By Sir WILLIAM THOMSON, F.R.S., LL.D., etc.
[1] A Lecture delivered at the Academy of Music, Philadelphia, under
the auspices of the Franklin Institute, September 29, 1884.
The subject upon which I am to speak to you this evening is happily for
me not new in Philadelphia. The beautiful lectures on light which were
given several years ago by President Morton, of the Stevens Institute,
and the succession of lectures on the same subject so admirably
illustrated by Prof. Tyndall, which many now present have heard, have
fully prepared you for anything I can tell you this evening in respect
to the wave theory of light.
It is indeed my humble part to bring before you some mathematical and
dynamical details of this great theory. I cannot have the pleasure
of illustrating them to you by anything comparable with the splendid
and instructive experiments which many of you have already seen. It
is satisfactory to me to know that so many of you now present are so
thoroughly prepared to understand anything I can say, that those who
have seen the experiments will not feel their absence at this time. At
the same time I wish to make them intelligible to those who have not
had the advantages to be gained by a systematic course of lectures. I
must say in the first place, without further preface, as time is short
and the subject is long, simply that sound and light are both due to
vibrations propagated in the manner of waves; and I shall endeavor in
the first place to define the manner of propagation and mode of motion
that constitute those two subjects of our senses, the sense of sound
and the sense of light.
Each is due to vibrations. The vibrations of light differ widely
from the vibrations of sound. Something that I can tell you more
easily than anything in the way of dynamics or mathematics respecting
the two classes of vibrations is, that there is a great difference
in the frequency of the vibrations of light when compared with the
frequency of the vibrations of sound. The term "frequency," applied to
vibrations, is a convenient term, applied by Lord Rayleigh in his book
on sound to a definite number of full vibrations of a vibrating body
per unit of time. Consider, then, in respect to sound, the frequency
of the vibrations of notes, which you all know in music represented
by letters, and by the syllables for singing the do, re, mi, etc.
The notes of the modern scale correspond to different frequencies of
vibrations. A certain note and the octave above it correspond to a
certain number of vibrations per second and double that number.
I may explain in the first place conveniently the note called "C;"
I mean the middle "C." I believe it is the C of the tenor voice,
that most nearly approaches the tones used in speaking. That note
corresponds to two hundred and fifty-six full vibrations per second,
two hundred and fifty-six times to and fro per second of time.
Think of one vibration per second of time. The seconds pendulum of the
clock performs one vibration in two seconds, or a half vibration in one
direction per second. Take a 10-inch pendulum of a drawing-room clock,
which vibrates twice as fast as the pendulum of an ordinary eight-day
clock, and it gives a vibration of one per second, a full period of one
per second to and fro. Now think of three vibrations per second. I can
move my hand three times per second easily, and by a violent effort I
can move it to and fro five times per second. With four times as great
force, if I could apply it, I could move it twice five times per second.
Let us think, then, of an exceedingly muscular arm that would cause it
to vibrate ten times per second, that is, ten times to the left and ten
times to the right. Think of twice ten times, that is, twenty times per
second, which would require four times as much force; three times ten,
or thirty times a second, which require nine times as much force. If a
person were nine times as strong as the most muscular arm can be, he
could vibrate his hand to and fro thirty times per second, and without
any other musical instrument could make a musical note by the movement
of his hand which would correspond to one of the pedal notes of an
organ.
If you want to know the length of a pedal pipe, you can calculate it in
this way. There are some numbers you must remember, and one of them is
this. You, in this country, are subjected to the British insularity in
weights and measures; you use the foot and inch and yard. I am obliged
to use that system, but I apologize to you for doing so, because it
is so inconvenient, and I hope all Americans will do everything in
their power to introduce the French metrical system. I hope the evil
action performed by an English minister whose name I need not mention,
because I do not wish to throw obloquy on any one, may be remedied. He
abrogated a useful rule, which for a short time was followed and which
I hope will soon be again enjoined, that the French metrical system
be taught in all our national schools. I do not know how it is in
America. The school system seems to be very admirable, and I hope the
teaching of the metrical system will not be let slip in the American
schools any more than the use of the globes.
I say this seriously. I do not think any one knows how seriously
I speak of it. I look upon our English system as a wickedly
brain-destroying piece of bondage under which we suffer. The reason
why we continue to use it is the imaginary difficulty of making a
change, and nothing else; but I do not think that in America any such
difficulty should stand in the way of adopting so splendidly useful a
reform.
I know the velocity of sound in feet per second. If I remember rightly,
it is 1,089 feet per second in dry air at the freezing point, and 1,115
feet per second in air of what we call moderate temperature, 59 or 60
degrees (I do not know whether that temperature is ever attained in
Philadelphia or not; I have had no experience of it, but people tell
me it is sometimes 59 or 60 degrees in Philadelphia, and I believe
them); in round numbers let us call it 1,000 feet per second. Sometimes
we call it a thousand musical feet per second, it saves trouble in
calculating the length of organ pipes; the time of vibration in an
organ pipe is the time it takes a vibration to run from one end to the
other and back. In an organ pipe 500 feet long the period would be one
per second; in an organ pipe 10 feet long the period would be 50 per
second; in an organ pipe 20 feet long the period would be 25 per second
at the same rate. Thus 25 per second and 50 per second of frequencies
correspond to the periods of organ pipes of 20 feet and 10 feet.
