From Newton to Einstein; changing conceptions of the universe

SIR ISAAC NEWTON

From NEWTON
to EINSTEIN

Changing Conceptions of
THE UNIVERSE

BY

BENJAMIN HARROW, PH.D.

SECOND EDITION, REVISED AND ENLARGED

WITH ARTICLES BY PROF. EINSTEIN, PROF. J. S. AMES
(JOHNS HOPKINS), SIR FRANK DYSON (ASTRONOMER
ROYAL), PROF. A. S. EDDINQTON (CAMBRIDGE) AND SIR
J. J. THOMSON (PRESIDENT OF THE ROYAL SOCIETY)

Portraits and Illustrations

NEW YORK

D. VAN NOSTRAND COMPANY

EIGHT WARREN STREET

1920

First Edition, May, 1920
Second Edition, October, 19ZO

f$&

Copyright, 1920

BY

D. VAN NOSTRAND COMPANY

PREFACE

EINSTEIN'S contributions to our ideas of time
and space, and to our knowledge of the universe
in general, are of so momentous a nature, that
they easily take their place among the two or
three greatest achievements of the twentieth cen-
tury. This little book attempts to give, in
popular form, an account of this work. As,
however, Einstein's work is so largely dependent
upon the work of Newton and Newton's success-
ors, the first two chapters are devoted to the
latter.

B.H.

PREFACE TO SECOND EDITION

THE preparation of this new edition has made
it possible to correct errors, to further amplify
certain portions of the text and to enlarge the
ever-increasing bibliography on the subject.
Photographs of Professors J. J. Thomson, Michel-
son, Minkowski and Lorentz are also new features
in this edition.

The explanatory notes and articles in the
Appendix will, I believe, present no difficulties to
readers who have mastered the contents of the
book. They are in fact "popular expositions" of
various phases of the Einstein theory; but
experience has shown that even "popular exposi-
tions" of the theory need further "popular intro-
ductions."

I wish to take this opportunity of thanking
Prof. Einstein, Prof. A. A. Michelson of the
University of Chicago, Prof. J. S. Ames of Johns
Hopkins University, and Professor G. B. Pegram
of Columbia University for help in various ways
which they were good enough to extend to me.
Prof. J. S. Ames and the editor of Science have
been kind enough to allow me to reprint the for-
mer's excellent presidential address on Einstein's
theory, delivered before the members of the
American Physical Society.

B. H.

TABLE OF CONTENTS

PAGE

I. NEWTON 1

II. THE ETHER AND ITS CONSEQUENCES . 27

III. EINSTEIN 41

IV. APPENDIX 81

Time, Space and Gravitation, by Prof.

Einstein 88

Einstein's Law of Gravitation, by Prof.

J. S. Ames 93

The Reflection of light by Gravitation
and the Einstein Theory of Relativity,
by Sir Frank Dyson, Prof. A. S. Ed-
dington and Sir J. J. Thomson . .

NEWTON

"Newton was the greatest genius that ever
existed." — Lagrange, one of the greatest of French
mathematicians.

"The efforts of the great philosopher were
always superhuman; the questions which he did
not solve were incapable of solution in his time."
— Arago, famous French astronomer.

EINSTEIN

"This is the most important result obtained in
connection with the theory of gravitation since
Newton's day. Einstein's reasoning is the result
of one of the highest achievements of human
thought." — Sir J. J. Thomson, president of the
British Royal Society and professor of physics at
the University of Cambridge.

"It surpasses in boldness everything previously
suggested in speculative natural philosophy and
even in the philosophical theories of knowledge.
The revolution introduced into the physical
conceptions of the world is only to be compared
in extent and depth with that brought about by
the introduction of the Copernican system of
the universe." — Prof. Max Plancky professor of
physics at the University of Berlin and winner of
the Nobel Prize.

NEWTON

speaking of Newton we are tempted
to paraphrase a line from the Scrip-
tures: Before Newton the Solar
System was without form, and void;
then Newton came and there was light. To
have discovered a law not only applicable to
matter on this earth, but to the planets and sun
and stars beyond, is a triumph which places
Newton among the super-men.

What Newton's law of gravitation must have
meant to the people of his day can be pictured only
if we conceive what the effect upon us would be
if someone — say Marconi — were actually to
succeed in getting into touch with beings on an-
other planet. Newton's law increased confidence
in the universality of earthly laws; and it
strengthened belief in the cosmos as a law-
abiding mechanism.

Newton's Law. The attraction between any
two bodies is proportional to their masses and
inversely proportional to the square of the dis-
tance that separates them. This is the concen-
1

' Ffom Newton to Einstein

trated form of Newton's law. If we apply this
law to two such bodies as the sun and the earth,
we can state that the sun attracts the earth,
and the earth, the sun. Furthermore, this
attractive power will depend upon the distance
between these two bodies. Newton showed
that if the distance between the sun and the
earth were doubled the attractive power would
be reduced not to one-half, but to one-fourth;
if trebled, the attractive power would be re-
duced to one-ninth. If, on the other hand, the
distance were halved, the attractive power
would be not merely twice, but four times as
great. And what is true of the sun and the
earth is true of every body in the firmament,
and, as Professor Rutherford has recently shown,
even of the bodies which make up the solar sys-
tem of the almost infinitesimal atom.

This mysterious attractive power that one body
possesses for another is called "gravitation,"
and the law which regulates the motion of bodies
when under the spell of gravitation is the law of
gravitation. This law we owe to Newton's
genius.

Newton' *s Predecessors. We can best appreciate
Newton's momentous contribution to astronomy
by casting a rapid glance over the state of the

From Newton to Einstein

science prior to the seventeenth century — that is,
prior to Newton's day. Ptolemy's conception of
the earth as the center of the universe held un-
disputed sway throughout the middle ages. In
those days Ptolemy was in astronomy what
Aristotle was in all other knowledge: they were
the gods who could not but be right. Did not
Aristotle say that earth, air, fire and water con-
stituted the four elements? Did not Ptolemy
say that the earth was the center around which
the sun revolved? Why, then, question further?
Questioning was a sacrilege.

Copernicus (1473-1543), however, did ques-
tion. He studied much and thought much. He
devoted his whole life to the investigation of the
movements of the heavenly bodies. And he
came to the conclusion that Ptolemy and his fol-
lowers in succeeding ages had expounded views
which were diametrically opposed to the truth.
The sun, said Copernicus, did not move at all,
but the earth did; and far from the earth being
the center of the universe, it was but one of sev-
eral planets revolving around the sun.

The influence of the church, coupled with man's
inclination to exalt his own importance, strongly
tended against the acceptance of such heterodox
views. Among the many hostile critics of the

From Newton to Einstein

Copernican system, Tycho Brahe (1546-1601)
stands out pre-eminently. This conscientious
observer bitterly assailed Copernicus for his
suggestion that the earth moved, and developed
a scheme of his own which postulated that the
planets revolved around the sun, and planets
and sun in turn revolved around the earth.

The majority applauded Tycho; a small, very
small group of insurgents had faith in Copernicus.
The illustrious Galileo (1564-1642) belonged to
the minority. The telescope of his invention
unfolded a view of the universe which belied the
assertions of the many, and strengthened his be-
lief in the Copernican theory. "It (the Coper-
nican theory) explains to me the cause of many
phenomena which under the generally accepted
theory are quite unintelligible. I have collected
arguments for refuting the latter, but I do not
venture to bring them to publication." So wrote
Galileo to his friend, Kepler. "I do not ven-
ture to bring them to publication." How sig-
nificant of the times — of any time, one ventures
to add.

Galileo did overcome his hesitancy and pub-
lished his views. They aroused a storm. "Look
through my telescope," he pleaded. But the
professors would not; neither would the body of

-

From Newton to Einstein

Inquisitors. The Inquisition condemned him:
"The proposition that the sun is in the center of
the earth and immovable from its place is absurd,
philosophically false and formally heretical; be-
cause it is expressly contrary to the Holy Scrip-
tures." And poor Galileo was made to utter
words which were as far removed *-^m his
thoughts as his oppressors' ideas were from the
truth: "I abjure, curse and detest the said
errors and heresies."

The truth will out. Others arose who defied
the majority and the powerful Inquisition. Most
prominent of all of these was Galileo's friend,
Kepler. t Though a student of Tycho, Kepler
did not hesitate to espouse the Copernican sys-
tem; but his adoption of it did not mean unquali-
fied approval. Kepler's criticism was particu-
larly directed against the Copernican theory that
the planets revolve vin circles. This was bold-
ness in the extreme. Ever since Aristotle's dis-
course on the circle as a perfect figure, it was
taken for granted that motion in space was cir-
cular. Nature is perfect; the circle is perfect;
hence, if the sun revolves, it revolves in circles.
So strongly were men imbued with this "per-
fection," that Copernicus himself fell victim.
The sun no longer moved, but the earth and the

From Newton to Einstein

=

planets did, and they moved in a circle. Rad-
ical as Copernicus was, a few atoms of conserv-
atism remained with him still.

Not so Kepler. Tycho had taught him the
importance of careful observation, — to such good
effect, that Kepler came to th^ conclusion that
the revolution of the earth around the sun takes
the form of an ellipse rather than a circle, the
sun being stationed at one of the foci of the ellipse.

To picture this ellipse, we shall ask the reader
to stick two pins a short distance apart into a
piece of cardboard, and to place over the pins a
loop of string. With the point of a pencil draw
the loop taut. As the pencil moves around the
two pins the curve so produced will be an ellipse.
The positions of the two pins represent the two
foci.

Kepler's observation of the elliptical rotation
of the planets was the first of three laws, quanti-
tatively expressed, which paved the way for
Newton's law. Why did the planets move in
just this way? Kepler tried to answer this
also, but failed. It remained for Newton to
supply the answer to this question.
. Newton9 s Law of Gravitation. The Great Plague
of 1666 drove Newton from Cambridge to his
home in Lincolnshire. There, according to the

From Newton to Einstein

celebrated legend, the philosopher sitting in his
little garden one fine afternoon, fell into a deep
reverie. This was interrupted by the fall of an
apple, and the thinker turned his attention to
the apple and its fall.

It must not be supposed that Newton "dis-
covered" gravity. Apples had been seen to fall
before Newton's time, and the reason for their
return to earth was correctly attributed to this
mysterious force of attraction possessed by the
earth, to which the name "gravity" had been
given. Newton's great triumph consisted in
showing that this "gravity," which was supposed
to be a peculiar property residing in the earth]
was a universal property of matter; that it ap-j'
plied to the moon and the sun as well as to the
earth; that, in fact, the motions of the moon and
the planets could be explained on the basis of
gravitation. But_ his^ supreme^ triumph was
to give, in o^^ublinie^genera^ation, quanti-
tative expression teethe motion^ regulating heav-
enTy^bodies.

Let us follow Newton in his train of thought.
An apple falls from a tree 50 yards high. It
would fall from a tree 500 yards high. It would
fall from the highest mountain top several miles
above sea level. It would probably fall from a

From Newton to Einstein

-

height much above the mountain top. Why not?
Probably the further up you go the less does the
earth attract the apple, but at what distance does
this attraction stop entirely?

The nearest body in space to the earth is the
moon, some 240,000 miles away. Would an
apple reach the earth if thrown from the moon?
But perhaps the moon itself has attractive power?
If so, since the apple would be much nearer the
moon than the earth, the probabilities are that
the apple would never reach the earth.

But hold! The apple is not the only object
that falls to the ground. What is true of the
apple is true of all other bodies — of all matter,
large and small. Now there is the moon itself, a
very large body. Does the earth exert any
gravitational pull on the moon? To be sure, the
moon is many thousands of miles away, but the
moon is a very large body, and perhaps this size
is in some way related to the power of attraction?

But then if the earth attracts the moon, why
does not the moon fall to the earth?

A glance at the accompanying figure will help
to answer this question. We must remember
that the moon is not stationary, but travelling at
tremendous speed — so much so, that it circles
the entire earth every month. Now if the earth

From Newton to Einstein

were absent the path of the moon would be a
straight line, say MB. If, however, the earth
exerts attraction, the moon would be pulled in-

M B

ward. Instead of following the line MB it would
follow the curved path MB'. And again, the
moon having arrived at B', is prevented from fol-
lowing the line E'C, but rather B'C'. So that
the path instead of being a straight line tends
to become curved. From Kepler's researches the
probabilities were that this curve would assume
the shape of an ellipse rather than a circle.

The only reason, then, why the moon does not
fall to the earth is on account of its motion. Were
it to stop moving even for the fraction of a second
it would come straight down to us, and probably
few would live to tell the tale.

10 From Newton to Einstein

Newton reasoned that what keeps the moon
revolving around the earth is the gravitational
pull of the latter. The next important step was
to discover the law regulating this motion.
Here Kepler's observations of the movements of
the planets around the sun was of inestimable
value; for from these Newton deduced the
hypothesis that attraction varies inversely as
the square of the distance. Making use of this
hypothesis, Newton calculated what the attractive
power possessed by the earth must be in order
that the moon may continue in its path. He
next compared this force with the force exerted
by the earth in pulling the apple to the ground,
and found the forces to be identical! "I com-
pared," he writes, "the force necessary to keep
the moon in her orb with the force of gravity
at the surface of the earth, and found them
answer pretty nearly." One and the same force
pulls the moon and pulls the apple — the force
of gravity. Further, the hypothesis that the
force of gravity varies inversely as the square of
the distance had now received experimental con-
firmation.

The next step was perfectly clear. If the
moon's motion is controlled by the earth's gravi-
tational pull, why is it not possible that the earth's

From Newton to Einstein 11

motion, in turn, is controlled by the sun's gravi-
tational pull? that, in fact, not only the earth's
motion, but the motion of all the planets is reg-
ulated by the same means?

Here again Kepler's pioneer work was a foun-
dation comparable to reinforced concrete. Kep-
ler, as we have seen, had shown that the earth
revolves around the sun in the form of an ellipse,
one of the foci of this ellipse being occupied by
the sun. \ Newton now proved that such an ellip-
tic path was possible only if the intensity of the
attractive force between sun and planet varied
inversely as the square of the distance — the very
same relationship that had been applied with
such success in explaining the motion of the moon
around the earth!

Newton showed that the moon, the sun, the
planets — every body in space conformed to this
law. The earth attracts the moon; but so does
the moon the earth. If the moon revolves around
the earth rather than the earth around the moon,
it is because the earth is a much larger body, and
hence its gravitational pull is stronger. The
same is true of the relationship existing between
the earth and the sun.

Further Developments of Newton's Law of
Gravitation. When we speak of the earth attract-

From Newton to Einstein

ing the moon, and the moon the earth, what we
really mean is that every one of the myriad par-
ticles composing the earth attracts every one of
the myriad particles composing the moon, and
vice versa. If in dealing with the attractive
forces existing between a planet and its satellite,
or a planet and the sun, the power exerted by
every one of these myriad particles would have
to be considered separately, then the mathemat-
ical task of computing such forces might well
appear hopeless. Newton was able to present
the problem in a very simple form by pointing
out that in a sphere such as the earth or the moon,
the entire mass might be considered as residing
in the center of the sphere. For purposes of com-
putation, the earth can be considered a particle,
with its entire mass concentrated at the center
of the particle. This viewpoint enabled Newton
to extend his law of inverse squares to the re-
motest bodies in the universe.

If this great law of Newton's found such gen-
eral application beyond our planet, it served an
equally useful purpose in explaining a number of
puzzling features on this planet. The ebb
and flow of the tides was one of these puzzles.
Even in ancient times it had been noticed that a
full moon and a high tide went hand in hand, and

From Newton to Einstein 13

various mysterious powers were attributed to the
satellite and the ocean. . Newton pointed out
that the height of the water was a direct conse-
quence of the attractive power of the moon, and,
to a lesser extent, because further away, of the
sun.

