UNIVERSITY OF CALIFORNIA. FRO\\ THH LIBRARY Ol BENJAMIN PARKE AVERY. GIFT OF MRS. AVERY, August, 1806. s No. i /- fj iw A-^u . V LIGHT AND ELECTRICITY: l^OTES OF TWO COURSES OF LECTURES BEFORE THE ROYAL INSTITUTION OF GREAT BRITAIN. BY JOHN TYNDALL, LL. D., F. E. S., AUTHOB OP "HEAT AS A MODE OF MOTION," "LECTURES ON SOUND," "FRAGMENTS OF SCIENCE FOB UNSCIENTIFIC PEOPLE, 11 " HOURS OF EXEECISE IN- THE ALPS," ETC., ETC.; PROFESSOR OF NATURAL PHILOSOPHY IN THE EOYAL INSTITUTION OF GREAT BRITAIN. NEW YOEK: D. APPLETON AND COMPANY, 549 & 551 BROADWAY. 1871. PREFACE TO THE AMERICAN EDITION. FOE the benefit of those who attended his lectures on Light and Electricity at the Royal Institution, Prof. Tyndall prepared with much care a series of Notes, sum- ming up briefly and clearly the leading facts and princi- ples of these sciences. The Notes proved so serviceable to those for whom they were designed, that they were widely sought by students and teachers, and Prof. Tyndall accordingly had them reprinted in two small books. Under the conviction that they will be equally appreciated by instructors and .learners in this country, they are here combined and republished in a single volume. No intelligent teacher or earnest student needs to be reminded of the importance of repetition and recapitula- tion to give permanence to mental impressions. But it is neither possible nor desirable to retain in the memory the copious details which may be necessary to the first comprehension of a subject. Hence, after listening to a course of lectures, or going through an extended work in which facts, experimental proofs, and speculations, have 4 PREFACE TO THE AMERICAN EDITION. been elaborately presented, it is invaluable to retravcrsc the field, concentrating attention upon the prominent and established principles of the subject. This is an in- dispensable condition of all solid acquisition ; and, in thus clearly and sharply stating the fundamental principles of Electrical and Optical Science, Prof. Tyndall has earned the cordial thanks of all interested in education. NEW YORK, April, 1871. CONTENTS. LIGHT. PAGE General Considerations. Eectilinear Propagation of Light . . 11 Formation of Images through Small Apertures . . . 12 Shadows . . . . . . .13 Enfeeblement of Light by Distance : Law of Inverse Squares . 15 Photometry, or the Measurement of Light . . . .16 Brightness . . . . . . .17 Light requires Tune to pass through Space . . . .19 Aberration of Light . . . . .20 Reflection of Light (Catoptrics) Plane Mirrors . . .22 Verification of the Law of Reflection . . . . 22 Reflection from Curved Surfaces : Concave Mirrors . . .27 Caustics by Reflection (Catacaustics) . . . . 31 Convex Mirrors . . . . . . .32 Refraction of Light (Dioptrics) . . 33 Opacity of Transparent Mixtures . . . . .39 Total Reflection . . . . . . .41 Lenses . . . . . . . .44 Converging Lenses . . . . . .44 Diverging Lenses . . . . . . .44 Vision and the Eye . . . . . .46 Adjustment of the Eye : Use of Spectacles . . . .48 The Punctum Co3cmn 50 6 CONTENTS. PAGE Persistence of Impressions . . . . . .61 Bodies seen within the Eye . . . . . 52 The Stereoscope . . . . . . .64 Nature of Light ; Physical Theory of Reflection and Refraction 57 Theory of Emission . . . . . .57 s Theory of Undulation . . . . . .59 Prisms ........ 64 Prismatic Analysis of Light : Dispersion . . . .65 Invisible Rays : Calorescence and Fluorescence . . . 66 Doctrine of Visual Periods . . . . . .68 Doctrine of Colors ...... 69 Chromatic Aberration. Achromatism . . . .71 Subjective Colors ....... 72 Spectrum Analysis . . . . . . .74 Further Definition of Radiation and Absorption ... 75 The pure Spectrum : Fraunhofer's Lines . . . .77 Reciprocity of Radiation and Absorption . . . 78 Solar Chemistry . . . . . . .80 Planetary Chemistry . . . . . .81 Stellar Chemistry . . . . . . .82 Nebular Chemistry ...... 82 The Red Prominences and Envelope of the Sun . . .82 The Rainbow ....... 84 Interference of Light . . . . . . .86 Diffraction, or the Inflection of Light . . . . 88 Measurement of the Waves of Light . . . . .93 Colors of Thin Plates . . . . . .96 Double Refraction . . . . . . .101 Phenomena presented by Iceland Spar . . . ' . 104 Polarization of Light . . . . . .106 Polarization of Light by Reflection .... 108 Polarization of Light by Refraction . . . . .110 Polarization of Light by Double Refraction . . .110 CONTENTS. 7 PAGE Examination of Light transmitted through Iceland Spar . .111 Colors of Double-refracting Crystals in Polarized Light . . 114 Rings surrounding the Axes of Crystals in Polarized Light . ,119 Elliptic and Circular Polarization . . . .120 Rotatory Polarization . . . . . .121 CONCLUSION 123 ELECTRICITY. Voltaic Electricity : the Voltaic Battery . . . 131 Electro-Magnetism : Elementary Phenomena . . .133 Electro-Magnetic Engines . . . . . 135 Physical Effects of Magnetization . . . . .136 Character of Magnetic Force . . . . .138 Magnetism of Helix : Strength of Electro-Magnets . . .140 Electro-Magnetic Attractions : Law of Squares . . . 140 Inference from Law of Squares ; Theoretic Notions . . . 143 Diamagnetism : Magne-Crystallic Action . . . 144 Frictional Electricity: Attraction and Repulsion: Conduction and Insulation ....... 145 Theories of Electricity : Electric Fluids .';"-. . . 147 Electric Induction : the Condenser : the Electrophorus . . 148 The Electric Machine : the Leyden-jar .... 149 The Electric Current . . . . . . .150 The Electric Discharge : Thunder and Lightning . . 151 Electric Density : Action of Points ..... 152 Relation of Voltaic to Frictional Electricity . . . 153 Historic Jottings, concerning Conduction and the Leyden-jar . 155 Historic Jottings, concerning the Electric Telegraph . . 156 Phenomena observed in Telegraph-Cables .... 159 Artificial Cables ....... 163 Sketch of Ohm's Theory and Kohlrausch's Verification . .165 8 CONTENTS. PAGE Electro-chemistry. Chemical Actions in the Voltaic Cell : Origin of the Current ...... 168 Chemical Actions at a Distance : Electrolysis . . . .170 Measures of the Electric Current . . . .174 Electric Polarization : Ritter's Secondary Pile . . .175 Faraday's Electrolytic Law . . . . .177 Nobili's Iris Rings . . . . . .178 Distribution of Heat in the Circuit . . . .179 Relation of Heat to Current and to Resistance . . .180 Magneto-Electricity : Induced Currents . . . . 181 Relation of Induced Currents to the Lines of Magnetic Force. Rota- tory Magnetism . . . . . .184 The Extra-Current . . . . .186 Influence of Time on Intensity of Discharge. The Condenser . 187 Electric Discharge through rarefied Gases and Vapors . . 188 Action of Magnets on the Luminous Discharge . . .190 Magneto-electric Machines. Saxton's Machine. Siemens's Armature 191 Wilde's Machine . . . . . . .192 Siemens's and Wheatstone's Machine . . . .193 Induced Currents of the Leyden-Battery . . . . 1 94 NOTES OF A COURSE OF NINE LECTURES ON LIGHT. UHI7ERSIT7 NOTES ON LIGHT. General Considerations. Rectilinear Propagation of Light. 1. THE ancients supposed light to be produced and vision excited by something emitted from the eye. The moderns hold vision to be excited by something that strikes the eye from without. What that something is we shall consider more closely subsequently. 2. Luminous bodies are independent sources of light. They generate it and emit it, and do not receive their light from other bodies. The sun, a star, a candle-flame, are examples. 3. Illuminated bodies are such as receive the light by which they are seen from luminous bodies. A house, a tree, a man, are examples. Such bodies scatter in all directions the light which they receive ; this light reaches the eye, and through its action the illuminated bodies are rendered visible. 4. All illuminated bodies scatter or reflect light, and they are distinguished from each other by the excess or defect of light which they send to the eye. A white cloud in a dark-blue firmament is distinguished by its excess of light ; a dark pine-tree projected against the same cloud is distinguished through its defect of light. 5. Look at any point of a visible object. The light comes from that point in straight lines to the eye. The 12 NOTES ON LIGHT. lines of light, or rays as they are called, that reach the pupil form a cone, with the pupil for a base, and with the point for an apex. The point is always seen at the place where the rays which form the surface of this cone inter- sect each other, or, as we shall learn immediately, where they seem to intersect each other. 6. Light, it has just been said, moves in straight lines ; you see a luminous object by means of the rays which it sends to the eye, but you cannot see round a corner. A small obstacle that intercepts the view of a visible point is always in the straight line between the eye and the point. In a dark room let a small hole be made in a win- dow-shutter, and let the sun shine through the hole. A narrow luminous beam will mark its course on the dust of the room, and the track of the beam will be perfectly straight. 7. Imagine the aperture to diminish in size until the beam passing through it and marking itself upon the dust of the room shall dwindle to a mere line in thickness. In this condition the beam is what we call a ray of light. Formation of Images through Small Apertures. 8. Instead of permitting the direct sunlight to enter the room by the small aperture, let the light from some body illuminated by the sun a tree, a house, a man, for example be permitted to enter. Let this light be re- ceived upon a white screen placed in the dark room. Every visible point of the object sends a straight ray of light through the aperture. The ray carries with it the color of the point from which it issues, and imprints the color upon the screen. The sum total of the rays falling thus upon the screen produces an inverted image of that object. The image is inverted because the rays cross each other at the aperture. SHADOWS. 13 9. Experimental Illustration. Place a lighted candle in a small camera with a small orifice in one of its sides, or a large one covered by tin-foil. Prick the tin-foil with a needle ; the inverted image of the flame will immediate- ly appear upon a screen placed to receive it. By ap- proaching the camera to the screen, or the screen to the camera, the size of the image is diminished ; by augment- ing the distance between them, the size of the image is increased. 10. The boundary of the image is formed by drawing from every point of the outline of the object straight lines through the aperture, and producing these lines until they cut the screen. This could not be the case if the straight lines and the light rays were not coincident. 11. Some bodies have the power of permitting light to pass freely through them; they are transparent bodies. Others have the power of rapidly quenching the light that enters them ; they are opaque bodies. There is no such thing as perfect transparency or perfect opacity. The purest glass and crystal quench some rays; the most opaque metal, if thin enough, permits some rays to pass through it. The redness of the London sun in smoky weather is due to the partial transparency of soot for the red light. Pure water at great depths is blue; it quenches more or less the red rays. Ice when seen in large masses in the glaciers of the Alps is blue also. Shadows. 12. As a consequence of the rectilinear motion of light, opaque bodies cast shadows. If the source of light be a point, the shadow is sharply defined; if the source be a luminous surface, the perfect shadow is fringed by aft imperfect shadow called a penumbra. 13. When light emanates from a point, the shadow of 14 NOTES ON LIGHT. a sphere placed in the light is a divergent cone sharply defined. 14. When light emanates from a luminous globe, the perfect shadow of a sphere equal to the globe in size will be a cylinder it will be bordered by a penumbra. 15. If the luminous sphere l>e the larger of the two, the perfect shadow will be a convergent cone / it will be surrounded by a penumbra. This is the character of the shadows cast by the earth and moon in space ; for the sun is a sphere larger than either the earth or the moon. 16. To an eye placed in the true conical shadow of the moon, the sun is totally eclipsed ; to an eye in the penum- bra, the sun appears horned ; while to an eye placed be- yond the apex of the conical shadow and within the space enclosed by the surface of the cone produced, the eclipse is annular. All these eclipses are actually seen from time to time from the earth's surface. 17. The influence of magnitude may be experimentally illustrated by means of a bat's-wing or fish-tail flame ; or by a flat oil or paraffine flame. Holding an opaque rod between the flame and a white screen, the shadow is sharp when the edge of the flame is turned toward the rod. When the broad surface of the flame is pointed to the rod, the real shadow is fringed by a penumbra. 18. As the distance from the screen increases, the penumbra encroaches more and more upon the perfect shadow, and finally obliterates it. 19. It is the angular magnitude of the sun that de- stroys the sharpness of solar shadows. In sunlight, for example, the shadow of a hair is sensibly washed away at a few inches distance from the surface on which it falls. The electric light, on the contrary, emanating as it does from small carbon points, casts a defined shadow of a hair upon a screen many feet distant. ENFEEBLEMENT OF LIGHT BY DISTANCE. 15 Enfeeblement of Light Tyy Distance / Law of Inverse Squares. 20. Light diminishes in intensity as we recede from the source of light. If the luminous source be a point, the intensity diminishes as the square of the distance in- creases. Calling the quantity of light falling upon a given surface at the distance of a foot or a yard 1, the quantity falling on it at a distance of 2 feet or 2 yards is |-, at a distance of 3 feet or 3 yards it is {-, at a distance of 10 feet or 10 yards it would be yj^, and so on. This is the mean- ing of the law of inverse squares as applied to light. 21. Experimental Illustrations. Place your source of light, which may be a candle-flame though the law is in strictness true only for points at a distance say of 9 feet from a white screen. Hold a square of pasteboard, or some other suitable material, at a distance of 2 feet from the flame, or th of the distance of the screen. The square casts a shadow upon the screen. 22. Assure yourself that the area of this shadow is sixteen times that of the square which casts it ; a student of Euclid will see in a moment that this must be the case, and those who are not geometers can readily satisfy them- selves by actual measurement. Dividing, for example, each side of a square sheet of paper into four equal parts, and folding the sheet at the opposite points of division, a small square is obtained y^-th of the area of the large one. Let this small square, or one equal to it, be your shadow- casting body. Held at 2J feet from the flame, its shadow upon the screen 9 feet distant will be exactly covered by the entire sheet of paper. "Wlien, therefore, the small square is removed, the light that fell upon it is diffused over sixteen times the area on the screen; it is therefore diluted to y^th of its former intensity. That is to say, by 16 NOTES ON LIGHT. augmenting the distance fourfold we diminish tLe light sixteenfold. 23. Make the same experiment by placing a square at a distance of 3 feet from the source of light and 6 from the screen. The shadow now cast by the square will have nine times the area of the square itself ; hence the light falling on the square is diffused over nine times the surface upon the screen. It is, therefore, reduced to ^th of its intensity. That is to say, by trebling the distance from the source of light we diminish the light ninefold. 24. Make the same experiment at a distance of 4J fcet from the source. The shadow here will be four times the area of the shadow-casting square, and the light diffused over the greater square will be reduced to Jth of its former intensity. Thus, by doubling the distance from the source of light we reduce the intensity of the light fourfold. 25. Instead of beginning with a distance of 2 feet from the source, we might have begun with a distance of 1 foot. The area of the shadow in this case would be eighty-one times that of the square which casts it ; prov- ing that at 9 feet distance the intensity of the light is -^ of what it is at 1 foot distance. 26. Thus when the distances are 1, 2, 3, 4, 5, 6, V, 8, 9, etc., the relative intensities are 1> i, l> Ty A> &, t A> -fa, -fa, e tc. This is the numerical expression of the law of inverse squares. Photometry, or the Measurement of Light. 27. The law just established enables us to compare one light with another, and to express by numbers their relative illuminating powers. BRIGHTNESS. 17 28. The more intense a light, the darker is the shadow which it casts ; in other words, the greater is the contrast between the illuminated and unilluminated surface. 29. Place an upright rod in front of a white screen and a candle-flame at some distance behind the rod, the rod casts a shadow upon the screen. 30. Place a second flame by the side of the first, a second shadow is cast, and it is easy to arrange matters so that the shadows shall be close to each other, thus offering themselves for easy comparison to the eye. If when the lights are at the same distance from the screen the two shadows are equally dark, then the two lights have the same illuminating power. 31. But if one of the shadows be darker than the other, it is because its corresponding light is brighter than the other. Remove the brighter light farther from the screen, the shadows gradually approximate in depth, and at length the eye can perceive no difference between them. The shadow corresponding to each light is now illuminated by the other light, and if the shadows are equal it is be- cause the quantities of light cast by both upon the screen are equal. 