Full text of "Light waves and their uses"

See other formats

THE DECENNIAL PUBLICATIONS OF
THE UNIVERSITY OF CHICAGO

THE DECENNIAL PUBLICATIONS

ISSUED IN COMMEMORATION OP THE COMPLETION OP THE FIRST TEN
YEARS OF THE UNIVERSITY'S EXISTENCE

AUTHORIZED BY THE BOARD OP TRUSTEES ON THE RECOMMENDATION
OP THE PRESIDENT AND SENATE

EDITED BY A COMMITTEE APPOINTED BY THE SENATE

EDWARD CAPP8

STARE WILLARD CUTTING ROLLIN D. SALISBURY

JAMES ROWLAND ANGELL WILLIAM I. THOMAS SHAILER MATHEWS

CARL DARLING BUCK FREDERIC IVES CARPENTER OSKAR BOLZA

JULIUS STIEGLITZ JACQUES LOEB

THESE VOLUMES ARE DEDICATED

TO THE MEN AND WOMEN

OF OUR TIME AND COUNTRY WHO BY WISE AND GENEROUS GIVING

HAVE ENCOURAGED THE SEARCH AFTER TRUTH

IN ALL DEPARTMENTS OF KNOWLEDGE

LIGHT WAVES AND THEIR USES

LIGHT WAVES AND THEIR

USES

A. A. MICHELSON

OF THE DEPARTMENT OF PHYSICS

THE DECENNIAL PUBLICATIONS
SECOND SERIES VOLUME III

THE

UNIVSflSITY

CHICAGO

THE UNIVERSITY OF CHICAGO PRESS
1903

Copyrif/ltt 1H02

BY THK UXIVERSITY OF CHICAGO

PREFACE

THIS series of eight lectures on "Light Waves and Their
Uses" was delivered in the spring of 1899 at the Lowell
Institute. In the preparation of the experiments and the
lantern projections I was ably assisted by Mr. C. R. Mann,
to whom I am further indebted for editing this volume.

I have endeavored, possibly at the risk of inelegance of
diction, to present the lectures as nearly as possible in the
words in which they were originally given, trusting that
thereby some of the interest of the spoken addresses might
be retained.

While it is hoped that the work will be intelligible to the
general reader, it is also possible that some of the ideas may
be of interest to physicists and astronomers who may not
have had occasion to read the somewhat scattered published
papers.

A. A. MICHELSON.
RYERSON PHYSICAL LABORATORY
The University of Chicago
October, 1902

127058

CONTENTS

LECTURE I. Wave Motion and Interference - 1

LECTURE II. Comparison of the Efficiency of the Micro-
scope Telescope, and Interferometer - - 19

LECTURE III. Application of Interference Methods to Meas-
urements of Distances and Angles 44

LECTURE IV. Application of Interference Methods to Spec-

troscopy 60

LECTURE V. Light Waves as Standards of Length - 84

LECTURE VI. Analysis of the Action of Magnetism on
Light Waves by the Interferometer and
the Echelon 107

LECTURE VII. Application of Interference Methods to

Astronomy - 128

LECTURE VIII. The Ether - - 147
INDEX 165

LECTURE I
WAVE MOTION AND INTERFERENCE

SCIENCE, when it has to communicate the results of its
labor, is under the disadvantage that its language is but
little understood. Hence it is that circumlocution is inevi-
table and repetitions are difficult to avoid. Scientific men
are necessarily educated to economize expression so as to
condense whole sentences into a single word and a whole
chapter into a single sentence. These words and sentences
come to be so familiar to the investigator as expressions of
summarized work — it may be of years — that only by con-
siderable effort can he remember that to others his ideas
need constant explanation and elucidation which lead to
inartistic and wearying repetition. To few is it given to
combine the talent of investigation with the happy faculty
of making the subject of their work interesting to others. I
do not claim to be one of these fortunate few; and if I am
not as successful as I could wish in this respect, I can only
beg your indulgence for myself, but not for the subject I
have chosen. This, to my mind, is one of the most fasci-
nating, not only of the departments of science, but of human
knowledge. If a poet could at the same time be a physicist,
he might convey to others the pleasure, the satisfaction,
almost the reverence, which the subject inspires. The
aesthetic side of the subject is, I confess, by no means the
least attractive to me. Especially is its fascination felt in
the branch which deals with light, and I hope the day may
be near when a Ruskin will be found equal to the descrip-
tion of the beauties of coloring, the exquisite gradations of
light and shade, and the intricate wonders of symmetrical

LIGHT WAVES AND THEIR USES

forms and combinations of forms which are encountered at
every turn.

Indeed, so strongly do these color phenomena appeal to
me that I venture to predict that in the not very distant
future there may be a color art analogous to the art of
sound — a color music, in which the performer, seated be-
fore a literally chromatic scale, can play the colors of the
spectrum in any succession or combination, flashing on a
screen all possible gradations of color, simultaneously or in
any desired succession, producing at will the most delicate
and subtle modulations of light and color, or the most
gorgeous and startling contrasts and color chords ! It seems
to me that we have here at least as great a possibility of
rendering all the fancies, moods, and emotions of the human
mind as in the older art.

These beauties of form and color, so constantly recurring
in the varied phenomena of refraction, diffraction, and inter-
ference, are, however, only incidentals ; and, though a never-
failing source of aesthetic delight, must be resolutely ignored
if we would perceive the still higher beauties which appeal
to the mind, not directly through the senses, but through
the reasoning faculty; for what can surpass in beauty the
wonderful adaptation of Nature's means to her ends, and the
never-failing rule of law and order which governs even the
most apparently irregular and complicated of her manifes-
tations? These laws it is the object of the scientific
investigator to discover and apply. In such successful
investigation consists at once his keenest delight as well as
his highest reward.

It is my purpose to bring before you in the following
lectures an outline of a number of investigations which are
based on the use of light waves. I trust I may be pardoned
for citing, as illustrations of these uses, examples which are
taken almost entirely from my own work. I do this because

WAVE MOTION AND INTERFERENCE 3

I believe that I shall be much more likely to interest you by
telling what I know, than by repeating what someone else
knows.

In order to discuss intelligently these applications of
light waves, it will be necessary to recall some fundamental
facts about light and especially about wave motion. These
facts, though doubtless familiar to most of us here, need em-
phasis and illustration in order that we may avoid, as far as
possible, the tedious repetition against which we were warned.

Doubtless there are but few who have not watched with
interest the circular waves produced by a stone cast into a
still pond of water, the ever-widening circles, going farther
and farther from the center of disturbance, until they are
lost in the distance or break on the shore. Even if we had
no knowledge of the original disturbance, its character, in a
general way, might be correctly inferred from the waves.
For instance, the direction and distance of the source can be
determined with considerable accuracy by drawing two lines
perpendicular to the front of the wave ; the source would lie
at their intersection. The size of the waves will give infor-
mation concerning the size of the object thrown. If the waves
continue to beat regularly on the shore, the disturbance is
continuous and regular ; and, if regular, the frequency (i. e.,
the number of waves per second) determines whether the
disturbance is due to the splash of oars, to the paddles of a
steamer, or to the wings of an insect struggling to escape.

In a precisely similar manner, though usually without
conscious reasoning about the matter on our part, the sound
waves which reach the ear give information regarding the
source of the sound. Such information may be classified as
follows :

1. Direction (not precise).

2. Magnitude (loudness).

LIGHT WAVES AND THEIR USES

3. Frequency (pitch).

4. Form (character).

Light gives precisely the same kinds of information, and
hence it is only natural to infer that light also is a wave motion.
We know, in fact, that it is so ; but before giving the evi-
dence to prove it, it will be well to make a little preliminary
study of the chief characteristics of wave motion.^

FIG. i

One of the difficulties encountered in studying wave
motion is the rapidity of the propagation of the waves. A
fairly moderate speed is attained by the waves propagated
along a spiral spring. If one end of such a spring be
fastened to a wooden box on the wall of the lecture-room,
while the other end is held in the hand, we can see that any
motion communicated by the hand is successively trans-
mitted to the different parts of the spring until it reaches
the wall. Here it is reflected back toward the hand, but
with diminished amplitude. We can also see that any kind
of transverse motion, /. r., motion at right angles to the
length of the spring, whether regular or irregular, gives
rise to a corresponding wave form which travels along the
spring with a velocity that is the same in every case.

If the spring be very suddenly stretched or relaxed, a

WAVE MOTION AND INTERFERENCE 5

wave of longitudinal vibrations passes along it, announcing
its arrival at the other end by a sound at the box; the time
occupied in the passage being perceptibly less than that
required for the transverse wave.1

The velocity of the wave is in both cases too great to ad-
mit of convenient investigation. In order to familiarize the
student with wave |

motion, a number
of mechanical de-
vices have been
constructed, such
as that shown in
Fig. 1. Such me- FIG. 2

chanical models imitate wave motions rather than produce
them. They are purely kinematic illustrations, and not
true wave motions; for in the latter the propagation is de-
termined by the forces and inertias which exist within the
system of particles through which the wave is moving.

The wave model of Lord Kelvin is free from this objec-
tion. It consists of a vertical steel wire on which blocks
of wood are fastened at regular intervals. It is very essen-
tial that these blocks should not slip on the wire, and this
end is best accomplished by bending the wire, in the middle
of each block, around three small nails, as shown in Fig. 2.
For the sake of symmetry two such pieces may be fastened
together, with the wire passing between them. Attention
may be fixed upon the motion of the ends of the blocks, by
driving into them large, gilt, upholstering tacks — a device
which adds considerably to the attractiveness of the experi-
ment. The complete apparatus is shown in Fig. 3.

On giving the lowest element a twist, the torsion pro-
duced in the wire will communicate the twist to the next
element, etc. The twist thus travels along the entire row,

i 1 am indebted to Professor Cross for this illustration.

LIGHT WAVES AND THEIR USES

moving more slowly the smaller the wire and
the heavier the blocks, so that, by varying
these two factors, any desired speed may be
obtained.

The wave form which is propagated in any
of the various possible cases is, in general,
very complicated. It can be shown, however,
that it is always possible to express such forms,
however complex, by a series of simple sine
curves such as that represented in Fig. 4.
The study of wave motion may be much sim-
plified by this device. Accordingly, in all that
follows, except where the contrary is expressly
stated, it will be assumed that we are dealing
with waves of this simple type.

There are certain characteristics of wave
motion of which we shall have to speak fre-
quently in what follows, and which therefore
need definition. In the first place, the shape
of the wave illustrated in Fig. 4 is important.
It is the curve which would be drawn by a
pendulum, carrying a marker, upon a piece of
smoked glass moving uniformly'at right angles
to the motion of the pendulum. Since the
pendulum moves in what is called simple har-
monic motion, the curve is called a simple har-
monic curve, or a sine curve. The amplitude
of the wave is the maximum distance of a crest
or a trough from the position of rest, i. <>., from
the straight line drawn through the middle of
the curve. The period of the vibration is the
time it takes one particle to execute one com-
plete vibration ; i. e., to revert to the pendulum,
it is the time it takes the pendulum to execute

FIG. 3

WAVE MOTION AND INTERFERENCE 7

t
one complete swing.1 The phase of any particle along the

curve is the portion of a complete vibration which the par-
ticle has executed. The wave length is the distance between
two particles in the same phase. Thus it is the distance

FIG. 4

between two consecutive crests or between two consecutive
troughs. When all the particles vibrate in one plane, e. g.,
the plane of the drawing, the wave is said to be polarized in
a plane. The velocity of propagation of the wave is the dis-
tance traveled by any given crest in one second.

As has just been stated, the type of wave motion illus-
strated in Fig. 4 may be approximately realized by impart-
ing the motion of a pendulum or a tuning-fork to one end
of a very long cord. It can be shown that after a time
every particle of the cord will vibrate with precisely the

FIG. 5

same motion as that of the pendulum or tuning-fork from
which the disturbance starts. Any particular phase of the
motion occurs a little later in every succeeding particle ; and
it is this transmission of a given phase along the cord
which constitutes the wave motion.

i In some works the half of this is taken, /. e., the time it takes a pendulum to
move from the extreme left to the extreme right.

8 LIGHT WAVES AND THEIR USES

Very elementary considerations show that the length (I)
of the wave is connected with the period (p) of vibration of
the particles (the time of one complete cycle) and the
velocity (v) of transmission by the simple relation / — pv.

FIG. 6

In fact, if we could take instantaneous photographs of such
a train of waves at equal intervals of time, say one-eighth
of the period, they would appear as in Fig. 5. It will readily
be seen that in the eight-eighths of a period the wave has
advanced through just one wave length, while any particle
has gone once through all its phases.

Let us next consider the superposition of two similar trains
of waves of equal period and amplitude. If the phases of the
two wave trains coincide, the resulting wave train will have
twice the amplitude of the components, as shown in Fig. 6.
If, on the other hand, the phase of one train is half a period
ahead of that of the other, as in Fig. 7, the resulting ampli-

FIG. 7

tude is zero; that is, the two motions exactly neutralize
each other. In the case of sound waves, the first case cor-
responds to fourfold intensity, the second to absolute silence.
The principle of which these two cases are illustrations is
miscalled interference; in reality the result is that each wave
motion occurs exactly as if the other were not there to inter-

WAVE MOTION AND INTERFERENCE

fere. The name has, however, the sanction of long usage, and
will therefore be retained. The principle of interference is of

such fundamental importance that it will be worth while to

impress it upon the mind by a few experimental illustrations.

Fig. 8 represents an apparatus devised by Professor

Quincke for illustrating interference of sound. An organ

LIGHT WAVES AND THEIR USES

pipe is sounded near the base of the instrument. Thence
the sound waves are conducted through the two vertical
tubes, one of which is capable of being lengthened, like a
trombone. They then reunite and are conducted by a

FIG. 9

single tube to a " manometric capsule," which impresses the
resulting vibrations on a gas jet, the trembling of the jet
being rendered visible in a revolving mirror.

When the two branch tubes are of equal length, the
waves reach the flame in the same phase, causing it to

FIG. 10

vibrate, as shown by the character of the image in the
revolving mirror, Fig. 9; while, if one of the branches be
made half a wave1 longer than the other, the disturbance
disappears, and the image appears as shown in Fig. 10.

A very simple and instructive experiment may be made

i The length required will depend on the tone of the organ pipe. For middle C
(256 vibrations per second) the double length required is two feet.

WAVE MOTION AND INTERFERENCE

by throwing simultaneously two stones into still water, and
a number of interesting variations may be obtained by
varying the size of the stones and their distance apart.

The experiment may be arranged for projection by using
a surface of mercury instead of one of water, and agitating
it by means of a tuning-
fork, to the ends of whose
prongs are attached light
pieces of iron wire which
dip slightly into the mer-
cury.

The arrangement of
the apparatus is shown in
Fig. 11. The light of an
electric lamp is concen-
trated on a small mirror,
by which it is reflected
through a lens to the
tuning-fork, whose ends
dip into a surface of mer-
cury. It is reflected by
the mercury surface back through the lens and passes to
another mirror, by which it is reflected to form an image
on a distant screen. Fig. 12 shows the resulting disturbance
of the surface. The circular ripples which diverge from the
points of contact of the forks are represented by the circles.
These move too rapidly to be seen in the actual experiment,
but may be readily recognized in an instantaneous photo-
graph. The heavy lines are the lines of maximum disturb-
ance, where the two systems of waves meet, always in the
same phase ; while the lighter parts between represent the
quiescent portions of the surface, where the crests of one
system meet the troughs of the other, forming stationary
waves. Fig. 13 is a photograph of the actual appearance.

FIG. 11

12 LIGHT WAVES AND THEIR USES

Another striking instance of interference is furnished by
two tuning-forks of nearly the same pitch. Take, first, two
similar forks mounted on resonators. When these are sounded
by a cello bow, the resultant tone may or may not be louder
than the component tones, but it is constant — or, at least, dies
away very slowly. If, now, one of the forks be loaded by

FIG. 12

fastening a small weight to the prong, the sound sinks and
swells at regular intervals, producing the well-known phenom-
enon of "beats." The maximum occurs when the two vibra-
tions are in the same phase. Gradually the loaded fork loses
on the other until it is half a vibration behind ; then there is
a brief silence. This may be shown graphically by allowing
each fork to trace its own record along a piece of smoked
glass, and by adding the two sine curves, as shown in Fig. 14.

The matter of the interference of light waves requires
special treatment on account of the enormous rapidity of
the vibrations. This statement, however, inverts the actual
chronology, for this rapidity is inferred from the interference
experiments themselves.

WAVE MOTION AND INTERFERENCE

A beautiful instance of such interference occurs in a
soap film. Ordinarily, however, such films have the form

of a soap bubble; and, while the disturbing causes usually
in operation enhance wonderfully the beauty of the appear-
ance, they do not permit the accurate investigation of the

\AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAW
AAAAAAAAAAAAAAAAAAAAAAAAAAAA

W\A/V\A/-W\/\^^

FIG. 14

phenomenon. These disturbing elements are very much
diminished in the arrangement which follows:

LIGHT WAVES AND THEIR USES

A soap solution is made up as follows : One part of fresh
Castile soap is dissolved in forty parts of warm water ; when
cool, three parts of the solution are mixed with two parts

^ of glycerine. The
mixture is cooled
to a temperature
of 3° or 4° C., and
filtered. A soap
film is formed by
dipping into the
solution a short
piece of wide glass
tubing. Remov-
ing the tube and
placing it so that
the film is vertical,
a series of beauti-
fully colored bands
appear, the colors
being deeper at the
top and gradually
fading into barely perceptible alternations of pink and green
near the bottom. The bands broaden out as the film gets
thinner, but the succession of colors remains the same and
may be described as follows: The top of the film is black;
then the colors in the first band are bluish gray, white, yellow,
and red ; those in the second band are, in order, violet, blue,
green, yellow, red; the third band is blue, green, yellow, and
red; and the succeeding bands green and red. The colors
are best observed by using the film as a mirror to reflect the
light from a white wall ; or the light from a lantern may be
reflected to a lens which forms an image of the film 011 a
screen.

The colors of thin films and of interference phenomena

FIG.

WAVE MOTION AND INTERFERENCE 15

generally are among the most beautiful in nature, and while
no artist could do justice to such a subject, much less a
lithographic plate, such a plate (Plate II) may be used to
recall the more striking characteristics.

For the scientific investigation of the interference of light
waves, however, the soap film is rather unsatisfac-
tory on account of the excessive mobility of its parts
and the resulting changes in thickness. A much more
satisfactory arrangement for this purpose is the fol-
lowing: Two pieces of glass with optically plane
surfaces are carefully cleaned and freed from dust
particles. A single fiber of silk is placed on one of
the surfaces near the edge, and the other is pressed
against it, thus forming an extremely thin wedge
of air, between the two plates, as shown in Fig. 16.

It will be found that in this case the succession of colored
bands will resemble in every respect those in the soap film,
except that they are now permanent. The light is reflected
from all four surfaces, and hence the purity of the colors is
somewhat dimmed by the first and the fourth reflections.
These may be obviated by using wedges of glass instead of
plates.

To account for the colored fringes it will be best to begin
with the simpler case of monochromatic light. If a piece of
red glass is interposed anywhere in the path of the light,
the bands are no longer colored, but are alternately red and
black. They are rather more numerous than before, and a
trifle wider. If a blue glass is interposed, the bands con-
sist of alternations of blue and black, and are somewhat
narrower (c/. Plate II).

Let us suppose now that red light consists of waves of
very small length. The train of waves reflected by the first
surface of the film will be in advance of that reflected by the
second surface. At the point where the two surfaces touch

16 LIGHT WAVES AND THEIR USES

each other the advance is, of course, zero; and here we
should have the two wave trains in the same phase, with a
consequent maximum of light. Where the thickness of the
film is such that the second wave train is half a wave behind,
there should be a dark band ; at one whole wave retardation,
a bright band; and so on.

The alternations of light and dark bands are thus
accounted for, but the experiment shows that the first band
is dark instead of bright. This discrepancy is due to the
assumption that both reflections took place under like condi-
tions, and that the phase of the two trains of waves would be
equally affected by the act of reflection. This assumption
is wrong, for the first reflection takes place from the inner
surface of the first glass, while the second occurs at the outer
surface of the second glass. The first reflection is from a
rarer medium — the air; while the second is from a denser
medium — the glass. A simple experiment with the Kelvin
wave apparatus will illustrate the difference between the two
kinds of reflection. The upper end of this apparatus is fixed,
while the lower end is free ; the fixed end, therefore, represents
the surface of a denser medium, the free end that of a rarer
medium. If now a wave be started at the lower end by
twisting the lowest element to the right, the twist travels
upward till it reaches the ceiling, whence it returns with a
twist to the left — i. e., in the opposite phase. When, how-
ever, this left twist reaches the lowest element, it is reflected
and returns as a twist to the left — so that the reflection is
in the same phase.

There is thus a difference of phase of one-half a period
between the two reflections, and, when this is taken into
account, experiment and theory fully agree. We may now
make use of the experiment to find a rough approximation
to the length of the light waves.

If we measure by the microscope the diameter of the fila-

WAVE MOTION AND INTERFERENCE

ment which separates the glasses, it will be found to be,
say, two and seven-tenths microns.1 Counting the number
of dark bands in red light, we find there are eight; and
hence we conclude that at the thickest part of the air film
the retardation is eight waves, and hence the distance sepa-
rating the glasses — that is, the thickness of the filament-
is four waves, which gives about sixty-eight hundredths of

V
B

FIG. 17

a micron for the wave length of red light. If blue light is
used, there will be twelve dark bands, whence the wave
length of blue light is forty-five hundredths of a micron.

The following table gives the approximate wave lengths
of the principal colors:

Red 0.68 microns
Orange .63 "

Yellow .58

Green .53 "

Blue .48 "

Violet .43 "

Fig. 17 gives a diagram of the wave lengths of the dif-
ferent colors, magnified about twenty thousand times.

SUMMARY

Waves give information concerning direction, distance,
magnitude, and character of the source. Light does the
same ; hence the presumption in favor of the hypothesis that
light consists of waves.

1 A micron is a thousandth of a millimeter, or about a twenty-five thousandth of
an inch.

18 LIGHT WAVES AND THEIR USES

Wave trains may destroy each other by "interference."
Light added to light may produce darkness.

The reason why interference is not more frequently
apparent in the case of light is that light waves are exceed-
ingly minute.

By the measurement of interference fringes it is possible
to measure the length of light waves, and the results of such
measurements show that the wave lengths are different for
different colors.

LECTURE II

COMPARISON OF THE MICROSCOPE AND TELESCOPE
WITH THE INTERFEROMETER

ONE of the principal objections which have been urged
against the wave theory of light is the fact that light appears
to travel in straight lines, whereas sound, which is known
to be a wave motion, does not cast a shadow; in other
words, the sound waves are capable of bending around an
obstacle in the path of the waves.

We shall now not only try to show that both of these two
statements are untrue, or, at least, only approximately true,
but we shall actually show that sound waves do cast a shadow
and that light waves do not move in straight lines. The
effect, in fact, depends on the length of the wave, and we
may say roughly that the reason why a sound shadow is
not ordinarily observed is that the obstacles themselves are
of the same order of magnitude as the length of the sound
waves. If, therefore, we wish to cast a sound shadow, it
will be necessary to use either very large screens or very
short waves — that is, high sounds. Indeed, the effect will
be most evident if we use sounds that are barely within the
limits of audition, or in some cases higher than can be per-
ceived by the ear; and it will be interesting to trace the
relation between the definiteness of the sound shadow and
the shortness of the sound wave.

I have here a whistle whose length is about one inch. It
produces, therefore, a sound wave of the length of four
inches. In order to show to an audience the effect of the
whistle at different points on the other side of an obstacle, it
is convenient to use what is termed a "sensitive flame."

20 LIGHT WAVES AND THEIR USES

This flame is produced by allowing a jet of gas to issue
under considerable pressure from a small nozzle, and by
gradually increasing the pressure until the flame is on the
point of flaring. On blowing the whistle, we observe that
the flame ducks; it is lowered to perhaps one-third or one-
fourth of its height, and broadens out at the same time.
On placing the whistle behind an obstacle, we observe by
the ducking of the flame that it responds to the whistle
almost as readily as when no obstacle was present.

I now take a shorter whistle, half an inch long; which,
therefore, produces a sound wave two inches long. The
flame responds even more readily to this than to the longer
whistle, and when the shorter whistle is sounded behind
the obstacle the flame ducks, but to a much less marked
degree than before.

I have here the means of producing still higher sounds.
Strung on a piece of wire are a number of iron washers —
rings of iron about an inch in diameter. When these are
shaken they produce vibrations whose wave length is even
shorter than that produced by the whistle just sounded. On
shaking the rings you perceive the immediate response of
the flame, and on shaking the rings behind the obstacle the
flame responds still, but much more feebly. I take a new
set of rings one-half inch in diameter.- On shaking these
the flame responds as before, but when I place the rings
behind the obstacle the flame scarcely responds at all. I
take a still smaller series of discs. These are approximately
only one -fourth of an inch in diameter and produce a wave
whose length is approximately one-half inch. On shaking
the last set of discs outside the obstacle the flame responds
not quite so strongly as before, because the total amount of
energy in this case is very small ; but, on shaking the discs
behind the obstacle, the flame is absolutely quiescent, show-
ing that the sound shadow is perfect. In moving the discs

MICROSCOPE, TELESCOPE, INTERFEROMETER 21

to and fro while shaking them, the geometrical limit of the
shadow can be definitely marked to within something like half
an inch ; that is, a quantity of the same order as the length
of the sound wave which is being used.

It is evident from the foregoing that, if we wish to inves-
tigate the bending of light waves around a shadow, we must
take into account the fact which has already been established,
namely, that the light waves themselves are exceedingly
small — something of the order of a fifty-thousandth of an
inch. The corresponding bending around an obstacle might,
therefore, be expected to be a quantity of this same order;
hence, in order to observe this effect, special means would
have to be adopted for magnifying it.

The diffraction of sound waves is beautifully shown by
the following experiment : 1 A bird call is sounded about ten
feet from a sensitive flame, and a circular disc of glass about
a foot in diameter is interposed. If the adjustment is imper-
fect, the sound waves are completely cut off; but when the
centering of the plate is exact, the sound waves are just as
efficient as though the obstacle were removed.

