- 
 cific gravity of the earth, as obtained from the attraction of 
 Arthur's Seat, near Edinburgh, is 5'316, a result which accords 
 satisfactorily with the mean of the results obtained by the torsion, 
 balance. Of the accuracy of this important work it is sufficient to 
 observe, that when the length of each of the measured bases in 
 Salisbury Plain, and on the shores of Lough Foyle was computed 
 from the other, through the whole series of intermediate triangles, 
 the difference from the measured length was only 5 inches in a 
 length of from 5 to 7 miles. 
 
 Our knowledge of the laws of the Tides has received an im- 
 portant accession, in the results of the Tidal Observations made 
 around the Irish coasts in 1851, under the direction of the Eoyal 
 Irish Academy. The discussion of these observations was under- 
 taken by Professor Haughton, and that portion of it which relates 
 to the diurnal tides has been already completed and published. 
 The most important result of this discussion is the separation of the 
 effects of the Sun and Moon in the diurnal tide a problem which 
 was proposed by the Academy, as one of the objects to be attained 
 by the contemplated observations, and which has been now for the 
 first time solved. From the comparison of these effects Professor 
 Haughton has drawn some remarkable conclusions relative to the 
 mean depth of the sea in the Atlantic. In the dynamical theory of 
 the tides, the ratio of the solar to the lunar effect depends not only 
 on the masses, distances, and periodic times, of the two lumina- 
 ries, but also on the depth of the sea; and this, accordingly,
 
 FOR THE ADVANCEMENT OF SCIENCE, 1857. 491 
 
 may be computed when the other quantities are known. In this 
 manner Professor Haughton has deduced, from the solar and lunar 
 coefficients of the diurnal tide, a mean depth of 5 '12 miles a 
 result which accords in a remarkable manner with that inferred 
 from the ratio of the semidiurnal coefficients, as obtained by 
 Laplace from the Brest observations. The subject, however, is 
 far from being exhausted. The depth of the sea, deduced from 
 the solar and lunar tidal intervals, and from the age of the lunar 
 diurnal tide, is somewhat more than double of the foregoing ; and 
 the consistency of the individual results is such as to indicate that 
 their wide difference from the former is no't attributable to errors 
 of observation. Professor Haughton throws out the conjecture 
 that the depth, deduced from the tidal intervals and ages, cor- 
 responds to a different part of the ocean from that inferred from 
 the heights. 
 
 The phenomena of Terrestrial Magnetism present many close- 
 analogies with those of the tides ; and their study has been, in a 
 peculiar manner, connected with the labours of this Association. 
 To this Body, and by the hands of its present General Secretary, 
 were presented those Reports on the distribution of the Terrestrial 
 Magnetic Force which re-awakened the attention of the scientific 
 world to the subject. It was in the Committee-rooms of this 
 Association that the first step was taken towards that great 
 magnetic organization which has borne so much fruit; it was 
 here that the philosophical sagacity of Herschel guided its earlier 
 career ; and it was here again that the cultivators of the science 
 assembled, from every part of Europe, to deliberate about its 
 future progress. It was natural, therefore, that the results ob- 
 tained from such beginnings should form a prominent topic in the 
 addresses which have been annually delivered from this Chair; 
 and the same circumstances will plead my excuse, if I now revert 
 to some of them which have been already touched upon by my 
 predecessors. 
 
 It has been long known that the elements of the earth's 
 magnetic force were subject to certain regular and recurring 
 changes, whose periods were, respectively, a day and a year, and 
 which, therefore, were referred to the Sun as their source. To 
 these periodical changes Dr. Lament, of Munich, added another 
 of ten years, the diurnal range of the magnetic declination having
 
 492 ADDRESS DELIVERED BEFORE THE BRITISH ASSOCIATION 
 
 been found to pass from a maximum to a minimum, and back 
 again, in about that time. 
 
 But besides these slow and regular changes, there are others 
 of a different class, which recur at irregular intervals, and which 
 are characterized by a large deviation of the magnetic elements 
 from their normal state, and generally also by rapid fluctuation 
 and change. These phenomena, called by Humboldt " magnetic 
 storms," have been observed to occur simultaneously in the most 
 distant parts of the earth, and therefore indicate the operation of 
 causes affecting the entire globe. But, casual as they seem, they 
 are found to be subject to laws of their own. Professor Kreil was 
 the first to discover that, at a given place, they recurred more 
 frequently at certain hours of the day than at others ; and that, 
 consequently, in their mean effects, they were subject to periodical 
 laws, depending upon the hour at each station. 
 
 The laws of this periodicity have been ably worked out by 
 General Sabine, in his discussion of the results of the British 
 Colonial Observatories; and he has added the important fact, 
 that the same phenomena observe also the two other periods 
 already noticed namely, the annual and the decennial periods. 
 He has further arrived at the very remarkable result, that the 
 decennial magnetic period coincides, both in its duration and 
 in its epochs of maxima and minima, with the period ob- 
 served by Schwabe in the solar spots ; from which it is to be 
 inferred that the Sun exercises a magnetic influence upon the 
 earth, dependent on the condition of its luminous envelope. 
 