The period of vibration of an organ pipe, open at both ends, is
approximately the time it takes sound to travel from one end to the
other and back. You remember that the velocity in dry air in a pipe
10 feet long is a little more than 50 periods per second; going up to
256 periods per second, the vibrations correspond to those of a pipe 2
feet long. Let us take 512 periods per second; that corresponds to a
pipe about a foot long. In a flute, open at both ends, the holes are so
arranged that the length of the sound wave is about 1 foot, for one of
the chief "open notes." Higher musical notes correspond to greater and
greater frequency of vibration, viz., 1,000, 2,000, 4,000 vibrations
per second; 4,000 vibrations per second correspond to a piccolo flute
of exceedingly small length; it would be but one and a half inches
long. Think of a note from a little dog call, or other whistle one and
a half inches long, open at both ends, or from a little key having a
tube three-quarters of an inch long, closed at one end; you will then
have 4,000 vibrations per second.
A wave length of sound is the distance traversed in the period of
vibration. I will illustrate what the vibrations of sound are by this
condensation traveling along our picture on the screen. Alternate
condensations and rarefactions of the air are made continuously by a
sounding body. When I pass my hand vigorously in one direction, the
air before it becomes dense, and the air on the other side becomes
rarefied. When I move it in the other direction, these things become
reversed; there is a spreading out of condensation from the place
where my hand moves in one direction and then in the reverse. Each
condensation is succeeded by a rarefaction. Rarefaction succeeds
condensation at an interval of one-half what we call "wave lengths."
Condensation succeeds condensation at the full interval of what we call
wave lengths.
We have here these luminous particles on this scale,[2] representing
portions of the air close together, dense; a little higher up, portions
of air less dense. I now slowly turn the handle of the apparatus in
the lantern, and you see the luminous sectors showing condensation
traveling slowly upward on the screen; now you have another
condensation; making one wave length.
[2] Alluding to a moving diagram of wave motion of sound produced by a
working slide for lantern projection.
This picture or chart represents a wave length of four feet. It
represents a wave of sound four feet long. The fourth part of a
thousand is 250. What we see now of the actual scale represents the
lower note C of the tenor voice. The air from the mouth of a singer is
alternately condensed and rarefied just as you see here.
But that process shoots forward at the rate of one thousand feet per
second; the exact period of the motion is 256 vibrations per second for
the actual case before you. Follow one particle of the air forming part
of a sound wave, as represented by these moving spots of light on the
screen; now it goes down, then another portion goes down rapidly; now
it stops going down; now it begins to go up; now it goes down and up
again.
As the maximum of condensation is approached, it is going up with
diminishing maximum velocity. The maximum of rarefaction has now
reached it, and the particle stops going up and begins to move down.
When it is of mean density the particles are moving with maximum
velocity, one way or the other. You can easily follow these motions,
and you will see that each particle moves to and fro, and the thing
that we call _condensation_ travels along.
I shall show the distinction between these vibrations and the
vibrations of light. Here is the fixed appearance of the particles when
displaced but not in motion. You can imagine particles of something,
the thing whose motion constitutes light. This thing we call the
luminiferous ether. That is the only substance we are confident of
in dynamics. One thing we are sure of, and that is the reality and
substantiality of the luminiferous ether. This instrument is merely
a method of giving motion to a diagram designed for the purpose of
illustrating wave motion of light. I will show you the same thing in a
fixed diagram, but this arrangement shows the mode of motion.
Now follow the motion of each particle. This represents a particle of
the luminiferous ether, moving at the greatest speed when it is at the
middle position.
You see two modes of vibration,[3] sound and light now moving
together--the traveling of the wave of condensation and rarefaction,
and the traveling of the wave of transverse displacement. Note the
direction of propagation. Here it is from your left to your right, as
you look at it. Look at the motion when made faster. We have now the
direction reversed. The propagation of the wave is from right to left,
again the propagation of the wave is from left to right; each particle
moves perpendicularly to the line of propagation.
[3] Showing two moving diagrams, simultaneously, on the screen,
depicting a wave motion of light, the other a sound vibration.
I have given you an illustration of the vibration of sound waves,
but I must tell you that the movement illustrating the condensation
and rarefaction represented in that moving diagram are necessarily
very much exaggerated to let the motion be perceptible, whereas the
greatest condensation in actual sound motion is not more than one or
two per cent, or a small fraction of a per cent. Except that the amount
of condensation was exaggerated in the diagram for sound, you have a
correct representation of what actually takes in the low note C.
On the other hand, in the moving diagram representing light waves what
had we? We had a great exaggeration of the inclination of the line of
particles. You must first imagine a line of particles in a straight
line, and then you must imagine them disturbed into a wave curve, the
shape of the curve corresponding to the disturbance. Having seen what
the propagation of the wave is, look at this diagram and then look at
that one. This, in light, corresponds to the different sounds I spoke
of at first. The wave length of light is the distance from crest to
crest of the wave, or from hollow to hollow. I speak of crests and
hollows, because we have a diagram of ups and downs as the diagram is
placed.