This surprising result was first indicated by Poisson,
and was considered a very serious objection to the undula-
tory theory of light. It was naturally considered absurd to
say that in the very center of a geometrical shadow there
should not only be light, but that the brightness should be fully
as great as though no obstacle were present. The experi-
ment was actually tried, however, and abundantly confirmed
the remarkable prediction.

The experiment cannot be shown to an audience by pro-
jecting on a screen, but an individual need have no difficulty
in observing the effect. The image of an arc light (or, better,
of the sun) is concentrated on a pinhole in a card, and the
light passing through is observed by a lens of two or three

i Exhibited by Lord Rayleigh at the Royal Institute.

22 LIGHT WAVES AND THEIR USES

inches' focal length some twenty feet distant. About half-
way a disc of about a quarter-inch diameter, and very
smoothly and accurately turned, is suspended by three
threads,1 so that its center is accurately in line with the pin-
hole and the center of the lens. The field of the lens will
now be quite dark, except at the center of the shadow, where
a bright point of light is seen.

We shall now attempt to show the analogue of the sound-
shadow experiment by means of light waves. The light is

FIG. 18

concentrated on a very narrow slit A (Fig. 18), which may
be supposed to act as the source of light waves. Another
slit B, about an inch wide, is placed at a distance of about
eight feet, and beyond this a screen C receives the light
which has passed through B. The borders bb of the shadow
of the slit B are quite sharply defined (though a very slight
bending of the light around the edges may be observed by
means of a lens focused on 6). But if the slit be made
narrow, as at B' , the sharp boundary which should appear
at cc is diffuse and colored, the light being bent into the
geometrical shadow as indicated by the dotted lines. The
narrower the second slit is made, the wider and more diffuse
will be the image on the screen; that is to say, the greater
will be the amount of bending into the shadow. An inter-
esting variation of the experiment is made by using two slits
instead of the second slit B. In this case, in addition to the

i The disc may be glued to a piece of optical glass, care being taken that no
trace of glue appears beyond the edge of the disc.

MICROSCOPE, TELESCOPE, INTERFEROMETER 23

bending of the rays from their geometrical path, we have
the interference of the light from the two slits, producing
interference bands whose distance apart is greater the closer
the two slits are together. If instead of two slits we have a
very large number, such as would be produced by a number
of very fine parallel wires, we have, in addition to the cen-
tral, sharp image, two lateral, colored images, which, when
carefully examined, show in their proper order all the
colors of the spectrum. This arrangement is known as a
diffraction grating, and, though mentioned here simply
as an instance of diffraction or bending of the rays from
their geometrical path, will be shown in a subsequent lec-
ture to have a very important application in spectrum
analysis.

We have thus shown that light consists of waves of
exceeding minuteness, and have found approximate values of
the lengths of the waves by measuring the very small inter-
val between the surfaces at the thicker end of our air wedge.
It can be shown also that this same measurement may be
accomplished with a grating if we know the small interval
between its lines. The question naturally arises: Might
it not be advantageous to reverse the process, and, utilizing
this extreme minuteness of light waves, make our measure-
ments of length or angle with a correspondingly high order
of accuracy? The principal object of these lectures is to
illustrate the various means which have been devised for
accomplishing this result.

Before entering into these details, however, it may be well
to reply to the very natural question: What would be the
use of such extreme refinement in the science of measure-
ment? Very briefly and in general terms the answer would
be that in this direction the greater part of all future dis-
covery must lie. The more important fundamental laws and
facts of physical science have all been discovered, and these

24 LIGHT WAVES AND THEIR USES

are now so firmly established that the possibility of their ever
being supplanted in consequence of new discoveries is exceed-
ingly remote. Nevertheless, it has been found that there
are apparent exceptions to most of these laws, and this is
particularly true when the observations are pushed to a limit,
i. e., whenever the circumstances of experiment are such that
extreme cases can be examined. Such examination almost
surely leads, not to the overthrow of the law, but to the dis-
covery of other facts and laws whose action produces the
apparent exceptions.

As instances of such discoveries, which are in most cases
due to the increasing order of accuracy made possible by
improvements in measuring instruments, may be mentioned :
first, the departure of actual gases from the simple laws of the
so-called perfect gas, one of the practical results being the
liquefaction of air and all known gases; second, the discov-
ery of the velocity of light by astronomical means, depend-
ing on the accuracy of telescopes and of astronomical clocks ;
third, the determination of distances of stars and the orbits
of double stars, which depend on measurements of the order
of accuracy of one-tenth of a second — an angle which may be
represented as that which a pin's head subtends at a distance
of a mile. But perhaps the most striking of such instances
are the discovery of a new planet by observations of the small
irregularities noticed by Leverier in the motions of the
planet Uranus, and the more recent brilliant discovery by
Lord Rayleigh of a new element in the atmosphere through
the minute but unexplained anomalies found in weighing a
given volume of nitrogen. Many other instances might be
cited, but these will suffice to justify the statement that "our
future discoveries must be looked for in the sixth place of
decimals." It follows that every means which facilitates
accuracy in measurement is a possible factor in a future dis-
covery, and this will, I trust, be a sufficient excuse for bring-

MICROSCOPE, TELESCOPE, INTERFEROMETER 25

ing to your notice the various methods and results which
form the subject-matter of these lectures.

Before the properties of lenses were known, linear meas-
urements were made by the unaided eye, as they are at pres-
ent in the greater part of the everyday work of the car-
penter or the machinist; though in many cases this is
supplemented by the "touch" or "contact" method, which
is, in fact, susceptible of a very high degree of accuracy.
For angular measurements, or the determination of direc-
tion, the sight-tube was employed, which is used today in the
alidade and, in modified form, in the gun-sight — a fact
which shows that even this comparatively rough means,
when properly employed, will give fairly accurate results.

The question then arises whether this accuracy can be
increased by sufficiently reducing the size of the apertures.

The answer is: Yes, it can, but only up to a certain limit,
beyond which, apart from the diminution in brightness, the
diffraction phenomena just described intervene. This limit
occurs practically when the diameter of two openings a
meter apart has been reduced to about two millimeters, so
that the order of accuracy is about ^X¥^7, or ^-gVo"' ^or
measurements of angle. Calling ten inches the limit of dis-
tinct vision, this means that about ^^ of an inch is the
limit for linear measurement. An enormous improvement
in accuracy is effected by the introduction of the micro-
scope and telescope, the former for linear, the latter for
angular measurements. Both depend upon the property
of the objective lens of gathering together waves from a
point, so that they meet again in a point, thus producing an
image.

This is illustrated in Fig. 19. A train of plane waves
traveling in the direction of the arrows encounters a convex
lens. The velocity is less in glass, and since the lens is

LIGHT WAVES AND THEIR USES

thickest at the center, the retardation is greatest there, gradu-
ally diminishing toward the edge. The effect is to change
the form of the wave front from a plane to a spherical shell,

FIG. 19

which advances toward the focus at O, and produces at this
point a maximum of light, which is the image of the point
whence the waves started.

Fig. 20 illustrates the case where the convex waves
diverging from a luminous point O are changed to concave
waves converging to form the image at O ' .

It can readily be shown that the luminous point and its
image are in the same line with the center of the lens —

FIG. 20

sufficiently near for a first approximation. Accordingly, if
we take separate points of an object, we can construct its
image by drawing straight lines from these through the cen-
ter of the lens, as shown in Fig. 21. The size of the image
will be greater the greater the distance from the lens, so that

MICROSCOPE, TELESCOPEL J»NTERFEROMETER 27

the magnification is proportional to the ratio of the distances
from object and image respectively to the center of the lens ;
hence in the microscope an error in determining the position
of the image means a much smaller error in the determination

FIG. 21

of the position of the point source. This error could be
diminished indefinitely by increasing the magnifying power,
were it not for the attendant loss of light and the fact that
the light waves, though very minute, are not infinitesimally
small. In fact, the same diffraction effects again limit the
possibility of indefinite accuracy of measurement. What,
then, is the new limit?

Let p, Fig. 22, represent the center of the geometrical

FIG. 22

image of a luminous point. This will be a point of maximum
brightness, because all parts of the concave wave which con-
verges toward p reach this point at the same time, and there-
fore in the same phase. Let us consider an adjacent point q.
The parts of the converging wave are no longer at equal

28 LIGHT WAVES AND THEIR USES

distances from this point, and hence will not arrive in the
same phase, and the brightness will be less than at p. At
a certain distance pq there will be no light at all. This
occurs when the difference of phase between the extreme
ray and the central ray is half a wave, that is, calling
the wave length Z, when cq — bq — J I; for these two pairs of
rays destroy each other, and the same is true of every two
such pairs of rays.

The same is equally true of every point about p at this
same distance; hence there will be a dark ring about the
bright image. This is succeeded by a bright ring, a second
dark ring, and so on.

The radius of the first dark ring may be calculated as
follows :

Draw qt at right angles to bp. Then cq — bq = ^l. But
cq = cp, very nearly, and cp — bp, and bq = bt, so that
bp — bq = pt = 1 1.

But the triangles pqt and pbc are similar, whence pt : pq =
be : bp; or, calling r the radius of the first dark ring, F
the focal length of the lens, and D the diameter of the lens,

Tfl

r~ —I; that is, the radius of the dark ring is greater than

the length of the light wave, in the same proportion as the
focal length of the lens is greater than its diameter.1 For
example, if the length of the light wave be taken as one
fifty-thousandth of an inch, and the focal length of the lens
as one hundred times the diameter, then this radius will be
one five-hundredth of an inch — a quantity readily percep-
tible with a moderate eyepiece. The lack of distinctness of
the image would be of the same order, and would be further
aggravated by greater magnification, resembling a drawing
made with a blunt point.

1 Strictly, this is about one-fourth greater on account of the fact that the aper-
ture is circular instead of rectangular.

MICROSCOPE, TELESCOPE, INTERFEROMETER 29

In most cases these diffraction rings are so small that they
escape notice, unless the air is unusually quiet and the lens
exceptionally good. If these conditions are satisfied, and
the instrument is focused on a very small or distant bright
object (a star, or a pinhole in front of an electric arc), the
rings are readily vis-
ible with a sufficiently
high-power eye-piece.
They may be much
more readily ob-
served, however, if the
ratio of diameter to
focal length be di-
minished by placing
a circular aperture
before the lens. The
smaller the aperture,
the larger will be the
diffraction rings.

Fig. 23 is a photograph of the phenomenon, showing the
appearance of the rings when the diameter of a lens of five
meters' focal length has been reduced to one centimeter.

In the case of a telescope the corresponding limiting

angle is the angle subtended by r at the distance F, i. c., „,

and this, by the formula, is the same as the angle subtended
by the light wave at the distance D — the diameter of the
objective. This limiting angle for a five-inch lens would,
therefore, be -g-^ oV~o"o~ °^ an incn? *"• #•> about the size of a
quarter of a dollar viewed at the distance of a mile. This
could be measured to within one-fifth of its value, so that
the accuracy of measurement in this case corresponds to
TTTOTTUT as against -g-or without the lens; i. e., the order of
accuracy is increased about five hundred times.

LIGHT WAVES AND THEIR USES

For a microscope it will be simpler to proceed a little
differently. The magnification increases as the object ap-
proaches the front of the objective lens. Suppose it is almost
in contact. The waves from p (Fig. 24) reach o in the same
phase, but those from q reach o more quickly through the
upper half of the lens than through the lower half. Let
the difference in the paths quo and qbo be /, that is, one of the
light waves. Then there will be darkness at o so far as the

FIG. 24

point q is concerned; i. e., the dark ring in the image of q
will lie at o and will thus coincide with the bright center of the
image of p. This condition of affairs corresponds to a dis-
placement pq = ^l. Hence, if there were two luminous
points at a distance pq = \l apart, their diffraction images
would overlap so as to be indistinguishable from each other.
Hence ^Z, or y^nnnnr of an inch, is the "limit of resolution"
in any microscope, as against ^^ of an inch with the naked
eye. So that here again the increase in accuracy is about
four hundred times.

These theoretical deductions are amply confirmed by
actual observation, and since in this investigation we have
supposed a theoretically perfect lens, these results show
that our present microscopes and telescopes, when operated
under proper conditions, are almost perfect instruments.

Thus, Fig. 25 shows a micro-photograph of the specimen
called Amphipleura pellucida, whose markings are about

MICROSCOPE, TELESCOPE, INTERFEROMETER 31

100,000 to the inch. This is about the theoretical limit for
blue light. By using the portion of the spectrum beyond
the violet it might be possible to go still farther.

FIG. 25

Doubtless by a much higher magnification a much more
accurate setting on a given phase of the fringes could be
made, and hence a corresponding increase of accuracy of
measurement could be attained. But this involves a great
loss of light, since the intensity varies inversely as the
square of the magnification. Consequently, even with a
threefold magnification the intensity is diminished ninefold,
so that it would be difficult to see the image unless the illumi-

32 LIGHT WAVES AND THEIR USES

nation were so powerful as to endanger the specimen, or to
introduce temperature variations which would vitiate the
results of the measurement.

It is apparent from all that precedes that in all measure-
ments by the microscope or the telescope we are, in fact,

FIG. 26

making use of the interference of light waves. Let us see,
then, if we are making the best use of this interference, or
whether it may not be possible to increase the high degree
of accuracy already attained.

It has just been shown that, in the case of a telescope, the
angular magnitude of the diffraction rings, and with this the
accuracy of measurement of the position of the luminous
point, depends only on the diameter of the objective. Now,
the form of the fringes will of course vary with the form of
the aperture, and if this be square instead of circular, the
diffraction image will be represented by Fig. 26, which may
be compared with Fig. 23. The width of the fringes is but
little altered, while there is a perceptible increase in dis-

MICROSCOPE, TELESCOPE, INTERFEROMETER 33

FIG. 27

tinctness. Let the middle part of the aperture now be cov-
ered up, as in Fig. 27, so that the light can pass through
the uncovered portions, a and 6, only.
Fig. 28 shows the appearance of the
fringes in this case. The distribution is
somewhat different, but the distinctness
is considerably increased, so that the
position of the center of any fringe (the
central bright fringe, for instance) may
be measured with a decided increase in
accuracy. The utilization of the two
portions of a lens? at opposite ends of a diameter, converts
the telescope or microscope into an interferometer.

This term is used to denote any arrangement which sepa-
rates a beam of light into two parts and allows them to
reunite under conditions to produce interference. The path
of the separated pencils may be varied in every possible way ;

for instance, by interposing prisms
or mirrors, provided the optical
paths are nearly equal and the
angle between the two final direc-
tions very small. The first condi-
tion is essential only when the light
is not homogeneous. The reason
will be apparent when it is remem-
bered that the width of the inter-
ference bands depends on the wave
length of the light employed. If
the light is composite, as in the
case of white light, each component
will form interference bands whose width is proportional to
the wave length.

This is illustrated in Fig. 29, where the fringes due to
red, yellow, and blue light respectively are separated. In

FIG. 28

LIGHT WAVES AND THEIR USES

the actual experiment, however, they are all superposed.
At the middle point, where the two paths are equal, all the

colors will be superposed, the re-
sult being a white central band.
At no other point will this be true,
and the result will be a series of
colored fringes symmetrically dis-
posed about the central white
fringe, the succession of colors
being exactly the same as in the
case of thin films (c/. Plate II).

The breadth of the fringes is
determined by the smallness of the
angle under which the two pencils
meet. This is shown in Fig. 30.
In the right-hand figure the angle
between the pencils is smaller than

in the other, while the breadth of the fringes is correspond-
ingly greater in the former than in the latter. The exact

FIG. 29

FIG. 30

relation is readily obtained. We have only to note that ac
is the wave length I (very nearly) and be is (very nearly) the
width 6 of a fringe; whence, if e is the very minute angle

MICROSCOPE, TELESCOPE, INTERFEROMETER 35

at b (which is the same as the angle between the directions
of the interfering pencils), b = -; or, in other words, the

width of the fringes is proportional to the wave length of the
light, and inversely proportional to the angle between the
pencils.

Thus, if the pencils converge from two apertures a
quarter of an inch apart, and meet at a screen ten feet away,
the breadth of the fringes will be one-hundredth of an inch.

The importance of using a very small angle will be noted.

FIG. 31

In this simple form of interferometer the angle can be
made small only by bringing the two apertures very near
together, which seriously diminishes the efficiency of the
instrument ; or by increasing the distance from the openings
to the fringes, or by using a high magnification, which en-
feebles the light, already very faint in consequence of having
to start from a pinhole or a narrow slit s (Fig. 31) and
to pass through the narrow apertures a and b. There is,
therefore, but little advantage in this form of interferometer
over the corresponding older analogues (microscope and
telescope ) .

An important improvement may be effected by bending
one or both the rays op, bp by reflections in such a way as to
diminish the angle at p, as shown in Fig. 32.

A further improvement is effected by replacing the aper-
tures a and b by mirrors; and, finally, by replacing the slit

31)

LIGHT WAVES AND THEIR USES

8 by a plane surface. The interferometer is now changed
into the form illustrated in Fig. 33. It will now be
noted that the source need no longer be a point or a slit,
but may be a broad flame ; and the object whose position is to

FIG. 32

be measured is no longer a fine line or a slit, but a flat surface.
The width of the fringes may be made as great as we please
without any sacrifice in the brightness of the light. The corre-
sponding increase in accuracy is from twenty to one hundred
fold. We may conveniently restrict the term interferometer to
this arrangement, in which the division and the union of the
pencils of light are effected by a transparent plane parallel
plate. It is important to note that the path of the two pen-

cils after their separation by the first plate is entirely imma-
terial ; for example, either or both pencils may suffer any
number of reflections or refractions before they are reunited
by the second plate, without affecting in any essential point
the efficiency of the interferometer, provided that the differ-

MICKOSCOPE, TELESCOPE, INTERFEROMETER 37

ence in the path of the two pencils is not too great, and
provided that the two pencils are reunited at a sufficiently
small angle. By altering these conditions of reflection or

<-*; ---— \

\ N X

fc- A

Y-

FIG. .34

LIGHT WAVES AND THEIR USES

refraction we may obtain a very considerable number of
variations of form, as illustrated in Figs. 34, 35.

One of these types, enlarged in Fig. 36, has been arranged

FIG.

MICROSCOPE, TELESCOPE, INTERFEROMETER 39

in such a way as to show the extreme delicacy of the inter-
ferometer in measuring exceedingly small angles. For
this purpose two of the
mirrors, C and D, have been
mounted on a piece of steel
shafting P two inches in
diameter and six inches
long. When the length
of the paths of the two
pencils is the same to
within a few hundred thou- g^
sandths of an inch, the in-

terference fringes in white Q

light are readily observed, FIG 3,

or may be projected on the

screen. If, now, the steel shafting be twisted, one of the
paths is lengthened and the other diminished, and for every

movement of one
two-hundred-thou-
sandth of an inch
there would be a
motion of the
fringes equal to
the width of a
fringe. Now, tak-
ing the end of the
steel shafting be-
tween thumb and
forefinger, the ex-
ceedingly small
force which may
thus be applied
in this way is
FIG. 37 sufficient to twist

40 LIGHT WAVES AND THEIB USES

the solid steel shafting through an angle which is very
readilv observed by the movement of the fringes across the
field.

The form of interferometer which has proved most gen-
erally useful is that shown in Fig. 38. The light starts
t from source S and separates at

~~ C the rear of the plate A, part of

it being reflected to the plane
mirror C, returning exactly,
on its path through A, to O,
where it may be examined by a
telescope or received upon a
screen. The other part of the

1 ray goes through the glass plate
A, passes through 5, and is re-
flected by the plane mirror Z>,

returns on its path to the starting-point A, where it is
reflected so as nearly to coincide with the first ray. The
plane-parallel glass B is introduced to compensate for the
extra thickness of glass which the first portion of the ray
has traversed in passing twice through the plate A. With-
out it the two paths would not be optically identical, because
the first would contain more glass than the second.

Some light is reflected from the front surface of the plate
A, but its effect may be rendered insignificant by covering
the rear surface of A with a coating of silver of such thick-
ness that about equal portions of the incident light are
reflected and transmitted.

The plane -parallel plates A and B are worked originally
in a single piece, which is afterward cut in two. The two
pieces are placed parallel to each other, thus insuring exact
equality in the two optical paths AC and AD.

The foregoing principles are applied in concrete form in
the instrument shown in Figs. 39, 40. A rigid casting serves

MICROSCOPE, TELESCOPE, INTERFEROMETER 41

as the bed of the instrument. One end of this bed has
fastened to it a heavy metal plate H, which carries the
three glass plates A, D, and B. The plate A is held in
a metal frame which is rigidly fastened to the plate H.
The frame which holds B can be turned slightly about a
vertical axis to allow of adjust-
ing B so that it is parallel to A.
The mirror D is held by springs
against three adjusting screws
which are set in a vertical plate
attached to the end of the plate
H. Both C and D are silvered
on their front faces. The frame
which holds the mirror C is
firmly mounted on a metal slide
which can be moved by the screw
S along the ways EF. One very
essential feature of the apparatus
is that these ways shall be so true
that the mirror C shall remain
parallel to itself as it is moved
along. The accuracy of the ways
must be so great that the greatest
angle through which the mirror
C turns in passing along them is
less than one second of an arc.
This accuracy cannot be attained by the instrument maker,
but the final grinding must be done by the investigator
himself.

To adjust the instrument so that fringes are formed, a
small object like a pin is held between the source and the
plate A. Two images of this pin will be seen by an ob-
server at O — one formed by the light which is reflected from
O, and the other by that reflected from D. The fringes in

FIG. 39

LIGHT WAVES AND THEIB USES

monochromatic light will appear when these two images
have been made to coincide with the help of the adjusting
screws ss. The fringes in white light appear only when the
lengths of the two paths AD and AC are the same. The

FIG. 40

width and the position of the fringes in the field of view
can be varied by slightly moving the adjusting screws. We
shall have occasion to discuss this particular form of inter-
ferometer in a subsequent lecture.

SUMMARY

1. The objection to the wave theory of light, that light
moves in straight lines while sound waves can bend around
an obstacle, is shown to be groundless, since we have seen
that if the sound waves are sufficiently short they cast a
sound shadow, while by devices which take into account the

MICROSCOPE, TELESCOPE, INTERFEROMETER 43

extreme minuteness of light waves their bending around
obstacles may be readily observed.

2. The extreme minuteness of light waves renders it pos-
sible to utilize the microscope and the telescope as instru-
ments of great precision. These instruments depend on the
property of the objective of gathering together waves from
a point so that they are concentrated in the diffraction pat-
tern which is called the image.

3. The accuracy of measurement is still further increased
by modifying the telescope or microscope so as to utilize
only two pencils, thus converting these instruments into
interferometers.

4. By the device of separating the two pencils and
reuniting them by reflections from plane-parallel surfaces,
the fringes may be made as large as we please without
diminishing the brightness of the light, and hence the ac-
curacy of measurement may be correspondingly increased.

LECTURE III

APPLICATION OF INTERFERENCE METHODS TO MEAS-
UREMENTS OF DISTANCES AND ANGLES

IN the last lecture we considered the limitations of the
telescope and microscope when used as measuring instru-
ments, and showed how they may be transformed so that the
diffraction and interference fringes which place the limit
upon their resolving power may be made use of to increase
the accuracy of measurements of length and of angle. We
have named these new forms of instrument interferometers
and illustrated many of the forms in which they may be made.

It has been found that the particular form of interfer-
ometer described on p. 40 is the most generally useful, and
the principal subject of this lecture will be to illustrate the
applications which have already been made of this instrument.

But before passing to the first application of the interfer-
ometer, we may make a little digression, and consider briefly
the two theories which have been proposed to account for the
various phenomena of light. One of these is the undulatory
theory, which has already been explained ; the other is the
corpuscular theory, which for a long time held its ground
against the undulatory theory, principally in consequence of
the support of Newton.

The corpuscular theory supposes that a luminous body
shines in virtue of the emission of minute particles. These
corpuscles are shot out in all directions, and are supposed to
produce the sensation of vision when they strike the retina.
The corpuscular theory was for a long time felt to be unsatis-
factory because, whenever a new fact regarding light was
discovered, it was always necessary to make some supplemen-

APPLICATION OF INTERFERENCE METHODS 45

tary hypothesis to strengthen the theory ; whereas the undu-
latory theory was competent to explain everything without
the addition of extra hypotheses. Nevertheless, Newton
objected to the undulatory theory on the ground that it was
difficult to conceive that a medium which offers no resistance
to the motion of the planets could propagate vibrations which
are transverse (and we know that the light vibrations are trans-
verse because of the phenomena of polarization), for such
vibrations can be propagated only in a medium which has the
properties of a solid. Thus, if the end of a metal rod be
twisted, the twist travels along from one end to the other
with considerable velocity. If the rod were made of sealing
wax, the twist would rapidly subside. If such a rod could
be made of liquid, it would offer virtually no elastic resist-
ance to such a twist.

Notwithstanding this, the medium which propagates
light waves, and which was supposed to resist after the
fashion of an elastic solid, must offer no appreciable resist-
ance to such enormous velocities as those of the planets
revolving in their orbits around the sun. The earth, for
example, moves with a velocity of something like twenty
miles in a second, has been moving at that rate for millions
of years, and yet, as far as we know, there is no considerable
increase in the length of the year, such as would result
if it moved in a resisting medium. There are other
heavenly bodies far less dense than the earth, e. g., the
comets, and it seems almost incredible that such enormously
extended bodies with such an exceedingly small mass should
not meet with some resistance in passing through their
enormous orbits. The result of such resistance would be
an increase in the period of revolution of the comets, and
no such increase has been detected. We are thus required
to postulate a medium far more solid than steel and far less
viscous than the lightest known gas.

