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 <jfeecribe lines of light,
because of their rapid upward motion. These lines are
widened to the eye ; and thus a far greater apparent so-
lidity is imparted to the flame than in reality belongs to it.
189a. This augmentation of the true size of the optical
image is called Irradiation.
Bodies seen within the Eye.
190. Almost every eye contains bodies more or less
opaque distributed through its humors. The so-called
muscce volitantes are of this character ; so are the black
dots, snake-like lines, beads, and rings, which are strikingly
visible in many eyes. Were the area of the pupil con-
tracted to a point, such bodies might produce considerable
lUJCM
v s*v^i A
BODIES SEEN WITHIN THE EYE. 53
annoyance ; but because of the width of the pupil the
shadows which these small bodies would otherwise cast
upon the retina are practically obliterated, except when
they are very close to the back of the eye.* It is only
necessary to look at the firmament through a pinhole to
give these shadows greater definition upon the retina.
191. The veins and arteries of the retina itself also cast
their shadows upon its posterior surface ; but the shaded
spaces soon become so sensitive to light as to compensate
for the defect of light falling upon them. Hence under
ordinary circumstances the shadows are not seen. But if
the shadows be transported to a less sensitive portion of
the retina, the image of the vessels becomes distinctly
visible.
192. The best mode of obtaining the transference of the
shadow is to concentrate in a dark room, by means of a
pocket lens of short focus, a small image of the sun or of
the electric light upon the white of the eye. Care must be
taken not to send the beam through the pupil. When the
small lens is caused to move to and fro, the shadows are
caused to travel over different portions of the retina, and a
perfectly defined image of the veins and arteries is seen
projected in the darkness in front of the eye.
193. Looking into a dark space, and moving a candle
at the same time to and fro beside the eye, so that the rays
enter the pupil very obliquely, the shadow of the retinal
vessels is also obtained. In some eyes the suddenness and
vigor with which the spectral image displays itself are
extraordinary ; others find it difficult to obtain the effect.
194. Finally, a delicate image of the vessels maybe
obtained by looking through a pinhole at the bright sky,
and moving the aperture to and fro.
* See Notes 18 and 19.
54 NOTES ON LIGHT.
The Stereoscope.
195. Look with one eye at the edge of the hand, so that
the finger nearest the eye shall cover all the others. Then
open the second eye ; by it the other fingers will be seen
foreshortened. The images of the hand therefore within
the two eyes are different.
196. These two images are projected on the two retinoe ;
if by any means we could combine two drawings, executed
on a flat surface, so as to produce within the two eyes two
pictures similar to the two images of the solid hand, we
should obtain the impression of solidity. This is done by
the stereoscope.
197. The first form of this instrument was invented by
Sir Charles Wheatstone. He took drawings of solid objects
as seen by the two eyes, and looked at the images of these
drawings in two plane mirrors. Each eye looked at the
image which belonged to it, and the mirrors were so
arranged that the images overlapped, thus appearing to
come from the same object. By this combination of its
two plane projections, the object sketched was caused to
start forth as a solid.
198. In looking at and combining two such drawings,
the eyes receive the same impression, and go through the
same process as when they look at the real object. We
see only one point of an object distinctly at a time. If the
different points of an object be at different distances from
the eyes, to see the near points distinctly requires a greater
convergence of the axes of the eyes than to see the distant
ones. Now, besides the identity of the retinal images of
the stereoscopic drawings with those of the real object, the
eyes, in order to cause the corresponding pairs of points of
the two drawings to coalesce, have to go through the same
THE STEREOSCOPE. 55
variations of convergence that are necessary to see dis-
tinctly the various points of the actual object. Hence the
impression of solidity produced by the combination of such
drawings.
199. Measure the distance between two pairs of points,
which when combined by the stereoscope present two
single points at different distances from the eye. The dis-
tance between the one pair will be greater than that
between the other pair. Different degrees of convergence
are therefore necessary on the part of the eye to combine
the two pairs of points. It is to be noted that the coales-
cence produced in the stereoscope at any particular moment
is only partial. If one pair of corresponding points be
seen singly, the others must appear double. This is also
the case when an actual solid is looked at with both eyes ;
of those points of it which are at different distances from
the eyes one only is seen singly at a time.
200. The impression of solidity may be produced in an
exceedingly striking manner without any stereoscope at
all. Most easily, thus : Take two drawings projections,
as they are called of the frustum of a cone ; the one as it
is seen by the right eye, the other as it is seen by the left.
Holding them at some distance from the eyes, let the left-
hand drawing be looked at by the right eye, and the right-
hand drawing by the left. The lines of vision of the two
eyes here cross each other ; and it is easy, after a few trials
with a pencil-point placed in front of the eyes, to make two
corresponding points of the drawings coincide. The mo-
ment they coincide, the combined drawings start forth as
a single solid, suspended in the air at the place of intersec-
tion of the lines of vision. It depends upon the character
of the drawings whether the inside of the frustum is seen,
or the outside, whether its base or its top seems nearest to
the eye. For this experiment the drawings are best made
56 NOTES ON LIGHT.
in simple outline, and they may be immensely larger than
ordinary stereoscopic drawings.
Take notice that here also the different pairs of the
corresponding points are at different distances apart.
Two corresponding points, for example, of the top of the
frustum will not be the same distance asunder as two
points of the base.
201., Wheatstone's first instrument is called the Re-
flecting Stereoscope; but the methods of causing draw-
ings to coalesce so as to produce stereoscope effects are
almost numberless. The instrument most used by the
public is the Lenticular Stereoscope of Sir David Brews-
ter. In it the two projections are combined by means of
two half lenses with their edges turned inward. The len-
ticular stereoscope also magnifies.*
202. It has been stated in note 198 that for the dis-
tinct vision of a near point a greater convergence of the
lines of vision of the two eyes is necessary than that of a
distant one, By an instrument in which two rectangular
prisms are employed,! the rays from two points may be
caused to cross before they enter the eyes, the convergence
being thus rendered greater for the distant point than
for the near one. The consequence of this is, that the
near point appears distant, and the distant point near.
This is the principle of Wheatstone's pseudoscope. By
this instrument convex surfaces are rendered concave, and
concave surfaces convex. The inside of a hat or teacup
may be thus converted into its outside, while a globe may
be seen as a concave spherical surface.
* Fuller and clearer information regarding the stereoscope will be
found in the Journal of the PJiotographic Society, vol. iii. pp. 96, 116,
and 167.
See Note 150.
THEORY OF EMISSION. 57
Nature of Light ; Physical Theory of Reflection and
Refraction.
It is now time to redeem to some extent the promise
of our first note, that the "something" which excites the
sensation of light should be considered more closely sub-
sequently.
203. Every sensation corresponds to a motion excited
in our nerves. In the sense of touch, the nerves are
moved by the contact of the body felt ; in the sense of
smell, they are stirred by the infinitesimal particles of the
odorous body ; in the sense of hearing, they are shaken
by the vibrations of the air.
Theory of Emission.
204. Newton supposed light to consist of small parti-
cles shot out with inconceivable rapidity by luminous
bodies, and fine enough to pass through the pores of trans-
parent media. Crossing the humors of the eye, and strik-
ing the optic nerve behind the eye, these particles were
supposed to excite vision.
205. This is the Emission Theory or Corpuscular
Theory of Light.
206. Considering the enormous velocity of light, the
particles, if they exist, must be inconceivably small ; for
if of any conceivable weight, they would infallibly destroy
so delicate an organ as the eye. A bit of ordinary mat-
ter, one grain in weight, and moving with the velocity of
light, would possess the momentum of a cannon-ball 150
Ibs. weight, moving with a velocity of 1,000 feet a second.
207. Millions of these light particles, supposing them
to exist, concentrated by lenses and mirrors, have been
shot against a balance suspended by a single spider's
thread; this thread, though twisted 18,000 times, showed
58 NOTES ON LIGHT.
no tendency to untwist itself; it was therefore devoid of
torsion. But no motion due to the impact of the particles
was even in this case observed.*
208. If light consists of minute particles, they must be
shot out with the same velocity by all celestial bodies.
This seems exceedingly unlikely, when the different gravi-
tating forces of such different masses are taken into ac-
count. By the attractions of such diverse masses, the
particles would in all probability be pulled back with dif-
ferent degrees of force.
209. If, for example, a fixed star of the sun's density
possessed 250 times the sun's diameter, its attraction, sup-
posing light to be acted on like ordinary matter, would
be sufficient to finally stop the particles of light issuing
from it. Smaller masses would exert corresponding de-
grees of retardation ; and hence the light emitted by dif-
ferent bodies would move with different velocities. That
such is not the case that light moves with the same ve-
locity whatever be its source renders it probable that it
does not consist of particles thus darted forth.
But a more definite and formidable objection to the
Emission Theory may be stated after we have made our-
selves acquainted with the account it rendered of the phe-
nomena of reflection and refraction.
210. In direct reflection, according to the emission
theory, the light particles are first of all stopped in their
course by a repellent force exerted by the reflecting body,
and then driven in the contrary direction by the same
force.
211. This repulsion is, however, selective. The reflect-
ing substance singles out one portion of the group of par-
ticles composing a luminous beam and drives them back ;
* Bennett, Phil Trans., 1792.
THEORY OF UNDULATION. 59
but it attracts the remaining particles of the group and
transmits them.
212. When a light particle approaches a refractive
surface obliquely, if the particle be an attracted one, it is
drawn toward the surface, as an ordinary projectile is
drawn toward the earth. Refraction is thus accounted
for. Like the projectile, too, the velocity of the light par-
ticle is augmented during its deflection ; it enters the re-
fracting medium with this increased velocity, and once
within the medium, the attractions before and behind the
particle neutralizing each other, the increased velocity is
maintained.
213. Thus, it is an unavoidable consequence of the
theory of Newton, that the bending of a ray of light toward
the perpendicular is accompanied by an augmentation
of velocity that light in water moves more rapidly than
in air, in glass more rapidly than in water, in diamond
more rapidly than in glass. In short, that the higher the
refractive index, the greater the velocity of the light.
214. A decisive test of the emission theory was thus
suggested, and under that test the theory has broken
down. For it has been demonstrated, by the most rigid
experiments, that the velocity of light diminishes as the
index of refraction increases. The theory, however, had
yielded to the assaults made upon it long before this par-
ticular experiment was made.
Theory of Undulation.
215. The Emission Theory was first opposed by the
celebrated astronomer Huyghens, and the no less cele-
brated mathematician Euler, both of whom held that light,
like sound, was a product of wave-motion. Laplace, Malus,
Biot, and Brewster, supported Newton, and the emission
theory maintained its ground until it was finally over-
60 NOTES ON LIGHT.
thrown by the labors of Thomas Young * and Augustin
Fresnel.
216. These two eminent philosophers, while adducing
whole classes of facts inexplicable by the emission theory,
succeeded in establishing the most complete parallelism
between optical phenomena and those of wave-motion.
The justification of a theory consists in its exclusive com-
petence to account for phenomena. On such a basis the
Wave Theory , or the Undulatory Theory of light, now
rests, and every day's experience only makes its founda-
tions more secure. This theory must for the future
occupy much of our attention.
217. In the case of sound, the velocity depends upon
the relation of elasticity to density in the body which
transmits the sound. The greater the elasticity the greater
is the velocity, and the less the density the greater is the
velocity. To account for the enormous velocity of propa-
gation in the case of light, the substance which transmits
it is assumed to be of both extreme elasticity and of ex-
* Dr. Young was appointed Professor of Natural Philosophy in the
Royal Institution, August 3, 1801. From a marble slab in the village
church of Farnborough, near Bromley, Kent, I copied, on the llth of
April, the following inscription :
" Near this place are deposited the remains of THOMAS YOUNG, M. D.,
Fellow and Foreign Secretary of the Royal Society, Member of the Na-
tional Institute of France. A man alike eminent in almost every depart-
ment of human learning, whose many discoveries enlarged the bounds of
Natural Science, and who first penetrated the obscurity which had veiled
for ages the Hieroglyphics of Egypt.
" Endeared to his friends by his domestic virtues, Honored by the
world for his unrivalled acquirements, He died in the hope of the resur-
rection of the just.
"Born at Milverton, in Somersetshire, June 13, 1773.
"Died in Park Square, London, May 29, 1820,
" In the 56th year of his age."
THEORY OF UNDULATION. 61
trcme tenuity. This substance is called the Luminiferous
ether.
218. It fills space; it surrounds the atoms of bodies;
it extends, without solution of continuity, through the
humors of the eye. The molecules of luminous bodies are
in a state of vibration. The vibrations are taken up by
the ether, and transmitted through it in waves. These
waves impinging on the retina excite the sensation of
light.
219. In the case of sound, the air-particles oscillate to
and fro in the direction in which the sound is transmitted ;
in the case of light, the ether particles oscillate to and fro
across the direction in which the light is propagated. In
scientific language the vibrations of sound are longitudi-
nal, while the vibrations of light are transversal. In fact,
the mechanical properties of the ether are rather those of
a solid than of an air.
220. The intensity of the light depends on the distance
to which the ether particles move to and fro. This dis-
tance is called the amplitude of the vibration. The in-
tensity of light is proportional to the square of the ampli-
tude ; it is also proportional to the square of the maximum
velocity of the vibrating particle.
221. The amplitude of the vibrations diminishes simply
as the distance increases ; consequently the intensity,
which is expressed by the square of the amplitude, must
diminish inversely as the square of the distance. This,
in the language of the wave theory, is the law of inverse
squares.
222. The reflection of ether waves obeys the law es-
tablished in the case of light. The angle of incidence is
demonstrably equal to the angle of reflection.
223. To account for refraction, let us for the sake of
simplicity take a portion of a circular wave emitted by the
62 NOTES ON LIGHT.
sun or some other distant body. A short portion of such
a wave would be straight. Suppose it to impinge from
air upon a plate of glass, the wave being in the first in-
stance parallel to the surface of the glass. Such a wave
would go through the glass without change of direction.
224. But as the velocity in glass is less than the veloci-
ty in air, the wave would be retarded on passing into the
denser medium.
225. But suppose the wave, before impact, to be ob-
lique to the surface of the glass ; that end of the wave
which first reaches the glass will be first retarded, the
other portions being held back in succession. This retar-
dation of one end of the wave causes it to swing round ;
so that when the wave has fully entered the glass its course
is oblique to its first direction. It is refracted.
226. If the glass into which the wave enters be a plate
with parallel surfaces, the portion of the wave which
reached the upper surface first, and was first retarded,
will also reach its under surface first, and escape earliest
from the retarding medium. This produces a second
swinging round of the wave, by which its original direc-
tion is restored. In this simple way the Wave Theory
accounts for Refraction.
227. The convergence or divergence of beams of light
by lenses is immediately deduced from the fact that the
different points of the ether wave reach the lens, and are
retarded by the lens in succession,
228. The density of the ether is greater in liquids and
solids than in gases, and greater in gases than in vacuo.
A compressing force seems to be exerted on the ether by
the molecules of these bodies. Now if the elasticity of the
ether increased in the same proportion as its density, the
one would neutralize the other, and we should have no
retardation of the velocity of light. The diminished ve-
THEORY OF UNDULATION. G3
locity in highly-refracting bodies is accounted for by as-
suming that in such bodies the elasticity in relation to the
density is less than in vacuo. The observed phenomena
immediately flow from this assumption.
229. The case is precisely similar to that of sound in a
gas or vapor which does not obey the law of Mariotte.
The elasticity of such a gas or vapor, when compressed,
increases less rapidly than the density ; hence the dimin-
ished velocity of the sound.
230. But we are able to give a more distinct statement
as to the influence which a refracting body has upon the
velocity of light. Regard the lines o m and np in Fig. 2,
Note 113. These two lines represent the velocities of light
in the two media there considered; or, expressed more
generally, the sine of the angle of incidence represents the
velocity of light in the first medium, while the sine of the
angle of refraction represents the velocity in the second.
The index of refraction then is nothing else than the ratio
of the two velocities. Thus in the case of water, where the
index of refraction is -f , the velocity in air is to its velocity
in water as 4 is to 3. In glass also, where the index of
refraction is f , the velocity in air is to the velocity in glass
as 3 is to 2. In other words the velocity of light in air
is H times its velocity in water, and 1 J times its velocity
in glass. The velocity of light in air is about 2 times its
velocity in diamond, and nearly three times its velocity in
chromate of lead, the most powerfully refracting sub-
stance hitherto discovered. Strictly speaking, the index
of refraction refers to the passage of a ray of light, not
from air, but from a vacuum,* into the refracting body.
Dividing the velocity of light in vacuo by its velocity in
the refracting substance, the quotient is the index of re-
fraction of that substance.
* That is to say, a vacuum save as regards the ether itself
\
64 NOTES ON LIGHT.
231. In the wave theory, the rays of light are per-
pendiculars to the waves of ether. Unlike the icave, the
ray has no material existence ; it is merely a direction.
Prisms.
232. It has been stated, in Note 129, that in the case
of a plate of glass with parallel surfaces, the direction
possessed by an oblique ray, prior to its meeting the glass,
is restored when it quits the glass. This is not the case
if the two surfaces at which the ray enters and emerges
be not parallel.
233. When the ray passes through a wedge-shaped
transparent substance, in a direction perpendicular to the
edge of the wedge, it is permanently refracted. A body
of this shape is called a prism in optics, and the angle en-
closed by the two oblique sides of the wedge is called the
refracting angle.
234. The larger the refracting angle the greater is the
deflection of the ray from its original direction. But with
the self-same prism the amount of the refraction varies
with the direction pursued by the ray through the prism.
235. When that direction is such that the portion of
the ray within the prism makes equal angles with the two
sides of the prism, or, what is the same, with the ray be-
fore it reaches the prism and after it has quitted it, then
the total refraction is a minimum. This is capable both of
mathematical and experimental proof; and on this result
is based a method of determining the index of refraction.
236. The final direction of a refracted ray being un-
altered by its passage through glass plates with parallel
surfaces, we may employ hollow vessels composed of such
plates and filled with liquids, thus obtaining liquid
prisms.
PRISMATIC ANALYSIS OF LIGHT; DISPERSION. G5
Prismatic Analysis of Light / Dispersion.
237. Newton first unravelled the solar light, proving
it to be composed of an infinite number of rays of different
degrees of refrangibility ; when such light is sent through
a prism, its constituent rays are' drawn asunder. This act
of drawing apart is called dispersion.
238. The waves of ether generated by luminous bodies
are not all of the same length ; some are longer than
others. In refracting substances the short waves are more
retarded than the longer ones ; hence the short waves are
more refracted than the long ones. This is the cause of
dispersion.
239. The luminous image formed when a beam of white
light is thus decomposed by a prism is called a spectrum.
If the light employed be that of the sun, the image is
called the solar spectrum.
240. The solar spectrum consists of a series of vivid
colors, which, when reblended, produce the original white
light. Commencing with that which is least refracted,
we have the following order of colors in the solar spec-
trum : Red, Orange, Yellow, Green, Blue, Indigo, Violet.
241. The Color of Light is determined solely by its
Wave-length. The ether waves gradually diminish in
length from the red to the violet. The length of a wave
of red light is about Sa j 00 th of an inch ; that of the wave of
violet light is about g7 ^ 00 th of an inch. The waves which
produce the other colors of the spectrum lie between these
extremes.
242. The velocity of light being 192,000 miles in a
second, if we multiply this number by 39,000 we obtain
the number of waves of red light in 192,000 miles; the
product is 474,439,680,000,000. All these leaves enter the
eye in a second. In the same interval 699,000,000,000,000
66 NOTES ON LIGHT.
waves of violet light enter the eye. At this prodigious
rate is the retina hit by the waves of light.
243. Color, in fact, is to light what pitch is to sound.
The pitch of a note depends solely on the number of
aerial waves which strike the ear in a second. The color
of light depends on the number of ethereal waves which
strike the eye in a second. Thus the sensation of red is
produced by imparting to the optic nerve four hundred
and seventy-four millions of millions of impulses per
second, while the sensation of violet is produced by im-
parting to the nerve six hundred and ninety-nine millions
of millions of impulses per second. In the Emission
Theory numbers not less immense occur, " nor is there
any mode of conceiving the subject which does not call
upon us to admit the exertion of mechanical forces which
may well be termed infinite." *
Invisible Rays ; Calorescence and Fluorescence.
244. The spectrum extends in both directions beyond
its visible limits. Beyond the visible red we have rays
which possess a high heating power, though incompetent
to excite vision ; beyond the violet we have a vast body
of rays which, though feeble as regards heat, and power-
less as regards light, are of the highest importance be-
cause of their capacity to produce chemical action.
245. In the case of the electric light, the energy of the
non-luminous calorific rays emitted by the carbon points
is about eight times that of all the other rays taken to-
gether. The dark calorific rays of the sun also probably
exceed many times in power the luminous solar rays. It
is possible to sift the solar or the electric beam so as to
intercept the luminous rays, while the non-luminous ravs
are allowed free transmission.
* Sir John Herschel.