[Illustration: Waves of Red Light.]
[Illustration: Waves of Violet Light.]
Here, then, you have a wave length.[4] In this lower diagram you have
the wave length of violet light. It is but one-half the length of
the upper wave of red light; the period of vibration is but half as
long. Now, on an enormous scale, exaggerated not only as to slope, but
immensely magnified as to wave length, we have an illustration of the
waves of light. The drawing marked "red" corresponds to red light, and
this lower diagram corresponds to violet light. The upper curve really
corresponds to something a little below the red ray of light in the
spectrum, and the lower curve to something beyond the violet light. The
variation in length between the most extreme rays is in the proportion
of four and a half of red to eight of the violet, instead of four and
eight; the red waves are nearly as one to two of the violet.
[4] Exhibiting a large drawing, or chart, representing a red and a
violet wave of light.
To make a comparison between the number of vibrations for each wave
of sound and the number of vibrations constituting light waves, I may
say that 30 vibrations per second is about the smallest number which
will produce a musical sound; 50 per second give one of the grave pedal
notes of an organ, 100 or 200 per second give the low notes of the bass
voice, higher notes with 250 per second, 300 per second, 1,000, 4,000,
up to 8,000 per second, give about the shrillest notes audible to the
human ear.
Instead of the numbers, which we have, say, in the most commonly used
part of the musical scale, _i. e._, from 200 or 300 to 600 or 700 per
second, we have millions and millions of vibrations per second in light
waves; that is to say, 400 million million per second, instead of 400
per second. That number of vibrations is performed when we have red
light produced.
An exhibition of red light traveling through space from the remotest
star is due to the propagation by waves or vibrations, in which each
individual particle of the transmitting medium vibrates to and fro 400
million million times in a second.
Some people say they cannot understand a million million. Those people
cannot understand that twice two makes four. That is the way I put it
to people who talk to me about the incomprehensibility of such large
numbers. I say _finitude_ is incomprehensible, the infinite in the
universe _is_ comprehensible. Now apply a little logic to this. Is the
negation of infinitude incomprehensible? What would you think of a
universe in which you could travel one, ten, or a thousand miles, or
even to California, and then find it come to an end? Can you suppose an
end of matter, or an end of space? The idea is incomprehensible. Even
if you were to go millions and millions of miles, the idea of coming to
an end is incomprehensible.
You can understand one thousand per second as easily as you can
understand one per second. You can go from one to ten, and ten times
ten and then to a thousand without taxing your understanding, and then
you can go on to a thousand million and a million million. You can all
understand it.
Now 400 million million vibrations per second is the kind of thing
that exists as a factor in the illumination by red light. Violet
light, after what we have seen and have illustrated by that curve, I
need not tell you corresponds to vibrations of 800 million million per
second. There are recognizable qualities of light caused by vibrations
of much greater frequency and much less frequency than this. You may
imagine vibrations having about twice the frequency of violet light and
one fifteenth the frequency of red light, and still you do not pass
the limit of the range of continuous phenomena only a part of which
constitutes _visible_ light.
Everybody knows the "photographer's light," and has heard of
_invisible_ light producing visible effects upon the chemically
prepared plate in the camera. Speaking in round numbers, I may say
that, in going up to about twice the frequency I have mentioned for
violet light, you have gone to the extreme end of the range of known
light of the highest rates of vibration; I mean to say that you have
reached the greatest frequency that has yet been observed.
When you go below visible red light, what have you? We have something
we do not see with the eye, something that the ordinary photographer
does not bring out on his photographically sensitive plates. It is
light, but we do not see it. It is something so closely continuous with
light visible, that we may define it by the name of invisible light.
It is commonly called radiant heat; invisible radiant heat. Perhaps,
in this thorny path of logic, with hard words flying in our faces, the
least troublesome way of speaking of it is to call it radiant heat. The
heat effect you experience when you go near a bright, hot coal fire,
or a hot steam boiler; or when you go near, but not over, a set of hot
water pipes used for heating a house; the thing we perceive in our face
and hands when we go near a boiling pot and hold the hand on a level
with it, is radiant heat; the heat of the hands and face caused by a
hot fire, or a hot kettle when held under the kettle, is also radiant
heat.
You might readily make the experiment with an earthen teapot; it
radiates heat better than polished silver. Hold your hands below,
and you perceive a sense of heat; above the teapot you get more
heat; either way you perceive heat. If held over the teapot, you
readily understand that there is a little current of air rising. If
you put your hand under the teapot, you get cold air; the upper side
of your hand is heated by radiation, while the lower side is fanned
and is actually cooled by virtue of the heated kettle above it.
That perception by the sense of heat is the perception of something
actually continuous with light. We have knowledge of rays of radiant
heat perceptible down to (in round numbers) about four times the wave
length, or one-fourth the period of visible or red light. Let us take
red light at 400 million million vibrations per second; then the lowest
radiant heat, as yet investigated, is about 100 million million per
second in the way of frequency of vibration.