40 LIGHT WAVES AND THEIR USES

These two suppositions are possibly not as inconsistent
as they may at first seem to be, for we have a very important
analogy to guide us. Consider,, for example, shoemaker's
wax, or pitch, or asphaltum. These substances at ordinary
temperatures are hard, brittle solids. If you drop them, they
break into a thousand pieces; if you strike them (so lightly
that they do not break), they emit a sound which corresponds
to the transverse vibrations of a solid. If, however, we place
one of these substances on an inclined surface, it will gradually
flow down the incline like a liquid. Or if we support a cake
of shoemaker's wax on corks and place bullets on its upper
surface, after a time the bullets will have sunk to the bottom,
and the corks will be found floating on top. So in these
cases we have a gross and imperfect illustration of the co-
existence of apparently inconsistent properties such as are
required in our hypothetical medium.1 Nevertheless, it
seemed impossible to Newton to conceive a medium with
such incompatible properties, and this was, as stated above,
a serious obstacle in the way of his accepting the undula-
tory theory. There were others, which need not now be
mentioned.

For a long time after the various modifications that the
corpuscular theory had to receive had been made, both theo-
ries were actually capable of explaining all the phenomena
then known, and it seemed impossible to decide between
them until it was pointed out that the corpuscular theory
made it necessary to suppose that light traveled faster in a
denser medium, such as water or glass, than it does in a
rarer medium, such as air; while according to the undulatory
theory the case is reversed. We may illustrate briefly the
two cases: No matter what theory we accept, it is an
observed fact that refraction takes place when light passes

1 The specialization of the undulatory theory known as the electro-magnetic
theory does not remove this difficulty ; for it is even more difficult to account for
the properties of a medium which is the seat of electric and magnetic forces.

APPLICATION OF INTERFERENCE METHODS 47

from a denser to a rarer medium, and consists in a bending
of the incident ray toward the normal to the surface of the
denser medium. Suppose we have a plate of glass, for exam-
ple, and a ray of light falling upon the surface in any direc-
tion. According to the corpuscular theory, the substance
below the surface exerts
an attraction upon the
light corpuscles. Such
attraction can act only
in the direction of the
normal. If we separate
it into two components,
one in the surface and
one normal to it, the
normal one will be in-
creased. These two com-
ponents might be repre-
sented by OA and OB in Fig. 41, and the resultant of the
two would be OC. In consequence of the presence of the
denser medium, the normal component of the velocity of the
particle is increased, and the resultant is now OC' , which is
greater than OC.

Let us next consider refraction according to the wave
theory. A wave front ab (Fig. 42) is approaching the surface
ac of a denser medium in the direction ftc. This direction is
changed by refraction to ce, and the corresponding direction
of the new wave front is cd. During the time that the wave
ab moves through the distance be in the rarer medium, it
moves through the smaller distance ad in the denser. Thus
the results, according to the two theories, are exactly reversed.

Hence, if we could measure the enormous speed of light —
about 400,000 times as great as that of a rifle bullet — it would
be possible to put the two theories to the test. In order to

LIGHT WAVES AND THEIR USES

accomplish this we must compare the velocities of light in
air and in some denser, transparent medium — say water.
Now, the greatest length of a column of water which still
permits enough light to pass to enable us to measure the
very small quantities involved is something like thirty feet.

We should therefore
have to determine the
time it takes the light
to pass through thirty
feet of water, at the
rate of 150,000 miles
a second. This inter-
val of time is of the
order of one twenty-
millionth of a second.
But we must measure
a time interval even
smaller than this, for
we have to distinguish between the velocity in water and the
corresponding velocity in the air, /. <°., to determine the dif-
ference between two time intervals, each of which is of the
order of one twenty-millionth of a second. This, at first sight,
seems beyond the possibility of any physical experiment; but,
notwithstanding this exceedingly small interval of time, by
the combined genius of Wheatstone, Arago, Foucault, and
Fizeau the problem has been successfully solved. The
method proposed by Wheatstone for measuring the velocity
of electricity was this : A mirror was mounted so that it could
be revolved about an axis parallel to its surface at a very
high rate, and the light from the spark produced by the dis-
charge of a condenser was allowed to fall on the mirror. The
images of two sparks were observed in the revolving mirror;
the second spark passed after the electric current which pro-
duced it had passed through a considerable length of wire —

FIG. 42

APPLICATION OF INTERFERENCE METHODS 49

perhaps several miles; the first, after it had passed through
only a few feet of wire. If the mirror in this interval had
turned through a perceptible angle, the reflected light would
have moved through double that angle; and, knowing the
velocity of rotation of the mirror, and measuring this small
angle, the velocity of electricity could be determined. Arago
thought this same method might be adapted to the measure-
ment of the velocity of light.

FIG. 43

The principle of Arago 's method may be illustrated as
follows: Suppose we have a mirror R (Fig. 43), revolving
in the direction of the arrows, s is a spark from a con-
denser, which sends light directly to the mirror R, and also
to the distant mirror J/, whence it returns to R, and both
rays are reflected in the direction Sj. If, however, the light
takes an appreciable time to pass from s to M and back,
this light will reach the mirror R later, and the mirror will
have turned in the interval so as to reflect the light to s2.

If the angle s1J?s2 can be measured, the angle through
which the mirror moves is one-half as great ; and, knowing
the speed of the mirror, we know also the time it takes to
turn through this angle; and this is the time required for
light to traverse twice the distance slf, whence the velocity
of light.

The principle of Arago's method is sound, but it would
be extremely difficult to carry it into practice without an
important modification, due to Foucault, which is illustrated

50 LIGHT WAVES AND THEIR USES

in Fig. 44. Light from a source s falls on the revolving mir-
ror JR, and by means of a lens L forms an image of s at the
surface of a large concave mirror M. The light retraces its
path and forms an image which coincides with s if the mirror
R is at rest or is turning slowly. When the rotation is suf-
ficiently rapid the image is formed at Sj, and the displace-
ment ssj is readily measured.

FIG. 44

If the distance LM is occupied by a column of water,
the displacement would be less if the velocity of light is
greater in water than in air, as it should be according to the
corpuscular theory ; and if the undulatory theory is correct,
the displacement would be greater. Foucault found the
displacement greater, and thus the corpuscular theory re-
ceived its death-blow.

It remained for subsequent experiment to determine
whether the undulatory theory was true, because it was not
sufficient to show that the velocity was smaller in water ; it
was necessary to show that the ratio of the two velocities
was equal to the index of refraction of the water, which is
1.33. Experiments showed that the ratio of the two veloci-
ties is almost identical with this number, thus furnishing an
important confirmation of the undulatory theory.

Ordinarily the index of refraction is found by measuring
the amount of bending which a beam of light experiences in

APPLICATION OF INTERFERENCE METHODS 51

FIG. 45

passing from air into the medium in question. But if this
number is identical with the ratio of the velocities, the
index would evidently be determined if we knew the ratio
of the wave lengths, since the wave lengths are also propor-
tional to the velocities. This can be obtained by the inter-
ferometer. In fact, the origi-
nal name of the instrument is
' ' interf erential ref ractometer,"
because it was first used for
this purpose by Fresnel and
Arago in 1816; This name,
however, is as cumbersome as
it is inappropriate, for, as we
shall see, the range of useful-
ness of the instrument is by no means limited to this sort
of measurement.

The interferometer being adjusted for white light, the
colored interference fringes are thrown on the screen. If,
now, the number of waves in one of the paths be altered by
interposing a piece of glass, the adjustment will be disturbed
and the fringes will disappear; for the difference of path
thus introduced is several hundreds or thousands of waves;
and, as shown in the preceding lecture, the fringes appear
in white light only when the difference of path is very small.

The exact number of waves introduced can readily be

shown to be 2(n— 1)-; that is, twice the product of the

index less unity by the thickness of the glass divided by the
length of the light wave. Thus, if the index of the glass
plate is one and one-half and its thickness one millimeter,
and the wave length one-half micron, the difference in path
would be two thousand waves.

Let us take, therefore, an extremely thin piece of mica,
or a glass film such as may be obtained by blowing a

52 LIGHT WAVES AND THEIR USES

bubble of glass till it bursts. Covering only half the field with
the film, the fringes on the corresponding side are shifted in
position, as shown in Fig. 45, and the number of fringes in
the shift is the number of waves in the difference of path,
from which the index can be calculated by the formula.1

The interferometer is particu-
larly well adapted for showing very
slight differences in the paths of
the two interfering pencils, such,
for instance, as are produced by
inequalities in the temperature of
the air. The heat of the hand held
near one of the paths is quite suf-
ficient to cause a wavering of the
fringes; and a lighted match pro-
duces contortions such as are shown

in Fig. 46. The effect is due to the fact that the density
of the air varies with the temperature ; when the air is hot
its density diminishes, and with it the refractive index.

It follows that, if such an experiment were tried under
proper conditions, so that the displacement of the interfer-
ence fringes were regular and could be measured — which
means that the temperature is uniform throughout — then the
movement of the fringes would be an indication of tempera-
ture. Comparatively recently this method has been used to
measure very high temperatures, such as exist in the interior
of blast furnaces, etc.

In one of the preceding lectures an image of a soap film
was thrown on the screen, and it was shown that the thick-
ness of the film increased regularly from top to bottom,
and that where the thickness was sufficiently small the
interference fringes enable us to deduce the thickness of the

i For quantitative measurements it is necessary to employ monochromatic light.
The shifting of the central band of the colored fringes in white light does not give
even an approximately accurate result.

APPLICATION OF INTERFERENCE METHODS 53

film. It was also shown that at the top of the film, where
the thickness was very small, a black band appears, its lower
edge being sharply defined as though there were here a sud-
den change in thickness, as illustrated in Fig. 47.

Now, this "black spot" may be observed sufficiently long
to measure the displacement produced
in interference fringes when the film
is placed in the interferometer. It
is probable that over the area of the
"black spot" the two surfaces of the
film are as near together as possible;
and if the water is made up of mole-
cules, there are very few molecules
in this thickness — possibly only two

/ . FIG. 47

—so that a measurement or this

thickness would give at least an upper limit to the distance
between the molecules.

A soap solution of slightly different character from that
used in the last lecture is more serviceable for this purpose.1
With such a solution the film lasts a remarkably long time.
It is interesting to note that some time after the "black
spot" has formed, portions of its surface reflect even less
light than the rest, and these portions gradually increase
in size and number till the whole surface almost entirely
vanishes.

It is found on placing such a film as this in the inter-
ferometer that there is no appreciable change in the fringes.
The film is so thin that we cannot observe any displacement
at all ; if we place two films in the interferometer, the dis-
placement should be twice as great ; but even then it is inap-
preciable. To obtain a measurable displacement it was
found necessary to use fifty such films. The arrangement

iThis solution is made of caustic soda 1 gm., oleic acid 7 gm., dissolved in 600
c.c. of water.

LIGHT WAVES AND THEIR USES

of the interferometer for this experiment1 is shown in Fig. 48.

The films are introduced in the path AC, as indicated at

F. Yet even fifty films
produced a displacement
of only about half a
fringe, as shown in Fig.
49. Since the light
passed through each film
twice, this displacement
of half a fringe is what
would be produced by a
single passage through
one hundred films. One
film would therefore
produce a displacement

i i

FIG. 48

of one two-hundredths
of a fringe. A simple calculation tells us that the correspond-
ing distance between the water molecules is not greater than
six millionths of a millimeter. It may be much less than this.
^The interferometer is especially useful whenever it is
necessary to measure small changes in distance or angle.
One rather important instance of
such a measure is that of coefficient
expansion. Most bodies expand
with heat — certainly a very small
quantity: one or two parts in ten
thousand for a change of tempera-
ture of a single degree.

In some cases it may be neces-
sary to experiment upon a very
small specimen of the material in
question, and in such cases the whole change to be measured
may be of the order of a ten-thousandth part of an inch —

IE. S. JOIIONNOTT, Phil. Mag. (5), Vol. XL VII (1899), p. 501.

FIG. 49

APPLICATION OF INTERFERENCE METHODS 55

a quantity requiring a good microscope to perceive; but
such a quantity is very readily measured by the inter-
ferometer. It means a displacement amounting to several
fringes, and this displacement may be measured to within a
fiftieth of a fringe or less ; so that the whole displacement
may be measured to
within a fraction of 1 per
cent. Of course, with
long bars the attainable
degree of accuracy is far
greater.

Figs. 50 and 51 rep-
resent a piece of appa-
ratus designed by Pro-
fessors Morley and
Rogers,1 based on this
principle, b and c (Fig.
50) are the two plane-
parallel plates of the in-
terferometer, and the two
mirrors are at a and a' . Each mirror is divided into two
halves as at aa, so that a motion of each end of the bar to
be tested can be observed. The jackets gg serve to keep
the bars at any desired temperatures. One side of the instru-
ment, as aa, being kept at a constant temperature, a change
in the temperature of a' a' will cause the fringes to move,
and from this motion of the fringes the change in length,
which is caused by the change in temperature, can be very
accurately determined. Fig. 51 shows a perspective view of
the apparatus.

Evidently the same kind of instrument is suitable for
experiments in elasticity, and one of these was shown in the
last lecture, where a steel axle was twisted (c/. Figs. 36 and

i MOEL,EY AND ROGERS, Physical Review, Vol. IV (1896), pp. 1, 106.

FIG. 50

LIGHT WAVES AND THEIR USES

37, p. 39). If we measure the couple producing the twist,
and the number of fringes which pass by, we can find the
corresponding angle of twist, and a simple calculation gives
us the measure of our coefficient of rigidity.

The interferometer in this second form has also been

applied to the
balance. Fig.
52 shows such
an arrangement.
The mirrors of
the interferom-
eter are on the
upright metal
plate, the two
movable mirrors
being fastened
to the ends of
the arms of a
balance which
is just visible
within the horizontal box. The object of this particular
experiment was to determine the constant of gravitation;
in other words, to find the amount of attraction which a
sphere of lead exerted on a small sphere hung on an arm of
the balance. The amount of this attraction, when the two
spheres are as close together as possible, is proportional to
the diameter of the large sphere, which was something like
eight inches. The attraction on the small ball on the end
of the balance was thus the same fraction of its weight as
the diameter of the large ball was of the diameter of the
earth, i. e., something like one twenty-millionth.1 So the
force to be measured was one twenty-millionth of the weight

FIG. 51

1 This ratio takes into account the increased attraction due to the greater
density of the lead sphere.

APPLICATION OF INTERFERENCE METHODS 57

of this small ball. This force is so exceedingly small that
it is difficult to measure it by an ordinary balance, even
if the microscope is employed. But by the interference
method the approach of the large ball to the small one pro-
duced a displacement of seven whole fringes. The number
of fringes can be deter-
mined to something of the
order of one-twentieth of
the width of one fringe.
We therefore have with
this instrument the means
of measuring the gravita-
tion constant, and thence
the mass of the whole earth,
to within about T^Q- of the
whole. By still more sen-
sitive adjustment it would
be possible to exceed this
degree of accuracy.

An instrument in which
the interferometer is used
for testing the accuracy of
a screw is shown in Fig.
53. The screw which was
to be tested by this device was intended to be used in a
ruling engine for the manufacture of diffraction gratings.
Now, it is necessary, in ruling gratings, to make the dis-
tance between the lines the same to within a small frac-
tion of a micron. The error in the position of any of the
lines must be less than a ten-millionth part of an inch.
Ordinarily a screw from the best machinists has errors a
'thousand times as great. The screw must then be tested
and corrected. The testing is often done with the micro-
scope, but here the microscope is replaced by the inter-

FIG. 52

LIGHT WAVES AND THEIR USES

ferometer, with a corresponding increase in the delicacy of
the test.

I will conclude by showing how to measure the length of
light waves by means of the interferometer. By turning

FIG. 53

the head attached to the screw, one of the interferometer
mirrors (namely C, Fig. 39) can be moved very slowly.
This motion will produce a corresponding displacement of
the interference fringes. Count the number of interference
fringes which pass a fixed point while the mirror moves a
given distance. Then divide double the distance by the
number of fringes which have passed, and we have the
length of the wave. Using a scale marked from 0 to 10,
made of such a size and placed at such a distance that, when
a beam of light reflected from a mirror attached to the
screw moves over one division, a difference in path of one-

APPLICATION or INTERFERENCE METHODS 59

thousandth of a millimeter has been introduced, and project-
ing the interference fringes upon the screen, it will be noted
that while ten or twelve of these fringes move past the fiducial
line the spot of light will move over a corresponding dis-
tance on the scale. In moving through ten fringes the spot
of light moves through six of the divisions, and therefore
the length of one wave would be six-tenths of a micron,
which is very nearly the wave length of yellow light. If the
light passes through a piece of red glass, and the experiment
is repeated, the wave length will be greater; it is nearly
sixty-seven hundredths. It is easy to see how the process
may be extended so as to obtain very accurate measurements
of the length of the light wave.

SUMMARY

1. A comparison between the corpuscular and the undula-
tory theories of light shows that the speed of light in a
medium like water must be greater than in air according to
the former, and less according to the latter. In spite of the
inconceivable swiftness with which light is propagated, it
has been possible to prove experimentally that the speed is
less in water than in air, and thus the corpuscular theory is
proved erroneous.

2. A number of applications of the interferometer are
considered, namely, (a) the measurement of the index of
refraction ; (6) the coefficient of expansion ; (c) the coefficient
of elasticity; (d) the thickness of the "black spot;" (e) the
application to the balance ; (/) the testing of precision screws ;
((j) the measurement of the length of light waves.

LECTURE IV

THE APPLICATION OP INTERFERENCE METHODS TO
SPECTROSCOPY

DOUBTLESS most of us, at some time or other, have looked
through an old-fashioned prismatic chandelier pendant and
observed that when held horizontally it produces the very
curious effect of making objects appear to slope downward
as though going down hill; and certainly you have all
noticed the colored border which such a pendant produces
at the edge of luminous objects. This experiment was made
first under proper conditions by Newton, who allowed a
small beam of sunlight to pass through a narrow aperture
into a dark room and then through a glass prism. He
observed that the sun's image was drawn out into what we
call a spectrum, i. e., into a band of colors which succeed
one another in the well-known sequence — red, orange, yel-
low, green, blue, violet; the red being* least refracted and
the violet most.

If Newton had made his aperture sufficiently narrow
and, in addition, had introduced a lens in such a way
that a distinct image of tl^e slit through which the sun-
light passed was formed on the opposite wall, he would
have found that the spectrum of the sun was crossed by a
number of very fine lines at right angles to the direction in
which the colors extended. These lines, called after the dis-
coverer Fraunhofer's lines, have this very important char-
acteristic, that they always appear at certain definite positions
in the spectrum ; and hence they were used for a considerable
time for describing the location of the different colors of
the spectrum. We shall endeavor roughly to present this

INTERFERENCE METHODS IN SPECTROSCOPY 61

experiment. Not having sunlight, however, we shall take an
electric arc and produce a spectrum. It will be noticed that
this spectrum is not crossed by black lines, but that it is,
at least for our purpose, practically continuous, as shown on
Plate III, No. 1. Instead of using the electric light, let us
try a source which emits but a single color. For this pur-
pose we shall introduce into the electric arc a piece of
sodium glass. Instead of a spectrum of many colors, we
have one consisting mainly of one color, namely, of one
yellow band. This yellow band in reality consists of two
images of the slit, which are very close together, as can be
shown by making the slit narrower, for then the two lines
will also become narrower in proportion. If, instead of
sodium glass, we introduce a rod of zinc, then, instead of
one bright yellow line, the spectrum consists of lines in the
red, green, and violet — two or three in the violet, one in
the green, and one in the red. If we were to introduce
copper, the spectrum would consist of quite a number of lines
in the green; and if other substances were used, other lines
would appear in the spectrum (cf. Plate III, Nos. 3 and 4).
Now, the lines produced by any one substance are found to
occur always at a particular place in the spectrum, and are
thus characteristic of the substance which produces them. If,
instead of the electric light, we had used sunlight, we should
find, as Fraunhofer did, that the spectrum of the sun is crossed
by a number of fine, dark lines, perhaps as many as one
hundred thousand, distributed throughout the spectrum.
Some of the more important of these lines are shown in Fig.
54. The red end of the spectrum is at the bottom. Only the
visible portion of the spectrum of the sun is shown in the
figure. The pair of dark lines marked D coincide in position
with the bright lines which are produced by sodium, as
shown on Plate III, Nos. 2 and 3, and is an indication of the
presence of sodium in the sun's atmosphere.

LIGHT WAVES AND THEIR USES

FIG. 54

As was remarked above, this sodium line is
double, i. e., is really made up of two lines close
together. The "distance between these two lines is
a convenient standard of measurement for our sub-
sequent work. This distance is so small that a
single prism scarcely shows that the line is double.
As we increase the number of prisms, the lines are
separated more and more widely. If, instead of a
prism, we use one of the best grating spectroscopes,
the two lines are separated so far that we might
count sixty or eighty lines between ; and this fact
gives a fair idea of the resolving power of these
instruments. If we have two lines so close to-
gether as to be separated by only one-hundredth
of the distance between these two sodium lines,
the best spectroscope will hardly be able to sepa-
rate them; i. e., its limit of resolution has been
reached. ,

The difference in the character of the lines
from different substances is illustrated in Fig. 55.
The spectrum that you have just seen is a photo-
graph from a drawing, not a photograph from a
spectrum. These are from spectra. On the right
is a portion of the spectrum of irqji, the other the
corresponding portion of that of zinc. The enor-
mous diversity in the appearance of the lines will
be noted. Some are exceedingly fine — so fine that
they are not visible at all ; others are so broad that
they cover ten or twenty times the distance between
two sodium lines. This width of the lines de-
pends somewhat upon the conditions under which
the different substances are burned. If the incan-
descent vapor which sends out the lines is very
dense, then the lines are very broad; if it is very

INTERFERENCE METHODS IN SPECTROSCOPY 63

rare, then the lines are exceedingly narrow.
Some of the lines are double, some triple,
and some are very complex in their charac-
ter; and it is this complexity of character or
structure to which I wish particularly to
draw your attention.

This complexity of the character of the
lines indicates a corresponding complexity
in the molecules whose vibrations cause the
light which produces these lines; hence the
very considerable interest in studying the
structure of the lines themselves. In very
many cases — indeed, I may say, in most
cases — this structure is so fine that even
with the most powerful spectroscope it is
impossible to see it all. If this order of com-
plexity, or order of fineness, or closeness of
the component lines is something like one-
hundredth of the distance we have adopted
as our standard, it is practically just beyond
the range of the best spectroscopes. It
therefore becomes interesting to attempt to
discover the structure by means of inter-
ference methods.

In order to understand how interference
can be made use of, let us consider the nature
of the interference phenomena which would
be produced by an absolutely homogeneous
train of waves, •/. e., one which consisted of
only one definite simple harmonic vibra-
tion. If such a train of waves were sent into
an interferometer, it would produce a definite
set of fringes, and if the mirror C (Fig. 39)
of the interferometer were moved so as to

FIG. 55

64 LIGHT WAVES AND THEIR USES

increase the difference in path between the two interfering
beams, then, as was explained above on p. 58, these inter-
ference fringes would move across the field of view. Now,
in this case, since the light which we are using consists
of waves of a single period only, there will be but one set of
fringes formed, and consequently the difference of path be-
tween the two interfering beams can be increased indefinitely
without destroying the ability of the beams to produce inter-
ference. It is perhaps needless to say that this ideal case
of homogeneous waves is never practically realized in
nature.

What will be the effect on the interference phenomena if
our source of light sends out two homogeneous trains of
waves of slightly different periods? It is evident that each
train will independently produce its own set of interference
fringes. These two sets of fringes will coincide with each
other when the difference in the lengths of the two optical
paths in the interferometer is zero. When, however, this
difference in path is increased, the two sets of fringes move
across the field of view with different velocities, because they
are due to waves of different periods. Hence, one set must
sooner or later overtake the other by one-half a fringe, i. e.,
the two systems must come to overlap in such a way that a
bright band of one coincides with a dark band of the other.
When this occurs the interference fringes disappear. It is
further evident that the difference of path which must be
introduced to bring about this result depends entirely on
the difference in the periods of the two trains of waves, i. e.,
on the difference in the wave lengths, and that this disap-
pearance of the fringes takes place when the difference of
path contains half a wave more of the shorter waves than of
the longer. Hence we see that it is possible to determine
the difference in the lengths of two waves by observing the
distance through which the mirror C must be moved in

INTERFERENCE METHODS IN SPECTROSCOPY 65

passing from one position in which the fringes disappear to
the next.

If the two homogeneous trains of waves have the same
intensity, then the two sets of fringes will be of the same
brightness, and when the bright fringe of one falls on the
dark fringe of the other, the fringes disappear entirely. If,
however, the two trains have different intensities, one set of
fringes will be brighter than the other, and the fringes will
not entirely disappear when one set has gained half a fringe
on the other. In this case the fringes will merely pass
through a minimum of distinctness. We see then that, if
our source of light is double, i. e., sends out light of two
different wave lengths, we should expect to see the clearness
or visibility of the fringes vary as the difference of path
between the two interfering beams was increased.

If we invert this process and observe the interference
fringes as the difference in path is increased, and find this
variation in the clearness or visibility of the fringes, it is
proved with absolute certainty that we are dealing with a
double line. This is found to be the case with sodium
light, and, therefore, by measuring the distance between the
positions of the mirror at which the fringes disappear, we
find that we actually can determine accurately the difference
between the wave lengths of the two sodium lines. In
order to carry the analysis a step farther, suppose that
we magnify one of these two sodium lines. It would
probably appear somewhat like a broad, hazy band. For the
sake of simplicity, however, we will suppose that it looks like
a broad ribbon of light with sharp edges. The distance
between these edges, i. e., the width of this one line, if the
sodium vapor in the flame is not too dense, is something
like one-fiftieth, or, perhaps, in some cases as small as
one-hundredth, of the unit we have adopted — the distance
between the sodium lines.

66 LIGHT WAVES AND THEIR USES

This is proved by noting the greatest difference in path
which can be introduced before the fringes disappear entirely.
This distance is different for different substances, and the
greater it is the narrower the line, i. e., the more nearly does
it approach the ideal case of a source which emits waves of
one period only. Now, experiment shows that the fringes
formed by one sodium line will overtake those formed by the
other in a distance of about five hundred waves, correspond-
ing to about one-third of a millimeter, and that we can
observe interference fringes with sodium light, under proper
conditions, until the difference in path between the two
interfering beams is approximately thirty millimeters. This
means that the width of the band is something like one-
hundredth of the distance between the two bands. The
width of a single line can be appreciated in the ordinary
spectroscope when the sodium vapor is dense, and under
these conditions the fringes vanish when the difference in
path is only one-half inch, or even less. When we try to
make the source bright by increasing the temperature and
density of the sodium vapor in the flame, the band broadens
out to such an extent that the difference in path over which
interference can be observed may be less than one-hundredth
of an inch.