One of his first explanations, however, dealt
with certain irregularities in the moon's motion
around the earth. If the solar system would
consist of the earth and moon alone, then the
path of the moon would be that of an ellipse,
with one of the foci of this ellipse occupied by
the earth. Unfortunately for the simplicity of
the problem, there are other bodies relatively
near in space, particularly that huge body, the
sun. The sun not only exerts its pull on the earth
but also on the moon. However, as the sun is
much further away from the moon than is the
earth, the earth's attraction for its satellite is
much greater, despite the fact that the sun is
much huger and weighs far more than the earth.
The greater pull of the earth in one direction, and
a lesser pull of the sun in another, places the poor
moon between the devil and the deep sea. The
situation gives rise to a complexity of forces, the
net result of which is that the moon's orbit is not
quite that of an ellipse. Newton was able to

14 From Newton to Einstein

account for all the forces that come into play,
and he proved that the actual path of the moon
was a direct consequence of the law of inverse
squares in actual operation.

The "Principia" The law of gravitation,
embodying also laws of motion, which we shall
discuss presently, was first published in New-
ton's immortal "Principia" (1686). A selection
from the preface will disclose the contents of the
booky and, incidentally, the style of the au-
thor: "... We offer this work as mathematical
principles of philosophy; for all the difficulty in
philosophy seems to consist in this — from the
phenomena of motions to investigate the forces of
nature, and then from these forces to demonstrate
the other phenomena; and to this end the gen-
eral propositions in the first and second book are
directed. In the third book we give an example
of this in the explication of the system of the
world; for by the propositions mathematically
demonstrated in the first book, we there derive
from the celestial phenomena the forces of grav-
ity with which bodies tend to the sun and the
several planets. Then, from these forces, by
other propositions which are also mathematical,
we deduce the motions of the planets, the comets,
the moon and the sea. I wish we could derive

From Newton to Einstein 15

the rest of the phenomena of nature by the same
kind of reasoning from mechanical principles;
for I am induced by many reasons to suspect
that they may all depend upon certain forces by
which the particles of bodies, by some causes
hitherto unknown, are either mutually impelled
towards each other, and cohere in regular figures,
or are repelled and recede from each other. ..."

At this point we may state that neither New-
ton, nor any of Newton's successors including
Einstein, have been able to advance even a
plausible theory as to the nature of this gravita-
tional force. We know that this force pulls a
stone to the ground; we know, thanks to Newton,
the laws regulating the motions due to gravity;
but what this force we call gravity really is we
do not know. The mystery is as deep as the
mystery of the origin of life.

"Prof. Einstein," writes Prof. Eddington, "has
sought, and has not reached, any ultimate ex-
planation of its [that is, gravitation] cause. A
certain connection between the gravitational field
and the measurement of space has been postulated,
but this throws light rather on the nature of our
measurements than on gravitation itself. The
relativity theory is indifferent to hypotheses as

16 From Newton to Einstein

to the nature of gravitation, just as it is indiffer-
ent to hypotheses as to the nature of light."

Newton's Laws of Motion. In his Principia
Newton begins with a series of simple definitions
dealing with matter and force, and these are fol-
lowed by his three famous laws of motion. The
nature and amount of the effort required to start
a body moving, and the conditions required to
keep a body in motion, are included in these
laws. The Fundamentals, mass, time and space,
are exhibited in their various relationships. Of
importance to us particularly is that in these
laws, time and space are considered as definite
entities, and as two distinct and widely separated
manifestations. We shall see that in Einstein's
hands a very close relationship between these
two is brought about.

Both Newton and Einstein were led to their
theory of gravitation by profound studies of the
mathematics of motion, but as Newton's concep-
tion of motion differed from Einstein's, and as,
moreover, important discoveries into the nature
of matter and the relationship of motion to mat-
ter were made subsequent to Newton's time, we
need not wonder that the two theories show di-
vergence; that, as we shall see, Newton's is prob-
ably but an approximation of the truth. If we

From Newton to Einstein 17

confine our attention to our own solar system,
the deviation from Newton's law is, as a rule, so
small as to be negligible.

Newton's laws of motion are really axioms,
like the axioms of Euclid: they do not admit of
direct proof; but there is this difference, that the
axioms of Euclid seem more obviously true.
For example, when Euclid informs us that
"things which are equal to the same thing are
equal to one another," we have no hesitation in
accepting this statement, for it seems so self-
evident. When, however, we are told by New-
ton that " the alteration of motion is ever propor-
tional to the motive force impressed," we are at
first somewhat bewildered with the phraseology,
and then, even when that has been mastered, the
readiness with which we respond will probably
depend upon the amount of scientific training we
have received.

"Every body continues in its state of rest or of
uniform motion in a straight line, unless it is
compelled to change that state by forces impressed
thereon." So runs Newton's first law of motion.
A body does not move unless something causes it
to move; to make the body move you must
overcome the inertia of the body. On the other
hand, if a body is moving, it tends to continue

18 From Newton to Einstein

moving, as witness our forward movement when
the train is brought to a standstill. It may be
asked, why does not a bullet continue moving
indefinitely once it has left the barrel of the gun?
Because of the resistance of the air which it has
to overcome; and the path of the bullet is not
straight because gravity acts on it and tends to
pull it downwards.

We have no definite means of proving that a
body once set in motion would continue moving,
for an indefinite time, and along a straight line.
What Newton meant was that a body would
continue moving provided no external force
acted on it; but in actual practise such a con-
dition is unknown.

Newton's first law defines force as that action
necessary to change a state of rest or of uniform
motion, and tells us that force alone changes the
motion of a body. His second law deals with
the relation of the force applied and the resulting
change of motion of the body; that is, it shows us
how force may be measured. "The alteration
of motion is ever proportional to the motive force
impressed, and is made in the direction of the
right line in which that force is impressed."

Newton's third law runs — -"To every action
there is always opposed an equal reaction." The

From Newton to Einstein 19

very fact that you have to use force means that
you have to overcome something of an opposite
nature. The forward pull of a horse towing a
boat equals the backward pull of the tow-rope
connecting boat and horse. "Many people,"
says Prof. Watson, "find a difficulty in accepting
this statement . . . since they think that if the
force exerted by the horse on the rope were not a
little greater than the backward force exerted by
the rope on the horse, the boat would not progress.
In this case we must, however, remember that,
as far as their relative positions are concerned,
the horse and the boat are at rest, and form a
single body, and the action and reaction between
them, due to the tension on the rope, must be
equal and opposite, for otherwise there would be
relative motion, one with respect to the other."

It may well be asked, what bearing have these
laws of Newton on the question of time and space?
Simply this, that to measure force the factors
necessary are the masses of the bodies concerned,
the time involved and the space covered; and
Newton's equations for measuring forces assume
time and space to be quite independent of one
another. As we shall see, this is in striking
contrast to Einstein's view.

Newton's Researches on Light. In 1665, when

20 From Newton to Einstein

-

but 23 years old, Newton invented the binomial
theorem and the infinitesimal calculus, two
phases of pure mathematics which have been the
cause of many a sleepless night to college fresh-
men. Had Newton done nothing else his fame
would have been secure. But we have already
glanced at his law of inverse squares and the law
of gravitation. We now have to turn to some of
Newton's contributions to optics, because here
more than elsewhere we shall find the starting
point to a series of researches which have cul-
minated so brilliantly in the work of Einstein.

Newton turned his attention to optics in 1666
when he proved that the light from the sun, which
appears white to us, is in reality a mixture of all
the colors of the rainbow. This he showed by
placing a prism between the ray of light and a
screen. A spectrum showing all the colors from
red to violet appeared on the screen.

Another notable achievement of his was the
design of a telescope which brought objects to a
sharp focus and prevented the blurring effects
which had occasioned so much annoyance to
Newton and his predecessors in all their astronom-
ical observations.

These and other discoveries of very great in-
terest were brought together in a volume on optics

From Newton to Einstein 21

which Newton published in 1704. Our particular
concern here is to examine the views advanced
by him as to the nature of light.

That the nature of light should have been a
subject for speculation even to the ancients need
not surprise us. If other senses, as touch, for
example, convey impressions of objects, it is
true to say that the sense of sight conveys the
most complete impression. Oiir conception of
the external world is largely based upon the sense
of sight; particularly so when we deal with ob-
jects beyond our reach. In astronomy, there-
fore, a study of the properties of light is
indispensable.*

But what is this light? We open our eyes and
we see; we close our eyes and we fail to see. At
night in a da.'k room we may have our eyes open
and yet we do not see; light, then, must be
absent. Evidently, light does not wholly depend
upon whether our eyes are open or closed. This
much is certain: the eye functions and some-
thing else functions. What is this "something
else"?

Strangely enough, Plato and Aristotle re-
garded light as a property of the eye and the eye

* See Note 1 at the end of the volume.

From Newton to Einstein

alone. Out of the eye tentacles were shot which
intercepted the object and so illuminated it.
From what has already been said, such a view
seems highly unlikely. Far more consistent
with their philosophy in other directions would
have been the theory that light has its source in
the object and not in the eye, and travels from
object to eye rather than the reverse. How little
substance the Aristotelian contribution possesses
is immediately seen when we refer to the art of
photography. Here light rays produce effects
which are independent of any property of the
eye. The blind man may click the camera and
produce the impression on the plate.

Newton, of course, could have fallen into no
such error as did Plato and Aristotle. The
source of light to him was the luminous body.
Such a body had the power of emitting minute
particles at great speed, and these when coming in
contact with the retina produce the sensation of
sight.

This emission or corpuscular theory of Newton's
was combated very strongly by his illustrious
Dutch contemporary, Huyghens, who maintained
that light was a wave phenomenon, the dis-
turbance starting at the luminous body and

From Newton to Einstein 23

spreading out in all directions. The wave mo-
tions of the sea offer a certain analogy.

Newton's strongest objection to Huyghens'
wave theory was that it seemed to offer no satis-
factory explanation as to why light travelled in
straight lines. He says: "To me the funda-
mental supposition itself seems impossible, namely
that the waves or vibrations of any fluid can,
like the rays of light, be propagated in straight
lines, without a continual and very extravagant
bending and spreading every way into the
quiescent medium, where they are terminated by
it. I mistake if there be not both experiment
and demonstration to the contrary."

In the corpuscular theory the particles emitted
by the luminous body were supposed to travel in
straight lines. In empty space the particles
travelled in straight lines and spread in all
directions. To explain how light could traverse
some types of matter — liquids, for example —
Newton supposed tEat .> these light particles
travelled in the spaces [between the molecules
of the liquid.

Newton's objection to the wave theory was not
answered very convincingly by Huyghens. To-
day we know that light waves of high frequency
tend to travel in straight lines, but may be pre-

From Newton to Einstein

-

vented from doing so by gravitational forces of
bodies near its path. But this is Einstein's
discovery.

A very famous experiment by Foucault in 1853
proved beyond the shadow of a doubt that
Newton's corpuscular theory was untenable.
According to Newton's theory, the velocity
of light must be greater in a denser medium
(such as water) than in a lighter one (such as
air). According to the wave theory the reverse
is true. Foucault showed that light does travel
more slowly in water than in air. The facts
were against Newton and in favor of Huyghens;
and where facts and theory clash there is but
one thing to do: discard the theory.

Some Facts about Newton. Newton was a
Cambridge man, and Newton made Cambridge
famous as a mathematical center. Since New-
ton's day Cambridge has boasted of a Clerk Max-
well and a Rayleigh, and her Larmor, her J. J.
Thomson and her Rutherford are still with us.
Newton entered Trinity College when he was 18
and soon threw himself into higher mathematics.
In 1669, when but 27 years old, he became
professor of mathematics at Cambridge, and
later represented that seat of learning in Parlia-
ment. When his friend Montague became Chan-

From Newton to Einstein 25

cellor of the Exchequer, Newton was offered, and
accepted, the lucrative position of Master of the
Mint. As president of the Royal Society Newton
was occasionally brought in contact with Queen
Anne. She held Newton in high esteem, and in
1705 she conferred the honor of knighthood on
him. He died in 1727.

"I do not know," wrote Newton, "what I may
appear to the world, but, to myself, I seem to
have been only like a boy playing on the sea-
shore, and directing myself in now and then
finding a smoother pebble or a prettier shell than
ordinary, whilst the great ocean of truth lay all
undiscovered before me."

Such was the modesty of one whom many
regard as the greatest intellect of all ages.

REFERENCES

An excellent account of Newton may be found
in Sir R. S. Ball's Great Astronomers (Sir Isaac
Pitman and Sons, Ltd., London). Sedgewick
and Tyler's A Short History of Science (Mac-
millan, 1918) and Cajori's A History of Mathe-
matics (Macmillan, 1917) may also be con-
sulted to advantage. The standard biography is
that by Brewster.

II

THE ETHER AND ITS CONSEQUENCES

JJUYGHENS' wave theory of light, now
so generally accepted, loses its entire
significance if a medium for the
propagation of these waves is left out
of consideration. This medium we call the ether.*
Huyghens' reasoning may be illustrated in some
such way as this : If a body moves a force pushes
or pulls it. That force itself is exemplified in
some kind of matter — say a horse. The horse
in pulling a cart is attached to the cart. The
horse in pulling a boat may not be attached to
the boat directly but to a rope, which in turn is
attached to the boat. In common cases where
one piece of matter affects another, there is some
direct contact, some go-between.

But cases are known where matter affects
matter without affording us any evidence of con-
tact. Take the case of a magnet's attraction for a
piece of iron. Where is the rope that pulls the
iron towards the magnet? Perhaps you think
the attraction due to the air in between the mag-

* See Note 2.

27

28 From Newton to Einstein

net and iron? But removing the air does not
stop the attraction. Yet how can we conceive
of the iron being drawn to the magnet unless there
is some go-between? some medium not readily
perceptible to the senses perhaps, and therefore
not strictly a form of matter?

If we can but picture some such medium we can
imagine our magnet giving rise to vibrations in
this medium which are carried to the iron. The
magnet may give rise to a disturbance in that
portion of the medium nearest to it; then this
portion hands over the disturbance to its neigh-
bor, the next portion of the medium; and so on,
until the disturbance reaches the iron. You
see, we are satisfying our sense-perception by
arguing in favor of action by actual contact
rather than some vague action at a distance;
the go-between instead of being a rope is the
medium called the ether.

Foucault's experiment completely shattered the
corpuscular theory of light, and for want of any
other more plausible alternative, we are thrown
back on Huyghens' wave theory. It will presently
appear that this wave theory has elements in it
which make it an excellent alternative. In the
meantime, if light is to be considered as a wave
motion, then the query immediately arises, what

From Newton to Einstein 29

is the medium through which these waves are
propagated? If water is the medium for the
waves of the sea, what is the medium for the
waves of light? Again we answer, the medium
is the ether.

What Is This "Ether"? Balloonists find con-
ditions more and more uncomfortable the higher
they ascend, for the density of the air (and there-
fore the amount of oxygen in a given volume of
air) becomes less and less. Meteorologists have
calculated that traces of the air we breathe may
reach a height of some 200 miles. But what is
beyond? Nothing but the ether, it is claimed.
Light from the sun and stars reaches us via the
ether.

But what is this ether? We cannot handle it.
We cannot see it. It fails to fall within the scope
of any of our senses, for every attempt to show its
presence has failed. It is spirit-like in the pop-
ular sense. It is Lodge's medium for the souls
of the departed.

Helmholtz and Kelvin tried to arrive at some
properties of this hypothetical substance from a
careful study of the manner in which waves were
propagated through this ether. If, as the wave
theory teaches us, the ether can be set in motion,
then according to laws of mechanics, the ether

30 From Newton to Einstein

has mass. If so it is smaller in amount than
anything which can be detected with our most
accurate balance. Further — and this is a diffi-
culty not easily explained — if this ether has any
mass, why does it offer no detectable resistance
to the velocity of the planets in it? Why is not
the velocity of the planets reduced in time, just
as the velocity of a rifle bullet decreases owing
to the resistance of the air?