INVISIBLE RAYS. 67
246. In this way perfectly dark foci may be obtained
where combustible bodies may be burned, non-refractory
metals fused, and refractory ones raised to the tempera-
ture of whiteness. The non-luminous calorific rays may
be thus transformed into luminous ones, which yield all
the colors of the spectrum. This passage, by the inter-
vention of a refractory body, from the non-luminous to the
luminous state, is called Calorescence.
247. So also as regards the ultra-violet rays; when
they are permitted to fall upon certain substances the
disulphate of quinine for example they render the sub-
stance luminous ; invisible rays are thereby rendered visi-
ble. The change here receives the name of Fluorescence.
248. In calorescence the atoms of the refractory body
are caused to vibrate more rapidly than the waves which
fall upon them ; the periods of the waves are quickened by
their impact on the atoms. The refrangibility of the rays
is, in fact, exalted. In fluorescence, on the contrary, the
impact of the waves throws the molecules of the fluores-
cent body into vibrations of slower periods than those
of the incident waves ; the refrangibility of the rays is
in fact lowered. Thus by exalting the refrangibility of
the ultra-red, and by lowering the refrangibility of the
ultra-violet rays, both classes of rays are rendered capable
of exciting vision.
249. Though the term is by no means faultless, those
rays, both ultra-red and ultra-violet, which are incom-
petent to excite vision, are called invisible rays. In
strictness we cannot speak of rays being either visible or
invisible ; it is not the rays themselves but the objects
they illuminate that become visible. " Space, though
travers'ed by the rays from all suns and all stars, is itself
unseen. Not even the ether which fills space, and whose
motions are the light of the world, is itself visible."*
* " Proceedings of the Royal Institution," vol. v., p. 456.
68 NOTES 0$ LIGHT.
Doctrine of Visual Periods.
250. A string tuned to a certain note resounds when
that note is sounded. If you sing into an open piano, the
string whose note is in unison with your voice will be
thrown into sonorous vibration. If there be discord be-
tween the note and the string, there is no resonance,
however powerful the note may be. A particular church-
pane is sometimes broken by a particular organ-peal,
through the coincidence of its period of vibration with
that of the organ.
251. In this way it is conceivable that a feeble note,
through the coincidence of its periods of vibration with
those of a sounding body, may produce effects which a
powerful note, because of its non-coincidence, is unable to
produce.
252. This, which is a known phenomenon of sound,
helps us to a conception of the deportment of the retina
toward light. The retina, or rather the brain in which
its fibres end, is, as it were, attuned to a certain range of
vibrations, and it is dead to all vibrations which lie with-
out that range, however powerful they may be.
253. The quantity of wave-motion sent to the eye at
night, by a candle a mile distant, suffices to render the
candle visible. Employing the powerful ultra-red rays of
the sun, or of the electric light, it is demonstrable that
ethereal waves possessing many millions of times the me-
chanical energy of those which produce the candle's
light, may be caused to impinge upon the retina with-
out exciting any sensation whatever. The periods of
succession of the waves, rather than their strength, are
here influential.
254. When in music two notes are separated from each
other by an octave, the higher note vibrates witli twice
DOCTRINE OF COLORS. 69
the rapidity of the lower. In Note 241 the lengths of the
wave of red light and of violet light are set down as -g-g^oir
of an inch and -^^nr of an inc k respectively ; but these
numbers refer to the mean red and the mean violet. The
waves of the extreme violet are about half the length of
those of the extreme red, and they strike the retina with
double the rapidity of the red. While, therefore, the music-
al scale, or the range of the ear, is known to embrace nearly
eleven octaves, the optical scale, or range of the eye, is
comprised within a single octave.
Doctrine of Colors.
255. Natural bodies possess the power of extinguish-
ing, or, as it is called, absorbing the light that enters them.
This power of absorption is selective, and hence, for the most
part, arise the phenomena of color.
256. When the light which enters a body is wholly
absorbed the body is black ; a body which absorbs all the
waves equally, but not totally, is gray ; while a body which
absorbs the various waves unequally is colored. Color is
due to the extinction of certain constituents of the white
light within the body, the remaining constituents which
return to the eye imparting to the body its color.
25*7. It is to be borne in mind that bodies of all colors,
illuminated by white light, reflect white light from their
exterior surfaces. It is the light which has plunged to a
certain depth within the body, which has been sifted there
by elective absorption, and then discharged from the body
by interior reflection that, in general, gives the body its
color.
258. A pure red glass interposed in the path of a beam
decomposed by a prism, either before or after the act of
decomposition, cuts off all the colors of the spectrum except
the red. A glass of any other pure color similarly inter-
70 NOTES ON LIGHT.
posed would cut off all the spectrum except that particular
portion which gives the glass its color. It is, however,
extremely difficult, if not impossible, to obtain pure pig-
ments of any kind. Thus a yellow glass not only allows
the yellow light of the spectrum to pass, but also a portion
of the adjacent green and orange ; while a blue glass not
only allows the blue to pass, but also a portion of the ad-
jacent green and indigo.
259. Hence, if a beam of white light be caused to pass
through a yellow glass and a blue glass at the same time,
the only transmissible color common to both is green.
This explains why blue and yellow powders, when mixed
together, produce green. The white light plunges into
the powder to a certain depth, and is discharged by inter-
nal reflection, minus its yellow and. its blue. The green
alone remains.
260. The effect is quite different when, instead of mix-
ing blue and yellow pigments, we mix blue and yellow
lights together. Here the mixture is a pure white. Blue
and yellow are complementary colors.
261. Any two colors whose mixture produces white are
called complementary colors. In the spectrum we have
the following pairs of such colors :
Red and greenish Blue.
Orange and cyanogen Blue.
Yellow and indigo Blue.
Greenish Yellow and Violet.
262. A body placed in a light which it is incompetent
to transmit appears black, however intense may be the
illumination. Thus, a stick of red sealing-wax, placed in
the vivid green of the spectrum, is perfectly black. A
bright-red solution similarly placed cannot be distinguished
from black ink ; and red cloth, on which the spectrum is
CHROMATIC ABERRATION. ACHROMATISM. 71
permitted to fall, shows its color vividly where the red
light falls upon it, but appears black beyond this position.
263. We have thus far dealt with the analysis of white
light. In reblending the constituent colors, so as to pro-
duce the original, we illustrate, by synthesis, the composi-
tion of white light.
264. Let the beam analyzed be a rectangular slice of
light. By means of a cylindrical lens we can recombine
the colors, and produce by their mixture the original white.
It is also possible, by the combination of the colors of its
spectrum, to build up a perfect image of the source of light.
The persistence of impressions on the retina also offers a
ready means of blending colors.
Chromatic Aberration. Achromatism.
265. Owing to the different refrangibility of the differ-
ent rays of the spectrum, it is impossible by a single
spherical lens to bring them all to a focus at the same
point. The blue rays, for example, being more refracted
than the red will intersect sooner than the red.
266. Hence, when a divergent cone of white light is
rendered convergent by a lens, the convergent beam, as far
as the point of intersection of the rays, will be surrounded
by a sheath of red ; while beyond the focus the divergent
cone will be surrounded by a sheath of blue. Hence, when
the refracted rays fall upon a screen placed between the
lens and the focus of blue rays, a white circle with a red
border is obtained ; while if the screen be placed beyond
the focus of red rays, the white circle will have a blue
border. It is impossible to produce a colorless image in
these positions of the screen.
267. This lack of power on the part of a lens to bring its
differently-colored constituents to a common focus, is called
the Chromatic aberration of the lens.
72 NOTES ON LIGHT.
268. Newton considered it impossible to get rid of
chromatic aberration ; for he supposed the dispersion of a
prism or lens to be proportional to its refraction, and that
if you destroyed the one you destroyed the other. This,
however, was an error.
269. For two prisms producing the same mean refrac-
tion may produce very different degrees of dispersion. By
diminishing the angle of the more highly-dispersive prism
we can make its dispersion sensibly equal to that of the
feebly dispersive one ; and we can neutralize the colors of-,
both prisms by placing them in opposition to each other,
without neutralizing the refraction.
270. When, for example, a prism of water is opposed
to a prism of flint-glass, after the dispersion of the water,
which is small, has been destroyed, the beam is still re-
fracted. If a prism of crown-glass be substituted for the
prism of water, substantially the same effect is produced.
The flint-glass is competent to neutralize the dispersion of
the crown before it neutralizes the refraction.
271. What is here said of prisms applies equally to
lenses. A convex crown-glass lens, opposed to a concave
flint-glass lens, may have its dispersion destroyed, and still
images may be formed by the combination of the two
lenses, because of the residual refraction.
272. A combination of lenses wherein color is destroyed
while a certain amount of refraction is preserved, is called an
achromatic combination, or more briefly an achromatic lens.
273. The human eye is not achromatic. It suffers from
chromatic aberration as well as from spherical aberration.
Subjective Colors.
274. By the action of light the optic nerve is rendered
less sensitive. When we pass from bright daylight into a
moderately-lighted room, the room appears dark,
SUBJECTIVE COLORS. 73
275. This is also true of individual colors; when light
of any particular color falls upon the eye, the optic nerve
is rendered less sensitive to that color. It is, in fact, par-
tially blinded to its perception.
276. If the eyes be steadily fixed upon a red wafer
placed on white paper, after a little time the wafer will be
surrounded by a greenish rim, and if the wafer be moved
away, the place on which it rested will appear green.
277. This is thus explained : the eye by looking at the
wafer has its sensibility to red light diminished ; hence,
when the wafer is removed, the white light falling upon
the spot of the retina on which the image of the wafer
rested, will have its red constituent virtually removed, and
will therefore appear of the complementary color. The
first rim of green light observed is due to the extension of
the red light of the wafer a little beyond its geometrical
image on the retina, in consequence of the spherical aberra-
tion of 'the eye.
278. Colored shadows are reducible to the same cause.
Let a strong red light, for example, fall upon a white screen.
A body interposed between the light and the screen will
cast a shadow, and if this shadow be moderately illumi-
nated by a second white light it will appear green. If the
original light be blue, the shadow will appear yellow ; if
the original light be green, the shadow will appear red.
The reason is, that the eye in the first instance is partially
blinded to the perception of the color cast upon the screen ;
hence the white light, which reaches the eye from the
shadow, will have that color partially withdrawn, and the
shadow will appear of the complementary color.
279. Colors of this kind are called subjective colors ;
they depend upon the condition of the eye, and do not ex-
press external facts of color.
4
74 NOTES ON LIGHT.
Spectrum Analysis.
280. Metals and their compounds impart to flames pe-
culiar colors, which are characteristic of the metals. Thus
the almost lightless flame t>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<nr of an inch.
396. The entire series of bright rings were formed at
the following successive thicknesses :
TTsWir tnftrjnri TtArhn inAooj etc -i
and the series of dark rings, separating the bright ones, at
the thicknesses
'1 f SO'OO) 1180005 TT8 UTTF5 n 8 6 * C '
397. To account for the rings, Newton assumed that
the light particles were endowed withes of easy transmis-
COLORS OF THIN PLATES. 99
sion and of easy reflection. He probably figured those
particles as endowed at the same time with a motion of
translation through space, and a motion of rotation round
their own axes. If we suppose such particles to resemble
little magnets which present alternately attractive and
repulsive poles to the surface which they approach, we
have a conception in conformity w T ith the notion of New-
ton.
398. According to this conception ordinary reflection
and refraction would depend upon the presentation of the
repulsive or the attractive poles of the particles to the
reflecting or refracting surface.
399. Figure then the rotating light particles entering
the film of air between Newton's lens and plate. If the
distance between both be such as to enable the light
particle to perform a complete rotation, it will present at
the second surface of the film of air the same pole that* it
presented at the first. It will therefore be transmitted,
and will not return to the eye.
400. This effect would also take place if the distance
between the plate and lens were such as to enable the light
particle to perform two, three, four, etc., complete rota-
tions. The dark rings of Newton were thus accounted for.
They occurred at places where the light particles, instead
of being sent back to the eye from the second surface of
the film, were transmitted through that surface.
401. But if the thickness of the film be such as to allow
the light particle which has entered the first surface to
perform only half a rotation before it arrives at the second
surface ; then a repulsive pole will be presented to the
latter, and the particle will be driven back to the eye.
The same will occur if the distance be such as to enable
the light particle to perform three, or five, or seven, etc.,
semi-rotations. The bright rings of Newton were thus
100 NOTES ON LIGHT.
accounted for they occurred at places where the light
particles on reaching the second surface of the film were
reflected back to the eye.
402. The theory of emission is here at direct issue with
the theory of undulation. Newton assumes that the action
which produces the alternate bright and dark rings takes
place at a single surface ; i. e., the second surface of the
film. The undulatory theory affirms that the rings are
caused by the interference of rays reflected from both
surfaces. This has been proved to be the case. By
employing polarized light (to be subsequently described
and explained) we can destroy the reflection at the first
surface of the film, and when this is done the rings vanish
altogether.
403. The beauty and subtlety of Newton's conception
are, however, manifest ; and the theory was apparently
supported by the fact that rings of feeble intensity are
actually formed by transmitted light, and that the bright
rings by transmitted light correspond to thicknesses which
produce dark rings in reflected light.
404. The transmitted rings are referred by the un-
dulatory theory to the interference of rays which have
passed directly through the film, with others which have
undergone two reflections within the film. They are thus
completely accounted for.
NOTE. The thickness 1 ^^ 0o - 5 - of an inch referred to in
Note 396, as that corresponding to the first bright ring, is
one-fourth of the length of an undulation of the light em-
ployed by Newton. Hence, in passing to and fro through
the film, the rays reflected at the second surface are half
an undulation behind those reflected at the first surface.
At this thickness, therefore, the ring ought, according to
the principles of interference, to be darJc instead of bright.
The same remarks apply to the thicknesses
DOUBLE REFRACTION. 101
T __5___ 5 etc. ; the former corresponds to a retardation of
three, and the latter to a retardation of five semi-undula-
tions. With regard to the dark rings, the first of them
occurs at a thickness the double of which is the length of
a whole undulation ; the second of them occurs at a thick-
ness which, when doubled, is equal to two wave-lengths ;
the third at a thickness the double of which is three wave-
lengths. Hence, if we take the thickness of the film alone
into account, the bright rings ought to be dark, and the
dark rings bright.
But something besides thickness is to be considered
here. In the case of the first surface of the film the wave
passes from the dense ethej?-Qf the glass into the rare ether
of the air. In the case of the second surface of the film
the wave passes from the rare ether of the air into the
dense ether of the glass. This difference at the two re-
flecting surfaces of the film can be proved to be equivalent
to the addition of half a wave-length to the thickness of
the film. To the absolute thickness, therefore, as meas-
ured by Newton, half a wave-length is in each case to be
added ; when this is done the rings follow each other in
exact accordance with the law of interference enunciated
in Notes 348 to 350.
Double Refraction.
405. In air, water, and well-annealed glass, the luminif-
erous ether has the same elasticity in all directions. There
is nothing in the molecular grouping of these substances
to interfere with the perfect homogeneity of tbe ether.
406. But when water crystallizes to ice, the case is
different; here the molecules are constrained by their
proper forces to arrange themselves in a certain determi-
nate manner. They are, for example, closer together in
102 NOTES ON LIGHT.
some directions than in others. This arrangement of the
molecules carries along with it an arrangement of the sur-
rounding ether, which causes it to possess different degrees
of elasticity in different directions.
407. In a plate of ice, for example, the elasticity of the
ether in a direction perpendicular to the surface of freezing
is different from its elasticity in a direction parallel to the
same surface.
408. This difference is displayed in a peculiarly strik-
ing manner by Iceland spar, which is crystallized car-
bonate of lime ; and in consequence of the existence of
these two different elasticities, a wave of light passing
through the spar is divided into two ; the one rapid, cor-
responding to the greater elasticity, and the other slow,
corresponding to the lesser elasticity*
409. Where the velocity is greatest, the refraction is
least ; and where the velocity is least the refraction is
greatest. Hence in Iceland spar, as we have two waves
moving with different velocities, we have double refrac-
tion.
410. This is also true of the greater number of crys-
talline bodies. If the grouping of the molecules be not
in all directions alike, the ether will not be in all direc-
tions equally elastic, and double refraction will infallibly
result.
411. In rock-salt, alum, and other crystals, this homo-
geneous grouping of the molecules actually occurs, and
such crystals behave like glass, water, or air.
412. In certain doubly refracting crystals the molecules
are arranged in the same manner on all sides of a certain
direction. For example, in the case of ice the molecular
arrangement is the same all round the perpendiculars to
the surface of freezing.
413. In like manner, in Iceland spar the molecules are
DOUBLE REFRACTION. 103
arranged symmetrically round the crystallographic axis,
that is, round the shortest diagonal of the rhomb into
which the crystal may be cloven.*
414. When a beam of light passes through ice per-
pendicular to the surface of freezing, or through Iceland
spar parallel to the crystallographic axis, there is no
double refraction. These cases are representative ; that
is to say, there is no double refraction in the direction
round which the molecular arrangement is in all directions
the same.
415. This direction of no double refraction is called the
optic axis of the crystal.
NOTE. The vibrations of the ether being transverse
to the direction of the ray, the elasticity which determines
the rapidity of transmission is that at right angles to the
ray's direction. In Iceland spar the velocity is slowest
in the direction of the axis ; hence the elasticity at right
angles to the axis is a minimum. The ray, on the other
hand, whose vibrations are executed along the axis is the
most rapid ; hence the elasticity of the ether along the
axis is a maximum. In perfectly homogeneous bodies
the surface of elasticity would be spherical ; it would be
measured by the same length of radius in all directions.
In the case of Iceland spar the surface of elasticity is an
ellipsoid whose longer axis coincides with the axis of the
crystal.
* The arrangement of the molecules is such, that Iceland spar may
be cloven with great and equal facility in three different directions. The
planes of cleavage are here oblique to each other. Rock-salt also cleaves
readily and equally in three directions, the planes of cleavage being at
right angles to each other. Hence, while rock-salt cleaves into cubes,
Iceland spar cleaves into rhombs. Many crystals cleave with different
facilities in different directions. Selenite and crystallized sugar (sugar-
candy) are examples.
104 NOTES ON LIGHT.
Phenomena presented by Iceland Spar.
416. The two beams into which the incident beam is
divided by the spar do not behave alike. One of them
obeys the ordinary law of refraction ; its index of refrac-
tion is perfectly constant and independent of its direction
through the crystal. The angles of incidence and refrac-
tion are in the same plane, as in the case of ordinary re-
fraction. The ray which behaves thus is called the ordi-
nary ray. In its case the sine of the angle of incidence
is to the sine of the angle of refraction, or the velocity of
light in air is to its velocity in the crystal, in the constant
ratio of 1.654 to 1.. The number 1.654 is the ordinary
index of Iceland spar.
417. But the other beam acts differently. Its index
of refraction is not constant, nor is the angle of refraction
as a general rule in the same plane as the angle of inci-
dence. The ray which behaves thus is called the extraor-
dinary ray. If a prism be formed of the spar with its
refracting angle parallel to the optic axis, when the
incident beam traverses the prism at right angles to the
optic axis, the separation of its two parts is a maximum.
Here the full difference of elasticity between the axial
direction and that perpendicular to it comes into play,
and the extraordinary ray suffers its minimum retarda-
tion, and therefore its minimum refraction. Its refractive
index is then 1.483.
418. The index of refraction of the extraordinary ray
varies with its direction through the crystal from 1.483 to
1.654. The minimum value of the ratio of the two sines,
or of the two velocities, viz., 1.483, is called the extraordi-
nary index.
419. When a small aperture through which light
passes is regarded through a rhomb of Iceland spar two
PHENOMENA PRESENTED BY ICELAND SPAR. 105
apertures are seen. If the rhomb be placed over a black
dot on a sheet of white paper, two dots will be seen ; and
if the spar be turned, one of the images of the aperture or
of the dot will rotate round the other.
420. The rotating image is that formed by the ex-
traordinary ray.
421. One of the two images of the dot is also nearer
than the other. The ordinary ray behaves as if it came
from a more highly refractive medium, and the greater
the refraction the nearer must the image appear. The ap-
parent shallowness of water is referred to in Notes 131
and 132. With bisulphide of carbon the shallowness
would be more pronounced, because the refraction is
greater. In Iceland spar the ordinary index bears nearly
the same relation to the extraordinary as the index of
bisulphide of carbon to that of water; hence the ordi-
nary image must appear nearer than the extraordinary
one.
422. Brewster showed that a great number of crystals
possessed two optic axes, or two directions on which a
beam passes through the crystal without division. Crys-
tallized sugar, mica, heavy spar, sulphate of lime, and topaz,
are examples.
423. Thus crystals divide themselves into
I. Single refracting crystals, such as rock-salt, alum,
and fluor-spar ; and
II. Double refracting crystals, of which we have two
kinds, viz. :
a. Uniaxal crystals, or those with a single optic axis,
such as Iceland spar, rock-crystal, and tourmaline ; and
b. Biaxal crystals, or those which possess two optic
axes, such as arragonite, felspar, and those mentioned in
422.
