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THE PRINCIPLE OF RELATIVITY

LIGHT OF THE PHILOSOPHY OF SCIENCE

The Principle of Relativity

In the

Light of the Philosophy of Science

By

Paul Cams

With an Appendix Containing a Letter from the Rev. James Bradley
on the Motion of the Fixed Stars, IJ2J

Chicago

The Open Court Publishing Company

^9U

75^ ^r

COPYRIGHT BY

The Open Court Publishing Ca
1913

TABLE OF CONTENTS.

PAGE

Introductory i

On the Absolute

3

Tricks of Cognition 7

Comstock on Relativity 12

The A Priori - 15

On Absolute Motion 23

Absolute Space 25

Ernst Mach 34

Objectivity 42

Primary Concepts 51

Some Physical Problems of Relativity 66

The Principle of Relativity as a Phase in the Development of Science TJ

Conclusion 82

Appendix : The Rev. James Bradley on the Motion of the Fixed Stars ... 89

8S9854

THE PRINCIPLE OF RELATIVITY.

INTRODUCTORY.

PHYSICAL science seems to have entered into a new
phase, the slogan of the new school being The Prin-
ciple OF Relativity. In some quarters the current modes
of thought are declared antiquated, and the promise is
made that the old truths will acquire a new meaning.
Physicists speak of the relativity of time and space, and
we will add that they ought as well speak of the relativity
of things, of the whole actual world in all its parts and
interrelations.

Many who have watched the origin and rise of the
new movement are startled at the paradoxical statements
which some prominent physicists have made, and it is re-
markable that the most materialistic sciences, mechanics
and physics, seem to surround us with a mist of mysticism.
The old self-contradictory statements of the Eleatic school
revive in a modernized form, and common sense is baffled
in its attempt to understand how the same thing may be
longer and shorter at the same time, how a clock will
strike the hour later or sooner according to the point of
view from which it is watched; and the answer of this
most recent conception of physics to the question. How is
this all possible? is based on the principle of the relativity
of time and space.

The man who started this movement and was the first
to formulate it in concise language and to base it upon close

2 THE PRINCIPLE OF RELATIVITY.

argument was Professor Einstein/ who was followed by
Lorentz,^ and so we hear often of the Einstein-Lorentz
theory. The strangest thing about it is that the question
is seriously debated whether or not this theory is true, and
the answer is expected from experiments; while in our
opinion we are here confronted with a method, and the
problem is simply how we can best deal with certain diffi-
culties due to the relativity of all things. These difficulties
have originated through the need of a greater exactness
in measurements, but the underlying truth — the relativity
of all things — is not a question of fact, but a recognition
of certain complications with which we must learn to deal.

On reading recent expositions of the principle of rela-
tivity the man of good education, or the one who has at-
tended universities without being a specialist in either
mathematics or physics, feels the terra Urma give way
under his feet, and when he finds that the principle of
identity seems to fail in his comprehension of things, a
dizziness comes over his intellect and he sinks into the
bottomless abyss of the incomprehensibility of existence.
A general earthquake seems to quiver through his mind.
Everything totters around him and he stands in awe at the
significance of the new thought. Nor is there any one
who dares to contradict; for the most learned arguments
are adduced, the mathematical and logical conclusions of
which bristle with formidable formulas, — yea, experiments
are made to prove the truth of the relativity of time and
space.

For the sake of convenience we will speak of the repre-
sentatives of this new conception ^s the "relativity physi-
cists" in contradistinction to the old-fashioned physicists
of the old school. It has been said that the former repre-
sent more the mathematical aspect of physics while the

^ Jahrhuch der Radioaktivitdf und Elektronik, 1905-1908.
' H. A. Lorentz, Theory of Electrons (Teubner) 1910.

THE PRINCIPLE OF RELATIVITY. 3

latter are the realistic physicists proper, too realistic to
understand the significance of the new truth.

In order to facilitate a comprehension of the situation
as well as our own conception, we will here at once and
dogmatically state that the relativity physicists are per-
fectly right; what they claim is really and truly a matter
of course, and if they only would present their proposition
without dressing up their theory in paradoxical statements,
nobody would in the least hesitate to accept the new view.
But as soon as this is done people will at the same time
find out that the new view is not novel. Its importance
has been greatly exaggerated, for the principle has been
tacitly understood in the correct way by all preceding phys-
icists who, at the time however, ignored, or better did not
enter into, the problem, because they had other more press-
ing work on hand. Nor is it unlikely that they regarded
this problem of relativity as a philosophical question which
strictly speaking had no place before the forum of physics.

ON THE ABSOLUTE.

Perhaps the easiest way of elucidating the true mean-
ing of the relativity of time and space will be by setting
forth our own position as we held it long before the prin-
ciple of relativity gained prominence or had even been men-
tioned or alluded to.

The writer's book Fundamental Problems contains the
following statement under "Definitions and Explanations"
(first edition, page 254; seecond edition, page 252) :

"Absolute existence (in fact everything absolute) is
impossible. Reality is properly called Wirklichkeit in Ger-
man, derived from wirken, to take efifect. Reality is not
immovable and unchangeable absoluteness, but the effec-
tiveness of things in their relations. Reality therefore im-
plies not only existence, but the manifestation of existence

4 THE PRINCIPLE OF RELATIVITY.

also. Existence and its manifestation are not two different
things; both are one."

Since the da3^s of Heraclitus it has been a trite truism
that all existence is in a flux. There is no rest anywhere,
and actuality consists in the effects which these changes
exercise upon one another by action and reaction. Upon
this lack of stability, resulting from a universal and in-
trinsic relativity, Mr. Spencer bases one of the strongest,
though quite untenable, arguments of his agnosticism. He
seems to expect that time, space, motion, and matter are
or should be things-in-themselves, and forgets that they
represent relations, i. e., certain features of reality. We
will here quote his exposition of the unknowableness of
motion in space. In his First Principles Spencer says:

"Here, for instance, is a ship which, for simplicity's sake, we
will suppose to be anchored at the equator with her head to the
west. When the captain walks from stem to stern, in what direction
does he move? East, is the obvious answer, — an answer which for
the moment may pass without criticism. But now the anchor is
heaved, and the vessel sails to the west with a velocity equal to
that at which the captain walks. In what direction does he now move
when he goes from stem to stern? You cannot say east, for the
vessel is carrying him as fast towards the west as he walks to the
east ; and you cannot say west for the converse reason. In respect to
surrounding space he is stationary ; though to all on board the ship
he seems to be moving. But now are we quite sure of this conclusion?
Is he really stationary? When we take into account the earth's
motion round its axis, we find that instead of being stationary he is
traveling at the rate of 1000 miles per hour to the east; so that
neither the perception of one who looks at him, nor the inference
of one who allows for the ship's motion, is anything like the truth.
Nor indeed, on further consideration, shall we find this revised con-
clusion to be much better. For we have forgotten to allow for the
earth's motion in its orbit. This being some 68,000 miles per hour
it follows that, assuming the time to be midday, he is moving, not at
the rate of 1000 miles per hour to the east, but at the rate of 67,000
miles per hour to the west. Nay, not even now have we discovered
the true rate and the true direction of his movement. With the

THE PRINCIPLE OF RELATIVITY. 5

earth's progress in its orbit, we have to join that of the whole solar
system towards the constellation of Hercules ; and when we do this,
we perceive that he is moving neither east nor west, but in a line
inclined to the plane of the ecliptic, and at a velocity greater or less
(according to the time of the year) than that above named. To
which let us add, that were the dynamic arrangements of our sidereal
svstem fully known to us, we should probably discover the direction
and rate of his actual movement to differ considerably even from
these. How illusive are our ideas of motion, is thus made sufficiently
manifest. That which seems moving proves to be stationary ; that
which seems stationary proves to be moving; while that which we
conclude to be going rapidly in one direction, turns out to be going
much more rapidly in the opposite direction. And so we are taught
that what we are conscious of is not the real motion of any object,
either in its rate or direction ; but merely its motion as measured
from an assigned position — either the position we ourselves occupy
or some other."

The same argument of the captain walking the deck
of a ship was made before Spencer, though mostly it was
a ball rolling on deck; Bradley refers to it as well known
in his time, 1727, and the same story has been repeated
after Spencer. In fact it is one of the arguments of the
relativity of space among modern relativity physicists.

The principle upon which the representatives of the
new view take their stand is a consideration of actual life.
Things are in a flux, and this is an undeniable fact. We
must bear in mind that the way of making knowledge pos-
sible at all in the flux of being is to ignore what has nothing
to do with the problem under investigation. Our method
is based upon a fiction or, if you please, upon an artificial
trick, viz., to ignore complications and to consider a certain
thing as fixed; but there are cases in which we must re-
member that we ourselves change and that the very posi-
tion we assume is moving.

This trick of assuming that our position is stable is easy
enough because man does not at once notice that there is
any change; but all things are in a flux and he himself

O THE PRINCIPLE OF RELATIVITY.

changes unconsciously. A primitive unsophisticated man
does not know that the earth on which he stands is whirhng
around itself at the rate of 1037 miles an hour, on the
equator, further that it is also revolving with incredible
speed around the sun, and that with the sun it is proceeding
in a spiral motion towards one of the constellations, prob-
ably the constellation Heracles, around an unknown center
situated somewhere in the Milky Way. God only knows
what else takes place and what kind of whirling dances
the Milky Way performs. The savage has not the slightest
idea of all this, and so it is easy for him to ignore the mo-
tion of which he unconsciously partakes.

If man really w^ere aware of all the events which in-
fluence him, his head would swim, and he would be inca-
pable of thinking any sober thought. Fortunately he is
concerned solely with his own narrow interests. The more
man in the further growth of his mind becomes familiar
with these unnoticeable events, the more he discovers that
for any particular purpose he must ignore what does not
belong to the solution of the special problem under con-
sideration.

This way of ignoring what does not concern us at the
time is an artificial process, a process of abstraction and
elimination, of cutting off all disturbing incidents, and in
doing so the philosophically minded scientist will become
aware of the fiction of arbitrarily laying down a point of
reference which is treated as if it were stable while in fact,
like everything else, it too is caught in the maelstrom of
cosmic existence.

There is nothing wrong or harmful in this fiction; on
the contrary it is an indispensable part of our method of
comprehending things. The universe is too complicated to
be understood or viewed at a glance, and knowledge, sci-
ence, cognition as well as all mental processes become pos-
sible merely by concentration, i. e., by selecting a point of

THE PRINCIPLE OF RELATIVITY. 7

view as being a certain fixed location from which we ob-
serve a change, an event, a transformation, in order to
gain a comprehension of this or that piece of existence in
contrast to others of the same or of a different kind. Such
is the nature of cognition, and this artificial trick is an
essential condition of observation.

Knowledge is relative. It is the relation between sub-
ject and object, the thinker and the thing, and this, far
from being objectionable, is only the universal condition of
all existence; for all existence is relative. All reality is the
result of action and reaction; it is a forming and being
formed under definite conditions; it is transformation.
There is no existence in and by itself. Relativity is the
principle of all real and actual being.

TRICKS OF COGNITION.

If the standpoint of an observer changes, the thing ob-
served will naturally change too in its relation to him.
Formerly physicists were in the habit of not seriously bear-
ing in mind that the fixedness of their standpoint was an
assumption; they did not follow this principle to its ulti-
mate consequences. For their special problems it was not
necessary to do so, and there is very little use in bearing
it constantly in mind. The difference in time between the
moment when the observer looks at an object and that in
which the rays of light indispensa1)le for observation strike
his eye is too inconsiderable to be taken into account ; it is
a negligible quantity. But if the object under considera-
tion is at such an enormous distance that it takes the rays
of light thousands of years to reach the eye of the astron-
omer it does make a difference, and so James Bradley was
astonished to register the fact that the fixed stars in the sky
were not always in the same place but that they pendulated
semi-annually above us with the motion of the earth around
the sun. The direction in which we see them swings from

8 THE PRINCIPLE OF RELATIVITY.

the aphelion to the periheHon, and a closer consideration
of the facts shows that the rays of very distant stars which
we catch in the aphelion are not caused at the moment when
we see them but started thousands of years prior to the
moment in which they strike the lens of the astronomer's
telescope, and so the transference of rays of light from the
star to the astronomer's eye at this enormous distance rep-
resents a relation which most forcibly drives the truth
home to us that there is nothing absolute.

The same is true of all things. The object before us
seems to stand there in a perfect and quiet completeness,
and yet the changes that work unnoticed by our dull senses
are constant, continuous and rapid. Heraclitus used to say
that he could not come out of the same river into which he
had stepped a moment before, because the water was al-
ways rushing by. Never is a drop of it the same, and this
is true of all things, even of ourselves. The observer has
to exclude from his methods of observation the fact that
he himself, his senses and his mind, are in a constant flux.

In order to elucidate the significance of the nature of
cognition as being a limitation and concentration upon one
point and constructing artificial units, the writer has on
former occasions used the analogy of the kinematoscope,
the machine which produces moving pictures.

In order to make any picture possible we need a lens,
and the lens focuses the rays of light so as to throw rays
from the same spot upon one and the same place on the
plane vv^iere the picture appears. The rays of light which
proceed from an object scatter in all directions, and unless
we use a lens to concentrate the rays, the formation of a
picture of the object w^ould remain impossible. Thus the
method of producing a picture is by concentration.

The lens produces a picture by focusing rays of light,
that is by throwing the same rays upon the same spot;
but it would also be possible to produce a picture by cutting

THE PRINCIPLE OF RELATIVITY. 9

off the redundant rays of light and singhng out one or
very few rays, each one coming from each of the several
points of the object. Accordingly we can photograph ob-
jects through a pinhole; there is only this difference that
the picture is weak and needs long exposure. This proves
that the process of concentration is fundamentally a pro-
cess of abstraction, of leaving out, of omitting the disturb-
ing multiplicity of the innumerable facts of real life as
represented in the totality of objective experience.