32. Measure the distances of the two lights from the screen, and square these distances. The two squares will express the relative illuminating powers of the two lights. Supposing one distance to be 3 feet and the other 5, the relative illuminating powers are as 9 to 25- Brightness. 33. But if light diminishes so rapidly with the distance if, for example, the light of a candle at the distance of a yard is 100 times more intense than at the distance of 10 yards how is it that on looking at lights in churches or theatres, or in large rooms, or at our street-lamps, a light 18 NOTES ON LIGHT. 10 yards off appears almost, if not quite, as bright as one close at hand ? 34. To answer this question I must anticipate matters so far as to say that at the back of the eye is a screen, woven of nerve-filaments, named the retina; and that when we see a light distinctly, its image is formed upon this screen. This point will be fully developed when we come to treat of the eye. ISTow the sense of external brightness depends upon the brightness of this internal retinal image, and not upon its size. As we retreat from a light, its image upon the retina becomes smaller, and it is easy to prove that the diminution follows the law of inverse squares ; that at a double distance the area of the retinal image is reduced to one-fourth, at a treble dis- tance to one-ninth, and so on. The concentration of light accompanying this decrease of magnitude exactly atones for the diminution due to distance ; hence, if the air be clear, the light, within wide variations of distance, appears equally bright to the observer. 35. If an eye could be placed behind the retina, the augmentation or diminution of the image, with the de- crease or increase of distance, might be actually observed. An exceedingly simple apparatus enables us to illustrate this point. Take a pasteboard or tin tube, three or four inches wide and three or four inches long, and cover one end of it with a sheet of tin-foil, and the other with tracing-paper, or ordinary letter-paper wetted with oil or turpentine. Prick the tin-foil with a needle, and turn the aperture toward a candle-flame. An inverted image of the flame will be seen on the translucent paper screen by the eye behind it. As you approach the flame the image becomes larger, as you recede from the flame the image becomes smaller ; but the brightness remains through- out the same. It is so with the image upon the retina. LIGHT REQUIRES TIME TO PASS THROUGH SPACE. 19 36. If a sunbeam be permitted to enter a room through a small aperture, the spot of light formed on a distant screen will be round, whatever be the shape of the aper- ture ; this curious effect is due to the angular magnitude of the sun. Were the sun a point, the light spot would be accurately of the same shape as the aperture. Supposing, then, the aperture to be square, every point of light round the sun's periphery sends a small square to the screen. These small squares are ranged round a circle correspond- ing to the periphery of the sun ; through their blending and overlapping they produce a rounded outline. The spots of light which fall through the apertures of a tree's foliage on the ground are rounded for the same reason. Light requires Time to pass through Space. 37. This was proved in 1675 and 1676 by an eminent Dane, named Olaf Koemer, who was then engaged with Cassini in Paris in observing the eclipses of Jupiter's moons. The planet, whose distance from the sun is 475,- 693,000 miles, has four satellites. We are now only con- cerned with the one nearest to the planet. Rcemer watched this moon, saw it move round in front of the planet, pass to the other side of it, and then plunge into Jupiter's shadow, behaving like a lamp suddenly extinguished : at the other edge of the shadow he saw it reappear like a lamp suddenly lighted. The moon thus acted the part of a signal-light to the astronomer, which enabled him to tell exactly its time of revolution. The period between two successive lightings up of the lunar lamp gave this time. It was found to be 42 hours, 28 minutes, and 35 seconds. 38. This observation was so accurate, that having de- termined the moment when the moon emerged from the shadow, the moment of its hundredth appearance could 2Q NOTES ON LIGHT. also be determined. In fact, it would be 100 times 42 hours, 28 minutes, 35 seconds, from the first observa- tion. 39. Rcemer's first observation was made when the earth was in the part of its orbit nearest Jupiter. About six months afterward, when the little moon ought to make its appearance for the hundredth time, it was found un- punctual, being fully 15 minutes behind its calculated time. Its appearance, moreover, had been growing grad- ually later, as the earth retreated toward the part of its orbit most distant from Jupiter. 40. Roemer reasoned thus: "Had I been able to re- main at the other side of the earth's orbit, the moon might have appeared always at the proper instant ; an observer placed there would probably have seen the moon 15 minutes ago, the retardation in my case being due to the fact that the light requires 15 minutes to travel from the place where my first observation was made to my present position." 41. This flash of genius was immediately succeeded by another. " If this surmise be correct," Rremer reasoned, " then as I approach Jupiter along the other side of the earth's orbit, the retardation ought to become gradually less, and when I reach the place of my first observation there ought to be no retardation at all." He found this to be the case, and thus proved not only that light re- quired time to pass through space, but also determined its rate of propagation. 42. The velocity of light as determined by Roemer is 192,500 miles in a second. The Aberration of Light. The astounding velocity assigned to light by the ob- servations of Roamer received the most striking confirma- THE ABERRATION OF LIGHT. 21 tion from the English astronomer Bradley in the year 1723. In Kew Gardens to the present hour there is a sundial to mark the spot where Bradley discovered the aberration of light. 43. If we move quickly through a rain-shower which falls vertically downward, the drops will no longer seem to fall vertically, but will appear to meet us. A similar deflection of the stellar rays by the motion of the earth in its orbit is called the aberration of light. 44. Knowing the speed at which we move through a vertical rain-shower, and knowing the angle at which the rain-drops appear to descend, we can readily calculate the velocity of the falling drops of rain. So, likewise, know- ing the velocity of the earth in its orbit, and the deflec- tion of the rays of light produced by the earth's motion, we can immediately calculate the velocity of light. 45. The velocity of light, as determined by Bradley, is 191,515 miles per second a most striking agreement with the result of Rcemer. 46. This velocity has also been determined by experi- ments over terrestrial distances. M. Fizeau found it thus to be 194,677 miles a second, while the later experiments of M. Foucault made it 185,177 miles a second. 47. "A cannon-ball," says Sir John Herschel, "would require seventeen years to reach the sun, yet light travels over the same space in eight minutes. The swiftest bird, at its utmost speed, would require nearly three weeks to make the tour of the earth. Light performs the same dis- tance in much less time than is necessary for a single stroke of its wing ; yet its rapidity is but commensurate with the distance it has to travel. It is demonstrable that light cannot reach our system from the nearest of the fixed stars in less than five years, and telescopes disclose to us objects probably many times more remote." 22 NOTES ON LIGHT. The Reflection of Light (Catoptrics) Plane Mirrors. 48. When light passes from one optical medium to an- other, a portion of it is always turned back or reflected. 49. Light is regularly reflected by a polished surface ; but if the surface be not polished, the light is irregularly reflected or scattered. 50. Thus a piece of ordinary drawing-paper will scat- ter a beam of light that falls upon it so as to illuminate a room. A plane mirror receiving the sunbeam will reflect it "in a definite direction, and illuminate intensely a small portion of the room. 51. If the polish of the mirror were perfect it would be invisible, we should simply see in it the images of other objects ; if the room were without dust-particles, the beam passing through the air would also be invisible. It is the light scattered by the mirror and by the particles suspended in the air which renders them visible. 52. A ray of light striking as a perpendicular against a reflecting surface is reflected back along the perpen- dicular ; it simply retraces its own course. If it strike the surface obliquely, it is reflected obliquely. 53. Draw a perpendicular to the surface at the point where the ray strikes it ; the angle enclosed between the direct ray and this perpendicular is called the angle of in- cidence. The angle enclosed by the reflected ray and the perpendicular is called the angle of reflection. 54. It is a fundamental law of optics that the angle of incidence is equal to the angle of reflection. Verification of the Law of Reflection. 55. Fill a basin with water to the brim, the water be- ing blackened by a little ink. Let a small -plummet a small lead bullet, for example suspended by a thread, VERIFICATION OF THE LAW OF REFLECTION. 23 hang into the water. The water is to be our horizontal mirror, and the plumb-line our perpendicular. Let the plummet hang from the centre of a horizontal scale, with inches marked upon it right and left from the point of suspension, which is to be the zero of the scale. A lighted candle is to be placed on one side of the plumb-line, the observer's eye being at the other. 56. The question to be solved is this : How is the ray which strikes the liquid surface at the foot of the plumb- line reflected ? Moving the candle along the scale, so that the tip of its flame shall stand opposite different numbers, it is found that, to see the reflected tip of the flame in the direction of the foot of the plumb-line, the line of vision must cut the scale as far on the one side of that line as the candle is on the other. In other words, the ray reflect- ed from the foot of the perpendicular cuts the scale accurately at the candle's distance on the other side of the perpendicular. From this it immediately follows that the angle of incidence is equal to the angle of reflec- tion. 57. With an artificial horizon of this kind, and employ- ing a theodolite to take the necessary angles, the law has been established with the most rigid accuracy. The angle of elevation to a star being taken by the instrument, the telescope is then pointed downward to the image of the star reflected from the artificial horizon. It is always found that the direct and reflected rays enclose equal angles with the horizontal axis of the telescope, the reflected ray being as far below the horizontal axis as the direct ray is above it. On account of the star's distance the ray which strikes the reflecting surface is parallel with the ray which reaches the telescope directly, and from this follows, by a brief }mt rigid demonstration, the law above enun- ciated. 24 NOTES ON LIGHT. 58. The path described by the direct and reflected rays is the shortest possible. 59. When the reflecting surface is roughened, rays from different points, more or less distant from each other, reach the eye. Thus, a breeze crisping the surface of the Thames or Serpentine sends to the eye, instead of single images of the lamps upon their margin, pillars of light. Blowing upon our basin of water, we also convert the reflected light of our candle into a luminous column. 60. Light is reflected with different energy by different substances. At a perpendicular incidence, only 18 rays out of -every 1,000 are reflected by water, 25 rays per 1,000 by glass, while 666 per 1,000 are reflected by mercury. 61. When the rays strike obliquely, a greater amount of light than that stated in 60, is reflected by water and glass. Thus, at an incidence of 40, water reflects 22 rays ; at 60, 65 rays ; at 80, 333 rays ; and at 89j (almost grazing the surface), it reflects 721 rays out of every 1,000. This is as much as mercury reflects at the same incidence. 62. The augmentation of the light reflected as the obliquity of incidence is increased may be illustrated by our basin of water. Hold the candle so that its rays en- close a large angle with the liquid surface, and notice the brightness of its image. Lower both the candle and the eye until the direct and reflected rays as nearly as possible graze the liquid surface ; the image of the flame is now much brighter than before. Reflection from Looking-glasses. Various instructive experiments with a looking-glass may be here performed and understood. 63. Note first when a candle is placed between the glass and the eye, so that a line from the eye through the candle is perpendicular to the glass, that one well-denned image of the candle only is seen. VERIFICATION OF THE LAW OF REFLECTION. 25 G4. Let the eye now be moved so as to receive an ob- lique reflection ; the image is no longer single, a series of images at first partially overlapping each other being seen. By rendering the incidence sufficiently oblique these images, if the glass be sufficiently thick, may be completely separated from each other. 65. The first image of the series arises from the reflection of the light from the anterior surface of the glass. 66. The second image, which is usually much the bright- est, arises from reflection at the silvered surface of the glass. At large incidences, as we have just learned, metallic re- flection far transcends that from glass. 67. The other images of the series are produced by the reverberation of the light. from surface to surface of the glass. At every return from the silvered surface a portion of the light quits the glass and reaches the eye, forming an image ; a portion is also sent back to the silvered sur- face, where it is again reflected. Part of this reflected beam also reaches the eye and yields another image. This process continues : the quantity of light reaching the eye growing gradually less, and, as a consequence, the succes- sive images growing dimmer, until finally they become too dim to be visible. 68. A very instructive experiment illustrative of the augmentation of the reflection from glass, through aug- mented obliquity, may here be made. Causing the candle and the eye to approach the looking-glass, the first image becomes gradually brighter ; and you end by rendering the image reflected from the glass brighter, more lumi- nous, than that reflected from the metal. Irregularities in the reflection from looking-glasses often show themselves ; but with a good glass and there are few glasses so de- fective as not to possess, at all events, some good portions the succession of images is that here indicated. 2 26 NOTES ON LIGHT. 69. Position and Character of Images in Plane Mir- rors. The image in a plane mirror appears as far behind the mirror as the object is in front of it. This follows im- mediately from the law which announces the equality of the angles of incidence and reflection. Draw a line repre- senting the section of a plane mirror ; place a point in front of it. Rays issue from that point, are reflected from the mirror, and strike the pupil of the eye. The pupil is the base of a cone of such rays. Produce the rays backward ; they will intersect behind the mirror, and the point will be seen as if it existed at the place of intersection. The place of intersection is easily proved to be as far behind the mirror as the point is in front of it. 70. Exercises in determining the positions of images in a plane mirror, the positions of the objects being given, are here desirable. The image is always found by simply letting fall a perpendicular from each point of the object, and producing it behind the mirror, so as to make the part behind equal to the part in front. We thus learn that the image is of the same size and shape as the object, agreeing with it in all respects save one the image is a lateral in- version of the object. 71. This inversion enables us, by means of a mirror, to read writing written backward, as if it were written in the usual way. Compositors arrange their type in this back- ward fashion, the type being reversed by the process of printing. A looking-glass enables us to read the type as the printed page. 72. Lateral inversion comes into play when we look at our own faces in a glass. The right cheek of the object, for example, is the left cheek of the image ; the right hand of the object the left hand of the image, etc. The hair parted on the left in the object is seen parted to the right of the image, etc. REFLECTION FROM CURVED SURFACES. 27 73. A plane mirror half the height of an object gives an image which embraces the whole height. This is readily deduced from what has gone before. 74. If a plane mirror be caused to move parallel with itself, the motion of an image in the mirror moves with twice its rapidity. 75. The same is true of a rotating mirror: when a plane mirror is caused to rotate, the angle described by the image is twice that described by the mirror. 76. In a mirror inclined at an angle of 45 degrees to the horizon, the image of an erect object appears hori- zontal, while the image of a horizontal object appears erect. 