Lodge, in arguing in favor of an ether, holds
that its presence cannot be detected because it
pervades all space and all matter. His favorite
analogy is to point out the extreme unlikelihood
of a deep-sea fish discovering the presence of the
water with which it is surrounded on all sides; —
all of which tells us nothing about the ether, but
does try to tell us why we cannot detect it.*

In short, answering the query at the head of
this paragraph, we may say that we do not know.

Waves Set up in This Ether. The waves are
not all of the same length. Those that produce
the sensation of sight are not the smallest waves
known, yet their length is so small that it would
take anywhere from one to two million of them to
cover a yard. Curiously enough, our eye is not
sensitive to wave lengths beyond either side of
these limits; yet much smaller, and much larger

* See Note 3.

From Newton to Einstein 81

waves are known. The smallest are the famous
X-rays, which are scarcely one ten-thousandth
the size of light waves. Waves which have a
powerful chemical action — those which act on a
photographic plate, for example — are longer
than X-rays, yet smaller than light waves.
Waves larger than light waves are those which
produce the sensation of heat, and those used in
wireless telegraphy. The latter may reach the
enormous length of 5,000 yards. X-ray, actinic,
or chemically active ray, light ray, heat ray,
wireless ray — they differ in size, yet they all have
this in common: they travel with the same speed
(186,000 miles per second).

The Electromagnetic Theory of Light. Power-
ful support to the conception that space is per-
vaded by ether was given when Maxwell dis-
covered light to be an electro-magnetic phe-
nomenon. From purely theoretical considera-
tions this gifted English physicist was led to the
view that waves could be set up as a result of
electrical disturbances. He proved that such
waves would travel with the same velocity as light
waves. As air is not needed to transmit elec-
trical phenomena — for you can pump all air out
of a system and produce a vacuum, and electrical
phenomena will continue — Maxwell was forced to

32 From Newton to Einstein

the conclusion that the waves set up by electrical
disturbances and transmitted with the same veloc-
ity as light, were enabled to do so with the help
of the same medium as light, namely, the ether.

It was now but a step for Maxwell to formulate
the theory that light itself is nothing but an elec-
trical phenomenon, the sensation of light being
due to the passage of electric waves through the
ether. This theory met with considerable oppo-
sition at first. Physicists had been brought up
in a school which had taught that light and elec-
tricity were two entirely unrelated phenomena,
and it was difficult for them to loosen the shackles
that bound them to the older school. But two
startling discoveries helped to fasten attention
upon Maxwell's theory. One was an experi-
mental confirmation of Maxwell's theoretical
deduction. Hertz, a pupil of Helmholtz, showed
how the discharge from a Ley den jar set up
oscillations, which in turn gave rise to waves in
the ether, comparable, in so far as velocity is
concerned, to light waves, but differing from the
latter in wave length, the Hertzian waves being
much longer. At a later date these waves were
further investigated by Marconi, with the result
that wireless messages soon began to be flashed
from one place to another.

From Newton to Einstein 33

Just as there is a close connection between light
and electricity, so there is between light and
magnetism. The first to point out such a rela-
tionship was the illustrious Michael Faraday, but
we owe to Zeeman the most extensive investiga-
tions in this field.

If we throw some common salt into a flame, and,
with the help of a spectroscope, examine the
spectrum produced, we are struck by two bright
lines which stand out very prominently. These
lines, yellow in color, are known as the D-lines
and serve to identify even minute traces of sodium.
What is true of sodium is true of other elements:
they all produce very characteristic spectra.
Now Zeeman found that if the flame is placed
between a powerful magnet, and then some com-
mon salt thrown into the flame, the two yellow
lines give place to ten yellow lines. Such is one of
the results of the effect of a magnetic field on
light.

The Electron. The "Zeeman effect" led to
several theories regarding its nature. The most
successful of these was one proposed by Larmor
and more fully treated by Lorentz. It has
already been pointed out that the only difference
between wireless and light waves is that the
former are much "longer," and, we may now add,

34 From Newton to Einstein

their vibrations are much slower. Light and
wireless waves bear a relationship to one another
comparable to the relationship born by high and
low-pitched sounds. To produce wireless waves
we allow a charge of electricity to oscillate to and
fro. These oscillations, or oscillating charges,
are the cause of such waves. What charges give
rise to light waves? Lorentz, from a study of the
Zeeman effect, ascribed them to minute particles
of matter, smaller than the chemical atom, to
which the name "electron" was given.

The unit of electricity is the electron. Elec-
trons in motion give rise to electricity, and elec-
trons in vibration, to light. The Zeeman effect
gave Lorentz enough data to calculate the mass
of such electrons. He then showed that these
electrons in a magnetic field would be disturbed
by precisely the amount to which Zeeman's obser-
vations pointed. In other words, the assumption
of the electron fitted in most admirably with
Zeeman's experiments on magnetism and light.

In the meantime, a study of the discharge of
electricity through gases, and, later, the discovery
of radium, led, among other things, to a study of
beta or cathode rays — negatively charged par-
ticles of electricity. Through a series of strik-
ingly original experiments J. J. Thomson ascer-

From Newton to Einstein 35

tained the mass of such particles or corpuscles,
and then the very striking fact was brought out
that Thomson's corpuscle weighed the same as
Lorentz's electron. The electron was not merely
the unit of electricity but the smallest particle
of matter.

The Nature of Matter. All matter is made up
of some eighty-odd elements. Oxygen, copper,
lead are examples of such elements. Each element
in turn consists of an innumerable number of
atoms, of a size so small, that 300 million of them
could be placed alongside of one another without
their total length exceeding one inch.

John Dalton more than a hundred years ago
postulated a theory, now known as the atomic
theory, to explain one of the fundamental laws in
chemistry. This theory started out with an old '
Greek assumption that matter cannot be divided
indefinitely, but that, by continued subdivision,
a point would be reached beyond which no further
breaking up would be possible. The particles
at this stage Dalton called atoms.

Dalton's atomic hypothesis became one of the
pillars upon which the whole superstructure of
chemistry rested, and this because it explained a
number of perplexing difficulties so much more
satisfactorily than any other hypothesis.

.

36 From Newton to Einstein

For nearly a century Dalton stood as firm as a
rock. But early in the nineties some epoch-
making experiments on the discharge of elec-
tricity through gases were begun by a group of
physicists, particularly Crookes, Rutherford, Le-
nard, Roentgen, Becquerel, and, above all, J. J.
Thomson, which pointed very clearly to the fact
that the atoms are not the smallest particles of
matter at all; that, in fact, they could be broken
up into electrons, of a diameter one one-hundred-
thousandth that of an atom.

It remained for the illustrious Madame Curie
to confirm this beyond all doubt by her isolation
of radium. Here, as Madame Curie showed, was
an element whose atoms were actually breaking
up under one's very eyes, so to speak.

So far have we advanced since Dalton's day,
— -that,Dalton's unit, the atom, is now pictured as a
complex particle patterned after our solar system,
with a nucleus of positive electricity in the center,
and particles of negative electricity, or electrons,
surrounding the nucleus.

All this leads to one inevitable conclusion:
matter is electrical in nature. But now if matter
and light have the same origin, and matter is sub-
ject to gravitation, why not light also? So rea-
soned Einstein.

From Newton to Einstein 37

Summary. Newton's studies of matter in
motion led to his theory of gravitation, and, in-
cidentally, to his conception of time and space
as definite entities. As we shall see, Einstein in
his theory of gravitation based it upon discoveries
belonging to the post-Newtonian period. One of
these is Minkowski's theory of time and space as
one and inseparable. This theory we shall dis-
cuss at some length in the next chapter.

Other important discoveries which led up to
Einstein's work are the researches which cul-
minated in the electron theory of matter. The
origin of this theory may be traced to studies
dealing with the nature of light.

Here again Newton appears as a pioneer. New-
ton's corpuscular theory, however, proved wholly
untenable when Foucault showed that the velocity
of light in water is less than in air, which is the
very reverse of what the corpuscular theory de-
mands, but which does agree with Huyghens' wave
theory.

But Huyghens' wave theory postulated some
medium in which the waves can act. To this
medium the name "ether" was given. However,
all attempts to show the presence of such an ether
failed. Naturally enough, some began to doubt
the existence of an ether altogether.

38 From Newton to Einstein

Huyghens' wave theory received a new lease of
life with Maxwell's discovery that light is an
electromagnetic phenomenon; that the waves
set up by a source of light were comparable to
waves set up by an electrical disturbance.

Zeeman next showed that magnetism was also,
closely related to light.

A study of Zeeman's experiments led Lorentz
to the conclusion that electrical phenomena are
due to the motion of charged particles called
"electrons," and that the vibrations of these elec-
trons give rise to light.

The conception of the electron as the very fun-
damental of matter was arrived at in an entirely
different way: from studies dealing with the dis-
charge of electricity through gases and the
breaking up of the atoms of radium.

If matter and light have the same origin, and if
matter is subject to gravitation, why not light
also?

REFERENCES

For the general subject of light the reader must
be referred to a rather technical work, but one of
the best in the English language: Edwin Edser,
Light for Students (Macmillan, 1907).

The nature of matter and electricity is excel-

From Newton to Einstein 39

lently discussed in several books of a popular
variety. The very best and most complete of
its kind that has come to the author's attention
is Comstock and Troland's The Nature of Matter
and Electricity (D. Van Nostrand Co., 1919). Two
other very readable books are Soddy's Matter
and Energy (Henry Holt and Co.) and Crehore's
The Mystery of Matter and Energy (D. Van Nos-
trand Co., 1917).

C. Wide World

ALBERT EINSTEIN

Ill

EINSTEIN

J HIS is the most important result
obtained in connection with the
theory of gravitation since Newton's
day. Einstein's reasoning is the
result of one of the highest achievements of
human thought."

These words were uttered by Sir J. J. Thomson,
the president of the Royal Society, at a meeting
of that body held on November 6, 1919, to discuss
the results of the Eclipse Expedition.

Einstein another Newton — and this from the
lips of J. J. Thomson, England's most illustrious
physicist! If ever man weighed words carefully
it is this Cambridge professor, whose own re-
searches have assured him immortality for all
time.

What has this Albert Einstein done to merit
such extraordinary praise? With the world in
turmoil, with classes and races in a death struggle,
with millions suffering and starving, why do we
find time to turn our attention to this Jew?
41

42 From Newton to Einstein

His ideas have no bearing on Europe's calamity.
They will not add one bushel of wheat to starving
populations.

The answer is not hard to find. Men come and
men go, but the mystery of the universe remains.
It is Einstein's glory to have given us a deeper
insight into the universe. Our scientists are
Huxley's agnostics: they do not deny activities
beyond our planet; they merely center their
attention on the knowable on this earth. Our
philosophers, on the other hand, go far afield.
Some of them soar so high that, like one poet's
opinion of Shelley, the bubble bursts. Einstein,
using the tools of the scientist — the experimental-
ist— builded a skyscraper which ultimately
reached the philosophical school. His r61e is the
r61e of alcohol in causing water and ether (the
anaesthetic) to mix. Ether and water will mix no
better than oil and water, without the presence of
alcohol; in its presence a uniform mixture is
obtained.

The Object of the Eclipse Expedition. Einstein
prophesied that a ray of light passing near the
sun would be pulled out of its course, due to the
action of gravity. He went even further. He
predicted how much out of its course<the ray
would be deflected. This prediction was based

From Newton to Einstein 43

on a theory of gravitation which Einstein had
developed in great mathematical detail. The
object of the British Eclipse Expedition was either
to prove or disprove Einstein's assumption.

The Result of the Expedition. Einstein's pro-
phecy was fulfilled almost to the letter.

The Significance of the Result. Since Einstein's
theory of gravitation is intimately associated with
certain revolutionary ideas concerning time and
space, and, therefore, with Fundamentals of the
Universe, the net result of the expedition was to
strengthen our belief in the validity of his new
view of the universe.

It is our intention in the following pages to dis-
cuss the expedition and the larger aspects of
Einstein's theory that follow from it. But before
we do so we must have a clear idea of our solar
system.

Our Solar System. In the center of our system
is the sun, a flaming mass of fire, much bigger than
our own earth, and very, very far away. The
sun has its family of eight planets — of which the
earth is one — which travel around the sun; and
around some of the planets there travel satel-
lites, or moons. The earth has such a satellite,
the moon.

Now we have good reasons for believing that

44 From Newton to Einstein

every star which twinkles in the sky is a sun com-
parable to our own, having also its own planets
and its own moons. These stars, or suns, are so
much further away from us than our own sun,
that but a speck of their light reaches us, and
then only at night, when, as the poets would say,
our sun has gone to its resting place.

The distances between bodies in the solar sys-
tem is so immense that, like the number of dollars
spent in the Great War, the number of miles con-
veys little, or no impression. But picture your-
self in an express train going at the average rate
of 30 miles an hour. If you start from New York
and travel continuously you would reach San
Francisco in 4 days. If you could continue your
journey around the earth at the same rate you
would complete it in 35 days. If now you could
travel into space and to the moon, still with the
same velocity, you would reach it in 350 days.
Having reached the moon, you could circumscribe
it with the same express train in 8 days, as com-
pared to the 35 days it would take you to circum-
scribe the earth. If instead of travelling to the
moon you would book your passage for the sun
you, or rather your descendants, would get there
in 350 years, and it would then take them 10
additional years to travel around the sun.

From Newton to Einstein 45

Immense as these distances are, they are small
as compared to the distances that separate us
from the stars. It takes light which, instead of
travelling 30 miles an hour, travels 186,000 miles
a second, about 8 minutes to get to us from the
sun, and a little over 4 years to reach us from the
nearest star. The light from some of the other
stars do not reach us for several hundred years.

The Eclipse of the Sun. Now to return to an
infinitesimal part of the universe — our solar
system. We have seen that the earth travels
around the sun, and the moon around the earth.
At some time in the course of these revolutions
the moon must come directly between the earth
and the sun. Then we get the eclipse of the sun.
As the moon is smaller than the earth, only a
portion of the earth's surface will be cut off from
the sun's rays. That portion which is so cut off
suffers a total eclipse. This explains why the
eclipse of May, 1919, which was a total one for
Brazil, was but a partial one for us.

Einstein9 s Assertion Re-stated. Einstein claimed
that a ray of light from one of the stars, if passing
near enough to the surface of the sun, would be
appreciably deflected from its course; and he
calculated the exact amount of this deflection.
To begin with, why should Einstein suppose that

46 From Newton to Einstein

the path of a ray of light would be affected by the
sun?

Newton's law of gravitation made it clear that
bodies which have mass attract one another. If
light has mass — and very recent work tends to
show that it has — there is no reason why light
should not be attracted by the sun, or any other
planetary body. The question that agitated
scientists was not so much whether a ray of light
would be deviated from its path, but to what
extent this deviation would take place. Would
Einstein's figures be confirmed?

Of the bodies within our solar system the sun
is by far the largest, and therefore it would exert
a far greater pull than any of the planets on light
rays coming from the stars. Under ordinary
conditions, however* the sun itself shines with such
brilliancy, that objects around it, including rays
of light passing near its surface, are wholly
dimmed. Hence the necessity of putting our
theory to the test only when the moon covers up
the sun — when there is a total eclipse of the sun.

A Graphical Representation. Imagine a star A>
so selected that as its light comes to us the ray
just grazes the sun. If the path of the ray is
straight — if the sun has no influence on it — then
the path can be represented by the line AB. If,

From Newton to Einstein

47

however, the sun does exert a gravitational pull,
then its real path will be AB', and to an observer
on the earth the star will have appeared to shift
from A to A'.

What the Eclipse Expedition Set Out to Do.
Photographs of stars around the sun were to be
taken during the eclipse, and these photographs
compared with others of the same region taken at
night, with the sun absent. Any apparent shift-
ing of the stars could be determined by measuring
the distances between the stars as shown on the
photographic plates.