The kinematoscope involves not only the static form
of things, their spatial expression, the juxtaposition of
parts, but it also adds the changes that are taking place in
time. The film of the kinematoscope consists of a series of
pictures, one always a little different from another, and
if these are presented in rapid succession the series is fused
into one picture in which the succeeding differences appear
as motion. This is accomplished by the introduction of a
little winged wheel which in rapid succession covers and
uncovers the several pictures. If we would take this little
wheel v/ith its wings out of the kinematoscope, and if other-
wise the pictures on the film would succeed one another
in a rapid continuous motion without this artificial separa-
tion by the wings of the v.^heel, we would see no picture at
all but simply have a blur on the canvas. In order to
have distinct pictures appear on the canvas, we must cut
the flux of motion into little separate moments which we
may allegorically characterize as atoms of time.

Reality is a continuoi-i^^fliix,- but m order to J^^^ it
step by step we must do the same thing that the mathema-
tician does with his differential calculus. In the calculus
the curve is cut up into infinitesimal lines, which in con-
tinuous succession change their directions, and the smaller
we conceive these lines to be, the less is the mistake made
by this fiction, if they are treated like straight lines.

The method of the calculus, based upon the fiction of

lO THE PRINCIPLE OF RELATIVITY.

substituting for a continuous curve a series of little straight
lines constantly changing their direction, is not so very
different from the method of cognition in general. Nor
is there anything wrong in it, only we must remain con-
scious of the fiction. In a similar way we must know that
existence itself is a continuous system of relations, or in
other words, that relativity is the principle of all existence
in the world of actual life as well as in the domain of
thought. We must cut up the general flux according to the
needs of our investigation and lay down artificial limits.
^ ^ ■^

If we view the new physics under this aspect, it will
lose its mystic glamor and at the same tinie appear intelli-
gible. In fact we shall understand that the principle of
relativity is a matter of course, and if we cut up reality
into things, as if they were things-in-themselves, into units
or atoms, we employ a trick of cognition which makes it
possible to focus things and picture them distinctly in our
mind.

There are large numbers of scientists possessed of an
odium philosophicwn because philosophy means to them
some abstruse metaphysical system of thought which ig-
nores the natural sciences and, spiderlike, spins a world-
conception out of pure thought derived from the thinker's
subjectivity. The result is that they are soon perplexed in
their own science by philosophical problems ; for true phi-
losophy— the philosophy of science — is an indispensable
factor of cognition, and its influence extends into the fabric
of all scientific labors. Thus it happens that problems of
a philosophical character arise unexpectedly, and then the
information given by nature in reply to experiments is apt
to be misunderstood.

If the reference point (R) from which an observer
measures is in motion toward Ri, and the object observed
(O) also possesses a motion of its own, we are confronted

THE PRINCIPLE OF RELATIVITY. II

with a complicated phenomenon. If R moves toward O,
the object measured will be shorter than if it stands still,
and it will be longer if R moves with O in the same direc-
tion. We have only to forget, after the fashion of the
pragmatist, that there is an ideal of objective cognition,
and assume that all there is about size or the objective
measure of things consists in the result of our measuring
and we have the clue to the paradoxes of the physics of
relativity. If the point of reference is not stationary and
if we neglect to account for its motion, the result of our
measurement is necessarily vitiated thereby as much as
the pragmatist's philosophy by his personal equation.

O

Ri

Fig. I.

There are further complications of measurement. The
time needed for the transmission of signals must also be
taken into consideration. The rays of light travel at an
enormous velocity but the distances in the starry heavens
are also enormous and the distance between O and R is
less than between O and Ri. The rays which were sent
out from O at the moment of measurement have already
passed the track of the observer at R, while this same ob-
server has moved on to Ri, and there he catches the rays
sent out from O in its position at O ; in the meantime how-
ever the object O has in its turn also changed its place.
From Ri it appears at O, where it stood while the observer
was stationed at R, but in fact it stands no longer at O but
has in the meantime proceeded on its own path whither-
soever that may have led O, backward or forward, in any

12 TPIE PRINCIPLE OF RELATIVITY.

Other direction than R, possibly in the same direction as R.
Such phenomena are necessary resuUs of the relativity of
existence, and we must bear them in mind when confronted
with complicated conditions which present themselves, for
instance in astronomical cases. Here the mistakes rising
from the fiction of assuming our reference point to be stable
are considerable enough to enforce attention, and in that
case we shall have to make allowance for the instability of
our reference point, as well as for the time which the rays
of light need for their travel through space.

That was exactly Bradley's case as set forth in his
essay written in 1727, one hundred and eighty-five years
ago, and thus he became the forerunner of the relativity
physicists. To state it in other terms, Bradley correctly
solved a problem which in our days led to the formulation
of the principle of relativity, and he did so without men-
tioning this theory, yea without feeling the need of formu-
lating it. He simply took it for granted that he had in this
case to consider the motion of the earth that served him
as a reference point — the place of his observations.

COMSTOCK ON RELATIVITY.

The most popular and at the same time the most exact
characterization of the principle of relativity comes from
the pen of Prof. D. F. Comstock, of the Massachusetts
Institute of Technology. It appeared in Science (Vol.
XXXI, 1909, p. 767), and we quote from it the passages
which contain the statement of the problem:

Professor Comstock starts with the following two pos-
tulates :

"The uniform translatory motion of any system can not be de-
tected by an observer traveling with the system and making obser-
vations on it alone.

"The velocity of light is independent of the relative velocity
of the source of light and observer."

THE PRINCIPLE OF RELATIVITY. I3

The main passages of his exposition state the problem
thus :

"The whole principle of relativity may be based on an answer
to the question : When are two events which happen at some dis-
tance from each other to be considered simultaneous? The answer,
'When they happen at the same time,' only shifts the problem. The
question is, how can we make two events happen at the same time
when there is a considerable distance between them.

"Most people will, I think, agree that one of the very best
practical and simple ways would be to send a signal to each point
from a point half-way between them. The velocity with which
signals travel through space is of course the characteristic 'space
velocity,' the velocity of light.

"Two clocks, one at A and the other at B, can therefore be set
running in unison by means of a light signal sent to each from a
place midway between them.

2 C >- B

Fig. 2.

"Now suppose both clock A and clock B are on a kind of
sidewalk or platform moving uniformly past us with velocity v.
In Fig. 2 (2) is the moving platform and (1) is the fixed one,
on which we consider ourselves placed. Since the observer on
platform (2) is moving uniformly he can have no reason to con-
sider himself moving at all, and he will use just the method we
have indicated to set his two clocks A and B in unison. He will
send a light flash from C, the point midway between A and B,
and when this flash reaches the two clocks he will start them with
the same reading.

"To us on the fixed platform, however, it will of course be
evident that the clock B is really a little behind clock A, for, since
the whole system is moving in the direction of the arrow, light will
take longer to go from C to B than from C to A. Thus the clock
on the moving platform which leads the other will be behind in time.

"Now it is very important to see that the two clocks are in uni-
son for the observer moving with them (in the only sense in which
the word 'unison' has any meaning for him), for if we adopt the first

14 THE PRINCIPLE OF RELATIVITY.

postulate of relativity, there is no way in which he can know that he
is moving. In other words, he has just as much fundamental right
to consider himself stationary as we have to consider ourselves sta-
tionary, and therefore just as much right to apply the midway signal
method to set his clocks in unison as we have in the setting of our
'stationary clocks.' 'Stationary,' is, therefore, a relative term and
anything which we can say about the moving system dependent on
its motion, can with absolutely equal right be said by the moving
observer about our system.

"We are, therefore, forced to the conclusion that, unless we
discard one of the two relativity postulates, the simultaneity of two
distant events means a different thing to two different observers if
they are moving with respect to each other."

We quote further:

"It must be emphasized that, because of the first fundamental
postulate, there is no universal standard to be applied in settling such
a difference of opinion. Neither the standpoint of the 'moving' ob-
server nor our standpoint is wrong. The two merely represent two
different sides of reality. Any one could ask: What is the 'true'
length of a metal rod? Two observers working at different tem-
peratures come to different conclusions as to the 'true length.' Both
are right. It depends on what is meant by 'true.' Again, asking
a question which might have been asked centuries ago, is a man
walking toward the stern of an eastbound ship really moving west?
We must answer 'That depends' and we must have knowledge of the
questioner's view-point before we can answer yes or no."

The question of the man walking on a ship not only
"might have been asked centuries ago," but it has been
asked centuries ago. Our forebears were more conscious
of the relativity of existence than the relativity physicists
credit them.

Professor Comstock continues:

"It must be remembered that the results of the principle of
relativity are as true and no truer than its postulates. If future
experience bears out these postulates then the length of the body,
even of a geometrical line, in fact the very meaning of 'length,'
depends on the point of view, that is, on the relative motion of the
observer and the object measured."

THE PRINCIPLE OF RELATIVITY. 1 5

Professor Comstock's verdict of the case is summarized
in this paragraph:

"The results of the principle for uniform translation are simply
as true as its two postulates. If either of these postulates be proved
false in the future, then the structure erected can not be true in its
present form. The question is, therefore, an experimental one."

Here we demur. We claim that the question is not ex-
perimental but belongs to the department of a priori rea-
soning.

Professor Comstock does not enter into questions of
mass connected with the principle of relativity but is satis-
fied with this comment:

"The apparent transverse mass is, I think, best derived by Lewis
and Tolman,^ in their excellent paper on the principle of relativity,
and the relation between transverse and longitudinal mass is shown
in the most direct and simple way by Bumstead* making use of the
torsion pendulum. Any one interested in the subject should read
these two papers."

THE A PRIORI.

It is characteristic of modern science to denounce the
principle of the a priori and to extol experiment and expe-
rience. Now it is true that experience and experiment are
indispensable factors in science, and in all the specialties
of science. In experience and experiments we deal with
the facts presented to us by nature; but the method of
reasoning is not a thing which is derived from sense ex-
perience.

The method of reasoning is, as Kant truly said, a priori
and, let us add, the a priori is nothing mystical or mysteri-
ous; it is simply the result of pure thought or reflection
from which the data of the senses have been excluded.
Pure thought (or better, purely formal thought) is a men-
tal construction, or, if you prefer, a fiction. We omit every-

*Phil. Mag., i8, 510-523, 1909.

* Am. Jour, of Science, 26, pp. 493-508, 1909.

l6 THE PRINCIPLE OF RELATIVITY.

thing concrete and thus we retain a field of abstract possi-
bihties. Elsewhere we have called it a field of anyness.^
Obliterating in our mind all particularity we retain noth-
ing concrete and in this field of nothingness we build up
pure relations. From this domain all real things, com-
prising everything which we subsume under the categories
of matter and energy, has been excluded. But these pure
relations, i. e., pure forms which are non-material con-
structions lacking all concrete qualities such as all real
things possess, serve us as models for the relations of any
possible purely mental or actual existence. Our doings in
this field of abstraction consist in the fiction of pure lines,
pure numbers, pure motion, pure ideas and their inter-
relations such as genera and species, and thus we are ca-
pable of building up a world of purely formal or relational
thought, the totality of which in space is called geometry,
and in the domain of numbers which originate by counting
a series of single units, arithmetic, etc. In the domain of
pure thought, consisting of genera and species, we call the
laws that govern their relations logic, and the law of trans-
formation, of which the positive aspect is properly called
causality, and its negative counterpart the law of conser-
vation of matter and energy, has been called by Kant pure
natural science.

All systems of mental constructions have the advantage
of picturing in our mind any possible configuration of rela-
tivity, and in this sense pure thought (Kant's a priori) is
a field of anyness. It can be applied to any fact or set of
facts of existence, actual or fictitious, and these systems
of mental constructions therefore furnish us with the key
to determine the relations of real nature. They render
possible the systematization of sense impressions and thus

^ See Philosophy of Form, the chapter on "The Foundation of Mathe-
matics and Logic," pp. 7-10. For further details see also the chapter "Form
and Formal Thought" in the author's Fundamental Problems, pp. 26-60.

THE PRINCIPLE OF RELATIVITY. IJ

these systems of pure thought in the field of anyness are
the methods of scientific operation.

Let us not therefore speak contemptuously of the a
priori, or denounce apriorism as something medieval and
elusive, for even here in the attempt at establishing the
principle of relativity in time and space, the arguments of
the physicists are absolutely aprioristic. There is not one
of these so-called experiments, invented to prove the rela-
tivity of time and space, which does not ultimately resolve
itself into a machine that renders visible aprioristic con-
siderations.

The ultimate arguments in all the experiments made
to prove the relativity of time and space move in a domain
of purely formal thought, and the force of them is ulti-
mately of the same kind as the Q. E. D. of Euclidean theo-
rems. We think here mainly of such propositions as locate
an observer on the sun and another on the earth. Their
clocks actually agree, but when compared they are found
to dififer. About eight minutes have elapsed when the
observer on earth registers the time as the rays of the sun
reach the earth, and vice versa when the clock on earth
is observed as the rays from the earth strike the sun. The
imitation of the same conditions for the sake of comparing
the registration of two moving systems in an actual ex-
periment amounts to nothing more than the pencil draw-
ings of a Euclidean or logical figure in which the a priori
reasoning is visibly presented as a deuwustratio ad oculos.
The argument remains in either case one of pure thought.

The photograph of such an apparatus built for the pur-
pose of making an experiment in the relativity of time and
space to show the difiference between a solar clock and a
terrestrial clock may be found in the article of Emil Cohn
of Strassburg, 'Thysikalisches liber Raum und Zeit" in
Himmel und Erde, Vol. XXIII. To be sure the instru-
ment does not fulfil the conditions either of distance or of

l8 THE PRINCIPLE OF RELATIVITY.

the velocity of the transference of the signal, ''but," says
Professor Cohn, "that is of secondary importance."