 We are thus in the presence of two facts, which appear at first 
 sight opposed namely, the absolute simultaneity of magnetic dis- 
 turbances at all parts of the earth, and their predominance at 
 certain local hours at each place. General Sabine accounts for this 
 apparent discrepancy by the circumstance, that the hours of maxi- 
 mum disturbance are different for the different elements ; so that 
 there may be an abnormal condition of the magnetic force, operat- 
 ing at the same instant over the whole globe, but manifesting 
 itself at one place chiefly in one element, and at another place in 
 another. I would venture to suggest, as a subject of inquiry, 
 whether the phenomena which have been hitherto grouped together 
 as "occasional" effects may not possibly include two distinct 
 classes of changes, obeying separate laws one of them being 
 strictly periodic, and constituting a part of the regular diurnal
 
 FOR THE ADVANCEMENT OF SCIENCE, 1857. 493 
 
 change ; while the other is strictly abnormal, and simultaneous. 
 If this be so, it would follow that we are not justified in separat- 
 ing the larger changes from the rest, merely on the ground of 
 their magnitude ; and that a different analysis of the phenomenon 
 will be required. 
 
 The effects hitherto considered are all referrible to the Sun as 
 their cause. Professor Kreil discovered, however, that another 
 body of our System namely, our own satellite exerted an effect 
 upon the magnetic needle ; and that the magnetic decimation under- 
 went a small and very regular variation, whose amount was 
 dependent on the lunar hour-angle, and whose period was there- 
 fore a lunar day. This singular result was subsequently confirmed 
 by Mr. Broun, in his discussion of the Makerstoun observations ; 
 and its laws have since been fully traced, for all the magnetic 
 elements, by General Sabine, in the results obtained at the 
 Colonial Magnetic Observatories. 
 
 The foregoing facts bear closely upon the debated question of 
 the causes of the magnetic variations. It has been usual to ascribe 
 the periodical changes of the earth's magnetic force to the thermic 
 action of the Sun, operating either directly upon the magnetism 
 of the earth, or affecting it indirectly by the induction of thermo- 
 electric currents. Here, however, we have a distinct case of 
 magnetic action, unaccompanied by heat ; and the question is 
 naturally suggested, whether the solar diurnal change may not 
 also be independent of temperature. 
 
 The most important fact, in its bearing upon this question, 
 is the existence of an annual inequality in the diurnal variation, 
 dependent on the Sun's declination, recently pointed out by 
 General Sabine. If we deduct the ordinate of the curve, which 
 represents the mean diurnal variation for the entire year, from 
 those for the summer and winter half-yearly curves respectively, 
 the differences are found to be equal and opposite ; and the curves 
 which represent them are, consequently, similar, but oppositely 
 placed with respect to the axis of abscissae. From this, General 
 Sabine draws the inference, that the diurnal variation is a direct 
 fft'cct of solar action, and not a result of its thermic agency. 
 
 The most important step which has been recently taken in 
 this country, to advance the science of Meteorology, has been tin- 
 formation of a department connected with the Board of Trade, for
 
 494 ADDRESS DELIVERED BEFORE THE BRITISH ASSOCIATION 
 
 the collection and discussion of Meteorological Observations made 
 fit sea. The practical results of a similar undertaking in the 
 United States are now well known. The charts and sailing 
 directions, published by Lieutenant Maury, have enabled navi- 
 gators to shorten their passages, in many cases by one-fourth of 
 the time, and in some even to a greater extent. The commercial 
 importance of such results could not fail to attract general 
 attention ; and accordingly, when the United States Government 
 invited other maritime nations to co-operate in the undertak- 
 ing, the invitation was cordially accepted. A conference was held 
 at Brussels in 1853, at which meteorologists deputed by those 
 Powers attended; and a Eeport was made, recommending the 
 course to be pursued in a general system of marine meteorological 
 observations. This Report was laid before the British Parliament 
 soon after, and a sum of money was voted for the necessary ex- 
 penditure. The British Association undertook to supply verified 
 instruments, by means of its Observatory at Kew ; and the Eoyal 
 Society, in consultation with the most eminent meteorologists of 
 Europe and America, addressed an able Eeport to the Board of 
 Trade, in which the objects to be attended to, so as to render the 
 system of observation most available for Science, were clearly set 
 forth. With this co-operation on the part of the two leading 
 Scientific Societies, the establishment was soon organized. It was 
 placed under the direction of a distinguished naval officer, Admiral 
 Fitz-Eoy : and in the beginning of 1855 it was in operation. 
 Agents were established at the principal ports for the supply of 
 instruments, books, and instructions ; and there are now more 
 than 200 British ships so furnished, whose officers have under- 
 taken to make and record the required observations, and to 
 transmit them from time to time to the Department. At the 
 present time 700 months of logs have been received, from nearly 
 100 merchant ships, and are in process of tabulation. 
 
 Holland is taking similar steps ; and the Meteorological Insti- 
 tute of that country, under the direction of M. Buys Bellot, has 
 already published three volumes of nautical information, obtained 
 from Dutch vessels in the Atlantic and Indian Oceans. 
 
 For the purposes of Meteorological Science this system cannot 
 be considered as complete, until observations on land are included. 
 Most of the greater atmospheric changes are due to the distribu- 
 tion of land and water, and to the different effects of the Sun's rays
 
 FOR THE ADVANCEMENT OF SCIENCE, 1857. 495 
 
 on each. Observation alone can furnish the data from which the 
 effects of these agencies may he calculated ; and we can therefore 
 probably make no great advance in the knowledge of the meteoro- 
 logy of the globe, without a concurrent investigation of its two 
 leading departments. Land observations exist in great numbers. 
 In Prussia, in Eussia, in Austria, and in Belgium, such ob- 
 servations are organized under Government direction, or at least 
 with Government support. In other parts of Europe, as in Britain, 
 the labour is left to individuals or scientific societies. "What is 
 needed is to give unity to these isolated labours to connect them 
 with one another, and with the results obtained at sea ; and the 
 first step to this seems to be, to give them, in each country, that 
 permanence and uniformity of system which can only be insured 
 in measures adopted by the State. 
 