Three Possibilities Anticipated. According to
Newton's assumption, light consists of corpuscles,
or minute particles, emitted from the source of
light. If this be true these particles, having
mass, should be affected by the gravitational pull
of the sun. If we apply Newton's theory of
gravitation and make use of his formula, it can
be shown that such a gravitational pull would dis-

48 From* Newton to 'Einstein

place the ray of light by an average amount equal
to 0.75 (seconds of angular distance.)* .On the
other hand, where lig^t is regarded as waves set
in motion in the "ether" of space (the wave
theory of light), and wjiere weight is denied light
altogether, no deviation need be expected. Finaljfo
there is a third alternative: Einstein's. \Liglft,
says Einstein, has mass, and therefore pro^ajaljr
weight. Mass is the matter light contains;
weight represents pull by gravity. Light rays
will be attracted by the sun, but according to
Einstein's theory of gravitation the sun's gravi-
tational pull will displace the rays by an average
amount equal to 1.75 (seconds of angular dis-
tance).

The Expeditions. That science is highly inter-
national, despite many recent examples to the
contrary, is evidenced by this British Eclipse
Expedition. Here was a theory propounded by
one who had accepted a chair of physics in the
university of Berlin, and across the English Chan-
nel were Germany's mortal enemies making elab-
orate preparations to test the validity of the
Berlin professor's theory.

* A circle — in our case the horizon — is measured by divid-
ing the circumference into 360 parts; each part is called a
degree. Each degree is divided into 60 minutes, and each
minute into 60 seconds.

From Newton to Einstein 49

The British Astronomical Society began to plan
the eclipse expedition even before the outbreak
of the Great War. During the years that fol-
lowed, despite the destinies of nations which hung
on threads from day to day, despite the darkest
hours in the history of the British people, our
English astronomers continued to give attention
to the details of the proposed expedition. When
the day of the eclipse came all was in readiness.

One expedition under Dr. Crommelin was sent
to Sobral, Brazil; another, under Prof. Edding-
ton, to Principe, an island off the west coast of
Africa. In both these places a total eclipse was
anticipated.

The eclipse occurred on May 29, 1919. It
lasted for six to eight minutes. Some 15 photo-
graphs, with an average exposure of five to six
seconds, were taken. Two months later another
series of photographs of the same region were
taken, but this time the sun was no longer in the
midst of these stars.

The photographs were brought to the famous
Greenwich Observatory, near London, and the
astronomers and mathematicians began their
laborious measurements and calculations.

On November 6, at the meeting of the Royal
Society, the result was announced. The Sobral

50 From Newton to Einstein

expedition reported 1.98; the Principe expedition
1.62. The aver age was 1.8. Einstein had predicted
1.75, Newton might have predicted 0.75, and
the orthodox scientists would have predicted 0.
There could now no longer be any question as to
which of the three theories rested on a sure foun-
dation. To quote Sir Frank Dyson, the Astron-
omer Royal: "After a careful study of the plates
I am prepared to say that there can be no doubt
that they confirm Einstein's prediction. A very
definite result has been obtained that light is
deflected in accordance with Einstein's law of
gravitation." *

Where Did Einstein Get His Idea of Gravitation?
In 1905 Einstein published the first of a series of
papers supporting and extending a theory of time
and space to which the name "the theory of
relativity" had been given. These views as
expounded by Einstein came into direct conflict
with Newton's ideas of time and space, and also
with Newton's law of gravitation. Since Ein-
stein Had more faith in his theory of relativity
than in Newton's theory of gravitation, Einstein
so changed the latter as to make it harmonize with
the former. More will be said on this subject.

* See page 113.

From Newton to Einstein 51

Let not the reader misunderstand. Newton
was not wholly in the wrong; he was only ap-
proximately right. With the knowledge existing
in Newton's day Newton could have done no
more than he did; no mortal could have done
more. But since Newton's day physics — and
science in general — has advanced in great strides,
and Einstein can interpret present-day knowledge
in the same masterful fashion that Newton could
in his day. With more facts to build upon, Ein-
stein's law of gravitation is more universal than
Newton's; it really includes Newton's.

But now we must turn our attention very briefly
to the theory of relativity — the theory that led
up to Einstein's law of gravitation.

The Theory of Relativity. The story goes that
Einstein was led to his ideas by watching a man
fall from a roof. This story bears a striking
similarity to Newton and the apple. Perhaps
one is as true as the other.*

However that may be, the principle of rela-
tivity is as old as philosophical thought, for it
denies the possibility of measuring absolute time,
or absolute space. All things are relative. We
say that it takes a "long time" to get from New
York to Albany; long as compared to what?

* See Note 4.

52 From Newton to Einstein

long, perhaps, as compared to the time it takes to
go from New York City to Brooklyn. We say
the White House is "large"; large when compared
to a room in an apartment. But we can just as
well reverse our ideas of time and distance. The
time it takes to go from New York to Albany is
"short" when compared to the time it takes to
go from New York to San Francisco. The size of
the White House is "small" when compared to
the size of the city of Washington.

Let us take another illustration. Every time
the earth turns on its axis we mark down as a day.
With this as a basis, we say that it takes a little
over 365 days for the earth to complete its revo-
lution around the sun, and our 365 days we call a
year. But now consider some of our other
planets. With our time as a basis, it takes Jupi-
ter or Saturn 10 hours to turn on its axis, as com-
pared to the 24 hours it takes the earth to turn.
Saturn's day is less than one-half our day, and
our day is more than twice Saturn's — that is,
according to the calculations of the inhabitants
of the earth. Mercury completes her circuit
around the sun in 88 days; Neptune, in 164
years. Mercury's year is but one-fourth ours,
Neptune's, 164 times ours. And observers at
Mercury and Neptune would regard us from

From Newton to Einstein 53

their standard of time, which differs from our
standard.

You may say, why not take our standard of
time as the standard, and measure everything by
it? But why should you? Such a selection
would be quite arbitrary. It would not be
based on anything absolute, but would merely
depend on our velocity around the sun.

These ideas are old enough in metaphysics.
Einstein's improvement of them consists not
merely in speculating about them, but in giving
them mathematical form.

The Origin of the Theory of Relativity. A train
moves with reference to the earth. The earth
moves with reference to the sun. We say the
sun is stationary and the earth moves around
the sun. But how do we know that the sun itself
does not move with reference to some other body?
How do we know that our planetary system, and
the stars, and the cosmos as a whole is not in
motion?

There is no way of answering such a question
unless we could get a point of reference which is
fixed — fixed absolutely in space.

We have already alluded to our view of the
nature of light, known as the wave theory of
light. This theory postulates the existence of

54 From Newton to Einstein

an all-pervading "ether" in space. Light sets up
wave disturbances in this ether, and is thus
propagated. If the ocean were the ether, the
waves of the ocean would compare with the waves
set up by the ether.

But what is this ether? It cannot be seen. It
defies weight. It permeates all space. It per-
meates all matter. So say the exponents of
this ether. To the layman this sounds very
much like another name for the Deity. To Sir
Oliver Lodge it represents the spirits of the de-
parted.

To us, of importance is the conception that this
ether is absolutely stationary. Such a concep-
tion is logical if the various developments in
optics and electricity are considered. But if
absolutely stationary, then the ether is the long-
sought-for point of reference, the guide to deter-
mine the motion of all bodies in the universe.

The Famous Experiment Performed by Prof.
Michelson. If there is an ether, and a stationary
ether, and if the earth moves with reference to
this ether, the earth, in moving, must set up
ether "currents" — just as when a train moves it
sets up air currents. So reasoned Michelson, a
young Annapolis graduate at the time. And
forthwith he devised a crucial experiment the

From Newton to Einstein 55

explanation of which we can simplify by the fol-
lowing analogy:

Which is the quicker, to swim up stream a cer-
tain length, say a hundred yards, and back again,
or across stream the same length and back again?
The swimmer will answer that the up-and-down
journey is longer.*

Our river is the ether. The earth, if moving in
this ether, will set up an ether stream, the up
stream being parallel to the earth's motion. Now
suppose we send a beam of light a certain distance
up this ether stream and back, and note the time;
and then turn the beam of light at right angles
and send it an equal distance across the stream
and back, and note the time. How will the time
taken for light to travel in these two directions
compare? Reasoning by analogy, the up-and-
down stream should take longer.

Michelson's results did not accord with analogy.
No difference in time could be detected between
the beam of light travelling up-and-down, and
across-and-back.

But this was contrary to all reason if the pos-
tulate of an ether was sound. Must we then
revise our ideas of an ether? Perhaps after all
there is no ether.

* See Note 5.

56 From Newton to Einstein

But if no ether, how are we to explain the
propagation of light in space, and various elec-
trical phenomena connected with it, such as the
Hertzian, or wireless waves?

There was another alternative, one suggested
by Larmor in England and Lorentz in Holland, —
that matter is contracted in the direction of its
motion through the ether current. To say that
bodies are actually shortened in the direction of
their motion — by an amount which increases as
the velocity of these bodies approaches that of
light — is so revolutionary an idea that Larmor
and Lorentz would hardly have adopted such a
viewpoint but for the fact that recent investiga-
tions into the nature of matter gave basis for such
belief.

Matter, it has been shown, is electrical in na-
ture. The forces which hold the particles to-
gether are electrical. Lorentz showed that math-
ematical formulas for electrical forces could be
developed which would inevitably lead to the
view that material bodies contract in the direc-
tion of their motion.*

"But this is ridiculous," you say; "if I am
shorter in one direction than in another I would
notice it." You would if some things were
shortened and others were not. But if all things

* See Note 6.

From Newton to Einstein 57

pointing in a certain direction are shortened to
an equal extent, how are you going to notice it?
Will you apply the yard stick? That has been
shortened. Will you pass judgment with the
help of your eyes? But your retina has also
contracted. In brief, if all things contract to
the same amount it is as if there were no con-
traction at all.

Lorentz's Plausible Explanation Really Deepens
the Mystery. The startling ideas just outlined
have opened up several new vistas, but they have
left unanswered the two problems we set out to
solve: whether there is an ether, and if so,
what is the velocity of the earth in reference to
this ether? Lorentz maintains that there is an
ether, but the velocities of bodies relative to it
must forever remain a mystery. As you change
your position your distances change; you change;
everything about you changes accordingly; and
all basis for comparison is lost. Nature has
entered into a conspiracy to keep you ignorant.

Einstein Comes upon the Scene. Einstein
starts with the assumption that there is no pos-
sible way of identifying this ether. Suppose we
ignore the ether altogether, what then?*

If we do ignore the ether we no longer have

* See Note 7.

58 From Newton to Einstein

any absolute point of reference; for if the ether
is considered stationary the velocity of all bodies
within the ether may be referred to it; any point
in space may be considered a fixed point. If,
however, there is no ether, or if we are to ignore
it, how are we to get the velocity of bodies in
space?

The Principle of Relativity. If we are to
believe in the "causal relationship between only
such things as lie within the realm of observation,"
then observation teaches us that bodies move only
relative to one another, and that the idea of
absolute motion of a body in space is meaning-
less. Einstein, therefore, postulates that there
is no such thing as absolute motion, and that all
we can discuss is the relative motion of one
body with respect to another. This is just as
logical a deduction from Michelson's experiment
as the attempt to explain Michelson's anomalous
results in the light of an all-pervading ether.

Consider for a moment Newton's scheme. This
great pioneer pictured an absolute standard of
position in space relative to which all velocities
are measured. Velocities were measured by
noting the distance covered and dividing the result
by the time taken to cover the distance. Space
was a definite entity; and so was time. "Time,"

From Newton to Einstein 59

said Newton, "flows evenly on," independent of
aught else. To Newton time and space were
entirely different, in no way to be confounded.

Just as Newton conceived of absolute space, so
he conceived of absolute time. From the latter
standard of reference the idea of a "simultaneity
of events" at different places arose. But now if
there is no standard of reference, if the ether does
not exist or does not function, if two points A and
B cannot be referred to a third, and fixed point C,
how can we talk of "simultaneity of events" at
A and B? *

In fact, Einstein shows that if all you can speak
about is relative motion, then one event which

H

B <iA

takes say one minute on one planet would not
take one minute on another. For consider two
bodies in space, say the planets Venus and the
earth, with an observer B on Venus and another
A on the earth. B notes the time taken for a
ray of light to travel from B to the distance M .
* See Note 8.

60 From Newton to Einstein

on the earth has means of observing the same
event. B records one minute. A is puzzled,
for his watch records a little more than one
minute. What is the explanation? Granting
that the two clocks register the same time to
start with, and assuming further Einstein's hy-^
pothesis that the velocity of light is independent of
its source, the difference in time is due to the fact
that the planet Venus moves with reference to
the observer on the earth; so that A in reality
does not measure the path BM and M B, but
BM' and M'B', where BB' represents the dis-
tance Venus itself has moved in the interval.
And if you put yourself in J5's position on Venus
the situation is exactly reversed. All of which is
simply another way of saying that what is a cer-
tain time on one body in space is another time on
another body in space. There is nothing definite
in time.

Prof. Cohen's Illustration. Further bewildering
possibilities are clearly outlined in this apt illus-
tration: "If when you are going away on a long
and continuous journey you write home at regular
intervals, you should not be surprised that with
the best possible mail service your letters will
reach home at progressively longer intervals,
since each letter will have a greater distance to

From Newton to Einstein 61

travel than its predecessor. If you were armed
with instruments to hear the home clock ticking,
you would find that as your distance from home
keeps on increasing, the intervals between the suc-
cessive ticks (that is, its seconds) grow longer, so
that if you travelled with the velocity of sound
the home clock would seem to slow down to a
standstill — you would never hear the next tick.

"Precisely the same is true if you substitute
light rays for sound waves. If with the naked
eye or with a telescope you watch a clock moving
away from you, you will find that its minute hand
takes a longer time to cover its five-minute inter-
vals than does the chronometer in your hand, and
if the clock travelled with the velocity of light
you would forever see the minute hand at pre-
cisely the same point. That which is true of the
clock is, of course, also true of all time intervals
which it measures, so that if you moved away
from the earth with the velocity of light every-
thing on it would appear as still as on a painted
canvas."

Your time has apparently come to a standstill
in one position and is moving in another! All
this seems absurd enough, but it does show that
time alone has little meaning.

Minkowski's Conclusion. The relativity the-

From Newton to Einstein

ory requires that we thoroughly reorganise our
method of measuring time. But this is inti-
mately associated with our method of measuring
space, the distance between two points. As we
proceed we find that space without time has little
meaning, and vice versa. This leads Minkowski
to the conclusion that "time by itself and space
by itself are mere shadows; they are only two
aspects of a single and indivisible manner of co-
ordinating the facts of the physical world." Ein-
stein incorporated this time-space idea in his
theory of relativity.

How We Measure a Point in Space. Suppose
I say to you that the chemical laboratory of
Columbia University faces Broadway; would
that locate the laboratory? Hardly, for any
building along Broadway would face Broadway.
But suppose I add that it is situated at Broadway
and 117th Street, south-east? there could be little
doubt then. But if, further, this laboratory
would occupy but part of the building, say the
third floor; then the situation would be specified
by naming Broadway, 117th Street S. E., third
floor. If Broadway represents length, 117th
Street width, and third floor height, we can see
what is meant when we say that three dimensions
are required to locate a position in space.

From Newton to Einstein 63

The Fourth Dimension. A point on a line may
be located by one dimension; a point on a wall
requires two dimensions; a point in the room, like
the chemical laboratory above ground, needs
three. The layman cannot grasp the meaning
of a fourth dimension; yet the mathematician
does imagine it, and plays with it in mathemat-
ical terms. Minkowski and Einstein picture
time as the fourth dimension. To them time
occupies no more important position than length,
breadth, or thickness, and is as intimately related
to these three as the three are to one another.
H. G. Wells, the novelist, has beautifully caught
this spirit when in his novel, "The Time Ma-
chine," he makes his hero travel backwards and
forwards along time just as a man might go north
or south. When the man with his time machine
goes forward he is in the future; when he goes
backwards he is in the past.