I had hoped to be able to give you a lower figure. Prof. Langley
has made splendid experiments on the top of Mount Whitney, at the
height of 1,500 feet above the sea level, with his "bolometer," and
has made actual measurements of the wave lengths of radiant heat
down to exceedingly low figures. I will read you one of the figures;
I have not got it by heart yet, because I am expecting more from
him.[5] I learned a year and a half ago that the lowest radiant heat
observed by the diffraction method of Prof. Langley corresponded to 28
one-hundred-thousandths of a centimeter for wave length, 28 as compared
with red light, which is 7.3, or nearly fourfold. Thus wave lengths of
four times the amplitude or one-fourth the frequency per second of red
light have been experimented on by Prof. Langley, and recognized as
radiant heat.
[5] Since my lecture I have heard from Prof. Langley that he has
measured the refrangibility by a rock salt prism, and inferred the wave
length of heat rays from a "Leslie cube" (a metal vessel of hot water
radiating from a blackened side). The greatest wave length he has thus
found is one one-thousandth of a centimeter, which is seventeen times
that of sodium light. The corresponding period is about thirty million
million to the second.--W.T.
Photographic or actinic light, as far as our knowledge extends at
present, takes us to a little less than one-half the wave length of
violet light. You will thus see that while our acquaintance with wave
motion below the red extends down to one-quarter of the slowest rate
which affects the eye, our knowledge of vibrations at the other end of
the scale only comprehends those having twice the frequency of violet
light. In round numbers, we have four octaves of light, corresponding
to four octaves of sound in music. In music the octave has a range to a
note of double frequency. In light we have one octave of visible light,
one octave above the visible range, and two octaves below the visible
range. We have one hundred per second, two hundred per second, four
hundred per second (million million understood) for invisible radiant
heat, eight hundred per second for visible light, and one thousand six
hundred per second for invisible light.
One thing in common to the whole is the heat effect. It is extremely
small in moonlight, so small that nobody until recently knew there was
any heat in the moon's rays. Herschel thought it was perceptible in
our atmosphere by noticing that it dissolved away very light clouds,
an effect which seemed to show in full moonlight more than when we
have less than full moon. Herschel, however, pointed this out as
doubtful, but now, instead of its being a doubtful question, we have
Prof. Langley giving as a fact that the light from the moon drives the
indicator of his sensitive instrument clear across the scale, and with
a comparatively prodigious heating effect!
I must tell you that if any of you want to experiment with the heat of
the moonlight, you must compare the heat with whatever comes within the
influence of the moon's rays only. This is a very necessary precaution;
if, for instance, you should take your bolometer or other heat detecter
from a comparatively warm room into the night air, you would obtain an
indication of a fall in temperature owing to this change. You must be
sure that your apparatus is in thermal equilibrium with the surrounding
air, then take your burning glass, and first point it to the moon and
then to space in the sky beside the moon; you thus get a differential
measurement in which you compare the radiation of the moon with the
radiation of the sky. You will then see that the moon has a distinctly
heating effect.
To continue our study of visible light, that is, undulations extending
from red to violet in the spectrum (which I am going to show you
presently), I would first point out on this chart that in the section
from letter A to letter D, we have visual effect and heating effect
only; but no ordinary chemical or photographic effect.
[Illustration: The Solar Spectrum.]
Photographers can leave their usual sensitive, chemically prepared
plates exposed to yellow light and red light without experiencing any
sensible effect; but when you get toward the blue end of the spectrum,
the photographic effect begins to tell, more and more as you get toward
the violet end. When you get beyond the violet, there is the invisible
light known chiefly by its chemical action. From yellow to violet we
have visual effect, heating effect, and chemical effect, all three;
above the violet, only chemical and heating effect, and so little of
the heating effect that it is scarcely perceptible.
The prismatic spectrum is Newton's discovery of the composition of
white light. White light consists of every variety of color from red
to violet. Here, now, we have Newton's prismatic spectrum produced by
a prism. I will illustrate a little in regard to the nature of color
by putting something before the light which is like colored glass;
it is colored gelatin. I will put in a plate of red gelatin which is
carefully prepared of chemical materials, and see what that will do. Of
all the light passing to it from violet to red, it only lets through
the red and orange, giving a mixed reddish color.
Here is another plate of green gelatin. The green absorbs all the red,
giving only green. Here is another plate absorbing something from each
portion of the spectrum, taking away a great deal of the violet and
giving a yellow or orange appearance to the light. Here is another
absorbing out the green, leaving red, orange, and a very little faint
green, and absorbing out all the violet.
When the spectrum is very carefully produced, far more perfectly than
Newton knew how to show it, we have a homogeneous spectrum. It must
be noticed that Newton did not understand what we call a homogeneous
spectrum; he did not produce it, and does not point out in his writings
the conditions for producing it. With an exceedingly fine line of light
we can bring it out as in sunlight, like this upper picture, red,
orange, yellow, green, blue, indigo, and violet according to Newton's
nomenclature. Newton never used a narrow beam of light, and so could
not have had a homogeneous spectrum.