 Here, however, we encounter an objection, upon which it is ne- 
 cessary to say a few words. 
 
 It has been objected to the Science of Meteorology, as it is 
 usually studied, that it proceeds upon a false method ; and that, 
 consequently, it has led and can lead to no results. I feel 
 myself in a manner compelled to notice this grave objection, in 
 the first place because it proceeds from men whose opinions on 
 this (or almost any other scientific question) are entitled to the 
 highest deference; and secondly, because this Association must 
 bear no inconsiderable measure of the reproach, if it be well 
 founded. 
 
 First, then, as to results. I am free to admit that the number 
 of those engaged in the discussion of meteorological observations is 
 /f ^proportionately small, and that the results obtained probably fall 
 far short of what may be expected from the data already accumu- 
 lated. But that the methods have led, and can lead, to no results, 
 is, I think, sufficiently disproved by the labours of a single man 
 Professor Dove of Berlin. And if it be true that the course pur- 
 sued in the science has yielded much fruit, in proportion to the 
 labour bestowed on the discussion, it will hardly be deemed widely 
 erroneous. Still, as it is possible that the methods pursued 
 though not fruitless may be inadequate, it seems necessary to 
 notice the objection somewhat more minutely. 
 
 It is asserted, hen, that the capital vice of the Science of 
 Meteorology, as at present pursued, is that it has no definite aim ; 
 that it ought to embrace an inquiry into the physical constitution of
 
 496 ADDRESS DELIVERED BEFORE THE BRITISH ASSOCIATION 
 
 the objects with which the science is concerned, and an investiga- 
 tion of causes as well as laics of phenomena. 
 
 It may be admitted, at once, in reference to this objection, that 
 the physical constitution of the bodies whose changes we are inves- 
 tigating is a proper object of study to the physicist ; but it does 
 not seem to follow that it should necessarily be conducted by the 
 same individuals who are in search for the laws of the phenomena, 
 or even that the former knowledge is essential to the progress of 
 the latter. The noblest of all the physical sciences, Astronomy, 
 is little more than a science of laics laws, too, of the simplest kind 
 of change ; and the knowledge of these laws is wholly independent 
 of the physical constitution of the masses whose movements it studies. 
 A similar observation maybe made regarding the science of Terres- 
 trial Magnetism ; and the case is one which brings us still nearer 
 to the question at issue, inasmuch as the laws which have been 
 obtained and they are numerous have resulted from a method 
 of inquiry altogether similar to that adopted in Meteorology. 
 
 Time will not permit me to inquire whether there is not a 
 misconception of a metaphysical kind at the root of this objection. 
 I may observe, however, before leaving the subject, that there are 
 two modes of studying the sequences of natural phenomena, one 
 in their relation to time, and which is best accomplished by obser- 
 vations at stated periods, and the other in the relation of the 
 successive phases of the phenomena to one another. Of these, the 
 latter, although not wholly neglected, has not been so much 
 followed as it deserves ; and I cannot but think that it would, 
 if more systematically followed, enrich the science of Meteorology 
 with a new harvest of results. 
 
 The most important of the recent additions to the theory of 
 Light have been those made by M. Jamin. It has been long 
 known that metals differed from transparent bodies, in their 
 action on light, in this, that plane-polarized light reflected from 
 their surfaces became elliptically-polarized ; and the phenomenon 
 is explained, on the principles of the wave-theory, by the assump- 
 tion that the vibration of the ether undergoes a change of phase at 
 the instant of reflexion, the amount of which is dependent on its. 
 direction, and on the angle of incidence. This supposed distinc- 
 tion, however, was soon found not to be absolute. Mr. Airy 
 showed that diamond reflected light in a manner similar to metals ;
 
 FOR THE ADVANCEMENT OF SCIENCE, 1857. 497 
 
 and Mr. Dale and Professor Powell extended the property to all 
 bodies having a high refractive power. But it was not until 
 lately that M. Jamin proved that there is no distinction, in this 
 respect, between transparent and metallic bodies; and that all 
 bodies transform plane-polarized into elliptically-polarized light, 
 and impress a change of phase at the moment of reflexion. 
 Professor Haughton has followed up the researches of M. Jamin, 
 and established the existence of circularly-polarized light by reflex- 
 ion from transparent surfaces. 
 
 The theoretical investigations connected with this subject afford 
 a remarkable illustration of one of those impediments to the pro- 
 gress of natural philosophy, which Bacon has put in the foremost 
 place among his examples of the Idola : I mean the tendency of 
 the human mind to suppose a greater simplicity and uniformity 
 in nature than exists there. The phenomena of polarization 
 compel us to admit that the sensible luminous vibrations are 
 transversal, or in the plane of the wave itself ; and it was naturally 
 supposed by Fresnel, and after him by M'Cullagh and Neumann, 
 either that no normal vibrations were propagated, or that, if they 
 were, they were unconnected with the phenomena of light. We 
 now learn that it is by them that the phase is modified in the act 
 of reflexion ; and that, consequently, no dynamical theory which 
 neglects them, or sets them aside, can be complete. 
 