106 NOTES ON LIGHT.
424. When on a plate of Iceland spar cut perpen-
dicular to the axis, a beam of light falls obliquely, the
ordinary ray being the more refracted is nearer to the
axis than the extraordinary. The extraordinary ray is as
it were repelled by the axis. But Biot showed that there
are many crystals in which the reverse occurs, in which, that
is to say, the extraordinary ray is nearer to the axis than
the ordinary, being as it were attracted. The former class
he called repulsive or negative crystals ; Iceland spar, ruby,
sapphire, emerald, beryl, and tourmaline, being examples.
The latter class he called attractive or positive crystals,
rock-crystal, ice, zircon, being examples.
The Polarization of Light.
425. The double refraction of Iceland spar was dis-
covered by Erasmus Bartholinus, and was first described
by him in a work published in Copenhagen in 1669. The
celebrated Huyghens sought to account for the phenome-
non on the principles of a wave theory, and he succeeded
in doing so.
426. In his experiments on this subject, Huyghens
found that when a common luminous beam passes through
Iceland spar in any direction save one (that of the optic
axis), it is always divided into two beams of equal intensi-
ty / but that when either of these two half-beams is sent
through a second piece of spar, it is usually divided into
two of unequal intensity ; and that there are two posi-
tions of the spar in which one of the beams vanishes alto-
gether.
427. On turning the spar round this position of absolute
disappearance, the missing beam appeared ; its companion
at the same time becoming dimmer ; both of them then
passed through a phase of equal intensity, and when the
THE POLARIZATION OF LIGHT. 107
rotation was continued, the beam which was first trans-
mitted disappeared.
428. Reflecting on this experiment Newton came to
the conclusion that the divided beam had acquired sides
by its passage through the Iceland spar, and that its inter-
ception and transmission depended on the way on which
those sides presented themselves to the molecules of the
second crystal. He compared this two-sidedness of a beam
of light to the two-endedness of a magnet known as its
polarity ; and a luminous beam exhibiting, this two-sided-
ness was afterward said to be polarized.
429. In 1808, Mains, while looking through a bire-
fracting prism at one of the windows of the Luxembourg
Palace, from which the solar light was reflected, found
that in a certain position of the spar, the ordinary image
of the window almost wholly disappeared ; while, in a
position perpendicular to this, the extraordinary image
disappeared. He discerned the analogy between this
action and that discovered by Huyghensin Iceland spar,
and came to the conclusion that the effect was due to
some new property impressed upon the light by its reflec-
tion from the glass.
430. What is this property ? It may be most simply
studied and understood by means of the crystal called
tourmaline. This crystal is birefractive ; it divides a
beam of light incident upon it into two, but its molecular
grouping, and the consequent disposition of the ether
within it, are such that one of these beams is rapidly
quenched, while the other is transmitted with comparative
freedom.
431. It is to be borne in mind that the motions of the
individual ether particles are transverse to the direction in
which the light is propagated (read Note 219). In a
108 NOTES ON LIGHT.
learn of ordinary light the mirations occur in all direc-
tions round the line of propagation.
432. The change suffered by light in passing through
a plate of tourmaline, of sufficient thickness, and cut paral-
lel to the axis is this : All vibrations save those executed
parallel to the axis are quenched within the crystal. Hence
the beam emergent from the plate of tourmaline has all its
vibrations reduced to a single plane. In this condition it
is a beam of plane polarized l^ahh^
433. Imagine a cylindrical beam of light with all its
ether particles vibrating in the same direction say hori-
zontally looked down upon vertically, the ether particles,
if large enough, would be seen performing their excursions
to and fro across the direction of the beam. Looked at
crosswise horizontally, the particles would be seen ad-
vancing and retreating, but their paths would be invisible,
every ether particle covering its own path. In the one
case we should see the lines of excursion ; in the other case,
the ends of the lines only. In this, according to the
undulatory theory, consists the two-sidedness discovered
by Huyghens, and commented on by Newton.
Polarization of Light by ^Reflection.
434. The quality of two-sidedness is also impressed
upon light by reflection. This is the great discovery of
Malus. A beam reflected from glass is in part polarized
at all oblique incidences, a portion of its vibrations being
reduced to a common plane. At one particular incidence
the beam is perfectly polarized, all its vibrations being
reduced to the same plane. The angle of incidence which
corresponds to this perfect polarization is called the polar-
izing angle.
435. The polarizing angle is connected with the index
POLARIZATION OF LIGHT BY REFLECTION. 109
of refraction of the medium by a very beautiful law dis-
covered by Sir David Brewster.* When a luminous beam
is incident upon a transparent substance, it is in part
reflected and in part refracted. At one particular inci-
dence the reflected and refracted portions of the beam are
at right angles to each other. The angle of incidence is
then the polarizing angle. This is the geometrical expres-
sion of the law of Brewster.
436. The polarizing angle augments with the refractive
index of the medium. For water it is 53, for glass 58,
and for diamond 68.
437. Thus a beam of ordinary light, whose vibrations
are executed in all directions, impinging upon a plate of
glass at the polarizing angle, has, after reflection, all its
vibrations reduced to a common plane. The direction of
the vibrations of the polarized beam is parallel to the polar-
izing surface.
438. Let a beam thus polarized by reflection at the
surface of one plate of glass impinge upon a second plate
at the polarizing angle. In one position of this plate the
beam suffers its maximum reflection. In a certain other
position the beam is wholly transmitted, there is no reflec-
tion. In this experiment the angle of incidence remains
unchanged, nothing being altered save the side of the ray
which strikes the reflecting surface.
439. The reflection of the polarized beam is a maxi-
mum when the lines along which the ether particles vibrate
are parallel to the reflecting surface. It is wholly trans-
mitted w T hen the lines of vibration strike the reflecting
surface at the polarizing angle. The reflection is then
zero. By taking advantage of this fact, the reflection
from the first surface of a thin film has been abolished,
* The index of refraction of the medium is the tangent of the polar-
izing angle.
110 NOTES ON LIGHT.
Newton's rings being thereby rendered incapable of for-
mation, as stated in Note 402.
440. A beam which meets the first surface of a plate
of glass with parallel sides at the polarizing angle meets
the second surface also at its polarizing angle, and is in
part reflected there perfectly polarized. Hence, by aug-
menting the number of plates, the repeated reflections at
their limiting surfaces furnish a polarized beam of greater
intensity than that obtained by reflection at a single
surface.
Polarization of Light by Refraction.
441. We have hitherto directed our attention to the
reflected portion of the beam ; but the refracted portion,
which enters the glass, is also partially polarized. The
quantities of polarized light in the reflected and refracted
beams are always equal to each other.
442. The plane of vibration in the refracted beam is at
right angles to that in the reflected beam.
443. When several plates of glass are placed parallel
to each other, and a beam is permitted to fall upon them
at the polarizing angle, at every passage from plate to
plate a portion of the light is reflected polarized, an equal
portion of polarized light entering the glass at the same
time. By duly augmenting the number of plates, the
polarization by the successive refractions may be ren-
dered sensibly perfect. When this occurs, if any further
plates be added to the bundle, reflection entirely ceases at
their limiting surfaces, the beam afterward being wholly
transmitted.
Polarization of Light by Double Refraction.
444. In the case last considered the light was polarized
by ordinary refraction. The polarization of light by double
LIGHT TRANSMITTED THROUGH ICELAND SPAR. HI
refraction has been already touched upon in Notes 432
and 433. We shall now extend our examination of the
crystal of tourmaline there referred to, and turn it to ac-
count in the examination of other crystals.
445. If a beam of light which has passed through one
plate of tourmaline impinge upon a second plate, it will
pass through both, if the axes of the two plates be parallel.
But if they are perpendicular to each other, then the light
transmitted by the one is quenched by the other, dark-
ness marking the space where the two plates are super-
posed.
446. If the two axes be oblique to each other, a portion
of the light will pass through both plates. For, in a
manner similar to the resolution of forces in ordinary me-
chanics, an oblique vibration may be resolved into two,
one parallel to the axis of the tourmaline, the other per-
pendicular to the axis. The latter component is quenched,
but the former is transmitted.
447. Hence if the axes of two plates of tourmaline be
perpendicular to each other, a third plate of tourmaline
introduced obliquely between them, or a plate of any other
crystal which acts in a manner similar to the tourmaline,
will transmit a portion of the light emergent from the
first crystal. The plane of vibration of this light being
oblique to the axis of the second crystal, a portion of the
light will also pass through the latter. By the intro-
duction, therefore, of a third crystal, with its axis oblique,
we abolish in part the darkness of the space where the two
rectangular plates are superposed.
Examination of Light transmitted through Iceland Spar.
448. We have now to examine, by means of a plate
of tourmaline, the two parts into which a luminous beam
is divided in its passage through Iceland spar.
NOTES ON LIGHT.
449. Confining our attention to one of the two beams,
it is immediately found that in a certain position of the
plate the light is freely transmitted, while in the per-
pendicular position it is completely stopped. This proves
the beam emergent from the spar to be polarized.
450. From the position of the tourmaline we can im-
mediately infer the direction of vibration in the polarized
beam. If transmission occur when the axis 6f the plate
of tourmaline is vertical, the vibrations are vertical ; if
transmission occur when the tourmaline is horizontal, the
vibrations are horizontal. The same mode of investiga-
tion teaches us that the second beam emergent from the
spar is also polarized.
451. The vibrations of the ether particles in the two
beams are executed in planes which are at right angles to
each other. If the vibrations in the one beam be vertical,
in the other they are horizontal. A plate of tourmaline
with its axis vertical transmits the former and quenches
the latter; while the same plate held horizontally, quenches
the former and transmits the latter.
452. A tourmaline plate placed with its axis vertical,
in front of the electric lamp, has its image cast by a lens
upon a screen. A piece of Iceland spar, with one of its
planes of vibration horizontal and the other vertical,
placed in front of the lens divides the beam into two, and
yields two images of the tourmaline. One of these images
is bright, the other is dark. The reason is, that in the
light emergent from the tourmaline the vibrations are
vertical, and they can only be transmitted through the
spar in company with its vertically vibrating beam., In
the horizontally vibrating beam the tourmaline must ap-
pear black.
453. It is also black if the light emergent from it, and
surrounding it, meet, at the polarizing angle, a plate of
LIGHT TRANSMITTED THROUGH ICELAND SPAR. H3
glass whose plane of reflection is vertical y while it is
bright when the light is reflected horizontally. These
effects are consequences of the law of polarization by re-
flection.
454. Not only do crystallized bodies possess this
power of double refraction and polarization; but all bodies
whose atomic grouping is such as to cause the ether with-
in them to possess different elasticities in different direc-
tions do the same.
455. Thus organic structures are usually double re-
fracting. A double refracting structure may also be con-
ferred on ordinary glass by either strain or pressure.
Strains and pressures due to unequal heating also produce
double refraction. Unannealed glass behaves like a crys-
tal. A plate of common window-glass, which under ordi-
nary circumstances shows no trace of double refraction, if
heated at a single point, is rendered doubly refractive by
the strains and pressures propagated round the heated
point. The introduction of any of these bodies between
the crossed plates of tourmaline partly abolishes the dark-
ness caused by the superposition of the plates.
456. Two plates of tourmaline, between which bodies
may be introduced and examined by polarized light, con-
stitute a simple form of the polariscope. The plate at
which the light first enters is called the polarizer, while
the second plate is called the analyzer.
457. But the tourmalines are small, usually colored,
and under no circumstances competent to furnish an in-
tense beam of polarized light. If one of the parts into
which a prism of Iceland spar divides a beam of light
could be abolished, the remaining beam would be polar-
ized, and, because of the transparency of the spar, it
would be far more intense than any beam obtainable from
tourmaline.
114 NOTES ON LIGHT.
458. This has been accomplished with great skill by
Nicol. He cut a long parallelopiped of spar into two by
a very oblique section; polished the two surfaces, and
united them by Canada balsam. The refrangibility of
the balsam lies between those of the ordinary and the ex-
traordinary rays in Iceland spar, being less than the
former and greater than the latter. When, therefore, a
beam of light is sent along the parallelopiped, the ordi-
nary ray, to enter the balsam, must pass from a denser to
a rarer medium. In consequence of the obliquity of its
incidence it is totally reflected, and is thus got rid of.
The extraordinary ray, on the contrary, in passing from
the spar to the balsam passes from a rarer to a denser
medium, and is therefore transmitted. In this way we
obtain a single intense beam of polarized light (read Notes
123, 141, and 142).
459. A parallelopiped prepared in the fashion here de-
scribed is called a NicoVs prism.
460. Nicol's prisms are of immense use in experiments
on polarization. With them the best polariscopes are
constructed. Reflecting polariscopes are also constructed,
consisting of two plates of glass, one of which polarizes
the light by reflection, the other examining the light so
polarized. The beam reflected from the polarizer is in this
case reflected or quenched by the analyzer according as
the planes of reflection of the two mirrors are parallel or
at right angles to each other.
Colors of Double-refracting Crystals in Polarized Light.
461. A large class of these colors may be illustrated
and explained by reference to the deportment of thin
plates of gypsum (crystallized sulphate of lime, commonly
called selenite) between the polarizer and analyzer of the
polariscope.
COLORS OF DOUBLE-REFRACTING CRYSTALS. H5
462. The crystal cleaves with 'great freedom in one
direction ; it cleaves with less freedom in two others ; the
latter two cleavages are also unequal. In other words,
gypsum possesses three planes of cleavage, no two of
which are equal in value, but one of which particularly
signalizes itself by its perfection.
463. By following these three cleavages it is easy to
obtain from the crystal diamond-shaped laminaB of any re-
quired thinness.
464.. The crystal, as might be expected from the char-
acter of its cleavages, is double-refracting. A beam of
ordinary light impinging at right angles on a plate of
gypsum, whose surfaces are those of most perfect cleavage,
has . its vibrations reduced to two planes at right angles
to each other ; that is to say, the beam whose ether, prior
to entering the gypsum, vibrates in all transverse direc-
tions, after it has entered the gypsum, and after its
emergence from it, vibrates in two rectangular directions
only.
465. The elasticity of the ether is different in these
two rectangular directions ; consequently the one beam
passes more rapidly through the gypsum than the other.
466. In refracting bodies generally the retardation of
the light consists in a diminution of the wave-length of
the light. The rate of vibration is unchanged during
the passage of the light through the refracting body.
The case is exactly similar to that of a musical sound
transmitted from water into air. The velocity is reduced
to one-fourth by the transfer, because the wave-length is
reduced to one-fourth. But the pitch, depending as it
does on the number of waves which reach the ear in a
second, is unaltered.
467. Because of the difference of elasticity between
the two rectangular directions of vibration in gypsum, the
116 NOTES OX LIGHT.
waves of ether in the one direction arc more shortened
than in the other.
468. In the experiments with a plate of gypsnm now
to be described and explained, we shall employ as polar-
izer a piece of Iceland spar, one of whose beams is in-
tercepted by a diaphragm. A Nicol's prism shall be our
analyzer.
469. When the planes of vibration of the spar and
of the Mcol coincide, the light passes through both and
may be received upon a screen. When the planes of
vibration are at right angles to each other, the light emer-
gent from the spar is intercepted by the Nicol, and the
screen is dark.
470. If a plate of selenite be placed between the
polarizer and analyzer, with either of its planes of vibra-
tion coincident with that of the polarizer or analyzer, it
produces no change upon the screen. If the screen be
light, it remains light ; if it be dark, it remains dark after
the introduction of the gypsum, which here behaves like
a plate of ordinary glass.
471. Let us assume the screen to be dark. Interpos-
ing a thick plate of gypsum with its directions of vibra-
tion oblique to that of the polarizer or analyzer, white light
reaches the screen. If the plate be thin, the light which
reaches the screen is colored. If the plate be of uniform
thickness, the color is uniform. If of different thicknesses,
or if in cleaving thin scales cling to the surface of the film,
some portions of the plate will be differently colored from
the rest.
472. When thick plates are employed, the different
colors, as in the case of thin plates, are superposed, and re-
blended to white light.
473. The quantity of light which reaches the eye is a
maximum when the planes of vibration of the gypsum
COLORS OF DOUBLE-REFRACTING CRYSTALS. H7
enclose an angle of 45 with those of the polarizer and
analyzer.
474. If the plate of selenite be a thin wedge, and if the
light be monochromatic, say red, alternately bright (red)
and dark bands are thrown upon the screen.
475. If, instead of red light, blue be employed, the
blue bands are found to occur at smaller thicknesses than
those which produced the red : other colors occur at inter-
mediate thicknesses. Hence when white light is employed,
instead of bands of brightness separated from each other
by bands of darkness, we have a series of iris-colored
bands.
476. If, instead of a wedge gradually augmenting in
thickness from the edge toward the back, we employ a disk
gradually augmenting in thickness from the centre out-
ward ; instead of a series of parallel bands we obtain under
similar circumstances, in white light, a series of concentric
iris-colored circles.
477. Here, then, we have in the first instance a beam
of plane polarized light impinging on the selenite. The
direction of vibration of this beam is resolved into two
others at right angles to each other; namely, into the
two directions in which the ether vibrates within the crys-
tal. One of these systems of waves is retarded with refer-
ence to the other.
478. But as long as the rays vibrate at right angles to
each other, they cannot interfere so as to augment or di-
minish the intensity. To effect such interference the rays
must vibrate in the same place.
479. The function of the analyzer is to reduce the two
rectangular wave-systems to a single plane. Here the
effect of retardation is at once felt, and the waves conspire
or oppose each other according as their vibrations are in
the same phase or in opposite phases.
118 - NOTES OX LIGHT.
480. When the vibration planes of the polarizer and
analyzer are parallel^ a thickness of the gypsum crystal
which produces a retardation of half an undulation causes
the light to be extinguished by the analyzer.
481. When the polarizer and analyzer are crossed, a
retardation of half an undulation, or of any odd number
of half undulations, within the crystal does not produce
extinction when these vibrations are compounded by the
analyzer. A retardation of a whole undulation, or of any
number of whole undulations, produces in this case extinc-
tion. This, when followed out, is a plain consequence of
the composition of the vibrations.
482. Expressed generally, the phenomena exhibited by
the parallel and crossed polarizer and analyzer are com-
plementary. If the field be dark when they are crossed,
it is bright when they are parallel. If the field be green
when they are crossed, it is red when they are parallel ;
if yellow when they are crossed, it is blue when they are
parallel. Thus a rotation of 90 always brings out the
complementary color.
483. If instead of the Mcol we employ a birefracting
prism of Iceland spar, the colors of the selejiite produced
by the two oppositely-polarized beams will be comple-
mentary. The overlapping of the two colors always pro-
duces white. Any other double-refracting substance,
whether crystallized, organized, mechanically pressed or
strained, exhibits, on examination by polarized light, phe-
nomena similar to those of the gypsum.
484. A common beam of light is equivalent in all its
effects to two beams vibrating in two rectangular planes.
As two such beams cannot interfere, we cannot have the
colors of the selenite in common light.
KINGS SURROUNDING THE AXES OF CRYSTALS. H9
Rings surrounding the Axes of Crystals in Polarized
Light.
485. A pencil of rays passing along the axis through
Iceland spar suffers no division ; but if inclined to the axis,
however slightly, the pencil is divided into two, which
vibrate in rectangular planes, and one of which is more
retarded than the other.
486. If the incident light be polarized, on quitting the
spar, oblique to the axis, it will be in a condition similar
to the light emergent from the plates of gypsum already
referred to. When two rectangular vibrations, passing
through the same ether, are reduced to the same plane by
the analyzer, interference occurs ; the two rays either con-
spiring or opposing each other.
487. Whether they conspire or not depends upon the
amount of relative retardation, and this again depends
upon the thickness of the spar traversed by the two rays.
If they conspire at a certain thickness they will also con-
spire at twice that thickness, thrice that thickness, etc.
Those thicknesses at which the rays conspire are separated
by others at which they oppose each other.
488. With a conical beam whose central ray passes
along the axis, the effects are symmetrical all round the
axis ; and when the crystal, illuminated by such a ray, is
examined by monochromatic polarized light, we have a
series of bright and dark circles surrounding the axis.
489. When the light is red the circles are larger than
when the light is blue ; the smaller the wave-length the
smaller are the circles. Hence, since the different colors
are not superposed, when white light is employed instead
of bands of alternate brightness and darkness we have ?
series of iris-colored circles.
120 NOTES ON LIGHT.
When the polarizer and analyzer are crossed the sys-
tem of bands is intersected by a "black cross, whose arms
are parallel to the planes of vibration in the polarizer and
analyzer. Those rays, whose planes of vibration within
the crystal coincide with the planes of either the polarizer
or analyzer, cannot get through either, and their complete
interception forms the two arms of the cross. Those rays
whose planes of vibration enclose an angle of 45 with
that of the polarizer or analyzer produce the greatest effect
when they conspire. At this inclination the bright ring
is at its maximum brilliancy, from which, right and left,
it becomes more feeble, until it finally merges into the
darkness of the cross.
490. A rotation of 90 produces here, as in other cases,
the complementary phenomena : the black cross becomes
white, and the circles change their tints to complementary
ones.
491. In crystals possessing two optic axes a series of
iris-colored bands surround both axes, each band forming
a curve, which its discoverer, James Bernoulli, called a
lemniscata.
Elliptic and Circular Polarization.