This is a diagram painted on glass and showing the colors as we know
them. It would take two or three hours if I were to explain the
subject of spectrum analysis to-night. We must tear ourselves away
from it. I will just read out to you the wave lengths corresponding
to the different positions in the sun's spectrum of certain dark
lines commonly called "Fraunhofer's lines." I will take as a unit the
one-hundred-thousandth of a centimeter. A centimeter is 0.4 of an
inch; it is a rather small half an inch. I take the thousandth of a
centimeter and the hundred of that as a unit. At the red end of the
spectrum the light in the neighborhood of that black line A has for its
wave length 7.6; B has 6.87; D has 5.89; the "frequency" for A is 3.9
times 100 million million; the frequency of D light is 5.1 times 100
million million per second.
Now, what force is concerned in those vibrations as compared with
sound at the rate of 400 vibrations per second? Suppose for a moment
the same matter was to move to and fro through the same range but
400 million million times per second. The force required is as the
square of the number expressing the frequency. Double frequency would
require quadruple force for the vibration of the same body. Suppose I
vibrate my hand again, as I did before. If I move it once per second, a
moderate force is required; for it to vibrate ten times per second, 100
times as much force is required; for 400 vibrations per second, 160,000
times as much force.
If I move my hand once per second through a space of a quarter of
an inch; a very small force is required; it would require very
considerable force to move it ten times a second, even through so small
a range; but think of the force required to move a tuning fork 400
times a second; compare that with the force required for a motion of
400 million million times a second. If the mass moved is the same, and
the range of motion is the same, then the force would be one million
million million million times as great as the force required to move
the prongs of the tuning fork. It is as easy to understand that number
as any number like 2, 3, or 4.
Consider gravely what that number means, and what we are to infer from
it. What force is there in space between my eye and that light? What
forces are there in space between our eyes and the sun and our eyes and
the remotest visible star! There is matter and there is motion, but
what magnitude of force may there be?
I move through this "luminiferous ether" as if it were nothing. But
were there vibrations with such frequency in a medium of steel or
brass, they would be measured by millions and millions and millions of
tons action on a square inch of matter. There are no such forces in our
air. Comets make a disturbance in the air, and perhaps the luminiferous
ether is split up by the motion of a comet through it. So when we
explain the nature of electricity, we explain it by a motion of the
luminiferous ether. We cannot say that it is electricity. What can this
luminiferous ether be? It is something that the planets move through
with the greatest ease. It permeates our air; it is nearly in the same
condition, so far as our means of judging are concerned, in our air and
in the interplanetary space. The air disturbs it but little; you may
reduce the air by air pumps to the hundred thousandth of its density,
and you make little effect in the transmission of light through it.
The luminiferous ether is an elastic solid. The nearest analogy I can
give you is this jelly which you see.[6] The nearest analogy to the
waves of light is the motion, which you can imagine, of this elastic
jelly, with a ball of wood floating in the middle of it. Look there,
when with my hand I vibrate the little red ball up and down, or when I
turn it quickly round the vertical diameter, alternately in opposite
directions; that is the nearest representation I can give you of the
vibrations of luminiferous ether.
[6] Exhibiting a large bowl of clear jelly with a small red wooden ball
embedded in the surface near the center.
Another illustration is Scottish shoemaker's wax or Burgundy pitch, but
I know Scottish shoemaker's wax better. It is heavier than water, and
absolutely answers my purpose. I take a large slab of the wax, place it
in a glass jar filled with water, place a number of corks on the lower
side and bullets on the upper side. It is brittle like the Trinidad or
Burgundy pitch which I have in my hand. You can see how hard it is, but
if left to itself it flows like a fluid. The shoemaker's wax breaks
with a brittle fracture, but it is viscous, and gradually yields.
What we know of the luminiferous ether is that it has the rigidity of
a solid, and gradually yields. Whether or not it is brittle and cracks
we cannot yet tell, but I believe the discoveries in electricity, and
the motions of comets and the marvelous spurts of light from them,
tend to show cracks in the luminiferous ether--show a correspondence
between the electric flash and the aurora borealis and cracks in the
luminiferous ether. Do not take this as an assertion, it is hardly
more than a vague scientific dream; but you may regard the existence
of the luminiferous ether as a reality of science, that is, we have
an all-pervading medium, an elastic solid, with a great degree of
rigidity; its rigidity is so prodigious in proportion to its density
that the vibrations of light in it have the frequencies I have
mentioned, with the wave lengths I have mentioned.
The fundamental question as to whether or not luminiferous ether
has gravity has not been answered. We have no knowledge that the
luminiferous ether is attracted by gravity; it is sometimes called
imponderable because some people vainly imagine that it has no weight.
I call it matter with the same kind of rigidity that this elastic jelly
has.