There are two motions both constant and both stand-
ing in a definite proportion. The sun with its clocks has
been made to stand still. The earth with its two clocks
moves, and there is an arrangement by which to represent
the transference of signals. The main thing is that "their
velocities stand in definite proportions and all that concerns
us are these proportions. That we have here replaced the
enormous velocity of light by a velocity of a few centi-
meters per seecond is unessential. It is essential, however,
that the velocity of the earth is three-fourths the velocity
of light, while the real ratio is i : 10,000."

Newton's laws are a priori, and Newton proves that
these laws hold good in, and are serviceable as, interpreta-
tions of the actual world of fact. The empiricist ought to
rebel against Newton's laws, because they never have been
nor ever can be proved by either experience or experiment.
Whoever saw a body moving in a straight line? and has
Newton (from the standpoint of the empiricist) any right
at all to make such sweeping statements of movements
which have never occurred in the experience of anybody?
V The most general principle at the bottom of scientific
work is perhaps the so-called law of the conservation of
matter and energy, and even this law is based on purely
\a priori arguments.

Incidentally we will say that the law does not hold
good if we restrict the notion of matter to matter in the
sense of the physicist which is mass, i. e., to concrete par-
ticles of existence that are extended and possess weight.
It holds good only if we understand by matter the substance
of being, its objective reality. We had better therefore
speak of the conservation not of matter but of substance,
for gross matter, consisting of the chemical elements, is
constantly being produced before our eyes in the starry

TKt PRINCIPLE OF RELATIVITY. IQ

heavens where the astronomers can watch the process
through their telescopes. In the nebulas we see now the
commotion of whirls with which gradually first the lighter
and then the heavier chemical elements are being manu-
factured out of the original world-substance which we
assume to be the same as the luminiferous ether.

Therefore we may surrender the law of conservation
of gross matter, ])ut we still hold to the conception that
tliere is a conservation of stuff or substance, and the same
is true of energy. There may be energy in the shape of
a stress incorporated in the same wonderful world stuff,
the ether, and this stress may be set free and become actual
motion or kinetic energy, by some cause which creates
those whirls that start the formation of nebulas.

And what proves the law of this conservation of sub-
stance and energy? It is the necessity of a priori thought
which compels us to assume the principle that nothing
originates from nothing and nothing disappears into noth-
ing, which thought rests ultimately on the idea that all
processes of existence are transformations. Everything
that originates is formed by combination from something
tliat existed before.

It has been maintained that the principle of relativity
must be proved experimentally, but this is a mistake. Real-
ity is everywhere a system of interrelations, yea every
single concrete thing, every phenomenon, every piece of
existence is a bundle of relations. It can be analyzed into
its elements, which are actions and reactions; and that is
all that reality means. Space as well as time are merely
the measures, the former of arrangement or position, the
latter of succession. Space denotes the interrelation of
parts constituting figures or shapes affording a mode of
determining direction and distance. Time measures the
duration of events which is done by counting uniform
cyclical motions or parts thereof. And so we must grant

20 THE PRINCIPLE OF RELATIVITY.

that the relativity of time and space, as well as of all real
, things is a universal and inalienable condition of all exist-
ence. We can not think of any actuality which would not
be dominated by relativity; which means we must regard
the principle of relativity as an a priori postulate.

The principle of relativity is not established by expe-
rience but is ultimately based upon reflection and pure
ratiocination. It belongs to the category of purely formal
thought as much as all arithmetical and geometrical propo-
sitions.

If any proposition of purely formal thought, such as
2X2 = 4, does not hold good in our experience, we doubt
the correctness of our counting or measuring, but we do
not doubt our a priori proposition. We revise our obser-
vation, not our logic, our arithmetic, our mathematics; and
suppose our observation proves true, suppose that 2X2
rabbits shut up in a cage are on recounting their number
found to be more than four, say six or ten or any higher
amount, we do not upset our arithmetic or any of our
purely formal propositions, but seek the cause of the ir-
regularity in the objects, in the things or animals counted.
In that case we are positive that some transformation of
the concrete material has set in which adds to the number
to be expected according to arithmetical law.

If the reference point (R) belongs to the same system
of motion as the object observed (O), our measurement
will be correct and indicate the size of the object ade-
quately. But if R moves in a direction and with a velocity
of its own, different from O, the measurement will not be
adequate; it will be warped in an exact proportion to the
motion of R, and this rule holds good in the same way as
all mathematical, logical and generally purely formal theo-
rems.

The reliability of purely formal truths is not merely
theoretical, but finds its application in practical life, in the

THE PRINCIPLE OF RELATIVITY. 21

objective world of matter and motion, and can be verified
by experience and experiment. And this is true also of
the relativity of time and space.

If for instance a photographer takes the picture of a
rapid express train in motion with a camera provided
with a curtain shutter, the wheels will not be round but
oval in the photograph, and the relativity photographer
who identifies the picture with the thing, in the same way
as the relativity physicist identifies the result of measur-
ing with the objective size of the object measured, will
claim that in proportion to the velocity of the train times
the inverse proportion of the velocity of the slit in the
curtain of the shutter, the wheels will increase their hori-
zontal diameters and become that much more oval. Yea
they will insist that the very same wheel will be at the
same time in one camera, only a little more, in another
one much more oval according to the quickness with which
the slit of the curtain passes over the sensitive plate.

The relativity photographer will claim that the wheels /
in motion are oval while common mortals think that they
only appear oval in the photograph.

Photographs do not lie; they show the objects photo-
graphed without any personal equation on the part of the
photographer; their objectivity and impartiality can not \
be doubted, and here we see the wheels oval. They are
oval, and their ovality, viz., their deviation from true cir-
cles, depends on the velocity of certain motions. An en- ;
thusiast for the principle of relativity can justly claim that \
every photograph of a rapid train which shows the oval ]
form of the wheels is a successful experiment in the demon-
stration of the relativity of figure in space.

The truth of the principle of relativity in the domain
of photography can be explained by a priori considerations.
It is a matter of course, and if we argue the subject in our
mind in pure reflection, we find out what we must expect,

22 THE PRINCIPLE OF RELATIVITY.

and if finally we make the experiment, the principle proves
true.

In the same way all the experiments made by machin-
ery so constructed as to represent terrestrial and solar
clocks or yard sticks, and to point out the unavoidable dif-
ference of measurements in both time and size resultant
from their respective motions of the earth and the sun as
well as the time it takes to transmit signals, are not experi-
ments in the physicist's sense but expositions and demon-
strations of purely formal truths which belong to the cat-
egory of mathematics.

If the principle of relativity does not hold good in any
domain of actual life, we must seek the cause in the mate-
rial used and not in the principle of relativity. In other
words we would be confronted with a purely physical prob-
lem which demands a physical solution, and this seems to
be the case of the Fizeau experiment.

Prof. Emil Cohn, of Strassburg,® says:

"It is strange that the relativity principle of mechanics does not
hold good in radiation — in radiation and therewith in electrodynamics,
for that the spread of radiation is an electrical process we may con-
sider since Heinrich Hertz as an assured matter of experience. The
decisive experiment which has been made by Fizeau is this: In a
liquid, flowing with a uniform velocity, light is to be propagated in
the direction of the current. According to the relativity principle
an observer drifting in the current should find the velocity of propa-
gation to be the same as if the liquid were at rest, and an outside
observer should find the velocity of the light augmented by the full
velocity of the current in the liquid. (Think, e. g., of the ball
rolling on the deck of a ship in motion.) But such is not the case.
There is added only a certain portion, viz., the index of refraction."

The very result of the experiment proves that one of
the determinant factors is the physical property of the
fluid.

When the principle of relativity is applied to positive

''Loc. cit., p. 7.

THE PRINCIPLE OF RELATIVITY. 23

facts we reach slippery ground, on which we must be on
our guard to avoid mystification, for it would seem as if
the law of the conservation of matter and energy were
upset and all objectivity of scientific truth were lost. Ex-
periments have been made to prove the principle of rela-
tivity with the result that Hupka and Bucherer,^ the former
with cathode rays, the latter with radium rays, demon-
strate that mass increases with velocity as the relativity
principle demands. Kaufmann, however, comes to the
conclusion that there is an increase of mass but not as
ought to be expected according to the principle of relativ-
ity, while Michelson and Morley demonstrate with great
exactness that in spite of the motion of the earth the trans-
mission of light is not changed at all, not within one hun-
dred millionth of its proportion nor even a fraction thereof.

It would lead us too far to discuss the experiments .
made to apply the principle of relativity to physics and
electrodynamics; we will only mention that (as a priori
might be expected) they tend to corroborate its applica-
bility in these domains. ^

ON ABSOLUTE MOTION.

Dr. Philipp Frank in his discussion "Does Absolute
Motion Exist ?"^ declares that motion in physics always
means "motion with reference to some definite body," and
he recognizes that "this question is a philosophical one^
but it is certainly not a physical question." The answer
is the first Newtonian law, viz., "A body not affected by
an exterior force moves in a straight line with a constant

' A. H. Bucherer, "Die experimentelle Bestatigung des Relativitatsprin-
zips" in Annalen der Physik, XXVIII. p. 513; "Messungen an Becquerel-
strahlen" in Physikalische Zeitschrift, IX, pp. 755-760.

'"Gibt es eine absolute Bewegung?" Lecture delivered December 4, 1909,
at the University of Vienna before the Philosophical Society. Wissenschaft-
liche Beilage, 1910.

* Dr. Frank adds here : "Perhaps the psychologist would call it a psycho-
logical one," but this would be a mistake. Psychology has nothing to do
with the subject.

24 THE PRINCIPLE OF RELATIVITY.

velocity which of course may be zero/" This is called the
law of inertia."

If another force affects the moving body it is subject to
the second law, the law of the parallelogram of forces, ac-
cording to which the body will move along the diagonal of
the two forces.

The following extracts translated from Dr. Frank's
essay on absolute motion will prove instructive:

"The system of the fixed stars constitutes a fundamental body.
Even in shooting a cannon ball towards the south we see no devia-
tion from the law of inertia if we consider it with reference to the
fixed stars. The ball remains in the same plane ; but this plane does
not retain the same relative position to the meridian of the earth,
wherefore, of course, with reference to the earth the law of inertia
is violated. On the whole it is evident that we really recover all the
observed motor phenomena when we refer Newton's laws of motion
to the fixed stars. Not until they are referred to the fixed stars do
these laws acquire an exact sense which makes it possible to apply
them to concrete conditions.

"We shall call those motions which are referred to a fundamental
body 'true movements' and those related to any other body of ref-
erence 'apparent movements.' For instance the immobility of my
chair is only apparent, for when referred to the fixed stars it is in
motion.

"We now ask whether there arc any other fundamental bodies
aside from the system of the fixed stars. Obviously not any body
revolving in an opposite direction to the fixed stars can be such a
fundamental body, for considered with reference to such a body all
rectilinear movements are curved. Therefore the law of inertia
could not hold with reference to the body in question if it is valid
with reference to the fixed stars. Then too a fundamental body can
possess no acceleration with reference to the fixed stars, because
otherwise there would be no uniformity of the motion of inertia with
reference to it. However, these conditions are not only necessary
but they are sufficient to characterize a fundamental body. All bodies
moving uniformly and in a straight line with reference to the fixed
stars will also be fundamental bodies inasmuch as rectilinearity and

" The original reads thus : "Corpus omne perseverare in statu suo quies-
cendi vel movendi uniformiter in directum nisi quatenus a viribus impressis
cogitur statum ilium mutare."

THE PRINCIPLE OF RELATIVITY. 25

uniformity continue to hold for them, as do likewise the supple-
mentary velocities determined by the second law. Accordingly New-
ton's laws do not indicate one single fundamental body, but an in-
finite number moving in opposite directions with a uniform and
rectilinear motion.

"Hence we may well speak of 'true' in contrast to apparent
rotary motion ; for all bodies revolving with reference to a funda-
mental body revolve with reference to all other bodies. The same
is true of true acceleration because an acceleration with respect to
a fundamental body is also acceleration (i. e., change of velocity)
with respect to all the rest. On the other hand, there is no sense
in speaking of 'true' uniform rectilinear motion ; for if a body pos-
sesses a uniform velocity with respect to the fixed stars, it is itself a
fundamental body possessing of course with respect to itself a
velocity of zero; it is at rest.

"Accordingly there is true acceleration, but not true velocity.
From this is easily derived a proposition established by Newton
which is called the principle of relativity of mechanics, namely that
a uniform rectilinear movement of the system as a whole makes no
change in the processes within the system ; that is to say, we can not
tell from the processes within the system what velocity the uniform
rectilinear movement possesses with reference to the fixed stars.
On the other hand, the rotary motion of a system has indeed an in-
fluence on the processes within the system, as for instance in the
phenomena of centrifugal force ; thus the earth has become flattened
at its poles because of its rotation, or if I revolve a dish full of water
the water will rise at the sides."

ABSOLUTE SPACE.

If we make measurements of motions which are lim-
ited to terrestrial conditions, the earth is and must be the
system which, though not absolute, must for the nonce be
so considered, and in that case the earth is called the funda-
tnental or inertial body, of our measurements. But in
many purely terrestrial motions we observe in very precise
and exact measurements, deviations which compel us to
seek for another fundamental body.