 Attention has been lately recalled to a fundamental position of 
 the wave-theory of light, respecting which opposite assumptions 
 have been made. The vibrations of a polarized ray are all parallel 
 to a fixed direction in the plane of the wave ; but that direction 
 may be either parallel, or perpendicular, to the plane of polarization. 
 In the original theory of Fresnel the latter was assumed to be the 
 fact ; and in this assumption Fresnel has been followed by Cauchy. 
 In the modified theories of M'Cullagh and Neumann, on the 
 other hand, the vibrations are supposed to be parallel to the plane 
 of polarization. This opposition of the two theories was compen- 
 sated, as respects the results, by other differences in their hypothe- 
 tical principles; and both of them have led to conclusions which 
 observation has verified. There seemed, therefore, to be no means 
 left to the theorist to decide between these conflicting hypotheses, 
 until Professor Stokes, recently, in applying the dynamical theory 
 of light to other classes of phenomena, found one in wlii >h tlm 
 effects should differ on the two assumptions. When light is 
 
 2K
 
 498 ADDRESS DELIVERED BEFORE THE BRITISH ASSOCIATION 
 
 transmitted through a fine grating, it is turned aside, or dif- 
 fracted, according to laws which the wave-theory has explained. 
 Now Professor Stokes has shown that, when the incident light 
 is polarized, the plane of vibration of the diffracted ray must differ 
 from that of the incident, the two planes being connected by a 
 very simple relation. It only remained, therefore, for observa- 
 tion to determine whether the planes of polarization of the incident 
 and refracted rays were similarly related, or not. The experiment 
 was undertaken by Professor Stokes himself, and he has inferred 
 from it that the original hypothesis of Fresnel is the true one ; 
 but, as an opposite result has been obtained by M. Holtzmann, on 
 repeating the experiment, the question must be regarded as still un- 
 determined. The difference in the experimental results is ascribed 
 by Professor Stokes to the difference in the nature of the gratings 
 employed, the substance of the diffracting body being supposed to 
 exert an effect upon the polarization of the light, which is diffrac- 
 ted by it under a great obliquity. I learn from Professor Stokes 
 that he proposes to resume the experimental inquiry, and to test 
 this supposition by employing gratings of various substances. If 
 the conjecture should prove to be well founded, it will, unfor- 
 tunately, greatly complicate the dynamical theory of light. In 
 the meantime the hypothesis is one of importance in itself, and 
 deserves to be verified or disproved by independent means. I 
 would venture to suggest that it may be effectively tested by 
 means of the beautiful interference-refractor of M. Jamin, which 
 the inventor has already applied to the study of the effects upon 
 light* produced by grazing a plate of any soluble substance in- 
 closed in a fluid. 
 
 It is well known that the refractive index of bodies increases 
 with their density ; and the theory of emission has even expressed 
 the law of their mutual dependence. That theory, it is true, is 
 now completely overthrown by the decisive experimentum cruets 
 of MM. Fizeau and Foucault. It was, therefore, probable, a 
 priori, that this law the only one peculiar to the theory would 
 be found wanting. Its truth has recently been put to an experi- 
 mental test by M. Jamin. Water, it is known, has its maximum 
 of density at about 40 of Fahrenheit ; so that, if Newton's law 
 were true, its refractive index should also have a maximum value 
 at the same temperature. This has been disproved by M. Jamin, 
 by observing the interference of two rays, one of which has passed
 
 FOR THE ADVANCEMENT OF SCIENCE, 1857. 499 
 
 through air, and the other through water ; and thus the last con- 
 clusion of the emission-theory has been set aside. 
 
 It would occupy too much of your time were I to touch, even 
 lightly, upon the subject of the chemical action of light, and the 
 many beautiful and important discoveries of the Art to which it 
 has given rise. I may, however, mention, as one of the latest of 
 the marvels of photography, that M. Poitevin has succeeded in pro- 
 ducing plates in relief , for the purposes of engraving, by the action 
 of light alone. The process depends upon the change in the 
 affinity for water, produced by the action of light upon a thin 
 plate of gelatine, which is impregnated with bichromate of potash. 
 
 In the whole range of experimental science there is no fact 
 more familiar, or longer known, than the development of Heat by 
 friction. The most ignorant savage is acquainted with it, and it was 
 probably known to the first generation of mankind. Yet, familiar 
 as it is, the science of which it is the germ dates back but a very 
 few years. 
 
 It was known from the time of Black, that heat disappeared in 
 producing certain changes of state in bodies, and reappeared when 
 the order of those changes was reversed ; and that the amount of 
 heat, thus converted, had a given relation to the effect produced. 
 In one of these changes namely, evaporation a definite mecha- 
 nical force is developed, which is again absorbed when the vapour 
 is restored by pressure to the liquid state. It was, therefore, not 
 unnatural to conjecture, that in all cases in which heat is deve- 
 loped by mechanical action, or vice versa, a definite relation would 
 be found to subsist between the amount of the action, and that of 
 the heat developed or absorbed. 
 
 This conjecture was put to the test of experiment by Mayer 
 and Joule, in 1842, and was verified by the result. It was found 
 that heat and mechanical power were mutually convertible; and that 
 the relation between them was definite, 772 foot-pounds of motive 
 power being equivalent to a unit of heat that is, to the amount of 
 heat requisite to raise a pound of water through one degree of 
 Fahrenheit. The science of Thermo-dynamics, based upon this 
 fact, and upon a few other obvious facts, or self-evident principles, 
 has grown up in the hands of Clausius, Thomson, and Kankine, 
 into large proportions, and is each day making fresh conquests 
 from the region of the unknown. 
 
 2x2
 
 500 ADDRESS DELIVERED BEFORE THE BRITISH ASSOCIATION 
 
 Thus far the science of Heat is made to rest wholly upon the 
 facts of experiment, and is independent of any hypothesis respect- 
 ing the molecular constitution of bodies. The dynamical theory of 
 Heat, however, has materially aided in establishing true physical 
 conceptions of the nature of heat. The old hypothesis of caloric, as 
 a separate substance, was indeed rendered improbable by the 
 experiments of Eumford and Davy, and by the reasonings of 
 Young ; but it continued to hold its ground, and was interwoven 
 into the language of science. It is now clearly shown to be self- 
 contradictory ; and to lead to the result, that the amount of heat 
 in the universe may be indefinitely augmented. On the other 
 hand, the identification of radiant heat with light, and the esta- 
 blishment of the wave-theory, left little doubt that heat consisted in 
 a vibratory movement either of the molecules of bodies, or of the 
 ether within them. Still, the relation of heat to bodies, and the 
 phenomena of conduction, indicate a mechanism of a more compli- 
 cated kind than that of light, and leave ample room for further 
 speculation. 
 