Here are two tourmalines; if you look through them toward the light,
you see the white light all around, _i. e._, they are transparent. If
I turn round one of these tourmalines the light is extinguished, it is
absolutely black, as though the tourmalines were opaque. This is an
illustration of what is called polarization of light. I cannot speak
to you about qualities of light without speaking of the polarization
of light. I want to show you a most beautiful effect of polarizing
light, before illustrating a little further by means of this large
mechanical illustration which you have in the bowl of jelly. Now I put
in the lantern another instrument called a "Nicol prism." What you
saw first were two plates of the crystal tourmaline which came from
Brazil, I believe, having the property of letting light pass when both
plates are placed in one particular direction as regards their axes of
crystallization, and extinguishing it when it passes through the first
plate held in another direction. We have now an instrument which also
gives rays of polarized light. A Nico prism is a piece of Iceland spar,
cut in two and turned, one part relatively to the other, in a very
ingenious way, and put together again, and cemented into one by Canada
balsam. The Nicol prism takes advantage of the property which the spar
has of double refraction, and produces the phenomenon which I now show
you.
I turn one prism round in a certain direction and you get light,
a maximum of light. I turn it through a right angle and you get
blackness. I turn it one-quarter round again and get maximum light;
one-quarter more, maximum blackness; one-quarter more, and bright
light. We rarely have such a grand specimen of a Nicol prism as this.
There is another way of producing polarized light. I stand before that
light, and look at its reflection in a plate of glass on the table
through one of the Nicol prisms, which I turn round, so. Now I must
incline that piece of glass at a particular angle, rather more than
forty-five degrees; I find a particular angle in which, if I look at
it and then turn the prism round in the hand, the effect is absolutely
to extinguish the light in one position and to give it maximum
brightness in another position. I use the term "absolute" somewhat
rashly. It is only a reduction to a very small quantity of light, not
an absolute annulment as we have in the case of the two Nicol prisms
used conjointly. Those of you who have never heard of this before would
not know what I am talking about. As to the mechanics of the thing,
it could only be explained to you by a course of lectures on physical
optics. The thing is this: vibrations of light must be in a definite
direction relatively to the line in which the light travels.
Look at this diagram: the light goes from left to right; we have
vibrations perpendicular to the line of transmission. There is a
line up and down, which is the line of vibration. Imagine here a
source of light, violet light, and here in front of it is the line of
propagation. Sound vibrations are to and fro; this is transverse to the
line of propagation. Here is another, perpendicular to the diagram,
still following the law of transverse vibration; here is another
circular vibration. Imagine a long rope: you whirl one end of it, and
you send a screw-like motion running along; you can get the circular
motion in one direction or in the opposite.
Plane polarized light is light with the vibrations all in a single
plane, perpendicular to the plane through the ray, which is technically
called the "plane of polarization." Circular polarized light consists
of undulations of luminiferous ether having a circular motion.
Elliptically polarized light is something between the two, not in a
straight line, and not in a circular line; the course of vibration
is an ellipse. Polarized light is light that performs its motions
continually in one mode or direction. If in a straight line, it is
plane polarized; if in a circular direction, it is circularly polarized
light; when elliptical, it is elliptically polarized light.
With Iceland spar, one unpolarized ray of light divides on entering
it into two rays of polarized light, by reason of its power of double
refraction, and the vibrations are perpendicular to one another in the
two emerging rays. Light is always polarized when it is reflected from
a plate of unsilvered glass, or water, at a certain definite angle of
fifty-six degrees for glass, fifty-two degrees for water, the angle
being reckoned in each case from a perpendicular to the surface. The
angle for water is the angle whose tangent is 1.4. I wish you to look
at the polarization with your own eyes. Light from glass at fifty
six degrees and from water at fifty-two degrees goes away vibrating
perpendicularly to the plane of incidence and plane of reflection.
We can distinguish it without the aid of an instrument. There is a
phenomenon well known in physical optics as "Haidinger's brushes." The
discoverer is well known in Philadelphia as a mineralogist, and the
phenomenon I speak of goes by his name. Look at the sky in a direction
of ninety degrees from the sun, and you will see a yellow and blue
cross, with the yellow toward the sun, and from the sun, spreading
out like two foxes' tails with blue between, and then two red brushes
in the space at right angles to the blue. If you do not see it, it is
because your eyes are not sensitive enough, but a little training will
give them the needed sensitiveness.
If you cannot see it in this way, try another method. Look into a pail
of water with a black bottom; or take a clear glass dish of water, rest
it on a black cloth and look down at the surface of the water on a
day with a white cloudy sky (if there is such a thing ever to be seen
in Philadelphia). You will see the white sky reflected in the basin
of water at an angle of about fifty degrees. Look at it with the head
tipped to one side, and then again with the head tipped to the other
side, keeping your eyes on the water, and you will see Haidinger's
brushes. Do not do it fast, or you will make yourself giddy. The
explanation of this is the refreshing of the sensibility of the retina.
The Haidinger's brush is always there, but you do not see it because
your eye is not sensitive enough. After once seeing it, you always see
it; it does not thrust itself inconveniently before you when you do not
want to see it. You can readily see it in a piece of glass with dark
cloth below it, or in a basin of water.
I am going to conclude by telling you how we know the wave lengths
of light and how we know the frequency of the vibrations. We shall
actually make a measurement of the wave length of the yellow light. I
am going to show you the diffraction spectrum.