This happens in the case of the Foucault pendulum ex-
periments and may also be observed in a cannon ball which

26 THE PRINCIPLE OF RELATIVITY.

if shot south along the meridian will at a great distance
show a deviation toward the west. Such experiments
point out that the entire system of the fixed stars ought
to be regarded as the fundamental body which thus would
represent to us absolute space. I say here on purpose
"represent to us," not "be," because we are most probably
in the same predicament as persons moving in a train to
whom the train and its interrelations, so long as the train
does not move in a curve, represent the fundamental body
or absolute space, viz., the ultimate system of reference.

It stands to reason that bodies in translation ( in which
the entire system as a whole moves in the same direction
with the same velocity and without any internal change
even of its smallest particles) behave as if they vv'ere at
rest, and so the motion of a straight line cannot be observed
so long as the observer remains limited to his own system.
Every deviation from a straight line, however, implies a
retardation on the inner side of the curve, or, what means
the same, an acceleration on the outside of the curved path
of motion. Accordingly all rotations bear witness to the
character of their motion as appears in the Foucault pen-
dulum experiment and in the flattening of the earth at the
poles. Since further the idea of a rectilinear motion is a
mere a priori postulate which can never be realized in
actual nature, we see that every motion that takes place
anywhere is affected by the totality of the universe. We
must assume that its existence (the existence indeed of
every particular thing or the recurrence of any event) must
be understood to be a part of the whole. It bears traces of
all the influences of all masses, and of all forces of the rest
of the world according to the way it is interrelated with its
surrounding conditions.

The fixed stars have so far proved sufficient for our
terrestrial needs to serve us as a fundamental body for

THE PRINCIPLE OF RELATIVITY. 2/

calculations of a mechanical nature; but here the problem
of absolute space presents itself.

We know positively that though the fixed stars are
practically a fundamental body to us for mechanical meas-
urements, they are shifting about among themselves and no
more constitute something absolute than does our own
earth ; and yet there has risen a controversy on this subject
in which Ernst Mach applies the principle of relativity
throughout the universe while Prof. Alois Hofler stands up
for what he calls the absolutist theory. We will hear what
Dr. Frank has to say on this point :

"Is it to a certain extent accidental, or is it essential, that the
^aHty of the fixed stars coincides with that fundamental body in
relation to which the laws of Newton hold valid? Or to put it
more clearly : If the fixed stars were set violently in motion among
each other and hence could no longer constitute a fixed body of
reference, would the mechanical processes on earth proceed exactly
as they did before? For instance, would the Foucault pendulum
move just as at present, even though it now turns with the fixed
stars, whereas in that case it would not be quite clear which con-
stellation's revolution it should join?

"Were everything to remain as of old the fundamental system
of reference would not be determined by the fixed stars but would
only accidentally coincide with them, and would in reality be
some merely ideal or yet undiscovered body. In the other case all
mechanical occurrences on earth would have to be completely altered
to correspond with the promiscuous movements of the fixed stars.

"It is well known that this is the view held by Ernst Mach. It
alone holds with consistent firmness to physical relativism, and it
alone answers the second main question of physics in the relativistic
sense.

"The opposite view is represented by Alois Hofler in his studies
on the current philosophy of mechanics, and lately by G. Hamel, pro-
fessor of mechanics at the technical high school of Briinn, in an
essay which appeared in the annual report of the German mathemat-
ical society of 1909 on 'Space, Time and Energy as a priori Forms
of Thought.'

"Before I enter ui)on the controversy itself I would like further

28 THE PRINCIPLE OF RELATIVITY.

to elucidate Mach's view by carrying out its results somewhat farther.
In his well-known essay on the History and Root of the Principle
of the Conservation of Energy^^ Mach ascribes to the distant masses
in space a direct influence on the motor phenomena of the earth
which supplements the influence afforded by gravitation. Of course
no effect of gravitation from the fixed stars upon the earth can be ob-
served, yet in spite of this they influence, for instance, the plane of
oscillation of the Foucault pendulum because in Mach's opinion it
remains parallel to them.

"The question now arises according to what general law of
nature this influence operates which does not, like gravity, produce
accelerations but velocities instead. Obviously this influence must
be a property belonging to every mass, for according to our present
conception the fixed stars of course are precisely the same sort of
masses as earthly bodies. ^

"However, experience teaches us that terrestrial masses have
no more influence on the plane of oscillation of the Foucault pendu-
lum than has the changing position of the moon, sun and planets ;
but on the other hand it is exactly the most distant masses, the fixed
stars, which determine its plane of oscillation. Accordingly we must
either assume that the effect is directly proportional to the distance
of the masses (which would be very strange indeed) or simply
assume that this effect is proportional to the effective masses and
independent of the distance, whence the dominant influence of the
more remote, as the far greater and more numerous, bodies would
naturally follow, and Mach inclines to this latter view.

"Mach's view shows most clearly in his position with regard
to Newton's famous bucket experiment. In this Newton intended
to show that the centrifugal force produced by a revolving body is
due not to its relative but to its absolute velocity of rotation. He
suspended a bucket filled with water by a vertical cord, twisted the
cord quite tightly and then let it untwist itself, in this way setting the
bucket to revolve rapidly. At first the water did not rotate with the
bucket and therefore the bucket had a velocity of rotation with
reference to the water while in the meantime the surface of the
water remained undisturbed. In time, however, friction caused the
water to become so affected by the rotary motion that bucket and
water revolved like one homogeneous mass whereby the centrifugal

" Second edition, Leipsic, 1909 ; English translation by P. E. B. Jourdain,
Chicago, 191 1.

THE PRINCIPLE OF RELATIVITY. 29

force caused the water to rise at the sides of the bucket and the sur-
face became concave.

"Hence it is evident that the centrifugal force reached its great-
est strength at the moment when the relative motion of the water
with respect to the bucket became zero ; hence according to New-
ton this force can be produced only by the absolute rotary motion of
the water.

"To this now Mach justly protests that only the relative rotation
of the water with reference to the fixed stars is to be considered, for
this system of the fixed stars and not the bucket is the fundamental
body. And indeed at first the water was at rest with reference to the
fixed stars, but at the close of the experiment it was revolving.
The mass of the bucket compared to the mass of the fixed stars is
an entirely negligible quantity, so that it does not depend in the
least upon the rotation. But we can not know, adds Mach, how
the experiment would turn out if the sides of the bucket were miles
thick ; and by this he apparently means so thick that their mass would
be considerable even when compared with the mass of the system of
fixed stars. Then indeed might the rotation of the bucket disturb
the action of the fixed stars.

"Hofler protests, on the other hand, that a system which is
symmetrical round its axis could not according to all our experience
in mechanics produce by its rotation that sort of an effect on the
water within it.

"This also is quite true. But the effect of the masses assumed
by Mach is such that it can not be expressed in our ordinary ex-
periences with mechanics except by means of the facts of the iner-
tia of all motion with reference to the fixed stars. New conditions
such as the rotation of an enormously thick bucket might give rise
to new phenomena. If we agree with Mach's view that the rotation
of the plane of the Foucault pendulum is directly produced by the
masses of the fixed stars, we must likewise admit, in order to be con-
sistent, that the relative rotation of the very thick bucket might give
rise to similar effects with reference to the water, as the rotation of
the system of the fixed stars with reference to the earth to the plane
of oscillation.

"Hofler expresses his contention against Mach's thesis in the
form of the following question: If in Galileo's time the sky had
been clouded over and had never become clear again so that we
would never have been able to have taken the stars into our calcu-
lation, would it then have been impossible to have established our

30 THE PRINCIPLE OF RELATIVITY.

present mechanics solely by • the aid of terrestrial experiments ?
By this question Hofler means to say that if the connection with the
fixed stars were a constituent of the concept of uniform motion, we
would never have been able in such an overclouded world to have
established the law of inertia, for instance, whereas in reality it is
clear that this would nevertheless have been possible.

"I will not dwell on the more psychological question as to
whether or how easily this would have been possible, but will only
consider now the logical construction of mechanics in such a dark-
ened world on the hypothesis that easily or with difficulty in one
way or another we would have attained to our present knowledge
of mechanics.

"Let us for a moment imagine ourselves in such a world.
Above our heads extends a uniform vault of uninterrupted gray or
black. Were we to shoot projectiles toward the south we would
see that they describe paths which are curved towards the west ; if
we started pendulums to vibrating we would see that they would re-
volve their planes of oscillation in mysterious periods — I say mys-
terious because we might perhaps be able to perceive the change of
day and night as an alternation of light and darkness, but would not
be able to refer it to the movements of celestial bodies. Perhaps
at first we would surmise that the motion of the pendulum could be
ascribed to optical influences. I would like to see placed in such a
world one of the philosophers who regard the law of inertia as an
a priori truth. In the face of these mysterious curvatures and de-
flections he would probably find no adherents and he would not
know himself what to make of his own standpoint.

"Finally, let us assume, there arises a dauntless man, the Coper-
nicus of this starless world, who says that all motions proceed spon-
taneously in a straight line, but that this straight line is not straight
with reference to the earth but with respect to a purely ideal system
of reference which turns in a direction opposite to that of the earth.
The period of this rotation is supplied by the period of the Foucault
pendulum.

"This man would of course deny physical relativism upon the
earth, for in his opinion terrestrial processes would not depend only
on the relative velocities of terrestrial bodies but on something
else besides, viz., their velocities with respect to a purely ideal sys-
tem of reference. Nevertheless, he would not introduce any non-
physical element because for the purpose of the physicist a purely
ideal system of reference whose motion with respect to an em-

THE PRINCIPLE OE RELATIVITY. 3 1

pirical system is known serves the same purpose as would the em-
pirical system itself. This bold innovator might finally refer the
words 'true rest' and 'true motion' to his ideal fundamental body
and so ascribe true motion and only apparent rest to the earth, thus
maintaining a mechanics which would coincide literally with that of
ours to-day, except that no small luminous points would be seen
sparkling in connection with the fundamental body.

"Hence we see that physical relativism is not a necessary tool
of the physicist. Apart, perhaps, from the psychological improb-
ability— of which, however, nothing more positive can be said — the
possibility of the development here indicated is logically free from
objections throughout, and therefore the same is also true of the
possibility of a nonrelativistic physics.

"But I would like to strengthen the argument of Hofler even
somewhat further. That is to say, I would ask whether the world
in which we live is then really so essentially different from that
fictitious one. Imagine the dark roof which conceals the sky placed
somewhat higher so that there is room beneath it for the fixed stars,
perhaps as the dark background which may be seen nightly in the
starry sky. The whole difference then consists in the fact that not
only the Foucault pendulum and similar appliances move with ref-
erence to the earth, but enormously greater masses as well — all the
twinkling lights of the sky by which the thought of a fundamental
body in motion with respect to the earth is psychologically greatly
facilitated, but logically is not much changed. Now imagine the
sky of this earlier dark world suddenly illuminated ; then we would
see that the fictitious system of reference is closely linked to enormous
cosmic masses, and it would be easy enough to accept Mach's hy-
pothesis that these masses condition the fundamental system ....

"If a distinction must be drawn between the respective values
of the conceptions of Mach and Hofler, it is as follows : Mach's view
adds decidedly more to the observed facts ; for that it retains phys-
ical relativism does not involve freedom from hypothesis, because
at best this relativism is theory and not fact. Mach sets up, hypo-
thetically of course, a new formal natural lav/ with regard to the
action of masses existing side by side with gravitation, affecting
the experiment very materially but unable to raise any claim to the
simplest description of actual conditions.

"The other view, which simply introduces the system of ref-
erence procured by observation of the terrestrial and celestial move-
ments without asking whence all this is derived, represents the pres-

32 THE PRINCIPLE OF RELATIVITY.

ent state of our knowledge most adequately without any arbitrary
addendum but also without giving the spirit of inquiry any incentive
to new experiments.

"It is the old contrast between the most exact and least hypo-
thetical representation possible of the known science, and progressive
inquiry after new things in more or less daring and fantastic hypoth-
eses. But Mach in this case stands in the opposite camp as in most
other cases where his repugnance to all hypothesis has made him a
pioneer in the phenomenological direction ....

"I therefore believe I have proved that we can grant the follow-
ing: Physical phenomena do not depend only on the relative motion
of bodies without at the same time admitting the possibility of the
concept of an absolute motion in the philosophical sense."*

Strange that Mach, with his reluctance to introduce
anything hypothetical except what is absolutely indispen-
sable, should range on the side of the theorists, and after
some reflection I believe that there may be a slight hitch in
Dr. Frank's interpretation of Mach's view.

First I myself, from my own point of view, would refuse
to call the principle of relativity an hypothesis; it is an
a priori proposition, a theorem, or if you prefer, a postu-
late of pure thought which either holds good universally,
or has no validity whatever. So far as I know, Mach has
not discussed this side of the subject but he has instinctively
acted upon this view, and I would say that there is a
greater hypothetical element in the assumption that the
theorem 2X2 = 4, or any other proposition of the same
kind, holds good only for our earth but not for Mars and
Venus, than to say that it holds good also for the fixed
stars and in the possible worlds outside of our Milky Way.
Accordingly, whatever Mach's personal opinion may be,
I would regard the universal application of the principle
of relativity as less complicated and more free from hypo-

* This last paragraph is printed in spaced letters which indicates the em-
phasis of the author, and so we print the text of his summary in the original.
Dr. Frank says : "Die physikalischen Erscheinungen hangen nicht nur von der
Relativbewegung der Korper ab, ohne doch damit die Moglichkeit des Be-
grifFes einer absoluten Bewegung im philosophischen Sinne zuzugeben."

THE PRINCIPLE OF RELATIVITY. 33

thetical elements than its limitation to a portion of the
world.

I can not as yet make up my mind to believe that our
system of the Milky Way which furnishes us the grand
sight of the fixed stars is an ultimate possessing the charac-
teristics of absolute space.