77. An object placed between two mirrors enclosing an angle yields a number of images depending upon the angle enclosed by the mirrors. The smaller the angle, the greater is the number of images. To find the number of images, divide 360 by the number of degrees in the angle enclosed by the two mirrors, the quotient, if a whole number, will be the number of images, plus one, or it will include the images and the object. The construction of the kaleidoscope depends on this. 78. When the angle becomes in other words, when the mirrors are parallel the number of images is infinite. Practically, however, we see between parallel mirrors a long succession of images, which become gradually feebler, and finally cease to be sensible to the eye. Reflection from Curved Surf aces : Concave Mirrors. 79. It has been already stated and illustrated that light moves in straight lines, which receive the name of rays. Such rays may be either divergent, parallel, or convergent. 80. Rays issuing from terrestrial points are necessarily divergent. Rays from the sun or stars are, in consequence 28 NOTES ON LIGHT. of the immense distances of these objects, sensibly par- allel. 81. By suitably reflecting them, we can render the rays from terrestrial sources either parallel or convergent. This is done by means of concave mirrors. 82. In its reflection from such mirrors, light obeys the law already enunciated for plane mirrors. The angle of incidence is equal to the angle of reflection. FIG. 1. M 83. Let M N be a very small portion of the circum- ference of a circle with its centre at O. Let the line a or, passing through the centre, cut the arc M N" into two equal parts at a. Then imagine the curve M N twirled round a x as a fixed axis ; the curve would describe part of a spherical surface. Suppose the surface turned toward x to be silvered over, we should then have a concave spherical reflector ; and we have now to understand the action of this reflector upon light. 84. The line a x is the principal axis of the mirror. .85. All rays from a point placed at the centre O strike the surface of the mirror as perpendiculars, and after re- flection return to O. 86. A luminous point placed on the axis beyond O, say REFLECTION FROM CURVED SURFACES. 29 at jc, throws a divergent cone of rays upon the mirror. These rays are rendered convergent on reflection, and they intersect each other at some point on the axis between the centre O and the mirror. In every case the direct and the reflected rays (xm and mx' for example) enclose equal angles with the radius (O m) drawn to the point of inci- dence. 87. Supposing x to be exceedingly distant, say as far away as the sun from the small mirror or, more cor- rectly, supposing it to be infinitely distant then the rays falling upon the mirror will be parallel. After reflection such rays intersect each other, at a point midway between the mirror and its centre. 88. This point, which is marked F in the figure, is the principal focus of the mirror ; that is to say, the principal focus is the focus of parallel rays. 89. The distance between the surface of the mirror and its principal focus is called the focal distance. 90. In optics, the position of an object and of its image are always exchangeable. If a luminous point be placed in the principal focus, the rays from it will, after reflection, be parallel. If the point be placed anywhere between the principal focus and the centre O, the rays after reflection will cut the axis at some point beyond the centre. 91. If the point be placed between the principal focus F and the mirror, the rays after reflection will be divergent they will not intersect at all there will be no real focus. 92. But if these divergent rays be produced backward, they will intersect behind the mirror, and form there what is called a virtual, or imaginary focus. Before proceeding further, it is necessary that these simple details should be thoroughly mastered. Given the position of a point in the axis of a concave mirror, no dif- 30 NOTES ON LIGHT. ficulty must be experienced in finding the position of the image of that point, nor in determining whether the focus is virtual or real. 93. It will thus become evident that, while a point moves from an infinite distance to the centre of a spherical mirror, the image of that point moves only over the dis- tance between the principal focus and the centre. Con- versely, it will be seen that during the passage of a lumi- nous point from the centre to the principal focus, the image of the point moves from the centre to an infinite distance. 94. The point and its image occupy what are called conjugate foci. If the last note be understood, it will be seen that the conjugate foci move in opposite directions, and that they coincide at the centre of the mirror. 95. If instead of a point an object of sensible dimen- sions be placed beyond the centre of the mirror, an in- verted image of the object diminished in size will be formed between the centre and the principal focus. 96. If the object be placed between the centre and the principal focus, an inverted and magnified image of the object will be formed beyond the centre. The positions of the image and its object are, it will be remembered, convertible. 97. In the two cases mentioned in 95 and 96 the image is formed in the air in front of the mirror. It is a real image. But if the object be placed between the principal focus and the mirror, an erect and magnified image of the object is seen behind the mirror. The image is here virtual. The rays enter the eye as if they came from an object be- hind the mirror. 98. It is plain that the images seen in a common look- ing-glass are all virtual images. 99. It is now to be noted that what has been here CAUSTICS BY REFLECTION. 31 stated regarding the gathering of rays to a single focus by a spherical mirror is only true when the mirror forms a small fraction of the spherical surface. Even then it is only practically, not strictly and theoretically, true. Caustics by Reflection ( Catacaustics). 100. When a large fraction of the spherical surface is employed as a mirror, the rays are not all collected to a point; their intersections, on the contrary, form a lumi- nous surface, which in optics is called a caustic (German, Brennflache). 101. The interior surface of a common drinking-glass is a curved reflector. Let the glass be nearly filled with milk, and a lighted candle placed beside it; a caustic curve will be drawn upon the surface of the milk. A carefully-bent hoop, silvered within, also shows the caustic very beautifully. The focus of a spherical mirror is the cusp of its caustic. 102. Aberration. The deviation of any ray from this cusp is called the aberration of the ray. The inability of a spherical mirror to collect all the rays falling upon it to a single point is called the spherical aberration of the mirror. 103. Heal images, as already stated, are formed in the air in front of a concave mirror, and they may be seen in the air by an eye placed among the divergent rays be- yond the image. If an opaque screen, say of thick paper, intersect the image, it is projected on the screen and is seen in all positions by an eye placed in front of the screen. If the screen be semi-transparent, say of ground glass or tracing-paper, the image is seen by an eye placed either in front of the screen or behind it. The images in phantas- magoria are thus formed. Concave spherical surfaces are usually employed as 32 NOTES ON LIGHT. burning-mirrors. By condensing the sunbeams with a mirror 3 feet in diameter and of 2 feet focal distance, very powerful effects may be obtained. At the focus, water is rapidly boiled, and combustible bodies are immediately set on fire. Thick paper bursts into flame with explosive violence, and a plank is pierced as with a hot iron. Convex Mirrors. 104. In the case of a convex spherical mirror the posi- tions of its foci and of its images are found as in the case of a concave mirror. But all the foci and all the images of a convex mirror are virtual. 105. Thus to find the principal focus you draw parallel rays which, on reflection, enclose angles with the radii equal to those enclosed by the direct rays. The reflected rays are here divergent / but on being produced back- ward, they intersect at the principal focus behind the mirror. 106. The drawing of two lines suffices to fix the posi- tion of the image of any point of an object either in con- cave or convex spherical mirrors. A ray drawn from the point through the centre of the mirror will be reflected through the centre ; a ray drawn parallel to the axis of the mirror will, after reflection, pass, or its production will pass, through the principal focus. The intersection of these two reflected rays determines the position of the image of the point. Applying this construction to objects of sensible magnitude, it follows that the image of an object in a convex mirror is always erect and diminished. 107. If the mirror be parabolic instead of spherical, all parallel rays falling upon the mirror are collected to a point at its focus ; conversely, a luminous point placed at the focus sends forth parallel rays : there is no aberration. If the mirror be elliptical, all rays emitted from one of the REFRACTION OF LIGHT. 33 foci of the ellipsoid are collected together at the other. Parabolic reflectors are employed in light-houses, where it is an object to send a powerful beam, consisting of rays as nearly as possible parallel, far out to sea. In this case the centre of the flame is placed in the focus of the mirror ; but, inasmuch as the flame is of sensible magnitude, and not a mere point, the rays of the reflected beam are not accurately parallel. The Refraction of Light (Dioptrics). 108. We have hitherto confined our attention to the portion of a beam of light which rebounds from the re- flecting surface. But, in general, a portion of the beam also enters the reflecting substance, being rapidly quenched when the substance is opaque (see note 11), and freely transmitted when the substance is transparent. 109. Thus in the case of water, mentioned in note 60, when the incidence is perpendicular all the rays are trans- mitted, save the 18 referred to as being reflected. That is to say, 982 out of every 1,000 rays enter the water and pass through it. 110. So likewise in the case of mercury, mentioned in the same note; 334 out of every 1,000 rays falling on the mercury at a perpendicular incidence, enter the metal and are quenched at a minute depth beneath its surface. We have now to consider that portion of the luminous beam which enters the reflecting substance ; taking, as an illustrative case, the passage from air into water. 111. If the beam fall upon the water as a perpendicu- lar, it pursues a straight course through the water : if the incidence be oblique, the direction of the beam is changed at the point where it enters the water. 34 NOTES ON LIGHT. 112. This bending of the beam is called refraction. Its amount is different in different substances. FIG. 2. m 113. The refraction of light obeys a perfectly rigid law which must be clearly understood. Let A B C D, Fig. 2, be the section of a cylindrical vessel which is half filled with water, its surface being AC. E is the centre of the circular section of the cylinder, and B D is a perpendicular to the surface at E. Let the cylindrical envelope of the vessel be opaque, say of brass or tin, and let an aperture be imagined in it at B, through which a narrow light- beam passes to the point E. The beam will pursue a straight course to D without turning to the right or to the left. 114. Let the aperture be imagined at m, the beam striking the surface of the water at E obliquely. Its course on entering the liquid will be changed ; it will pursue the track E n. 115. Draw the line m o perpendicular to B D, and also the line n p perpendicular to the same B D. It is always found that m o divided by n p is a constant quantity, no matter what may be the angle at which the ray enters the water. REFRACTION OF LIGHT. 35 116. The angle marked x above the surface is called the angle of incidence ; the angle at y below the surface is called the angle of refraction ; and if we regard the radius of the circle A B C D as unity or 1, the line m o will be the sine of the angle of incidence ; while the line n p will be the sine of the angle of refraction. 11V. Hence the ill-important optical law The sine of the angle of incidence divided by the sine of the angle of refraction is a constant quantity. However these angles may vary in size, this bond of relationship is never severed. If one of them be lessened or augmented, the other must diminish or increase so as to obey this law. Thus if the incidence be along the dotted line m' E, the refraction will be along the line E n\ but the ratio of m' o' to n' p' will be precisely the same as that of m o to n p. 118. The constant quantity here referred to is called the index of refraction. 119. One word more is necessary to the full compre- hension of the term sine, and of the experimental demon- stration of the law of refraction. When one number is divided by another the quotient is called the ratio of the one number to the other. Thus 1 divided by 2 is ^, and this is the ratio of 1 to 2. Thus also 2 divided by 1 is 2, and this is the ratio of 2 to 1. In like manner 12 divided by 3 is 4, and this is the ratio of 12 to 3. Conversely, 3 di- vided by 12 is ^, and this is the ratio of 3 to 12. 120. In a right-angled triangle the ratio of any side to the hypothenuse is found by dividing that side by the hypothenuse. This ratio is the sine of the angle opposite to the side, however large or small the triangle may be. Thus in Fig. 2 the sine of the angle x in the right-angled triangle E o m is really the ratio of the line o m to the hypothenuse E m it would be expressed in a fractional form thus, ^ . In like manner the sine of y is the ratio Hi m 36 NOTES ON LIGHT, of the line np to the hypothenuse E w, and would be ex- pressed in a fractional form thus, *j~. These fractions are the sines of the respective angles, whatever be the length of the line E m or E n. In the particular case above re- ferred to, where these lines are considered as units, the f , . mo _ n p tractions -y- and --, or in other words m o and n p^ be- come, as stated, the sines of the respective angles. We are now prepared to understand a simple but rigid dem- onstration of the law of refraction. FIG. 3. r H - - 121. ML J K is a cell with parallel glass sides and one opaque end M L The light of a candle placed at A falls into the vessel, the end ML casting a shadow which reaches to the point E. Fill the vessel with water the shadow retreats to PI through the refraction of the light at the point where it enters the water. 122. The angle enclosed between M E and M L is equal to the angle of incidence a?, and, in accordance with the L definition given in 120,-^- ^ is its sine sine of the angle of refraction y. All these lines can be while - - is the REFRACTION OF LIGHT. 37 either measured or calculated. If they be thus determined, and if the division be actually made, it will always be found T TM T TT that the two quotient s-^-^ and ^ ==rStand in a constant ratio to each other, whatever the angle may be at which the light from A strikes the surface of the liquid. This 4 ratio in the case of water is , or, expressed in decimals, 1.333.* 123. When the light passes from air into water, the refracted ray is bent toward the perpendicular. This is generally, but not always, the case when the light passes from a rarer to a denser medium. 124. The principle of reversibility which runs through the whole of optics finds illustration here. When the ray passes from water to air it is bent/rom the perpendicular: it accurately reverses its course. 125. If instead of water we employed vinegar the ratio would be 1.344 ; with brandy it would be 1.360 ; with rec- tified spirit. of wine 1.372 ; with oil of almonds or with olive oil 1.470; with spirit of turpentine 1.605; w T ithoilof aniseseed 1.538; with oil of bitter almonds 1.471; with bisulphide of carbon 1.678 ; with phosphorus 2.24. 126. These numbers express the indices of refraction of the various substances mentioned ; all of them refract the light more powerfully than water, and it is worthy of remark that, all of them, except vinegar, are combustible substances. 127. It was the observation on the part of Newton, that, having regard to their density, "unctuous sub- stances" as a general rule refracted light powerfully, coupled with the fact that the index of refraction of the diamond reached, according. to his measurements, so high . * More accurately, 1.33G. 38 NOTES ON LIGHT. a figure as 2.439, that caused him to foresee the possible combustible nature of the diamond. The bold prophecy of Newton* has been fulfilled, the combustion of a dia- mond being one of the commonest experiments of modern chemistry. 128. It is here worth noting that the refraction by spirit of turpentine is greater than that by water, though the density of the spirit is to that of the water as 874 is to 1,000. A ray passing obliquely from the spirit of turpen- tine into water is bent from the perpendicular, though it passes from a rarer to a denser medium ; while a ray pass- ing from water into the spirit of turpentine is bent toward the perpendicular, though it passes from a denser to a rarer medium. Hence the necessity for the words " not always " employed in 123. 129. If a ray of light pass through a refracting plate with parallel surfaces, or through any number of plates with parallel surfaces, on regaining the medium from which it started, its original direction is restored. This follows from the principle of reversibility already re- ferred to. 130. In passing through a refracting body, or through any number of refracting bodies, the light accomplishes its transit in the minimum of time. That is to say, given the velocity of light in the various media, the path chosen by the ray, or, in other words, the path which its refraction imposes upon the ray, enables it to perform its journey in the most rapid manner possible. 