492. Two rays of light vibrating at right angles to
each other, however the one system of vibrations may be
retarded with reference to the other, cannot, as already
stated, interfere so as to produce either an increase or a
diminution of the light.
493. But though the intensity remains unchanged, the
rays act upon each other. If one of them differs from the
other by any exact number of semi-undulations, the two
rays are compounded to a single rectilinear vibration. In
all other cases the resultant vibration is elliptical / in one
ROTARY POLARIZATION. 121
particular case the ellipse in which the individual particles
of ether move is converted into a circle. This occurs when
one of the systems of waves is an exact quarter of an
undulation behind the other ; we have then circular polar-
ization.
494. This compounding of ethereal vibration is me-
chanically the same as the compounding of the vibrations
of an ordinary pendulum ; or as the compounding of the
vibrations of two rectangular tuning-forks by the method
of Lissajous.*
495. Elliptic polarization is the rule and not the excep-
tion. It is particularly manifested in reflection from
metals, and from transparent bodies which possess a high
index of refraction. Jamin has detected it in light reflected
from all bodies.
Rotary Polarization.
496. A polarized ray of monochromatic light, as al-
ready stated, suffers no change during its transmission
through Iceland spar in the direction of the optic axis.
497. But if transmitted through rock-crystal (quartz)
in the direction of the optic axis, its plane of vibration is
turned by the crystal. Supposing the polarizer and ana-
lyzer of the polariscope to be crossed so as to produce
perfect darkness before the crystal is introduced between
them, on its introduction light will pass, and to quench
the light the analyzer must be turned into a new position.
The angle through which the analyzer is turned measures
the rotation of the plane of vibration.
498. Some specimens of rock-crystal turn the plane of
vibration to the right, and others to the left. The former
are called right-handed and the latter left-handed crystals.
* See Lectures on Sound, 1st ed., p. 307.
6
122 NOTES ON LIGHT.
Sir John Herschel connected this optical difference with a
visible difference of crystalline form.
499. In the celebrated experiment of Faraday, with a
bar of heavy glass, the plane of vibration was caused to
rotate both by a magnet and an electric current ; the
direction of rotation bearing a constant relation to the
polarity of the magnet and to the direction of the current.
500. The subject of rotary polarization was examined
with great care and completeness by Biot, and he estab-
lished certain laws regarding it, two of which may be
enunciated here :
1. The amount of the rotation is proportional to the
thickness of the plate of rock-crystal.
2. The rotation of the plane of vibration is different
for the different rays of the spectrum, increasing with the
refrangibility of the light.
Thus with a plate of rock-crystal one millimetre thick,
he obtained the following rotations for the mean rays of
the respective colors of the spectrum :
Red, 19.
Orange, 21'
Yellow, 23 C
Green, 28 C
Blue, 32.
Indio 36
Violet, 41
With a plate two millimetres in thickness the rotation for
red is 38 and for violet 82.
501. Since, then, the rays of different colors emerge
from the rock-crystal vibrating in different planes, when
such light falls upon the analyzer that color only whose
plane of vibration coincides with that of the analyzer will
be transmitted. By turning the analyzer we allow the
other colors to pass in succession.
502. The phenomena of rotary polarization are pro-
duced by the interference of two circularly-polarized pen-
of light, which are propagated along the axis with
CONCLUSION. 123
unequal velocities, the one revolving from left to right,
and the other revolving in the opposite direction.*
CONCLUSION.
I have endeavored in these lectures to bring before
you the views at present entertained by all eminent scien-
tific thinkers regarding the nature of light. I have en-
deavored to make as clear to you as possible that bold
theory according to which space is filled with an elastic
substance capable of transmitting the motions of light and
heat. And consider how impossible it is to escape from
this or some similar theory to avoid ascribing to light,
in space, a material basis. Solar light and heat require
about eight minutes to travel from the sun to the earth.
During this time the light and heat are .detached from
both. Enclose, in idea, a portion of the intervening space
say a cubic mile of it occupied for a moment by light
and heat. Ask yourselves what they are. The first in-
quiry toward a solution is, What can they do ? We only
know things by their effects. What, then, are the effects
which this cubic mile of light and heat can produce ? At
the earth, where we can operate upon them, we find them
capable of producing motion. We can lift weights with
them ; we can turn wheels with them ; we can urge locomo-
tives with them ; we can fire projectiles with them. What
other conclusion can you come to than that the light and
heat which thus produce motion are themselves motions f \
One cubic mile of space, then, is for a measurable time
the vehicle of motion. But is it in the human mind to
imagine motion without at the same time imagining some-
* See Lloyd, Wave Theory, p. 199, etc.
f Sir William Thomson has attempted to calculate " the mechanical
value of a cubic mile of sunlight."
124 NOTES ON LIGHT.
thing moved ? Certainly not. The very conception of
motion necessarily includes that of a moving body. What,
then, is the thing moved in the case of our cubic mile of
sunlight ? The undulatory theory replies that it is a sub-
stance of determinate mechanical properties, a body which
may or may not be a form of ordinary matter, but to
which, whether it is or not, we give the name of ether.
Let us tolerate no vagueness here ; for the greatest dis-
service that could be done to science the surest way to
give error a long lease of life is to enshroud scientific
theories in vagueness. The motion of the ether com-
municated to material substances throws them into mo-
tion. It is, therefore, itself a material substance, for we
have no knowledge that in nature any thing but a material
substance can throw other material substances into mo-
tion. Two modes of motion are possible to the ether.
Either it is shot through space as a projectile, or it is the
vehicle of wave-motion. The projectile theory, though
enunciated by Newton, and supported by such men as
Laplace, Biot, Brewster, and Malus, has hopelessly broken
down. Wave-motion, then, of one kind or another, we
must fall back upon. But how does the Wave Theory
account for the phenomena? Throughout the greater
part of these lectures we have been answering this ques-
tion. The cases brought before you are representative.
Thousands of facts might be cited in illustration of each
of them, and not one of these facts is left unexplained by
the undulatory theory. It accounts for all the phenomena
of reflection ; for all the phenomena of refraction, single
and double ; for all the phenomena of dispersion ; for all
the phenomena of diffraction ; for the colors of thick plates
and thin, as well as for the colors of all natural bodies. It
accounts for all the phenomena of polarization ; for all
those wonderful affections, those chromatic splendors ex-
CONCLUSION. 125
hibited by crystals in polarized light. Thousands of iso-
lated facts might, as I have said, be ranged under each
of these heads ; the undulatory theory accounts for them
all. It traces out illuminated paths through what would
otherwise be the most hopeless jungle of phenomena in
which human thought could be involved. This is why
the foremost men of the age accept the ether not as a
vague dream, but as a real entity a substance endowed
with inertia, and capable, in accordance with the estab-
lished laws of motion, of imparting its thrill to other sub-
stances. If there is one conception more firmly fixed in
modern scientific thought than another, it is that heat is
a mode of motion. Ask yourselves how the vast amount
of mechanical energy actually transmitted in the form
of heat reaches the earth from the sun. Matter must be
its vehicle, and the matter is according to theory the
luminiferous ether.
Thomas Young never saw with his eyes the waves of
sound; but he had the force of imagination to picture
them and the intellect to investigate them. And he rose
from the investigation of the unseen waves of air to that
of the unseen waves of ether ; his belief in the one being
little, if at all, inferior to his belief in the other. One ex-
pression of his will illustrate the perfect definiteness of
his ideas. To account for the aberration of light he
thought it necessary to assume that the ether which en-
compasses the earth does not partake of the motion of our
planet through space. His words are : " The ether passes
through the solid mass of the earth as the wind passes
through a grove of trees." This bold assumption has
been shown to be unnecessary by Prof. Stokes, who proves
that, by ascribing to the ether properties analogous to
those of an elastic solid, aberration would be accounted
126 NOTES ON LIGHT.
for, without supposing the earth to be thus permeable.
Stokes believes in the ether as firmly as Young did.
I may add, that one of the most refined experimenters
in France, M. Fizeau, who is also a a member of the Insti-
tute, undertook to determine, some years ago, whether a
moving body drags the ether along with it in its motion.
His conclusion is, that part of the ether adheres to the
molecules of the body, and is transferred along with
them. This conclusion may or may not be correct ; but
the mere fact that such experiments were undertaken by
such a man illustrates the distinctness with which this
idea of an ether is held by the most eminent scientific
workers of the age.
But while I have endeavored to place before you with
the utmost possible clearness the basis of the undulatory
theory, do I therefore wish to close your eyes against any
evidence that may arise of its incorrectness ? Far from
it. You may say, and justly say, that a hundred years
ago another theory was held by the most eminent men,
and that, as the theory then held had to yield, the undu-
latory theory may have to yield also. This is perfectly
logical. Just in the same way, a person in the time of
Newton, or even in our own time, might reason thus : The
great Ptolemy, and numbers of great men after him, be-
lieved that the earth was the centre of the solar system.
Ptolemy's theory had to give way, and the theory of
gravitation may, in its turn, have to give way also. This
is just as logical as the former argument. The strength
of the theory of gravitation rests on its competence to ac-
count for all the phenomena of the solar system ; and how
strong that theory is will be understood by those who
have heard in this room Prof. Grant's lucid account of all
CONCLUSION. 127
that it explains. On a precisely similar basis rests the
undulatory theory of light ; only that the phenomena which
it explains are far more varied and complex than the phe-
nomena of gravitation. You regard, and justly so, the
discovery of Neptune as a triumph of theory. Guided by
it, Adams and Leverrier calculated the position of a plane-
tary mass competent to produce the disturbances of Uranus.
Leverrier communicated the result of his calculation to
Galle, of Berlin ; and that same night Galle pointed the
telescope of the Berlin Observatory to the portion of the
heavens indicated by Leverrier, and found there a planet
36,000 miles in diameter.
It so happens that the undulatory theory has also its
Neptune. Fresnel had determined the mathematical ex-
pression for the wave-surface in crystals possessing two
optic axes ; but he did not appear to have an idea of any
refraction in such crystals other than double refraction.
While the subject was in this condition the late Sir Wil-
liam Hamilton, of Dublin, a profound mathematician,
took it up, and proved the theory to lead to the conclu-
sion that at four special points of the wave-surface the
ray was divided not in two parts, but into an infinite
number of parts ; forming at those points a continuous
conical envelope instead of two images. No human eye
had ever seen this envelope when Sir William Hamilton
inferred its existence. If the theory of gravitation be
true, said Leverrier, in effect, to Dr. Galle, a planet ought
to be there : if the theory of undulation be true, said Sir
William Hamilton to Dr. Lloyd, my luminous envelope
ought to be there. Lloyd took a crystal of Arragonite,
and following with the most scrupulous exactness the in-
dications of theory, discovered the envelope which had
previously been an idea in the mind of the mathematician.
128 NOTES ON LIGHT.
Whatever may be the strength which the theory of gravi-
tation derives from the discovery of Neptune, it is matched
by the strength which the undulatory theory derives from
the discovery of conical refraction.
NOTE.
I would strongly recommend for perusal the essay on
Light, published in Sir John Herschel's " Familiar Lectures
on Scientific Subjects."
J. T.
NOTES
OF A COURSE OF SEVEN LECTURES ON
ELECTRICITY.
NOTES ON EL-EGTEIOITT.
Voltaic ^Electricity : the Voltaic Battery.
1. IF two pieces of the same metal (pure zinc or pure
platinum, for example) be immersed in water, which has
been rendered sour by the addition of a little sulphuric
acid, the acidulated water attacks neither.
The ordinary zinc of commerce being rendered impure
by the admixture of other metals is attacked by the acid.
It may, however, be enabled to withstand the acid by
covering its surface with mercury. The zinc is dissolved
by the mercury, detached from its impurities, and pre-
sented to the liquid. This process is called amalga-
mation.
2. If two pieces of two different metals (pure zinc and
platinum, for example) be immersed in acidulated water,
no sensible action occurs as long as the metals do not touch
each other but the moment they touch, and as long as
they continue in contact, the zinc is attacked by the acid-
ulated water and dissolves, while bubbles of gas rise
from the surface of the platinum.
3. This gas when collected proves to have the specific
gravity of hydrogen ; like hydrogen it also burns in the
air. The water, in fact, is decomposed by the touching
metals ; its oxygen unites with the zinc to form oxide of
zinc, while its hydrogen escapes from the platinum.
132 NOTES ON ELECTRICITY.
4. If the two metals be only partially plunged into the
acidulated water, it does not matter whether contact oc-
curs within the liquid or outside of it. The effect in both
cases is the decomposition of the water, the solution of
the zinc, and the liberation of the hydrogen gas.
5. When the two partially immersed metals arc con-
nected outside the liquid by a long wire (say of copper)
the effect is the same as when they touch directly. In
both cases a circuit is said to be formed, consisting of the
two metals and the liquid. In the case last mentioned
the copper wire is said to complete the circuit.
For these experiments a strip of platinum and a strip
of amalgamated zinc are employed. The liquid is placed
in a glass cell with parallel sides, through which is sent a
beam of light, and by means of a lens a magnified image
of the cell and its two strips is cast upon a screen. The
chemical action consequent upon touching the metals,
or on completing the circuit with a wire, and its suspension
when contact is interrupted, are then very plainly seen.
6. The wire is also said to be the vehicle of an electric
current which flows round the circuit. It is also called a
Voltaic current, because the action here described was
discovered by the celebrated Italian philosopher Yolta.
These terms, however, convey to ug, as yet, no meaning.
Our sole business during the present lecture is to examine
the wire which completes the circuit, and to determine
wherein it differs from an ordinary wire.
7. And to enable ourselves to do this effectually, we
shall employ an arrangement, or a combination, of zinc
and platinum plates and acids, known as a voltaic battery.
We shall subsequently analyze this battery, and de-
termine what occurs within it. For the present, as afore-
said, we shall confine ourselves to the examination of the
wire which completes the circuit outside the battery.
ELECTRO-MAGNETISM: ELEMENTARY PHENOMENA. 133
Electro-Magnetism : Elementary Phenomena.
8. Interrupting the circuit, and immersing the wire in
iron filings, it shows no power of attraction over them.
Establishing the circuit, on reimmersing the wire in the
filings they cluster round it and cling to it. If the wire
be raised out of the filings, they form an envelope round
it. The moment, however, the circuit is interrupted, the
filings fall.
9. If the wire be disconnected from the plates of plat-
inum and zinc, and stretched under and parallel to a sus-
pended bar magnet, no action is observed ; but on mak-
ing the wire, stretched beneath the magnet, form part of
a voltaic circuit, the magnet is deflected from the mag-
netic meridian. This is OErsted's discovery.
10. To the eye the wire, if tolerably thick, is un-
changed by its connection with the zinc and platinum.
But if for the thick copper wire a thin platinum wire be
substituted it is sensibly heated, and may even be caused
to glow brightly. The wire therefore must be the vehicle
of some power or condition, which is competent to pro-
duce both magnetic and thermal phenomena.
11. If a naked wire, forming part of a voltaic circuit, be
wound round a bar of iron, the power of which the wire
was the vehicle is in great part transmitted to the iron
which becomes part of the circuit.
12. But if the wire be overspun with cotton, or still
better with silk, this transmission of the power from the
wire to the iron bar is prevented. The wire may then be
coiled round the bar while the power is compelled to pass
in succession through all the convolutions of the wire.
Here the iron bar is not at all in the circuit.
13. But though not in the circuit it is powerfully ex-
cited by the surrounding wire. Every convolution of the
134 NOTES ON ELECTRICITY.
wire evokes a certain amount of magnetism in the bar ;
and by rendering the convolutions sufficiently numerous,
a magnet of enormous strength may be thus generated.
This is Sturgeon's application of Arago's discovery.
14. Such a magnet is called an Electro-magnet to dis-
tinguish it from ordinary permanent steel magnets. When
the circuit is broken the power of the electro-magnet
ceases. It then falls from its highly-excited condition to
the condition of ordinary iron.
15. For electro-magnetic purposes the covered wire is
usually coiled round a hollow reel, several layers of coil
being sometimes superposed upon each other. In this
condition the reel is called an electro-magnetic helix. The
iron bar to be magnetized is placed within the helix, form-
ing its core. The electro-magnet may be either straight,
shaped like a horseshoe, or it may be caused to assume
other forms.
16. The smooth bar of iron placed across the ends, or
poles, of a horseshoe magnet, is sometimes called a keeper,
sometimes an armature, and sometimes a sub-magnet.
17. It is not necessary that the convolutions of the
helix should be close to the core. A hoop, for example,
a yard in diameter, round which covered wire is coiled,
magnetizes an iron bar placed across it at its centre. The
magnetized body is here nearly 18 inches from the mag-
netizing coil. How is the power transmitted from the one
to the other ? Is it an action at a distance, or does it re-
quire a medium for its propagation ? I do not know.
The question at present profoundly interests investiga-
tors.
18. If a covered wire forming part of a voltaic circuit
be coiled round an iron bar near one of its ends, there is a
propagation of the excitement along the bar toward the
distant end. As the coils augment in number the attrac-
ELECTRO-MAGNETIC ENGINES. 135
tive power of the distant end increases. On undoing the
coils the magnetism gradually falls. The process resem-
bles more or less the conduction of heat. The augmenta-
tion of the coils answering to the increasing of the tem-
perature, and the undoing of the coils answering to the
cooling of the end of the bar.
Electro-Magnetic Engines.
19. When the end -of a cylinder of iron is partially in-
troduced into an electro-magnetic helix, on completing the
circuit a force of suction is exerted upon it tending to draw
it into the helix. Page turned this force to account in the
construction of an electro-magnetic engine.
Hollow iron cylinders, which pass freely into the
helix, are employed for this experiment. The end only
of the hollow cylinder being introduced, when the circuit
is completed the cylinder is suddenly and strongly
sucked in.
20. Others have turned to account mechanically the
attraction exerted by electro-magnetic cores on bars of
iron. The distinguished electro-mechanician Froment pro-
duced rotatory motion in this way. A series of electro-
magnets are so ranged that their poles lie facing each
other along the circumference of a circle ; and a series of
transverse bars of iron are so connected together as to be
able to approach the poles in succession, and rotate as a
system. "When the circuit is established, these bars are
attracted, motion being thus imparted to the system. The
bars on arriving at the poles which attract them suddenly
cease to be attracted ; the magnetism being temporarily
suspended to allow each bar to pass forward, with the
velocity impressed upon it, to the next pair of attracting
poles. On reaching these the magnetism is again tem-
porarily suspended. Thus the bars are never pulled
136 NOTES ON ELECTRICITY.
back / and in this way a continuous motion of rotation is
maintained.
21. This rotatory motion can be applied in various
ways ; it may, for example, be caused to pump water, to
saw wood, or to drive piles.
One of Froment's electro-magnetic engines, and its
application to pumping and pile-driving, is employed to
illustrate this.
Physical Effects of Magnetization.
22. Sound is one of the physical effects which accom-
pany sudden magnetization and sudden demagnetization.
An ear placed close to an iron core hears a clink the mo-
ment the circuit is established round it. A clink is also
heard when the circuit is broken. This is Page's discovery.
Employing a contact-breaker (in a distant room to abolish
its noise) the coil may be magnetized and demagnetized
in quick succession ; the sounds then produced may be
heard by several hundreds at once.
A poker of good soft iron placed within an electro-
magnetic helix, and with its two ends supported on wooden
trays, produces a very good effect. The sound may be
rendered musical.
23. When an iron bar is magnetized its volume is un-
changed, but its shape is altered. It lengthens in the
direction of magnetization. This is Joule's discovery.
24. Joule employed a system of levers to augment the
effect, and a microscope to observe the elongation thus
augmented. Our method is this : The iron bar is magnet-
ized by an electro-magnetic helix which surrounds it.
Its elongation is first augmented fiftyfold by means of a
lever; and this motion is applied to turn the axis of a
rotating mirror. From the mirror is reflected a long beam
of light, which forms an index without weight. The re-
PHYSICAL EFFECTS OF MAGNETIZATION. 137
fleeted beam may be caused to print a circle of light upon
a white screen, and this circle when the bar is magnetized,
suffers a displacement due to the elongation of the bar.
This displacement may amount to a foot or more.
What is the cause of this elongation ? The discussion
of this question requires some preliminary knowledge.
25. If a sheet of paper or a square of glass be placed
over a magnet, iron filings scattered on the paper or on
the glass arrange themselves in lines, which Faraday called
Lines of Force. Along these lines the filings set their
longest dimensions, and they also attach themselves end
to end. A little bar of iron, or a small magnetic needle,
freely suspended, sets itself also along these lines of
force.
The formation and modifications of the magnetic curves,
or lines of force, are shown in this lecture by means of small
magnets held between plates of glass and strongly illumi-
nated. Magnified images of the curves are thrown upon
a screen about 40 feet distant. The shifting of the curves
by the tapping of the glass is plainly visible.
26. We may regard a bar of iron as made up of parti-
cles united by the force of cohesion, but still to some ex-
tent distinct. When iron is broken we see crystalline
facets on the surface of fracture. In fact, the bar is com-
posed of minute crystals of irregular shape. These, when
the bar is magnetized, try to set their longest dimensions
parallel to the direction of magnetization, that is to say,
in the direction of the bar itself. They succeed in this
effort to some slight extent, and thus produce the minute
and temporary lengthening of the bar. This is the ex-
planation of De la Rive. It is, I think, as true as it is
acute.