The above discussion of the case of the two sodium lines
may easily be extended to include lines of greater complex-
ity, and it will be found that, whatever the nature of the
source, the clearness or visibility of the fringes will vary as
the difference in path between the two interfering beams is
increased. It may also be shown that each particular com-
plex source will show variations in the visibility of the
fringes which are peculiar to it.

Inversely it is evident that by the observation of the
character of the curve which expresses the relation between
the clearness of the fringes and the difference of path — the

INTERFERENCE METHODS IN SPECTROSCOPY 67

FIG. 56

68 LIGHT WAVES AND THEIR USES

visibility curve, as it may be termed — we can draw con-
clusions as to the character of the radiations which cause the
interference phenomena, even when such investigation is
beyond the power of the best spectroscopes. In order to
make the method (it may perhaps be called the method of
light-wave analysis) an accurate process, it is necessary, in
the first place, to produce a number of visibility curves from
known sources. Thus, for example, we may take two lines
corresponding to the sodium lines, and produce their visibil-
ity curve, as we did before, by adding up the separate fringes
and obtaining the resultant ; we may then take three or four
or any number of lines, and determine the corresponding
visibility curves. Each of these, instead of being a single
line, may have an appreciable breadth, and the brightness
of the line may be distributed in various ways within the
breadth.

Now, the process of adding up such a series of simple
harmonic curves (for the interference fringes are represented
by simple harmonic curves) is very laborious. Hence the
instrument shown in Fig. 56, called a harmonic analyzer,
was devised to perform this work mechanically. It looks
very complex ; in reality it is very simple, the apparent
complexity arising from the considerable number of ele-
ments required. A single element is shown in Fig. 57.
A curved lever which is pivoted at o is represented at B.
One end of this lever is attached to the collar of the eccen-
tric A. When this eccentric revolves, it therefore transmits
to the lever B a motion which is very nearly simple har-
monic. The amount of the motion which is communicated
to the writing lever u is regulated by the distance of the
connecting rod R from the axis o. When the connecting
rod is on one side of the axis the motion is positive ; when
on the other side the motion would be negative. The end
of this lever is connected to another lever #, and the farther

INTERFERENCE METHODS IN SPECTROSCOPY 69

FIG. 57

70 LIGHT WAVES AND THEIR USES

end of this lever is connected with a small helical spring «.
There are eighty such elements arranged in a row, as shown
in Fig. 56. In order to add the force of all of the springs,
they are connected with the drum C, which can turn about
its axis, and counterbalanced by a very much larger spring
S connected to the other side of the drum. This gives us
the means of adding forces which are proportional to the
amount of displacement of the lever below, and hence the
sum of the forces of these eighty springs is in direct propor-
tion (at any rate to a close degree of approximation) to the
sum of the motions themselves. We have thus a mechanical
device for adding simple harmonic motions.

To illustrate this addition of simple harmonic motions
by means of our machine, one of the connecting rods is first
moved out to the extreme end of the lever. We shall then
have but one simple harmonic motion to deal with, and this
corresponds to an absolutely homogeneous source. The re-
suiting curve is the first one in Fig. 58. Each one of the
Oscillations corresponds to an interference fringe, and there
would be an infinite number of such if the difference in path
were indefinitely increased. Now we will take the case of two
simple harmonic motions. At 6, curve 2, the fringes have dis-
appeared completely. One series of fringes has just overtaken
the other by one-half a fringe, and, therefore, they neutral-
ize each other. At c the fringes have begun to appear again,
and at d they have attained a maximum visibility or clear-
ness. They then disappear and reappear again, and so on
indefinitely.

Curve 3 represents the case of the two sodium lines, each
of which is supposed to be double. It will be observed that
in this case there are two periods ; one, the same as that of
curve 2, which corresponds to the double sodium line, and
the other a longer period whose first minimum occurs at
e and which corresponds to the shorter distance between the

INTERFERENCE METHODS IN SPECTROSCOPY 71

two components of each line. The conclusion which can be
drawn from observation of such a curve as this is that the

l/WWVWVWW^^

? d

5 ||MM/VVV~V^^ — /www> ,/www .

iN-ww/vv^^

I a |||(1(W--^^

FIG. 58

source which was used in obtaining it was a double line, each
of whose components was double.

Curve 4 represents the visibility curve of two lines, one
of which is very much brighter than the other, but whose

72 LIGHT WAVES AND THEIR USES

distance apart is the same as that of the lines of curve 2.
The period of the visibility curve is the same as that of 2,
but instead of going to zero it merely goes to a minimum at
/. Inversely, when we get such a curve as this we know that
one of the lines is brighter than the other — just how much
brighter can be learned from the ratio of the maximum and
minimum ordinates.

Curve 5 is that due to a single broad source of uniform
intensity throughout. It will be noted how quickly the
fringes lose their distinctness. Curve 6 is that due to a broad
source which is brighter in the middle than at the edges.
The distribution in this case is supposed to follow the expo-
nential law. The corresponding visibility curve does not
exhibit maxima and minima, but gradually dies out and
remains at zero. Curve 7 corresponds to a double source
each of whose components is brighter in the middle. Curve
8 represents a triple source each of whose components is
a simple harmonic train of waves of the same intensity.
Curve 9 represents the visibility due to a triple source
in which the outer components are much fainter than the
middle one.

We might go on indefinitely constructing on the machine
the visibility curves which correspond to any assumed dis-
tribution of the light in the source. The curves presented
will suffice to make clear the fact that there is a close
connection between the distribution of light in any source
arid the visibility curve which can be obtained with the
use of that source. It is, however, the inverse problem,
i. e.y that of determining the nature of the source from
observation of the visibility curve, in which the greatest
interest lies.

In order to determine by this method the character of
the source with which we are dealing, we must find our visi-
bility curve by turning the micrometer screw of the inter-

INTERFERENCE METHODS IN SPECTROSCOPY 73

ferometer and noting the clearness of the fringes as the dif-
ference of the path varies. We then construct a curve
which shall represent this variation of visibility on a more
or less arbitrary scale, and compare it with one of the known
forms, such as those shown in Fig. 58. There is, however,
a more direct process. The explana-
tion of this process involves so much
mathematics that I shall not undertake
it here. It will be sufficient to state
that the harmonic analyzer cannot only
be used as has been described, but is
also capable of analyzing such visibility FIG> 59

curves. Thus, if we introduce into the instrument the curve
corresponding to the visibility curve, by making the distances
of the connecting rods from the axis proportional to the ordi-
nates of the visibility curve, and then turn the machine, it
produces directly a very close approximation to the char-
acter of the source. For example, take curve 2 of Fig.
58. By its derivation we know that it corresponds to a
double source each of whose components is absolutely homo-
geneous. If we introduce this curve, or rather the envelope
of it, into the machine, it will give a resultant which repre-
sents the character of the source to a close degree of approxi-
mation. The actual result is shown in Fig. 59, in which the
ordinates represent the intensity of the light. We thus see
that the machine can operate in both ways, i. e., that it can
add up a series of simple harmonic curves and give the
resultant, which in the case before us is the visibility curve,
and that it can take the resultant curve and analyze it into
its components, which here represent the distribution of the
light in the source.

Now the question naturally arises as to how the observa-
tions by which the visibility curve is determined are con-
ducted; also as to what units to adopt, and what scale

74 LIGHT WAVES AND THEIR USES

of measurement. It is apparently something very indefi-
nite. The visibility is not a quantity that can be measured,
as we can a distance or an angle — unless, to be sure, we
first define it. After defining it properly, we can pro-
duce, in accordance with that definition, interference fringes
that shall have any desired visibility. By the use of fringes
which have a known visibility we can educate the eye in
estimating visibility, or we may have these standard fringes
before us for comparison at the time of observation, and
may then determine when the two systems are of the same
clearness; and when they are of the same clearness, we say
that the desired visibility is the same as that whose value is
known from our formula. This is the more accurate method,
and is the one which was finally adopted ; but long before its
adoption it was found that fairly accurate visibility curves
could be obtained by merely agreeing to call the visibility
100 when it was perfect, 75 when good, and 50 when -fair.
Then 25 would be rather poor, 10 would be bad, and at zero
the fringes would vanish. Of course, there would be a
greater or less difference in what we should agree to call
good, but in general we can tell where the fringes were half
as clear as their perfect value, provided, of course, we had
this perfect value given, etc.

As a matter of fact, however, it is not of the utmost
importance to determine the visibility with great accuracy.
We know that we can measure a minimum or a maximum
independently of any scale, and these points are the really
important ones. For example, a curve may come to zero
gradually or abruptly — in both cases the distance between
the two lines which produced the curve would be exactly the
same. The two pairs might differ in character in other
ways, but the distance between the two components of each
pair would be the same. So, even without an absolute scale
that we have tested, and even without any very great amount

INTERFERENCE METHODS IN SPECTROSCOPY 75

FIG. 60

of experience in observation, we can get a very fair visi-
bility curve, and from that a very fair conception of the
nature of the spectrum of the particular source we are exam-
ining, by merely determining the points of maximum and
minimum clearness.

Before discussing some of the visi-
bility curves that have been obtained,
I should like to say a word concerning
the source of light. When the source
is under ordinary conditions, i. e.,
under atmospheric pressure, the mole-
cules are not vibrating freely, and dis-
turbing causes come in to make the
oscillations not perfectly homogeneous.
Hence the light from such a source,
instead of being a definite, sharp line, is a more or less
diffuse band. In order to obtain the character of the line
under the extreme conditions, i. e., under as small pres-
sure as possible, the substance must be placed in a vacuum
tube. The tube is then connected to an air pump and
exhausted until the pressure in it is reduced to a few thou-
sandths of an atmosphere.

When the exhaustion has become sufficient — the time
depending on the particular degree of exhaustion required
by the substance which we wish to examine — the tube is
heated to drive off the remaining water vapor, sealed up, and
is then ready for use. The residual gas is made luminous
by the spark from an induction coil. In some cases the
substance is sufficiently volatile to show the spectrum at
ordinary temperatures; e. </., that of mercury appears after
slight heating. In the case of such substances as cad-
mium and zinc the tube is placed in a brass box, as illus-
trated in Fig. 60, and heated until the substance is volatilized,
a thermometer giving us an idea of the temperature reached.

LIGHT WAVES AND THEIR USES

Fig. 61 illustrates the arrangement of the apparatus
as it is actually used. An ordinary prism spectroscope
gives a preliminary analysis of the light from the source.

?>a

FIG. 61

This is necessary because the spectra of most substances
consist of numerous lines. For example, the spectrum of
mercury contains two yellow lines, a very brilliant green
line, and a less brilliant violet line. If we pass all the
light together into the interferometer, we have a combina-
tion of all four. It is usually better to separate the various
radiations before they enter the interferometer. Accord-
ingly, the light from the vacuum tube at a passes through an

INTERFERENCE METHODS IN SPECTROSCOPY 77

ordinary spectroscope 6cd, and the light from only one of
the lines in the spectrum thus formed is allowed to pass
through the slit d into the interferometer.

As explained above, the light divides at the plate e, part
going to the mirror/, which is movable, and part passing
through to the mirror g. The first ray returns on the path/e/i.
The second returns to e, is reflected, and passes into the tele-
scope h. If the two paths are exactly equal, we have inter-
ference phenomena in white light; but for monochromatic
light the difference of path (from the point e to the mirror /,
and from the same point to the mirror g) may be very consid-
erable. Indeed, in some cases interference can be obtained
when the difference in the two paths amounts to over half a
million waves.

It is rather important to note that the surface of the
mirror g must be so set by means of the adjusting screws
at its back that its image in the mirror e shall be parallel
with the surface of the movable mirror f. When this is
the case the fringes, instead of being straight lines, as in
the case of the fringes in white light, are concentric circles
very similar in appearance to Newton's rings. Having thus
adjusted the interferometer so that the fringes are circles, the
difference in path is increased by turning the micrometer
screw a definite amount, say half a millimeter at a time. At
every half millimeter an observation is taken of the visibility,
and then these readings are plotted on co-ordinate paper as
ordinates, the corresponding difference of path serving as
abscissaB. The ends of these ordinates trace out the visi-
bility curve. This curve is then set on the harmonic ana-
lyzer, as described above, and the machine turns out the curve
corresponding to the distribution of the light in the line
examined.

In this way the radiations of many substances were
analyzed, and in almost every case it was found that the

LIGHT WAVES AND THEIR USES

line was not produced by homogeneous vibrations, but was
double, treble, or even more complex. The distances
between the components of these compound lines are so
small that it is practically impossible, except in a few cases,
to observe them in the ordinary spectroscope.

The following diagrams (Figs. 62-8) present a number
of these visibility curves. Thus Fig. 02 represents that
obtained from the red radiation of hydrogen. The curve
to the right represents the visibility curve, while on the
left the corresponding distribution of the light is drawn.
Beginning at a difference of path zero, the visibility was

FIG. 62

100, and at one millimeter it was somewhat less, and so on,
until at about seventeen millimeters we find a minimum.
As the difference in path increases, we find that there is a
maximum at twenty-three millimeters. After that the curve
slopes down, and at about thirty-five millimeters it disappears
entirely. Since the curve is periodic, we may be pretty sure
that this red line of hydrogen is a double line. This fact, I
believe, has never yet been observed, though the distance
between the two components is not beyond the range of a
good spectroscope, being about one-fortieth or one-fiftieth
of the distance between sodium lines.1

Fig. 63 represents the curve which was obtained from
sodium vapor in a vacuum tube. When we burn sodium at
atmospheric pressure — as, for example, when we place sodium

1 This prediction has since been amply confirmed by direct observation.

INTERFERENCE METHODS IN SPECTROSCOPY 79

glass in a Bunsen flame — the visibility curve due to its radi-
ations diminishes so rapidly that it reaches zero when the
difference of path is about forty millimeters ; it is practically

FIG. 63

impossible to go farther than this. It is seen that the curve
is periodic, which would indicate that each one of the
sodium lines is a double line. The intensity curve at the
left represents one of the sodium lines only. The other, on
the same scale, would be distant about half a meter. We
can from this get some idea of the relative sensitiveness of
this process of light-wave analysis, as compared with that of
ordinary spectrum analysis. It will be observed that the
intensity curve shows still another small component which
corresponds to still another longer period, but the existence
of these short companion lines is not absolutely certain.

FIG. 64

Fig. 64 represents the curve of thallium. The oscilla-
tion shows that it is a double line, and not very close. The
distance between the components is about one-sixtieth of the
distance between the sodium lines. We have also a longer
oscillation which shows that each one of the components is

80 LIGHT WAVES AND THEIR USES

double. The distance between these small components and
the larger ones is something like one-thousandth of the dis-
tance between sodium lines, corresponding to a separation
of lines far beyond the possible limit of the most powerful
spectroscope.

The curve of the green radiation of mercury is shown in
Fig. 65. This curve is really so complicated that the char-
acter of the source is still a little in doubt. The machine has
not quite enough elements to resolve it satisfactorily, having
but eighty when it ought to have eight hundred. The curve

FIG. 65

looks almost as though it were the exceptional result of this
particular series of measurements, and we might imagine that
another series of measurements would give quite a different
curve. But I have actually made over one hundred such
measurements, and each time obtained practically the same
results, even to the minutest details of secondary waves.
The nearest interpretation I can make as to the character
of the spectral source is given at the left of this diagram.
It will be noticed that the width of the whole structure
is, roughly speaking, one-sixtieth of the distance between
the sodium lines. The distance between the close compo-
nents of the brighter line is of the order of one-thousandth
of the distance between the sodium lines. The fringes
in this case remain visible up to a difference of path of
400 millimeters, and they have actually been observed
up to 480 millimeters, or nearly one-half meter's differ-
ence in path — corresponding to something like 780,000 .
waves.

INTEKFERENCE METHODS IN SPECTROSCOPY 81

In the curve of Fig. 66 we have quite a contrast to the
preceding. Here we have a radiation almost ideally homo-
geneous. Instead of having numerous maxima and minima
like the curves we have been considering, this visibility curve
diminishes very gradually according to a very simple mathe-
matical law, which tells us that the source of light is a
single line of extremely small breadth, the breadth being of
the order of one eight-hundredth to one-thousandth of the

FIG. 66

distance between the sodium lines. It is impossible to
indicate exactly the width of the line, because the distribu-
tion of intensity throughout it is not uniform. The impor-
tant point to which I wish to call attention, however, is that
this curve is of such a simple character that for a difference
of path of over 200 millimeters, or 400,000 light waves,
we can obtain interference fringes. This indicates that the
waves from this source are almost perfectly homogeneous.
It is therefore possible to use these light waves as a stand-
ard of length, as will be shown in a subsequent lecture.
The curve corresponds to the red radiation from cadmium
vapor in a vacuum tube. In using this red cadmium wave
as a standard of length it is very important to have other
radiations by which we can check our observations. The
cadmium has two other lines, which serve as a control or
check to the result obtained by the first.

Fig. 67 represents the green radiation of cadmium.
This curve is not quite so simple as that of the red, but

LIGHT WAVES AND THEIR USES

extends almost to 200 millimeters. The corresponding line
is shown to be a close double.

The curve corresponding to the violet light of cadmium
is shown in Fig. 68, and is seen to be comparatively simple.

FIG.

We have thus shown that spectral lines are complex dis-
tributions of light, whose resolution in general is beyond the
power of the spectroscope. This complexity of the spectral
lines is particularly interesting because it indicates a corre-
sponding complexity of the molecules which cause the vibra-
tions which give rise to the corresponding spectral lines.

FIG. G8

This complexity may be likened to the complexity of a solar
system ; and while this may bring dismay to the Keplers and
Newtons who may hope to unravel the mysteries of this pigmy
world, it certainly increases the interest in the problem.

INTERFERENCE METHODS IN SPECTROSCOPY 83

SUMMARY

1. The spectrum of the light emitted by incandescent
gases is not continuous, but is made up of a number of
bright lines whose position in the spectrum is very definite,
and which are characteristic of the elements which produce
them.

2. These "lines" are not such in a mathematical sense,
but have an appreciable width and a varying distribution of
light, and in some cases are highly complex.

3. This variation in distribution is, however, restricted to
such narrow limits that in most cases it is impossible to
investigate it by the best spectroscopes ; but by the method
of visibility curves the lines may be resolved into their
elements.

4. An important auxiliary for the interpretation of the
visibility curves is the harmonic analyzer — an instrument
which sums up any number of simple harmonic motions, and
which also analyzes any complex motion into its simple
harmonic elements.

LECTURE V
LIGHT WAVES AS STANDARDS OF LENGTH

IN the last lecture it was shown that in many cases the
interference fringes could be observed with a very large dif-
ference in path — a difference amounting to over 500,000
waves. It may be inferred from this that the wave length,
during the transmission of 500,000 or more waves, has
remained constant to this degree of accuracy; that is,
the waves must be alike to within one part in 500,000. The
idea at once suggests itself to use this invariable wave
length as a standard of length. The proposition to make
use of a light wave for this purpose is, I believe, due to Dr.
Gould, who mentioned it some twenty-five years ago. The
method proposed by him was to measure the angle of dif-
fraction for some particular radiation — sodium light, for
example — with a diffraction grating. If we suppose Fig. 69
to represent, on an enormously magnified scale, the trace
of such a grating, then the light for a particular wave
length — say one of the sodium lines — which passes through
one of the openings in a certain direction, as AB, is re-
tarded, over that which passes through the next adjacent
opening, by a constant difference of path ; and therefore
in the direction AB all the waves, even those which pass
through the last of a very large number of such apertures,
are in exactly the same phase. There will be then, if we
are observing in a spectrum of the first order, as many waves
in this distance AB as there are apertures in the distance
AC. A diffraction grating is made by ruling upon a glass or
a metal surface a great number of very fine lines by a ruling
diamond, the number being recorded by the ruling-machine

LIGHT WAVES AS STANDARDS OF LENGTH 85

itself, so that there can be no error in determining the number
of rulings. This number is usually very large, between 50,000
and 100,000. Since this number of lines is accurately known,
we know also the number of spaces in the whole distance AC.
This distance can be measured by comparing the two end
rulings with an intermediate

standard of length, which \ — \ — \ — \ — \ — \ — \— ^

has been compared with the
standard yard or the stand-
ard meter with as high a
degree of accuracy as is pos-
sible in mechanical measure-
ments. If, now, we know

also the angle ACS, we can calculate the distance AB; and
since we know the number of waves in this distance, which
is the same as the number of apertures, we have the means
of measuring the length of one wave. It will be observed,
in making such an absolute determination of wave length by
this means, that we have to depend entirely upon the accu-
racy of the distance between the lines on the grating — a
distance which is measured by a screw advancing through a
small proportion of its circumference for each line ruled. If
the intervals between the lines are not exactly equal, then
there will be an error introduced, notwithstanding every pre-
caution taken, which it is extremely difficult, if not impossible,
to correct.

Another error may be introduced in making the com-
parison of the two extreme lines on the grating with the
standard decimeter. This error may, roughly, be said to
amount to something like one-half a micron, i. e., one-half
of one-thousandth of a millimeter. If, then, the entire
length of the ruling is fifty millimeters, and the error, say,
one ten-thousandth of a millimeter, the wave length may be
measured to within one part in 500,000. This is the error

86 LIGHT WAVES AND THEIR USES

upon the supposition that our standard is absolutely cor-
rect. But the length of the standard decimeter itself has
to be determined by means of microscopic measurements, and
since the temperature plays a considerable role, it is difficult
to avoid errors very much larger than those due to the
microscope. If we combine all these errors, we can probably
attain at best an accuracy in all measurements involved of the
order of one part in 100,000. Finally, we have to measure
the angle ACB, and it is very much more difficult to
measure angles than lengths. All these errors — the measure-
ment of the angle, the error in the determination of the
distance -4C, that in the comparison of the intermediate
standard which we use, and that in the distribution of these
spaces — may combine in such a way that the total error may
amount to very much more than one part in 100,000; it
may be one in 20,000 or 30,000. This degree of accuracy,
however, is greater than that attained by either of the other
two methods which have been proposed for establishing an
absolute standard of length.

The first of these proposed standards was the length of
the pendulum which vibrates seconds at Paris. Such a
pendulum may be obtained by suspending from a knife
edge a steel rod upon which a large lens-shaped brass bob
is fastened. The steel rod carries another knife edge near
the other end, so that the pendulum can be turned over so
as to be suspended from this lower knife edge. The pen-
dulum must then be adjusted so that its time of vibration is
exactly the same in either position, which can be done with
but little difficulty. When such a pendulum vibrates seconds
in either position, the distance between the knife edges is
the length of a simple seconds pendulum.

We may also construct a simple pendulum by fastening a
sphere of metal to the end of a thin, fine wire. It is then
necessary to measure the time of oscillation, and the distance

LIGHT WAVES AS STANDARDS OF LENGTH 87

between the point of suspension and the center of gravity
of the spherical bob. This distance can be measured to a
very fair degree of accuracy. Unfortunately the different
observations vary among themselves by quantities even
greater than the errors of the diffraction method.

The second of these proposed standards was the circum-
ference of the earth measured along a meridian, as it was
believed that this distance is probably invariable. There
are, however, certain variations in the circumference of the
earth, for we know that the earth must be gradually cool-
ing and contracting. The change thus produced is prob-
ably exceedingly small, so that the errors in measuring this
circumference would not be due so much to this cause as to
others inherent to the method of measuring the distance
itself. For suppose we determine the latitude of two places,
one 45° north of the equator and one 45° south. The dif-
ference in latitude of these places can be determined
with astronomical precision. The distance between the
places is one-fourth of the entire circumference of the
earth. This distance must be measured by a system of tri-
angulation — a process which is enormously expensive and
requires considerable time and labor ; and it is found that
the results of these measurements vary among themselves
by a quantity even greater than do those reached with the
pendulum. So that none of these three methods is capable
of furnishing an absolute standard of length.

While it was intended that one meter should be the one
forty-millionth of the earth's circumference, in consequence
of these variations it was decided that the standard meter
should be defined as the arbitrary distance between two
lines ruled on a metal bar a little over a meter long, made
of an alloy of platinum and irridium. It was made of
these two substances principally on account of hardness and
durability. In order to bring the metal as nearly as possible

88 LIGHT WAVES AND THEIR USES

to what was termed its " permanent condition," these bars
were subjected to all sorts of treatment and maltreatment.
The originals were cast and recast a great many times, and
afterward they were cooled — a process which took several
months.

After such treatment it is believed that the alteration in
length of these bars will be exceedingly small, if anything
at all. But, as a matter of fact, it is practically impos-
sible to determine such small alterations, because, while
there have been a number of copies made from this funda-
mental standard, these copies are all made of the same metal
as the original; hence, if there were any change in the
original, there would probably be similar changes in all the
copies simultaneously, and it would therefore be impossible
to detect the change. The extreme variation, however, must
be of the order of one-thousandth of a millimeter or less
in the whole distance of 1,000 millimeters.

The question rightly arises then: Why require any other
standard, since this is known to be so accurate? The
answer is that the requirements of scientific measurement
are growing more and more rigorous every year. A
hundred years ago a measurement made to within one-
thousandth of an inch was considered rather phenomenal.
Now it is one of the modern requirements in the most
accurate machine work. At present a few measurements
are relied upon to within one ten-thousandth of an inch.
There are cases in which an accuracy of one-millionth of
an inch has been attained, and it is even possible to
detect differences of one five-millionth of an inch. Past
experience indicates that we are merely anticipating the
requirements of the not too distant future in producing
means for the determination of such small quantities.
Again, in order that the results of scientific work already
completed, or shortly to be completed, may be compared

LIGHT WAVES AS STANDARDS OF LENGTH 89

and checked with those of subsequent researches, it is essen-
tial that the units and standards employed should have the
same meaning then as now, and, therefore, that such stand-
ards should be capable of being reproduced with the
highest attainable order of accuracy. We may, perhaps, say
that the limit of such attainable accuracy is the accuracy
with which two of the standards can be compared, and
this is, roughly speaking, about one-half of a micron —
some say as small as three-tenths of a micron. For such
work neither of the three methods described above of pro-
ducing a standard is sufficiently accurate. As before stated,
the results obtained by them vary among themselves by
quantities of the order of one part in 50,000 to one part in
20,000. Since the whole meter is 1,000,000 microns, an
order of accuracy of one-half of a micron, which can be
obtained with a microscope, would mean one part in 2,000,-
000, which is far beyond the possibilities of any of the three
methods proposed.