131. Refraction always causes water to appear shal- lower, or a transparent plate of any kind thinner, than it * " Car ce grand homme, qui mettait la plus grande severitS dans ses experiences, et la plus grande reserve dans ses conjectures, n'hesitait jamais a suivre les consequences d!une verite aussi loin qu'elle pouvait le conduire." BIOT. OPACITY OF TRANSPARENT MIXTURES. 39 really is. The lifting up of the lower surface of a glass cube, through this cause, is very remarkable. 132. To understand why the water appears shallower, fix your attention on a point at its bottom, and suppose the line of vision from that point to the eye to be perpen- dicular to the surface of the water. Of all rays issuing from the point, the perpendicular one alone reaches the eye without refraction. Those close to the perpendicular, on emerging from the water, have their divergence augmented by refraction. Producing these divergent rays backward, they intersect at a point above the real bottom, and at this point the bottom will be seen. 133. The apparent shallowness is augmented by looking obliquely into the water. 134. In consequence of this apparent rise of the bottom, a straight stick thrust into the water is bent at the surface from the perpendicular. Note the difference between the deportment of the stick and of a luminous beam. The beam on entering the water is bent toward the perpendicular. 135. This apparent lifting of the bottom when water is poured into a basin brings into sight an object at the bot- tom of the basin which is unseen when the basin is empty. Opacity of Transparent Mixtures. 136. Reflection always accompanies refraction; and if one of these disappear, the other will disappear also. A solid body immersed in a liquid having the same refractive index as the solid, vanishes ; it is no more seen than a por- tion of the liquid itself of the same size would be seen. 137. But in the passage from one medium to another of a different refractive index, light is always reflected ; and this reflection may be so often repeated as to render the mixture of two transparent substances practically im- 40 NOTES ON LIGHT. pervious to light. It is the frequency of the reflections at the limiting surfaces of air and water that renders foam opaque. The blackest clouds owe their gloom to this re- peated reflection, which diminishes their transmitted light. Hence also their whiteness by reflected light. To a similar cause is due the whiteness and imperviousiiess of common salt, and of transparent bodies generally when crushed to powder. The individual particles transmit light freely; but the reflections at their surfaces are so numerous that the light is wasted in echoes before it can reach to any depth in the powder. 138. The whiteness and opacity of writing-paper are due mainly to the same cause. It is a web of transparent fibres, not in optical contact, which intercept the light by repeatedly reflecting it. 139. But if the interstices of the fibres be filled by a body of the same refractive index as the fibres themselves, the reflection at their limiting surfaces is destroyed, and the paper is rendered transparent. This is the philosophy of the tracing-paper used by engineers. It is saturated with some kind of oil, the lines of maps and drawings being easily copied through it afterward. Water aug- ments the transparency of paper, as it darkens a white towel ; but its refractive index is too low to confer on either any high degree of transparency. It, however, renders certain minerals, which are opaque when dry, translucent. 140. The higher the refractive index the more copious is the reflection. The refractive index of water, for ex- ample, is 1.336; that of glass is 1.5. Hence the different quantities of light reflected by water and glass at a per- pendicular incidence, as mentioned in note 60. It is its enormous refractive strength that confers such brilliancy upon the diamond. TOTAL REFLECTION. 41 Total Reflection. Read notes 123 and 124 ; then continue here. 141. When the angle of incidence from air into water is nearly 90, that is to say, when the ray before entering the water just grazes its surface, the angle of refraction is "48^. Conversely, when a ray passing from water into air strikes the surface at an angle of 48J- , it will, on its emer- gence, just graze the surface of the water. 142. If the angle which the ray in water encloses with the perpendicular to the surface be greater than 48-|-, the ray will not quit the water at all : it will be totally reflected at the surface. 143. The angle which marks the limit where total re- flection begins is called the limiting angle of the medium. For water this angle is 48 27', for flint glass it is 38 41', while for diamond it is 23 42'. 144. Realize clearly that a bundle of light rays filling an angular space of 90 before they enter the water, are squeezed into an angular space of 48 27' within the water, and that in the case of diamond the condensation is from 90 to 23 42'. 145. To an eye in still water its margin must appear- lifted up. A fish, for example, sees objects, as it were, through a circular aperture of about 97 (twice 47 27') in diameter overhead. All objects down to the horizon will be visible in this space, and those near the horizon will be much distorted and contracted in dimensions, especially in height. Beyond the limits of this circle will be seen the bottom of the water totally reflected, and therefore de- picted as vividly as if seen by direct vision.* 146. A similar effect, exerted by the atmosphere (when 16 Sir John Hcrschcl. 42 NOTES ON LIGHT. no clouds cross the orbs), gives the sun and moon at rising and setting a slightly flattened appearance. 147. Experimental Illustrations. Place a shilling in a drinking-glass ; cover it with water to about the depth of an inch, and tilt the glass so as to obtain the necessary obliquity of incidence at the surface. Looking upward toward the surface, the image of the shilling will be seen shining there, and, as the reflection is total, the image will be as bright as the shilling itself. A spoon suitably dipped into the glass also yields an image due to total re- flection. 148. Thrust the closed end of an empty test-tube into a glass of water. Incline the tube, until the horizontal light falling upon it shall be totally reflected upward. When looked down upon, the tube appears shining like burnished silver. Pour a little water into the tube : as the liquid rises, it abolishes total reflection, and with it the lustre, leaving a gradually diminishing lustrous zone, which disappears wholly when the level of the water within rises to, or above, that of the water without. A tube of any kind stopped water-tight will answer for this experiment, which is both beautiful and instructive. 149. If a ray of light fall as a perpendicular on the side of a right-angled isosceles glass prism, it will enter the glass and strike the hypothenuse at an angle of 45. This exceeds the limiting angle of glass ; the ray will therefore be totally reflected ; and, in accordance with the law mentioned in note 54, the direct and reflected rays will be at right angles to each other. When such a change of direction is required in optical instruments, a right- angled isosceles prism is usually employed. 150. When the ray enters the prism parallel to the hypothenuse, it will be refracted, and will strike the hy- pothenuse at an angle greater than the limiting angle. It TOTAL REFLECTION. 43 will, therefore, be totally reflected. If the object, instead of being a point, be of sensible magnitude, the rays from its extremities will cross each other within the prism, and hence the object will appear inverted when looked at through the prism. Dove has applied the " reversion prism " to render erect the inverted images of the astronomical telescope. 151. The mirage of the desert and various other phan- tasmal appearances in the atmosphere are, in part, due to total reflection. When the sun heats an expanse of sand, the layer of air in contact with the sand becomes lighter than the superincumbent air. The rays from a distant object, a tree for example, striking very obliquely upon the upper surface of this layer, may be totally reflected, thus showing images similar to those produced by a sur- face of water. The thirsty soldiers of the French army were tantalized by such appearances in Egypt. 152. Gases, like liquids and solids, can refract and re- flect light ; but, in consequence of the lowness of their refractive indices, both reflection and refraction are feeble. Still, atmospheric refraction has to be taken into account by the astronomer, and by those engaged in trigonomet- rical surveys. The refraction of the atmosphere causes the sun to be seen before it actually rises, and after it act- ually sets. 153. The quivering of objects seen through air rising over a heated surface is due to irregular refraction, which incessantly shifts the directions of the rays of light. In the air this shifting of the rays is never entirely absent, and it is often a source of grievous annoyance to the astronomer who needs a homogeneous atmos- phere. 154. The flame of a candle or of a gas-lamp, and the column of heated air above the flame ; the air rising from 44 NOTES ON LIGHT. a red-hot iron ; the pouring of a heavy gas, such as car- bonic acid, downward into air; and the issue of a lighter one, such as hydrogen, upward may all be made to reveal themselves by their action upon a sufficiently in- tense light. The transparent gases interposed between such a light and a white screen are seen to rise like smoke upon the screen through the effects of refraction. Lenses. 155. A lens in optics is a portion of a refracting sub- stance, such as glass, which is bounded by curved sur- faces. If the surface be spherical, the lens is called a spherical lens. 156. Lenses divide themselves into two classes, one of which renders parallel rays convergent, the other of which renders such rays divergent. Each class comprises three kinds of lenses, which are named as follows : Converging Lenses. 1. Double convex, with both surfaces convex. 2. Plano-convex, with one surface plane and the other convex. 3. Concavo-convex (Meniscus), with a concave and a convex surface, the convex surface being the most strongly curved. Diverging Lenses. 1. Double concave, with both surfaces concave. 2. Plano-concave, with one surface plane and the other concave. 3. Convexo-concave, with a convex and a concave surface, the concave surface being the most strongly curved. LENSES. 45 157. A straight line drawn through the centre of the lens, and perpendicular to its two convex surfaces, is the principal axis of the lens. 158. A luminous beam falling on a convex lens parallel to the axis, has its constituent rays brought to intersec- tion at a point in the axis behind the lens. This point is the principal focus of the lens. As before, the principal focus is the focus of parallel rays. 159. The rays from a luminous point placed beyond the focus intersect at the opposite side of the lens, an image of the point being formed at the place of intersec- tion. As the point approaches the principal focus its image retreats from it, and when the point actually reaches the principal focus, its image is at an infinite distance. 160. If the principal focus be passed, and the point come between that focus and the lens, the rays after pass- ing through the lens will be still divergent. Producing them backward, they will intersect on that side of the lens on which stands the luminous point. The focus here is virtual. A body of sensible magnitude placed between the focus and the lens would have a virtual image. 161. When an object of sensible dimensions is placed anywhere beyond the principal focus, a real image of the object will be formed in the air behind the lens. The image maybe either greater or less than the object in size, but the image will always be inverted. 162. The .positions of the image and the object are, as before, convertible. 163. In the case of concave lenses the images are al- ways virtual. 164. A spherical lens is incompetent to bring all the rays that fall upon it to the same focus. The rays which pass through the lens near its circumference are more 46 NOTES ON LIGHT. refracted than those which pass through the central por- tions, and they intersect earlier. Where perfect definition is required it is therefore usual, though at the expense of illumination, to make use of the central rays only. 165. This difference of focal distance between the cen- tral and circumferential rays is called the spherical aberra- tion of the lens. A lens so curved as to bring all rays to the same focus is called aplanatic / a spherical lens cannot be rendered aplanatic. 166. As in the case of spherical mirrors, spherical lenses have their caustic curves and surfaces (diacaustics) formed by the intersection of the refracted rays. "Vision and the Eye. 167. The human eye is a compound lens, consisting of three principal parts : the aqueous humor, the crystal- line lens, and the vitreous humor. 1C 8. The aqueous humor is held in front of the eye by the cornea, a transparent, horny capsule, resembling a watch-glass in shape. Behind the aqueous humor, and immediately in front of the Crystalline lens, is the iris, which surrounds the pupil. Then follow the lens and the vitreous humor, which last constitutes the main body of the eye. The average diameter of the human eye is 10.9 lines.* 169. When the optic nerve enters the eye from behind, .it divides into a series of filaments, which are woven to- gether to form the retina, a delicate net-work spread as a screen at the back of the eye. The retina rests upon a black pigment, which reduces to a minimum all internal reflection. 1*70. By means of the iris the size of the pupil may be caused to vary within certain limits. When the light is * A line is -^ th of an inch. VISION AND THE EYE. 47 feeble the pupil expands, 'when it is intense the pupil con- tracts ; thus the quantity of light admitted into the eye is, to some extent, regulated. The pupil also diminishes when the eye is fixed upon a near object, and expands when it is fixed upon a distant one. 171. The pupil appears black; partly because of the ' internal black coating, but mainly for another reason. Could we illuminate the retina, and see at the same time the illuminated spot, the pupil would appear bright. But the principle of reversibility, so often spoken of, comes into play here. The light of the illuminated spot in re- turning outward retraces its steps, and finally falls upon the source of illumination. Hence, to receive the return- ing rays, the observer's eye ought to be placed between the source and the retina. But in this position it would cut off the illumination. If the light be thrown into the eye by a mirror pierced with a small orifice, or with a small portion of the silvering removed, then the eye of the observer placed behind the mirror, and looking through the orifice, may see the illuminated retina. The pupil under these circumstances glows like a live coal. This is the principle of the Ophthalmoscope (Augenspiegel, Helin- holtz), an instrument by which the interior of the eye may be scanned, and its condition in health or disease noted. 172. In the case of albinos, or of white rabbits, the black pigment is absent, and the pupil is seen red by light which passes through the sclerotica, or white of the eye. When this light is cut off, the pupil of an albino appears black. In some animals the black pigment is displaced by a reflecting membrane, the tapetum. It is the light reflected from the tapetum which causes a cat's eye to shine in partial darkness. The light in this case is not internal, for when the darkness is total the cat's eyes do not shine. 48 NOTES ON LIGHT. 173. In the camera obscura'of the photographer the images of external objects formed by a convex lens are received upon a plate of ground glass, the lens being pushed in or out until the image upon the glass is sharply defined. 174. The eye is a camera obscura, with its refracting lenses, the retina playing the part of the plate of ground glass in the ordinary camera. For perfectly distinct vision it is necessary that the image upon the retina should be perfectly defined ; in other words, that the rays from every point of the object looked at should be converged to a point upon the retina. 175. The image upon the retina is inverted. Adjustment of the Eye : Use of Spectacles. 176. If the letters of a book held at some distance from the eye be looked at through a gauze veil placed nearer the eye, it will be found that when the letters are seen distinctly, the veil is seen indistinctly ; conversely, if the veil be seen distinctly, the letters will be seen indistinct- ly. This demonstrates that the images of objects at dif- ferent distances from the eye cannot be defined at the same time upon the retina. 177. Were the eye a rigid mass, like a glass lens, in- capable of change of form, distinct vision would only be possible at one particular distance. We know, however, that the eye possesses a power of adjustment for different distances. This adjustment is effected, not by pushing the front of the eye backward or forward, but by chan- ging the curvature of the crystalline lens. 178. The image of a candle reflected from the forward or backward surface of the lens is seen to diminish when the eye changes from distant to near vision, thus proving ADJUSTMENT OF THE EYE: USE OF SPECTACLES. 49 ' .. the curvature of the lens to be greater for near than for distant vision. 