According to Kant the totality of the fixed stars which
are thickest in the Milky Way forms a great system (the
system of the Milky Way) and our sun^as well as all the
visible fixed stars^belongs to it. Kant believes that this, our
own universe, which in the Milky Way appears to us as an
enormous ring but together with the totality of the fixed
stars must resemble an oblate spheroid, is not the only cosmic
system, but that there are other similar systems outside of it
and that they too whirl on through the infinity of space, in
company with our Milky Way system, around some center
of their own; and this very center of many Milky Ways
may partake of a motion the observation of which lies
hopelessly beyond our ken. Accordingly the space condi-
tions of the Milky Way may serve its as absolute space,
but there is a probability that this space is not more abso-
lute than are the space relations in a quick but quietly mov-
ing train to the passengers.

Another point where we feel justified in doubting Dr.
Frank's exposition is the statement that Mach hypothet-
ically assumes a new law of nature as to the efficacy of
masses, besides the law of gravitation. The passage in
Mach's writings to which Dr. Frank refers does not (in
my opinion) suggest the idea of an additional law of nature
according to which the distant fixed stars should exercise
a mysterious influence on the Foucault pendulum. We will
later on let Mach speak for himself. In our opinion it
seems that it would be sufficient to ascribe the rotation of
the pendulum to its inertia while the earth revolves round
itself, and this takes place in the space in which the earth

34 THE PRINCIPLE OF RELATIVITY.

has its motion, viz., the space of the Milky Way system.
The pendulum remains in the plane of oscillation in which
it started while the earth turns around vmderneath. If
there are influences at work beyond the expanse of the
space of the fixed stars in our Milky Way system, they
must affect the totality of our system and would therefore
be contained in its space conditions ; acting with an unfail-
ing constancy they could not be separated from the prop-
erties of our space and would scarcely be discoverable.

There seems to me no need of inventing a new force
besides gravitation. The law of inertia seems to explain
the Foucault pendulum experiment satisfactorily.

The fixed stars as a totality remain in their places (at
least as far as concerns the experiment) and the plane in
which the pendulum swings keeps its original direction;
thus the apparent motions of both coincide. Their space
relations (the space relations of the pendulum and of the
fixed stars) are the same, and there is no need to assume
the existence of any unknown force exercised by the fixed
stars upon the pendulum.

ERNST MACH.

We will let Mach state his views in his own words :

"Obviously it does not matter whether we think of the earth as
turning round on its axis, or at rest while the celestial bodies revolve
round it. Geometrically these are exactly the same case of a relative
rotation of the earth and of the celestial bodies with respect to one
another. Only, the first representation is astronomically more con-
venient and simpler.

"But if we think of the earth at rest and the other celestial
bodies revolving round it, there is no flattening of the earth, no
Foucault's experiment, and so on — at least according to our usual
conception of the law of inertia.

"Now, one can solve the difficulty in two ways: Either all mo-
tion is absolute, or our law of inertia is wrongly expressed. Neu-
mann'- preferred the first supposition, I, the second. The law of
" Ueber die Principien der Galilei-Newton* schen Theorie. Leipsic, 1870.

THE PRINCIPLE OF RELATIVITY. 35

inertia must be so conceived that exactly the same thing results
from the second supposition as from the first. By this it will be evi-
dent that, in its expression, regard must be paid to the masses of
the universe.

"In ordinary terrestrial cases, it will answer our purposes quite
well to reckon the direction and velocity with respect to the top of a
tower or a corner of a room ; in ordinary astronomical cases, one
or other of the stars will suffice. But because we can also choose
other corners of rooms, another pinnacle, or other stars, the view
may easily arise that we do not need such a point at all from which
to reckon. But this is a mistake ; such a system of coordinates has
a value only if it can be determined by means of bodies. . . .

"If we wish to apply the law of inertia in an earthquake, the
terrestrial points of reference would leave us in the lurch, and, con-
vinced of their uselessness, we would grope after celestial ones.
But, with these better ones, the same thing would happen as soon
as the stars showed movements which were very noticeable. When
the variations of the positions of the fixed stars with respect to one
another cannot be disregarded, the laying down of a system of co-
ordinates has reached an end. It ceases to be immaterial whether
we take this or that star as point of reference ; and we can no longer
reduce these systems to one another. We ask for the first time
which star we are to choose, and in this case easily see that the stars
cannot be treated indifferently, but that because we can give prefer-
ence to none, the influence of all must be taken into consideration.

"We can, in the application of the law of inertia, disregard any
particular body, provided that we have enough other bodies which
are fixed with respect to one another. If a tower falls, this does not
matter to us ; we have others. If Sirius alone, like a shooting star,
shot through the heavens, it would not disturb us very much ; other
stars would be there. But what would become of the law of inertia
if the whole of the heavens began to move and the stars swarmed
in confusion? How would we apply it then? How would it have
to be expressed then? We need not worry about one body as long
as we have others enough. Only in the case of a shattering of the
universe we learn that all bodies, each with its share, are of im-
portance in the law of inertia ....

"Yet another example : A free body, when acted upon by an in-
stantaneous couple, moves so that its central ellipsoid with fixed cen-
ter rolls without slipping on a tangent-plane parallel to the plane of
the couple. This is a motion in consequence of inertia. Here the bodv

36 THE PRINCIPLE OF RELATIVITY.

makes very strange motions with respect to the celestial bodies.
Now, do we think that these bodies, without which one cannot
describe the motion imagined, are without influence on this motion?
Does not that to which one must appeal explicitly or implicitly when
one wishes to describe a phenomenon belong to the most essential
conditions, to the causal nexus of the phenomenon? The distant
heavenly bodies have, in our example, no influence on the accelera-
tion, but they have on the velocity."

Now follows the passage to which Dr. Frank obviously
refers :

"Now, what share has every mass in the determination of direc-
tion and velocity in the law of inertia? No definite answer can be
given to this by our experiences. We only know that the share of
the nearest masses vanishes in comparison with that of the farthest.
We would, then, be able completely to make out the facts known to
us if, for example, we were to make the simple supposition that all
bodies act in the way of determination proportionately to their
masses and independently of the distance, or proportionately to the
distance, and so on. Another expression would be: In so far as
bodies are so distant from one another that they contribute no notice-
able acceleration to one another, all distances vary proportionately
to one another."

We do not here understand Mach to fall back on the
assumption of a new kind of force, and if we must grant
that the distant masses exercise a dominant influence while
the influence of the nearest ones (of the earth, the moon,
and the sun) vanishes, we would say that this is due to the
constancy of the distant masses which, as it were, is an
inherent and inalienable part of all mass in the entire sys-
tem and may be said to characterize its space conditions.

In speaking of "space conditions" I am conscious of
using a term which Mach would repudiate, for he claims
that for a comprehension of the concatenation of events,
the notions of time and space are redundant. He says
(loc. cit. pp. 60-61) :

"To say the least, it is superfluous in our consideration of causal-
ity to drag in time and space. Since we only recognize what we

THE PRINCIPLE OF RELATIVITY. 37

call time and space by certain phenomena, spatial and temporal deter-
minations are only determinations by means of other phenomena.
If, for example, we express the positions of earthly bodies as func-
tions of the time, that is to say, as functions of the earth's angle of
rotation, we have simply determined the dependence of the positions
of the earthly bodies on one another.

"The earth's angle of rotation is very ready to our hand, and
thus we easily substitute it for other phenomena which are connected
with it but less accessible to us ; it is a kind of money which we spend
to avoid the inconvenient trading with phenomena, so that the pro-
verb "Time is money" has also here a meaning. We can elim-
inate time from every law of nature by putting in its place a phenom-
enon dependent on the earth's angle of rotation.

"The same holds of space. We know positions in space by the
affection of our retina, or our optical or other measuring apparatus.
And our x, y, s in the equations of physics are, indeed, nothing else
than convenient names for these affections. Spatial determinations
are, therefore, again determinations of phenomena by means of other
phenomena.

"The present tendency of physics is to represent every phenom-
enon as a function of other phenomena and of certain spatial and
temporal positions. If, now, we imagine the spatial and temporal
positions replaced in the above manner, in the equations in question,
we obtain simply every phenomenon as function of other phenomena.

"Thus the law of causality is sufficiently characterized by saying
that it is the presupposition of the mutual dependence of phenomena.
Certain idle questions, for example, whether the cause precedes or
is simultaneous with the effect, then vanish by themselves."

We understand that Mach endeavors to eliminate the
terms time and space, because he wishes to correct the
common notion which regards space as a big box into
which the world has been packed. Mach says:

"Space and time are not here conceived as independent entities,
but as forms of the dependence of the phenomena on one another.
I subscribe, then, to the principle of relativity, which is also firmly
upheld in my Mechanics and JVdnuelehre."^^

" Cf. "Zeit und Raum physikalisch betrachtet," in Erkenntnis tind Irrtum,
Leipsic, 1905 (2d ed. 1906, pp. 434-448) ; See also Space and Geometry, pp. 94 ff.

38 THE PRINCIPLE OF RELATIVITY.

We agree with Mach. There is no time in itself ; there
is no space in itself. Nevertheless, Mach has given much
attention to physical space and appreciates the important
part which it plays not only in the formation of our space-
conception, but also in the actual world, for every spot of
space possesses physical qualities according to the particles
of mass which are there aggregated. Mach says :

"Since the positions in space of the material parts can be recog-
nized only by their states, we can also say that all the states of the
material parts depend upon one another.

"The physical space which I have in mind — and which, at the
same time, contains time in itself — is thus nothing other than de-
pendence of phenomena on one another. A complete physics, which
would know this fundamental dependence, would have no more need
of special considerations of space and time, for these latter consid-
erations would already be included in the former knowledge."

The same idea is expressed by Mach in his Essay
"Ueber den Zeitsinn des Ohres:^''

"Physics sets out to represent every phenomenon as a function
of time. The motion of a pendulum serves as the measure of time.
Thus, physics really expresses every phenomenon as a function of
the length of the pendulum. We may remark that this also happens
when forces, say, are represented as functions of the distance ; for
the conception of force (acceleration) already contains that of time.
If one were to succeed in expressing every phenomenon — physical
and psychical — as a function of the phenomenon of pendulum-
motion, this would only prove that all phenomena are so connected
that any one of them can be represented as a function of any other.
Physically, then, time is the representability of any phenomenon as
a function of any other one."

We do not deny the truth of Mach's view. Neverthe-
less time and space are very convenient terms denoting
two categories of certain interrelations (he w^ould call
them interdependencies) in the flux of things. Popular
terms mostly originate because there is a need of them,

'^* Sitzh. der Wien. Akad., 1865. Compare Conservaiinn of Energy, V- 00.

THE PRINCIPLE OF RELATIVITY. 39

and it seems to me it would be wiser to correct the errors
connected with them than to drop them. If we pursue the
latter policy we shall find ourselves obliged to reinvent a
new collective term for certain classes of relations which
belong together and can not be identified with other rela-
tions. The space and time relations are radically different
from those of a purely physical, chemical or psychological
nature.

We need not fear to retain the old terms, space and
time, if we only bear in mind that there is neither absolute
space nor absolute time but that the words denote relations.
It seems to me that when Kant speaks of the ideality of
space and time and insists on their non-existence as ob-
jective beings (JVescn or Jf'esculicifcn) he attempts to say
the same as Mach who declares that they are not "inde-
pendent entities."

The conclusion at which we arrive in considering the
nature of time and of space, be it from our standpoint of
philosophy or from Mach's physical point of view, may
be expressed in one word, that their most obvious char-
acteristic is relativity.

Professor Mach says in one of his notes quoted above,
"I subscribe then to the principle of relativity," and so do
I. Indeed I go one step further. I consider relativity as
an inherent quality of existence and so I adopt the prin-
ciple of it not as a result of experience but on a priori
grounds. The principle of relativity, however, is fre-
quently stated by relativity physicists as if the old ideal
of science in its objective significance had to be abandoned,
as if physics had to be remodeled, and as if the proclama-
tion of the principle of relativity indicated a new departure
from our traditional methods. This is not so, and I must
insist that the principle of relativity has always been sub-
consciouslv in the minds of scientists. Onlv it has latelv

40 THE PRINCIPLE OF RELATIVITY.

been forced upon the attention of physicists by the progress
in astronomical measurements.

How helpful the emphasis recently laid upon the prin-
ciple of relativity will prove remains to be seen. Its ardent
adherents exhibit great zeal which in many directions
seems to be misdirected, and it appears to me that in spite
of the correctness of the underlying idea their hopes are
greatly exaggerated. After a while when the opponents
of the principle of relativity will understand that its truth
is as much a matter of course as the truth of the law of
conservation of matter and energy, the contentions about
it will cease and the evolution of science will no longer
show evidence of excitement but will continue in its old
quiet way.

There is more philosophy in our science than the school
of empiricists are inclined to believe. It is very desirable
that in familiarizing themselves with philosophy, these
scientists should not fall back on the old systems of a vision-
ary absolute, but they should adopt the philosophy of sci-
ence, the only philosophy which is not a mere ingenious
dream, and possesses objective significance.

The philosophy of science is the philosophy. It is the
indispensable introduction to the study of any science and
furnishes the basis for scientific method as well as a general
survey of the assured results of all the several sciences.
If the philosophy of science had been better known, the
principle of relativity had at once been rightly understood
and the vagaries of many mystifying contentions would
have been avoided.

In order to appreciate the sense and historic signifi-
cance of the principle of relativity, we must bear in mind
that in dealing with the several innumerable problems of
existence science introduces a method which possesses cer-

THE PRINCIPLE OF RELATIVITY. 4I

tain limitations due to conditions which originate through
some fictions of an apparently arbitrary nature assumed
for the sake of isolating the object of investigation and
concentrating upon it our attention.