You see on the screen,[7] on each side of a central white bar of light,
a set of bars of light variegated colors, the first one, on each side,
showing blue or indigo color, about four inches from the central white
bar and red about four inches farther, with vivid green between the
blue and the red. That effect is produced by a grating with 400 lines
to the centimeter, engraved on glass, which I now hold in my hand.
The next grating has 3,000 lines on a Paris inch. You see the central
space, and on each side a large number of spectrums, blue at one end
and red at the other. The fact that, in the first spectrum, red is
about twice as far from the center as the blue, proves that a wave
length of red light is double that of blue light.
[7] Showing the chromatic bands thrown upon the screen from a
diffraction grating.
I will now show you the operation of measuring the length of a wave of
sodium light, that is, a light like that marked D on the spectrum, a
light produced by a spirit lamp with salt in it. The sodium vapor is
heated up to several thousand degrees, when it becomes self-luminous,
and gives such a light as we get by throwing salt upon a spirit lamp in
the game of snap dragon.
I hold in my hand a beautiful grating of glass silvered by Liebig's
process of metallic silver, a grating with 6,480 lines to the inch,
belonging to my friend Prof. Barker, which he has kindly brought here
for us this evening. You will see the brilliancy of color as I turn the
light reflected from the grating toward you and pass the beam around
the room. You have now seen directly with your own eyes these brilliant
colors reflected from the grating, and you have also seen them thrown
upon the screen from a grating placed in the lantern. With a grating
of 17,000 lines, a much greater number of lines per inch than the
other, you will see how much further from the central bright space the
first spectrum is; how much more this grating changes the direction or
diffraction of the beam of light. Here is the center of the grating,
and there is the first spectrum. You will note that the violet light
is least diffracted and the red light is most diffracted. This
diffraction of light first proved to us definitely the reality of the
undulatory theory of light.
You ask, Why does not light go round the corner as sound does? Light
goes round a corner in these diffraction spectrums; it is shown going
round a corner, it passes through these bars and is turned round an
angle of thirty degrees. Light going round a corner by instruments
adapted to show the result, and to measure the angles at which it is
turned, is called the diffraction of light.
I can show you an instrument which will measure the wave lengths of
light. Without proving the formula, let me tell it to you. A spirit
lamp with salt sprinkled on the wick gives very nearly homogeneous
light, that is to say, light all of one wave length, or all of the
same period. I have a little grating that I take in my hand. I look
through this grating, and see that candle before me. Close behind it
you see a blackened slip of wood with two white marks on it ten inches
asunder. The line on which they are marked is placed perpendicular
to the line at which I shall go from it. When I look at this salted
spirit lamp, I see a series of spectrums of yellow light. As I am
somewhat short-sighted, I am making my eye see with this eye-glass
and the natural lenses of the eye what a long-sighted person would
make out without an eye-glass. On that screen you saw a succession of
spectrums. I now look direct at the candle, and what do I see? I see a
succession of five or six brilliantly colored spectrums on each side
of the candle. But when I look at the salted spirit lamp, now I see
ten spectrums on one side and ten on the other, each of which is a
monochromatic band of light.
I will measure the wave lengths of light thus: I walk away to a
considerable distance, and look at the candle and marks. I see a set of
spectrums. The first white line is exactly behind the candle. I want
the first spectrum to the right of that white line to fall exactly on
the other white line, which is ten inches from the first. As I walk
away from it, I see it is now very near it; it is now on it. Now the
distance from my eye is to be measured, and the problem is again to
reduce feet to inches. The distance from the spectrum of the flame
to my eye is thirty-four feet nine inches. Mr. President, how many
inches is that? Four hundred and seventeen inches, in round numbers
420 inches. Then we have the proportion, as 420 is to 10 so is the
length from bar to bar of the grating to the wave length of sodium
light--that is to say, as forty-two is to one. The distance from bar to
bar is the four-hundredth of a centimeter; therefore the 42d part of
the four-hundredth of a centimeter is the required wave length, or the
16,800th of a centimeter is the wave length according to our simple,
and easy, and hasty experiment. The true wave length of sodium light,
according to the most accurate measurement, is about a 17,000th of a
centimeter, which differs by scarcely more than one per cent. from our
result!
The only apparatus you see is this little grating; it is a piece of
glass with four-tenths of an inch ruled with 400 fine lines. Any of you
who will take the trouble to buy one may measure the wave lengths of a
candle flame himself. I hope some of you will be induced to make the
experiment for yourselves.
If I put salt on the flame of a spirit lamp, what do I see through this
grating? I see merely a sharply defined yellow light, constituting
the spectrum of vaporized sodium, while from the candle flame I see
an exquisitely colored spectrum, far more beautiful than I showed you
on the screen. I see, in fact, a series of spectrums on the two sides
with the blue toward the candle flame and the red further out. I cannot
get one definite thing to measure from in the spectrum from the candle
flame as I can with the flame of a spirit lamp with the salt thrown on
it, which gives, as I have said, a simple yellow light. The highest
blue light I see in the candle flame is now exactly on the line. Now
measure to my eye; it is forty-four feet four inches, or 532 inches.