We now turn to the interference method. Some pre-
liminary experiments showed that there were possibilities in
this method. The fact to which we have just drawn atten-
tion— namely, that the wave lengths are the same to at least
one part in 500,000 — looks particularly promising and leads
us to believe that, if we had the proper means of using the
waves and of multiplying them up to moderately long dis-
tances, without multiplying the errors, they could be used
as a standard of length which would meet the requirement.
This requirement is that a sufficient number of waves shall
produce a length which may be reproduced with such a
degree of accuracy that the difference between the new
standard and the one now serving as the standard cannot
be detected by the microscope.

The process is, in principle, an ideally simple one, and

90 LIGHT WAVES AND THEIR USES

consists in counting the number of waves in a given distance.
However, in counting such an enormous number, of the
order of several hundred thousands, one is liable to make a
blunder — not an error in a scientific sense, but a blunder.
Of course, ultimately, this would be detected by the process
of repetition.

The investigation, in a concrete form, presents a number
of interesting points, involving problems of construction of
a unique character which had to be solved before the process
could be said to be perfectly successful.

The construction and operation of the apparatus will be
much more readily understood if we first dwell a little upon
the conditions that are to be fulfilled. Suppose, for illustra-
tion, that it is required to find the distance between two-
mile posts on a railroad track. The most convenient method
for measuring such a distance would be by a hundred-
foot steel tape stretched by a known stretching force and
applied to the steel rails. The rails are mentioned simply
in order that there should not be any sag of the tape which
would introduce still another error. The zero mark of the
tape being placed against a mark on the rail which serves
as the starting-point, a second mark is made on the rail
opposite the hundred-foot mark of the tape. The tape
is then placed in position a second time with one end on
the second mark, and a third mark is placed at the farther
end ; and so on indefinitely. This is the first process. By
it we have divided the mile into the nearest whole number
of hundred-foot spaces. Then we measure the fractions.

The second operation consists in verifying the length of
the steel tape, which we must do by comparing it with a
standard yard or foot by the same stepping-off process.

The process of measuring the meter in light waves is
essentially the same as that described above, the meter
answering to the distance of a mile of track, and the

LIGHT WAVES AS STANDARDS OF LENGTH 91

hundred-foot tape corresponding to a considerably smaller
distance. This smaller distance is what I have termed an
"intermediate standard." There is in this latter case the
additional operation of finding the number of light waves in
the intermediate standard ; so that, in reality, there are three
distinct processes to be considered.

In the first operation it is evident that, if an error is com-
mitted whenever we lift the tape and place it down again,
the smaller the number of times we lift it and place it down,
the smaller the total error produced ; hence, one of the essen-
tial conditions of our apparatus would be to make this small
standard as long as possible. The length of the intermediate
standard is, however, limited by the distance at which we can
observe interference fringes. The limit, as was stated in the
last lecture, is reached when this distance is of the order of
several hundred thousand waves. At this distance the inter-
ference fringes are rather faint, and it seemed better for
such determinations not to make use of the extreme distance,
but of such a smaller distance as would insure distinct inter-
ference fringes. It was found convenient to use, as the max-
imum length of the intermediate standard, one decimeter.
The number of light waves in the difference of path (which
is twice the actual distance, because the light is reflected
back) would be something of the order of three or four
hundred thousand waves. With such a difference of path we
can still see interference fringes comparatively clearly, if we
choose the radiating substance properly.

The investigations described in the last lecture showed
that the radiations emitted by quite a number of the sub-
stances which were examined were more or less highly com-
plex. One remarkable exception, however, was found in
the red radiation of cadmium vapor. This particular radia-
tion proved to be almost ideally homogeneous, i. e., to con-

92 LIGHT WAVES AND THEIR USES

sist very nearly of a series of simple harmonic vibrations.
This radiation was therefore eminently suited to the purpose,
and was adopted as the standard wave length.

Most substances produce a more or less complicated spec-
trum involving quite a number of lines, but in the case of
cadmium vapor, though there are three different radiations,
these three are all so nearly homogeneous that each one can
be used; and the complexity of the spectrum is in this case
an advantage, as will be shown below. To produce the cad-
mium radiation, metallic cadmium is placed in a glass tube
which contains two aluminum electrodes. The tube is then
connected by glass tubing with an air pump and exhausted
of air. The tube is also. heated so as to drive off all residual
gas and vapor, and when the required degree of exhaustion
is reached, it is hermetically sealed and in condition to use.
The cadmium is not very volatile, and at ordinary tempera-
tures we should see scarcely anything of the cadmium light
when the electric discharge passes. The tube is therefore
placed in a metal box, as shown in Fig. 60, which is furnished
with a window of mica and has a thermometer introduced into
one side. If the box be heated by a Bunsen burner to a
temperature in the neighborhood of 300° C., the cadmium
vapor fills the tube, and can then be rendered luminous by
the passage of the electric spark.

Now, it is found most convenient not to make this first
intermediate standard in the form of a bar like the standard
meter, with two lines drawn upon it ; for then we should intro-
duce errors of the microscope at every reading, and these
errors would be added together. Thus, since this is one-
tenth of the whole meter, we might have, in adding up, ten
times the error of the microscope, which we said was of the
order of one-half a micron ; we could thus have, in the end,
an error of five microns. The interference method gives us
the means of multiplying the length of the intermediate

LIGHT WAVES AS STANDARDS OF LENGTH

FIG. 70

standard with the slightest possible error, amounting, per-
haps, to one-twentieth of a micron ; in some cases a little less.
If two plane surfaces be parallel to one another and a given
distance apart, then, with the interferometer, we may locate
the position of either one of these surfaces by means of
the interference
fringes in white
light to within
one-twentieth of
a fringe, which
means one-for-
tieth of a wave,
or one-eightieth
of a micron. It
has been found
most convenient

to use glass surfaces very carefully polished and made as
nearly plane as possible, and silvered on the front. The
two surfaces are mounted on a brass casting, and care-
fully adjusted so as to be as nearly parallel as possible,
so that it does not matter what part of the surface is used.
This parallelism of the two surfaces must be arranged
with extraordinary accuracy; the greatest deviation from
true parallelism must be of the order of one-half of a
fringe, which would be one-fourth of a wave length, or
one -eighth of a micron. Since the width of the surface
is something like two centimeters, the allowable angle
between the two surfaces is something like one part in
two hundred thousand.

A section of the intermediate standard we have been de-
scribing is represented in Fig. 70. The two glass surfaces
are about two centimeters square and silvered on their front
surfaces, which are very nearly true planes. Their rear
surfaces press against three small pins. These are adjusted

LIGHT WAVES AND THEIR USES

for parallelism by riling until the requisite degree of accuracy
is obtained. The parallelism cannot be made altogether
perfect, and, as a matter of fact, in some cases the error may
amount to as much as one-tenth of a micron or more.

Fig. 71 represents a perspective view of the same thing.

In this figure
the intermedi-
ate standard
rests on a car-
riage by means
of which it may
be moved as
necessary for
the purpose of
comparing it

FIG. 71

with the whole
meter. In mak-
ing this comparison the surfaces must be parallel to the mirror
which serves as a reference plane in the interferometer. The
parallelism in this case must be of the same order of accu-
racy as that between the surfaces themselves. The adjust-
ment is made by the screws at the rear, one of which turns
the whole standard about a vertical axis and the other about
a horizontal one.

In determining the number of waves in the meter, the
first operation is to find the number of whole waves in this
intermediate standard. It can readily be conceived that the
counting of something like 300,000 waves would be no small
matter; in fact, a little calculation would show that, if we
counted two per second, it would take over forty hours
to make the count. Probably a number of methods will
suggest themselves of making such a process of counting
automatic. Indeed, several experiments have been made,
and with some promise of success ; but the possibility

LIGHT WAVES AS STANDARDS OF LENGTH 95

of skipping over one fringe, through some accident, is
serious. It was therefore thought desirable to use another
process, very much longer and more tedious, but very much
surer. This process consists in dividing the distances to be
measured into a very much smaller number of parts, so that
the distances to be measured in waves would be very much
smaller. Thus a distance of ten centimeters contains 300.-
000 waves; half of this distance would contain 150,000. If
we go on dividing in this way, until we get to the last one
of nine such steps, we reach an intermediate standard whose
length is something of the order of one-half millimeter.
The total number of waves in this standard is about 1,200,
and this number it is a comparatively simple matter to count.
The method of proceeding in counting these fringes
is the same as that described above. The reference plane,
as we will call the movable mirror in the interferometer,
is moved gradually from coincidence with the first sur-
face to coincidence with the second, and the fringes which
pass are counted. Such a count was made for the three
standard radiations, namely, the red, green, and blue of
cadmium vapor. The result was 1,212.37 for red, 1,534.79
for green, and 1,626.18 for blue. Now, an important point
is that we can measure these fractions with an extraordi-
nary degree of accuracy; so the second decimal place is
probably correct to within two or three units. The whole
number we know to be correct by repeating the count and,
getting the same result. Having thus obtained this number,
including also the fractions of waves on the shorter standard
to a very close approximation, we compare it with the
second, which is, approximately, twice as long. This com-
parison gives us, without further counting, the whole number
of waves in the second standard by multiplying the number
in the first by two. We have the same possibility of meas-
uring fractions on the second standard, and so can determine

9(5

LIGHT WAVES AND THEIR USES

the number of waves in its length with an equal degree of

accuracy.

I will give the description of this process somewhat more

in detail. In Fig. 72 mm' represents the first or the shorter

standard viewed
from above. This
standard rests on a
carriage which can
be moved with a
screw. The second
standard nri is twice
as long as the first,
and is placed as close
as possible to the
first and rigidly con-
nected with some

FIG. 72

part of the frame.
The mirror d is the
reference plane.1
The two front mirrors of the two standards are adjusted to
give fringes in white light with the reference plane. The
central fringe in the white-light system is black; the others
are colored. Hence we can always distinguish the central
fringe. When the central fringes occur in the same rela-
tive position upon the two front mirrors m and ?i, then
these two surfaces are exactly in the same plane. Now, if we
move the reference plane backward through the length of the
shorter standard, its surface will coincide with the mirror m',
and at this instant fringes in white light will appear. Thus
we have the means of knowing when the reference plane
has been moved the length of the first standard to an order
of accuracy of one- tenth or one -twentieth of a fringe.

1 Better, the image of d in a and />, which in the figure would coincide with the
front surfaces of m and n.

LIGHT WAVES AS STANDARDS OF LENGTH 97

The next process is to move the first standard backward
through the same distance. Then the white-light fringes
will again appear on the front mirror m. Finally we move
the reference plane again through the same distance and, if
the second standard is twice as long as the first, we get inter-
ference fringes on the two rear mirrors of the two interme-
diate standards. If there is any difference, then the central
fringe of the white-light system will not be in the same
position on both mirrors, and we shall know that one is twice
as long as the other less, say, two fringes, which would mean
less one-half micron. In this way we can tell whether one is
exactly twice as long as the other or not; and if not, we can
determine the difference to within a very small fraction of a
wave.

When we multiply the number of waves in the first
standard by two, any error in the fractional excess is, of
course, also multiplied by two. So the fraction of a
wave which must be added to the second number is uncer-
tain. If we observe the fringes produced by one radiation,
for example the red, we get a system of circular fringes upon
both mirrors of the standard ; and if these two systems have
the same appearance on the upper mirror as on the lower,
then we know this fraction is zero ; and the number of waves
in the second standard is then the nearest whole number
to the number determined. If this is not the case, we can
by a simple process tell what the fraction is, and can obtain
this fractional excess to any required degree of accuracy.
As an example, we may multiply the numbers obtained for
the first standard by two, and we find 2,424.74 for the
number of red waves in standard No. 2. The correct value
of this fraction for red light was found to be .93 instead of
.74. Thus the same degree of accuracy which was obtained
in measuring the first standard can be obtained in all the
standards up to the last. We have thus the means of find-

LIGHT WAVES AND THEIR USES

ing accurately the whole number of waves in the last
standard. The whole number obtained by this process of
"stepping off" for the red radiation of cadmium was found
to be 310,678. The fraction was then determined by the
circular fringes, as described above, and found to be .48.
In the same way the number for the green radiation was
determined as 393,307.93; and for the blue radiation as
416,735.86. To give an idea of the order of accuracy,
I would state that there were three separate determina-
tions made at different times and by different individuals,
as follows:

Determination

Red

Green

Blue

I ..

310,678.48

393,307.92

416,735.86

310 678 65

393 308 10

416 736 07

III .

310 678 68

39330809

416 736 02

The fact that these determinations were made at entirely
different times, separated by an interval of whole months,
and by different individuals, and that we still were able to
get, not only the same whole number of waves, but also so
nearly the same fractions, gives us a confidence, which
we could not otherwise feel, in the possibilities of the
process.

In comparing the standards with one another the tem-
perature made no difference, if only it were uniform through-
out the instrument, because two intermediate standards side
by side, made of the same substance, would expand in ex-
actly the same way, provided we could be sure that both had
the same temperature. But in the determination of the num-
ber of waves in standard No. 9 it is extremely important
to know the temperature with the very highest degree of
accuracy. For this purpose some of the best thermome-

f MWV

S AS ST3

^3/TY )

LIGHT WAVES AS S T A^ B A gtfs o F LENGTH 99

ters obtainable were placed in the instrument, and the
thermometers themselves were carefully tested, their errors
determined, and other well-known precautions taken. In
this way the temperature at which the intermediate standard
No. 9 contains the number of waves given above was deter-
mined to within one-hundredth of a degree.

The final step in the process is the comparison of the
decimeter standard with the standard meter. This is a com-
paratively simple affair. In fact, it is exactly the same as
the comparison of the first intermediate standard with the
second, except that the second standard is now ten times as
long — which necessitates going through the process ten
times instead of twice.

Since in this case also we use the fringes for determining
when one end of the standard and the reference plane are
in the same plane, the error, as before stated, may be as
small as one-twentieth of a wave ; so that all the errors added
together would be of the order of one-half of a wave, or
one quarter of a micron.

The conditions which had to be fulfilled by the instru-
ment which was used for this purpose are, then, these: We
have, in the first place, to provide for the displacement of
the intermediate standard and of the reference plane in such
a way that the parallelism of the mirrors is not disturbed.
This necessitates that the ways along which the carriage
supporting the mirrors moves be exceedingly true. It took
a whole month to perform this part of the work — to get the
ways so nearly true that there should be no change in the
position of the fringes as the mirrors were moved back and
forth. In the second place, we must be able to know the
position of the mirrors inside of the box which is placed
over the instrument to protect it from temperature changes.
To secure this, the carriage which holds the mirrors must be
moved by means of a long screw carefully calibrated to

100 LIGHT WAVES AND THEIR USES

within two microns or so. In the third place, since there
will be slight displacements, owing to the impossibility of
getting the ways absolutely true, it must be possible to cor-
rect these displacements. The adjustments for effecting this
are shown in Fig. 71. Fourth, we must have a firm sup-
port for the longer of the two standards to be compared,

FIG. 73

and a movable support, which moves parallel with itself, for
the shorter standard.

The last standard, the auxiliary meter, has to be com-
pared with the standard meter itself, and, therefore, the two
must be of similar construction. In other words, in this
last comparison we have to resort to the microscope again.
For the meter bar which we had in the interferometer itself
had two lines upon it as nearly as possible one meter apart,
as determined by a rough comparison with the prototype
meter. The standard No. 9 had to be compared with
this. For this purpose an arm which had a fine mark 011
it was rigidly fastened to the standard No. 9, and arranged to
come in the focus of the microscope. In making this com-
parison, we must admit, the order of accuracy is not so great.

LIGHT WAVES AS STANDARDS OF LENGTH 101

But there are only two of these to make, so that the possible
error is the same as that to which we are liable in comparing
two meter bars. This error is unavoidable.

The whole instrument had to be placed in a box, which
protected it from temperature changes and drafts of air, and
had to be placed on a firm pier so as to keep it as free from

FIG. 74

vibration as possible. Finally, the conditions which have been
mentioned above for producing a suitable source of light
had to be fulfilled. We have thus a fair idea of what condi-
tions had to be met in constructing the complete apparatus
for making this comparison.

We shall now show how these conditions were actually
fulfilled in the apparatus that was used for the experiment.

Fig. 73 gives a plan of the entire arrangement. It is
easy to recognize the vacuum tube which serves as a
source of light and the arrangement of the plates in the
interferometer. This arrangement is the same as that
shown in Fig. 72. In order to have but one radiation at a
time in the instrument, the light from the tube is passed

102

LIGHT WAVES AND THEIR USES

through an ordinary spectroscope. Thus the light from the
tube Z is brought to a focus on the slit /j. It is then made
parallel by means of the lens x^ and passes through the
prism TF, which is filled with bisulphide of carbon. The

lens «r3 forms the
spectral images
of the slit ti in
the plane of the
slit t2. The arm
Z IF of the spec-
troscope can be
moved so as to
bring either the
red, the green,
or the blue spec-
tral image upon
this slit, from
which it passes
into the instru-
ment.

Fig. 74 is a
view of the plan
of part of the in-
strument. The
arrangement of

surfaces shown diagramatically in Fig. 72 is readily recog-
nized. All of the plates, I may state, instead of being
rectangular, have a circular border, because in this form
they can be worked true more readily.

Fig. 75 represents a vertical cross-section of the same in-
strument. It will be noted that the reference plane is divided
into sections. This is done in order to enable us to determine
very accurately the position of the interference fringes. The
two intermediate standards will be recognized at the right.

FIG. 73

LIGHT WAVES AS STANDARDS OF LENGTH 103

Fig. 76 represents the actual instrument in perspective.
In this the two microscopes, with their arrangement for pro-
ducing an illumination on the meter bar by means of reflected
light, are shown. On the left are the handles which turn the
two screws. One of these moves the intermediate standard

FIG. 76

and the other moves the reference plane. The complete
instrument in the case which protects it against tempera-
ture changes is shown in Fig. 77.

This investigation was reported in the spring of 1892 to
Dr. Gould, who at that time represented the United States in
the International Committee of Weights and Measures. It
was principally through his goodness that I was asked to
carry out the actual experiments at the International Bureau
of Weights and Measures at Sevres. Many of the acces-
sories that were required for the instrument which has just
been described had to be made in this country, and were

104

LIGHT WAVES AND THEIR USES

taken Over and installed in one of the laboratories of the
Bureau.

The standard meter itself is kept in a vault underground
and under double lock and key, and is inspected only once
in ten years, and even then it is not handled any more than

FIG. 77

is absolutely necessary. It took the better part of an entire
year to accomplish the work as it has been described. The
final result of the investigation was that the number of
light waves in a standard meter was found to be, for the red
radiation of cadmium 1,553,163.5, for the green 1,966,249.7,
for the blue 2,083,372.1— all in air at 15° C. and at normal
atmospheric pressure.

It is also worth noting that the fractions of a wave are
important, because, while the absolute accuracy of this
measurement may be roughly stated as about one part in
two million, the relative accuracy is much greater, and is
probably about one part in twenty million.

LIGHT WAVES AS STANDARDS OF LENGTH 105

The question may be asked: What is the object of mak-
ing such determinations, when we know that the standard
itself would not change by any amount which would vitiate
any ordinary measurements ? The reply would be that,
while the care taken of the standards is pretty sure to secure
them from any serious accident, yet we have no means of
knowing that any of these standards are not going through
some slow process of change, on account of a gradual
rearrangement of the molecules. Now that we have com-
pared the meter with an invariable standard, we have the
means of detecting any slow change and of correcting the
standard which has been vitiated by such process. Thus it
is now possible to control, by reference to the standard light
waves, the standard of length. The standard light waves
are not alterable ; they depend on the properties of the atoms
and upon the universal ether ; and these are unalterable. It
may be suggested that the whole solar system is moving
through space, and that the properties of ether may differ
in different portions of space. I would say that such a
change, if it occurs, would not produce any material effect in
a period of less than twenty millions of years, and by that
time we shall probably have less interest in the problem.

SUMMARY

1. We find that three propositions for expressing our
standard of length in terms of some invariable length in
nature have been made, namely:

a) Measurement of the seconds pendulum.

6) Measurement of the earth's circumference.

c) Measurement of light waves.

The first two, as well as the first plan proposed for carry-
ing out the third, i. e., the method of the diffraction grating,
have been found deficient in accuracy.

2. The second or interference method of utilizing light

106 LIGHT WAVES AND THEIB USES

waves, while ideally simple in theory, necessitates in practice
an elaborate and complicated piece of apparatus for its
realization. But, notwithstanding the delicacy of the opera-
tion, it is capable of giving results of such extraordinary
accuracy that, were the fundamental standard lost or de-
stroyed, it could be replaced by this method with duplicates
which could not be distinguished from the originals.

LECTURE VI

ANALYSIS OF THE ACTION OP MAGNETISM ON LIGHT
WAVES BY THE INTERFEROMETER AND THE ECHELON

A LITTLE over a year ago the scientific world was startled
by the announcement that Professor Zeeman had discovered
a new effect of magnetism on light. The experiment that
he tried may be briefly described in the following way: If
we place a sodium flame in front of the slit of a spectroscope,
we get in the field of view a bright double line. If tho flame
is placed between the poles of a powerful electro-magnet, it is
found that the lines are very much broadened; at least this
was the way in which the announcement of the discovery was
first made. It may be mentioned that a somewhat similar
observation was made by M. Fievez a long time before. He
found that the sodium lines in the spectrum were modified by
the magnetic field, but not quite in the way that Zeeman
announced ; instead of the lines being broadened, he thought
that each separate sodium line was doubled or quadrupled. It
seems that, long before this, the experiment had actually been
tried by Faraday, who, guided by theoretical reasons, con-
jectured that there should be some effect produced by a
powerful magnetic field upon radiations.

The only reason why Faraday did not succeed in observ-
ing what Fievez and Zeeman observed afterward was that the
spectroscopic means at his disposal at the time were far from
being sufficiently powerful. The effect is very small at best.
The distance between the sodium lines being taken as a kind
of unit for reference, the separate sodium lines, as was shown
in a preceding lecture, have a width of about one-hundredth
of the distance between the two. The broadening, or

107

108 LIGHT WAVES AND THEIR USES

doubling, or other modification which is produced in the
spectrum by the magnetic field, is of the order of one-fortieth,
or perhaps one-thirtieth, of the distance between the sodium
lines. Hence, in order to see this effect at all, the highest
spectroscopic power at our disposal must be employed.
Subsequent investigation has shown, indeed, that still other
modifications ensue, which are very much smaller even than
this, and which cover a space of perhaps only one-hundredth
to one hundred-and-fiftieth of the distance between the so-
dium lines. They are, therefore, beyond reach of the most
powerful spectroscope.

It occurred to me at once to try this experiment by the
interference method, which is particularly adapted to the
examination of just such cases as this, in which the. effect to
be observed is beyond the range of the spectroscopic method.
The investigation was repeated in very much the same way
as described by Zeeman, namely: A little blow-pipe flame
was placed between the poles of a powerful electro-magnet;
a piece of glass was placed in the flame to color it with so-
dium light. The light, instead of passing into the spectro-
scope, was sent into an interferometer and analvzed by the
method described in Lecture IV. The visibility curves
which were thus obtained showed that, instead of a broad-
ening, as was first announced by Zeeman, each of the so-
dium lines appeared to be double. The visibility curves
which were observed are shown in Fig. 78, and in Fig. 79,
the curves which give the corresponding distribution of the
light in the source. In the former figure the vertical
distances of the different curves represent the clearness of
the fringes, and the horizontal distances the differences
in path. In curve A, as the difference in the paths
increases, the fringes become less and less distinct, until at
forty millimeters the fringes have almost entirely disap-
peared. This curve represents the visibility of the sodium

ACTION OF MAGNETISM ON LIGHT WAVES 109

flame without any magnetic field. The corresponding
intensity curve A (Fig. 79) shows that the center of the line
has the greatest in-
tensity and that the
intensity falls off rap-
idly on either side,
the width of the line
corresponding to
something like one-
hundredth of the dis-
tance between the two
sodium lines. When
the field was created
by simply closing the
current through the
magnet, the visibility
curve assumed the
form indicated in
curve B. The cor-
responding distribu-
tion of light is shown in the second of the intensity
curves, B (Fig. 79) and we see that the line shows simply a
broadening, with a possible indication of doubling. The

field was then increased
considerably ; curve C
(Fig. 78) represents the
visibility. The corre-
sponding intensity curve
shows clearly that the
line is double. The

FIG. 78

FIG. 79

other curves were ob-
tained by increasing
the field gradually, and it will be noted that the result
is an increasing separation of the line and, at the same

110 LIGHT WAVES AND THEIR USES

time, a considerable broadening out of the two separate
elements.

This same experiment was tried with other substances,
especially with cadmium, and it was found that almost iden-
tical results were obtained with cadmium light as with
sodium. It was therefore inferred that the observations an-
nounced by Zeeman were, at any rate, incomplete, and it
was thought that possibly the instruments at his command
were not sufficiently powerful to show the phenomena of the
doubling. Shortly after this experiment was published an-
other announcement was made by Zeeman. In this he states
that there is not simply a broadening of the lines, but a sepa-
ration of them into three components, and, what was very
much more interesting, that these three components are
polarized in directions at right angles with each other: the
middle line polarized in one plane and the two outer lines
in another.