 The only mechanical hypothesis (so far as I am aware) which 
 is consistent with the present state of our knowledge of the pheno- 
 mena of heat, is the theory of molecular vortices of Mr. Bankine. 
 In this theory all bodies are supposed to consist of atoms, composed 
 of nuclei surrounded with elastic atmospheres. The radiation of light 
 and heat is ascribed to the transmission of oscillations of the nuclei ; 
 while thcrmometric heat is supposed to consist in circulating cur- 
 rents, or vortices, amongst the particles of their atmospheres, where- 
 by they tend to recede from the nuclei, and to occupy a greater 
 space. From this hypothesis Mr. Eankine has deduced all the 
 laws of thermo-dynamics, by the application of known mechanical 
 principles. He has also, from the same principles, deduced rela- 
 tions (which have been confirmed by experiment) between the 
 pressure, density, and absolute temperature of elastic fluids, and 
 between the pressure and temperature of ebullition of liquids. 
 
 The dynamical theory of heat enables us to frame some conjec- 
 tures to account for the continuance of its supply, and even to 
 speculate as to its source. The heat of the Sun is dissipated and lost 
 by radiation : and must be progressively diminished unless its 
 thermal energy be supplied. According to the measurements of 
 M. Pouillet, the quantity of heat, given out by the Sun in a year, 
 is equal to that which would be produced by the combustion of a
 
 FOR THE ADVANCEMENT OF SCIENCE, 1857. 501 
 
 stratum of coal seventeen miles in thickness : and if the Sun's 
 capacity for heat be assumed equal to that of water, and the heat 
 be supposed to be drawn uniformly from its entire mass, its tem- 
 perature would thereby undergo a diminution of 2'4 Fahr. 
 annually. 
 
 On the other hand, there is a vast store of force in our System 
 capable of conversion into heat. If, as is indicated by the small 
 density of the Sun, and by other circumstances, that body has not 
 yet reached the condition of incompressibility, we have, in the 
 future approximation of its parts, a fund of heat probably quite 
 large enough to supply the wants of the human family to the end 
 of its sojourn here. It has been calculated that an amount of con- 
 densation, which would diminish the diameter of the Sun by only 
 the ten-thousandth part, would suffice to restore the heat emitted 
 in 2000 years. 
 
 Again, on our own earth, vis viva is destroyed by friction in 
 the ebb and flow of every tide, and must therefore reappear as heat. 
 The amount of this must be considerable, and should not be over- 
 looked in any estimation of the physical changes of our globe. 
 According to the computations of Bessel, 25,000 cubic miles of 
 water flow, in every six hours, from one quarter of the earth to 
 another. The store of mechanical force is thus diminished, and 
 the temperature of our globe augmented, by every tide. We do 
 not possess the data which would enable us to calculate the magni- 
 tude of these effects. All that we know with certainty is, that the 
 resultant effect of all the thermal agencies, to which the earth is 
 exposed, has undergone no perceptible change within the historic 
 period. We owe this fine deduction to Arago. In order that the 
 date palm should ripen its fruit, the mean temperature of the place 
 must exceed 70 Fahr. ; and, on the other hand, the vine cannot be 
 cultivated successfully when the mean temperature is 72 or up- 
 wards. Hence, the mean temperature of any place, at which these 
 two plants flourished and bore fruit, must lie between these narrow 
 limits, i. e. could not differ from 71 Fahr. by more than a single 
 degree. Now, from the Bible we learn that both plants were 
 simultaneously cultivated in the central valleys of Palestine, in the 
 time of Moses ; and its then temperature is thus definitively deter- 
 mined. It is the same at the present time ; so that the mean tem- 
 perature of this portion of the globe has not sensibly altered in the 
 course of thirty-three centuries.
 
 502 ADDRESS DELIVERED BEFORE THE BRITISH ASSOCIATION 
 
 The future of physical science seems to lie in the path upon 
 which three of our ablest British physicists have so boldly entered, 
 and in which they have already made such large advances. I may 
 therefore be permitted briefly to touch upon the successive steps in 
 this lofty generalization, and to indicate the goal to which they 
 tend. 
 
 It has been long known that many of the forces of nature are 
 related. Thus, heat is produced by mechanical action, when that is 
 applied in bringing the atoms of bodies nearer by compression, or 
 when it is expended in friction. Heat is developed by electricity r 
 when the free passage of the latter is impeded ; it is produced 
 whenever light is absorbed; and it is generated by chemical 
 action. A like interchangeability probably exists among all the 
 other forces of nature, although in many the relations have not 
 been so long perceived. Thus, the development of electricity from 
 chemical action dates from the observations of Gralvani ; and the 
 production of magnetism by electricity from the discovery of 
 Oersted. 
 
 The next great step was to perceive that the relation of the 
 physical forces was mutual ; and that of any two, compared toge- 
 gether, either may stand to the other in the relation of cause. 
 