In reality, if we stop to think a minute, there
is no valid reason for the non-existence of a fourth
dimension. If one, two and three dimensions,
why not four — and five and six, for that matter?
Theoretically at least there is no reason why the
limit should be set at three. However, our minds
become sluggish when we attempt to picture
dimensions beyond three; just as an extraordi-

64 From Newton to Einstein

nary effort on our part is needed to follow Einstein
when he "juggles" with space and time.

Our difficulty in imagining four dimensions may
be likened to the difficulty two-dimensioned
beings would experience in imagining us, beings of
the conventional three dimensions. Suppose
these two-dimensional beings were living on the
surface of the earth; what could they see?
They could see nothing below and nothing above
the surface. They would see shifting surfaces
as we walked about, but being sensitive to length
and breadth only, and not to height, they could
gain no notion whatsoever of what we really
look like. It is thus with us when we attempt
to picture four-dimensional space.

Perhaps the analogy of the motion picture may
help us somewhat. As everybody knows, these
motion pictures consist of a series of photographs
which are shown in rapid succession on the screen.
Each photograph by itself conveys a sensation of
space, that is, of three dimensions; but one pho-
tograph rapidly following another conveys the
sensation of space and time — four dimensions.
Space and time are interlinked.

The Time-space Idea Further Developed. We
tave already alluded to the fact that objects in
space moving with different velocities build up

^msc

From Newton to Einstein 65

different time intervals. Thus the velocity of the
star Arcturus, if compared with reference to the
earth, moves at the rate of 200 miles a second.
Its motion through space is different from ours.
Objects which, according to Lorentz, contract
in the direction of their motion to an extent
proportional to their velocity, will contract dif-
ferently on the surface of Arcturus than on the
earth. Our space is not Arcturus' space; neither
is Arcturus' time our time. And what is true
of the discrepancies existing between the space
and time conceptions of the earth and Arcturus is
true of any other two bodies in space moving at
different velocities.

But is there no relationship existing between
the space and time of one body in the universe as
compared to the space and time of another? Can
we not find something which holds good for all
bodies in the universe? We can. We can express
it mathematically. It is the concept of time and
space interlinked; of time as the fourth dimen-
sion, length, breadth and thickness being the
other three; of time as one of four co-ordinates
and at right angles to the other three (a situation
which requires a terrific stretch of the imagina-
tion to visualize) . The four dimensions are suffi-
cient to co-ordinate the time-space relationships

66 From Newton to Einstein

of all bodies in the cosmos, and hence have a
universality which is totally lacking when time
and space are used independently of one another.
The four components of our time-space are up-
and-down, right-and-left, backwards-and-for-
wards, and sooner-and-later.

"Strain" and "Distortion" in Space. The
four-dimensional unit has been given the name
"world-line," for the "world-line" of any particle
in space is in reality a complete history of that
particle as it moves about in space. Particles,
we know, attract one another. If each particle is
represented by a world-line these world-lines will
be deflected from their course owing to such
attraction.

Imagine a bladder representing the universe,
with lines on it representing world-lines. Now
squeeze the bladder. The world-lines are bent
in various directions; they are "distorted."
This illustrates the influence of gravity on these
world-lines; it is the "strain" brought about due
to the force of attraction. The distorted bladder
illustrates even more, for it is a true representa-
tion of the real world.

How Einstein's Conception of Time and Space
Led to a New View of Gravitation. In our con-
ventional language we speak of the sun as exerting

From Newton to Einstein 67

a "force" on the earth. We have seen, however,
that this force brings about a "distortion" or
"strain" in world-lines; or, what amounts to the
same thing, a "distortion" or "strain" of time
and space. The sun's "force," the "force" of
any body in space, is the "force" due to gravity;
and these "forces" may now be treated in terms
of the laws of time and space. "The earth,"
Prof. Eddington tells us, "moves in a curved
orbit, not because the sun exerts any direct pull,
but because the earth is trying to find the short-
est way through a space and time which have
been tangled up by an influence radiating from
the sun." *

At this point Newton's conceptions fail, for
his views and his laws do not include "strains"
in space. Newton's law of gravitation must be
supplanted by one which does include such dis-
tortions. It is Einstein's great glory to have sup-
plied us with this new law.

Einstein's Law of Gravitation. This appears to
be the only law which meets all requirements.
It includes Newton's law, and cannot be distin-
guished from it if our experiments are confined
to the earth and deal with relatively small
velocities. But when we betake ourselves to

* See Note 9.

68 From Newton to Einstein

some orbits in space, with a gravitational pull
much greater than the earth's, and when we deal
with velocities comparable to that of light, the
differences become marked.

Einstein9 s Theory Scores Its First Great Victory.
In the beginning of this chapter we referred to
the elaborate eclipse expedition sent by the Brit-
ish to test the validity of Einstein's new theory
of gravitation. The British scientists would
hardly have expended so much time and energy
on this theory of Einstein's but for the fact that
Einstein had already scored one great victory.
What was it?

Imagine but a single planet revolving about the
sun. According to Newton's law of gravitation,
the planet's path would be that of an ellipse —
that is, oval — and the planet would travel indef-
initely along this path. According to Einstein
the path would also be elliptical, but before a
revolution would be quite completed, the planet
would start along a slightly advanced line, form-
ing a new ellipse slightly in advance of the first.
The elliptic orbit slowly turns in the direction in
which the planet is moving. After many years —
centuries — the orbit will be in a different direction.

The rapidity of the orbit's change of direction
depends on the velocity of the planet^ Mercury

From Newton to Einstein

moving at the rate of 30 miles a secon$ is the fast-
est among the planets. It has the further ad-
vantage over Venus or the earth in that its orbit,
as we have said, is an ellipse, whereas the orbits
of Venus and the earth are nearly circular; and
how are you going to tell in which direction a
circle is pointing?

Observation tells us that the orbit of Mercury
is advancing at the rate of 574 seconds (of arc)
per century. We can calculate how much of this
is due to the gravitational influence of other
planets. It amounts to 532 seconds per century.
What of the remaining 42 seconds?

You might be inclined to attribute this short-
coming to experimental error. But when all
such possibilities are allowed for our mathe-
maticians assure us that the discrepancy is 30
times greater than any possible experimental
error.

This discrepancy between theory and observa-
tion remained one of the great puzzles in astron-
omy until Einstein cleared up the mystery.
According to Einstein's theory the mathematics of
the situation is simply this: in one revolution of
the planet the orbit will advance by a fraction of a
revolution equal to three times the square of the
ratio of the velocity of the planet to the velocity

70 From Newton to Einstein

of light. When we allow mathematicians to
work this out we get the figure 43, which is
certainly close enough to 42 to be called identical
with it.

Stitt Another Victory? Einstein's third pre-
diction— the shifting of spectral lines toward the
red end of the spectrum in the case of light coming
to us from the stars of appreciable mass — seems
to have been confirmed recently (March, 1920).
"The young physicists in Bonn," writes Prof.
Einstein to a friend, "have now as good as
certainty (so gut wie sicker) proved the red
displacement of the spectral lines and have
cleared up the grounds of a previous disappoint-
ment."

Summary. Velocity, or movement in space, is
at the basis of Einstein's work, as it was at the
basis of Newton's. But time and space no longer
have the distinct meanings that they had when
examined with the help of Newton's equations.
Time and space are not independent but inter-
dependent. They are meaningless when treated
as separate entities, giving results which may
hold for one body in the universe but do not hold
for any other body. To get general laws which
are applicable to the cosmos as a whole the Fun-
damentals of Mechanics must be united.

From Newton to Einstein 71

Einstein's great achievement consists in apply-
ing this revised conception of space and time to
elucidate cosmical problems. "World-lines,"
representing the progress of particles in space,
consisting of space-time combinations (the four
dimensions), are "strained" or "distorted" in
space due to the attraction that bodies exhibit
for one another (the force of gravitation). On
the other hand, gravitation itself — more universal
than anything else in the universe — may be inter-
preted in terms of strains on world-lines, or, what
amounts to the same thing, strains of space-time
combinations. This brings gravitation within
the field of Einstein's conception of time and
space.

That Einstein's conception of the universe is an
improvement upon that of Newton's is evidenced
by the fact that Einstein's law explains all that
Newton's law does, and also other facts which
Newton's law is incapable of explaining. Among
these may be mentioned the distortion of the oval
orbits of planets round the sun (confirmed in the
case of the planet Mercury), and the deviation of
light rays in a gravitational field (confirmed by
the English Solar Eclipse Expedition).

Einstein's Theories and the Inferences to be
Drawn from Them. Einstein's theories, sup-

72 From Newton to Einstein

ported as they are by very convincing experi-
ments, will probably profoundly influence philo-
sophic and perhaps religious thought, but they
can hardly be said to be of immediate consequence
to the man in the street. As I have said else-
where, Einstein's theories are not going to add
one bushel of wheat to war-torn and devastated
Europe, but in their conception of a cosmos
decidedly at variance with anything yet con-
ceived by any school of philosophy, they will
attract the universal attention of thinking men
in all countries. The scientist is immediately
struck by the way Einstein has utilized the
various achievements in physics and mathe-
matics to build up a co-ordinated system showing
connecting links where heretofore none were per-
ceived. The philosopher is equally fascinated
with a theory, which, in detail extremely com-
plex, shows a singular beauty of unity in design
when viewed as a whole. The revolutionary
ideas propounded regarding time and space, the
brilliant way in which the most universal property
of matter, gravitation, is for the first time linked
up with other properties of matter, and, above all,
the experimental confirmation of several of his
more startling predictions — always the finest test
of scientific merit — stamps Einstein as one of

From Newton to Einstein 73

those super-men who from time to time are sent
to us to give us a peep into the beyond.

Some Facts about Einstein Himself. Albert
Einstein was born in Germany some 45 years
ago. At first he was engaged at the Patent
Bureau in Berne, and later became professor at
the Zurich Polytechnic. After a short stay at
Prague University he accepted one of those tempt-
ing "Akademiker" professorships at the uni-
versity of Berlin — professorships which insure a
comfortable income to the recipient of one of
them, little university work beyond, perhaps,
one lecture a week, and splendid facilities for
research. A similar inducement enticed the
chemical philosopher, van 't Hoff, to leave his
Amsterdam, and the Swedes came perilously near
losing their most illustrious scientist, Arrhenius.

Einstein published his first paper on relativity
in 1905, when not more than 30 years old. Of
this paper Planck, the Nobel Laureate in physics
this year, has offered this opinion: "It surpasses
in boldness everything previously suggested in
speculative natural philosophy and even in the
philosophical theories of knowledge. The rev-
olution introduced into the physical conceptions
of the world is only to be compared in extent
and depth with that brought about by the in-

74 From Newton to Einstein

(reduction of the Copernican system of the
universe."

Einstein published a full exposition of the rel-
ativity theory in 1916.

During the momentous years of 1914-19, Ein-
stein quietly pursued his labors. There seems to
be some foundation for the belief that the ways of
the German High Command found little favor in
his eyes. At any rate, he was not one of the forty
professors who signed the famous manifesto extol-
ling Germany's aims. "We know for a fact,"
writes Dr. O. A. Rankine, of the Imperial College
of Science and Technology, London, "that Ein-
stein never was employed on war work. What-
ever may have been Germany's mistakes in other
directions, she left her men of science severely
alone. In fact, they were encouraged to continue
in their normal occupations. Einstein undoubt-
edly received a large measure of support from the
Imperial Government, even when the German
armies were being driven back across Belgium."

Quite recently (June, 1920) the Barnard Medal
of Columbia University was conferred on him "in
recognition of his highly original and fruitful
development of the fundamental concepts of
physics through application of mathematics." In
acknowledging the honor, Prof. Einstein wrote to

From Newton to Einstein 75

President Butler that "... quite apart from
the personal satisfaction, I believe I may regard
your decision [to confer the medal upon him]
as a harbinger of a better time in which a sense of
international solidarity will once more unite
scholars of the various countries."

REFERENCES

For those lacking all astronomical knowledge,
an excellent plan would be to read the first 40
pages of W. H. Snyder's Everyday Science (Allyn
and Bacon), in which may be found a clear and
simple account of the solar system. This could
be followed with Bertrand Russell's chapter on
The Nature of Matter in his little volume, The
Problems of Philosophy (Henry Holt and Co.).
Here the reader will be introduced to the purely
philosophical side of the question — quite a neces-
sary equipment for the understanding of Einstein's
theory.

Of the non-mathematical articles which have
appeared, those by Prof. A. S. Eddington (Nature,
volume 101, pages 15 and 34, 1918) and Prof.
M. R. Cohen (The New Republic, Jan. 21, 1920)
are the best which have come to the author's
notice. Other articles on Einstein's theory, some
easily comprehensible, others somewhat con-

76 From Newton to Einstein

fusing, and still others full of noise and rather
empty, are by H. A. Lorentz, The New York Times,
Dec. 21, 1919 (since reprinted in book form by
Brentano's, New York, 1920); J. Q. Stewart,
Scientific American, Jan. 3, 1920; E. Cunningham,
Nature, volume 104, pages 354 and 374, 1919; F.
H. Loring, Chemical News, volume 112, pages 226,
236, 248, and 260, 1915; E. B. Wilson, Scientific
Monthly, volume 10, page 217, 1920; J. S. Ames,
Science, volume 51, page 253, 1920*; L. A. Bauer,
Science, volume 51, page 301 (1920, and volume
51, page 581 (1920); Sir Oliver Lodge, Scientific
Monthly, volume 10, page 378, 1920; E. E.
Slosson, Independent, Nov. 29, Dec. 13, Dec. 20,
Dec. 27, 1919 (since collected and published hi
book form by Harcourt, Brace and Howe) ; Isabel
M. Lewis, Electrical Experimenter, Jan., 1920;
A. J. Lotka, Harper's Magazine, March, 1920,
page 477; and R. D. Carmichael, New York
Times, March 28, 1920. Einstein himself is
responsible for a brief article in English which
first appeared in the London Times, and was
later reprinted in Science, volume 51, page 8, 1920
(see the Appendix).

A number of books deal with the subject, and
all of them are more or less mathematical. How-
ever, in every one of these volumes certain chap-

f See page 93.

From Newton to Einstein 77

ters, or portions of chapters, may be read with
profit even by the non-mathematical reader.
Some of these books are: Erwin Freundlich, The
Foundations of Einstein's Theory of Gravitation
(University Press, Cambridge, 1920). (A very
complete list of references — up to Feb., 1920 — is
also given); A. S. Eddington, Report on the
Relativity Theory of Gravitation for the Physical
Society of London (Fleetway Press, Ltd., Lon-
don, 1920); R. C. Tolman, Theory of the Relativity
of Motion (University of California Press, 1917);
E. Cunningham, Relativity and the Electron Theory-
(Longmans, Green and Co., 1915); R. D. Car-
michael, The Theory of Relativity (John Wiley and
Sons, 1913) ; L. Silberstein, The Theory of Rela-
tivity (Macmillan, 1914); and E. Cunningham,
The Principle of Relativity (University Press,
Cambridge, England, 1914).

To those familiar with the German language
Einstein's book, Ueber die spezielle und die allge-
meine Relativitats-theorie (Friedr. Vieweg und
Sohn, Braunschweig, 1920), may be recom-
mended.*

The mathematical student may be referred to a

* This has since been translated into English by Dr. Law-
son and published by Methuen (London).

Since the above has been written two excellent books have

78 From Newton to Einstein

volume incorporating the more important papers
of Einstein, Minkowski and Lorentz: Das Rela-
tivitdtsprinzip, (B. G. Teubner, Berlin, 1913).