27. Magnetic oxide of iron may be suspended as a
powder in water contained in a cylindrical vessel with flat
138 NOTES ON ELECTRICITY.
glass ends. Let the vessel be surrounded by a coil of
covered wire. Looking at a candle through the muddy
liquid, and making the coil part of a voltaic circuit, the
candle brightens at the moment the circuit is made.
Breaking the circuit, dimness again supervenes. This is
due to an arrangement of the particles of suspended oxide
similar to that of the iron filings. They set their longest
dimensions parallel to the beam of light, and thus obstruct
its passage less. They also attach themselves end to end,
and form lines like the lines of filings. This beautiful ex-
periment is due to Grove.
Projecting a magnified image of the end of the cylin-
drical cell on a screen, and sending through it the beam
of the electric lamp whenever the circuit is established,
an illuminated disk, 2 or 3 feet in diameter, flashes out
upon the screen.
Character of Magnetic Force.
It is necessary to our further progress to have clear
and definite ideas as to the character of the magnetic
force.
28. The magnetic power of a magnet, or of a mag-
netic needle, though really distributed throughout its
mass, appears to be concentrated at two points near the
ends. These points are called the poles of the magnet or
needle.
29. The magnetic power of the earth is doubtless also
distributed through the mass of the earth, but a concen-
tration similar to that just noticed endows the earth also
with magnetic poles.
30. The action of the earth upon a magnetic needle is
this: the north terrestrial pole repels one end of the
needle and attracts the other ; the south magnetic pole
also attracts one end of the needle and repels the other.
CHARACTER OF MAGNETIC FORCE. 139
But the end attracted by the north terrestrial pole is re-
pelled by the south, while the end attracted by the south
is repelled by the north.
31. Thus to each terrestrial magnetic pole the needle
presents two ends which are differently endowed. Two
opposite kinds of magnetism may be supposed to be con-
centrated at the two ends. In this douUeness of the mag-
netic force consists what is called magnetic polarity.
32. Each of the two distinct 'kinds of magnetism may
be regarded as self-repellent. North repels north, and
south repels south. But different kinds of magnetism are
mutually attractive ; south attracts north, and north at-
tracts south.
33. When a magnet, or a magnetic needle, is suspended
with the line joining its poles oblique to the magnetic
meridian, the earth's action on the needle resolves itself
into what in mechanics is called " a couple," tending to
turn the needle into the magnetic meridian.
34. When the needle is in the meridian, the two forces
which constitute the couple are opposite and equal. The
tendency to produce rotation then ceases ; the needle is
in its position of equilibrium.
35. When the forces are equal and opposite they must
neutralize each other ; no motion of translation of the
needle being, therefore, possible. Thus, when the needle
is caused to swim on water, or on mercury, it does not
move toward either of the terrestrial magnetic poles.
36. One pole of a bar magnet repels the one end and
attracts the other end of a magnetic needle. At the other
pole of the magnet the attraction and repulsion are
reversed. In the middle of the magnet is the magnetic
equator, where neither end of the needle is attracted or
repelled.
140 NOTES ON ELECTRICITY.
Magnetism of Helix : Strength of Electro-Magnets.
3V. An electro-magnetic helix, even without a core of
iron, behaves exactly like a magnet. It attracts iron.
Its two ends, moreover, are opposite poles, and between
them is a magnetic equator. When, however, a core is
placed within the helix, the magnetism of the combined
system is far more intense than that of the helix alone.
38. The strength of a" magnet is measured by its power
to deflect a magnetic needle from its meridian ; the mag-
netic strength of a helix alone, and of a helix and core
combined, are similarly determined.
39. To obtain the magnetic strength of the core alone,
we first determine the strength of the helix alone, then
that of the helix and core combined; subtracting the
former strength from the latter, we obtain the magnetic
strength of the core.
40. If the cores be thick and formed of good iron, the
magnetic strength of the core is exactly proportional to
that of the helix. A helix of double power will produce
an electro-magnet of double strength ; a helix of treble
power, an electro-magnet of treble strength, and so on.
Thus by varying the strength of the helix we vary in like
degree the strength of the iron core within it.
Electro-Magnetic Attractions : Law of Squares.
41. And here an important point arises. When we
allow a core of double power to act upon a piece of good
iron, nearly but not quite in contact with the core, the
attraction of the iron is not doubled, but quadrupled. If
the core be of treble power, the attraction is not only
trebled, but it increases ninefold. If the magnetic
strength of the core be quadrupled, the attraction of the
iron is augmented sixteenfold. In fact, the attraction is
ELECTRO-MAGNETIC ATTRACTIONS. 141
proportional, not to the strength simply, but to the
strength multiplied by itself, or to the square of the
strength of the electro-magnet.
We must be very clear as to the cause of this action,
and must, therefore, contrast for a moment the magnetic
action of hard steel with that of soft iron.
42. Soft iron is easily magnetized, but it loses its mag-
netism when the magnetizing force is withdrawn. Steel
is magnetized with difficulty, but it retains its magnetism
even after the withdrawal of the magnetizing magnet.
43. This obstinacy on the part of steel in declining to
accept the magnetic state, and this retentiveness on the
part of steel when the magnetic condition has been once
imposed upon it, are called coercive force. It is not a
happy term, but it is the one employed.
44. Supposing a piece of magnetized steel to possess a
coercive force so high as to resist further magnetization,
its attraction by an electro-magnet would be directly pro-
portional, not to the square of the strength, but simply to
the strength of the electro-magnet.
45. Why, then, does the iron follow the law of the
square of the strength ? It is because the magnetic con-
dition of the iron is not constant, but rises with the
strength of the magnet. When the magnetism of the
core is doubled, the magnetism of the iron is also doubled ;
when the magnetism of the core is trebled, the magnetism
of the iron is trebled. The resultant attraction is found
by multiplying the magnetism of the iron by the magnet-
ism of the core, and this product is the expression of the
law of squares just referred to.
46. To make the matter clearer, let us figure the mag-
netism of the core as due to particles of magnetism, which
are introduced into the core in gradually-increasing num-
bers. Let us start with a core possessing one magnetic
142 NOTES ON ELECTKICITY.
particle, and let it act upon a piece of hard steel also pos-
sessing one magnetic particle; the resulting attraction will
be unity or 1. Let two particles be now thrown into the
core : the steel in virtue of its coercive force remains un-
changed, but its particle being now pulled by two parti-
cles instead of one, the resulting attraction will be 2. If
three particles of magnetism be thrown into the core, all
of them pulling at the single particle of the steel will pro-
duce a treble attraction, and so on.
47. ISTow let us start with a core possessing, as before,
a single particle of magnetism, and with a piece of iron
also possessing a single particle generated by the core ;
the attraction, as before, is here unity. On introducing
two particles into the core, they generate immediately two
particles in the iron. But two particles each pulled by
twice the force first exerted, makes the attraction four
times what it was at the outset.
It is to be remembered that every particle is attracted
as if the other particles were absent.
48. In like manner, if three particles be thrown into
the core, three particles are also generated in the iron.
Each of these iron magnetic particles is pulled by the three
particles of the electro-magnet ; that is to say, each of the
iron particles is pulled with three times the primitive force.
But there are three particles so pulled ; hence the attrac-
tion is nine times what it was at the outset.
49. Let us compare this action for a moment with that
of gravity. Two masses of matter attract each other with
a force which we shall take as our unit. If the one mass
be doubled, the attraction is doubled ; if both masses be
doubled, the attraction is increased fourfold. If one
mass be trebled, the attraction is trebled ; if both masses
be trebled, the attraction is increased ninefold. When,
therefore, both the masses are doubled and trebled, we
INFERENCE FROM LAW OF SQUARES. 143
have the law of squares. Now, it is this doubling and
trebling, in both cases, of the thing which causes magnetic
attraction, which causes it to follow the same law.
Inference from Law of Squares : Theoretic Notions.
50. Why do I lead you through these considerations ?
Simply to make clear to you, that if " the law of squares "
here developed show itself in the action of a magnet upon
matter, we may infallibly infer that the condition of that
matter is not a constant condition ; but that it rises and
falls with the condition of the magnet. Matter thus af-
fected is said to be magnetized by influence or by induc-
tion. It is attracted or repelled (for we shall come im-
mediately to the repulsion of matter by a magnei) in virtue
of some condition into which it is temporarily thrown by
the influencing magnet.
51. What then is the thing that causes magnetic attrac-
tion? The human mind has long striven to realize it.
Thales (600 B. c.) thought that the magnet possessed a
soul. Cornelius Gemma in 1535 supposed invisible lines
to stretch from the magnet to the attracted body, a con-
ception which reminds us of Faraday's Lines of Force.
Others thought the iron the natural nutriment of the
magnet. Descartes embraced magnetic phenomena in
his celebrated theory of vortices, and in our day Clerk
Maxwell has worked in this direction. ^Epinus assumed
the existence of a magnetic fluid. Coulomb assumed the
existence of two fluids, each self-repellent, but mutually
attractive. Ampere deemed a magnet an assemblage of
minute electric currents, which circulated round the atoms
of the magnetized body. These conceptions are some-
times exceedingly useful as a means of connection and
classification, even when we do not believe them true.
William Thomson deduces magnetic phenomena from
144 NOTES ON ELECTRICITY.
" imaginary magnetic matter," thus giving the mind tne
conception while distinctly releasing it from belief. The
real origin of magnetism is yet to be revealed.
Diamagnetism : Magne- Crystallic Action.
52. Brugmans, in 1778, first observed the repulsion of
bismuth by a magnet. In 1827 Le Baillif described the
repulsion of antimony. Saigey, Seebeck, and Becquerel,
also observed certain actions of the kind.
53. In 1845 Faraday generalized these observations
by demonstrating the magnetic condition of all matter.
He showed that bodies divided themselves into two great
classes, the one attracted, the other repelled by the poles
of a magnet.
54. To the force producing this repulsion, Faraday gave
the name of Diamagnetism.
What is the nature of this force ? Is it inherent and
constant, or is it induced ?
55. The repulsion of diamagnetic bodies follows accu-
rately the law of squares above developed. A double
force produces a quadruple repulsion ; a treble force pro-
duces a ninefold repulsion, and so on.
56. Hence we may infer, with certainty, that the con-
dition of diamagnetic bodies in virtue of which they are
repelled by a magnet, is a condition induced by the mag-
net, rising and falling as the strength of the magnet rises
and falls.
57. The force of diamagnetism is vastly feebler than
that of ordinary magnetism. Of all diamagnetic sub-
stances, for example, bismuth is the most strongly repelled ;
but its repulsion is almost incomparably less than the at-
traction of iron. According to Weber, the magnetism of
a thin bar of iron exceeds the diamagnetism of an equal
mass of bismuth about two and a half million times.
FRICTIONAL ELECTTJCITY. 145
58. Diamagnetic bodies under magnetic excitement
exhibit a polarity the reverse of that of magnetic bodies.
In all cases, whether we operate with helices or with
magnets, or with helices and magnets combined, the
actions of magnetic and diamagnetic bodies are anti-
thetical.
59. An iron statue standing erect on the earth's sur-
face is converted into a magnet by the earth's magnetism ;
a marble statue, or a man standing erect, is converted by
the same force into a diamagnet ; for marble is diamag-
netic, and so are all the tissues and all the solids and
fluids of the human body. The poles of the man are those
of the iron statue reversed.
60. Organic bodies, and most crystals, are magnetized
with different degrees of intensity in different directions.
They are endowed with axes of magnetic induction.
61. Thus in the case of Iceland spar (carbonate of
lime), the repulsion along the axis is a maximum. In the
case of carbonate of iron, a crystal of the same shape and
structure as carbonate of lime, the attraction along the
axis is a maximum.
62. The position assumed by a crystal when suspended
between the poles of a magnet, depends on its magnetie
axes.
Frictional Electricity : Attraction and Repulsion : Con-
duction and Insulation.
63. By the friction of a woollen cloth amber is en-
dowed with the power of attracting light bodies. This
substance was called Electron by the Greeks ; hence the
name Electricity was applied to the power of attraction
exhibited by amber. This attraction remained an isolated
fact for more than 2,000 years.
64. In the year 1600 Dr. Gilbert of Colchester, physi-
7
146 NOTES ON ELECTRICITY.
cian to Queen Elizabeth, showed that the power of attrac-
tion was shared by many other substances. Dry glass,
for example, when rubbed by silk, and dry sealing-wax
when rubbed by flannel, exhibit this attractive power.
When they do so they are said to be electrified.
65. An electrified body attracts and is attracted by all
kinds of unelectrified matter ; but repulsion may also come
into play. Thus, rubbed glass repels rubbed glass, and
rubbed sealing-wax repels rubbed sealing-wax ; while
rubbed glass attracts rubbed sealing-wax, and rubbed
sealing-wax attracts rubbed glass.
66. Hence the notion of two kinds of electricity: one
proper to vitreous bodies, and therefore called vitreous
electricity ; the other proper to resinous bodies, and there-
fore called resinous electricity.
67. These terms are improper; because by employing
suitable rubbers we can obtain the electricity of sealing-
wax from glass, and the electricity of glass from sealing-
wax. We now use the term positive electricity to denote
that developed on glass by the friction of silk ; and nega-
tive electricity to denote that developed on sealing-wax
by the friction of flannel.
68. Bodies endowed with the same electricity repel
each other, while bodies endowed with opposite electrici-
ties attract each other. This is the fundamental law of
electric action.
69. The rubber and the body rubbed are always en-
dowed with opposite electricities. They always attract
each other. The work done in overcoming this attraction
appears as heat in the electric spark.
70. To find the kind of electricity with which a body
is endowed we must ascertain, by trial, the electricity by
which the body is repelled. This, we mayi)e sure, is the
electricity of the body. Attraction does not furnish a
safe test, because unelectrified bodies are attracted.
THEORIES OF ELECTRICITY. 147
71 Some substances possess in a very high degree the
capacity of transmitting the electric power, or condition ;
others possess in a high degree the capacity of intercept-
ing it. The former bodies are called conductors, the latter
bodies, insulators.
12. The insulators were formerly called electrics, be-
cause they could be electrified by friction when held in
the hand. The conductors were called non-electrics, be-
cause they could not be so electrified. The division is
improper, because if a conductor be insulated it can
readily be electrified. To keep it electrified an insulator
must be introduced between it and the earth.
Theories of Electricity : JZZectric Fluids.
73. What is electricity? Why should it adhere so
tenaciously to some substances, and flow so freely through
or along others ? The human mind has made many
attempts to imagine the inner cause of electric action, and
it still continues to make such attempts. Formerly it was
thought that magnetism and electricity, as well as light
and heat, were all the work of " imponderable matter,"
associated with the ordinary matter. In the case of light
and heat, this conception has undergone profound modi-
fication ; and we seem to see clearly the mechanical cause
of both. But no similar clearness has as yet been at
tained with regard to electricity, though a strong presump-
tion exists that our notions of it are destined soon to
undergo a modification equally profound.
74. Meanwhile we may employ the provisional con-
ception furnished by the theory of electric fluids. It will
enable us to classify our facts, though it is not to be re-
garded as demonstrated.
75. According to this theory, electrical attractions and
repulsions arise from two invisible fluids, each self-re-
.
148 NOTES ON ELECTRICITY.
pulsive but both mutually attractive. The fluids are
supposed to be mixed together to form a compound neu-
tral fluid in unelectrified bodies.
76. The act of electrification, by friction, consists in
the forcible separation of the two fluids, one of which is
diffused over the rubber, and the other over the body
rubbed. But they may also be separated in another way
now to be illustrated.
Electric Induction : the Condenser : the jElectrophorus.
77. If an electrified body be brought near an insulated
unelectrified conductor, but not into contact with it, the
electrified body will decompose the compound fluid of the
conductor ; attracting one of its constituents and repelling
the other. When the electrified body is withdrawn, the
separated fluids reunite and neutralize each other.
78. This forcible separation of the two fluids of a
neutral conductor, by the mere proximity of an electrified
body, is called electric induction. Bodies in this state are
also said to be electrified by influence. Neutral bodies are
attracted because they are first excited by induction.
79. When an insulated conductor is acted on by an
electrified body, its repelled electricity is free, but its
attracted electricity is held captive by the inducing elec-
trified body. Connecting the conductor for a moment
with the earth, its free electricity escapes ; and then, on
the removal of the electrified inducing body, the captive
electricity is liberated and diffused over the surface of the
conductor.
80. Thus by the mere proximity of the electrified body,
and without establishing contact between it and the
neutral conductor, we can charge the latter with the oppo-
site electricity.
81. Two sheets of tin-foil (conductors) being separated
THE ELECTRIC MACHINE: THE LEYDEN-JAR. 149
from each other by- a sheet of glass (an insulator), if one
sheet have electricity imparted to it, it will act through
the glass, and decompose the neutral electricity of the
opposite sheet attracting the one constituent and repelling
the other.
82. If the second sheet be connected with the earth
"the repelled electricity will flow away, and we shall have
two mutually attractive layers of electricity separated
from each other by the glass.
83. If the one sheet of tin -foil be united with the other
by a conductor,, the two opposite electricities will flow
together ; the tin-foil is then said to be discharged. This
discharge usually assumes the form of a spark.
84. If the surface of a cake of resin, or of a sheet of
vulcanized india-rubber be electrified, a plate of metal
laid upon it will have its neutral fluid decomposed ; its
positive fluid being attracted and its negative repelled.
On touching the metal plate its free (repelled) electricity
flows to the earth ; and now if the plate be raised by an
insulating handle, it will appear charged with positive
electricity. This is the principle of the Electrophorus.
TJie Electric Machine : the Ley den-jar.
85. An Electric Machine consists of two parts : the
insulator, which is excited by friction, and the prime con-
ductor.
86. The first electric machine consisted of a ball of
sulphur, which was rubbed against the hand. It was in-
vented by Otto von Guericke, burgomaster of Magdeburg,
in the year 1671. A sphere of glass was afterward intro-
duced, then a cylinder of glass, and finally a round glass
plate, which was rubbed with dry silk.
87. The prime conductor is thus charged: When the
glass plate is turned by a handle it passes between the silk
150 NOTES ON ELECTEICITY.
rubbers and is positively electrified. The electrified glass
then acts by induction upon the prime conductor, attract-
ing the negative electricity and repelling its positive.
The conductor is furnished with points, from which the
negative electricity streams out against the excited glass.
Thus the prime conductor is charged, not by directly
communicating to it positive electricity, but by robbing
it of its negative, the positive remaining behind.
88. The arrangement mentioned in Note 81 is virtually
a Leyden-jar. Were the plate of glass there referred to
moulded into the shape of a jar, one sheet of foil would
cover its interior and the other its exterior. When the
jar is connected with an electric machine, its charged in-
terior coating acts by induction across the glass on the
exterior coating, attracting the opposite and repelling the
similar electricity.
89. In the experiment which led to the discovery
of the Leyden-jar the hand of the experimentalist served
as the outer coating.
90. The escape of the repefl^d electricity of the outer
coating to the earth leaves the cVptive electricity exposed
solely to the attraction of that within the jar, and enables
the jar to take a strong charge.
The Electric Current.
91. When the outer and the inner coatings are con-
nected by a conductor, an electric current passes from the
one to the other.
92. The current starts at the same instant from the
inner and outer coatings; the middle point of the conduct-
or being reached last by the current. This indicates that
there are two currents which start at the same moment
from the inner and outer coatings.
THE ELECTRIC DISCHARGE. 151
93. It is agreed to call the direction in which the
positive electricity flows the direction of the current.
The Electric Discharge : Thunder and Lightning.
94. "When an electric current encounters resistance in
its passage, heat is developed : this heat is sometimes so
intense as to reduce metals to a state of vapor.
95. When a body is intensely electrified, it will dis-
charge its electricity to an unelectrified body across an
interval of air in the form of an electric spark. Two
bodies oppositely electrified discharge to each other in the
same way.
96. When two oppositely electrified clouds discharge
toward each other, the track of the lightning marks the
course of an electric current, and the sound of the thunder
is the sound of an electric spark.
97. An electrified cloud, if it 'come near the earth, may
discharge its electricity to the earth jn the*same way.
98. If the body througli which the atmospheric elec-
tricity passes be a good conductor, and of sufficient size,
no harm is done; but the resistance offered by trees,
houses, and animals, to the passage of the electricity
usually causes their destruction.
99. The nervous system Acquires a certain interval of
time to become conscious of pain. The time of an electric
discharge is but a small fraction of this interval ; hence
as a sentient apparatus the nervous system is destroyed
before consciousness can set in. If this be true and there
are the strongest grounds for believing it to be true
death from lightning must be painless.
100. When an electrified cloud passes over a pointed
lightning-conductor, the opposite electricity of the earth
is discharged from the point of the conductor against the
152 NOTES ON ELECTRICITY.
cloud. The cloud is thus neutralized, and, in general,
without producing thunder.