 With respect to heat and mechanical force, this has been long 
 known. When a body is compressed by mechanical force, it gives 
 out heat ; and, on the other hand, when it is healed, it dilates, and 
 evolves power. The knowledge of the action of electricity, in dis- 
 solving the bonds of chemical union, followed closely upon that of 
 the inverse phenomenon : and the discovery of electro-magnetism 
 by Oersted was soon followed by that of magneto-electricity by 
 Faraday. With reason, therefore, it occurred to many minds that 
 the relations of any two of the forces of nature were mutual; 
 that that which is the cause, in one mode of interaction, may be- 
 come the effect, when the order of the phenomena is changed ; 
 and that therefore, in the words of Mr. Grove, one of the able 
 expounders of these views, while they are " correlative," or recipro- 
 cally dependent, " neither, taken abstractedly, can be said to be the 
 essential cause of the others." 
 
 But a further step remained to be taken. If these forces were 
 not only related, but mutually related, was it not probable that the 
 relation was also a definite one ? Thus, when heat is developed by 
 mechanical action, ought we not to expect a certain definite proper-
 
 FOR THE ADVANCEMENT OP SCIENCE, 1857. 503 
 
 tion to subsist between the interacting forces, so that if one were 
 doubled or trebled in amount, the other should undergo a propor- 
 tionate change ? This anticipation, it has been already stated, has 
 been realized by Mayer and Joule. The discovery of the mechanical 
 equivalent of heat has been rapidly followed by that of other 
 forces ; and we now know not only that electricity, magnetism, and 
 chemical action, in given quantities, will produce each a definite 
 amount of mechanical work, but we know further chiefly through 
 the labours of Mr. Joule what that relation is, or, in other words, 
 the mechanical equivalent of each force. 
 
 The first step in this important career of discovery though 
 long unperceived in its relation to the rest was, undoubtedly ? 
 Faraday's proof of the definite chemical effect of the voltaic cur- 
 rent. The last will probably be to reduce all these phenomena to 
 /nodes of motion, and to apply to them the known principles of 
 dynamics, in such a way as not only to express the laws of each 
 kind of movement, as it is in itself, but also the connexion and 
 dependence of the different classes of the phenomena. 
 
 A bold attempt at such a generalization has been made by 
 M. Helmholtz. The science of Thermo-dynamics starts from the 
 principle, that perpetual motion is impossible, or, in other words, that 
 we cannot, by any combination of natural bodies, produce force out 
 of nothing. In mechanical force, this principle is reducible to the 
 known law of the conservation of living force ; and M. Helmholtz 
 has accordingly endeavoured to show that this law is maintained in 
 the interaction of all the natural forces ; while, at the same time, 
 the assumption of its truth leads to some new consequences in 
 physics, not yet experimentally confirmed. Expressed in its most . 
 general form, this principle asserts that the gain of vis viva during the 
 motion of a sj stern is equal to the force consumed in producing it 
 from which it follows, that the sum of the vires vivce, and of the 
 existing forces, is constant. This principle M. Helmholtz deno- 
 minates the conservation of force. A very important consequence of 
 its establishment must be, that all the actions of nature are due to 
 attractive and repulsive forces, whose intensity is a function of 
 the distance, the conservation of vis viva holding only for such 
 forces. 
 
 It is usually stated, in mechanical works, that there is a loss of 
 vis rit'a in the collision of inelastic bodies, and in friction. This 
 is true with respect to the motion of masses, which forms the sub-
 
 504 ADDRESS DELIVERED BEFORE THE BRITISH ASSOCIATION 
 
 ject of mechanical science as at present limited ; but it is not true 
 in a larger sense. In these, and such-like cases, the movement of 
 masses is transformed into molecular motion, and thus reappears as 
 heat, electricity, or chemical action ; and the amount of the 
 transformed action definitely corresponds to the mechanical force 
 which was apparently lost. 
 
 In the cases just considered, mechanical action is converted 
 into molecular. But molecular actions of different kinds are 
 themselves in like manner interchangeable. Thus, when light is 
 absorbed, m viva is apparently lost ; but not to speak of phoxpho 
 rescence, in which the light absorbed, or a portion of it, is again 
 given out in all such cases, heat and chemical action are de- 
 veloped, and in amount corresponding to the loss. Hence the 
 apparent exceptions to the principle are in reality confirmations of 
 it ; and we learn that the quantity of force in nature is as un- 
 changeable as the quantity of matter. 
 
 This, however, is not true of the quantity of available force. It 
 follows from Carnot's law, that heat can be converted into me- 
 chanical work only when it passes from a warmer to a colder 
 body. But the radiation and conduction, by which this is effected, 
 tend to bring about an equilibrium of temperature, and therefore to 
 annihilate mechanical force : and the same destruction of energy 
 is going forward in the other processes of nature. Thus, it follows 
 from the law of Carnot, as Professor Thomson has shown, that the 
 Universe tends to a state of eternal rest ; and that its store of 
 available force must be at length exhausted, unless replenished by 
 a new act of Creative Power. 
 
 Mr. Rankine has attempted, in another method, to combine the 
 physical sciences into one system, by distinguishing the properties 
 which the various classes of physical phenomena possess in common, 
 and by taking for axioms propositions which comprehend their 
 laws. The principles thus obtained are applicable to all physical 
 change ; and they possess all the certainty of the facts from which 
 they are derived by induction. The subject-matter of the science 
 so constituted is energy, or the capacity to effect changes ; and its 
 fundamental principles are 1st, that all kinds of energy and work 
 are homogeneous or, in other words, that any kind of energy may 
 be made the means of performing any kind of work; and 2nd, that 
 the total energy of a substance cannot be altered by the mutual 
 action of its parts. From these principles the author has deduced
 
 FOR THE ADVANCEMENT OF SCIENCE, 1857- 505 
 
 some very general' laws of the transformation of energy, which in- 
 clude the known relations of physical forces. 
 