To make the meaning of this clear, we shall have to make
a brief digression into the subject of the polarization of
light. It will be remembered that in one of the first
illustrations of wave motion light waves were compared
with the waves along a cord, and it was stated that
the vibrations which caused the phenomena of light are
known to be vibrations of this character rather than of the
character of sound waves. The sound waves consist of
vibrations in the direction of the propagation of the sound
itself. The motion of the particles in the light waves are
at right angles to their direction of propagation. These
transverse vibrations, as they are called, may be vertical or
horizontal, or they may be diagonal, or they may move in a
curved path, for instance in circles or ellipses.

In the case of ordinary light the vibrations are so mixed
up together in all possible planes that it is impossible to sepa-
rate any one particular vibration from the rest without

ACTION OF MAGNETISM ON LIGHT WAVES 111

special devices, and such devices are termed " polarizers."
They may be likened very roughly to a grating the aper-
tures of which determine the plane of vibration. Through
such a grating we can transmit vibrations along a cord only
in the plane of the apertures. A vibration at right angles
to this plane will not travel along the cord beyond the grat-
ing. The corresponding light phenomena may be illustrated
by attempting to pass a beam of light which has been polar-
ized through a medium which acts toward the light waves
as does the grating toward the waves on the cord. It
is found that crystals act as such media. Thus a plate
of tourmaline possesses this property. For, as is well
known, if two plates of tourmaline be placed so that their
optical axes are parallel with each other, almost as much
light will pass throiigh the two as through either one alone.
But if the axes are set at right angles to each other by turn-
ing one of them through 90°, the light is entirely cut off.
Turning again through 90°, the light again appears, etc.
In the case of the tourmaline the vibrations which have
passed through one plate are all in one plane.

There is another important case in which the light is said
to be polarized, namely, when the motion of the particles is
circular. We may have two such circular vibrations — one in
which the motion is in the direction of the hands of a watch,
called right-handed, and the other in which the motion is in
the direction opposite to that of the hands of a watch, and
which is therefore called left-handed. We may consider that
each one of these vibrations is compounded of two plane
vibrations of equal intensity, in one of which the motion is
horizontal and in the other vertical, and which differ from one
another in phase, this difference being one-fourth of a period
for the left-handed and three-fourths of a period for the right-
handed. If we add together two such circular vibrations
of equal intensity, their horizontal components would exactly

112

LIGHT WAVES AND THEIR USES

FIG. 80

neutralize- each other, so that there would be no horizontal
motion at all. The vertical components, however, being in
the same direction, will add to each other,
so that the resultant of two beams of light
polarized circularly in opposite directions
and of equal intensity is a plane polarized
ray.

To return, now, to Zeeman's phenome-
non. Fig. 80 represents one of the sodium
lines when examined in a direction at right
angles to the magnetic field. The upper
line represents the appearance when the
light is polarized so that only horizontal
vibrations reach the spectroscope.- If,
however, the polarizer is rotated through 90°, so that only
vertical vibrations pass, the appearance is that of the lower
half of the diagram, the two side lines appearing and the
central line disappearing. Finally, if the light is examined
in the direction of the magnetic field, which can be accom-
plished by boring a hole through the pole of the magnet,
it is found that only two are visible — the two outside ones;
and one of these is composed of light which vibrates cir-
cularly in the direction of the hands of a watch, and the
other is circularly polarized in the opposite
direction.

An extremely beautiful and simple ex-
planation of this phenomenon has been
given by Lorentz, Larmor, Fitzgerald, and
a number of others. At the risk of intro-
ducing a few technicalities, I will venture
to repeat this explanation in a simple form.
For this purpose it is necessary to know that
the particles or atoms of matter are each supposed to be asso-
ciated with an electric charge, and that such a charged par-

FIG. 81

ACTION OF MAGNETISM ON LIGHT WAVES 113

ticle is termed an " electron." This hypothesis, made long
before Zeeman made his discovery, was found necessary to
account for the facts of electrolysis. For the decomposition
of an electrolyte by an electric current is most simply
explained upon the hypothesis that it contains positively
and negatively charged particles, and that the positively
charged atoms go toward the negative pole, and the nega-
tively charged toward the positive pole. They then give
up their electricity, and this giving up of electricity consti-
tutes an electric current. Hence this assumption, which is
useful in explaining the Zeeman effect, is nothing new. It
is known, also, that the vibrations of these particles, or of
their electric charges, produce the disturbance in the ether
which is propagated in the form of light waves \ and that
the period of any light wave corresponds to the period of
vibration of the electric charge which produces it.

The most general form of path of such a vibrating
electric charge would be an ellipse. Now, an elliptical vibra-
tion can always be resolved into a circular vibration and a
plane one, so that any polarized ray may be resolved into a
plane polarized ray and a circularly polarized ray. So all
we need to consider are plane and circularly polarized rays.
But we may suppose that a plane vibration is due to two
oscillations in a circle, one going in a direction opposite to
that of the hands of a watch, and the other in their direction.
Hence, we need consider only circular vibrations. Now,
if the electric charge is moving in a circle, it can be shown
that when the plane of the circle is at right angles to the
direction between the two poles of the magnet, the effect of the
field would be to accelerate the motion when the rotation is,
say, counter-clockwise, but to retard it when it is clockwise.

It was shown above that the position of a spectral line
in the spectrum depends on the period of the light which
produces it. Hence the position of the line will be altered

114 LIGHT WAVES AND THEIR USES

when any current is passing about the electro-magnet. When
the current is passing in a certain direction, the velocity of
rotation of the particles moving, say counter-clockwise, is
increased. Hence the period of vibration is smaller; i. e.,
the number of vibrations, or the frequency, is greater. In
this case there will be a shifting toward the blue end of
the spectrum by an amount corresponding to the amount of
the acceleration. Those particles which are rotating in an
opposite direction, /. e., clockwise, will be retarded, the
frequency will be less, and the spectral lines will be shifted
toward the red. These two shiftings would account, then,
for the double line. It is further clear that those vibrations
which occurred in planes parallel to the lines of force of the
magnetic field would be unaltered. These vibrations would
then produce the middle line, which is not shifted from its
position by the magnetic field.

Again, if we are viewing the light in a direction at right
angles to the lines of force of the field, the vibrations of
those particles which are affected by the field would have no
components parallel to the field. If the particles are re-
volving in a plane perpendicular to the field, then, when
viewed in this direction, they would appear to be moving
only up and down; i. e., they would send out plane polarized
light whose vibrations are vertical. These two vertical vibra-
tions form the two outer lines of the triplet, and it can be
shown that the light is plane polarized by passing it through
a polarizer. Those particles which are vibrating horizontally
do not have their period of vibration altered by the field.
Consequently we get a single line whose position in the
spectrum is not changed, and which is plane polarized in a
plane at right angles to that of the other two.

When this second announcement of Zeeman appeared,
it seemed worth while to repeat the experiments with the

ACTION OF MAGNETISM ON LIGHT WAVES 115

interferometer, especially as it was pointed out that proba-
bly the reason why a single or a double line appeared,
instead of a triple line, was because part of the light corre-
sponding to the middle line was cut off by the reflection
from the separating plate of the interferometer. The light
thus reflected is polarized, and most of the light which
should have formed the central image is thus cut off. It
was therefore determined to repeat these experiments under

FIG. 82

such conditions that we could be perfectly sure that light
which reached the interferometer vibrated in only one plane.
To accomplish this it is necessary merely to introduce a
polarizer into the path of the light.

Fig. 82 represents the arrangement of the experiment
with the interferometer. The source of light, instead of
being sodium in a Bunsen flame, is vapor in a vacuum tube,
illuminated by an electric discharge. The capillary part of
the tube is placed between the poles of the magnet.

The light is first passed through an ordinary spectro-
scope, so that there is formed at s a spectrum, any part of
which we may examine. The slit at s allows only one radia-
tion to pass into the interferometer. Thus, if we examine
cadmium light, we may allow the red to pass through, or the
green, or the blue. The light is made parallel by a lens and
then passes into the interferometer. The arrangement for

116

LIGHT WAVES AND THEIR USES

examining separately the vertical vibrations alone and the
horizontal vibrations alone is represented at N, and consists
merely of a Nicol prism which can be rotated about a hori-
zontal axis.

With this arrangement a different set of visibility curves

was obtained. These are
shown in Figs. 83, 84, 85.

The upper curve of Fig.
83 represents the visibility
curve produced by the hori-
zontal vibrations of the red
cadmium light in a strong
magnetic field. For the ver-
tical vibrations the visibility
curve is something totally
different, and is shown in the
lower half of the figure. The
effect of the field is readily
appreciated by comparing
this figure with Fig. 66, which corresponds to the red cad-
mium line without any magnetic field.

The upper curve of Fig. 84 represents the visibility curve
of the blue cadmium vapor when the horizontal vibrations
only are allowed to pass through. When vertical vibrations
only are allowed to pass through, the curve has the form
shown in the lower half of the figure.

The case of the green radiation, when there is no field,
is shown in Fig. 67 above. When the magnetic field is
on, and when the horizontal vibrations only are allowed to
pass through, the visibility curve has the form of the upper
curve in Fig. 85. When vertical vibrations are allowed to
pass through, it has the form of the lower curve.

The intensity curves corresponding to Figs. 83, 84, and
85 are shown in Fig. 86. The upper three correspond to

ACTION OP MAGNETISM ON LIGHT WAVES 117

the horizontal vibrations, while the lower three correspond
to the vertical vibrations. In the case of the red radiations
it will be noted that, whether there is a magnetic field or
not, there is no particular change for red cadmium light
when the horizontal vibrations alone are considered. When
the field is on, the vertical
vibrations give a double line,
or possibly one of more com-
plex form.

In the case of the blue
radiations, however, when
there is a magnetic field and
only horizontal vibrations
are allowed to pass through,
the line is double. The
doubling is very distinct,
and the separation is so wide
that it should be easily seen
by means of the spectroscope. When the vertical vibra-
tions alone are allowed to pass through, there is a very much
more complicated effect. In all cases we can see that the
line is double, as in the case of red cadmium light, but in
this case each component of the double lines is at least
quadruple, or even more complex.

In the case of the green radiation, when horizontal vibra-
tions only are considered, we have a triple line for the cen-
tral line of the Zeeman triplet. When horizontal vibrations
alone are allowed to pass through without a magnetic field,
it resembles in general character the red line (c/. Fig. 67).
When vertical vibrations are examined in the magnetic
field, the line is highly complex ; and in this case it is abso-
lutely certain that each of the components of the double
consists of at least three separate lines. The phenomenon
is perfectly symmetrical about the central line.

FIG. 81

118 LIGHT WAVES AND THEIB USES

It appears from these results that the Zeeman effect is a
much more complex phenomenon than was at first supposed,
and therefore the simple explanation that was given above
no longer applies. At any rate, it rriust be very seriously
modified in order to account for the much more highly com-
plex character of the phe-
nomena, as here described.
The complete theory has not
yet been worked out, and
meanwhile we must gather
whatever information we
can concerning the behavior
of as many different radia-
tions as possible. Every
attempt to deduce some gen-
eral law which will cover
all cases at present known
has thus far proved unsuc-
cessful. There are a number of anomalies which seem even
more difficult to account for than the doubling of this middle
line and the multiplication of the side lines. For example, in
one of the radiations examined, the line without any magnetic
field appeared as quadruple, but when the magnetic field was
on, it appeared as a single line.

There are quite a number of other interesting cases, which
we have not time to consider now. The explanation of these
anomalies will probably not be given until long after the
explanation of the doubling and tripling and multiplication
of separate lines.

The examination of spectral lines by means of the inter-
ferometer, while in some respects ideally perfect, is still
objectionable for several reasons. In particular, it requires
a very long time to make a set of observations, and we can

ACTION OF MAGNETISM ON LIGHT WAVES 119

examine only one line at a time. The method of observa-
tion requires us to stop at each turn of the screw, and note
the visibility of the fringes at each stopping-place. During
the comparatively long time which it takes to do this the
character of the radiations themselves may change. Besides,
we have the trouble of translating our visibility curves into
distribution curves. Hence it is rather easy for errors to
creep in.

On account of these limitations of the interferometer
method, attention was directed to something which should

Type I. Type II. Type HI.

FIG. 86

be more expeditious, and the most promising method of
attack seemed to be to try to improve the ordinary diffrac-
tion grating. The grating, as briefly explained in one of
the preceding lectures, consists of a series of bars very close
together, which permit light to pass through the intervals
between them. The first gratings ever made were of this
nature, for they consisted of a series of wires wound around
two screws, one above and one below. This first form
of grating answered very well for the preliminary work,
but is objectionable because the interval between the
wires is necessarily rather large, i. e., the grating is rather
coarse. If we allow light to pass through these intervals,
each interval may be considered to act as a source of light.

120

LIGHT WAVES AND THEIR USES

From eaeh of these sources it is spread out in circular waves.
If the incident wave is plane and falls normally upon the
grating, all these waves start from the separate openings in
the same phase of vibration. Hence, in a plane parallel to
the grating we should have, as the resultant of all these
waves, a plane wave traveling in the direction of the normal
to the grating. When this wave is concentrated in the focus
of a lens, it produces a single bright line, which is the image
of the slit and is just as though the grating were not present.

FIG. 87

Suppose we consider another direction, say AC (Fig. 87).
We have a spherical wave, starting from the point 5,
another in the same phase from the point a, etc. Now, if
the direction AC is such that the distance ab from the
opening a to the line through B perpendicular to A C is
just one wave, then along the line BC the light from the
openings B and a differ in phase by one whole wave. When
ab is equal to one wave, cd will be equal to two waves;
hence, along BC the light from the opening c will be one
wave behind the light from a^etc. ; and if these waves are
brought to a focus, they will produce a bright image of the
source. Since the wave lengths are different for different
colors, the direction AC in which this condition is fulfilled
will be different for different colors. A grating will there-

ACTION OF MAGNETISM ON LIGHT WAVES 121

fore sort out the colors from a source of light ind bend them
at different angles, forming a spectrum. Since the blue
waves are shorter than the red, the blue will be bent least
and the red most, the intervening colors coming in their
proper order between. Again, we may also have an image
formed when the direction AC is such that this difference
in phase of the light from successive openings, instead of one
wave, is two. The spectrum thus formed is said to be of
the second order. When this difference in phase is three
waves, the spectrum is said to be of the third order, etc.

Plate I, Fig. 2, represents the spectrum produced by a
coarse grating. The source of light was a narrow slit illumi-
nated by sunlight. The central image appears just as though
no grating were present, and on either side are diffuse spec-
tral images colored as on Plate I. Three such images,
which are the spectra of the first, second, and third orders,
may be counted on the right, and the same on the left. The
grating used in producing this picture had about six hun-
dred openings to the inch. Now, a finer grating produces a
much greater separation of the colors. The large concave
gratings used for the best grade of spectroscopic work pro-
duce spectra of the first order which are four feet long.
Those of higher order are correspondingly longer.

The efficiency of such gratings depends on the total dif-
ference of path in wave lengths between the first wave and
the last. Thus in the grating shown in Fig. 87 there will be,
in the case of the first spectrum, as many waves along AC as
there are openings between A and B. If we call the total
number of openings in the grating n, then there will be n
waves along AC. In the second spectrum, then, since each
one of the intervals corresponds to two waves, the total
difference in the path is twice as great, so that the number of
waves in AC will be 2n. For the third spectrum the num-
ber would be 3 n, and for the mth spectrum mn.

122 LIGHT WAVES AND THEIR USES

The efficiency of the grating depends on the order m
of the spectrum and the number n of lines in the grating,
/. e., on the product of the two. Hitherto the efforts of
makers of gratings have been directed toward increasing n
as much as possible by making the total number of lines in
the grating as great as possible. It has been found that as
many as 100,000 lines can be ruled side by side on a metallic
surface; but in ruling 100,000 lines it is extremely difficult

FIG. 88

to get them in their proper position. Very little attention
has as yet been directed toward producing a spectrum of a
very high order. The chief reason for this is that the inten-
sity of the light in the spectra of higher orders diminishes
very rapidly as the order increases. The first spectrum is by
far the brightest; the second has an intensity of something
like one -third of the first, and the succeeding spectra are
still fainter. There have been, occasionally, gratings in
which the diamond point happened to rule in such a way as
to throw an abnormal proportion of light in one spectrum.
Such are exceedingly rare and exceedingly valuable. It
seems to be a matter of chance whether the diamond rules
such gratings or not. It was with the double purpose of
multiplying the order of the spectrum, and at the same time
of throwing all the light in one spectrum, that the instrument
shown in Fig. 88 was devised.

ACTION OF MAGNETISM ON LIGHT WAVES 123

The method of reasoning which led to the invention of
this instrument may be of interest. We will suppose that,
in order to throw the light in one spectrum, the diamond
point could be made to rule a grating with a section like that
shown in Fig. 89, the distance between the steps being exactly
equal and the sur-
faces of the grooves
perfectly polished.
Suppose that the light
came in the direction
indicated nearly nor-
mal to the surface of
the groove. The light
would be reflected
back in the opposite
direction, and that
which came from each

r lli. o»

successive groove

would differ in phase from that from the adjacent grooves
by a number of waves corresponding to double the difference
in path. The retardation, instead of being one wave, would
be twice the number of waves in this distance. If the dis-
tance between the grooves were very large, the number of
waves in this distance would also be very large, so that the
order of the resulting spectrum would be correspondingly
high. Further, almost all the light returns in one direction,
so that the spectrum we are using will be as bright as possible.
We have thus shown, at least theoretically, the possi-
bility of producing a very high order of spectrum, and at the
same time of getting almost all the light in one spectrum.
However, the necessary condition is that the distances
between the grooves be equal within a very small fraction
of a light wave. This is a difficult, but not a hopeless,
problem. In fact, we may obtain the desired retardation

124 LIGHT WAVES AND THEIR USES

by piling up plates of glass of the same thickness. These
plates of glass can be made originally of a single piece, as
nearly uniform in thickness as possible. It has been possible
to obtain plates, plane parallel, so accurate that the thickness
was the same all over to within one-hundredth of a light
wave; that is, less than one five-millionth of an inch. If
we could place a number of such plates in contact with each
other, we should have the means of producing any desired
retardation of light reflected from one surface over the light
reflected from the next nearest surface, and should be able to
make this retardation exactly the same number of waves for
all the intervals. The difficulty lies in the fact that we can-
not place the plates in contact even by applying a pressure
large enough to distort the glasses, because of dust particles.
The thickness of such particles is of the order of a light
wave. It is therefore difficult to get the plates much closer
together than about three waves. If this distance were
constant, no harm would be done, but it varies in different
cases ; so the extreme accuracy of the thickness of the glass
is practically valueless.

Fortunately there is a way of getting around the diffi-
culty, and this way has, at the same time, other advantages.
Suppose that, instead of reflecting the light from such a pile
of glass plates, we allow it to go through. The light travels
more slowly in glass than in air — in the ratio of one and one-
half to one — and the retardations produced by the successive
plates in the light which has passed through are now exactly
the same. In this way it has been found possible to utilize as
many as twenty or thirty of such plates, and the retardation
produced by each plate would correspond to the difference in
the optical path between a layer of air and an equally thick
layer of glass. Some of these plates have been made as
thick as one inch. Roughly speaking, there are 50,000
waves in an inch of air; the number in an equal thickness of

ACTION OF MAGNETISM ON LIGHT WAVES 125

glass would be one and one-half times as great, so that the
difference in path would beJ25,000 waves. But the resolving
power is the order of spectrum multiplied by the number of
plates. If we are observing, therefore, in the 25,000th
spectrum, and there are thirty such plates, the resolving power
would be 750,000; whereas the resolving power of the best
gratings is about 100,000.

There are, however, disadvantages in the use of this in-
strument. One of these may be illustrated as follows: Sup-
pose we take the case of the ordinary grating; the first
spectral image is rather widely separated from the central
image of the slit, the second spectral image is twice as far
away as the first, and the third spectral image will start
three times as far away as the first, and will also be three
times as long. The result is that parts of the second and
third overlap. The overlapping becomes greater and greater
as the order of the spectrum increases, so that when the
25,000th spectrum is reached the spectra are inextricably
confused. Where we have to deal with a few simple radia-
tions, however, as in cadmium or sodium, this overlapping is
not so serious as might be supposed. We have a very
simple means of getting rid of the worst of it by analyzing
the light by means of a prism before it enters the pile of
plates.

The construction of the instrument is not very different
from that of the ordinary spectroscope. The light passes
through a slit and then through a lens, by which it is made
parallel. It then passes through the pile of plates — the
echelon, as it has been named — and into the observing tele-
scope. With this instrument the results obtained by the
method of visibility curves have been confirmed. Thus Fig.
81 shows the appearance of the green mercury line in the
field of view of the echelon when the source is in a strong
magnetic field. In the three central components the vibra-

126 LIGHT WAVES AND THEIR USES

tions are horizontal, while in the outer three on both sides
the vibrations are vertical. An idea of the power of this
instrument can be obtained by comparing Fig. 81 with Fig.
80, which gives the appearance of the line as seen in the best
grating spectroscope.

SUMMARY

1. The investigation of the changes produced in the radia-
tions of substances by placing them in the magnetic field is in
general a phenomenon barely within the range of the best
spectroscopes, and there are some features of it which it
would be entirely hopeless to attack by this method.

2. Such investigations, however, are precisely the kind
for which the interference method is particularly adapted.
In fact, the results of the investigation by the method of
visibility curves have furnished a number of new and interest-
ing developments which could only with difficulty have been
obtained by the ordinary spectrometer methods.

3. Fertile as this method has shown itself to be, there are,
nevertheless, a number of serious drawbacks. In order to
obviate these a new instrument was devised, the echelon
spectroscope, which has all the advantages of the grating spec-
troscope, together with a resolving power many times as great.
With the aid of this instrument all the preceding deductions
have been amply verified and a number of new and interest-
ing facts added to the store of our knowledge of the Zeeman
effect.

LECTUKE VII

APPLICATION OF INTERFERENCE METHODS TO
ASTRONOMY

OUR knowledge of the heavenly bodies is still very limited.
The little that we have learned has been acquired almost en-
tirely with the assistance of the telescope, or the telescope
compounded with the spectroscope. Without these, the stars
and the planets would always remain, even to the most
perfect unaided vision, as simple points of light. With
these aids we are every year adding very much to our knowl-
edge of their constitution, their form, their structure, and their
motions. For example, the spectroscope gives information
concerning the elements contained in the sun and the stars ;
for by means of the dark or bright lines in the spectrum we
are able to identify elements by the position of their spec-
tral lines, and from this identification we are able to infer,
with almost absolute certainty, the presence of the corre-
sponding material in the heavenly body which is examined.
The same is true of comets and nebulae. By the general
character of the spectrum we may also distinguish whether
these bodies are in the form of incandescent gases, or
whether they are in solid or liquid form; and we can, to a
certain extent, infer their temperature. We can even deter-
mine whether the body is approaching or receding. For
example, if the body is approaching, the waves are crowded
together so that their wave length will be shortened, and
hence they have a correspondingly altered position in the
spectrum, i. e., the line will be shifted toward the blue end
of the spectrum. If the body is receding, the spectral line
is shifted in position toward the red end of the spectrum.

127

128 LIGHT WAVES AND THEIR USES

By the telescope we have discovered that all the planets,
including many of the minor planets, have discs of appre-
ciable size. We have found markings on the planets, have
discovered the satellites of Jupiter and the rings of Saturn,
and have observed various interesting details concerning the
structure of these rings. The strange markings on the
planet Mars, which bear such a remarkable resemblance to
the works of intelligent beings, are among the most interest-
ing of the recent revelations of the telescope.

It is hard to realize that such observations concern
bodies that are distant millions of miles from us; in fact,
the distance is so great that it can be more readily ex-
pressed by the time light takes to reach us from these
bodies. In some cases this may be as much as several
years. We can compare this distance with the circumference
of the earth, by considering that light or a telegram will
go around the earth seven times in a second, while from
these bodies it would take several hours for light to reach us.
Yet these are our nearest neighbors, or, rather, members of
our immediate family. Our farther neighbors are so remote
that probably the light from many of them has not yet
reached us. To these more distant bodies our own little
family of planets is probably invisible; even the sun itself
is a second-rate star. If, however, Jupiter were sufficiently
bright, then the sun and Jupiter together would form what
is called a " double star," and to an inhabitant of a distant
planet which might be traveling about this distant star it
would appear as a double star with a separation of about one
second, which may be expressed as the angle subtended by
two luminous points about one-half inch apart when at a
distance of three miles. They would therefore be entirely
invisible to the naked eye as separate objects.

One of the most serious difficulties in the way of further
progress in the investigation of the telescopic characteristics

INTERFERENCE METHODS IN ASTRONOMY 129

of the planets and of the constitution of star systems, is what
is called bad " seeing." It must be remembered that light, in
order to reach a telescope, must pass through from forty to
one hundred miles of atmosphere. This atmosphere is not
homogeneous. If the atmosphere were homogeneous, there
would not be any very serious objection. The intensity of the
light from the object would be practically as great as if there
were no air present. But the air is unequally heated, and
therefore has unequal densities in different portions. Hence
the different portions of a beam of light which have passed
through different parts of the atmosphere and reached
different parts of the objective of the telescope would be
differently retarded, and these differences in retardation
would not be constant, but would vary, sometimes rapidly
and sometimes slowly, producing what is technically called
"boiling."

This unsteadiness of the image is the most serious diffi-
culty with which astronomers have to contend; there is no
instrumental remedy. The best that can be done is to
choose an appropriate site, and it seems to be the general
opinion of astronomers that such a site is best chosen on
some very high plateau or tableland. By some it is con-
sidered that a high mountain top is a desirable location, and
there is no question that such a site possesses very marked
advantages in consequence of the rarity of the air. If the
air were very rare,. k' boiling" would have less effect than
it has in dense air. But to compensate this advantage we
have the very bad effect of currents of heated air traveling
up the side of the mountain. As a matter of fact, however,
even in the worst locations, there are occasional nights when
the astronomer has almost perfect seeing — when even the
largest instruments attain almost their theoretical limit of
accuracy. This theoretical efficiency may be most con-
veniently tested by observations on double stars.