101. The duration of an electric spark amounts only to
an extremely small fraction of a second. On this account,
when moving bodies are suddenly illuminated by the
spark from a Ley den-jar, they appear to rest for a short in-
terval in the position which they occupied when the flash
fell upon them. A moving cannon-ball illuminated by a
flash of lightning appears to stand still about one-eighth
of a second, this being about the interval during which an
impression, once made, persists upon the retina.
102. The unretarded electric spark will scatter gun-
powder, but will not ignite it. To produce ignition it is
necessary to retard the discharge by sending it through a
wet string.
Electric Density : Action of Points.
103. If we double the quantity of electricity imparted
to the same conductor, the density of the electricity is
said to be doubled ; if we treble the quantity, the density
is said to be trebled ; and so on.
104. On a sphere the density of the electricity is the
same at all points of its surface ; on a plate the density
is greatest at the edges ; and on an elongated conductor
the density is greatest at the 'ends.
105. When the conductor ends in a sharp point the
electric density at the point is so great that the electricity
discharges itself into the air.
106. The air thus electrified is self-repellent, and is also
repelled by the point, the so-called " electric wind " being
produced.
107. By causing an electric wind to issue from opposite
points of a light body, the reaction of the two winds
RELATION OF VOLTAIC TO FRICTIONAL ELECTRICITY. 153
may make the body to float in stable equilibrium in the
air.
Relation of Voltaic to Frictional Electricity.
108. The outer ends of two pieces of zinc and platinum,
partially immersed in acidulated water, are in opposite
electrical conditions. The free platinum end shows posi-
tive electricity, while the free zinc end shows negative
electricity.
109. When both plates are united by a wire, the posi-
tive flows along the wire toward the negative, and the
negative toward the positive. But, as mentioned in
Note 93, it is agreed to call the direction in which the
positive electricity flows the direction of the current.
110. The force which urges this current forward (the
electro-motive force) is enormously less than that which
urges forward a current of frictional electricity. The
consequence -is, that the latter is able to surmount resist-
ances which are totally un surmountable by the former.
111. But by linking cells together we cause the voltaic
current to approach more and more to the character of
the frictional current. It requires, however, a battery of
more than a thousand cells to make the current from a
voltaic battery jump over an interval of air I6 * 00 th of an
inch in length. An electric machine of moderate power,
and furnished with a suitable conductor, is competent to
urge its current across an interval ten thousand times as
great as this.
112. The electric spark passes through air by the
agency of the particles of the conductor from which it
springs, and which are carried forward by the discharge.
113. But measured by other standards the frictional
current is almost incomparably more feeble than the vol-
taic current. For example: it is not without special
154 NOTES ON ELECTRICITY.
arrangements for multiplying the effect that the current
from a large electrical machine is enabled to deflect a mag-
netic needle.
114. Faraday immersed two wires, the one of zinc and
the other of platinum, each -^th of an inch in diameter, in
a cell of acidulated water. The depth of immersion was
only -|ths of an inch, and the time of immersion only J^ths
of a second. Still he found that the electricity generated
by this small apparatus, in this brief time, produced a
distinctly greater effect upon a magnetic needle than 28
turns of the large electric machine of the Royal Institu-
tion.
115. A cubic inch of air, if compressed with sufficient
power, may be able to rupture a very rigid envelope ; while
a cubic yard of air, if not so compressed, may exert but
a feeble pressure upon the surfaces which bound it. Now
the electricity of the machine is in a condition analogous
to the compressed air. Its density, or, as it fs sometimes
called, its intensity, or tension, is great. The electricity
from the voltaic battery, on the other hand, resembles the
uncompressed air. It exceeds enormously in quantity
that from the machine ; but it falls enormously below it
in intensity.
116. The deflection of a magnetic needle and other
actions of the voltaic current depend solely upon quantity,
hence the vast superiority of the voltaic current in pro-
ducing such deflection.
117. Faraday found the quantity of electricity dis-
engaged by the decomposition of a single grain of water
in a voltaic cell (see Note 5) to be equal to that liberated
in 800,000 discharges of the great Leyden battery of the
Royal Institution. This, if concentrated in a single dis-
charge, would be equal to a great flash of lightning. He
also estimated the quantity of electricity liberated by the
HISTORIC JOTTINGS. 155
chemical action of a single grain of water on four grains
of zinc to be equal in quantity to that of a powerful
thunder-storm.
118. Weber and Kohlrausch have found that the quan-
tity of electricity associated with one milligramme of
hydrogen in water, if diffused over a cloud 1,000 metres
above the earth, would exert upon an equal quantity of
the opposite electricity at the earth's surface an attractive
force of 2,268,000 kilogrammes.*
Historic Jottings^ concerning Conduction and the
Leyden-jar.
119. In 1729, Stephen Grey, pensioner of the Charter
House, discovered electric conduction. Connecting an end
of a wire 700 feet long with a glass tube and supporting
the wire on loops of silk, he found that on rubbing the
tube the distant end of his wire became electrified and
attracted light bodies. He also found that a wire loop did
not answer as a support, as the electricity escaped through
it ; hence arose the division of bodies into conductors and
insulators. Grey's observations were written down by
the secretary of the Royal Society the day before his
death.
120. In October, 1 745, Von Kleist, a bishop of Cammin,
in Pomerania, charged with electricity a flask containing
sometimes mercury, sometimes alcohol. Through a cork
in the neck of the flask passed an iron nail, which was
brought into contact with the conductor of an electrical
machine. On touching the nail Yon Kleist experienced a
violent shock.
121. In January, 1746, Cunseus of Leyden received also
a shock, and his experiment was repeated by Allamand
* The metre is a yard and one-eleventh in length ; the milligramme
is - G L 5 th of a grain ; the kilogramme is 2 Ibs. 3^ oz.
156 NOTES ON ELECTRICITY.
and Musschenbroek. A wire passed from the conductor
of the machine into a flask filled with water. Musschen-
broek held the flask in the right hand, the machine was
turned, and then with the left hand he drew a spark from
the conductor. The shock received was, according to
Musschenbroek so terrible, that he declared he would not
receive a second for the crown of France. Musschen-
broek observed that it was only the person who held the
flask in his hand that felt the shock. Kleist failed to
recognize this condition.
122. In Germany the jar is sometimes called Kleist's
jar, but more commonly, because of the failure just referred
to, the Ley den-jar. The theory of it, and other similar
apparatus, was given by Franklin in September, 1747.
(See Notes 81, 88, 89, 90.)
123. In 1747, Dr. Watson, Bishop of Llandaff, sent the
discharge from a Leyden-jar through 2,800 feet of wire,
and through the same distance of earth. Subsequently, in
the same year, he sent the discharge through 10,600 feet
of wire, supported by insulators of baked wood. The ex-
periment was made on Shooter's Hill.
124. In 1748 similar experiments were made by Frank-
lin across the Schuylkill, and by De Luc across the Lake
of Geneva.
Historic Jottings^ concerning the Electric Telegraph.
125. The first proposal of an electric telegraph was
made by an anonymous contributor to the Scot's Maga-
zine for 17 53. Various attempts to apply frictional elec-
tricity for this purpose were subsequently made. They
culminated in the exceedingly ingenious arrangement of
Mr. (now Sir Francis) Ronalds, published in 1823.
126. The voltaic pile was described by Volta in a
letter to Sir Joseph Banks, written from Como in 1800.
HISTORIC JOTTINGS. 157
127. Immediately afterward Nicholson and Carlisle
discovered the decomposition of water by the voltaic
current.
128. In 1808 Sommering proposed a system of tele-
graphy based on the discovery of Nicholson and Carlisle.
A similar system was proposed about the same time by
Prof. Coxe, of Pennsylvania.
129. In 1820 GErsted discovered the deflection of a
magnetic needle by an electric current.*
130. The idea of employing the deflection of the
needle for telegraphic purposes occurred to the cele-
brated French mathematician, La Place; the problem
was partly worked out by Ampere, and still further ad-
vanced by Ritchie, Professor of Natural Philosophy in the
Royal Institution.
131. In 1832 Baron Schilling constructed models of a
telegraphic apparatus which were exhibited before the
Emperors Alexander and Nicholas.
132. In 1833 Gauss and Weber established an electric
telegraph between the Physical Cabinet and the Astro-
nomical and Magnetic Observatories of Gottingen, em-
bracing a distance of nearly 10,000 feet. Faraday's elec-
tricity instead of Volta's was employed by Gauss and
Weber.
133. Steinheil was requested by Gauss to pursue the
subject. To the telegraph he made many highly-impor-
* In his exceedingly useful little book on the Telegraph, published in
Weale's "Rudimentary Series," Mr. Robert Sabine quotes the following
remarkable passage from a work on magnetism, published in Paris, by
Prof. Izarn, in 1804: "D'apres les observations de Romagnesi, physicien
de Trente, 1'aiguille deja aimantee, et que 1'on soumet ainsi au courant
galvanique, eprouve une declinaison; et d'apres celles de J. Majon,
savant chemiste de Genes, les aiguilles non-aimentees acquierent par ce
moyen une sorte de polarite magnetique." The work containing this
passage was lent to Mr. Sabine by Mr. Latimer Clark!
158 NOTES ON ELECTRICITY.
tant contributions and suggestions. In 1837 lie had estab-
lished a system of wires about 40,000 feet in length, con-
necting various points in the city of Munich and its
neighborhood. The most considerable discovery of Stein-
lieil, and, indeed, one of the most practically important
hitherto made in connection with telegraphy, is that the
" return wire " between two stations might be dispensed
with, and the earth employed in its stead.
134. In 1834 Wheatstone, by means of a rotating mir-
ror, made his celebrated experiments on the velocity of
electricity. In the following year he exhibited one of
BarOn Schilling's telegraphs in his lectures at King's
College.
135. In 1836 Mr. William Fothergill Cooke saw in the
lectures of Prof. Muncke, at Heidelberg, the performance
of a similar instrument. Struck by its obvious practical
importance, he devised a system of telegraphy, and, in
partnership with Wheatstone, dating from June, 1837,
succeeded in introducing the telegraphic system into
England.
136. From 1832 to 1836 Morse sought to apply chemi-
cal decomposition by the electric current to telegraphic
purposes; he abandoned this for his electro-magnetic
system devised in 1836. This method consists in stamp-
ing, by means of the attraction of an electro-magnet, dots
and lines upon a slip of paper caused to move by proper
mechanism over the circumference of a wheel.
137. In 1850 the first submarine cable was laid by
Mr. Brett between Dover and Calais. It survived only a
day. In 1851 another cable was laid down, which proved
successful.
138. On the 5th of August, 1858, the submergence of
the first Atlantic cable was completed, and messages were
sent between England and America. The cable ceased
PHENOMENA IN TELEGRAPH-CABLES. 159
to act on the 4th of September, or about a month after its
submersion.
139. In 1865 the second Atlantic cable was laid and
lost. In 1866 a cable was successfully laid, and in the
same year the cable of 1865 was recovered. Messages are
now sent between England and America at the rate of
fourteen words a minute.
Phenomena observed in Telegraph- Cables*
140. Davy showed ("Elements of Chemical Philoso-
phy," 1812, p. 154) that a Leyden-battery could be charged
with voltaic electricity.*
* Davy thus describes the celebrated battery with which he made
this experiment. The spirit to which the battery owed its birth has not
diminished among the members of the Royal Institution : " The most
powerful combination that exists in which number of alternations is com-
bined with extent of surface, is that constructed by the subscriptions of
a few zealous cultivators and patrons of science, in the laboratory of the
Royal Institution (in 1808). It consists of two hundred instruments,
connected together in regular order, each composed of ten double plates
arranged in cells of porcelain, and containing in each plate thirty-two
square inches ; so that the whole number of double plates is 2,000, and
the whole surface 128,000 square inches. This battery, when the cells
were filled with 60 parts of water mixed with one part of nitric acid,
and one part of sulphuric acid, afforded a series of brilliant and im-
pressive effects. When pieces of charcoal about an inch long and one-
sixth of an inch in diameter, were brought near each other (within the
thirtieth or fortieth part of an inch) a bright spark was produced, and
more than half the volume of the charcoal became ignited to whiteness,
and by withdrawing the points from each other a constant discharge
took place through the heated air, in a space equal at least to four
inches, producing a most brilliant ascending arch of light, broad, and
conical in form in the middle. When any substance was introduced
into this arch, it instantly became ignited ; platina melted as readily in
it as wax in the flame of a common candle ; quartz, the sapphire, mag-
nesia, lime, all entered into fusion ; fragments of diamond, and points
of charcoal and plumbago, rapidly disappeared, and seemed to evapo-
1GO NOTES ON ELECTRICITY.
141. Dr. Werner Siemens was the first to employ (in
1847) gutta-percha as a means of insulating subterranean
telegraph-wires. On the 18th of January, 1850, in a paper
communicated to the Physical Society of Berlin, he stated
that a subterranean wire covered with gutta-percha, and
surrounded by the moisture of the earth, behaved like a
colossal Leyden-jar. He also found that ordinary tele-
graph-wires charged themselves, though in a much smaller
degree than the subterranean wires.
142. In 1838 Faraday predicted the retardation of the
electric discharge by its own inductive action. (" Experi-
rate in it, even when the connection was made in a receiver exhausted
by the air-pump ; but there was no evidence of their having previously
undergone fusion.
" When the communication between .the points positively and nega-
tively electrified was made in air, rarefied in the receiver of the air-
pump, the distance at which the discharge took place increased as the
exhaustion was made, and when the atmosphere in the vessel supported
only one-fourth of an inch of mercury in the barometrical gauge, the
sparks passed through a space of nearly half an inch ; and by withdraw-
ing the points from each other, the discharge was made through six
or seven inches, producing a most beautiful coruscation of purple light,
the charcoal became intensely ignited, and some platina wire attached
to it, fused with brilliant scintillations, and fell in large globules upon
the plate of the pump. All the phenomena of chemical decomposition
were produced with intense rapidity by this combination. When the
points of charcoal were brought near each other in non-conducting fluids,
such as oils, ether, and oxymuriatic compounds, brilliant sparks occurred,
and elastic matter was rapidly generated ; and such was the intensity of
the electricity, that sparks were produced, even in good imperfect con-
ductors, such as the nitric and sulphuric acids.
" When the two conductors from the ends of the combination were
connected with a Leyden-battery, one with the internal, the other with
the external coating, the battery instantly became charged, and on re-
moving the wires, and making the proper connections, either a shock or
a spark could be perceived ; and the least possible time of contact was
sufficient to renew the charge to its full intensity."
PHENOMENA IN TELEGRAPH-CABLES. 161
mental Researches," 1333. "Faraday as a Discoverer,"
new edition, p. 89.)
143. In 1854 Faraday experimented with cables at
the gutta-percha works of the Electric Telegraph Company.
One hundred miles of gutta-percha covered wire were im-
mersed in water, and a second hundred miles of a similar
wire were placed in a dry tank. We will call the former
the water wire, and the latter the air wire.
144. Connecting one pole of a battery with the earth,
and connecting the other pole with one of the two insu-
lated ends of the water wire, on breaking the connection
and touching the wire a powerful shock was received ; the
discharge from the wire was also competent to ignite a
Statham fuze. When, after having been in contact with
the battery, the wire was separated and connected with
a galvanometer, the instrument was powerfully affected.
145. A rush of electricity into the wire was declared
by the galvanometer when contact was made ; a rush out
of the wire was declared when the wire between the bat-
tery and the galvanometer was connected with the earth.
None of these effects were observed with the 100 miles of
air wire.
146. Faraday, like Werner Siemens, rightly explained
the effect by likening the cable to an enormous Leyden-
jar, the wire constituting the interior, the water the ex-
terior coating, with the gutta-percha insulator between
them. In fact, the surface of the wire in these experi-
ments amounted to 8,300 square feet, while the surface of
the outer coating of water was 33,000 square feet. To the
charge and discharge of this apparatus the effects observed
were due.
147. In a subterranean line of telegraph 1,500 miles
long were placed three galvanometers : one, , at the be-
ginning of the wire ; a second, #, in the middle ; and a
162 NOTES ON ELECTRICITY.
third, c, at the end, which was also connected with the
earth.
148. Connecting the battery with the wire of the galva-
nometer a, that instrument was instantly affected ; after
a sensible time b was affected ; and after a still longer
time, c. It required, in fact, two seconds for the electric
stream to reach the last instrument.
149. All the instruments being deflected, when the
battery was suddenly cut off at a, that instrument in-
stantly fell to zero, b fell subsequently, and c after a still
longer interval.
150. By a brief touch of the battery-pole against #,
that instrument was deflected, and could be allowed to
fall back into its neutral condition before the electric
power had reached b / b in its turn would be affected, and
left neutral before the power had reached c.
151. In this case a wave of force was sent into the wire
which gradually travelled along it, appearing in different
parts of the wire at successive intervals of time.
152. It was even possible, by adjusted touches of
the battery, to make several successive waves coexist in
the wire.
153. When, after making and breaking contact at a,
that galvanometer was connected with the earth, part
of the electricity sent into the wire returned, and de-
flected a in the reverse direction ; here currents flowed
in opposite directions out of both extremities of the wire.
154. These effects of induction enabled Werner Sie-
mens and Faraday to explain the widely-different veloci-
ties assigned by different experimenters to the electric
current.
155. To pass through any conductor electricity re-
quires time, the time being directly proportional to the
lengtJi of the conductor.
ARTIFICIAL CABLES. 163
156. But in the case of a submarine cable another cause
of retardation comes into play, namely, the charging of
the cable; the retardation here is proportional to the
square of the length of the cable.
Artificial Cables.
157. It was to illustrate points like these and to deter-
mine the dimensions to be given to the Atlantic cables,
that Mr. Cromwell Yarley devised his artificial cables.
158. In one of these cables a resistance equal to that
of a real cable 14,000 miles in length is obtained by intro-
ducing into the path of the current feebly-conducting
liquids instead of metallic wires. The inductive action
is obtained by means of condensers of tin-foil. In another
artificial cable coils of wire are employed to give the
necessary resistance.
159. The arrangement described in Note 81 is a con-
denser. But those constructed by Mr. Varley are of
enormously greater area, the condensing sheets being
separated from each other not by plates of glass, but by
thin sheets of paper and paraiBne. The vastness of the
area and the proximity of the inducing surfaces combine
to exalt the effect.
160. When the condensers themselves are charged by
a battery, on discharging them they exhibit phenomena
similar to those of a Leyden-jar. The shock, spark, and
other effects of frictional electricity, are readily obtained.
161. A series of 50 condensers, for example, joined " in
cascade," that is to say, with the outer coating of each
joined to the inner coating of the next, when charged with
a battery of 1,000 cells, yield powerful sparks, and defla-
grate wires.
162. If the wire be bent and introduced into a glass of
water, the glass is shattered by the discharge.
1G4 NOTES ON ELECTRICITY.
163. In the 14,000-mile artificial cable are introduced
a series of eleven tubes containing the resisting liquid.
Into these dip wires. One end of the charging battery is
connected with the earth, and the other end can, at will,
be connected with the artificial cable. A series of ten
galvanometers are placed between the resisting tubes
along the artificial cable.
164. When no condensers are employed, on making
connection with the battery all the galvanometers appear
to be simultaneously deflected.
165. When the condenser is introduced between each
pair of resisting cells ten condensers in all the current
has to charge each condenser to a certain degree be-
fore it can sensibly affect the galvanometer beyond the
condenser. Hence, when the condensers are attached,
the action on the galvanometers is successive, not con-
temporaneous.
166. Mr. Varley supposed his 14,000-mile artificial
cable divided into sections representing stations in Lon-
don, at Gibraltar, Malta, Suez, Aden, Bombay, Calcutta,
Rangoon, Singapore, Java, and Australia. Supposing
an actual cable laid, and galvanometers placed at these
stations, the deflections obtained on establishing battery
contact would be successive. They are represented by
the deflections of the galvanometers associated with the
artificial cable.
16V. By varying the resistance and the amount of in-
ductive condenser-surface, a representation of any other
cable may readily be produced.
168. Connected with the needle of each of the ten gal-
vanometers is a reflecting mirror, from which a brilliant
spot of light is cast upon a screen. When the cable is not
in action, the ten spots form a row along the same ver-
tical line ; when the battery contact is made, the successive
SKETCH OF OHM'S THEORY. 165
deflections of the galvanometers is declared by the suc-
cessive motion of the spots.
Sketch of Ohm's Theory and KolilrauscK s Verification.
169. I have already spoken (Note 110) of the force
which urges forward the electric current (the electro-
motive force). The amount of this force may be deduced
from the action of the current, when opposed by different
resistances, upon a freely-suspended magnetic needle.
170. If the wire which carries the current be cut
across, the current ceases to flow. The electricity ceases
to be dynamic. But at the two ends of the severed wire
we have static electricity.
171. By suitable instruments the amount of this stati-
cal charge may be determined ; it increases with the num-
ber of elements of the battery.
172. It is, moreover, proportional to the strength of
the current obtained when the wires are reunited.
173. In this way the statical charge becomes a meas-
ure of dynamical action : electricity at rest is connected
with electricity in motion.
174. In experiments on the electroscopic properties of
the voltaic circuit it is necessary that the battery should
be well insulated.