Einstein's papers have appeared in the Annalen
der Physiky Leipzig, volume 17, page 132, 1905,
volume 49, page 769, 1916, and volume 55, page
241, 1918.

have been published. One is by Prof. A. S. Eddington,
Space, Time and Gravitation (Cambridge Univ. Press, 1920).
The other, somewhat more of a philosophical work, is Prof.
Moritz Schlick's Space and Time in Contemporary Physics
(Oxford Univ. Press, 1920).

Though published as early as 1897, Bertrand Russell's
An Essay on the Foundations of Geometry (Cambridge Univ.
Press, 1897) contains a fine account of non-Euclidean geom-
etry.

APPENDIX

APPENDIX

NOTE 1 (page 21)

"On this earth there is indeed a tiny corner of the universe
accessible to other senses [than the sense of sight] : but feeling
and taste act only at those minute distances which separate
particles of matter when 'in contact:* smell ranges over,
at the utmost, a mile or two, and the greatest distance which
sound is ever known to have traveled (when Krakatoa
exploded in 1883) is but a few thousand miles — a mere fraction
of the earth's girdle." — Prof. H. H. Turner of Oxford,

NOTE 2 (page 27)

Huyghens and Leibnitz both objected to Newton's inverse
square law because it postulated "action at a distance,"
— for example, the attractive force of the sun and the earth.
This desire for "continuity" in physical laws led to the
supposition of an "ether." We may here anticipate and
state that the reason which prompted Huyghens to object
to Newton's law led Einstein in our own day to raise objec-
tions to the "ether" theory. "In the formulation of physical
laws, only those things were to be regarded as being in causal
connection which were capable of being actually observed."
And the "ether" has not been "actually observed."

The idea of "continuity" implies distances between adja-
cent points that are infinitesimal in extent; hence the idea
of "continuity" comes in direct opposition with the finite
distances of Newton.

81

82 Appendix

The statement relating to causal connection — the refusal
to accept an "ether" as an absolute base of reference —
leads to the principle of the relativity of motion.

NOTE 3 (page 30)

Sir Oliver Lodge goes to the extreme of pinning his faith in
the reality of this ether rather than in that of matter. Witness
the following statement he made recently before a New
York audience:

"To my mind the ether of space is a substantial reality
with extraordinarily perfect properties, with an immense
amount of energy stored up in it, with a constitution which
we must discover, but a substantial reality far more impres-
sive than that of matter. Empty space, as we call it, is
full of ether, but it makes no appeal to our senses. The
appearance is as if it were nothing. It is the most important
thing in the material universe. I believe that matter is a
modification of ether, a very porous substance, a thing more
analogous to a cobweb or the Milky Way or something
very slight and unsubstantial, as compared to ether."

And again :

"The properties of ether seem to be perfect. Matter is
less so; it has friction and elasticity. No imperfection has
been discovered in the ether space. It doesn't wear out;
there is no dissipation of energy; there is no friction. Ether
is material, yet it is not matter; both are substantial realities in
physics, but it is the ether of space that holds things together
and acts as a cement. My business is to call attention to
the whole world of etherealness of things, and I have made
it a subject of thirty years' study, but we must admit that
there is no getting hold of ether except indirectly."

"I consider the ether of space," says Lodge, in conclusion,

Appendix 83

"the one substantial thing in the universe." And Lodge is
certainly entitled to his opinion.

NOTE 4 (page 51)

For the benefit of those readers who wish to gain a deeper
insight into the relativity principle, we shall here discuss it
very briefly.

Newton and Galileo had developed a relativity principle
in mechanics which may be stated as follows: If one system
of reference is in uniform rectilinear motion with respect
to another system of reference, then whatever physical laws
are deduced from the first system hold true for the second
system. The two systems are equivalent. If the two sys-
tems be represented by xyz and x'y'z' \ and if they move with
the velocity of v along the x-axis with respect to one another,
then the two systems are mathematically related thus:

x'=x— vt, y1 ' =y, z'=z, t' =t, ... (1)

and this immediately provides us with a means of trans-
forming the laws of one system to those of another.

With the development of electrodynamics (which we may
call electricity in motion) difficulties arose which equations
in mechanics of type (1) could no longer solve. These
difficulties merely increased when Maxwell showed that
light must be regarded as an electromagnetic phenomenon.
For suppose we wish to investigate the motion of a source
of light (which may be the equivalent of the motion of the
earth with reference to the sun) with respect to the velocity
of the light it emits — a typical example of the study of moving
systems — how are we to coordinate the electrodynamical
and mechanical elements? Or, again, suppose we wish to

84 Appendix

investigate the velocity of electrons shot out from radium
with a speed comparable to that of light, how are we to
coordinate the two branches in tracing the course of these
negative particles of electricity?

It was difficulties such as these that led to the Lorentz-
Einstein modifications of the Newton-Galileo relativity
equations (1). The Lorentz-Einstein equations are expressed
in the form:

.. (2)

c denoting the velocity of light in vacuo (which, according to
all observations, is the same, irrespective of the observer's
state of motion). Here, you see, electrodynamical systems
(light and therefore "ray" velocities such as those due to
electrons) are brought into play.

This gives us Einstein's special theory of relativity. From
it Einstein deduced some startling conceptions of time and
space.

NOTE 5 (page 55)

The velocity (v) of an object in one system will have a
different velocity (v') if referred to another system in uniform
motion relative to the first. It had been supposed that
only a "something" endowed with infinite velocity would
show the same velocity in all systems, irrespective of the
motions of the latter. Michelson and Morley's results
actually point to the velocity of light as showing the proper-
ties of the imaginary "infinite velocity." The velocity of light
possesses universal significance; and this is the basis for
much of Einstein's earlier work.

Appendix 85

NOTE 6 (page 56)

"Euclid assumes that parallel lines never meet, which they
cannot do of course if they be defined as equidistant. But are
there such lines? And if not, why not assume that all lines
drawn through a point outside a given line will eventually
intersect it? Such an assumption leads to a geometry in
which all lines are conceived as being drawn on the surface of
a sphere or an ellipse, and in it the three angles of a triangle
are never quite equal to two right angles, nor the circum-
ference of a circle quite TT times its diameter. But that is pre-
cisely what the contraction effect due to motion requires."

(DR. WALKER)

NOTE 7 (page 57)

Einstein had become tired of assumptions. He had no
particular objection to the "ether" theory beyond the fact
that this "ether" did not come within the range of our senses;
it could not be "observed." "The consistent fulfilment of
the two postulates — * action by contact' and causal relation-
ship between only such things as lie within the realm of
observation [see Note 2] combined together is, I believe,
the mainspring of Einstein's method of investigation ..."
(Prof. Freundlich).

NOTE 8 (page 59)

That the conception of the "simultaneity" of events is
devoid of meaning can be deduced from equation (2) [see
NOTE 4]. We owe the proof to Einstein. "It is possible to
select a suitable time-coordinate in such a way that a time-
measurement enters into physical laws in exactly the same
manner as regards its significance as a space measurement
(that is, they are fully equivalent symbolically), and has

Appendix

likewise a definite coordinate direction ... It never
occurred to anyone that the use of a light-signal as a means
of connection between the moving-body and the observer,
which is necessary in practice in order to determine simul-
taneity, might affect the final result, i.e., of time measurements
in different systems." (Freundlich). But that is just what
Einstein shows, because time-measurements are based on
"simultaneity of events," and this, as pointed out above,
is devoid of meaning.

Had the older masters the occasion to study enormous
velocities, such as the velocity of light, rather than relatively
small ones — and even the velocity of the earth around the
sun is small as compared to the velocity of light — dis-
crepancies between theory and experiment would have
become apparent.

NOTE 9 (page 67)

How the special theory of relativity (see Note 4) led to
the general theory of relativity (which included gravitation)
may now be briefly traced.

When we speak of electrons, or negative particles of elec-
tricity, in motion, we are speaking of energy in motion. Now
these electrons when in motion exhibit properties that are
very similar to matter in motion. Whatever deviations there
are are due to the enormous velocity of these electrons,
and this velocity, as has already been pointed out, is com-
parable to that of light; whereas before the advent of the
electron, the velocity of no particles comparable to that of
light had ever been measured.

According to present views "all inertia of matter consists
only of the inertia of the latent energy in it; ... every-

Appendix 87

thing that we know of the inertia of energy holds without
exception for the inertia of matter."

Now it is on the assumption that inertial mass and gravi-
tational "pull" are equivalent that the mass of a body is
determined by its weight. What is true of matter should
be true of energy.

The special theory of relativity, however, takes into
account only inertia ("inertial mass") but not gravitation
(gravitational pull or weight) of energy. When a body absorbs
energy equation 2 (see Note 4) will record a gain in inertia
but not in weight — which is contrary to one of the funda-
mental facts in mechanics.

This means that a more general theory of relativity is re-
quired to include gravitational phenomena. Hence Einstein's
General Theory of Relativity. Hence the approach to a new
theory of gravitation. Hence "the setting up of a differential
equation which comprises the motion of a body under the
influence of both inertia and gravity, and which symbolically
expresses the relativity of motions . . . The differential
law must always preserve the same form, irrespective of
the sytem of coordinates to which it is referred, so that
no system of coordinates enjoys a preference to any other."
(For the general form of the equation and for an excellent
discussion of its significance, see Freundlich's monograph,
pages 27-33.)

TIME, SPACE AND GRAVITATION*

BY

PROF. ALBERT EINSTEIN

THERE are several kinds of theory in physics. Most of
them are constructive. These attempt to build a picture of
complex phenomena out of some relatively simple proposition.
The kinetic theory of gases, for instance, attempts to refer
to molecular movement the mechanical thermal, and dif-
fusional properties of gases. When we say that we under-
stand a group of natural phenomena, we mean that we have
found a constructive theory which embraces them.

Theories of Principle. — But in addition to this most weighty
group of theories, there is another group consisting of what I
call theories of principle. These employ the analytic, not
the synthetic method. Their starting-point and foundation
are not hypothetical constituents, but empirically observed
general properties of phenomena, principles from which math-
ematical formulae are deduced of such a kind that they apply
to every case which presents itself. Thermodynamics, for
instance, starting from the fact that perpetual motion never
occurs in ordinary experience, attempts to deduce from this,
by analytic processes, a theory which will apply in every case.
The merit of constructive theories is their comprehensiveness,
adaptability, and clarity, that of the theories of principle,
their logical perfection, and the security of their foundation.

The theory of relativity is a theory of principle. To under-
stand it, the principles on which it rests must be grasped.
But before stating these it is necessary to point out that
the theory of relativity is like a house with two separate

* Republished by permission from "Science."
88

Appendix

stories, the special relativity theory and the general theory
of relativity.

Since the time of the ancient Greeks it has been well known
that in describing the motion of a body we must refer to
another body. The motion of a railway train is described
with reference to the ground, of a planet with reference to
the total assemblage of visible fixed stars. In physics the
bodies to which motions are spatially referred are termed
systems of coordinates. The laws of mechanics of Galileo
and Newton can be formulated only by using a system of
coordinates.

The state of motion of a system of coordinates can not be
chosen arbitrarily if the laws of mechanics are to hold good
(it must be free from twisting and from acceleration). The
system of coordinates employed in mechanics is called an
inertia-system. The state of motion of an inertia-system,
so far as mechanics are concerned, is not restricted by nature
to one condition. The condition in the following proposition
suffices; a system of coordinates moving in the same direction
and at the same rate as a system of inertia is itself a system of
inertia. The special relativity theory is therefore the appli-
cation of the following proposition to any natural process:
"Every law of nature which holds good with respect to a
coordinate system K must also hold good for any other system
Kf provided that K and K' are in uniform movement of trans-
lation."

The second principle on which the special relativity theory
rests is that of the constancy of the velocity of light in a vac-
uum. Light in a vacuum has a definite and constant velocity,
independent of the velocity of its source. Physicists owe
their confidence in this proposition to the Maxwell-Lorentz
theory of electro-dynamics.

90 Appendix

The two principles which I have mentioned have received
strong experimental confirmation, but do not seem to be
logically compatible. The special relativity theory achieved
their logical reconciliation by making a change in kinematics,
that is to say, in the doctrine of the physical laws of space and
time. It became evident that a statement of the coincidence
of two events could have a meaning only in connection with a
system of coordinates, that the mass of bodies and the rate of
movement of clocks must depend on their state of motion
with regard to the coordinates.

The Older Physics. — But the older physics, including the
laws of motion of Galileo and Newton, clashed with the
relativistic kinematics that I have indicated. The latter gave
origin to certain generalized mathematical conditions with
which the laws of nature would have to conform if the two
fundamental principles were compatible. Physics had to be
modified. The most notable change was a new law of motion
for (very rapidly) moving mass-points, and this soon came
to be verified in the case of electrically-laden particles. The
most important result of the special relativity system con-
cerned the inert mass of a material system. It became evident
that the inertia of such a system must depend on its energy-
content, so that we were driven to the conception that inert
mass was nothing else than latent energy. The doctrine
of the conservation of mass lost its independence and became
merged in the doctrine of conservation of energy.

The special relativity theory which was simply a systematic
extension of the electro-dynamics of Maxwell and Lorentz,
had consequences which reached beyond itself. Must the
independence of physical laws with regard to a system of
coordinates be limited to systems of coordinates in uniform
movement of translation with regard to one another? What

Appendix

has nature to do with the coordinate systems that we pro-
pose and with their motions? Although it may be necessary
for our descriptions of nature to employ systems of coordinates
that we have selected arbitrarily, the choice should not be
limited in any way so far as their state of motion is concerned.
(General theory of relativity.) The application of this gen-
eral theory of relativity was found to be in conflict with a
well-known experiment, according to which it appeared that
the weight and the inertia of a body depended on the same
constants (identity of inert and heavy masses). Consider
the case of a system of coordinates which is conceived as being
in stable rotation relative to a system of inertia in the New-
tonian sense. The forces which, relatively to this system, are
centrifugal must, in the Newtonian sense, be attributed to
inertia. But these centrifugal forces are, like gravitation,
proportional to the mass of the bodies. Is it not, then, pos-
sible to regard the system of coordinates as at rest, and the
centrifugal forces as gravitational? The interpretation seemed
obvious, but classical mechanics forbade it.

This slight sketch indicates how a generalized theory of
relativity must include the laws of gravitation, and actual
pursuit of the conception has justified the hope. But the
way was harder than was expected, because it contradicted
Euclidian geometry. In other words, the laws according to
which material bodies are arranged in space do not exactly
agree with the laws of space prescribed by the Euclidian
geometry of solids. This is what is meant by the phrase "a
warp in space." The fundamental concepts "straight,"
"plane," etc., accordingly lose their exact meaning in physics.

In the generalized theory of relativity, the doctrine of space
and time, kinematics, is no longer one of the absolute founda-
tions of general physics. The geometrical states of bodies

92 Appendix

and the rates of clocks depend in the first place on their gravi-
tational fields, which again are produced by the material system
concerned.

Thus the new theory of gravitation diverges widely from
that of Newton with respect to its basal principle. But in
practical application the two agree so closely that it has been
difficult to find cases in which the actual differences could be
subjected to observation. As yet only the following have
been suggested:

1. The distortion of the oval orbits of planets round the sun
(confirmed in the case of the planet Mercury).

2. The deviation of light-rays in a gravitational field (con-
firmed by the English Solar Eclipse expedition).

3. The shifting of spectral lines towards the red end of the
spectrum in the case of light coming to us from stars of appre-
ciable mass (not yet confirmed).

The great attraction of the theory is its logical consistency.
If any deduction from it should prove untenable, it must be
given up. A modification of it seems impossible without
destruction of the whole.

No one must think that Newton's great creation can be
overthrown in any real sense by this or by any other theory.
His clear and wide ideas will for ever retain their significance
as the foundation on which our modern conceptions of physics
have been built.