130

LIGHT WAVES AND THEIR USES

The resolving power, as shown in one of the preced-
ing lectures, depends on the size of the diffraction rings
which are produced about the image of a star. It was also
shown that the smallest angle which a telescope could
resolve was that subtended at the center of the lens by the

radius of the first dark ring,
and this angle is equal to the
ratio of the length of the light
wave to the diameter of the
objective. For example, if
we consider a 4-inch glass,
the length of the light wave
being ^^ of an inch, this
angle would be ^njVo~o- If
the lens were a 40-inch glass,
the angle would be something

FIG. 90

200 0000'

which can be

represented by the angle sub-
tended by a dime at the distance of fifteen miles. Hence, if
we had two such dimes placed side by side, the largest glass
would scarcely separate them.

Fig. 90 is an actual photograph of the image of a point
of light taken with an aperture smaller than that of a tele-
scope, but otherwise under the same conditions under which
a telescope is used. It is easy to see that, surrounding the
point of the image, there is a more or less defined white
disc, and beyond this a dark ring. Outside of this dark ring
there are a bright ring and another dark ring. Theoretically,
there are a great number of those rings; practically, we see
only one or two under the most favorable conditions.

This figure represents the appearance of the image of one
of Jupiter's satellites as it would be observed in one of the
largest telescopes under the most favorable conditions. If
it be required to measure the diameter of one of these very

INTERFERENCE METHODS IN ASTRONOMY 131

FIG. 91

distant objects, a pair of parallel wires is placed as nearly as
possible upon what is usually called the edge of the disc, as
shown in Fig. 91. The position
of this edge varies enormously
with the observer. One observer
will suppose it well within the
white portion; another, on the
edge of the black portion. Then,
too, the images vary with atmos-
pheric conditions. In the case
of an object relatively distinct
there may be an error of as much
as 5 to 10 per cent. In many
cases we are liable to an error
which may amount to 15 per

cent., while in some measurements there are errors of 20
to 30 per cent.

Suppose the object viewed were a double star. In
general, the appearance would be very much like that repre-
sented in Fig. 92, except that, as before stated, in the actual

case the appearance would be
troubled by " boiling." It will
be noted that as long as the
diffraction rings are well clear
of each other we need not have
the slightest hesitation in say-
ing that the object viewed is a
double star.

Fig. 93 represents under ex-
actly the same conditions two
points, artificial double stars,
but very much closer together.
In this case the diffraction rings overlap each other. It
will be seen that the central spot is elongated, and the expert

FIG. 92

132 LIGHT WAVES AND THEIB USES

astronpmer may decide that the star is double. This elon-
gation can under favorable circumstances be detected even a

considerable time after the
diffraction rings merge into
each other. If the atmospheric
conditions were a little worse,
such a close double would be
indistinguishable from the
single star, and if the stars
were a little closer together,
it would be practically impos-
sible to separate them.

Fig. 94 represents the case

FIG. 93 . .

of a triple star whose compo-
nents are so close together as to be barely within the limit of
resolution of the telescope. In this case the object would
probably be taken as triple because its central portion is trian-
gular. If the three stars were a little closer together, it
would be impossible to say whether the object viewed were a
single or a double star, or a triple
star, or a circular disc.

If now, in measuring the
distance between two double
stars, or the diameter of a disc
such as that presented by a
small satellite or one of the
minor planets, instead of at-
tempting to measure what is
usually called the "edge" of
the disc — which, as before
stated, is a very uncertain thing
and varies with the observer and

with atmospheric conditions — we try to find a relation be-
tween the size and shape of the object and the clearness of

INTERFERENCE METHODS IN ASTRONOMY 133

the interference fringes, we should have a means of making
an independent measurement of the size of objects which are
practically beyond the power of resolution of the most power-
ful telescope. The principal object of this lecture is to show
the feasibility of such methods of measurement. For this
purpose, however, the circular
fringes that we have been in-
vestigating are not very well
adapted; they are not very
sharply defined; there is not
enough contrast between them.
However, there is a relation
which can be traced oat be-
tween the clearness of the dif-
fraction fringes and the size
and shape of the object viewed.

rm • x- FIG- 95

This relation is very complex.

The result of such calculation is that the intensity is
greatest at the center, whence it rapidly falls off to zero at
the first dark band. It then increases to a second maxi-
mum, where it is not more than one-ninth as great as in
the center. What we should have to observe, then, is the
contrast between these two parts — one but one-ninth as
marked as the other and confused more or less by atmos-
pheric disturbances. In case of a rectangular aperture the
intensity curve is somewhat different, in that the maxima
on either side of the central band are considerably greater,
so that it is somewhat easier to see the fringes. ' In case
of the rectangular aperture the fringes are parallel to the
long sides of the rectangle. The appearance of the dif-
fraction phenomenon in this case is illustrated in Fig.
95. The pattern consists of a broad central space, whose
sides are parallel to the sides of the rectangular slit, arid
of a succession of fringes diminishing in intensity 011

134 LIGHT WAVES AND THEIR USES

either skle. The corresponding intensity curve is shown
in Fig. 96.'

If we had two such apertures instead of one, the ap-
pearance would be all the more
definite ; but the two apertures to-
gether produce, in addition, inter-
ference fringes very much finer
than the others, but very sharp
and clear. The intensity curve cor-
responding to these two slits is shown in Fig. 97. In this
case it is easy to distinguish the successive maxima, and the
atmospheric disturbances are very much less harmful than
in the case of the more indefinite phenomenon.

Fig. 98 represents the appearance of the diffraction pat-
tern due to two slits when a slit, instead of a point, is used
as the source of light. The appearance of the two patterns
is not essentially different, that due to the slit being very
much brighter. In the case of a point source there is so
little light that it is more difficult to see the fringes. Here
the same large fringes are visible as before, but over the
central bright space there is a number of very fine fringes.
The two central ones are particularly sharp, so that it is
easy to locate their position if necessary, but still easier to
determine their visibility. This clearness
is the essential point we have to consider,
because the size of the object determines
the clearness of the fringes. We find that
if we gradually increase the width of the
source, the fringes grow less and less dis-

n L • T£ FIG' 9T

tinct, and finally disappear entirely, it
we note the instant when the fringes disappear, we can calcu-
late from the dimensions of the apparatus the width of the

i This ignores the diffraction bands parallel to the shorter sides of the rect-
angle, which are usually inconspicuous.

Jl/Vv

INTERFERENCE METHODS IN ASTRONOMY 135

source. Or, if we alter the dimensions of the apparatus
and observe when the fringes cease to be visible in our
observing telescope, we have the means of measuring the
diameter of the source, which may be a double star, or the
disc of one of Jupiter's satellites, or one of the minor planets.

We may get some notion
of the relation which exists
between the clearness of the
fringes and the size of the ob-
ject when the fringes disap-
pear, by considering a simple
case like that of a double star.
Suppose we have two slits in
front of the object glass of a
telescope focused on a single
star. At the focus the rays
from the two slits come to-
gether in condition to produce

interference fringes, and the fringes always appear when the
source is a point. Suppose we have in the field of view
another star. It will produce its own series of fringes in the
focus of the telescope. We shall then have two similar sets
of fringes in the field of view. If, now, the two stars are
so near together that the central bright fringes of the
two systems coincide, then the two sets of fringes will
reinforce each other. If, however, one of the stars is just
so far away from the other that the angle between them
is equal to the angle between the central bright band and
its first adjacent minimum, then the maximum of one sys-
tem of fringes will fall upon the minimum of the other set,
and the two will efface each other so that the fringes dis-
appear. Hence the fringes disappear when the angle sub-
tended by the source is equal to the angle subtended by
half the breadth of the fringes, viewed from the objec-

FIG. 98

136 LIGHT WAVES AND THEIR USES

tive. This angle is easily calculated. Thus if I represent the
wave length and s is the distance between the two slits, then

the angle is equal to „ • - . Hence, if we know the length

of the light wave (we can take it as one fifty-thousandth of
an inch if we choose) , by measuring the distance between
our slits when the fringes disappear we have the means of
measuring the angular distance between double stars.
^ In the case of a single-slit source we can also get some
sort of an idea of the conditions which prevail when the
fringes disappear. For we may conceive the slit source to
be divided into a number of line sources, parallel and
adjacent to each other. Then each line source would form
its own set of fringes, and when the angle between the two
outside lines, i. e., the edges of the slit, is equal to the angle
subtended by the distance of the first dark band from the
center, the fringes again overlap in such a way as to dis-
appear. The value of this angle is easily found to be -. So,

supposing that we had such an object in the heavens as a nar-
row band of light, we have the means of finding its width. If,
instead of a slit, we used a circular opening as a source, there
is a little more difficulty in the mathematical analysis. In this

case the coefficient of - , instead of being 1 as in the second
s

case, or ^ as in the first case, is found to be 1.22. In observ-
ing such an object we measure the distance between our two
slits when the interference fringes have just vanished, and
compute the angular magnitude of the object by using this
coefficient. If we knew the distance to the object, we could
calculate also its actual diameter.

The curve representing the clearness of the fringes as the
slits approach is rather interesting. It varies with the form

INTERFERENCE METHODS IN ASTRONOMY 137

of the object viewed. In the case of a double star it falls very
rapidly from its maximum to zero ; then it rises again, and if
the two slits themselves could possibly be infinitely narrow
and the light perfectly homogeneous, it would rise to its origi-
nal value. But because the slits themselves have a certain
width, and because the observation is usually made with white
light, this second maximum is usually less than the first.

If the source is a single point of light, then the fringes
are equally distinct, no matter what the distance between the
slits; whereas, when the source is a disc of appreciable
angular width, the fringes fade out as the distance between
the slits increases, so that there is no possibility of a doubt
as to whether we are looking at a point or a source of appre-
ciable size.

Suppose we are looking at a disc of a given diameter
through such a pair of slits which are close together. If
we gradually increase the distance between the slits, the
visibility becomes smaller and smaller until the fringes dis-
appear entirely. As the distance between the slits increases
again, the clearness increases, and so on; i. e., there are sub-
sequent maxima and minima which may be measured, if it be
considered desirable. It is necessary, however, to measure
this distance between the two slits at the time the fringes
first disappear; we may measure this distance at the sub-
sequent disappearances if we choose, but it is not essential,
for we are able to find the diameter of the object (the
distance between two objects in the case of the double star)
if we know the distance between the slits at the first dis-
appearance. If, however, we do not know the shape of the
source, we must observe at least one more disappearance.

In Fig. 99 the visibility curves which characterize a slit,
a uniformly illuminated disc, and a disc whose intensity is
greater at the center, are shown. The full curve cor-
responds to a slit, the dotted one to a disc, and the dashed

LIGHT WAVES AND THEIR USES

one to the disc which is brighter at the center. It will be
noted that in the case of the slit the distances between the
zero points are all alike. In the case of the disc the curve
is still of the same general form, but the distance to the first
zero position is no longer equal to the others, but is 1 .22 as
great. Hence, if the distances between the zero points are
equal, as shown in the figure for the full curve, we know the

FIG. 99

source is rectangular. But if the distance to the first zero
point is 1.22 times as great as the distances between the
succeeding zero points, we know that we are observing a
uniformly illuminated circular object. The next interval
would determine in this case, as in the first, the diameter of
the object viewed.

In the case of the slit the distances between the zero
points are rigorously equal, and it may be of interest to note
that the visibility at the second maximum is something like
one-fourth of the visibility at the first. So there is no pos-
sibility of deception in noting the point at which the fringes
disappear ; indeed, the disappearance can be so sharply deter-
mined that we may measure the corresponding distance be-

INTERFERENCE METHODS IN ASTRONOMY 139

tween the slits to within 1 per cent, of its whole value, and
so determine the width of the line source with a corre-
sponding degree of accuracy.

The visibility curve shown in Fig. 100 represents the case
in which the source is a double disc — a double star, for
instance, in which the
discs have apprecia-
ble magnitude. The
envelope of the curve,
which is drawn full,
corresponds to the
circular form of the
separate discs, and
from this curve we can
determine the size of
the separate discs,
provided they are
equal. The dotted
curve tells us that we
are dealing with a

double object. Hence, if in observing a heavenly body we
obtain a visibility curve of this form, we infer that we are
dealing with a double star.

There is a difficulty in carrying out such observations,
especially when we are observing a very small object or a
very close double star. For in this case the slits have to be
separated rather widely, and the angle between the rays
from the two slits, when they come together, is rather large.
Hence, the distance between the interference fringes is
correspondingly small, as was shown in a previous lecture,
and this distance becomes less and less as the angle becomes
greater and greater. When we approach the limit of reso-
lution of the telescope, the fringes are so small that a
rather high power eyepiece must be used in order to see

FIG. 100

140

LIGHT WAVES AND THEIB USES

them, and the light is correspondingly feeble. We may over-
come this difficulty in the same way as we did in our trans-
formation of the microscope into the interferometer, by using
mirrors to change the direction of the beam of light, instead of
allowing it to pass through two apertures in front of the lens.
Fig. 101 represents two arrangements by which this may
be accomplished. The light falls from above upon the two

FIG. 101

mirrors a and &, which correspond to the two slits. By
these mirrors we can bend the light at any angle we choose,
and bring the two beams together again at as small an angle
as we wish, by means of the plane-parallel plate. Thus we
can make the fringes as broad as we choose. In the second
diagram we have a rather more complex arrangement of
mirrors, but the effect is the same. The paths of the two
rays can be easily traced in the diagrams.

If we wish to observe with such an arrangement a body
of the size of a small satellite, we should have to construct
the instrument so that the distance between the two mirrors
could be altered, because these mirrors correspond to the

INTERFERENCE METHODS IN ASTRONOMY 141

two slits whose distance apart must be changed. This can
be done by mounting the mirror a and the mirror b on a
right- and left-handed screw. On turning the screw the
two mirrors would move in opposite directions through
equal distances, leaving everything 'else unchanged. Such
an instrument is represented in Fig. 102. The light falls
from below upon the two mirrors a and 6, which are
mounted on carriages which can be moved in opposite
directions by the right- and left-handed screw.

FIG. 102

Fig. 103 represents an actual instrument which was used
in making laboratory experiments to test the method. The
artificial double stars, or star discs, were pinholes made in a
sheet of platinum. These holes were as small as it was pos-
sible to make them, of such a diameter as to test the resolu-
tion of the telescope, with a bright source of light behind
them. The left-hand figure represents the double slit. It
is mounted on a right- and left-handed screw and can be
operated by the observer. The slits can thus be moved
by a measurable quantity, and their distance apart when the
fringes disappear can be determined.

After making a series of such experiments in the labora-
tory, I was invited to spend a few weeks at the Lick Observatory
at Mount Hamilton to test the method on Jupiter's satellites.
These satellites have angular magnitudes of something like
one second of arc, so that they should be measurable by this

LIGHT WAVES AND THEIR USES

method. The actual micrometric measurements which have
been made of these satellites with the largest telescopes give
results which vary considerably among themselves. Hence
the interest in trying the interferometer method. The appa-
ratus used was similar to that shown in Fig. 103, /. <?., it

consisted of two movable slits in front of the objective of the
eleven-inch glass at the Lick Observatory.

The atmospheric conditions at Mount Hamilton while the
work was in progress were not altogether favorable, so that

FIG. 103

out of the three weeks1 sojourn there there were only four
nights which were good enough to use, though one of these
nights was almost perfect ; and on this one night most of the
measurements were made. The results obtained, together
with those of four determinations which have been made by
the ordinary micrometer method, using the largest telescopes
available, are given in the following table:

Number of Satellite

A. A. M.

Eng.

St.

Ho.

Bu.

1 02

1 08

1 02

1 11

0.94

0.91

0.98

1.00

Ill

1 37

1 54

1 49

1 78

1 31

1 28

1 27

1 46

1 61

The numbers in the column marked A. A. M. are the re-
sults in seconds of arc obtained by the interference method.
The other columns contain the results obtained by the ordi-
nary method by Engelmann, Struve, Hough, and Burnhaui

INTERFERENCE METHODS IN ASTRONOMY 143

respectively. The important point to be noted is that the
results by the interference method are near the mean of the
other results, and that the results obtained by the other
method differ widely among themselves.

It is also important to note that, while an eleven-inch
glass was used for the observations by the interference
method, the distance between the slits at which the fringes
disappear was very much less than eleven inches; on the
average, something like four inches. Now, with a six-inch
glass one can easily put two slits at a distance of four
inches. Hence a six-inch glass can be used with the same
effectiveness as the eleven-inch, and gives results by the
interference method which are equal in accuracy to those
obtained by the largest telescopes known. If this same
method were applied to the forty-inch glass of the Yerkes
Observatory, it would certainly be possible to obtain meas-
urements of objects only one-sixth as large as the satellites
of Jupiter.

The principal object of the method which has been
described was not, however, to measure the diameter of the
planets and satellites, or even of the double stars, though it
seems likely now that this will be one rather important
object that may be accomplished by it ; for some double stars
are so close together that it is impossible to separate them
in the largest telescope. A more ambitious problem, which
may not be entirely hopeless, is that of measuring the diam-
eter of the stars themselves. The nearest of these stars, as
before stated, is so far away that it takes several years
for light from it to reach us. They are about 100,000
times as far away as the sun. If they were as large as the
sun, the angle they would subtend would be about one-
hundredth of a second. A forty-inch telescope can resolve
angles of approximately one-tenth of a second, so that, if we
were to attempt to measure, or to observe, a disc of only

144 LIGHT WAVES AND THEIR USES

one-hundredth of a second, it would require an objective
whose diameter is of the order of forty feet — which, of
course, is out of the question. It is, however, not altogether
out of the question to construct an interference apparatus
such that the distance between its mirrors would be of this
order of magnitude.

But it is not altogether improbable that even some of
the nearer stars are considerably larger than the sun, and in
that case the angle which they subtend would be consider-
ably larger. Hence it might not be necessary to have an
instrument with mirrors forty feet apart. In addition it
may be noted that it is not absolutely necessary to observe
the disappearance of the fringes in order to show that
the object has definite magnitude ; for if the visibility of the
fringes varies at all, we know that the source is not a point.
For, suppose we observe the visibility curve of a star which
is so far away that we know it has no appreciable disc. The
visibility curve would correspond to a straight line. There
would be no appreciable difference in distinction of fringes
as the distance between the slits was increased indefinitely.
If we now observe a star which has a diameter of one-
hundredth of a second, we need only to observe that the
visibility for a large distance between the slits is less than in
the case of the distant star, in order to know that the second
object has an appreciable disc, even if the instruments were
not large enough to increase the distance sufficiently to
make the fringes disappear. From the difference between
two such visibility curves we might calculate rather roughly
the actual magnitude of the stars.

SUMMARY

1. The investigation of the size and structure of the
heavenly bodies is limited by the resolving power of the
observing telescope. When the bodies are so small or so

INTERFERENCE METHODS IN ASTRONOMY 145

distant that this limit of resolution is passed, the telescope
can give no information concerning them.

2. But an observation of the visibility curves of the
interference fringes due to such ,sources, when made by the
method of the double slit or its equivalent, and properly
interpreted, gives information concerning the size, shape, and
distribution of the components of the system. Even in the
case of a fixed star, which may subtend an angle of less than
one-hundredth of a second, it may not be an entirely hope-
less task to attempt to measure its diameter by this means.

LECTURE VIII

THE ETHER

THE velocity of light is so enormously greater than any-
thing with which we are accustomed to deal that the mind
has some little difficulty in grasping it. A bullet travels at
the rate of approximately half a mile a second. Sound, in a
steel wire, travels at the rate of three miles a second. From
this — if we agree to except the velocities of the heavenly
bodies — there is no intermediate step to the velocity of
light, which is about 186,000 miles a second. We can, per-
haps, give a better idea of this velocity by saying that light
will travel around the world seven times between two ticks
of a clock.

Now, the velocity of wave propagation can be seen, with-
out the aid of any mathematical analysis, to depend on the
elasticity of the medium and its density; for we can see
that if a medium is highly elastic the disturbance would be
propagated at a great speed. Also, if the medium is dense
the propagation would be slower than if it were rare. It
can easily be shown that if the elasticity were represented by
E, and the density by Z), the velocity would be represented
by the square root of E divided by D. So that, if the den-
sity of the medium which propagates light waves were as
great as the density of steel, the elasticity, since the velocity
of light is some 60,000 times as great as that of the propa-
gation of sound in a steel wire, must be 60,000 squared
times as great as the elasticity of steel. Thus, this medium
which propagates light vibrations would have to have an
elasticity of the order of 3,600,000,000 times the elasticity
of steel. Or, if the elasticity of the medium were the same

146

THE ETHER 147

as that of steel, the density would have to be 3,600,000,000
times as small as that of steel, that is to say, roughly
speaking, about 50,000 times as small as the density of hydro-
gen, the lightest known gas. Evidently, then, a medium
which propagates vibrations with such an enormous velocity
must have an enormously high elasticity or abnormally low
density. In any case, its properties would be of an entirely
different order from the properties of the substances with
which we are accustomed to deal, so that it belongs in a
category by itself.

Another course of reasoning which leads to this same
conclusion — namely, that this medium is not any ordinary
form of matter, such as air or gas or steel — is the following :
Sound is produced by a bell under a receiver of an air pump.
When the air has the same density inside the receiver as
outside, the sound reaches the ear of an observer without
difficulty. But when the air is gradually pumped out of the
receiver, the sound becomes fainter and fainter until it ceases
entirely. If the same thing were true of light, and we
exhausted a vessel in which a source of light — an incandes-
cent lamp, for example — had been placed, then, after a certain
degree of exhaustion was reached, we ought to see the light
less clearly than before. We know, however, that the con-
trary is the case, i. e., that the light is actually brighter and
clearer when the exhaustion of the receiver has been carried
to the highest possible degree. The probabilities are enor-
mously against the conclusion that light is transmitted by
the very small quantity of residual gas. There are other
theoretical reasons, into which we will not enter.

Whatever the process of reasoning, we are led to the
same result. We know that light vibrations are transverse
to the direction of propagation, while sound vibrations are in
the direction of propagation. We know also that in the case
of a solid body transverse vibrations can be readily trans-

148 LIGHT WAVES AND THEIR USES

mitted." -Thus, if we have a long cylindrical rod and we give
one end of it a twist, the twist will travel along from one end
to the other. If the' medium, instead of being a solid rod,
were a tube of liquid, and were twisted at one end, there
would be no corresponding transmission of the twist to the
other end, for a liquid cannot transmit a torsional strain.
Hence this reasoning leads to the conclusion that if the
medium which propagates light vibrations has the proper-
ties of ordinary matter, it must be considered to be an elastic
solid rather than a fluid.

This conclusion was considered one of the most formi-
dable objections to the undulatory theory that light con-
sists of waves. For this medium, notwithstanding the
necessity for the assumption that it has the properties of a
solid, must yet be of such a nature as to offer little resist-
ance to the motion of a body through it. Take, for example,
the motion of the planets around the sun. The resistance
of the medium is so small that the earth has been travel-
ing around the sun millions of years without any appre-
ciable increase in the length of the year. Even the vastly
lighter and more attenuated comets return to the same point
periodically, and the time of such periodical returns has
been carefully noted from the earliest historical times, and
yet no appreciable increase in it has been detected. We are
thus confronted with the apparent inconsistency of a solid
body which must at the same time possess in such a marked
degree the properties of a perfect fluid as to offer no appre-
ciable resistance to the motion of bodies so very light and
extended as the comets. We are, however, not without analo-
gies, for, as was stated in the first lecture, substances such
as shoemaker's wax show the properties of an elastic solid
when reacting against rapid motions, but act like a liquid
under pressures.

In the case of shoemaker's wax both of these contradictory

THE ETHER 149

properties are very imperfectly realized, but we can argue
from this fact that the medium which we are considering
might have the various properties which it must possess
in an enormously exaggerated degree. It is, at any rate,
not at all inconceivable that such a medium should at the
same time possess both properties. We know that the air
itself does not possess such properties, and that no matter
which we know possesses them in sufficient degree to
account for the propagation of light. Hence the conclusion
that light vibrations are not propagated by ordinary mat-
ter, but by something else. Cogent as these three lines
of reasoning may be, it is undoubtedly true that they do not
always carry conviction. There is, so far as I am aware,
no process of reasoning upon this subject which leads
to a result which is free from objection and absolutely
conclusive.

But these are not the only paradoxes connected with the
medium which transmits light. There was an observation
made by Bradley a great many years ago, for quite
another purpose. He found that when we observe the posi-
tion of a star by means of the telescope, the star seems
shifted from its actual position, by a certain small angle
called the angle of aberration. He attributed this effect to
the motion of the earth in its orbit, and gave an explana-
tion of the phenomenon which is based on the corpus-
cular theory and is apparently very simple. We will
give this explanation, notwithstanding the fact that we
know the corpuscular theory to be erroneous.

Let us suppose a raindrop to be falling vertically and an
observer to be carrying, say, a gun, the barrel being as
nearly vertical as he can hold it. If the observer is not
moving and the raindrop falls in the center of the upper
end of the barrel, it will fall centrally through the lower
end. Suppose, however, that the observer is in motion

150 LIGHT WAVES AND THEIR USES

in the direction bd (Fig. 104) ; the raindrop will still fall
exactly vertically, but if the gun advances laterally while
the raindrop is within the barrel, it strikes against the side.
In order to make the raindrop move centrally along
the axis of the barrel, it is evidently necessary to
incline the gun at an angle such as bad. The
gun barrel is now pointing, apparently, in the
wrong direction, by an angle whose tangent is the
ratio of the velocity of the observer to the velocity
of the raindrop.

According to the undulatory theory, the ex-
planation is a trifle more complex; but it can
easily be seen that, if the medium we are consider-
ing is motionless and the gun barrel represents a
telescope, and the waves from the star are moving
in the direction ad, they will be concentrated at a
point which is in the axis of the telescope, unless
the latter is in motion. But if the earth carrying
the telescope is moving with a velocity something
like twenty miles a second, and we are observing
the stars in a direction approximately at right
angles to the direction of that motion, the light
from the star will not come to a focus on the axis
of the telescope, but will form an image in a new
position, so that the telescope appears to be point-
• d ing in the wrong direction. In order to bring the
image on the axis of the instrument, we must turn
the telescope from its position through an angle
whose tangent is the ratio of the velocity of the earth in its
orbit to the velocity of light. The velocity of light is, as
before stated, 186,000 miles a second— 200,000 in round
numbers — and the velocity of the earth in its orbit is roughly
twenty miles a second. Hence the tangent of the angle of
aberration would be measured by the ratio of 1 to 10,000.