175. If the middle point of a wire which connects the
two poles of a voltaic battery be connected with the earth,
the tension of that point is null. The circuit gradually
rises in tension right and left to the two poles of the
battery. But on one side of the point we have exclusive-
ly positive electricity, while at the other side we have ex-
clusively negative electricity.
176. At equal distances, at opposite sides of the zero-
point, the tension is the same.
177. If any other point than the middle be connected
166 NOTES ON ELECTRICITY.
at the earth, it becomes the zero-point, right and left of
which as before we have the two opposite electricities.
178. If the negative end of the battery be connected
with the earth, the whole wire shows positive electricity ; if
the positive end be connected with the earth, the whole
wire shows negative electricity.
179. The wire offers a certain resistance to the passage
of the current. The battery itself is also in the circuit,
and the current has to overcome its resistance also. But
the resistance of the battery may be expressed by a
certain length of the external wire. When this is done
the sum of the lengths of both wires is called the reduced
length of the circuit.
180. Given the reduced length of the circuit and the
electro-motive force, we can determine" by a simple calcula-
tion the electric tension of every point in the circuit.
181. The circuit through which the current flows may
be represented by a horizontal line (called an abscissa) ;
the electric tension at every point of the circuit may be
represented by a vertical line (called an ordinate). If
ordinates be drawn to represent the electric tensions at a
great number of points of the circuit, the line joining the
ends of all the perpendiculars will represent the distribu-
tion of electric tension in the circuit. The steepness
of this line also represents what Ohm called the electric
fall.
182. More strictly, the electric fall is the decrease in
the length of the ordinate for the unit of length of the
abscissa.
183. The total charge of the wire is expressed by the
area of the triangle enclosed by the ordinate, abscissa,
and line of fall.
184. The laws of the voltaic circuit as enunciated by
Ohm, have been verified everywhere. The electroscopic
SKETCH OF OHM'S THEORY. 167
state of the circuit has been examined by Kohlrausch, and
found to be in strict accordance with Ohm's theory.
185. Ohm assumed the passage of the electric fluid
from one section to another of the connecting wire to be
due solely to the difference of electric tension between the
two sections ; he further assumed the quantity of electri-
city transmitted to be proportional to this difference of
tension, and from these fundamental assumptions he de-
duced the laws of the voltaic circuit.
186. These laws may be briefly stated thus :
. The strength of the current is directly proportional
to the electro-motive force.
b. The strength of the current is inversely propor-
tional to the resistance.
c. If the wire which unites the two poles of battery be
of the same material, and of the same thickness through-
out, the " electric fall " is the same throughout the wire.
d. If the wire be of the same material, but of different
thicknesses, the " fall " is steeper on the thin wire than on
the thick. The " fall " is inversely proportional to the
cross-section of the wire.
e. If the poles be connected by two wires of the same
thickness, but of different resisting powers, the electric
fall is steepest on the more resisting wire. The " fall " is
directly proportional to the specific resistances of the
wires.
187. In verifying these laws Kohlrausch employed a
condenser to augment the feeble charges obtained from
his voltaic cell, and he held this instrument to be essential.
By an exceedingly skilful device Sir Wm. Thomson has
rendered the condenser unnecessary, and has thus greatly
simplified the means of demonstration.
168 NOTES ON ELECTRICITY.
Electro-chemistry. Chemical Actions in the Voltaic Cell:
Origin of the Current.
188. Philosophers suppose matter to be made of ele-
mentary parts called atoms, which are practically indi-
visible.
189. The elementary atoms can be caused to unite to
form compound atoms, which are called molecules.
190. Thus water is formed of the combination of the
atoms of oxygen and hydrogen ; common salt is formed of
union of atoms of chlorine and sodium ; potash is formed
by the union of the atoms of potassium and oxygen ; the
sulphuric acid also which we employed to acidulate our
water is formed by the union of atoms of sulphur with
atoms of oxygen.
191. When, as in our first experiment, two strips of
zinc and platinum are dipped into acidulated water, the
zinc, as we know, exerts a very strong attraction on the
oxygen of the water. When the strips are united this
attraction triumphs ; the oxygen unites with the zinc, and
a voltaic current is established. .
192. The oxide of zinc here formed combines with the
sulphuric acid and forms sulphuric zinc.
193. By this removal of the oxide from its surface the
zinc is kept constantly clean, and thus enabled to attract
other atoms of oxygen from the surrounding liquid.
During this process the zinc gradually dissolves, and as
long as this continues the electric current will flow. In
fact, it is the constant dissolution of the zinc that main-
tains the permanent current.
194. The hydrogen of the water, as we have seen,
escapes as a free gas from the surface of the platinum,
which, unlike the zinc, is not dissolved.
195. We are not yet quite clear as to the precise way
ELECTRO-CHEMISTRY. 169
in which the electric current is supported by the solution
of the zinc, but the following facts and speculations ought
to be known to you.
196. When two different metals are brought into con-
tact, with no liquid between them, one of them charges
itself with positive and the other with negative electricity.
We have here the famous " contact force " which Volta
and his followers considered to be the urging power of the
voltaic current.
197. But the generation of heat, and the performance
of mechanical work, by the mere contact of two metals,
would be equivalent to a perpetual motion. It would be
at variance with the law which requires for the production
of any power an equivalent consumption of some other
power.
198. It is, however, a fact that when two different
metals touch each other the positive electricity resorts by
preference to one metal, and the negative electricity to
the other ; the two electricities are as it were attracted
differently by the two metals.
199. This difference of attraction, however, only causes
a momentary rearrangement of the two electricities,
which pass, when the contact is made, into a new condi-
tion of equilibrium. As long as the contact continues this
equilibrium is not disturbed ; there is no continuous cur-
rent.
200. We may regard the distinct atoms which enter
into the molecules of a compound as charged in a similar
manner. For example, the atoms of hydrogen and oxygen
when they unite to form a molecule of water, may be
looked upon as charged like the two touching metals.
This would be the case if the atoms, like the metals, pos-
sessed different attractions for the two electricities.
201. When strips of zinc and platinum are plunged
170 NOTES ON ELECTRICITY.
in such a liquid, the positively-charged atofn will turn
toward the one metal, and the negatively-charged atom
toward the other.
202. But, unless the metals touch each other, electrical
equilibrium immediately sets in, a constant state of electric
tension being set up at the free ends of the two metals.
203. The electricity at the ends may be permitted to
flow into a condenser, and may be thus stored up ; such a
condenser may thus be discharged through a covered wire
which passes round a magnetic needle, a deflection of the
needle being thus produced.
204. Thus in. Davy's experiment with his large voltaic
battery, wherewith he charged his battery of Leyden-jars,
the latter, after having been charged, might be discharged
through a galvanometer, a magnetic deflection being thus
produced.
205. But the metals, once relieved of their charge,
would immediately reload themselves with electricity, and
might be again employed to charge a Leyden battery, and
to produce a deflection of a magnetic needle.
206. At no moment during this process the battery
circuit would be complete ; still we should have a succes-
sion of magnetic actions similar to those observed with a
closed circuit.
207. In fact, in the closed circuit the solution of the
zinc incessantly removes the charged surface of that metal
by dissolving it away, and enables the zinc to take a fresh
charge ; an incessant effort, never fully satisfied, is made
to establish electric equilibrium ; the incessant renewal of
the effort maintains the electric current.
Chemical Actions at a Distance : Electrolysis.
208. Thus, then, in the cell where the voltaic current
is generated chemical action occurs. We have, on the one
CHEMICAL ACTIONS AT A DISTANCE. 171
hand, the decomposition of the water, and on the other the
combination of the zinc with the oxygen and the sulphu-
ric acid.
209. But a voltaic current can also produce chemical
action at a distance from its place of generation. This
discovery, as stated in Note 127, was made in the year
1800 by Nicholson and Carlisle.
210. We cannot decompose water by a single voltaic
cell ; but when two or more cells are united to form a
battery, the current from such a battery, when sent
through acidulated water, tears asunder the united atoms
of oxygen and hydrogen.
211. The oxygen is set free at the place where the
current enters ; the hydrogen is set free at the place
where the current quits the liquid. If the direction of the
current be reversed, the oxygen and hydrogen instantly
change places.
212. It must be clearly borne in mind that the direc-
tion of the current, as already defined, is the direction in
which the positive electricity moves. Knowing, therefore,
the places at which the oxygen and hydrogen are liber-
ated, we can infer with certainty the direction of the cur-
rent through the liquid.
213. For every volume of oxygen liberated in the de-
composition of water by a voltaic current, two volumes of
hydrogen are set free.
214. Electro-chemical decomposition is called electro-
lysis / and the compound liquid decomposed by the elec-
tric current is called an electrolyte.
215. The electric current formed a powerful means of
analysis in the famous experiments of Sir Humphry Davy
in 1807.
216. By operating with the current upon ordinary
potash, Davy found the base of this substance to be a
172 NOTES ON ELECTRICITY.
metal of exceeding lightness, and with an extraordinary
appetite for oxygen. When placed on water, it floated
on the liquid, and combined with its oxygen. By the
heat thus generated the liberated hydrogen was caused to
burst into flame. When a globule of the metal was placed
on ice, it burned with a bright flame, and the hole made
by the heat was filled with a solution of potash.
217. Soda, treated in the same manner, also yielded a
metal resembling that of potash. Thus Davy, by the use
of the voltaic current, decomposed the alkaline earths, and
greatly expanded our knowledge of chemistry.
218. To obtain these effects it is necessary to bring the
potash and the so.da to a state of fusion by heat. In the
solid state they are non-conductors of electricity. In fact,
the molecules, when rigid, cannot turn in the manner in-
dicated in Note 201. To conduct the current, it is neces-
sary that they should thus turn and be decomposed.
219. When the current is sent through a solution of
common salt, it decomposes both the water and the salt.
The chlorine of the salt, in company with the oxygen of
the water, appears where the current enters the liquid.
The sodium of the salt, in company with the hydrogen of
the water, appears where the current quits the liquid.
220. Chlorine possesses powerful bleaching properties ;
and if the solution of salt be colored with indigo or litmus,
the presence of the chlorine is declared by the destruction
of the color.
221. When a current is sent through a solution of
iodide of potassium, the brown substance iodine is set
free where the current enters, while the metal potassium
is set free where the current quits the solution. The ex-
periment may be made by moistening bibulous paper with
the dissolved iodide.
222. In electrolysis it is usual to immerse two plates of
ELECTROLYSIS. 173
platinum, or of some other suitable substance, in the
liquid to be decomposed, and to send the current from
plate to plate. The plate at which the current enters the
liquid is called the Positive Electrode, the plate at which
the current quits the liquid is called the Negative Elec-
trode. Without the liquid these electrodes would, as we
have already learned, charge themselves with positive
and negative electricity.
223. But inasmuch as electricities which attract each
other are of opposite qualities, the substance which is
liberated at the positive electrode is called the Electro-
ISTegative constituent, while the substance liberated at the
negative electrode is called the Electro-Positive constitu-
ent of the liquid.
224. Thus, in the examples above given the oxygen,
chlorine, and iodine, are the electro-negative elements ; the
hydrogen, sodium, and potassium, being the electro-posi-
tive elements.
225. The terms electro-positive and electro-negative
are, however, relative, for a substance may be electro-
positive in one combination, and electro-negative in an-
other.
226. If an electric current be conducted through a
solution of sulphate of soda, it separates the sulphuric acid
from the soda ; the presence of the acid may be proved by
its turning a vegetable color red.
227. When nitrate of silver or acetate of lead is decom-
posed by a voltaic current, crystals of silver, or of lead,
are deposited on the negative electrode.
228. The chemical actions of the electric current, some
examples of which are here given, constitute what is called
Electro-chemistry.
229. Electro-plating and gilding and the electrotype
process are important applications of electro-chemistry.
174 NOTES ON ELECTRICITY.
Here a chemical compound containing gold, silver, or
copper, is decomposed by a voltaic current, the metal
being deposited on the surface intended to be coated
with it.
230. If the surface on which the metal is deposited
have a design engraved upon it, the lines of the engrav-
ing are accurately filled by the metal which, when the
deposit is thick enough, may be detached, a perfect copy
of the design being thus obtained.
Measures of the Electric Current.
231. The tangent-compass, devised by Weber, con-
sists of a vertical ring of brass or copper, in the centre of
which swings a small compass-needle. The ring being
placed in the magnetic meridian, the needle is deflected
when a current is sent round the ring. The strength of
the current can be proved to be proportional to the tan-
gent of the angle of deflection ; hence the name of the
instrument.
232. The voltameter is an instrument devised by Fara-
day to measure the strength of an electric current. It
consists of a graduated tube which receives and measures
the quantity of gas generated by the current in a given
time.
233. The strengths of a series of currents measured by
the voltameter are accurately proportional to the same
strengths measured by the tangent-compass. Placing a
tangent-compass and a voltameter in the same series of
circuits, the tangents of the angles observed in the one
case are accurately proportional to the quantities of gas
generated in the other.
ELECTRIC POLARIZATION. 175
Electric Polarization : Hitter's Secondary Pile.
234. When an electric current is sent through acidu-
lated water a film of oxygen covers the positive electrode,
and a film of hydrogen covers the negative electrode.
One of these two substances being electro-positive, and the
other electro-negative, they act in the liquid like two dif-
ferent metals ; the hydrogen plays the part of zinc, and
the oxygen plays the part of platinum.
235. Interrupting the primary battery circuit, and
uniting together the two plates covered with their respec-
tive films, an electric current is obtained.
236. The direction of this current is from the hydro-
gen film to the oxygen film in the liquid, and from the
oxygen film to the hydrogen film through the connecting
wire.
237. Two electrodes thus covered with condensed
gaseous films are said to be polarized; and the currents
obtained from them are called currents of polarization.
238. Now the battery current being always from
oxygen to hydrogen (see Note 211), it is plain that the
current of polarization is always opposite in direction to
the battery current employed to polarize the electrodes.
239. When a decomposition cell with platinum plates
is introduced into a voltaic circuit, it is found that the
battery current, though strong at starting, gradually
sinks. This sinking is due to the gradual development
of the antagonistic current of polarization.
240. Also in the cells of the battery itself this current
of polarization may come prejudicially into play. When
two metals, say zinc and platinum, and one liquid, say
acidulated water, are employed, the platinum plate is
coated with a film of hydrogen.
241. This hydrogen, being electro-positive, resembles
176 NOTES ON ELECTRICITY.
a plate of zinc, so that when it is present we Lave, as it
were, zinc opposed to zinc in the battery.
242. Were both plates actually of zinc, we could have
no current ; and with the hydrogen film which approxi-
mates to zinc we have only a feeble current. To get
the full effect of the zinc and platinum some means must
be devised to remove from the platinum its film of hy-
drogen.
243. This is effected in Grove's battery by the em-
ployment of two liquids. The one is strong nitric acid,
which contains the plate of platinum ; the other is dilute
sulphuric acid, which contains the plate of zinc. The
nitric acid is placed in a vessel of porous earthenware,
which becomes saturated with the liquid and allows the
current to pass through it.
244. When the current passes, the hydrogen liberated
at the platinum electrode in Grove's cell is instantly oxi-
dized by the nitric acid, and prevented from forming a
film upon the surface of the platinum.
245. If instead of employing a single decomposition
cell and a single pair of platinum electrodes, we employ a
series of such cells, and send the same current through
them all, we convert every pair of such plates into an ac-
tive voltaic couple ; and if the number of such couples be
great, effects of great intensity may be obtained.
246. If instead of using decomposition cells we simply
employ a series of plates of the same metal, say a series
of half-crowns, separated from each other by pieces of
bibulous paper or by bits of cloth wetted with acidulated
water ; on sending a voltaic current through such a pile
of plates, we liberate on one of the surfaces of each plate
a film of oxygen, and on the other surface a film of hydro-
gen. These play the part of the two different metals in
the pile of Yolta.
FARADAY'S ELECTROLYTIC LAW. 177
247. The electro-motive force of such a pile maybe far
greater than that of the battery which charges it. It may
produce a far more brilliant spark, and urge its current
against resistances which would be quite insuperable to
the original battery current.
248. The discoverer of this form of pile was Bitter ; it
is sometimes called the secondary pile, to distinguish it
from the battery which charges it.
Faraday's Electrolytic, Law.
249. When the self-same current is sent through a
series of cells containing various compound liquids, the
same amount of liquid is not decomposed in all cases.
250. Let the current be sent in succession through a
series of cells containing water, oxide of lead, chloride of
lead, iodide of lead, and chloride of silver ; then taking
them in the above order, the weights of the liquids de-
composed are represented by the numbers 9, 111.5, 139,
230.5, 143.5.
251. The question now is, how are these weights of the
respective substances divided between the two electrodes?
Supposing the numbers to express grains, we should have
the following division between the electrodes :
At the positive electrode. At the negative electrode.
Water 8 grains oxygen. ... 1. grain hydrogen.
Oxide of lead. . . 8 " " 103.5 grains lead.
Chloride of lead. 35.5 " -chlorine... 103.5 " "
Iodide of lead.. 127 " iodine 103.5 " "
Chloride of silver 35.5 " chlorine... 108 " silver.
252. Now these numbers express the combining pro-
portions of the respective substances ; by the electric
current in all cases the law of combination as regards
quantity is exactly inverted. The substances combine in
equivalent proportions ; they are decomposed in precisely
178 NOTES ON ELECTRICITY.
the same proportions. This is the celebrated law of elec-
trolysis discovered by Faraday.
253. In no case in the body of the electrolyte is any
decomposition observed; in no case is any gas there liber-
ated. The substances set free appear at the electrodes,
and there alone.
254. Taking water as an illustration, the process is to
be figured thus : When the electrodes, charged with elec-
tricity from the battery, are plunged into the liquid, the
oxygen atom of the water turns toward the positive, and
the hydrogen atom toward the negative electrode.
255. If the electro-motive force be strong enough, the
oxygen is torn away from its hydrogen ; the free hydro-
gen immediately converges its attraction on the next
adjacent oxygen atom, and unites with it, dislodging at
the same time the hydrogen with which that atom
had been previously combined. Another atom of hydro-
gen is thus liberated, which in its turn decomposes the
adjacent water-molecule. Thus through the chain of
molecules run a series of decompositions, followed by im-
mediate recompositions, until the negative electrode is
reached. Here the hydrogen, having no further oxygen
with which to combine, is liberated as a gas. This is the
theory of Grotthuss, which at all events fairly embraces
the facts.
NobilPs Iris Rings.
256. The hardness of steel in tempering it is judged
by its color, which is due to a film of oxide overspreading
the steel. The oxide which forms on the surface of molten
lead also shows vivid colors.
257. These are the colors of thin plates investigated
by Newton and explained by Thomas Young.
258. By electro-chemical decomposition Nobili pro-
DISTRIBUTION OF HEAT IN THE CIRCUIT. 179
ciuced such colors in a very beautiful* manner. Placing,
for example, a polished steel plate in a dilute solution of
acetate of lead, and connecting the plate with the positive
pole of a voltaic battery, on dipping the end of a wire
connected with the negative pole into the solution, the
peroxide of lead is liberated on the surface of the steel
immediately under the wire ; and a film gradually dimin-
ishing in thickness spreads from that point outward.
Round this point we have a series of concentric circles
showing vivid iris colors.
259. These colors, like all those of thin plates, depend
upon the thickness of the film, which diminishes as the
distance traversed by the current increases.
(Du Bois-Reymond has shown that when the point
from the negative end of the battery is very near the
steel plate, the thickness of the film corresponding to the
different circles is inversely proportional to the cubes of
their radii.)
Distribution of Heat in the Circuit.
260. When the two ends of a voltaic battery are con-
nected by a thick wire of good conducting material the
wire is not sensibly heated ; the heat due to the oxidation
of the zinc is in this case confined to the battery itself.
261. But if the two ends of the battery be connected
by a wire that offers a resistance to the current, the wire
is heated, and may, if properly chosen, be raised to a
white heat.
262. Considering the battery as the hearth where the
zinc is burnt, we might be led to infer that the heat due
to the combustion of the zinc is liberated on the hearth
itself, and that its amount depends solely upon the quanti-
ty of zinc consumed.
263. This, however, is not the case. Let the battery,
180 NOTES ON ELECTRICITY.
with its two ends united by a thick wire, be surrounded
by a vessel of water, to which the heat developed by the
oxidation say of an ounce of zinc is communicated ; the
quantity of heat developed is measured by the rise of
temperature of the water.
264. Let the battery, with its two ends united by the
resisting wire, be placed in the same vessel, and let the
heat generated in the battery by the oxidation of an ounce
of . zinc be again determined ; this heat will be less than
that observed in the last experiment.
265. If the connecting wire be now enclosed in a sepa-
rate vessel, and if the heat generated in the wire be thus
determined, on adding this amount of heat to that lib-
erated in the battery, a total heat is obtained exactly
equal to that generated in the battery alone, when the
good conducting wire was employed.
266. In fact, the absolute amount of heat generated by
the oxidation of an ounce of zinc is perfectly constant ;
but it may be distributed in various proportions between
the battery and the external circuit.
Relation of Heat to Current and to Resistance.
267. On what does heat developed in a wire uniting
the two ends of a voltaic battery depend ?