 I have occupied your time so largely with the sciences of one 
 section, that I cannot do more than advert to one or two topics 
 connected with the others, which have struck my own mind, 
 although, from my limited acquaintance with the subjects, I could 
 not venture to say that they are absolutely the most deserving 
 >of notice. 
 
 Among the most remarkable of the recent discoveries in inor- 
 ganic chemistry are those of MM. Wohler and Deville, relative to 
 silicon and boron. Each of these substances is now proved to exist 
 in three very different states, analogous to the three known states 
 of carbon, to which they are thus closely allied, namely, charcoal, 
 graphite, and diamond. The last of these states is, of course, the 
 most interesting. Crystallized boron possesses a hardness, bright- 
 ness, and refractive power, comparable to those of diamond; it 
 burns in chlorine, without residue, and under circumstances resem- 
 bling those of the combustion of diamond in oxygen ; it is not 
 acted on by any of the acids, and appears to be the least alterable 
 of all the simple bodies. I have been informed that its powder is 
 already used in the arts, instead of diamond dust ; and it seems 
 not improbable that, when obtained by the chemist in crystals of 
 larger size, it may rival the diamond as a gem. 
 
 The science of Geology appears, of late years, to have entered 
 upon a new phase of its development, one characterized by a 
 stricter reference of its speculative views to the principles of those 
 sciences with which it is connected, and upon which it ought to be 
 based. The able memoirs of Mr. Hopkins, on what may be called 
 dynamical geology, afford a remarkable proof of this; and we have 
 another instance of the application of sound physical principles to 
 this science in the explanations which have been recently offered of 
 the phenomena of slaty cleavage. A report on this interesting 
 subject was presented to the Association by Professor Phillips at 
 its last Meeting, and will be found in the volume just published. 
 These sounder views Originate, I believe, with himself and with 
 Mr. Sharpe ; but they have been enlarged and confirmed by Mr. 
 Sorby, Dr. Tyndall, and Professor Haughton.
 
 506 ADDRESS DELIVERED BEFORE THE BRITISH ASSOCIATION 
 
 We have an interesting proof of the readiness of geologists of 
 the present day to submit their views to the test of exact observa- 
 tion, in the measurements undertaken by Mr. Horner for the pur- 
 pose of approximating to the age of the sedimentary deposits. Of 
 the geological changes still in operation, none is more remarkable 
 than the formation of deltas at the mouths of great rivers, and of 
 alluvial land by their overflow. Of changes of the latter kind, 
 perhaps the most remarkable is the great alluvial deposit formed in 
 the valley of the Nile by the annual inundations of that river ; and 
 here it fortunately happens that history comes to the aid of the 
 geologist. These sedimentary deposits have accumulated round the 
 bases of monuments of known age ; and we are, therefore, at once fur- 
 nished with a chronometric scale by which the rate of their formation 
 may be measured. The first of the series of measurements under- 
 taken by Mr. Horner was made, with the co-operation of the Egyp- 
 tian Government, around the obelisk of Heliopolis, a monument 
 built, according to Lepsius, 2300 years B. c. A more extensive 
 series of researches has been since undertaken in the district of 
 Memphis ; but Mr. Horner has not yet, I believe, published the 
 results. 
 
 The problems now to be solved in Palaeontology are clearly 
 defined in the enunciation of the problem recently proposed by the 
 French Academy of Sciences as one of its prize questions, viz., "to 
 study the laws of distribution of organic beings in the different 
 sedimentary rocks, according to the order of their superposition ; 
 to discuss the question of their appearance or disappearance, 
 whether simultaneous or successive ; and to determine the nature 
 of the relations which subsist between the existing organic king- 
 dom and its anterior states." The prize was obtained by Professor 
 Bronn, of Heidelberg ; and his memoir, of which I have only seen 
 an outline, appears to be characterized by views at once sound and 
 comprehensive. The leading result seems to be, that the genera and 
 species of plants and animals, which geology proves to have existed 
 successively on our globe, were created in succession, in adaptation 
 to the existing state of their abode, and not transmuted, or modified^ 
 as the theory of Lamark supposes, by the physical influences which 
 surrounded them. 
 
 I must now pass, from the results of science, to the administrative 
 measures which have been adopted by this Association for its
 
 FOR THE ADVANCEMENT OF SCIENCE, 1857. 507 
 
 advancement, and more especially to those which will be brought 
 under your consideration at the present Meeting. 
 
 One of the modes in which this Association most effectively 
 promotes the advancement of science is, you are aware, by the 
 preparation and publication of Eeports on the history, and actual 
 state, of its several branches. With the help of these, original 
 investigators may, with little labour, ascertain all that has been 
 accomplished in each department, before they proceed to increase 
 the store ; and so not only prepare their own minds for their task, 
 but also avoid the waste of time and toil which has been too often 
 incurred in the re-discovery of the same truths. 
 
 To further the same objects, it was proposed by Professor Henry, 
 of Washington, at the Glasgow meeting of the Association, that a 
 Catalogue of papers occurring in the Transactions of Scientific 
 Societies, and in the Scientific Journals, should be prepared by the- 
 Association, the Smithsonian Institution undertaking to execute 
 that part of the work which related to American Science. A 
 Committee, consisting of Mr. Cayley, Mr. Grant, and Professor 
 Stokes, was appointed to consider this proposal, and their report 
 was submitted to the Cheltenham meeting. The subject has since 
 been under the consideration of the Council of the Royal Society ; 
 and a preliminary Report has been drawn up by a sub-committee 
 of that body, which will probably be brought before your Com- 
 mittee at this Meeting. 
 