179. The principal refraction endured by rays of light in crossing the eye occurs at the surface of the cornea, where the passage is from air to a much denser medium. The refraction at the cornea alone would cause the rays to intersect at a point nearly half an inch behind the retina. The convergence is augmented by the crystalline lens, which brings the point of intersection forward to the retina itself. 180. A line drawn through the centre of the cornea and the centre of the whole eye to the retina is called the axis of the eye. The length of the axis, even in youth, is sometimes too small ; in other words, the retina is some- times too near the cornea ; so that the refracting part of the organ is unable to converge the rays from a luminous point so as to bring them to a point upon the retina. In old age also the refracting surfaces of the eye are slightly flattened, and thus rendered incompetent to refract the rays sufficiently. In both these cases the image would be formed behind the retina, instead of upon it, and hence the vision is indistinct. 181. The defect is remedied by holding the object at a distance from the eye, so as to lessen the divergence of its rays, or by placing in front of the eye a convex lens, which helps the eye to produce the necessary convergence. This is the use of spectacles. 182. The eye is also sometimes too long in the direc- tion of the axis, or the curvature of the refracting surfaces may be too great. In either case the rays entering the pupil are converged so as to intersect before reaching the retina. This defect is remedied either by holding the object very close to the eye, so as to augment the divergence of its rays, thus throwing back the point of intersection ; or 3 50 NOTES ON LIGHT. by placing in front of the eye a concave lens, which pro- duces the necessary divergence. 183. The eye is not adjusted at the same time for equally-distant horizontal and vertical objects. The dis- tance of distinct vision is greater for horizontal lines than for vertical ones. Draw with ink two lines at right angles to each other, the one vertical, the other horizontal : see one of them distinctly black and sharp ; the other appears indistinct, as if drawn in lighter ink. Adjust the eye for this latter line, the former will then appear indistinct. This difference in the curvature of the eye in two direc- tions may sometimes become so great as to render the application of cylindrical lenses necessary for its correc- tion. The Punctum Ccecum. 184. The spot where the optic nerve enters the eye, and from which it ramifies to form the net-work of the retina, is insensible to the action of light. An object whose image falls upon that spot is not seen. The image of a clock- face, of a human head, of the moon, may be caused to fall upon this " blind spot," and when this is the case the object is not visible. 185. To illustrate this point, proceed thus : Lay two white wafers on black paper, or two black ones on white paper, with an interval of 3 inches between them. Bring the right eye at a height of 10 or 11 inches exactly over the left-hand wafer, so that the line joining the two eyes shall be parallel to the line joining the two wafers. Closing the left eye, and looking steadily with the right at the left-hand wafer, the right-hand one ceases to be visible. In this position the image falls upon the " blind spot " of the right eye. If the eye be turned in the least degree to the right or left, or if the distance between it and the paper PERSISTENCE OF IMPRESSIONS. 51 be augmented or diminished, the wafer is immediately seen. Preserving these proportions as to size and distance, objects of far greater dimensions than the wafer may have their images thrown upon the blind spot, and be obliter- ated. Persistence of Impressions. 186. An impression of light once made upon the retina does not subside instantaneously. An electric spark is sensibly instantaneous ; but the impression it makes upon the eye remains for some time after the spark has passed away. This interval of persistence varies with different persons, and amounts to a sensible fraction of a second. 187. If, therefore, a succession of sparks follow each other at intervals less than the time which the impression endures, the separate impressions will unite to form a con- tinuous light. If a luminous point be caused to describe a circle in less than this interval, the circle will appear as a continuous closed curve. From this cause, also, the spokes of a rapidly-rotating wheel blend together to a shadowy surface. Wheatstone's Photometer is based on this persistence. It also explains the action of those instru- ments in which a series of objects in different positions being brought in rapid succession before the eye, the im- pression of motion is produced. 188. A jet of water descending from an orifice in the bottom of a vessel exhibits two distinct parts : a tranquil pellucid portion near the orifice, and a turbid or untranquil portion lower down. Both parts of the jet appear equally continuous. But when the jet in a dark room is illumi- nated by an electric spark, all the turbid portion reveals itself as a string of separate drops standing perfectly still. It is their quick succession that produces the impression of continuity. , The most rapid cannon-ball, illuminated by 52 NOTES ON LIGHT. a flash of lightning, would be seen for the fraction of a second perfectly motionless in the air. 189. The eye is by no means a perfect optical instru- ment. It suffers from spherical aberration; a scattered luminosity, more or less strong, always surrounding the defined images of luminous objects upon the retina. By this luminosity the image of the object is sensibly increased in size ; but with ordinary illumination the scattered light is too feeble to be noticed. When, however, bodies are intensely illuminated, more especially when the bodies are small, so that a slight extension of their images upon the retina becomes noticeable, such bodies appear larger than they really are. Thus, a platinum- wire raised to whiteness by a voltaic current has its apparent diameter enormously increased. Thus also the crescent moon seems to belong to a larger sphere than the dimmer mass of the satellite which it partially clasps. Thus also, at considerable dis- tances, the parallel flashes sent from a number of separate lamps and reflectors in a light-house encroach upon each other, and blend together to a single flash. The white- hot particles of carbon in a flame f a Bunsen's burner is rendered a brilliant yellow by the metal sodium, or by any vola- tilizible compound of that metal, such as chloride of sodium or common salt. The flame is rendered green by copper, purple by zinc, and red by strontian. 281. These colors are due to the vapors of the metals which are liberated in the flame. 282. When such incandescent metallic vapors are ex- amined by the prism, it is found that instead of emitting rays which form a continuous spectrum, one color passing gradually into another, they emit distinct groups of rays of definite, but different refrangibilities. The spectrum corresponding to these rays is a series of colored bands, separated from each other by intervals of darkness. Such bands are characteristic of luminous gases of all kinds. 283. Thus the spectrum of incandescent sodium-vapor consists of a brilliant band on the confines of the orange and yellow ; and the vapor is incompetent to shed forth any of the other light of the spectrum. When this band is more accurately analyzed it resolves itself into two dis- tinct bands ; greater delicacy of analysis resolves it into a group of bands with fine dark intervals between them. The spectrum of copper-vapor is signalized by a series of green bands, while the incandescent vapor of zinc produces brilliant bands of blue and red. 284. The light of the bands produced by metallic vapors is very intense, the whole of the light being con- centrated into a few narrow strips, and escaping in a great measure the dilution due to dispersion. 285. These colored bands are perfectly characteristic FURTHER DEFINITION OF RADIATION, ETC. 75 of the vapor ; from their position and number the sub- stance that produces them can be unerringly inferred. 286. If two or more metals be introduced into the flame at the same time, prismatic analysis reveals the bands of each metal as if the others were not there. This is also true when a mineral containing several metals is intro- duced into the flame. The constituent metals of the min- eral will give each its characteristic bands. 287. Hence, having made ourselves acquainted with the bands produced by all known metals, if entirely new bands show themselves, it is a proof that an entirely new metal is present in the flame. It is thus that Bunsen and KirchhofF, the founders of spectrum analysis, discovered Rubidium and Caesium ; and that Thallium, with its superb green band, was discovered by Mr. Crookes. 288. The permanent gases when heated to a sufficient temperature, as they may be by the electric discharge, also exhibit characteristic bands in their spectra. By these bands they may be recognized, even at stellar dis- tances. 289. The action of light upon the eye is a test of un,- rivalled delicacy. In specti*um analysis this action is brought specially into play; hence the power of this method of analysis.* Further Definition of Radiation and Absorption. 290. The terms ray, radiation, and absorption, were employed long prior to the views now entertained regard- * Many persons are incompetent to distinguish one color of the spec- trum from another ; red and green, for example, are often confounded. Dalton, the celebrated founder of the Atomic Theory, could only distin- guish by their form ripe red cherries from the green leaves of the tree. This point is now attended to in the choice of engine-drivers, who have to distinguish one colored signal from another. The defect is called color-blindness, and sometimes Daltonism. 76 NOTES ON LIGHT. ing the nature of light. It is necessary more clearly to understand the meaning attached by the undulatory theory to those terms. 291. And to complete our knowledge it is necessary to know that all bodies, whether luminous or non-luminous, are radiants ; if they do not radiate light they radiate heat. 292. It is also necessary to know that luminous rays are also heat rays ; that the self-same waves of ether falling on a thermometer produce the effects of heat ; and im- pinging upon the retina produce the sensation of light. The rays of greatest heat, however, as already explained, lie entirely without the visible spectrum. 293. The radiation both of light and heat consists in the communication of motion from the vibrating atoms of bodies to the ether which surrounds them. The ab- sorption of heat consists in the acceptance of motion, on the part of the atoms of a body, from ether which has been already agitated by a source of light or heat. In radia- tion, then, motion is yielded to the ether ; in absorption, motion is received from the ether. 294. When a ray of light or of heat passes through a body without loss ; in other words, when the waves are transmitted through the ether which surrounds the atoms of the body, without sensibly imparting motion to the atoms themselves, the body is transparent. If motion be in any degree transferred from the ether to the atoms, in that degree is the body opaque. 295. If either light or radiant heat be absorbed, the absorbing body is ic armed / if no absorption takes place, the light or radiant heat, whatever its intensity may be, passes through the body without affecting its tempera- ture. 296. Thus in the dark foci referred to in Note 246, or THE PURE SPECTRUM: FRAUXHOFER'S LINES. 77 in the focus of the most powerful burning mirror which concentrates the beams of the sun, the air might be of a freezing temperature, because the absorption of the heat by the air is insensible. A plate of clear rock-salt, more- over, placed at the focus, is scarcely sensibly heated, the absorption being small ; while a plate of glass is shivered, and a plate of blackened platinum raised to a white heat, or even fused, because of their powers of absorption. 297. It is here worth remarking that calculations of the temperatures of comets, founded on their distances from the sun> may be, and probably are, entirely fal- lacious. The comet, even when nearest to the sun, might be intensely cold. It might carry with it round its perihelion the chill of the most distant regions of space. If transparent to the solar rays it would be unaffected by the solar heat, as long as that heat maintained the radiant form. The Pure Spectrum : Fraunhofer^ s Lines. 298. When a beam of white light issuing from a slit is decomposed, the spectrum really consists of a series of colored images of the slit placed side by side. If the slit be wide, these images overlap but in a pure spectrum the colors must not overlap each other. 299. A pure spectrum is obtained by making the slit through which the decomposed beam passes very narrow, and by sending the beam through several prisms in suc- cession, thus augmenting the dispersion. 300. When the light of the sun is thus treated, the solar spectrum is found to be not perfectly continuous ; across it are drawn innumerable dark lines, the rays cor- responding to which are absent. Dr. Wollaston was the first to observe some of these lines. They were afterward studied with supreme skill by Fraunhofer, who lettered 78 NOTES ON LIGHT. them and made accurate maps of them, and from him they have been called Fraunhofer^ s lines. Reciprocity of Radiation and Absorption. 301. To account for the missing rays of the lines of Fraunhofer was long an enigma with philosophers. By the genius of Kirchhoff the enigma was solved. Its solu- tion carried with it a new theory of the constitution of the sun, and a demonstration of a method which enables us to determine the chemical composition of the sun, the stars, and the nebulae. The application of Kirchhoff's principles by Messrs. Huggins, Miller, Secchi, Janssen, and Lockyer, has been of especial interest and importance. 302. Kirchhoff's explanation of the lines of Fraunhofer is based upon the principle that every body is specially opaque to such rays as it can itself emit when rendered incandescent. 303. Thus the radiation from a carbonic-oxide flame, which contains carbonic acid at a high temparature, is in- tercepted in an astonishing degree by carbonic acid. If the rays from a sodium flame be sent through a second sodium flame, they will be stopped with particular energy by the second flame. The rays from incandescent thal- lium vapor are intercepted by thallium vapor, those from lithium vapor by lithium vapor, and so of the other metals. 304. In the language of the undulatory theory, waves of ether are absorbed with special energy their motion is taken up with special facility by atoms whose periods of vibration synchronize with the periods of the waves. This is another way of stating that a body absorbs with special energy the rays which it can itself emit. 305. If a beam of white light be sent through the in- tensely yellow flame of sodium vapor, the yellow con- RECIPROCITY OF RADIATION AND ABSORPTION. 79 stituent of the beam is intercepted by the flame, while rays of other refrangibilities are allowed free transmission. 306. Hence, when the spectrum of the electric light is thrown upon a white screen, the introduction of a sodium flame into the path of the rays cuts off the yellow compo- nent of the light, and the spectrum is furrowed by a dark band in place of the yellow. 307. Introducing other flames in the same manner in the path of the beam, if the quantity of metallic vapor in the flame be sufficient, each flame will cut out its own bands. And if the flame through which the light passes contain the vapors of several metals, we shall have the dark char- acteristic bands of all of them upon the screen. 308. Expanding in idea our electric light until it forms a globe equal to the sun in size, and wrapping round this incandescent globe an atmosphere of flame, that atmos- phere would cut off those rays of the globe which it can itself emit, the interception of the rays being declared by dark lines in the spectrum. 309. We thus arrive at a complete explanation of the lines of Fraunhofer, and a new theory of the constitution of the sun. The orb consists of a solid or molten nucleus, in a condition of intense incandescence, but it is sur- rounded by a gaseous photosphere containing vapors which absorb those rays of the nucleus which they them- selves emit. The lines of Fraunhofer are thus produced. 310. The lines of Fraunhofer are narrow bands of partial darkness ; they are really illuminated by the light of the gaseous envelope of the sun. But this is so feeble in comparison with the light of the nucleus intercepted by the envelope, that the bands appear dark in comparison with the adjacent brilliance. 311. Were the central nucleus abolished, the bands of Fraunhofer on a perfectly darlt ground would be trans- 80 NOTES ON LIGHT. formed into a series of bright bands. These would re- semble the spectra obtained from a flame charged with metallic vapors. They would constitute the spectrum of the solar atmosphere. 312. It is not necessary that the photosphere should be composed of pure vapor. Doubtless it contains vast masses of incandescent cloudy matter, composed of white hot molten particles. These intensely luminous white hot clouds may be the main origin of the light which the earth receives from the sun, and with them the true vapor of the photosphere may be more or less confusedly mingled. But the vapor which produces the lines of Fraunhofer musjb exist outside the clouds, as assumed by Kirchhoff. Solar Chemistry. 