The length of this wave then is the 532d part of the four-hundredth
of a centimeter, which would be the 21,280th of a centimeter, say the
21,000th of a centimeter. Then measure for the red, and you would find
something like the 11,000th for the lowest of the red light.
Lastly, how do we know the frequency of vibration?
Why, by the velocity of light. How do we know that? We know it in a
number of different ways, which I cannot explain now because time
forbids. Take the velocity of light. It is 187,000 British statute
miles per second. But it is much better to take a kilometer for
the unit. That is about six-tenths of a mile. The velocity is very
accurately 300,000 kilometers per second; that is, 30,000,000,000
centimeters per second. Take the wave length as the 17,000th of a
centimeter, and you find the frequency of the sodium light to be 510
million million per second. There, then, you find a calculation of
the frequency from a simple observation which you can all make for
yourselves.
[Illustration: Vibrating Spherule Imbedded in an Elastic Solid.]
Lastly, I must tell you about the color of the blue sky which was
illustrated by the spherule embedded in an elastic solid. I want to
explain to you in two minutes the mode of vibrations. Take the simplest
plane-polarized light. Here is a spherule which is producing it in
an elastic solid. Imagine the solid to extend miles horizontally and
miles down, and imagine this spherule to vibrate up and down. It is
quite clear that it will make transverse vibrations similarly in all
horizontal directions. The plane of polarization is defined as a plane
perpendicular to the line of vibration. Thus, light produced by a
molecule vibrating up and down, as this red globe in the jelly before
you, is polarized in a horizontal plane because the vibrations are
vertical.
Here is another mode of vibrations. Let me twist this spherule in
the jelly as I am doing it, and that will produce vibrations, also
spreading out equally in all horizontal directions. When I twist this
globe round, it draws the jelly round with it; twist it rapidly back,
and the jelly flies back. By the inertia of the jelly the vibrations
spread in all directions, and the lines of vibration are horizontal
all through the jelly. Everywhere, miles away, that solid is placed
in vibration. You do not see it, but you must understand that they
are there. If it flies back it makes vibration, and we have waves of
horizontal vibrations traveling out in all directions from the exciting
molecule.
I am now causing the red globe to vibrate to and fro horizontally. That
will cause vibrations to be produced which will be parallel to the line
of motion at all places of the plane perpendicular to the range of the
exciting molecule. What makes the blue sky? These are exactly the
motions that make the blue light of the sky which is due to spherules
in the luminiferous ether, but little modified by the air. Think of the
sun near the horizon, think of the light of the sun streaming through
and giving you the azure blue and violet overhead. Think first of any
one particle of the sun, and think of it moving in such a way as to
give horizontal and vertical vibrations and what not of circular and
elliptic vibrations.
You see the blue sky in high pressure steam blown into the air; you
see it in the experiment of Tyndall's blue sky, in which a delicate
condensation of vapor gives rise to exactly the azure blue of the sky.
Now the motion of the luminiferous ether relatively to the spherule
gives rise to the same effect as would an opposite motion impressed
upon the spherule quite independently by an independent force. So you
may think of the blue color coming from the sky as being produced by to
and fro vibrations of matter in the air, which vibrates much as this
little globe vibrates embedded in the jelly.
The result in a general way is this: The light coming from the blue
sky is polarized in a plane through the sun, but the blue light of
the sky is complicated by a great number of circumstances, and one of
them is this: that the air is illuminated not only by the sun, but by
the earth. If we could get the earth covered by a black cloth, then we
could study the polarized light of the sky with simplicity, which we
cannot do now. There are, in nature, reflections from seas, and rocks,
and hills, and waters in an indefinitely complicated manner.
Let observers observe the blue sky not only in winter, when the earth
is covered with snow, but in summer, when it is covered with dark
green foliage. This will help to unravel the complicated phenomena
in question. But the azure blue of the sky is light produced by the
reaction on the vibrating ether of little spherules of water, of
perhaps a fifty-thousandth or a hundred-thousandth of a centimeter
diameter, or perhaps little motes, or lumps, or crystals of common
salt, or particles of dust, or germs of vegetable or animal species
wafted about in the air. Now what is the luminiferous ether? It is
matter prodigiously less dense than air, millions and millions and
millions of times less dense than air. We can form some sort of idea of
its limitations. We believe it is a real thing, with great rigidity in
comparison with its density, and it may be made to vibrate 400 million
million times per second, and yet with such rigidity as not to produce
the slightest resistance to any body going through it.
Going back to the illustration of the shoemaker's wax; if a cork will
in the course of a year push its way up through a plate of that wax
when placed under water, and if a lead bullet will penetrate downward
to the bottom, what is the law of the resistance? It clearly depends on
time. The cork slowly in the course of a year works its way up through
two inches of that substance; give it one or two thousand years to do
it, and the resistance will be enormously less; thus the motion of a
cork or bullet, at the rate of one inch in 2,000 years, may be compared
with that of the earth, moving at the rate of six times ninety-three
million miles a year, or nineteen miles per second, through the
luminiferous ether, but when we have a thing elastic like jelly and
yielding like pitch, surely we have a large and solid ground for our
faith in the speculative hypothesis of an elastic luminiferous ether,
which constitutes the wave theory of light.