THE ETHER 151

More accurately, this angle is 20 f 445. The limit of accuracy
of the telescope, as was pointed out in several of the pre-
ceding lectures, is about one-tenth of a second; but, by
repeating these measurements under a great many variations
in the conditions of the problem, this limit may be passed,
and it is practically certain that this number is correct to the
second decimal place.

When this variation in the apparent position of the stars
was discovered, it was accounted for correctly by the as-
sumption that light travels with a finite velocity, and that,
by measuring the angle of aberration, and knowing the speed
of the earth in its orbit, the velocity of light could be found.
This velocity has since been determined much more accu-
rately by experimental means, so that now we use the velocity
of light to deduce the velocity of the earth and the radius
of its orbit.

The objection to this explanation was, however, raised
that if this angle were the ratio of the velocity of the
earth in its orbit to the velocity of light, and if we filled
a telescope with water, in which the velocity of light is
known to be only three-fourths of what it is in air, it would
take one and one-third times as long for the light to pass
from the center of the objective to the cross-wires, and
hence we ought to observe, not the actual angle of aberration,
but one which should be one-third greater. The experiment
was actually tried. A telescope was filled with water, and
observations on various stars were continued throughout the
greater part of the year, with the result that almost exactly
the same value was found for the angle of aberration.

This result was considered a very serious objection to the
undulatory theory until an explanation was found by Fresnel.
He proposed that we consider that the medium which trans-
mits the light vibrations is carried along by the motion of the
water in the telescope in the direction of the motion of the

152 LIGHT WAVES AND THEIR USES

earth around the sun. Now, if the light waves were carried
along with the full velocity of the earth in its orbit, we should
be in the same difficulty, or in a more serious difficulty, than
before. Fresnel, however, made the further supposition that
the velocity of the carrying along of the light waves by the
motion of the medium was less than the actual velocity of the
medium itself, by a quantity which depended on the index of
refraction of the substance. In the case of water the value
of this factor is seven-sixteenths.

This, at first sight, seems a rather forced explanation ;
indeed, at the time it was proposed it was treated with con-
siderable incredulity. An experiment was made by Fizeau,
however, to test the point — in my opinion one of the most
ingenious experiments that have ever been attempted in
the whole domain of physics. The problem is to find
the increase in the velocity of light due to a motion of the
medium. We have an analogous problem in the case of
sound, but in this case it is a very much simpler matter. We
know by actual experiment, as we should infer without experi-
ment, that the velocity of sound is increased by the velocity
of a wind which carries the air in the same direction, or
diminished if the wind moves in the opposite direction. But
in the case of light waves the velocity is so enormously
great that it would seem, at first sight, altogether out of the
question to compare it with any velocity which we might be
able to obtain in a transparent medium such as water or
glass. The problem consists in finding the change in the
velocity of light produced by the greatest velocity we can
get — about twenty feet a second — in a column of water
through which light waves pass. We thus have to find
a difference of the order of twenty feet in 186,000 miles,
i. e., of one part in 50,000,000. Besides, we can get only
a relatively small column of water to pass light through and
still see the light when it returns.

THE ETHER 153

The difficulty is met, however, by taking advantage of
the excessive minuteness of light waves themselves. This
double length of the water column is something like forty
feet. In this forty feet there are, in round numbers,
14,000,000 waves. Hence the difference due to a velocity
of twenty feet per second, which is the velocity of the water
current, would produce a displacement of the interference
fringes (produced by two beams, one of which passes down
the column and the other up the column of the moving
liquid) of about one-half a fringe, which corresponds to
a difference of one-half a light wave in the paths. Revers-
ing the water current should produce a shifting of one-half
a fringe in the opposite direction, so that the total shifting
would actually be of the order of one interference fringe.
But we can easily observe one -tenth of a fringe, or in some
cases even less than that. Now, one fringe would be the
displacement if water is the medium which transmits the
light waves. But this other medium we have been talking
about moves, according to Fresnel, with a smaller velocity
than the water, and the ratio of the velocity of the medium
to the velocity of the water should be a particular fraction,
namely, seven-sixteenths. In other words, then, instead of
the whole fringe we ought to get a displacement of seven-
sixteenths of a fringe by the reversal of the water current.
The experiment was actually tried by Fizeau, and the result
was that the fringes were shifted by a quantity less than
they should have been if water had been the medium; and
hence we conclude that the water was not the medium which
carried the vibrations.

The arrangement of the apparatus which was used in the
experiment is shown in Fig. 105. The light starts from a
narrow slit S, is rendered parallel by a lens L, and separated
into two pencils by apertures in front of the two tubes TT,
which carry the column of water. Both tubes are closed by

154

LIGHT WAVES AND THEIR USES

pieces of the same plane-parallel plate of glass. The light
passes through these two tubes and is brought to a focus by
the lens in condition to produce interference fringes. The
apparatus might have been arranged in this way but for
the fact that there would be changes in the position of the
interference fringes whenever the density or temperature
of the medium changed; and, in particular, whenever the
current changes direction there would be produced altera-
tions in length and changes in density ; and these exceedingly

FIG. 105

slight differences are quite sufficient to account for any motion
of the fringes. In order to avoid this disturbance, Fresnel had
the idea of placing at the focus of the lens the mirror M, so that
the two rays return, the one which came through the upper
tube going back through the lower, and vice versa for the
other ray. In this way the two rays pass through identical
paths and come together at the same point from which they
started. With this arrangement, if there is any shifting of
the fringes, it must be due to the reversal of the change
in velocity due to the current of water. For one of the
two beams, say the upper one, travels with the current
in both tubes; the other, starting at the same point, travels
against the current in both tubes. Upon reversing the
direction of the current of water the circumstances are
exactly the reverse: the beam which before traveled with
the current now travels against it, etc. The result of the
experiment, as before stated, was that there was produced a

THE ETHER

155

displacement of less than should have been produced by the
motion of the liquid. How much less was not determined.
To this extent the experiment was imperfect.

On this account, and also for the reason that the experiment
was regarded as one of the most important in the entire subject
of optics, it seemed to me that it was desirable to repeat it

FIG. 106

in order to determine, not only the fact that the displace-
ment was less than could be accounted for by the motion
of the water, but also, if possible, how much less. For this
purpose the apparatus was modified in several important
points, and is shown in Fig. 106.

It will be noted that the principle of the interferometer
has been used to produce interference fringes of consider-
able breadth without at the same time reducing the inten-
sity of the light. Otherwise, the experiment is essentially
the same as that made by Fizeau. The light starts from a
bright flame of ordinary gas light, is rendered parallel by
the lens, and then falls on the surface, which divides it into
two parts, one reflected and one transmitted. The reflected

15(5 LIGHT WAVES AND THEIR USES

portion goes down one tube, is reflected twice by the total
reflection prism P through the other tube, and passes, after
necessary reflection, into the observing telescope. The other
ray pursues the contrary path, and we see interference fringes
in the telescope as before, but enormously brighter and more
definite. This arrangement made it possible to make meas-
urements of the displacement of the fringes which were very
accurate. The result of the experiment was that the meas-
ured displacement was almost exactly seven-sixteenths of
what it would have been had the medium which transmits
the light waves moved with the velocity of the water.

It was at one time proposed to test this problem by utiliz-
ing the velocity of the earth in its orbit. Since this velocity
is so very much greater than anything we can produce at
the earth's surface, it was supposed that such measurements
could be made with considerable ease ; and they were actually
tried in quite a considerable number of different ways and
by very eminent men. The fact is, we cannot utilize the
velocity of the earth in its orbit for such experiments, for
the reason that we have to determine our directions by points
outside of the earth, and the only thing we have is the stars,
and the stars are displaced by this very element which we
want to measure; so the results would be entirely negative.
It was pointed out by Lorentz that it is impossible by any
measurements made on the surface of the earth to detect any
effect of the earth's motion.

Maxwell considered it possible, theoretically at least,
to deal with the square of the ratio of the two velocities;
that is, the square of ^1^, or Tinririinmr. He further
indicated that if we made two measurements of the velocity
of light, one in the direction in which the earth' is travel
ing in its orbit, and one in a direction at right angles to
this, then the time it takes light to pass over the same

THE ETHER 157

length of path is greater in the first case than in the
second.

We can easily appreciate the fact that the time is greater
in this case, by considering a man rowing in a boat, first in a
smooth pond and then in a river. If he rows at the rate of
four miles an hour, for example, and the distance between
the stations is twelve miles, then it would take him three
hours to pull there and three to pull back — six hours in
all. This is his time when there is no current. If there
is a current, suppose at the rate of one mile an hour,
then the time it would take to go from one point to
the other, would be, not 12 divided by 4, but 12 divided by
4+1, i. e., 2.4 hours. In coming back the time would be
12 divided by 4 — 1, which would be 4 hours, and this
added to the other time equals 6.4 instead of 6 hours. It
takes him longer, then, to pass back and forth when the
medium is in motion than when the medium is at rest.
We can understand, then, that it would take light longer to
travel back and forth in the direction of the motion of the
earth. The difference in the times is, however, so exceedingly
small, being of the order of 1 in 100,000,000, that Maxwell
considered it practically hopeless to attempt to detect it.

In spite of this apparently hopeless smallness of the
quantities to be observed, it was thought that the minute-
ness of the light waves might again come to our rescue.
As a matter of fact, an experiment was devised for detect-
ing this small quantity. The conditions which the appa-
ratus must fulfil are rather complex. The total distance
traveled must be as great as possible, something of the order
of one hundred million waves, for example. Another condi-
tion requires that we be able to interchange the direction
without altering the adjustment by even the one hundredth-
millionth part. Further, the apparatus must be absolutely
free from vibration.

158 LIGHT WAVES AND THEIR USES

The 'problem was practically solved by reflecting part of
the light back and forth a number of times and then returning
it to its starting-point. The other path was at right angles to
the first, and over it the light made a similar series of excur-
sions, and was also reflected back to the starting-point. This
starting-point was a separating plane in an interferometer,
and the two paths at right angles were the two arms of an
interferometer. Notwithstanding the very considerable dif-
ference in path, which must involve an exceedingly high order
of accuracy in the reflecting surfaces and a constancy of
temperature in the air between, it was possible to see fringes
and to keep them in position for several hours at a time.

These conditions having been fulfilled, the apparatus was
mounted on a stone support, about four feet square and one
foot thick, and this stone was mounted on a circular disc of
wood which floated in a tank of mercury. The resistance to
motion is thus exceedingly small, so that by a very slight
pressure on the circumference the whole could be kept in slow
and continuous rotation. It would take, perhaps, five minutes
to make one single turn. With this slight motion there
is practically no oscillation; the observer has to follow
around and at intervals to observe whether there is any
displacement of the fringes.

It was found that there was no displacement of the
interference fringes, so that the result of the experiment
was negative and would, therefore, show that there is still
a difficulty in the theory itself; and this difficulty, I may
say, has not yet been satisfactorily explained. I am present-
ing the case, not so much for solution, but as an illustration
of the applicability of light waves to new problems.

The actual arrangement of the experiment is shown in
Fig. 107. A lens makes the rays nearly parallel. The
dividing surface and the two paths are easily recognized. The
telescope was furnished with a micrometer screw to determine

THE ETHER

159

the amount of displacement of the fringes, if there were any.
The last mirror is mounted on a slide; so these two paths
may be made equal to the necessary degree of accuracy —
something of the order of one fifty-thousandth of an inch.

Fig. 108 represents the actual apparatus. The stone and
the circular disc of wood sup-
porting the stone in the tank
filled with mercury are readily
recognized; also the dividing
surface and the various mirrors.

It was considered that, if
this experiment gave a posi-
tive result, it would determine
the velocity, not merely of the
earth in its orbit, but of the
earth through the ether. With

good, reason it is supposed that
the sun and all the planets as
well are moving through space at a rate of perhaps twenty
miles per second in a certain particular direction. The velocity
is not very well determined, and it was hoped that with this
experiment we could measure this velocity of the whole solar
system through space. Since the result of the experiment
was negative, this problem is still demanding a solution.

The experiment is to me historically interesting, because
it was for the solution of this problem that the interferometer
was devised. I think it will be admitted that the problem,
by leading to the invention of the interferometer, more than
compensated for the fact that this particular experiment gave
a negative result.

From all that precedes it appears practically certain that
there must be a medium whose proper function it is to trans-
mit light waves. Such a medium is also necessary for the

160

LIGHT WAVES AND THEIR USES

transmission of electrical and magnetic effects. Indeed, it
is fairly well established that light is an electro-magnetic
disturbance, like that due to a discharge from an induction coil
or a condenser. Such electric waves can be reflected and
refracted and polarized, and be made to produce vibrations

FIG. 108

and other changes, just as the light waves can. The only
difference between them and the light waves is in the wave
length.

This difference may be enormous or quite moderate. For
example, a telegraphic wave, which is practically an electro-
magnetic disturbance, may be as long as one thousand miles.
The waves produced by the oscillations of a condenser, like
a Leyden jar, may be as short as one hundred feet; the waves
produced by a Hertz oscillator may be as short as one-tenth
of an inch. Between this and the longest light wave there
is not an enormous gap, for the latter has a length of about
one- thousandth of an inch. Thus the difference between the

THE ETHER 161

Hertz vibrations and the longest light wave is less than the
difference between the longest and shortest light waves, for
some of the shortest oscillations are only a few millionths of
an inch long. Doubtless even this gap will soon be bridged
over.

The settlement of the fact that light is a magneto-elec-
tric oscillation is in no sense an explanation of the nature
of light. It is only a transference of the problem, for the
question then arises as to the nature of the medium and of
the mechanical actions involved in such a medium which
sustains and transmits these electro-magnetic disturbances.

A suggestion which is very attractive on account of its
simplicity is that the ether itself is electricity ; a much more
probable one is that electricity is an ether strain — that a
displacement of the ether is equivalent to an electric current.
If this is true, we are returning to our elastic-solid theory.
I may quote a statement which Lord Kelvin made in reply
to a rather skeptical question as to the existence of a me-
dium about which so very little is supposed to be known.
The reply was: "Yes, ether is the only form of matter about
which we know anything at all." In fact, the moment we
begin to inquire into the nature of the ultimate particles o?
ordinary matter, we are at once enveloped in a sea of con-
jecture and hypotheses — all of great difficulty and complexity.

One of the most promising of these hypotheses is the
"ether vortex theory," which, if true, has the merit of intro-
ducing nothing new into the hypotheses already made, bi:t
only of specifying the particular form of motion required.
The most natural form of such vortex motions with which
to deal is that illustrated by ordinary smoke rings, such as
are frequently blown from the stack of a locomotive. Such
vortex rings may easily be produced by filling with smoke
a box which has a circular aperture at one end and a rubber
diaphragm at the other, and then tapping the rubber. The

102 LIGHT WAVES AND THEIR USES

friction against the side of the opening, as the puff of smoke
passes out, produces a rotary motion, and the result will be
smoke rings or vortices.

Investigation shows that these smoke rings possess, to a
certain degree, the properties which we are accustomed to
associate with atoms, notwithstanding the fact that the
medium in which these smoke rings exists is far from ideal.
If the medium were ideal, it would be devoid of friction,
and then the motion, when once started, would continue
indefinitely, and that part of the ether which is differentiated
by this motion would ever remain so.

Another peculiarity of the ring is that it cannot be cut

—it simply winds around the knife. Of course, in a very

short time the motion in a smoke ring ceases in consequence

of the viscosity of the air, but it would continue indefinitely

in such a frictionless medium as we suppose the ether to be.

There are a number of other analogies which we have
not time to enter into — quite a number of details and
instances of the interactions of the various atoms which have
been investigated. In fact, there are so many analogies
that we are tempted to think that the vortex ring is in reality
an enlarged image of the atom. The mathematics of the
subject is unfortunately very difficult, and this seems to be
one of the principal reasons for the slow progress made in
the theory.

Suppose that an ether strain corresponds to an electric
charge, an ether displacement to the electric current, these
ether vortices to the atoms — if we continue these supposi-
tions, we arrive at what may be one of the grandest general-
izations of modern science — of which we are tempted to say
that it ought to be true even if it is not — namely, that all
the phenomena of the physical universe are only different
manifestations of the various modes of motions of one all-
pervading substance — the ether.

THE ETHER 163

All modern investigation tends toward the elucidation of
this problem, and the day seems not far distant when the
converging lines from many apparently remote regions of
thought will meet on this common ground. Then the
nature of the atoms, and the forces called into play in their
chemical union; the interactions between these atoms and
the non-differentiated ether as manifested in the phenomena
of light and electricity ; the structures of the molecules and
molecular systems of which the atoms are the units; the
explanation of cohesion, elasticity, and gravitation — all
these will be marshaled into a single compact and consistent
body of scientific knowledge.

SUMMARY

1. A number of independent courses of reasoning lead to
the conclusion that the medium which propagates light waves
is not an ordinary form of matter. Little as we know about
it, we may say that our ignorance of ordinary matter is still
greater.

2. In all probability, it not only exists where ordinary
matter does not, but it also permeates all forms of matter.
The motion of a medium such as water is found not to add
its full value to the velocity of light moving through it, but
only such a fraction of it as is perhaps accounted for on the
hypothesis that the ether itself does not partake of this motion.

3. The phenomenon of the aberration of the fixed stars
can be accounted for on the hypothesis that the ether does
not partake of the earth's motion in its revolution about
the sun. All experiments for testing this hypothesis have,
however, given negative results, so that the theory may still
be said to be in an unsatisfactory condition.

INDEX.

ABERRATION, 149.

ACCURACY OF MEASUREMENT: value of
increasing, 23; limit without lenses,
25 ; limit with lenses, 27 ; increase due
to lenses, 30; increase due to interfer-
ometer, 36 ; of standards of length with
grating, 85 ; of length of seconds pen-
ulum, 86 ; of earth's circumference, 87 ;
of wave length with the interferometer,
98.

AIR WEDGE: interference produced by,
15.

AMPHIPLEURA PELLUCIDA : use as test of
resolution, 30.

AMPLITUDE, 6.

ANALYSIS : of periodic curves, 68 ; of the
nature of a source of light, 76.

ANALYZER : harmonic, 68.

ARAGO : velocity of light, 48 ; interfer-
ometer, 51.

BEATS : between tuning-forks, 12.

BLACK SPOT : on soap film, 53 ; thickness
of, 54.

BOILING OF STAR IMAGES, 129.

BRADLEY : aberration, 149.

BURNHAM : Jupiter's satellites, 142.

CADMIUM : analysis of radiations of, 81 ;
red radiation as standard of length,
91 ; number of waves in meter; 98 ; ac-
tion of magnetism on radiations of,
116.

COMETS : resistance by ether to motion
of, 45.

CORPUSCULAR THEORY, 44.

DIFFRACTION : of sound waves, 19 ; in
telescope and microscope, 29; by rec-
tangular opening, 32.

DIFFRACTION PATTERN : due to circular
opening, 29, 130; due to rectangular
opening, 133 ; due to two slits, 134.

DOUBLE SLIT: use of in astronomical
work, 134.

EARTH: resistance by ether to motion
of, 45, 148 ; circumference of as stand-
ard of length, 87.

ECHELON SPECTROSCOPE, 122.

EFFICIENCY: of microscope and tele-
scope, 25.

ELECTROLYSIS, 113.

ELECTROMAGNETIC NATURE OF LIGHT,
160.

ENGELMANN : Jupiter's satellites, 142.

ETHER: properties of, 45, 146; vortex-
theory of, 161.

EXPANSION : measurement of coefficient
of, 55.

FARADAY : action of magnetism on light,
107.

FIEVEZ: action of magnetism on light,
107.

FITZGERALD: action of magnetism on
light, 112.

FIZEAU: velocity of light, 48; in mov-
ing media, 152.

FOUCAULT : velocity of light, 48.

FRAUNHOFER: lines in solar spectrum,
60.

FRESNEL : measurement of index of re-
fraction, 51 ; moving media, 152.

FRINGES: t due to two openings, 33;
breadth of, 34 ; use of in spectrum anal-
ysis, 64.

GASES : liquefaction of, 24.

GOULD : standards of length, 84, 103.

GRATING : diffraction, 23, 84, 119 ; effici-
ency of, 121.

GRAVITATION CONSTANT : measurement
with interferometer, 56.

GUN SIGHT : use in measuring angles, 25.

HARMONIC MOTION, 6 ; analyzer, 68.

HERTZ : oscillator, 160. .

HOUGH : Jupiter's satellites, 142.

HYDROGEN : analysis of radiations of, 78.

IMAGE: formation of, 26.

INTERFERENCE : definition of, 8 ; of sound
waves, 9 ; of mercury ripples, 11 ; of
light in soap film, 12 ; of two trains of
waves, 64.

INTERFER9METER : definition of, 33, 36;
description of, 40; application of to
measure index of refraction, 51 ; to
measure thickness of soap film, 53 ; to
measure coefficient of expansion, 55;
to measure gravitation constant, 56 ;
to test screws, 57; to measure light
waves, 58; to analyze spectral lines,
60, 73, 78; to determine standards of
length, 89; to the Zeeman effect, 108,
114; to astronomical measurements,
127 ; to aberration, 157.

INTERMEDIATE STANDARDS OF LENGTH,
93.

IRON : spectrum of, 62.

JOHONNOTT: thickness of liquid films,
54.

JUPITER, 128; size of satellites, 141.

KELVIN: dynamic model of wave mo-
tion, 5, 16.

165

166

INDEX

LARMOR : action of magnetism on light,
112.

LENS : formation of image by, 26.

LEVERRIER: discovery of Uranus, 24.

LINEAR MEASUREMENTS : attainable ac-
curacy in, 25.

LORENTZ : action of magnetism on light,
112; aberration, 156.

MAGNETISM : action on light, 107.

MAGNIFICATION : produced by lens, 27 ;
loss of light in, 27 ; of fringes by inter-
ferometer, 32.

MANOMETRIC CAPSULE, 10.

MARS, 128.

MAXWELL : aberration, 156.

MERCURY : analysis of radiations of, 80.

METER: manufacture of, 87; value in
waves of cadmium light, 104.

MICROSCOPE : efficiency of, 25 ; limit of
resolution of, 30.

MOLECULES: complexity of, shown by
spectrum, 82.

MORLEY : measurement of coefficient of
expansion, 55.

MOVING MEDIA: effect on velocity of
light, 151.

Music : color, 2.

NEWTON: corpuscular theory, 45; spec-
trum, 60.

OBJECTIVE: relation to size of diffrac-
tion pattern, 30.

PENDULUM : motion of, 6 ; as standard of
length, 86.

PERIOD, 6.

PHASE: defined, 7; loss of by reflec-
tion, 16.

POISSON: diffraction, 21.

POLARIZATION, 110.

QUINCKE: interference of sound, 9.

RAYLEIGH : diffraction of sound, 21 ; dis-
covery of Argon, 24.

REFLECTION : change of phase on, 16.

REFRACTION : comparison of theories of,
47; index of, 50; measurement of in-
dex of, 51.

RESOLUTION: of telescope, 29,130 ; of mi-
croscope, 30; of spectroscope, 62; of
grating, 121 ; of echelon, 125.

REVOLVING MIRROR, 48.

RIPPLES : interference of on surface of
mercury, 11.

ROGERS: measurement of coefficient of
expansion, 55.

RUSKIN,!.

SATURN, 128.

SCREW: testing with interferometer, 57.

SENSITIVE FLAME, 19.

SIMPLE HARMONIC MOTION, 6 ; curve, 7.

SINE CURVE, 7.

SLIT: diffraction produced by, 22.

SOAP FILM : colors of, 14.

SODIUM: spectrum of, 61: distance be-
tween lines a standard of measure-
ment, 62; distance between lines of,
66 ; analysis of radiations of, 78 ; action
of magnetism on radiations of, 107.

SOUND WAVES : interference of, 9 ; dif-
fraction of, 19 ; shadow produced by,
20.

SOURCE OF LIGHT : distribution of, 75.

SPECTRAL LINES: structure of , 62 ; analy-
sis of with interferometer, 73.

SPECTRUM, 60; of sodium, 61, 78; of hy-
drogen, 78; of thallium, 79; of mer-
cury, 80; of cadmium, 81 ; order of, 121.

STANDARDS OF LENGTH, 86.

STAR DISCS : size of, 143.

STRUVE : Jupiter's satellites, 142.

TELESCOPE: efficiency of, 25; limit of
resolution of, 29, 130.

THALLIUM : analysis of radiations of, 79.

TUNING-FORKS : beats formed by, 12.

UNDULATORY THEORY, 44.

URANUS : discovery of, 24.

VACUUM TUBES : as sources of light, 75.

VELOCITY: of wave motion, 8, 146; of
light, 146.

VISIBILITY : defined, 68; curves with the
interferometer, 70; with the double
slit, 139.

VORTEX THEORY, 161.

WAVE LENGTH : definition of, 7 ; meas-
urement of , 17 ; as standard of length,
84.

WAVE MOTION, 3; kinetic model of, 4;
Kelvin's dynamic model of, 5 ; propa-
gation of, 7.

WHEATSTONE : velocity of light, 48.

YOUNG : interference, 22.

ZEEMAN: action of magnetism on light
107.

ZINC : spectrum of, 62.

PLATE I
2 1

PLATE II

PLATE III
2 3

RETURN TO the circulation desk of any
University of California Library

or to the

NORTHERN REGIONAL LIBRARY FACILITY
Bldg. 400, Richmond Field Station
University of California
Richmond, CA 94804-4698

ALL BOOKS MAY BE RECALLED AFTER 7 DAYS

• 2-month loans may be renewed by calling
(510)642-6753

• 1-year loans may be recharged by bringing
books to NRLF

• Renewals and recharges may be made
4 days prior to due date

DUE AS STAMPED BELOW

AUG 2 0 2005

DD20 12M 1-05

Internet Archive Audio

Featured

Top

Images

Featured

Top

Software

Featured

Top

Books

Featured

Top

Video

Featured

Top

Mobile Apps

Browser Extensions

Archive-It Subscription

Save Page Now

Full text of "Light waves and their uses"

See other formats