313. From the dark bands of the spectrum we can de- termine what substances enter into the composition of the solar atmosphere. 314. One example will illustrate the possibility of this. Lot the light from the sun and the light from incandes- cent sodium vapor pass side by side through the same slit, and be decomposed by the same prism. The solar light will produce its spectrum, and the sodium light its yellow band. This yellow band will coincide exactly in position with a characteristic dark band of the solar spectrum, which Fraunhofer distinguishes by the letter r>. 315. Were the solar nucleus absent, and did the va- porous photosphere alone emit light, the dark line D would be a bright one. Its character and position prove it to be the light emitted by sodium. This metal, therefore, is contained in the atmosphere of the sun.* * By reference to note 283 it will be seen that the sodium line is resolved by delicate analysis into a group of lines. The Fraunhofer dark band D is similarly resolved. It ought to be mentioned that both PLANETARY CHEMISTRY. 81 316. The result is still more convincing when a metal which gives a numerous series of bright bands finds each of its bands exactly coincident with a dark band of the solar spectrum. By this method Kirchhoff, to whom we owe, in all its completeness, this splendid generalization, established the existence of iron, calcium, magnesium, sodium, chromium, and other metals, in the solar atmos- phere ; and Mr. Huggins has extended the application of the method to the light of the planets, fixed stars, and nebulas.* Planetary Chemistry. 317. The light reflected from the moon and planets is solar light ; and, if unaffected by the planet's atmosphere, the spectrum of the planet would show the same lines as the solar spectrum. 318. The light of the moon shows no other lines. There is no evidence of an atmosphere round the moon. 319. The lines in the spectrum of Jupiter indicate a powerful absorption by the atmosphere of this planet. The atmosphere of Jupiter contains some of the gases or vapors present in the earth's atmosphere. Feeble lines, some of them identical with those of Jupiter, occur in the spectrum of Saturn. 320. The lines characterizing the atmospheres of Jupiter and Saturn are not present in the spectrum of Mars. The blue portion of the spectrum is mainly the seat of absorp- tion ; and this, by giving predominance to the red rays, may be the cause of the red color of Mars. 321. All the stronger lines of the solar spectrum are found in the spectrum of Venus, but no additional lines. Mr. Talbot and Sir John Herschel clearly foresaw the possibility of em- ploying spectrum analysis in detecting minute traces of bodies. * Prof. Stokes foresaw the possible application of spectrum analysis to solar chemistry. 82 NOTES OX LIGHT. Stellar Chemistry. 822. The atmosphere of the star Aldebaran contains hydrogen, sodium, magnesium, calcium, iron, bismuth, tellurium, antimony, mercury. The atmosphere of the star Alpha in Orion contains sodium, magnesium, calcium, iron, and bismuth. 323. No star sufficiently bright to give a spectrum has been observed to be without lines. Star differs from star only in the grouping and arrangement of the numerous fine lines by which their spectra are crossed. 324. The dark absorption lines are strongest in the spectra of yellow and red stars. In white stars the lines, though equally numerous, are very poor and faint. 325. A comparison of the spectra of stars of different colors suggests that the colors of the stars may be due to the action of their atmospheres. Those constituents of the white light of the star on which the lines of absorption fall thickest are subdued, the star being tinted by the residual color. Father Secchi, of Rome, has studied the light of many hundreds of stars, and has divided them into four classes. Nebular Chemistry. 326. Some nebula3 give spectra of bright bands, others give continuous spectra. The light from the former ema- nates from intensely heated matter existing in a state of gas. This may in part account for the weakness of the light of these nebula?. 327. It is probable that two of the constituents of the gaseous nebulae are hydrogen and nitrogen. The Red Prominences and Envelope of the Sun. 328. Astronomers had observed during total eclipses of the sun vast red prominences extending from the solar THE RED PROMINENCES OF THE SUN. 83 . limb many thousand miles into space. The intense illumi- nation of the circumsolar region of our atmosphere masks, under ordinary circumstances, the red prominences. They are quenched, as it were, by excess of light. 329. But when, by the intervention of the dark body of the moon, this light is cut off, the prominences are dis- tinctly seen. 330. It was proved by Mr. De la Hue and others that the red matter of the prominences was wrapped round a large portion of the sun's surface. According to the observations of Mr. Lockyer, the red matter forms a com- plete envelope round the sun. 331. Examined by the spectroscope the matter of the prominences shows itself to be, for the most part, incan- descent hydrogen. With it are mixed the vapors of sodium and magnesium. 332. Mr. Janssen, in India, and Mr. Lockyer subse- quently, but independently, in England, proved that the bright bands of the prominences might be seen without the aid of a total eclipse. The explanation of this dis- covery is glanced at in Note 284, where the intensity of the bright bands of incandescent gases was referred to the practical absence of dispersion. 333. By sending the light, which under ordinary cir- cumstances masks the hydrogen bands, through a sufficient number of prisms, it may be dispersed, and thereby en- feebled in any required degree. When sufficiently en- feebled the undispersed light of the incandescent hydrogen dominates over that of the continuous spectrum. By going completely round the periphery of the sun Mr. Lockyer found this hydrogen atmosphere everywhere present, its depth, generally about 5,000 miles, being indicated by the length of its characteristic bright lines. Where the hydrogen ocean is shallow, the bright bands are short ; J^ 84 NOTES ON LIGHT. where the prominences rise like vast waves above the level of the ocean, the bright lines are long. The prominences sometimes reach a height of 70,000 miles. The Rainbow. 334. A beam of solar light, falling obliquely on the surface of a rain-drop, is refracted on entering the drop ; it is in part reflected at the back of the drop, and on emerging from the drop it is again refracted. 335. By these two refractions on entrance and on emergence the beam of light is decomposed, and it quits the drop resolved into its colored constituents. It is re- ceived by the eye of an observer who faces the drop and turns his back to the sun. 336. In general the solar rays, when they quit the drop, are divergent, and therefore produce but a feeble effect upon the eye. But at one particular angle the rays, after having been twice refracted and once reflected, issue from the drop almost perfectly parallel. They thus preserve their intensity like rays reflected from a parabolic mirror, and produce a corresponding effect upon the eye. The angle at which this parallelism is established varies with the refrangibility of the light. 337. Draw a line from the sun to the observer's eye and prolong this line beyond the observer. Conceive an- other line drawn from the eye enclosing an angle of 42 30' with the line drawn to the sun. The rain-drop struck by this second line will send to the eye a parallel beam of red light. Every other drop similarly situated, that is to say, every drop at an angular distance of 42 30' from the line drawn to the sun, will do the same. We thus obtain a circular hand of red light, forming part of the base of a cone, by which the eye of the observer is the apex. Because THE RAINBOW. 85 of the angular magnitude of the sun the width of this band will be half a degree. 338. From the eye of the observer conceive another line to be drawn enclosing an angle of 40 30' with the line drawn to the sun. A drop struck by this line will send along the line an almost perfectly parallel beam of violet light to the eye. All drops at the same angular distance will do the same, and we shall obtain a band of violet light of the same width as the red. These two bands con- stitute the limiting colors of the rainbow, and between them the bands corresponding to the other colors lie. 339. The rainbow is in fact a spectrum, in which the rain-drops play the part of prisms. The width of the bow from red to violet is about two degrees. The size of the arc visible at any time manifestly depends upon the posi- tion of the sun. The bow is grandest when it is formed by the rising or the setting sun. An entire semicircle is then seen by an observer on a plain, while from a mountain- top a still greater arc is visible. 340. The angular distances and the order of colors here given correspond to the primary bow, but in addition to this we usually see a secondary bow of weaker hues, and in which the order of the colors is that of the primary in- verted. In the primary the red band forms the convex surface of the arch ; it is the largest band ; in the second- ary the violet band is outside, the red forming the con- cavity of the bow. 341. The secondary bow is produced by rays which have undergone two reflections within the drop, as well as two refractions at its surface. It is this double internal reflection that weakens the color. In the primary bow the incident rays strike the upper hemisphere of the drop, and emerge from the lower one ; in the secondary bow the in- cident rays strike the lower hemisphere of the drop, emerge 86 NOTES ON LIGHT. from the upper one, and then cross the incident rays to reach the eye of the observer. The secondary bow is 3^ degrees wide, and it is 7 1 degrees higher than the primary. From the space between the two bows part of the light reflected from the anterior surfaces of the rain-drops reaches the eye ; but no light whatever that enters the rain-drops in this space is reflected to the eye. Hence this region of the falling shower is darkest. Interference of Light. 342. In wave-motion we must clearly distinguish the motion of the wave from, the motion of the individual par- ticles which at any moment constitute the wave. For while the wave moves forward through great distances, the individual particles of water concerned in its propaga- tion perform a comparatively short excursion to and fro. A sea-fowl, for example, as the waves pass it, is not car- ried forward, but moves up and down.* 343. Here, as in other cases, the distance through which the individual water" particles oscillate, or through which the fowl moves vertically up and down, is called the amplitude of the oscillation. 344. When light from, two different sources passes through the same ether, the waves from the one source must be more or less affected by the waves from the other. This action is most easily illustrated by reference to water- waves. 345. Let two stones be cast at the same moment into still water. Round each of them will spread a series of circular waves. Let us fix our attention on a point A in the water, equally distant from the two centres of disturb- ance. The first two crests of both systems of waves reach -_.- '* Strictly speaking, the water particles .describe closed curves, and not straight vertical lines. INTERFERENCE OF LIGHT. 87 this point at the same moment, and it is lifted by their joint action to twice the height that it would attain through the action of either wave taken singly. 346. The first depression, or sinus as it is called, of the one system of waves also reaches the point A at the same moment as the first sinus of the other, and through their joint action the point is depressed to twice the depth that it would attain l)y the action of either sinus taken singly. 347. What is true of the first crest and the first de- pression is also true of all the succeeding ones. At the point A the successive crests will coincide, and the suc- cessive depressions will coincide, the agitation of the point being twice what it would be if acted upon by one only of the systems of waves. 348. The length of a wave is the distance from any crest, or any sinus, to the crest or sinus next preceding or succeeding. In the case of the two stones dropped at the same moment into still water, it is manifest that the coin- cidence of crest with crest and of sinus with sinus would also take place if the distance from the one stone to the point A exceeded the distance of the other stone from the same point by a whole wave-length. The only difference would be, that the second wave of the nearest stone would then coincide with the first wave of the most distant one. The one system of waves would here be retarded a whole wave-length behind the other system. 349. A little reflection will also make it clear that coincidence of crest with crest and of sinus with sinus will also occur at the point A when the retardation of the one system behind the other amounts to any number of ichole wave-lengths. 350. But if we suppose the point A to be half a wave- length more distant from the one stone than from the other, then as the waves pass the point A the crests of one 88 NOTES ON LIGHT. of the systems will always coincide with the sinuses of the other. When a wave of the one system tends to elevate the point A, a wave from the other system will, at the same moment, tend to depress it. As a consequence the point will neither rise nor sink, as it would do if acted upon by either system of waves taken singly. The same neutralization of motion occurs where the difference of path between the two stones and the point A amounts to any odd number of half wave-lengths. 351. Here, then, by adding motion to motion, we abolish motion and produce rest. In precisely the same way we can, by adding sound to sound, produce silence, one sys- tem of sound-waves being caused to neutralize another. So also by adding heat to heat we can produce cold, while by adding light to light we can produce darkness. It is this perfect identity of the deportment of light and radiant heat with the phenomena of wave-motion that constitutes the strength of tlie Theory of Undulation. 352. This action of one system of waves upon another, whereby the oscillatory motion is either augmented or diminished, is called Interference. In relation to optical phenomena it is called the Interference of Light. We shall henceforth have frequent occasion to apply this principle. Diffraction, or the Inflection of Light. 353. Newton, who was familiar with the idea of an ether, and indeed introduced it in some of his specula- tions, objected that if light were propagated by waves, shadows could not exist ; for that the waves would bend round opaque bodies, and abolish the shadows behind them. According to the wave theory this bending round of the w r aves actually occurs, but the different portions DIFFRACTION, OR THE INFLECTION OF LIGHT. 9 of the inflected waves destroy each other 'by their inter- ference. 354. This bending of the waves of light round the edges of opaque bodies, receives the name of Diffraction or In- flection (German, Beugung). We have now to consiclef some of the effects of diffraction. 355. And for this purpose it is necessary that our source of light should be a physical point or a fine line : for when an extensive luminous surface is employed, the effects of its different points in diffraction phenomena neutralize each other. 356. A. point of light may be obtained by converging, by a lens of short focus, the parallel rays of the sun, admitted through a small aperture into a dark room. The small image of the sun formed at the focus is here our luminous point. The image of the sun formed on the surface of a silvered bead, or indeed upon the convex fur- face of a glass lens, or of a watch-glass blackened within, also answers the purpose. 357. A line of light is obtained by admitting the sun- light through a slit, and sending the slice of light through a cylindrical lens. The rectangular beam is contracted to a physical line at the focus of the lens. A glass tube blackened within and placed in the light, reflects from its surface a luminous line which also answers the purpose. For many experiments, indeed, the circular aperture, or the slit itself, suffices without any condensation by a lens. 358. In the experiment now to be described, a slit of variable width is placed in front of the electric lamp, and this slit is looked at from a distance through another slit, also of variable aperture. The light of the lamp is ren- dered monochromatic by placing a pure red glass in front of the slit. 90 NOTES ON LIGHT. 359. With the eye placed in the straight line drawn through both slits from the incandescent carbon points of the electric lamp an extraordinary appearance is observed. Firstly, the slit in front of the lamp is seen as a vivid rectangle of light ; but right and left of it is a long series of rectangles, decreasing in vividness, and separated from each other by intervals of absolute darkness. 360. The breadth of the bands varies with the width of the slit placed in front of the eye. If the slit be widened, the images become narrower, and crowd more closely to- gether; if the slit be narrowed, the images widen and retreat from each other. 