We must bear in mind that we behold an object by
focusing our eyes upon it and that only thereby can we
form a picture of the object. It is a fiction to behold an
object as if it were a thing by itself and it is positively
impossible to see anything as it is in all its relations and
with all its changes, past, present and future. Nor would
such a comprehension of the object in all its entirety be
desirable, for in the omneity of its relations we would see
the whole universe while the special feature which concerns
us sinks into insignificance. The same is true of science.
Each of the several sciences selects its own field of investi-
gation and thus constitutes a definite domain of abstraction
for the sake of concentrating all attention upon it. For
mechanics and for the measurements of motion in space, we
need a reference point which must be able to be considered
stationary, and if that is not the case we must refer both
the movable place of observation, viz., the reference point
(R) and the object observed (O) to one common system,
which could be treated as, or must so far as R and O are
concerned, actually be, stable.

We repeat that there is nothing abgolu^^^^^
is relative; real and actual existences, concrete things and
happenings are relative, and if there is any thing that in a
certain sense deserves the name absolute it is the truth as
described in our mental fictions, the laws of purely formal
thought, the eternal uniformities of purely formal rela-
tions such as we know from mathematics and all the other
purely formal sciences ; but even they are absolute only in
the sense of constituting an entire system the truth of
which is absolute, viz., it stands aloof and is founded in it-
self as a world of necessary conclusions built up in the field

42 THE PRINCIPLE OF RELATIVITY.

of anyness to serve as models for any ccnditioiis^ in any
world actual or imaginary. And this absolute, this system
of mental construction, is after all a system of relations.

The more we ponder on the nature of existence, the
more we shall understand the sweeping significance of
relativity.

OBJECTIVITY.

Since the dawn of civilization man has groped after
truth. He has investigated it; he has pondered on it;
he has made guesses and proposed hypotheses ; he has ap-
proximated truth by allegories, foreshadowing it in verse
and fable ; and since he began to count and to measure he
has reduced the results of his inquiry to exact statements.

All observations are necessarily subjective, but man
is not satisfied with subjective truth, he wants objective
truth and objectivity of statement is the ideal of science.

Is objectivity impossible? Must we abandon our ideal
of science ? It seems to us that science has more and more
in its various fields approached its ideal of objective truth.
Standard measures have been invented and perfected. Time
is measured by a pendulum of definite size, even apparently
trivial factors have been considered such as latitude and
altitude; and our precision machines testify to the in-
genuity of man's genius in his attempt to eliminate per-
sonal equations as much as possible. The reliability of
scientific computation has reached a marvelous degree, but
it is almost more astonishing that we are still dissatis-
fied and that our measurements of minute fractions of the
wave lengths of light are no longer exact enough for our
needs.

In the face of the enormous accomplishmxcnts of science
in approximating the ideal of objectivity, a new school has
risen which goes so far as to deny all objectivity, and in-

THE PRINCIPLE OF RELATIVITY. 43

sisting upon the truth of relativity, it would make us be-
lieve that objectivity is a phantom.

The relativity principle was first pronounced by Ein-
stein in the Jahrhuch der Radioaktivitdt (Vol. IV, pp.
411 ff., 1907). It was invented to account for certain diffi-
culties in the explanation of optical and electrical phenom-
ena by considering the relativity of the movements in a
system that is not at rest, called a disturbed system in con-
trast to quiet systems. In all quiet systems the common
laws of dynamics hold good and the proposition of the
relativity principle has been made for the sake of account-
ing for the laws of disturbed systems.

The principle of relativity is an a priori postulate from
which certain theorems are derived whose truth is to be
verified or refuted by experiment. Mr. Norman Camp-
bell says:^

"The principle is what is more often termed a 'theory'
— that is to say, it is a set of propositions from which ex-
perimental laws may be logically deduced. It can be proved
to be true or false in a manner convincing to everybody
only by comparing the laws so deduced with those found
experimentally; but a theory which never conflicted with
experiment might yet (as I hold) be judged objectionable
on other grounds, and, conversely, a theory which was not
in complete accord with experiment might yet be judged
satisfactory."

Among the postulates of the principle of relativity there
is one, counted the second, which presents great difficulties.
It proclaims that "The velocity of light determined by all
observers who are not accelerated relatively to each other
is the same whatever may be the relative velocities of the
observer."

An unsophisticated thinker would naturally assume that

' See "The Common Sense of Relativity" in The Philosophical Magadne
for April 191 1, pp. 502 flf.

44 THE PRINCIPLE OF RELATIVITY.

the velocity of light must be expected to increase or de-
crease according to the velocity of the observer. But the
relativist assures us that light is an exception; on his as-
sumption light is like a shadow whose motion depends upon
the motion of its body representing the observer. The
relation of the shadow to its body remains the same, how-
ever its body's (the observer's) velocity may change.

The question as to the velocity of light is a question of
physics, not of philosophy, and we will touch upon it later.
Here we will state only that the main objection to the
relativity principle is the inference which implicates our
objective ideal of science.

Not all the relativists agree on all points of their doc-
trine, and contradictory statements are not uncommon.
We can here only characterize the general tendency and
will not enter into the individual interpretations too closely.

Relativists try to avoid a difficulty which we grant
exists, but is not insurmountable. Idealists of former days
have used more subtle methods to dispose of the belief in
objectivity of things, of time, and of space. They have
produced only quibbles and the relativists have succeeded
no better ; only it is strange that the movement has origi-
nated among the physicists.

In what precedes we have demonstrated the para-
mount importance of relativity, but for all that we see no
necessity for abandoning the old ideal of science. On the
contrary we feel inclined to insist on it more strongly than
ever. We do not deny the relativity of all existence
throughout and without exception, but we still cling to the
old scientific ideal of objectivity and we can not see that
the relativity principle, in the one-sided sense in which the
relativity physicists uphold it, is well established.

Having discussed in the article mentioned the part
which relativity plays in scientific method, we feel inclined
to add a few suggestions concerning the significance of

THE PRINCIPLE OF RELATIVITY. 45

the recent movement among physicists who emphasize the
principle of relativity and prophesy that through it a new
era in the scientific interpretation o£ the world will have
to begin.

We have seen that many of the paradoxes which are
proclaimed by the relativity physicists disappear on close
inspection, for the contradictions resolve themselves into
purely verbal contrasts. The same object is not in itself
longer or shorter, but the result of measurement will be
different according to the conditions under which the meas-
urements take place. And further, although time can be
eliminated, although it may be treated as a function of
space, or even be treated as a kind of fourth dimension,
the conception of time will nevertheless still remain of
great convenience. The. truth is that we must subsume
time and space under one common category which, with"
Kant and other thinkers of well-established classical tra-
dition since the days of Aristotle, has been called "form."
We- must always bear in mind the interrelation between
tim£L_and_§P-3^^-^'^d ^'^^w the two as.Jhe forms of ;:one and
the same reality. Time is the form of doing, of progressive
action, of change, of events, and space is the form of being,
of existence in its juxtaposition of parts. The former is
the order of procedure in which the latter is transformed.
Neither can be thought without the other, and the two are
one. The principle of simplicity requires us to consider both
in their interrelation. But for all that the traditional no-
tion of time still proves the best method for rendering
measurements of changes intuitively clear while an elimi-
nation of time as proposed by the Relativity Physicists is
apt to obscure the issue; and we come to the conclusion
that experience has not without good reasons found in the
proper terms "space" and "time" a very convenient, yea,
as it seems to me, the most appropriate, mode of represen-
tation.

V

46 THE PRINCIPLE OF RELATIVITY.

It is strange that the relativity principle has been pro-
posed for the very purpose of approximating objective
truth with greater exactness, but instead of accounting
for inexactness or inaccuracies in results and for apparent
contradictions by taking into consideration the mistakes
in calculation on account of the shifting conditions of this
world which is a constant flux, a panta rhei, the leaders of
the new movement cancel the old ideal of science which
has guided us thus far and propose a new standard strongly
tinged with subjectivism, built upon the basis of the rela-
tivity of all existence.

All experience is a mixture of objectivity and subjec-
tivity : it is due to the interrelation between a sentient sub-
ject and the sensed objects. So far science has tried to
eliminate the subjective side, the personal equation, while
the relativity physicists deny the legitimacy of the ideal of
objectivity, or as they call it, the concept of the real. Tt
is true that in clinging to the facts of observation without
trying to eliminate the subjective elements and thereby to
unify our results in an objective statement, we simplify
our calculations, but it is very doubtful whether this proce-
dure can be generally applied to other than optical and elec-
trical phenomena. Relativists deem the theory justified if
they simplify their own line of labors. Mr. Campbell ex-
claims in his enthusiasm:

"Anything more beautifully straightforward it would
be hard to conceive. Not only is the result magnificently
simple, but it furnishes us with a mathematical instrument
of extraordinary power. In place of the elaborate calcu-
lations which have hitherto been necessary in dealing with
moving systems, all that we have to do now is to solve the
problem under consideration for the limiting case of infini-
tesimal velocity, and then effect a mere algebraical trans-
formation. The only objection that seems likely to be
raised is that the principle proves too much, that it appears

THE PRINCIPLE OF RELATIVITY. 47

impossible that such far-reaching conclusions can be drawn
from such simple assumptions : the only difficulty, in fact, is
that the thing is too easy."

''The crudest arguments based on the oldest theory of
light lead to the conclusion that the rate of a clock as ob-
served by a certain observer must change with the relative
motion of clock and observer. For, it will be argued, the
observer does not see the clock 'as it really is at the mo-
ment,' but 'as it was a time T earlier, where T is the time
taken for light to reach the observer.' And on these lines
it is easy to show that the apparent rate of a clock moving
away from the observer with a velocity v is (i — v/c)
times^ the rate of the same clocks observed at rest. It is
only the magnitude of the change concerning which the
two theories differ.

" 'Yes,' says our objector, 'that is all very well : of
course the apparent rate of the clock changes with motion,
but does the real rate change?' We immediately incjuire
what the 'real rate' means. He is at first inclined to assert
that it is the rate observed by an observer traveling with
the clock, but when we inquire relative to what clock that
observer is to measure the rate he becomes uneasy. He
cannot compare another clock traveling with him, for if
the 'real rate' of one clock has changed, so has the 'real
rate' of the other ; and he cannot use a clock which is not
traveling with him, because he admits that he does not see
such a clock 'as it really is.'

"Pressing our inquiries, I think we shall get an answer
of this nature. 'If I take a pendulum clock to some place
where gravity is dift'erent, the rate of the clock will change.
It is a change of this nature which I call a change in the
"real rate," and I want to know whether there is any
change of that kind, on the theory of relativity, when the

* c denotes the universal velocity whatever it mav turn out to be. See ihid.
p. So8.

48 THE PRINCIPLE OF RELATIVITY.

clock is set in motion.' Now why does our objector call a
change of the first kind a change in the 'real rate'? The
reply is to be found in the history of the word 'real.' The
word is intimately associated with the philosophic doctrine
of realism, which holds that the most important thing that
we can know about any body is not what we observe about
it, but its 'real nature,' which is something that is inde-
pendent of observation.

Now, of course, a quantity which is wholly independent
of observation cannot play any part in an experimental
science, but there are quantities which are independent of
observation in the more limited sense that they are observed
to be the same by whatever observer the observation is
.made. The term 'real' has come to be transferred from the
philosophical conception to such quantities. The 'real rate'
of the clock is said to change when it is transferred to a
place where gravitation is dififerent, because all observers
agree that the rate of the clock which has been moved has
undergone an alteration relatively to that which has not
been moved.

"Now in the conditions which we are considering the
observers do not agree. If A and B, each carrying a clock
with him, are moving relatively to each other, they will not
agree as to the rate of either of their clocks relative to
A's standard or to B's standard or to any other standard.
The conditions which, in the case of the alteration of gravi-
tation, gave rise to the conception of a 'real rate' are not
present : in this case there is no 'real rate,' and it is as ab-
surd to ask whether it has changed as it would be to ask a
question about the properties of a round square. However,
some people, who in their eagerness to escape the reproach
of being metaphysicians have adopted without inquiry the
oldest and least satisfactory metaphysical doctrines, are so
enamoured of the conception of 'reality' that they refuse to
give it up. Finding that the'observations of different ob-

THE PRINCIPLE OF RELATIVITY. 49

servers do not agree, they define a new function of those
observations, such that it is the same for all observers, and
proceed to call this the 'real rate.' This function, according
to the principle of relativity, is Pii' where n' is the rate of
the clock as seen by an observer relative to whom it is trav-
eling with the velocity v. according to that principle, if
we substitute in that function the appropriate values for
any one observer, the resulting number will always be the
same. So far no overwhelming objection can be raised."

What the relativists call "real" we would call objective,
and we deem the ideal of objectivity to be the goal of sci-
ence. Mr. Campbell has much to say on the concept of
reality :

"It is the great merit of the principle of relativity that it
forces on our attention the true nature of the concepts of
'real time' and 'real space' which have caused such end-
less confusion. If we mean by them quantities which are
directly observed to be the same by all observers, there
simply is no real space and real time. If we mean by them,
as apparently we do mean nowadays, functions of the di-
rectly observed quantities which are the same for all ob-
servers, then they are derivative conceptions which depend
for their meaning on the acceptance of some theory as to
how the directly observed quantities will vary with the
motion, position, etc. of the observers. 'Real' quantities
can never be the starting point of a scientific argument ; by
their very nature they are not quantities which can be de-
termined by a single observation : the term 'real' has always
kept its original meaning of some property of a body which
is not observed simply.

"All the difficulties and apparent paradoxes of the prin-
ciple of relativity will vanish if the attention is kept rigidly
fixed upon the quantities which are actually observed. If
any one thinks he discovers that that principle predicts
some experimental result which is incomprehensible, let

50 THE PRINCIPLE OF RELATIVITY.

hini dismiss utterly from his mind the conception of reality.
Let him imagine himself in the laboratory actually per-
forming the experiment: let him consider the numbers
which he will record in his note-book and the subsequent
calculation which he will make. He may then find that the
result is somewhat unexpected — to meet with unexpected
results is the usual end of performing experiments, — but he
will not find any contradiction or any conclusion which is
not quite as simple as that which he expected.