 A still more important question has been, for some years, under 
 the consideration of this Association, and of the Royal Society the 
 question, namely, whether any measures could be adopted by the 
 Government, or Parliament, that would improve the position of 
 science, or its cultivators in this country. 
 
 The Parliamentary Committee of the Association have taken 
 much pains in the attempt to arrive at a solution of this large and 
 complex question. They consulted, in the first instance, several of 
 the most eminent scientific men of this country; and in their 
 first Report, presented to the Meeting of the Association at 
 Glasgow, they have analyzed the replies obtained, and have recom- 
 mended certain general measures founded thereon. The most 
 important of these recommendations are, the provision, at the cost 
 of the nation, of a central building in London, in which the prin-
 
 508 ADDRESS DELIVERED BEFORE THE BRITISH ASSOCIATION 
 
 cipal Scientific Societies of the metropolis may be locatedt ogether ; 
 and the formation of a Scientific Board, to have the control and 
 expenditure of the public funds allotted to the advancement of 
 science. This report was brought under the consideration of your 
 Committee of Recommendations at the last two Meetings of the 
 Association; and the opinions of the members of the General 
 Committee have been since invited in reference to its suggestions. 
 The Council of the Royal Society have likewise deliberated on the 
 same question, and have passed certain resolutions on the subject, 
 which accord in substance with the conclusions of the Parliament- 
 ary Committee. A copy of these resolutions was forwarded by 
 Lord Wrottesley, as President of the Society, to Lord Palmerston ; 
 and motions have been made in both Houses of Parliament for the 
 production of the correspondence. 
 
 The first of the objects above referred to namely, the juxta- 
 position of the Scientific Societies of London in one locality has 
 been since accomplished by the grant of Burlington House for the 
 use of the Royal, Linnsean, and Chemical Societies; and the result 
 affords a fresh instance of the readiness of Her Majesty's Govern- 
 ment to listen to, and comply with, the suggestions of men of 
 science, when deliberately and carefully made. I cannot but 
 think that this important step is fraught with consequences affect- 
 ing the promotion of science, and extending far beyond the ex- 
 ternal and obvious advantages, which it insures to the Scientific 
 Societies more immediately benefited. 
 
 Another mode in which this Association has materially aided 
 in the advancement of science is through the instrumentality of its 
 Observatory at Kew. The objects which are at present attained 
 by that important establishment are, the trial and improvement of 
 instrumental methods, and especially of those connected with the 
 photographic registration of natural phenomena ; the verification of 
 meteorological instruments, and the construction of standard 
 barometers and thermometers ; the supervision of apparatus to be 
 employed by scientific travellers, and the instruction of the ob- 
 servers in their use; and lastly, the conduct of special experimental 
 researches, undertaken by members of the Association at its request. 
 In all these various ways, the labours of the Kew Observatory 
 have tended, in no small degree, to the advancement of the sciences 
 of observation and experiment in this country ; and the result is
 
 FOR THE ADVANCEMENT OF SCIENCE, 1857. 509 
 
 due, not only to the sagacity of the Committee under whose manage- 
 ment it is placed, but also, and eminently, to the zeal and talents 
 of Mr. Welsh, the gentleman who has the immediate charge of the 
 establishment. 
 
 There is but one other topic connected with the administration 
 of the Association to which I feel it necessary to invite your atten- 
 tion before I conclude, I mean the change which has been made 
 in the constitution of one of the Sections, and which will come 
 into operation at the present Meeting. 
 
 By a resolution of your Committee, adopted at the last meet- 
 ing, the scope of the Statistical Section has been enlarged, and 
 it now embraces Economic Science in all its relations. I regard 
 it as a fortunate circumstance for the Association, that this im- 
 portant change will come into operation under the Presidency of 
 the distinguished prelate whose talents have been so long devoted 
 to the advancement of this science, and to whose munificence we 
 owe the formation of a school of Political Economy in the Univer- 
 sity of Dublin, which has already attained a high measure of cele- 
 brity. The Section will have the aid, on this occasion, of more 
 than one of those gentlemen who have filled the Chair of the 
 Whately Professorship, as well as of other members of the Sta- 
 tistical Society of Dublin ; and its proceedings will receive the 
 countenance and support of many foreigners who have devoted 
 themselves to the cultivation of Economic Science. 
 
 Gentlemen, suffer me now to thank you for the indulgent 
 attention with which you have favoured me. I am conscious 
 that the sketch of the recent progress of the Physical Sciences, 
 which I have endeavoured to present, is but a meagre and imper- 
 fect summary of what has been accomplished ; but it is enough, at 
 all events, to prove, that Science is not on the decline, and that 
 its cultivators have not been negligent in their high calling. I 
 now beg, in the name of the local members of this body, to 
 welcome you warmly to this city ; and I pray that your labours 
 here may redound to the glory of God, and to the welfare and 
 happiness of your fellow-men.
 
 NOTES. 
 
 TO TABLE VI., p. 289. 
 
 The values of the Magnetic Intensity at Munich and Prague, and at 
 the four Russian stations, were originally expressed in Gaussian units, in 
 which the unit of weight is the gramme, and that of length the metre. One 
 gramme is equal to 15-4426 grains, and one metre to 3-2809 feet. Accord- 
 ingly, to reduce the Gaussian measures of Horizontal Intensity to British 
 units (one grain and one foot), the values of X must be multiplied by 
 
 6 = 2-1695. This has been done in Table VI. 
 
 NOTE TO TABLES V. AND VIII., pp. 286 AND 291. 
 
 The unit of Intensity in Tables V. and VIII. is the ten-thousandth 
 part of the unit of Magnetic Force.
 
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 This book is DUE on the last date stamped below.
 
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