Appendix 93

EINSTEIN'S LAW OF GRAVITATION*

BT

PROF. J. S. AMES
Johns Hopkins University

... IN the treatment of Maxwell's equations of the electro-
magnetic field, several investigators realized the importance
of deducing the form of the equations when applied to a
system moving with a uniform velocity. One object of such
an investigation would be to determine such a set of trans-
formation formulae as would leave the mathematical form
of the equations unaltered. The necessary relations between
the new space-coordinates, those applying to the moving
system, and the original set were of course obvious; and ele-
mentary methods led to the deduction of a new variable which
should replace the time coordinate. This step was taken by
Lorentz and also, I believe, by Larmor and by Voigt. The
mathematical deductions and applications in the hands of
these men were extremely beautiful, and are probably well
known to you all.

Lorentz' paper on this subject appeared in the Proceedings
of the Amsterdam Academy in 1904. In the following year
there was published in the Annalen der Physik a paper by
Einstein, written without any knowledge of the work of
Lorentz, in which he arrived at the same transformation
equations as did the latter, but with an entirely different and
fundamentally new interpretation. Einstein called atten-^
tion in his paper to the lack of definiteness in the concepts
of time and space, as ordinarily stated and used. He analyzed
clearly the definitions and postulates which were necessary

* Presidential address delivered at the St. Louis meeting of the
Physical Society, December 30, 1919. Republished by permis-
sion from " Science."

94 Appendix

before one could speak with exactness of a length or of an
interval of time. He disposed forever of the propriety of*'
speaking of the "true'* length of a rod or of the "true"
duration of time, showing, in fact, that the numerical values
which we attach to lengths or intervals of time depend upon
the definitions and postulates which we adopt. The words
"absolute" space or time intervals are devoid of meaning.
As an illustration of what is meant Einstein discussed two
possible ways of measuring the length of a rod when it is
moving in the direction of its own length with a uniform
velocity, that is, after having adopted a scale of length, two
ways of assigning a number to the length of the rod con-
cerned. One method is to imagine the observer moving with
the rod, applying along its length the measuring scale, and
reading off the positions of the ends of the rod. Another
method would be to have two observers at rest on the body
with reference to which the rod has the uniform velocity, so
stationed along the line of motion of the rod that as the rod
moves past them they can note simultaneously on a stationary
measuring scale the positions of the two ends of the rod.
Einstein showed that, accepting two postulates which need
no defense at this time, the two methods of measurements
would lead to different numerical values, and, further, that
the divergence of the two results would increase as the velocity
of the rod was increased. In assigning a number, therefore,
to the length of a moving rod, one must make a choice of the
method to be used in measuring it. Obviously the preferable
method is to agree that the observer shall move with the rod,
carrying his measuring instrument with him. This disposes
of the problem of measuring space relations. The observed
fact that, if we measure the length of the rod on different
days, or when the rod is lying in different positions, we always

Appendix 95

obtain the same value offers no information concerning the
"real " length of the rod. It may have changed, or it may not.
It must always be remembered that measurement of the
length of a rod is simply a process of comparison between it
and an arbitrary standard, e.g., a meter-rod or yard-stick.
In regard to the problem of assigning numbers to intervals of
time, it must be borne in mind that, strictly speaking, we do
not "measure" such intervals, i.e., that we do not select a
unit interval of time and find how many times it is contained
in the interval in question. (Similarly, we do not "measure"
the pitch of a sound or the temperature of a room.) Our
practical instruments for assigning numbers to time-inter-
vals depend in the main upon our agreeing to believe that a
pendulum swings in a perfectly uniform manner, each vibra-
tion taking the same time as the next one. Of course we
cannot prove that this is true, it is, strictly speaking, a defini-
tion of what we mean by equal intervals of time; and it is
not a particularly good definition at that. Its limitations are
sufficiently obvious. The best way to proceed is to consider
the concept of uniform velocity, and then, using the idea
of some entity having such a uniform velocity, to define equal
intervals of time as such intervals as are required for the entity
to traverse equal lengths. These last we have already defined.
What is required in addition is to adopt some moving entity
as giving our definition of uniform velocity. Considering
our known universe it is self-evident that we should choose

our definition of uniform velocity the velocity of light, since
is selection could be made by an observer anywhere in our

i verse. Having agreed then to illustrate by the words
"uniform velocity" that of light, our definition of equal inter-
vals of time is complete. This implies, of course, that there is

uncertainty on our part as to the fact that the velocity of

96 Appendix

light always has the same value at any one point in the uni-
verse to any observer, quite regardless of the source of light.
In other words, the postulate that this is true underlies our
definition. Following this method Einstein developed a
system of measuring both space and time intervals. As a
matter of fact his system is identically that which we use in
daily life with reference to events here on the earth. He
further showed that if a man were to measure the length
of a rod, for instance, on the earth and then were able to carry
the rod and his measuring apparatus to Mars, the sun, or to
Arcturus he would obtain the same numerical value for the
length in all places and at all times. This doesn't mean that
any statement is implied as to whether the length of the rod
has remained unchanged or not; such words do not have any
meaning — remember that we can not speak of true length.
It is thus clear that an observer living on the earth would have
a definite system of units in terms of which to express space
and time intervals, i.e., he would have a definite system of
space coordinates (x, y, z) and a definite time coordinate (t) ;
and similarly an observer living on Mars would have his
system of coordinates (#', y', z', t'). Provided that one
observer has a definite uniform velocity with reference to the
other, it is a comparatively simple matter to deduce the
mathematical relations between the two sets of coordinates.
When Einstein did this, he arrived at the same transformation
formulae as those used by Lorentz in his development of
Maxwell's equations. The latter had shown that, using these
formulae, the form of the laws for all electromagnetic phe-
nomena maintained the same form; so Einstein's method
J proves that using his system of measurement an observer,
anywhere in the universe, would as the result of his own
investigation of electromagnetic phenomena arrive at the

Appendix 97

same mathematical statement of them as any other observer,
provided only that the relative- velocity of the two observers
was uniform.

Einstein discussed many other most important questions
at this time; but it is not necessary to refer to them in con-
nection with the present subject. So far as this is concerned,
the next important step to note is that taken in the famous
address of Minkowski, in 1908, on the subject of "Space and
Time." It would be difficult to overstate the importance of
the concepts advanced by Minkowski. They marked the '
beginning of a new period in the philosophy of physics. I
shall not attempt to explain his ideas in detail, but shall
confine myself to a few general statements. His point of view
and his line of development of the theme are absolutely dif-
ferent from those of Lorentz or of Einstein; but in the end
he makes use of the same transformation formulae. His
great contribution consists in giving us a new geometrical
picture of their meaning. It is scarcely fair to call Minkowski's
development a picture; for to us a picture can never have
more than three dimensions, our senses limit us; while his
picture calls for perception of four dimensions. It is this fact
that renders any even semi-popular discussion of Minkowski's
work so impossible. We can all see that for us to describe
any event a knowledge of four coordinates is necessary, three
for the space specification and one for the time. A com-
plete picture could be given then by a point in four dimen-
sions. All four coordinates are necessary: we never observe
an event except at a certain time, and we never observe an
instant of time except with reference to space. Discussing
the laws of electromagnetic phenomena, Minkowski showed
how in a space of four dimensions, by a suitable definition of
axes, the mathematical transformation of Lorentz and Ein-

98 Appendix

stein could be described by a rotation of the set of axes. We
are all accustomed to a rotation of our ordinary cartesian
set of axes describing the position of a point. We ordinarily
choose our axes at any location on the earth as follows: one
vertical, one east and west, one north and south. So if we
move from any one laboratory to another, we change our axes;
they are always orthogonal, but in moving from place to place
there is a rotation. Similarly, Minkowski showed that if we
choose four orthogonal axes at any point on the earth, accord-
ing to his method, to represent a space-time point using the
method of measuring space and time intervals as outlined by
Einstein; and, if an observer on Arcturus used a similar set
of axes and the method of measurement which he naturally
would, the set of axes of the latter could be obtained from those
of the observer on the earth by a pure rotation (and naturally
a transfer of the origin) . This is a beautiful geometrical result.
To complete my statement of the method, I must add that
instead of using as his fourth axis one along which numerical
values of time are laid off, Minkowski defined his fourth
coordinate as the product of time and the imaginary constant,
the square root of minus one. This introduction of imaginary
quantities might be expected, possibly, to introduce difficul-
ties; but, in reality, it is the very essence of the simplicity of
the geometrical description just given of the rotation of the
sets of axes. It thus appears that different observers situated
at different points in the universe would each have their own
set of axes, all different, yet all connected by the fact that
any one can be rotated so as to coincide with any other.
This means that there is no one direction in the four-dimen-
sional space that corresponds to time for all observers. Just
as with reference to the earth there is no direction which can
be called vertical for all observers living on the earth. In the

Appendix 99

sense of an absolute meaning the words "up and down,"
"before and after," "sooner or later," are entirely meaning-
less.

This concept of Minkowski's may be made clearer, perhaps,
by the following process of thought. If we take a section
through our three-dimensional space, we have a plane, i.e.,
a two-dimensional space. Similarly, if a section is made
through a four-dimensional space, one of three dimensions is
obtained. Thus, for an observer on the earth a definite
section of Minkowski's four-dimensional space will give us our
ordinary three-dimensional one; so that this section will, as it
were, break up Minkowski's space into our space and give us
our ordinary time. Similarly, a different section would have
to be used to the observer on Arcturus; but by a suitable
selection he would get his own familiar three-dimensional
space and his own time. Thus the space defined by Min-
kowski is completely isotropic in reference to measured lengths
and times, there is absolutely no difference between any two
directions in an absolute sense; for any particular observer, of
course, a particular section will cause the space to fall apart
so as to suit his habits of measurement; any section, however,
taken at random will do the same thing for some observer
somewhere. From another point of view, that of Lorentz
and Einstein, it is obvious that, since this four-dimensional
space is isotropic, the expression of the laws of electromagnetic
phenomena take identical mathematical forms when expressed
by any observer.

The question of course must be raised as to what can be
said in regard to phenomena which so far as we know do not
have an electromagnetic origin. In particular what can be
done with respect to gravitational phenomena? Before, how-
ever, showing how this problem was attacked by Einstein;

100 Appendix

and the fact that the subject of my address is Einstein's
work on gravitation shows that ultimately I shall explain this,
I must emphasize another feature of Minkowski's geometry.
To describe the space-time characteristics of any event a
point, defined by its four coordinates, is sufficient; so, if one
observes the life-history of any entity, e.g., a particle of matter,
a light- wave, etc., he observes a sequence of points in the space-
time continuum; that is, the life-history of any entity is
described fully by a line in this space. Such a line was called
by Minkowski a "world-line." Further, from a different point
of view, all of our observations of nature are in reality obser-
vations of coincidences, e.g., if one reads a thermometer, what
he does is to note the coincidence of the end of the column of
mercury with a certain scale division on the thermometer
tube. In other words, thinking of the world-line of the end
of the mercury column and the world-line of the scale division,
what we have observed was the intersection or crossing of
these lines. In a similar manner any observation may be
analyzed; and remembering that light rays, a point on the
retina of the eye, etc., all have their world-lines, it will be recog-
nized that it is a perfectly accurate statement to say that
every observation is the perception of the intersection of world-
lines. Further, since all we know of a world-line is the result
of observations, it is evident that we do not know a world-
line as a continuous series of points, but simply as a series of
discontinuous points, each point being where the particular
world-line in question is crossed by another world-line.

It is clear, moreover, that for the description of a world-line
we are not limited to the particular set of four orthogonal axes
adopted by Minkowski. We can choose any set of four-
dimensional axes we wrish. It is further evident that the
mathematical expression for the coincidence of two points is

-

Appendix 101

absolutely independent of our selection of reference axes. If
we change our axes, we will change the coordinates of both
points simultaneously, so that the question of axes ceases to be
of interest. But our so-called laws of nature are nothing but
descriptions in mathematical language of our observations;
we observe only coincidences; a sequence of coincidences when
put in mathematical terms takes a form which is independent
of the selection of reference axes; therefore the mathematical
expression of our laws of nature, of every character, must
be such that their form does not change if we make a trans-
formation of axes. This is a simple but far-reaching de-
duction.

There is a geometrical method of picturing the effect of a
change of axes of reference, i.e., of a mathematical transforma-
tion. To a man in a railway coach the path of a drop of water
does not appear vertical, i.e., it is not parallel to the edge of
the window; still less so does it appear vertical to a man per-
forming manoeuvres in an airplane. This means that whereas
with reference to axes fixed to the earth the path of the drop is
vertical; with reference to other axes, the path is not. Or,
stating the conclusion in general language, changing the axes
of reference (or effecting a mathematical transformation) in
general changes the shape of any line. If one imagines the
line forming a part of the space, it is evident that if the space is
deformed by compression or expansion the shape of the line
is changed, and if sufficient care is taken it is clearly possible,
by deforming the space, to make the line take any shape
desired, or better stated, any shape specified by the previous
change of axes. It is thus possible to picture a mathematical
transformation as a deformation of space. Thus I can draw a
line on a sheet of paper or of rubber and by bending and
stretching the sheet, I can make the line assume a great variety

Appendix

of shapes; each of these new shapes is a picture of a suitable
transformation.

Now, consider world-lines in our four-dimensional space.
The complete record of all our knowledge is a series of se-
quences of intersections of such lines. By analogy I can draw
in ordinary space a great number of intersecting lines on a sheet
of rubber; I can then bend and deform the sheet to please
myself; by so doing I do not introduce any new intersections
nor do I alter in the least the sequence of intersections. So
in the space of our world-lines, the space may be deformed in
any imaginable manner without introducing any new inter-
sections or changing the sequence of the existing intersections.
It is this sequence which gives us the mathematical expression
of our so-called experimental laws; a deformation of our space
is equivalent mathematically to a transformation of axes,
consequently we see why it is that the form of our laws must
be the same when referred to any and all sets of axes,
that is, must remain unaltered by any mathematical trans-
formation.

Now, at last we come to gravitation. We can not imagine
any world-line simpler than that of a particle of matter left
to itself; we shall therefore call it a "straight" line. Our
experience is that two particles of matter attract one another
Expressed in terms of world-lines, this means that, if the world-
lines of two isolated particles come near each other, the lines,
instead of being straight, will be deflected or bent in towards
each other. The world-line of any one particle is therefore
deformed; and we have just seen that a deformation is the
equivalent of a mathematical transformation. In other words,
for any one particle it is possible to replace the effect of a
gravitational field at any instant by a mathematical transfor-
mation of axes. The statement that this is always possible

Appendix 103

for any particle at any instant is Einstein's famous "Principle
of Equivalence."

Let us rest for a moment, while I call attention to a most
interesting coincidence, not to be thought of as an intersection
of world-lines . It is said that Newton' s thoughts were directed
to the observation of gravitational phenomena by an apple
falling on his head; from this striking event he passed by
natural steps to a consideration of the universality of gravita-
tion. Einstein in describing his mental process in the evolu-
tion of his law of gravitation says that his attention was called
to a new point of view by discussing his experiences with a
man whose fall from a high building he had just witnessed.
The man fortunately suffered no serious injuries and assured
Einstein that in the course of his fall he had not been conscious
in the least of any pull downward on his body. In mathe-
matical language, with reference to axes moving with the
man the force of gravity had disappeared. This is a case
where by the transfer of the axes from the earth itself to the
man, the force of the gravitational field is annulled. The
converse change of axes from the falling man to a point on the
earth could be considered as introducing the force of gravity
into the equations of motion. Another illustration of the
introduction into our equations of a force by a means of a
change of axes is furnished by the ordinary treatment of a
body in uniform rotation about an axis. For instance, in the
case of a so-called conical pendulum, that is, the motion of a
bob suspended from a fixed point by string, which is so set
in motion that the bob describes a horizontal circle and the
string therefore describes a circular cone, if we transfer our
axes from the earth and have them rotate around the vertical
line through the fixed point with the same angular velocity as
the bob, it is necessary to introduce into our equations of

104 Appendix

motion a fictitious "force" called the centrifugal force. No
one ever thinks of this force other than as a mathematical
quantity introduced into the equations for the sake of sim-
plicity of treatment; no physical meaning is attached to it.
Why should there be to any other so-called "force," which
like centrifugal force, is independent of the nature of the
matter? Again, here on the earth our sensation of weight is
interpreted mathematically by combining expressions for
centrifugal force and gravity; we have no distinct sensation
for either separately. Why then is there any difference in
the essence of the two? Why not consider them both as
brought into our equations by the agency of mathematical
transformations? This is Einstein's point of view.