268. It depends, in the first place, on the strength of
the current, but it is not simply proportional to that
strength.
269. Let the strengths of a series of currents, deter-
mined either by the tangent-compass or the voltameter,
be represented by the numbers 1, 2, 3, 4, then the quanti-
ties of heat developed in the same wire by these respec-
tive currents are expressed by the numbers 1, 4, 9,
and 16.
MAGNETO-ELECTRICITY. 181
270. The heat generated is therefore proportional to
the square of the strength of the current.
271. Preserving the strength of the current constant,
the heat generated is proportional to the electrical re-
sistance of the wire through which it passes. These im-
portant principles were established by Joule.
272. Thus if one of two equal currents pass through a
silver wire, and the other through a platinum wire of the
same length and thickness, the heat generated in the
platinum will be ten times that generated in the silver,
because the resistance of the former is ten times that of
the latter. To urge the current through the platinum in
this case would, however, require greater battery-power
than that necessary for the silver.
273. Hence, when the same current is sent through a
wire composed of alternate lengths of silver and platinum
of equal thickness, the platinum spaces may be raised to
a white heat, while the silver is not raised to the faintest
glow.
Magneto-Electricity: Induced Currents.
274. In a conductor near to, but not in contact with a
voltaic circuit, a current is aroused when the circuit is
established. "When the circuit is interrupted a current is
also aroused in the conductor.
275. Thus, supposing the voltaic circuit to be bent
into the shape of a ring ; and that a second ring, not in
the circuit, is placed near the first : at the completion, and
at the interruption of the circuit, a current will run round
the second ring.
276. The two currents in the second ring are called
secondary currents. They are of momentary duration.
They impart, in passing, a shock to. a magnetic needle
round which they are sent, and by the motion of which
182 NOTES ON ELECTRICITY.
their existence is demonstrated. But they vanish imme-
diately, being quenched by the resistance of the ring and
converted into heat.
277. These two momentary currents flow in opposite
directions through the ring. The secondary current, ex-
cited on making the circuit, is opposed in direction to the
primary exciting current; that started on interrupting
the circuit flows in the same direction as the primary.
278. These secondary currents are called induced cur-
rents. They were discovered by Faraday in 1830, and
described by him in his Philosophical papers for 1831.
279. If, instead of employing a single ring, we make
use of an electro-magnetic helix, every coil of the helix
will furnish its quota of current, and the sum total of effect
is much greater than when only a single ring or coil is
employed.
For the following experiments, two flat spirals, each
formed of covered copper wire, are used.
280. One of the spirals is laid flat upon a table, its two
ends being connected with a galvanometer; the other
spiral is connected with a voltaic battery, with which the
connection can be established or broken at pleasure. Let
us call this the inducing or primary spiral, and that con-
nected with the galvanometer the secondary or induced
spiral.
281. Laying one spiral upon the other, on sending a
current through the primary, the needle of the galva-
nometer is suddenly driven aside by the current induced
in the secondary ; but the force which acts upon the needle
passes away in an instant, the needle returning to its first
position.
282. On interrupting the current the needle also re-
ceives a shock, being deflected in the opposite direction.
It thus declares the existence of a second temporary cur-
MAGNETO-ELECTRICITY. 1 83
rent in the secondary spiral. The directions of these two
currents, with reference to that of the primary, have been
already indicated; Note 277.
283. Holding the secondary spiral at a distance from
the primary with the current flowing through the latter ;
on causing the secondary spiral to approach the primary,
a. current is aroused; this current ceases the moment the
motion toward the primary ceases.
284. On withdrawing the secondary spiral from the
primary, a current is also aroused; this current also ceases
the moment the motion of withdrawal ends.
285. The current excited by approach is opposed in
direction to the primary ; the current excited by with-
drawal is in the same direction as the primary.
286. Two electric currents flowing in the same direc-
tion attract each other ; if they flow in opposite directions
they repel each other.
287. Hence, to make the secondary spiral approach its
primary, we have to overcome a repulsion y while to with-
draw the secondary from the primary we have to over-
come an attraction. Thus in order to produce these in-
duced currents we must expend mechanical force.
288. The force thus expended appears as heat in the
secondary wire after the cessation of the induced current.
It is the mechanical equivalent of that heat.
289. The approach of a magnetic pole to the second-
ary spiral and the withdrawal of the pole from the same
spiral also arouse induced currents. But, as before, it is
only during the periods of approach and withdrawal that
the current appears.
290. Thus by the mere motion of a magnet, and with-
out any battery or machine, electric currents may be
produced.
291. Every change of the magnetic condition of the
184 NOTES ON ELECTRICITY.
space near a secondary coil, or within it, produces an in-
duced current in the coil. If the change be an augmenta-
tion of magnetism, the current is in one direction ; if it be
a diminution of magnetism, the current is in the opposite
direction.
292. When a long secondary coil surrounds a primary
coil with a core of iron, by breaking and making the cir-
cuit of the primary in rapid succession, a series of power-
ful discharges may be obtained. An automatic apparatus
is usually employed to make and break the circuit.
293. Such Induction Coils have been constructed with
great skill by Ruhmkorff, and are, therefore, sometimes
called Ruhmkorff 's coils. Mr. Apps has recently produced
induction coils of astonishing power.
294. The power of a coil depends mainly on the per-
fection of the insulation of its coils. The induced cur-
rents in a Ruhmkorff's coil may possess thousands of
times the electro-motive force of the primary which ex-
cites them. They are able, for example, to overleap as
sparks, distances thousands of times greater than that
possible to the primary.
Relation of Induced Currents to the Lines of Magnetic
Force. Rotatory Magnetism.
295. The foregoing phenomena and principles were all
laid bare by Faraday. He also established most important
relations between his induced currents and the lines of
force surrounding a magnet. See Note 25.
296. He proved that when a conductor moves along
the lines of force no induced currents appear ; but that
when it moves across the lines of force such currents are
generated.
297. He proved, for example, that when a metal disk
ROTATORY MAGNETISM. 185
is caused to rotate so as to be tangent to the lines of
force, no current appears ; while when the disk, in its rota-
tion, cuts the lines of force, currents flow along the disk,
from the centre to the circumference and from the circum-
ference to the centre. Closed circuits are thus established
in the disk.
208. This, in fact, is the "Magnetism of Rotation,"
discovered by Arago in 1820, which received complete
explanation at the hands of Faraday.
299. Faraday showed that the lines of force of terres-
trial magnetism suflice to produce induced currents when
they are intersected by the rotating disk. In fact, all the
efiects of magneto-electric induction may be obtained
from the magnetism of the earth.
300. When a conductor rotates round an axis which
is parallel to the lines of force, it experiences simply the
resistance due to the friction of the air ; but if the axis
of rotation be transverse to the lines of force, the rotation
is retarded by the interaction of the magnet and the in-
duced currents.
301. This retardation may become so powerful as in-
stantly to arrest the rotation. If, for example, a cube or
sphere of copper suspended from a twisted string be
caused to spin, by untwisting, between the poles of an un-
excited electro-magnet, it experiences the retardation
due to air friction only ; but on the supervention of the
magnetic force the rotation is suddenly arrested. Fara-
day also showed that in passing a plate of copper rapidly
to and fro Jbetween the magnetic poles you seem to be
cutting cheese, though nothing is visible. It is as if pure
space were a kind of solid.
302. If by mechanical means the conductor be com-
pelled to rotate or to move to and fro between the excited
poles, it will be heated. Joule first demonstrated this ;
186 NOTES ON ELECTRICITY.
but a very striking demonstration of it was given by
Foucault, who heated his celebrated gyroscope in this
way. The heat is readily rendered sufficiently intense to
melt fusible metal. Between the unexcited poles no effect
of this kind is produced.
303. The repulsion set up by induced currents be-
tween the helices and the moving masses of iron in an
electro-magnetic engine, would of itself limit the practi-
cal application of electricity as a motive power. Never-
theless, though such engines speedily reach the limit of
their action, the conversion of molecular force into me-
chanical effect may be rendered far more perfect than in
the case of the steam-engine.
The JEJxtra- Current.
304. If the secondary coil of a Ruhmkorff's machine
have its ends united, the secondary circuit being then
complete, the spark obtained in breaking the primary is
small. On separating the two ends of the secondary the
primary spark is instantly augmented.
305. The diminution of the spark is due to the reac-
tion of the completed secondary circuit upon the primary.
When the secondary circuit is interrupted this reaction
ceases.
306. The primary circuit in its turn can, when com-
plete, react upon the secondary. It is complete when-
ever contact is made by the automatic contact-breaker.
A great enfeeblement of the secondary current is the
consequence. When the primary circuit is interrupted
the reaction does not exist; there is no enfeeblement,
the full power of the secondary being developed. It is
on this account that in Ruhmkorff's coil we obtain dis-
charges in a single direction only, instead of discharges
alternating in direction.
THE EXTRA-CURRENT. 187
307. The reaction here referred to connects itself with
what is called the extra-current.
308. When a current is sent through a single primary
coil, the primary current excites in the wire which carries
it, a secondary current opposed in direction to the primary.
The primary arouses an antagonist in its own path, which,
however, immediately disappears.
309. When the primary circuit is broken, a secondary
current of momentary duration, and having the same
direction as the vanishing primary, is evoked in the
coil.
310. Each of the two currents evoked in the primary
circuit itself, at the commencement and at the cessation
of the primary current, has been called by Faraday an
extra-current.
311. The spark obtained on breaking the primary cir-
cuit is augmented in brilliancy and power by the extra-
current.
312. If a second circuit be associated with the primary ;
if, for example, two covered wires are wound round the
same reel ; on making one of them a primary circuit we
have the brilliant spark due to the extra-current, as long
as the ends of the second coil remain unconnected.
313. But the moment they are connected the extra-
current in the primary circuit disappears ; there is an in-
stant reduction in the brilliancy of the spark.
314. This is an example of the reaction referred to in
Note 304. By the closing of the secondary circuit the
extra-current is formed in it instead of in the primary one.
Here, in fact, the extra-current becomes an ordinary in-
duced current ; it is only so long as it remains in the
primary circuit that its distinctive name is applied to it.
188 NOTES ON ELECTRICITY.
Influence of Time on Intensity of Discharge. The
Condenser.
315. The intensity of the secondary current its "dis-
charging distance," for example depends upon the ra-
pidity with which the primary is interrupted.
316. I have already referred to the passage of particles
between the two severed terminals of a circuit. By these
particles the current may be kept up for a short time after
the terminals have been disunited. A gradual dying away
of the primary is the consequence.
317. But to produce the maximum secondary intensity
it is necessary that the primary should be extinguished at
once.
318. This is very effectually accomplished if the pri-
mary be broken between the poles of a strong magnet.
The secondary spark may be thus made to overleap dis-
tances, vast in comparison with those possible to it when
the rupture of contact occurs far away from the magnetic
poles.
319. The magnet quenches immediately the stream of
particles which accompany the spark. Thus, instead of
being spread over a very sensible interval, the whole
power of the primary is concentrated into an instant of
time.
320. This concentration is announced by the loudness
of the report of the primary spark. This augmentation
of loudness was first observed by Page ; it was explained
by Eijke, who also exalted in the way here indicated the
discharge of the secondary coil.
321. The injurious effect of the spark produced by the
rupture of contact in Ruhmkorff's coil is much diminished
by the employment of a condenser, which is attached to
the primary. It was introduced by Fizeau.
ELECTRIC DISCHARG. 189
Electric Discharge tJirough Rarefied Gases and Vapors.
322. The eleetricity from, the prime conductor of an
electrical machine passes through the air in the form of a
dense and brilliant spark, which produces a very audible
report.
323. When the discharge passes through rarefied air
the discharging distance is augmented, and by sufficiently
rarefying the air the discharge may be caused to pass
silently. It then fills the tube through which it passes
with a rosy light.
324. This rosy light has the same origin as that of
the Aurora Borealis ; it is due to the nitrogen of the air.
325. Every attenuated gas has its own characteristic
color when traversed by the electric discharge. When
examined by a prism the color resolves itself into distinct
bands ; the nature of the gas may, indeed, be inferred from,
the analysis of its spectrum.
326. The discharge of the induction coil through at-
tenuated media produces luminous effects similar to those
produced by the electric machine.
327. The tubes containing the attenuated gases or va-
pors are usually called vacuum tubes. Through the tubes
pass platinum wires which are fused into the glass, and
between which the discharge passes.
328. Such tubes are produced in great perfection by
Geissler, of Bonn, and are sometimes called Geissler's
tubes.
329. Under certain circumstances, the luminous dis-
charge is composed of distinct luminous strata separated
from each other by dark intervals transverse to the direc-
tion of the discharge. These strata were first observed
by Grove ; they were observed independently and finely
developed by Ruhmkorff.
190 NOTES ON ELECTRICITY.
330. The luminous strata were believed to arise from
the intermittent action of the contact-breaker of the in-
duction coil ; but Gassiot produced them both with the
electric machine, and with his battery of 3,500 cells, where
no contact-breaker is employed.
331. Every single discharge of the induction coil
through a properly-chosen medium resolves itself into a
series of pulses, which declare themselves as a stratified
discharge. Under similar circumstances the discharge
from the voltaic battery also is resolved into a series of
pulses which are declared by their stratifications.
Action of Magnets on the Luminous Discharge.
332. The luminous discharge is to all intents and pur-
poses an electric current, and is acted on by a magnet like
a wire carrying a current.
333. But the flexibility of the luminous current in
rarefied gases enables the magnet to act upon it in a man-
ner peculiarly interesting and instructive.
334. Placing, for example, a tube through which the
luminous discharge is passing between the poles of an
electro-magnet, by .exciting the magnet the stream of
light may be either deflected or wholly extinguished.
335. In the latter case, by interrupting the current
passing round the magnet, or by lifting the tube out of
the magnetic field, the luminous discharge is restored.
336. In certain cases, when the luminous discharge
consists simply of a feeble glow, the supervention of the
magnetic force draws a series of strongly-illuminated
strata from the positive terminal of the vacuum-tube ;
when the magnetism is interrupted, these strata retreat
again in succession, as if swallowed up by the positive
pole. A number of exceedingly beautiful experiments of
this character has been made by Gassiot.
MAGNETO-ELECTRIC MACHINES. 191
337. It has been stated in Note 306 that the dis-
charges from the induction coil proceed always in the
same direction ; hence, in each vacuum-tube we have a
positive terminal or pole, and a negative terminal or
pole.
338. When the light surrounding the negative ter-
minal is subjected to a magnet, it ranges itself exactly
along the lines of magnetic force ; the light at the posi-
tive terminal shows no such action. This discovery is due
to Plticker.
Magneto-electric Machines. Saxton^s Machine. Siemens* 's
Armature.
339. Faraday's discovery of Magneto-electricity was
announced in 1831. In 1833 a machine was constructed
by Saxton for the more copious development of magneto-
electric currents.
340. In it copper-wire coils, within which were placed
cores of iron, were caused to rotate before the poles of a
powerful magnet.
341. On the approach of a coil to one of the poles of
the magnet, a powerful current, whose direction depended
on the nature of the pole, was induced in the coil. When
the coil retreated from the magnetic pole, a current in the
opposite direction was induced. This production of op-
posite currents by approach and withdrawal has been
already referred to in Notes 283, 284.
342. By means of an instrument called a commutator,
which reversed one of the induced currents at the proper
moment, the opposite currents were caused to flow in the
same direction.
343. The cores of soft iron and their associated coils
constitute what is called an armature. In Saxton's arma-
ture the coils were wound transversely to the iron cores.
192 NOTES ON ELECTRICITY.
344. But by winding his coils longitudinally, or parallel
to the axis of the core, and placing the armature so formed
between the poles of a series of horseshoe magnets, Siemens
obtained magneto-electric currents much more powerful
than those of Saxton.
Wilde's Machine.
Things were in this state when, in 1866, Wilde made
an important addition to our knowledge of magneto-
electricity.
345. He conducted the current obtained by means of
Siemens's armature round an electro-magnet, and found
that the magnetism thus excited was far greater than
that of the entire series of steel magnets employed to
generate the magneto-electric current.
346. Thus, in one case, he found that whereas the
series of permanent magnets taken collectively was com-
petent to support a weight of 40 Ibs. only, the electro-
magnet which they excited sustained a weight of 1,088 Ibs.
347. To produce this effect, however, it was necessary
that the armature of the magneto-electric machine should
rotate with great rapidity.
348. But Wilde went farther. Forming his electro-
magnet from a large plate of iron, and placing between its
long poles a correspondingly long armature, similar in
shape and construction to that of the magneto-electric
machine, he obtained from this second armature currents
of enormously greater power than those obtainable from
the first.
349. These currents could in their turn be sent round a
second electro-magnet, formed from a larger plate of iron.
Furnished with a rotating armature, this second electro-
magnet produced effects previously unknown. Rods of
iron a quarter of an inch in thickness were fused by the
SIEMENS'S AND WHEAT-STONE'S MACHINE. 193
currents, and they were also found competent, when dis-
charged between carbon terminals, to produce a light of
intolerable brilliancy.
Siemens'* s and Wheatstone^s Machine.
350. The next great step in magneto-electricity was
made simultaneously by Dr. Werner Siemens and Sir
Charles Wheatstone.
351. Expressed generally, this discovery consists in
exalting, by means of its own action, to a high pitch of
intensity an infinitesimal amount of magnetism.
352. Conceive an electro-magnetic core with a very
small amount of residual magnetism, which is never wholly
absent when iron has been once magnetized. Let a sec-
ondary coil, with cores of soft iron, rotate before the poles
of such a magnet. Exceedingly feeble induced currents
will circulate in the secondary coil. Let these induced
currents, instead of being carried away, be sent round the
electro-magnet which produced them ; its magnetism will
be thereby exalted. It is then in a condition to produce
still stronger currents. These also being sent round the
magnet, raise its magnetism still higher ; a more copious
production of induced currents being the consequence.
Thus by a series of interactions between the electro-magnet
and the secondary helix, each in turn exalting the other,
the electro-magnet is raised from a state of almost perfect
neutrality to one of intense magnetization.
353. When the magnet has been raised to this con-
dition, other coils than those employed to magnetize it
may be caused to rotate before, or between, its poles ; the
currents from these coils may be carried away and made
use of, for magnetization, for chemical decomposition, or
for the electric light.
354. The first magneto-electric machine used to pro-
9
194 NOTES ON ELECTEICITY.
duce a light sufficiently intense for light-houses was con-
structed by Mr. Holmes. In it permanent steel magnets
and rotating helices were employed. Mr. Holmes has
lately constructed a very powerful machine on the prin-
ciple of Siemens and Wheatstone.
Induced Currents of the Ley den-Battery.
355. If a Ley den jar, or battery, be discharged through
a primary spiral, it evokes a current in a secondary spiral.
With a strong charge this secondary current may be caused
to deflagrate a foot of thin platinum wire.
356. If the current from the secondary spiral be led
round a third spiral which faces a fourth ; on discharging
the battery through the primary spiral, the secondary in
the third spiral acts the part of a primary, and evokes in
the fourth spiral a tertiary current.
357. With another pair of spirals this tertiary current
can he made to generate a current of the fourth order ;
this again, with another pair of spirals, a current of the
fifth order. All these currents can impart shocks, ignite
gunpowder, or deflagrate wires.
For the investigation of the Induced Currents of the
Leyden-Battery we are indebted to Prof. Joseph Henry,
Director of the Smithsonian Institution, and to Prof. Bless,
of Berlin.
THE END.
0?
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THE ORIGIN OF SPECIES,
By CHARLES DARWIN.
A new American edition of " The Origin of Species," later than the latest
English edition, has just been published, with the author's most recent cor-
rections and additions.
In the whole history of the progress of knowledge there is no case so re-
markable of a system of doctrines, at first generally condemned as false and
absurd, coming into general acceptance in the scientific world in a single
decade. From the following statements, the reader will infer the estimate
that is now placed upon the man and his works by the highest authorities.
"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."
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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.
" Even the charge of atheism, which was so violently urged against Mr. Dar-
win, is now rarely heard, and theologians, whose orthodoxy is unquestioned, have
ventured to admit that it is possible to believe both in Christianity and the Dar-
winian theory at the same time."
From the Charleston Courier.
"No one can rise from an ordinarily attentive consideration of Mr. Darwin's
treatise, without being impressed, not only with the extent and depth of the
knowledge which he has attained upon the subject under treatment, and his long,
unwearied labor in collecting facts, but also with his possession of qualities
equally rare the true scientific temper, the transparent candor, and the truth-
seeking soberness, with which he expresses to you his conclusions, and the pro-
cesses by which he reaches them.
" Whether you like his discourse or not though you may refuse to acquiesce
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^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-
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THE ORIGIN OP CIVILIZATION ;
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PRIMITIVE CONDITION OF MAN.
By SIR JOHN LUBBOCK, Bart., M. P., F. R. S.
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LAY
ADDEESSES, AND KEYIEWS,
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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.
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L By W. R. GROYE. The Correlation of Physical Forces.
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HI. By J. R. MAYER. 1. Remarks on the Forces of Inorganic Nature.
2. On Celestial Dynamics.
3. On the Mechanical Equivalent of Heat.
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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.
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