361. It may be proved that the width of the bands is inversely proportional to the width of the slit held in front of the eye. 362. Leaving every thing else unchanged, let a blue glass or a solution of ammonia sulphate of copper, which gives a very pure blue, be placed in the path of the light. A series of blue bands is thus obtained, exactly like the former in all respects save one; the blue rectangles are narrower^ and they are closer together, than the red ones. 363. If we employ colors of intermediate refrangibili- ties between red and blue, which we may do by causing the different colors of a spectrum to shine through the slit, we should obtain bands of color intermediate in width and occupying intermediate positions between those of the red and blue. Hence when white light passes through the slit the various colors are not superposed, and instead of a series of monochromatic bands, separated from each other by intervals of darkness, we have a series of colored spec- tra placed side by side, the most refrangible color of each spectrum being nearest to the slit. 364. When the slit in front of the camera is illuminated by a candle-flame, instead of the more intense electric light, DIFFRACTION, OR THE INFLECTION OF LIGHT. 01 substantially the same effects, though less brilliant, are observed. 365. What is the meaning of this experiment, and how are the lateral images of the slit produced ? Of these and certain accompanying results the emission theory is in- competent to offer any explanation. Let us see how they are accounted for by the theory of undulation. 366. For the sake of simplicity, we will consider the case of monochromatic light. Conceive a wave of ether advancing from the first slit toward the second, and finally filling the second slit. When the wave passes through the latter it not only pursues its direct course to the retina, but diverges right and left, tending to throw into motion the entire mass of the ether behind the slit. In fact, every point of the wave which Jills the slit is itself a centre of new wave-systems, which are transmitted in all directions through the ether behind the slit. We have now to examine how these secondary waves act upon each other. 367. First, let us regard the central rectangle of the series. It is manifest that the different parts of every transverse section of the wave, which in this case fills our slit, reach the retina at the same moment. They are in complete accordance, for no one portion is retarded in reference to any other portion. The rays thus coming direct from the source through the slit to the retina pro- duce the central band of the series. 368. But now let us consider those waves which diverse O obliquely from the slit. In this case, the waves from the two edges of the slit have, in order to reach the retina, to pass over unequal distances. Let us suppose the differ- ence in path of the two marginal rays to be a whole wave- length of the red light ; how must this difference affect the final illumination of the retina ? 92 NOTES ON LIGHT. 369. Fix your attention upon the particular ray or line of light that passes exactly through the centre of the slit to the retina. The difference of path between this central ray and the two marginal rays is, in the case here sup- posed, half a wave-length. The least reflection will make it clear that every ray on the one side of the central liue finds a ray upon the other side, from which its path differs by half an undulation, with which, therefore, it is in com- plete discordance. The consequence is that the light on the one side of the central line will completely abolish the light on the other side of that line, absolute darkness be- ing the result of their mutual extinction. The first darJc interval of our series of bands is thus accounted for. It is produced by an obliquity which causes the paths of the marginal rays to be a whole wave-length different from each other. 370. When the difference between the paths of the marginal rays is half a wave-length^ a partial destruction of the light is effected. The luminous intensity corre- sponding to this obliquity is a little less than one-half accurately 0.4 of that of the undiffracted light. 371. If the paths of the marginal rays be three semi-\ undulations different from each other, and if the whole beam be divided into three equal parts, two of these parts will completely neutralize each other, the third only being effective. Corresponding, therefore, to an obliquity which produces a difference of three semi-undulations in the marginal rays, we have a luminous band, but one of considerably less intensity than the undiffracted central band. 372. With a marginal difference of path of four semi- undulations we have a second extinction of the entire beam, a space of absolute darkness corresponding to this obliquity. In this way we might proceed further, the MEASUREMENT OF THE WAVES OF LIGHT. 93 general result being that, whenever the obliquity is such as to produce a marginal difference of path of an even number of semi-undulations, we have complete extinction ; while, when the marginal difference is an odd number of semi-undulations, we have only partial extinction, a por- tion of the beam remaining as a luminous band. 373. A moment's reflection will make it plain that the shorter the wave, the less will be the obliquity required to produce the necessary retardation. The maxima and minima of blue light must, therefore, fall nearer to the centre than the maxima and minima of red light. The maxima and minima of the other colors fall between these extremes. In this simple way the undulatory theory com- pletely accounts for the extraordinary appearance referred to in Note 359. When a slit and telescope are used, in- stead of the slit and naked eye, the effects are magnified and rendered more brilliant. Measurement of the Waves of Light. 374. We are now in a condition to solve the im- portant problem of measuring the length of a wave of light. 375. The first of our dark bands corresponds, as al- ready explained, to a difference of marginal path of one undulation ; our second dark band to a difference of path of two undulations ; our third dark band to a difference of three undulations, and so forth. With a slit 1.35 * mil- limetre wide, Schwerd found the angular distance of the first dark band from the centre of the field to be 1' 38". The angular distances of the other dark bands are twice, three times, four times, etc., this quantity, that is to say, they are in arithmetical progression. 376. Draw a diagram of the slit EC with the beam * The millimetre is about ^ of an inch. 94 NOTES ON LIGHT. passing through it at the obliquity corresponding to the first dark band. Let fall a perpendicular from one edge, E, of the slit on the marginal ray of the other edge at d. The distance, c d, between the foot of this perpendicular and the other ectge is the length of the wave of light. From the centre E, with the width E c as radius, suppose a semicircle to be described ; its radius being 1.35, the length of this semicircle is readily found to be 4.248 milli- metres. Now, the length of this semicircle is to the length cdof the wave as 180 to 1' 38", or as 648,000* to 98". Thus we have the proportion 648,000 : 98 :: 4.248 to the wave-length cd* Making the calculation, we find the wave-length for this particular kind of light (red), to be 0.000643 of a milli- metre, or 0.000026 of an inch. 377. Instead of receiving them directly upon the retina, the colored fringes may be received upon a screen. In this case it is desirable to employ a lens of considerable con- vergent power to bring the beam from the first slit to a focus, and to place the second slit or other diffracting edge or edges between the focus and the screen. The light in this case virtually emanates from the focus. 378. If the edge of a knife be placed in the beam paral? lei to the slit, the shadow of the edge upon the screen will be bounded by a series of parallel colored fringes. If the light be monochromatic the bands will be simply bright and dark. The back of the knife produces the same effect as its edge. A wooden or an ivory paper-knife produces precisely the same effect as a steel knife. The fringes are absolutely independent of the character of the substance round the edge of which the light is diffracted. * C d is so minute that it practically coincides with the circle drawn round E. MEASUREMENT OF THE WAVES OF LIGHT. 95 379. A thick wire placed in the beam lias colored fringes on each side of its shadow. If the wire be Jine, or if a human hair be employed, the geometric shadow itself will be found occupied by parallel stripes. The former are called the exterior fringes, the latter the interior fringes. In the hands of Young and Fresnel all these phenomena received their explanation as effects of interference. 380. A slit consists of two edges facing each other. When a slit is placed in the beam between the focus and the screen, the space between the edges is occupied by stripes of color. 381. Looking at a distant point of light through a small circular aperture the point is seen encircled by a series of colored bands. If monochromatic light be used these bands are simply bright and dark, but with white light the circles display iris-colors. 382. These results are capable of endless variation by varying the size, shape, and number of the apertures through which the point of light is observed. The street lamps at night, looked at through the meshes of a hand- kerchief, show diffraction phenomena. The diffraction effects obtained by Schwerd in looking through a bird's feathers are very gorgeous. The iridescence of Alpine clouds is also, an effect of diffraction.* * This may be imitated by the spores of Lycopodium. The diffrac- tion phenomena of " actinic clouds " are exceedingly splendid. One of the most interesting cases of diffraction by small particles that ever came before me was that of an artist whose vision was disturbed by vividly- colored circles. When he came to me he was in great dread of losing his sight ; assigning as a cause of his increased fear that the circles were becoming larger and the colors more vivid. I ascribed the colors to minute particles in the humors of the eye, and encouraged him by the assurance that the increase of size and vividness indicated that the dif- fracting particles were becoming smaller, and that they might finally be altogether absorbed. The prediction was verified. It is needless to say 96 NOTES ON LIGHT. 383. Following out the indications of theory, Poisson was led to the paradoxical result that in the case of an opaque circular disk the illumination of the centre of the shadow, caused by diffraction at the edge of the disk, is precisely the same as if the disk were altogether absent. This startling consequence of theory was afterward veri- fied experimentally by Arago. Colors of Thin Plates. 284. When a beam of monochromatic light say of pure red, which is most easily obtained by absorption falls upon a thin, transparent film, a portion of the light is reflected at the first surface of the film ; a portion enters the film, and is in part reflected at the second surface. 385. This second portion having crossed the film to and fro is retarded with reference to the light first reflected. The case resembles that of our two stones" dropped into still water at unequal distances from the point A (Note 345). 386. If the thickness of the film be such .as to retard the beam reflected from the second surface a whole wave- length, or any number of whole wave-lengths or, in other words, any even number of half wave-lengths the two reflected beams, travelling through the same ether, will be in complete accordance / they will therefore support each other, and make the film appear brighter than either of them would do taken singly. 387. But if the thickness of the film be such as to retard the beam reflected from the second surface half a wave- length, or any odd number of half- wave lengths, the two reflected beams will^c in complete discordance / and a destruction of light will follow. By the addition of light one word on the necessity of optical knowledge in the case of the prac- ticat oculist. COLORS OF THIN PLATES. 97 which has undergone more than one reflection at the second surface to the light which has undergone only one reflec- tion, the" beam reflected from the first surface may be totally destroyed. Where this total destruction of light occurs the film appears black. 388. If the film be of variable thickness, its various parts will appear bright or dark, according as the thick- ness favors the accordance or discordance of the reflected rays. 389. Because of the different lengths of the waves of light, the different colors of the spectrum require different thicknesses to produce accordance and discordance ; the longer the waves, the greater must be the thickness of the film. Hence those thicknesses which effect the extinction of one color will not effect the extinction of another. When, therefore, a film of variable thickness is illuminated by white light, it displays a variety of colors. 390. These colors are called the colors of thin plates. 391. The colors of the soap-bubble; of oil or tar upon water ; of tempered steel ; the brilliant colors of lead skim- mings ; ISTobili's metallo-chrome ; the flashing colors of certain insects' wings, are all colors of thin plates. The colors are produced by transparent films of all kinds. In the bodies of crystals we often see iridescent colors due to vacuous films produced by internal fracture. In cutting the dark ice under the moraines of glaciers internal frac- ture often occurs, and the colors of thin plates flash forth from the body of the ice with extraordinary brilliancy. 392. Newton placed a lens of small curvature in optical contact with a plane surface of glass. Between the lens and the surface he had a film of air, which gradually aug- mented in thickness from the point of contact outward. He thus obtained in monochromatic light a series of bright and dark rings, corresponding to the different thick- 5 98 NOTES ON LIGHT. nesses of the film of air, which produced alternate accord- ance and discordance. 393. The rings produced by violet he found to be smaller than those produced by red, while the rings pro- duced by the other colors fell between these extremes. Hence when white light is employed, " Newton's Rings " appear as a succession of circular bands of color. A far greater number of the rings is visible in monochromatic than in white light, because the differently-colored rings, after a certain thickness of film has been attained, become superposed and reblended to form white light. 394. Newton, considering the means at his disposal, measured the diameters of his rings with marvellous accuracy ; he also determined from its focal length and its refractive index the diameter of the sphere of which his lens formed a part. He found the squares of the diameters of his rings to be in arithmetical progression, and conse- quently that the thicknesses of the film of air correspond- ing to the diameters of the rings were also in arithmetical progression. 395. He determined the absolute thicknesses of the plates of air at which the rings were formed. Employing the most luminous rays of the spectrum, that is, the rays at the common boundary of the yellow and orange, he found the thickness corresponding to the first bright ring to be __V. APPLETON AND COMPANY. SYSTEM OF PHILOSOPHY I. FIKST PRINCIPLES. (New and Enlarged Edition.} PART I. THE UNKNOWABLE. PART II. LAWS OF THE KNOW ABLE. 659 pages. Price, . - - $2.53 II. THE PRINCIPLES OF BIOLOGY. VOL. I. PART I. THE DATA OP BIOLOGY. PART II. THE INDUCTIONS OF BIOLOGY. PART III. THE EVOLUTION OF LIFE. 475 pages. Price, $2.60 PRINCIPLES OF BIOLOGY. YOL. II. PART IV. MORPHOLOGICAL DEVELOPMENT. PART V. PHYSIOLOGICAL DEVELOPMENT. PART VI. LAWS OF MULTIPLICATION. 565 pages. Price, $2.50 III. THE PRINCIPLES OF PSYCHOLOGY. PART I. THE DATA OF PSYCHOLOGY. 144 pages. Price, - - $0.75 PART II. THE INDUCTIONS OF PSYCHOLOGY. 146 pages. Price, - $0.75 PART III. GENERAL SYNTHESIS. 100 pages. ) - . PART IV. SPECIAL SYNTHESIS. 112 pages. f Fnce > MISCELLANEOUS. I. ILLUSTRATIONS OF UNIVERSAL PROGRESS. THIRTEEN ARTICLES. 451 pages. Price, ..... $2.50 II. ESSAYS : MORAL, POLITICAL, AND ^ESTHETIC. TEN ESSAYS. 386 pages. Price, $2.50 III. 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"Personally and practically exercised in zoology, in minute anatomy, in geology ; a student of geographical distribution, not on maps and in museums only, but by long voyages and laborious collection ; having largely advanced each of these branches of science, and having spent many years in gathering and sifting materials for his present work, the store of accurately-registered facts upon which the author of the ' Origin of Species ' is able to draw at will is prodigious." Prof. T. H. HUXLEY. "Far abler men than myself may confess that they have not that imtiring patience in accumulating, and that wonderful skill in using, large masses of facts of the most varied kind that wide and accurate physiological knowl- edge that acuteness in devising, that skill in carrying out experiments, and that admirable style of composition, at once clear, persuasive, and judicial, qualities which, in their harmonious combination, mark out Mr. Darwin as the man, perhaps of all men now living, best fitted for the great work he has undertaken and accomplished." ALFRED RUSSELL WALLACE. In Germany these views are rapidly extending. Prof. GIEKIE, a distin- guished British geologist, attended the recent Congress of German Natural- ists and Physicians, at Innspruck, in which some eight hundred savants were present, and thus writes : "What specially struck me was the universal sway which the writings of Darwin now exercise over the German mind. You see it on every side, in private conversation, in printed papers, in all the many sections into which such a meeting as that at Innspruck divides. Darwin's name is often men- tioned, and always with the profoundest veneration. But even where no al- lusion is specially made to him, nay, even more markedly, where such allusion is absent, we see how thoroughly his doctrines have permeated the scientific mind, even in those departments of knowledge which might seem at first sight to be farthest from natural history. * You are still discussing in Eng- land,' said a German friend to me, * whether or not the theory of Darwin can be true. We have got a long way beyond that here. His theory is now our common starting-point.' And, so far as my experience went, I found it tc be so." 33. ^IPIT^EITON & CO.. THE DESCENT OF MAN, SELECTION IN RELATION TO SEX. BY CHAS. DARWIN, M, A., F. E, S. Two Vols., 12mo. PRICE, ..... $4.00 In these volumes Mr. Darwin has brought forward all the facts and arguments which science has to offer in favor of the doctrine that man has arisen by gradual development from the lowest point of animal life. He had originally intended this work as a posthumous publication, but the extensive acceptance of the views unfolded in his book on the " Origin of Species " induced him to believe that the public were ripe for the most advanced deductions from his theory of "Natural Selection." Aside from the logical purpose which Mr. Darwin had in view, his work is an original and fascinating contribution to the most interesting portion of natural history. From the London Spectator. "For our part, we find Dr. Darwin's vindication of the origin of man a far more wonderful vindication of Theism than Paley's ' Natural Theology,' though we do not know, so reticent is his style, whether or not he conceives it himsell." From the Citizen and Hound Table. 