Granting, then, the principle of equivalence, we can so
choose axes at any point at any instant that the gravitational
field will disappear; these axes are therefore of what Edding-
ton calls the "Galilean" type, the simplest possible. Con-
sider, that is, an observer in a box, or compartment, which is
falling with the acceleration of the gravitational field at that
point. He would not be conscious of the field. If there were
a projectile fired off in this compartment, the observer would
describe its path as being straight. In this space the infinites-
imal interval between two space-time points would then be
given by the formula

ds* = dx\+dx\+dx*a+dx24,

where ds is the interval and Xi, xz, #3, #4, are coordinates. If
we make a mathematical transformation, i.e., use another set
of axes, this interval would obviously take the form

ds* —
where x\t 3%, £3 and x\ are now coordinates referring to the new

Appendix 105

axes. This relation involves ten coefficients, the coefficients
defining the transformation.

But of course a certain dynamical value is also attached to
the g's, because by the transfer of our axes from the Galilean
type we have made a change which is equivalent to the intro-
duction of a gravitational field; and the g's must specify the
field. That is, these g's are the expressions of our experiences,
and hence their values can not depend upon the use of any
special axes; the values must be the same for all selections.
In other words, whatever function of the coordinates any one g
is for one set of axes, if other axes are chosen, this g must still
be the same function of the new coordinates. There are ten
g's defined by differential equations; so we have ten co variant
equations. Einstein showed how these g's could be regarded
as generalized potentials of the field. Our own experiments
and observations upon gravitation have given us a certain
knowledge concerning its potential; that is, we know a value
for it which must be so near the truth that we can properly
call it at least a first approximation. Or, stated differently, if
Einstein succeeds in deducing the rigid value for the gravi-
tational potential in any field, it must degenerate to the New-
tonian value for the great majority of cases with which we have
actual experience. Einstein's method, then, was to investigate
the functions (or equations) which would satisfy the mathe-
matical conditions just described. A transformation from
the axes used by the observer in the following box may be
made so as to introduce into the equations the gravitational
field recognized by an observer on the earth near the box;
but this, obviously, would not be the general gravitational
field, because the field changes as one moves over the surface
of the earth. A solution found, therefore, as just indicated,
would not be the one sought for the general field; and another

106 Appendix

must be found which is less stringent than the former but
reduces to it as a special case. He found himself at liberty
to make a selection from among several possibilities, and
for several reasons chose the simplest solution. He then
tested this decision by seeing if his formulae would degenerate
to Newton's law for the limiting case of velocities small when
compared with that of light, because this condition is satisfied
in those cases to which Newton's law applies. His formulae
satisfied this test, and he therefore was able to announce a
"law of gravitation," of which Newton's was a special form
for a simple case.

To the ordinary scholar the difficulties surmounted by Ein-
stein in his investigations appear stupendous. It is not im-
probable that the statement which he is alleged to have made
to his editor, that only ten men in the world could under-
stand his treatment of the subject, is true. I am fully pre-
pared to believe it, and wish to add that I certanily am not
one of the ten. But I can also say that, after a careful and
serious study of his papers, I feel confident that there is nothing
in them which I can not understand, given the time to become
familiar with the special mathematical processes used. The
more I work over Einstein's papers, the more impressed I am,
not simply by his genius in viewing the problem, but also by
his great technical skill.

Following the path outlined, Einstein, as just said, arrived
at certain mathematical laws for a gravitational field, laws
which reduced to Newton's form in most cases where observa-
tions are possible, but which led to different conclusions in a
few cases, knowledge concerning which we might obtain by
careful observations. I shall mention a few deductions from
Einstein's formulae.

1. If a heavy particle is put at the center of a circle, and, if

Appendix 107

108 Appendix

that there was actually such a change as just described in the
orbit of Mercury, amounting to 574" of arc per century;
and it has been shown that of this a rotation of 532" was due
to the direct action of other planets, thus leaving an unex-
plained rotation of 42" per century. Einstein's formulae
predicted a rotation of 43", a striking agreement.

4. In accordance with Einstein's formulae a ray of light
passing close to a heavy piece of matter, the sun, for instance,
should experience a sensible deflection in towards the sun.
This might be expected from "general" consideration of
energy in motion; energy and mass are generally considered
to be identical in the sense that an amount of energy E has
the mass Elcz where c is the velocity of light; and conse-
quently a ray of light might fall within the province of gravi-
tation and the amount of deflection to be expected could be
calculated by the ordinary formula for gravitation. Another
point of view is to consider again the observer inside the com-
partment falling with the acceleration of the gravitational
field. To him the path of a projectile and a ray of light would
both appear straight; so that, if the projectile had a velocity
equal to that of light, it and the light wave would travel side
by side. To an obesrver outside the compartment, e.g., to
one on the earth, both would then appear to have the same
deflection owing to the sun. But how much would the
path of the projectile be bent? What would be the shape of
its parabola? One might apply Newton's law; but, accord-
ing to Einstein's formulae, Newton's law should be used only
for small velocities. In the case of a ray passing close to the
sun it was decided that according to Einstein's formula there
should be a deflection of 1".75 whereas Newton's law of
gravitation predicted hah* this amount. Careful plans were
made by various astronomers, to investigate this question at

Appendix 109

the solar eclipse last May, and the result announced by Dyson,
Eddington and Crommelin, the leaders of astronomy in Eng-
land, was that there was a deflection of 1".9. Of course the
detection of such a minute deflection was an extraordinarily
difficult matter, so many corrections had to be applied to the
original observations; but the names of the men who record
the conclusions are such as to inspire confidence. Certainly
any effect of refraction seems to be excluded.

It is thus seen that the formulae deduced by Einstein have
been confirmed in a variety of ways and in a most brilliant
manner. In connection with these formulae one question
must arise in the minds of everyone; by what process, where
in the course of the mathematical development, does the idea
of mass reveal itself? It was not in the equations at the
beginning and yet here it is at the end. How does it appear?
As a matter of fact it is first seen as a constant of integration
in the discussion of the problem of the gravitational field
due to a single particle; and the identity of this constant
with mass is proved when one compares Einstein's formulae
with Newton's law which is simply its degenerated form.
This mass, though, is the mass of which we become aware
through our experiences with weight; and Einstein proceeded
to prove that this quantity which entered as a constant of
integration in his ideally simple problem also obeyed the laws
of conservation of mass and conservation of momentum when
he investigated the problems of two and more particles.
Therefore Einstein deduced from his study of gravitational
fields the well-known properties of matter which form the
basis of theoretical mechanics. A further logical consequence
of Einstein's development is to show that energy has mass, a
concept with which every one nowadays is familiar.

The description of Einstein's method which I have given so

110 Appendix

far is simply the story of one success after another; and it is
certainly fair to ask if we have at last reached finality in our
investigation of nature, if we have attained to truth. Are
there no outstanding difficulties? Is there no possibility of
error? Certainly, not until all the predictions made from
Einstein's formulae have been investigated can much be said;
and further, it must be seen whether any other lines of argu-
ment will lead to the same conclusions. But without waiting
for all this there is at least one difficulty which is apparent
at this time. We have discussed the laws of nature as inde-
pendent in their form of reference axes, a concept which appeals
strongly to our philosophy; yet it is not at ah1 clear, at first
sight, that we can be justified in our belief. We can not
imagine any way by which we can become conscious of the
translation of the earth in space; but by means of gyroscopes
we can learn a great deal about its rotation on its axis. We
could locate the positions of its two poles, and by watching a
Foucault pendulum or a gyroscope we can obtain a number
which we interpret as the angular velocity of rotation of axes
fixed in the earth; angular velocity with reference to what?
Where is the fundamental set of axes ? This is a real difficulty.
It can be surmounted in several ways. Einstein himself has
outlined a method which in the end amounts to assuming
the existence on the confines of space of vast quantities of
matter, a proposition which is not attractive. deSitter has
suggested a peculiar quality of the space to which we refer
our space-time coordinates. The consequences of this are
most interesting, but no decision can as yet be made as to the
justification of the hypothesis. In any case we can say that
the difficulty raised is not one that destroys the real value of
Einstein's work.

In conclusion I wish to emphasize the fact, which should

Appendix 111

be obvious, that Einstein has not attempted any explanation
of gravitation; he has been occupied with the deduction of its
laws. These laws, together with those of electromagnetic
phenomena, comprise our store of knowledge. There is not
the slightest indication of a mechanism, meaning by that a
picture in terms of our senses. In fact what we have learned
has been to realize that our desire to use such mechanisms is
futile.

THE REFLECTION OF LIGHT BY GRAVITATION

AND THE EINSTEIN THEORY

OF RELATIVITY.*

SIR FRANK DYSON
the Astronomer Royal

The purpose of the expedition was to determine whether
any displacement is caused to a ray of light by the gravitational
field of the sun, and if so, the amount of the displacement.
Einstein's theory predicted a displacement varying inversely
as the distance of the ray from the sun's center, amounting
to 1".75 for a star seen just grazing the sun. . .

"A study of the conditions of the 1919 eclipse showed that
the sun would be very favorably placed among a group of
bright stars — in fact, it would be in the most favorable possi-
ble position. A study of the conditions at various points
on the path of the eclipse, in which Mr. Hinks helped us,
pointed to Sobral, in Brazil, and Principe, an island off the
west coast of Africa, as the most favorable stations. . .

The Greenwich party, Dr. Crommelin and Mr. Davidson,
reached Brazil in ample time to prepare for the eclipse, and
the usual preliminary focusing by photographing stellar
fields was carried out. The day of the eclipse opened cloudy,
but cleared later, and the observations were carried out with
almost complete success. With the astrographic telescope
Mr. Davidson secured 15 out of 18 photographs showing the
required stellar images. Totality lasted 6 minutes, and the
average exposure of the plates was 5 to 6 seconds. Dr.

* From a report In The Observatory, of the Joint Eclipse Meeting
of the Royal Society and the Royal Astronomical Society,
NoTember 6, 1919.

Appendix 113

Oommelin with the other lens had 7 successful plates out of 8.
The unsuccessful plates were spoiled for this purpose by the
clouds, but show the remarkable prominence very well.

When the plates were developed the astrographic images
were found to be out of focus. This is attributed to the effect
of the sun's heat on the coelostat mirror. The images were
fuzzy and quite different from those on the check-plates
secured at night before and after the eclipse. Fortunately
the mirror which fed the 4-inch lens was not affected, and the
star images secured with this lens were good and similar to
those got by the night-plates. The observers stayed on in
Brazil until July to secure the field in the night sky at the
altitude of the eclipse epoch and under identical instrumental
conditions.

The plates were measured at Greenwich immediately after
the observers' return. Each plate was measured twice over
by Messrs. Davidson and Furner, and I am satisfied that such
faults as lie in the results are in the plates themselves and not
in the measures. The figures obtained may be briefly sum-
marized as follows: The astrographic plates gave 0".97 for
the displacement at the limb when the scale-value was deter-
mined from the plates themselves, and 1".40 when the scale-
value was assumed from the check plates. But the much
better plates gave for the displacement at the limb I". 98,
Einstein's predicted value being I". ,75. Further, for these
plates the agreement was all that could be expected. . . .

After a careful study of the plates I am prepared to say that
there can be no doubt that they confirm Einstein's prediction.
A very definite result has been obtained that light is deflected
according to Einstein's law of gravitation.

114 Appendix

PROFESSOR A. S. EDDINGTON
Royal Observatory

Mr. Cottingham and I left the other observers at Madeira
and arrived at Principe on April 23. ... We soon realiz
that the prospect of a clear sky at the end of May was not very
good. Not even a heavy thunderstorm on the morning of 1
eclipse, three weeks after the end of the wet season, saved 1
situation. The sky was completely cloudy at first contact
but about half an hour before totality we began to see glimp
of the sun's crescent through the clouds. We carried out on
program exactly as arranged, and the sky must have
clearer towards the end of totality. Of the 16 plates taken
during the five minutes of totality the first ten showed no stars
at all; of the later plates two showed five stars each, from which
a result could be obtained. Comparing them with the check-
plates secured at Oxford before we went out, we obtained as
the final result from the two plates for the value of the displace-
ment of the limb 1".6±O.S . . . This result supports the
figures obtained at Sobral. . . .

I will pass now to a few words on the meaning of the result.
It points to the larger of the two possible values of the deflec-
tion. The simplest interpretation of the bending of the ray
is to consider it as an effect of the weight of light. We know
that momentum is carried along on the path of a beam of light.
Gravity in acting creates momentum in a direction different
from that of the path of the ray and so causes it to bend. For
the half -effect we have to assume that gravity obeys Newton's
law; for the full effect which has been obtained we must
assume that gravity obeys the new law proposed by Einstein.
This is one of the most crucial tests between Newton's law
and the proposed new law. Einstein's law had already indi-
cated a perturbation, causing the orbit of Mercury to revolve.

Appendix 115

That confirms it for relatively small velocities. Going to the
limit, where the speed is that of light, the perturbation is
increased in such a way as to double the curvature of the
path, and this is now confirmed.

This effect may be taken as proving Einstein's law rather
than his theory. It is not affected by the failure to detect the
displacement of Fraunhofer lines on the sun. If this latter
failure is confirmed it will not affect Einstein's law of gravita-
tion, but it will affect the views on which the law was arrived
at. The law is right, though the fundamental ideas underly-
ing it may yet be questioned. . . .

One further point must be touched upon. Are we to
attribute the displacement to the gravitational field and not
to the refracting matter around the sun? The refractive index
required to produce the result at a distance of 15' from the
sun would be that given by gases at a pressure of WQ to afFo of
an atmosphere. This is of too great a density considering
the depth through which the light would have to pass.

Sm J. J. THOMSON
President of the Royal Society

... If the results obtained had been only that light was
affected by gravitation, it would have been of the greatest
importance. Newton, did, in fact, suggest this very point in
his "Optics," and his suggestion would presumably have led
to the half- value. But this result is not an isolated one; it
is part of a whole continent of scientific ideas affecting the most
fundamental concepts of physics. . . This is the most impor-
tant result obtained in connection with the theory of gravita-
tion since Newton's day, and it is fitting that it should be

116 Appendix

announced at a meeting of the society so closely connected
with him.

The difference between the laws of gravitation of Einstein
and Newton come only in special cases. The real interest of
Einstein's theory lies not so much in his results as in the
method by which he gets them. If his theory is right,
it makes us take an entirely new view of gravitation. If it is
sustained that Einstein's reasoning holds good — and it has
survived two very severe tests in connection with the perihelion
of mercury and the present eclipse — then it is the result of
one of the highest achievements of human thought. The
weak point in the theory is the great difficulty in expressing
it. It would seem that no one can understand the new law
of gravitation without a thorough knowledge of the theory of
invariants and of the calculus of variations.

One other point of physical interest arises from the discus-
sion. Light is deflected in passing near large bodies of matter.
This involves alterations in the electric and magnetic field.
This, again, implies the existence of electric and magnetic
forces outside matter — forces at present unknown, though
some idea of their nature may be got from the results of this
expedition.

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