"There is one further point sometimes raised in con-
nection with the principle on which a few words may be
said.

"It is sometimes objected that the principle 'has no phys-
ical meaning/ that it destroys utterly the old theory of
light based on an elastic ether and puts nothing in its place,
that, in fact, it sacrifices the needs of the physical to the
needs of the mathematical instinct. That the statement is
true there can be no doubt, but the absence of any substitute
for the elastic ether theory of light may simply be due to the
fact that the principle has been developed so far chiefly by
people who are primarily mathematicians. It is well to ask,
can any physical theory of light be produced which is con-
sistent with the principle?

"The answer depends on what is meant by a 'physical
theory.' Hitherto the term has always meant a 'mechan-
ical theory,' a theory of which the fundamental propositions
are statements about particles moving according to the
Newtonian dynamical formulae. In this sense a physical
theory is impossible if the principle of relativity be accepted,
for the same reason that a corpuscular theory of light is
impossible, if the undulatory theory of light be accepted.
Newtonian dynamics and the principle of relativity are two
theories which deal in part with the same range of facts;
they both pretend to be able to predict how the properties
of observed systems will be altered by movement. If they

THE TRTNCIPLE OF RELATIVITY. 5 I

are not logically equivalent they must be contradictory : in
either case an 'explanation' of one in terms of the other is
impossible. It can be easily shown that they are contra-
dictory: if the principle of relativity is true, Newtonian
dynamics must be abandoned."^

We start with ''the facts of observation," and try to es-
tablish the objective state of things, called also "the real";
but relativists ignore the latter, and since every observer
has his own particular observation, they declare that there
is neither real time nor real space. The real is ruled out
from observation.

Suppose, however, that the clocks which the relativ-
ist observes were the heartbeats of the relativist himself
and the observer were the diagnosing physician, would the
relativist insist that the physician had better drop out of
sight the notion of reality, that there is as little sense in
asking for "the real rate" of his heartbeat as it is absurd
"to inquire whether, if all triangles had four sides, all
circles would be square" ?' If we can not attain an abso-
lutely correct objective statement, we keep at least the
ideal in view and this ideal is not an empty dream.

The relativity principle is a mathematical view of cer-
tain problems worked out for the sake of most minute
measurements; and the attitude of the relativists is stern.
If the facts can not be clearly represented by it, the worse
for the facts, and if the physicists declare that their phys-
ical theories are incompatible with it, a new brand of physi-
cists has to be manufactured who will inaugurate a rela-
tivist reform in physics.

PRIMARY CONCEPTS.

The relativity problem would never have originated
had the philosophy of science been clearly and distinctly

* This conclusion is reached by Sommerfeld in a paper, Ann. d. Phys.,
XXXIII, p. 684, etc. (1910).

" See Campbell, loc, cit., p. 509. The comparison is not appropriate.

^

52 THE PRINCIPLE OF RELATIVITY.

understood by physicists, but they have famiharized them-
selves very little with even the problems, let alone reached
proper solutions which explain the elementary concepts of
our scientific terms, the difference between substance and
form, between energy and matter, and the significance of
the purely formal sciences.

As mathematicians are in the habit of starting with ax-
ioms, so the relativists begin with postulates and these
postulates come in collision with the primary concepts such
as have been formulated among the orthodox physicists
and mathematicians of the present day.
r" A truly scientific view will brook neither axioms in
^mathematics, nor postulates in philosophy, nor primary
(^concepts in physics.

There has been much talk about primary concepts, and
arguments have been oft'ered why time is not a primary
notion or why we should let it pass as such. The truth is
that time as well as space are two methods of describing
definite relations. Time is not so much a fourth dimension
of space, though we might look upon it as if it were such,
time is the measure of motion and space is the scope of mo-
tion. Both time and space are presupposed in the idea of
motion. There is no time in itself, there is no space in
itself. What Newton and others with him call absolute
space is ''space conception" and what they call absolute
time is "time conception." Such are the ideas which by
pure deduction on a priori arguments, physicists form of
time and of space, just as mathematicians formulate the
general conception of numbers, of distances and of other
relations, angles, areas, etc.

The idea of primary concepts is a very unfortunate de-
vice to lay a foundation for science. The faults of this
method will not show so long as specialists are concerned
about specialist problems, but the carelessness of taking
anything for granted shows itself as soon as any problem

THE PRINCIPLE OF RELATIVITY. 53

broadens out into a general inquiry when its connection
with universal problems is questioned. Such primary con-
cepts are assumed to be undefinable and self-evident. That
opens the door to an arbitrary interpretation as to the na-
ture of space and time and energy, and gives a wide berth
to mysticism.

Science brooks neither axioms nor primary concepts.-
Science starts with experience ; it quarries out of experience
the stones of the purely formal sciences which furnish all
the methods of both common sense knowledge and scien-
tific inquiry. The most general characteristic of experience
is activity. Activity manifests itself in change. Change
implies motion; it means either change of place, i. e., mov-
ing from here to there, or change of combination, viz., a
moving of particles among themselves. Change inter-
feres with existing relations, it modifies the old interrela-
tions and establishes new interrelations.

The nature of relations in one terse term is called form.
The word "form" comprises both outer shape and inner
structure, and all interrelations of things as well as thoughts
can be determined by the laws of pure form, arithmetic,
geometry, logic, etc. Under all circumstances change mod-
ifies relations and means "transformation." There is a
transformation in the juxtaposition of things or their parts,
and there is a succession of events. The scope of the former
w^e call "space," of the latter "time"; or better from the
former we deduce our notion of space, from the latter our
notion of time.

Physical inquiry is not helped by calling certain fea-
tures of experience "primary concepts" and least of all
(as has been done) should space, time and force, — these
highly complicated constructions of a priori thought — be
beclouded by this mystifying name. Both time and space
are features of the form of existence, and force is a general
term for that feature of existence which marks its activity

54 THE PRINCIPLE OF RELATIVITY.

as motion, viz., as change of place, or rather as that which
causes changes and is measured by the resistance over-
come.

If we adopt the relativist principle to ignore the scien-
tific ideal of objectivity, i. e., if we define size as the result
of measurement and moments of time as determinations of
measurement by units of duration, without regard to the
ideal of coincidental happenings, and a common standard
of time, we may produce incredible statements against
which common sense rebels, and Professor Magie in his
Presidential Address,*^ delivered before the Physical So-
ciety and Section B of the American Association for the
Advancement of Science, at Washington, D. C. (December
28, 191 1 ), says in comment thereof:

"A description of phenomena in terms of four dimen-
sions in space would be unsatisfactory to me as an explana-
tion, because by no stretch of my imagination can I make
myself believe in the reality of a fourth dimension. The
description of phenomena in terms of a time which is a
function of the velocity of the body on which I reside will
be, I fear, equally unsatisfactory to me, because, try I ever
so hard, I can not make myself realize that such a time

is conceivable I do not believe that there is any man

now living who can assert with truth that he can conceive
a time which is a function of velocity or is willing to go to
the stake for the conviction that his 'now' is another man's
'future' or still another man's 'past.'

"One of the members of this society, recognizing our
present inability to conceive of relative time, and conceiv-
ing our intuitions of space and time to be the result of
heredity operating through many generations of men who
lacked the light of relativity, once proposed to me that
every one who could get even a glimmer of the notion of
relative time should persistently exercise his mind therein

* Published in Science, February 23, 1912, pp. 281 ff :

THE PRINCIPLE OF RELATIVITY. 55

and teach it to his students, in the hope that in a few gene-
rations the notion would emerge with the force of an in-
tuition. It would not be fair to leave the impression that
he was solemnly serious when he made this suggestion."

Form (i. e., relativity) is, as much as matter and energy,
an ultimate generalization and may be called a fundamental
concept (not a primary concept), and all the work of sci-
ence is a tracing of transformations.

It is essential for the measurement of space and time to
employ as measures uniform unjts, for space of distance
and for time of duration. In the same way we need uni-
form units to measure force.

Besides a quantitative analysis of experience, there is
a qualitative analysis which traces such transformations
as build up parts into a higher unit, whereby through the
interrelation or the interaction of the parts a new thing-
originates possessed of properties which are absent in the
parts before their combination."^

The law of change is called causality. Cause is the
motion which starts the process of transformation ; effect
is the result of the change ; and reason is the general rule
(formulated as a so-called law of nature) from which we
understand why the cause must have this effect.^

The so-called law of the conservation of matter and'
energy is a deduction from the law of causality, which can
be made as soon as we understand that all happenings are
transformations, for if all changes are transformation, the
amount of existence, its that, remains the same, only its
form changes.

While investigating the several problems of our ex-
perience, scientists assume that they deal with real occur-
rences and thus they implicitly grant the that of existence,

' See for instance tlie author's exposition of the nature of quality in The
Monist, Vol. XV, p. 375- See also Philosophy of Form, p. 12.

'This has been repeatedly discussed, e. g., in the author's Fundamental
Problems, pp. 79 fif.

56 THE PRINCIPLE OF RELATIVITY.

popularly denoted "matter" and "energy," viz., thingish-
ness (or with a Latin term "reality") and actuality. The
existence of ether is but an extension of the concept matter
and so physicists have so far believed in the existence of
ether ; but the relativity physicists, in their anxiety to pro-
pound original ideas, deny the existence of ether. Says
Prof. William Francis Magie in his above mentioned Presi-
dential Address:

"The principle of relativity in this metaphysical form
professes to be able to abandon the hypothesis of an ether.
All the necessary descriptions of the crucial experiments
in optics and electricity by which the theories of the uni-
verse are now being tested can be given without the use
of that hypothesis. Indeed the principle asserts our inabil-
ity even to determine any one frame or reference that can
be distinguished from another, or, what means the same
thing, to detect any relative motion of the earth and the
ether, and so to ascribe to the ether any sort of motion;
from which it is concluded that the philosophical course is
to abandon the concept of the ether altogether. I may
venture to say that in my opinion the abandonment of the
hypothesis of an ether at the present time is a great and
serious retrograde step in the development of speculative
physics. The principle of relativity accounts for the nega-
tive result of the experiment of Michelson and Morley,
but without an ether how do we account for the interference
phenomena which made that experiment possible? There
are only two ways yet thought of to account for the passage
of light through space. Are the supporters of the theory
of relativity going to return to the corpuscles of Newton?
There is choice only between corpuscles and a me-
dium, and I submit that it is incumbent upon the advocates
of the new views to propose and develop an explanation
of the transmission of light and of the phenomena which

THE PRINCIPLE OF RELATIVITY. 57

have been interpreted for so long as demonstrating its
periodicity. Otherwise they are asking us to abandon what
has furnished a sound basis for the interpretation of phe-
nomena and for constructive work in order to preserve
the universahty of a metaphysical postulate."

The concepts substance, i. e., matter or mass, and en-
ergy are ultimate generalizations as much as form, but they
are very different from form. We could do without the
words ''matter" or "ether" by the use of some other indi-
cation to be introduced in our formulas which denotes real-
ity; but that would not disprove the truth of the popular
view, which describes every concrete bodily existence as
material, nor is it likely that the old method of nomencla-
ture will be rendered antiquated or erroneous.

We must not forget what matter means. Matter is a
word which denotes that quality of objects which all of
them have in common, viz., objectivity. An object is a
thing that is objected to us, that offers us resistance, that
impresses itself upon our existence and thereby affects our
senses, and by objectivity we understand the general prop-
erty of concrete existence, the that of experience, or its
reality, viz., its thingishness. To deny the reality of the
real, the thingishness of things, is as ridiculous as the
opposite mistake, i. e., to think of reality, or objectivity,
or of matter as a mysterious entity in itself. There is no
reality in abstract o, for every that of existence is of a
definite form which acts somehow, and the activity of things
we call their actuality, or, as we call it in physics, energy.

The same problem presents itself in the domain of the
phenomena of ether, i. e., of light and electricity. There
are some good reasons to assume that concrete matter has
originated by a contraction or condensation of a more prim-
itive substance which for all we know may prove to be the
luminiferous ether, that thin substance which has been as-
sumed to be the medium of light and electricitv- If it is

58 THE PRINCIPLE OF RELATIVITY.

claimed by modern physicists that the principle of relativity
disposes of the ether, that we no longer need it and can dis-
card a belief in it as a superstition, that all physical phe-
nomena can be accounted for without the assumption of
an ether, we confront the same situation as in the theory
of energetics, where the claim is made "There is no matter,
all is energy."

The truth of this position, so far as we freely grant it,
is this, that all scientific explanation describes the trans-
formation of things; it traces the changes that take place
according to the laws of form (mathematics and mechan-
ics). In experience we are confronted with the fact that
it is so, but the scientist inquires into the factors how it
has become so, how it acts, and how it changes. By describ-
ing the how in formulas (so-called laws of nature) we de-
note the several factors with algebraic letters, such as ^ =
gravity, t = seconds of time, d = the distance traversed
by a falling body and v = the velocity of the fall, etc., and
express their interrelation in equations, as

v = gt and d = V2gt^.

By this method the essential features of natural phe-
nomena are expressed in symbols, and he who has been
initiated into the secret meaning of the symbols and the
method of using them, will be able to predict the course of
events if he is in possession of the necessary data.

What we here call with one word "essential" Kirchhoff
characterizes in two words "most complete and most terse,"
or to use the common version "the most exhaustive and
simplest." We deem our term preferable, and we under-
stand by "essential" all that which is efficient to produce the
result, not more, not less.