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" Whether you like his discourse or not though you may refuse to acquiesce in his conclusions still you are compelled to bear your witness, that this man ^as not been laboring to find facts to support a preconceived theory, but that the 'heory is tlie irrepressible outgrowth of his accumulated facts.' 1 '' From the Evening Bulletin. " This theory is now indorsed by many eminent scientists, who at first com- bated it, including Sir Charles Lyell, probably the most learned of living geolo- gists, and even by a class of Christian divines like Dr. McCosh, who think that certain theories of cosmogony, like the nebular hypothesis and the law of evolu- tion, may be accepted without doing violence to faith." , to any address in the U. S., on receipt of the price. D. APPLETON & CO., Publishers. THE ORIGIN OP CIVILIZATION ; OR, THE PRIMITIVE CONDITION OF MAN. By SIR JOHN LUBBOCK, Bart., M. P., F. R. S. 38O [Pages. Illustrated. 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Detroit Free Press. " This interesting and valuable volume illustrates, to some extent, the tray in which the modern scientific spirit manages to extract a considerable treasure from the chaff and refuse neglected or thrown aside by former in quirers." London Saturday Review. D. APPLETON & CO.-, Publishers. D. Appleton & Company^ Publications. LAY ADDEESSES, AND KEYIEWS, BY THOMAS HENRY HUXLEY. Cloth, 12mo. 380 pages. Price, $1.75 THIS is the latest and most popular of the works of this -in- trepid and accomplished English thinker. The American edition of the work is the latest, and contains, in addition to the English edition, Professor Huxley's recent masterly address on " Spon- taneous Generation," delivered before the British Association for the Advancement of Science, of which he was president. The following is from an able article in the Independent : The " Lay Sermons, Addresses, and Reviews " is a book to be read by every one who would keep up with the advance of truth as well by those who are hostile as those who are friendly to his conclusions. In it, scientific and philosophical topics are handled with consummate abil- ity. It is remarkable for purity of style and power of expression. No- where, in any modern work, is the advancement of the pursuit of that natural knowledge, which is of vital importance to bodily and mental well-being, so ably handled. Professor Huxley is undoubtedly the representative scientific man of the age. His reverence for the right and devotion to truth have estab- lished his leadership of modern scientific thought. He leads the beliefs and aspirations of the increasingly powerful body of the younger men of science. His ability for research is marvellous. 'There is possible no more equipoise of judgment than that to which he brings the phenomena of Nature. Besides, he is not a mere scientist. His is a popularized phi- losophy ; social questions have been treated by his pen in a manner most masterly. In his popular addresses, embracing the widest range of top- ics, he treads on ground with which he seems thoroughly familiar. There are those who hold the name of Professor Huxley as synony. mous with irreverence and atheism. Plato's was so held, and Galileo's, and Descartes's, and Newton's, and Faraday's. There can be no greater mistake. No man has greater reverence for the Bible than Huxley. No one more acquaintance with the text of Scripture. He believes there is definite government of the universe ; that pleasures and pains are distrib- uted in accordance with law ; and that the certain proportion of evil woven up hi the life even of worms will help the man "who thinks to bear his own share with courage. In the estimate of Professor Huxley's future influence upon science, his youth and health form a large element. He has just passed his forty- fifth year. If God spare his life, truth can hardly fail to be the gainer from a mind that is stored with knowledge of the laws of the Creator's operations, and that has learned to love all beauty and hate ail vileness of Nature and art. SPENCERS SYSTEM OF PHILOSOPHY. THE PHILOSOPHY OF EVOLUTION, By HERBERT SPENCER. This great system of scientific thought, the most original and important men- tal undertaking of the age, to which Mr. Spencer has devoted his life, is now well advanced, the published volumes being: First Principles, The Principles of Bi- ology, two volumes, and The Principles of Psychology , vol. i., which will be shortly printed. This philosophical system differs from all its predecessors in being solidly based on the sciences of observation and induction ; in representing the order and course of Nature ; in bringing Nature and man, life, mind, and society, under one great law of action ; and in developing a method of thought which may serve for practical guidance in dealing with the affairs of life. That Mr. Spencer is the man for this great work will be evident from the following statements : " The only complete and systematic statement of the doctrine of Evolution with which I am acquainted is that contained in Mr. Herbert Spencer's ' System of Philosophy ; ' a work which should be carefully studied by all who desire to know whither scientific thought is tending." T. H. HUXLEY. " Of all our thinkers, he is the one who has formed to himself the largest new scheme of a systematic philosophy." Prof. MASSON. " If any individual influence is visibly encroaching on Mills in this country, it is his." ma. "Mr. Spencer is one of the most vigorous as well as boldest thinkers that English speculation has yet produced." JOHN SXUAKT MILL. " One of the acutest metaphysicians of modern times." Ibid. " One of our deepest thinkers." Dr. JOSEPH D. HOOKEB. It is questionable if any thinker of finer calibre has appearc/l in our coun- try." GEORGE HENRY LEWES. "He alone, of all British thinkers, has organized a philosophy." Ibid. " He is as keen an analyst as is known in the history of philo&ophy ; I do not except either Aristotle or Kant." GEORGE EIPLET. "If we were to give our own judgment, we should say that, since Newton, there has not in England been a philosopher of more remarkable speculative and ystematizing talent than (in spite of some errors and some narrowness) Mr. Her- bert Spencer." London Saturday Review. u We cannot refrain from offering our tribute of respect to one who, whether lor Ihe extent of his positive knowledge, or for the profundity of his speculative insight, has already achieved a name second to none in the whole range of Eng- lish philosophy, and whose works will worthily sustain the credit of Englisb thought in the present generation." Westminster Review. Woi Jcs of Herbert /Spencer published by D. Appleton & Co. A NEW SYSTEM OF PHILOSOPHY. FIRST PRINCIPLES. . Vol.: Large 12mo. 515 Pages. Price $2 50. CONTENTS : PART FIRST. TJie Unknowable. flaptei ju Religion and Science; II. Ultimate Ecligious Ideas; 111 Ultimate Scientific Ideas; IV. The Relativity of all Knowledge; V Thi Reconciliation. PART SECOND, Laws of the Knowable. I. Laws in General; II. The Law of Evolution; III. The same con- tinued; IY. The Causes of Evolution; V. Space, Time, Matter, Motion, and Force ; VL The Indestructibility of Matter ; VII. The Continuity of Motion ; VIE. The Persistence of Force ; IX. The Correlation and Equivalence of Forces; X. The Direction of Motion ; XI. The Rhythm of Motion; XII. The Conditions Essential to Evolution ; XIII. The Instability of the Homoge- neous ; XIV. The Multiplication of Effects ; XV. Differentiation *nd Inte- gration ; XVI. Equilibration ; XVII. Summary and Conclusion. In the first part of this work Mr. Spencer defines the province, limits, and relations of religion and science, and determines the legitimate scope of philosophy. In part second he unfolds those fundamental principles which have been arrived at within the sphere of the knowable ; which are true of all order* of phenonema, and thus constitute the foundation of all philosophy. The law of Evolution, Mr. Spencer maintains to be universal, and he has here worked it out as the basis of his system. These First Principles are the foundation of a system of Philosophy bolder, more elaborate, and comprehensive perhaps, than any other which oat been hitherto designed hi England. British Quarterly Review. A work lofty hi aim and remarkable in execution, CornJdll Magazine. In the works of Herbert Spencer we have the rudiments of a positrra Theology, and an immense step toward the perfection of the science of Psy- chology. Christian Examiner. If we mistake not, in spite of the very negative character of his own re Bolts, he has foreshadowed some strong arguments for tke doctrine of a poei- felre Christian Theology. New Englander. .As far as tke frontiers of knowledge, where the intellect may go, there ft so living man whose guidance may more safely be trusted. Sfwt&lv. D. APPLETON & CO:S PUBLICATIONS. THE Correlation and Conservation of Forces. WITH AN HTKODUCTION AND BEIEF BIOGE APHICAL NOTICES By EDWARD L. YOUMANS, M.D. 12mo, 490 pages. CONTENTS. L By W. R. GROYE. The Correlation of Physical Forces. H. By Prof. HELMHOLTZ. The Interaction of Natural Forces. HI. By J. R. MAYER. 1. Remarks on the Forces of Inorganic Nature. 2. On Celestial Dynamics. 3. On the Mechanical Equivalent of Heat. IV. By Dr. FARADAY. Some Thoughts on the Conservation of Forces. Y. By Prof. LIEBIG. The Connection and Equivalence of Forces. VI. By Dr. CARPENTER. The Correlation of the Physical and Vital Forces. "This work is a very welcome addition to our scientific literature, and will b particularly acceptable to those who wish to obtain a popular, but at the same time precise and clear view of what Faraday justly calls the highest law in physical scienca, the principle of the conservation of force. Sufficient attention has not been paid to the publication of collected monographs or memoirs upon special subjects. Dr. Youmans' work exhibits the value of such collections in a very striking manne^, and we earnestly hope his excellent example may be followed in other branches of science." American Journal of Science. "It was a happy thought which suggested the publication of this volume. The question is often asked, and not so easily answered, What are the new doctrines of the Correlation and Conservation of Forces? In this volume we have the answer, and with the reasons of its chief expounders ; those who are ignorant on that thcine, can thus question the original authorities. 1 ' New Englander. "We here have the original expositions of the new Philosophy of Forces, accompa- nied by an excellent exposition of both the expositions and the expositors; the wholo will be a rare treat to the lovers of advancing scientific thought." Methodist Quarterly Review. " This is, perhaps, the most remarkable book of the age. We have hero the latent discoveries, and the highest results of thought concerning the nature, laws, and con- aections of the forces of the universe. No higher or more sublime problem can engage the intellect of man than is discussed by these doctors of science intent alone on aniv tag at the truth." Detroit Free Press. 'This work presents a praiseworthy specimen of complete and faithful authorship, Bad it* publication at thie time will form an epoch in tha experience of army think ing mlnda." ibune. Works of Herbert Spencer published by D. Appleton & Co. ILLUSTRATIONS OF UNIVERSAL PROGRESS, A SERIES OF DISCUSSIONS. 1 Vol Large 12mo. 470 Paflrea. Price $2.50. . ' CONTENTS : American Notice of Spencer's New System of Philosophy. I. Progress : its Law and Cause. II, Manners and Fashion. III. The Genesis of Science. IV, The Physiology of Laughter. V. The Origin and Function of Music. VI. The Nebular Hypothesis. VII. Bain on the Emotions and the Will. VIII. Illogical Geology. IX. The Development Hypothesis. X. The Social Organism. XI. Use and Beauty. XH. The Sources of Architectural Types. XIII. The Dse of Anthropomorphism. These Essays constitute a body of massive and original thought upon a farge variety of important topics, and will be read with pleasure by all who appreciate a bold and powerful treatment of fundamental themes. The general thought which pervades this book is beyond doubt the most impor- tant that the human mind has yet reached. N. Y. Independent. Those who have read the work on Education, will remember the ana- lytic tendency of the author's mind his clear perception and admirable ex- position of first principles his wide grasp of facts his lucid and vigorous style, and the constant and controlling bearing of the discussion on practical results. These traits characterize all Mr. Spencer's -writings, and mark, in an eminent degree, the present volume. N. Y. Tribune. We regard the distinguishing feature of this work to be the peculiarly Interesting character of its matter to the general reader. This is a great literary as well as philosophic triumph. In the evolution of a system of Philosophy which demands serious attention, and a keen exercise of the in- tellect to fathom and appreciate, he has mingled much that is really popular *nd entertaining. Rochester Democrat. Works pubUsJted ly 2). Appleton <& Co. HEAT, CONSIDERED AS A MODE OF MOTION, Being a Course of Twelve Lectures delivered before th* Royal Institution of Great Britain. BY JOHN TYITDALL, F. E. S., FSOFKSSOB or NATUBAL PHILOSOPHY IN THE BOYAL INSTITTTTION AUTHOX 3* t "GLACIEES OF THE ALTS," ETC. "With One Hundred Illustrations. Svo, 480 pages. Price, $2. From tne American Journal of Science. With all the skill which has made Faraday the master of experimental science in Great Britain, Professor Tyndall enjoys the advantage of a superior general culture, and is thus enabled to set forth his philosophy with all the graces of eloquence and the finish of superior diction. "With a simplicity, and absence of technicalities, which render his explanations lucid to un- scientific minds, and at the same time a thoroughness and originality by which he in- structs the most learned, he unfolds all the modern philosophy of heat His work takes rank at once as a classic upon the subject. New York Times. Professor Tyndall's course of lectures on heat is one of the most beautiful illustrations of a mode of handling scientific subjects, which is com- paratively new, and which promises the best results, both to science and to literature generally ; we mean the treatment of subjects in a style at once profound and popu- lar. The title of Professor Tyndall's work indicates the theory of heat held by him, and indeed the only one now held by scientific men it is a mode of motion. Boston Journal. He exhibits the curious and beautiful workings of nature in A most delightful manner. Before the reader particles of water lock themselves or fly asunder with a movement regulated like a dance. They form themselves into liquid flowers with fine serrated petals, or into rosettes of frozen gauze ; they bound upward In boiling fountains, or creep slowly onward in stupendous glaciers. Flames burst into music and sing, or cease to sing, as the experimenter pleases, and metals paint them- selves upon a screen in dazzling hues as the painter touches his canvas. New York Tribune. The most original and important contribution that ha> yet been made to tho theory and literature of thermotics. Scientific American. The work is written in a charming style, and Is th most valuable contribution to scientific literature that has been published in many fears. It is the most popular exposition of the dynamical theory of heat that, haa yet appeared. The old material theory of heat may be said to be defunct. Louisville Democrat. This is one of the most delightful scientific works w htye ever met. The lectures are so full of life and spirit that we can almost imagine the lecturer before us, and see his brilliant experiments in every stage of their progress. The theory is so carefully and thoroughly explained that no one can fail to understand it. Such books as these create a love for science. Independent. Professor Tyndall's expositions and experiments are remarkably thoughtful, ingenious, clear, and convincing ; portions of the book have almost tb interest of a romance, so startling are the descriptions and elucidations. UNIVERSITY OP CALIFORN IA LiBRARY THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW 30w-l,'15 YB 09622 / / i