We speak of the three laws of Kepler and of the con-
densed statements of the law of gravitation as "formulas,"
and this term truly expresses the nature of these general-

THE PRINCIPLE OF RELATIVITY. 59

ized descriptions of certain types of uniformities. They are
reductions of events to their purely formal (i. e., purely
relational) conditions, and these purely formal conditions
are the determinant (i. e., the causative) factors in all pos-
sible phenomena of a special type.

This is not a new truth. How old it is may be inferred
from the Greek term "formal'"* which in its etymology
means "the causal" or "the causative" because the Greek
philosophers describe the formal factors as efficient in cau-
sation.

When we have traced the essential factors of a certain
type of changes, the scientist's work is finished. Whether
mankind will ever be able to complete a scientific compre-
hension of the world in all its details, must be regarded as
doubtful, but wherever science has succeeded in discovering
the essential factors and has reduced them to formulas, we
have been enabled to offer for every such phenomenon a
satisfactory explanation.

This procedure aft'ords us an insight into the reason
why the course of a certain phenomenon must be so, why
it can not be otherwise, and in this procedure the fJiat is the
basis, the hozv is the method of cognition. There is no ex-
planation possible for the that, for the reality of the real,
for the actuality of the fact ; all explanations refer to the
how. The that is a brutal fact, and the ultimate goal of
science is the how, the answer being the formulation of
laws of nature which explain to us by a use of the law of
pure form that under given circumstances definite trans-
formations will take place. Knowledge of the law^s of na-
ture helps man to adapt himself to nature and also to adjust
his surrounding natural conditions to himself.

In our explanation we can omit the tJiat as a matter of
course, for it is understood that reality is real. We can
describe the purely formal relations only, which are the

» t6 alriwdes, derived from aMa = cause.

6o THE PRINCIPLE OF RELATIVITY.

essential part of explanations. There is no sense in ex-
plaining the that. We have simply to state whether or not
a formula covers actual facts, but to deny the that and say
that there is only a how the world wags, but there is no
world, seems to us a proposition that misconceives the situ-
ation.

We must not forget that such a word as substance, de-
noting here both "matter" and "ether" or existence in gen-
eral, is a term that stands for objective reality. Ether is
the that of the phenomena of electricity and light, as matter
is the that of bodily objects, declaring that they are real,
that they are concrete, and the term "substance" covers
any kind of existence, it embraces both matter and ether
or whatever the ultimate world-stuff may be called. There
is no sense in denying their actuality, and all that may be
meant by such a denial can only be either the redundancy
of an express declaration that the formulas of physics refer
to real processes, or a denial of ether or of matter as exist-
ences in themselves apart from their manifestations in defi-
nite configurations or modes of motion — a proposition
which nowadays no one will seriously dispute.

A denial of the existence of substance (of matter and

ether) is a purely verbal quibble. We might as well deny

the existence of energy and declare that there is no energy,

that there are only changes of place. The truth is that the

faculty of existence which manifests itself in changes of

place is called energy. We must not conceive of energy

as something in itself.

* * *

I am told that my own view is the gist of the principle
of relativity, and if that be true, I would gladly hail a phi-
. losophy of relativity as another name for the philosophy of
science. I have myself characterized the philosophy of sci-
ence as a philosophy of form, and form denotes the re-
lations in their totalitv. However, I would add that the

THE PRINCIPLE OF RELATIVITY. DI

system in which I have formulated this philosophy of sci-
ence is simpler than the world-conception of the relativity
physicists, besides it rests on a more solid foundation and
is absolutely free from paradoxes.

While I deny that we can dispense with the idea^of
objectivity (be it called matter, or ether, or substance) I
claim that we need make no mention of it in our formulas.
In this sense we can dispense with the mention of ether.
While I would not take the several paradoxes of time and
space as serious and deny their objective truth, I grant
that by a little confusion of thought in calling time or space
relations the results of our different measurements, we can
legitimately produce these paradoxes by exhibiting the in-
evitable discrepancies which originate through measure-
ments from different standpoints as objective contradictions.
Finally I consider it the ideal of a scientific philosophy
to reduce all possible occurrences to relations, to resolve
them into questions of form, to look upon them as trans-
formations, and therefore I say that the ultimate aim of
science is to describe everything in formulas. I see no ob-
jection to the relativist claim that this is a postulate of sci-
ence. In fact, I deduce this postulate directly from my
conception of reality which presents itself everywhere in
our experience as transformation. Thus we would justify
the principle of relativity on the basis of the old traditional
basis of exact science.

The main claim of the relativists is based upon their
simplification of the electromagnetic equations, and this is
granted even by the adversaries of the principle of rela-
tivity. Professor Magie says:

'Tt is surely true that if it were not for this demand of
simplicity, immediately attainable and at present expressed
in the electromagnetic equations, the chief incentive to the
development of the theory of relativity would be wanting."

62 THE PRiNCIPLE OF RELATIVITY.

The one simplification of formulas is attempted by cer-
tain relativists by a generalization of time and space into
a higher four-dimensional system, and they call it a four-
dimensional space. We may note incidentally that Wag-
ner's Parsival has anticipated the doctrine of relativity,
for in his search he utters the mysterious words: '^Zum
Raitm zuird liier die ZeitT (Into space here changeth
time!) The relativists might as well have called their
four-dimensional space a four-dimensional time. We ab-
stain from giving it a name, but subsume time and space
under one and the same category as ''form" which enables
us to view time and space as two inseparable factors of the
cosmic system of interrelations, and we deem it wise to re-
member that they are different. If the relativity physicists
have this in mind and do not mean ulterior mystifications,
I would not hesitate to join their ranks on this point.
* * *

We may add one more comment about simplification.
Logical possibilities are wider than actualized reality. Re-
ality is one instance among many others which are not
actualized. The fictions of fairy tales, of Gulliver's Trav-
els, and of religious myth are instances of it. But in the
domain of pure logic even actually absurd conditions pa-
rade as legitimate potentialities. Actual space has three di-
mensions, but metageometricians have invented more-di-
mensional spaces. Why not? We have in the construction
of purely logical systems the undeniable right to general-
ize into the not actualized logical possibilities and mathe-
maticians can not be restrained from building up a pange-
ometry. While Euclidean space is homaloidal, they may
create all kinds of curved spaces, which are all legitimate
before the tribunal of pure logic, if they are but consistent
in themselves. The main gain derived from such construc-
tions which will naturally appear to the average man of
average common sense as gratuitous, if not positively non-

The principle of relativity. 63

sensical, consists in rising to a higher level and understand-
ing from this higher point of view the actualized reality
better than if he remains on the terra firma of a limited
sense-experience.

It might help our comprehension of causality as a trans-
formation according to the laws of form to conceive the
chain of causation as reversible, that the condition of causes
are turned into effects and that the final factors that bring-
about the effect become the causes. This view has been
humorously worked out by Fechner who for this purpose
assumes that the pendulum of events will go on for a while
in the direction it takes now, but the time will come when
it will swing back. And then it will appear to us as quite
natural and necessary that the decayed and waste material
from fields and polluted rivers pass into our bodies and are
changed in our bowels into juice to go forth from our
mouths on the dinner table as lovely fruit or cheese, with
bread and butter, and as roast venison or fish to go back
and constitute useful parts in the revived animal. It would
please us to see all this come about and the thought of the
resurrection of the lamb under the butcher's knife would
demonstrate that there is a purpose in the law of causation.
We would be accustomed to the outcome and deem it
natural. In fact some notions of an inverse world order
in the golden age when the lamb will feed on the wolf, when
the deer will hunt the hunter, when the rich shall be poor
and the poor rich, when the miserable will be comforted
while the fortunate will be tortured has now and then re-
ceived serious support in the religious hopes of the dis-
inherited classes of mankind, and we may find in the New
Testament an echo of this belief in those traditions which
come down to us from Ebionite sources, the parables of the
foolishness of the rich and the benediction of the poor.
Dives goes to Hell while Lazarus is carried by angels to
Abraham's bosom. Abraham says in Luke xvi : 25 : "Son,

64 THE PRINCIPLE OF RELATIVITY.

remember that thou in thy Hfetime receivedst thy good
things, and likewise Lazarus evil things: but now he is
comforted, and thou art tormented." No mention is made
that Dives was wicked and that Lazarus was good; the
only argument is that the other world must be reverted in
its order.

A view of this kind which generalizes the mechanical
constitution of the world and sees the possibility of an in-
verted causation, just as an engine may be reversed, may
widen our comprehension and simplify our formulas of
moral action, but we need not for that reason believe in
its actualization. It is simply an instructive Insits imagina-
fionis, an ingenious and helpful fiction — like our conception
of four-dimensional space.

The mathematician who limits his studies to the Euclid-
ean plane will understand his problems better if he becomes
familiar with the theorems of stereometry, or if he views the
figures of plane geometry as projections ; or again if he re-
gards a certain set of curves as conic sections. And further
many problems of stereometry find a simpler formulation
if viewed from the more comprehensive, though purely
imaginary, view-point of a four-dimensional geometry. All
this indicates that the simplifications of which the relativity
physicists boast, may be (and I am inclined to believe that
they are) very harmless. For all I can say, judging merely
from the acceptance they have found, they must be true,
but I can not see why they should be subversive of the sci-
entific world-conception of the past.

A peculiar view of time which has been proposed in all
seriousness, although common sense might consider it as
absurd, is the concept of time and space as consisting of
discrete ultimate units. Do not our years, and days, and
our hours too begin at definite moments ? We become fifty
or sixty years old suddenly with the beginning of a definite
minute, According to this, time would run in jerks like

THE PRINCIPLE OF RELATIVITY. 65

the jumping second hands, and it would ultimately consist
of infinitesimally small units of duration. Space also would
be stippled and not continuous. Every motion would have
to proceed in hopping from spot to spot, and the surface of
a plane would be not unlike a half-tone picture which pro-
duces the impression of a continuous level but consists in
reality of different dots more or less deeply tinged with
ink. Such conceptions of time and space are quite con-
ceivable although our classical and well-established views
of both present them as continua. If space and time were
actual entities endowed with positive qualities, if they were
not merely potentialities of motion, a scope in which we
move about, we could discover the nature of space by ex-
periment. However, as they are constructions made in the
abstract domain of anyness we should not refuse to con-
sider seriously all kinds of propositions as to the nature of
time and space. ^^

In comment on theories of this kind we would say that
duration is continuous, but time consists of discrete units
of duration ; and again the scope of motion shows us an un-
interrupted expanse while geometry exhibits definite lines
of definite direction and of definite length. Geometrical
space in its classical Euclidean form is not stippled, never-
theless every construction is particular. Geometrical points
have no extension, but they possess a definite location, be-
ing determined, e. g., by two crossing lines. Thus space is

'" The Monist of October 1912 contained an article on "Atomic Theories
of Energy" by Mr. Arthur E. Bostwick, which is of interest both to those
who accept and those who do not accept this theory. In comment we would
say that Mr. Bostwick's defense of an atomic theory of energy is certainly
true of definite amounts of energy, and his theory holds good also in his
comparison of energy to amounts of money values deposited in a bank account.
If deposits were made in specie, we could trace every dollar of a deposit. It
is true we can not do so, but this we can not do only because no one cares to
receive definite and individual coins, but is satisfied with money in any form.
Therefore the bank is like a reservoir of water which receives and gives out
water as it happens to come. The bank gives credit for amounts received and
pays out amounts according to request. Thus the individual coin is lost sight
of as the many drops of water are definite and concrete masses, and every
dollar in a bank represents some concrete value somewhere.

66 THE PRINCIPLE OF RELATIVITY.

not the totality of all points, but the totality of our scope
of motion and anywhere in space points may be laid down.
In a word: Time and geometrical space are constructions
invented for the purpose of making measurements possible
in a scope of potentialities.

Actual existence is always definite, pure forms however
as well as purely formal thoughts, are always potential.

It seems as if the beginning of actuality must consist
in establishing something that is limited and concrete. In
this way it appears plausible that a potential world would
be continuous as an ocean of pure ether might be, but
an actual world ought to consist of a group of units, of
atoms, of definite particular specks of existence endowed
with definite amounts of energy, and we ought to be able to
trace every definite amount of existence through all the
changes which in the process of evolution it will undergo;
and this ought to be true as regards every amount of both
matter and energy.

SOME PHYSICAL PROBLEMS OF RELATIVITY.

The physical problems presenting themselves in the ex-
periments which have become connected with the move-
ment of relativity do not seem to have any direct bearing
on the principle of relativity itself. Relations are of a
purely formal nature and relativity therefore belongs to
the same kind of knowledge as arithmetic, geometry and
logic. Relativity can and must be applied to physics just
as much as there is an applied mathematics, but as the
Pythagorean theorem is independent from its applications
in experience, so applied relativity can neither establish
nor refute the principle of relativity. This is true above all
of the well-known and most important Michelson-Morley
experiment.

The instrument made in Berlin by Schmidt & Haensch
was so delicate that it was of no use in Berlin, and even

THE PRINCIPLE OF RELATIVITY. 67

when placed upon the foundation for the pier of the equa-
torial in the Astrophysical Observatory at Potsdam the
fringe of interference rings disappeared by stamping upon
the pavement at a distance of about lOO meters. Every
detail of consequence was taken into consideration, not only
the motion of the earth through the ether but also the
motion of the whole solar system towards the constellation
of Heracles. The expansion of the brass arms of the in-
strument through a change in temperature, and also the
bending of the arms through rotation were duly considered
and the difficulties arising therefrom met. A scale ruled
on glass was employed in order to dispense with the mi-
crometer screw w^hich here proved useless. Yellow light
was used, because its wavelength is least difficult to meas-
ure.

If the ether is at rest while the earth moves through
it, the time required for light to pass from one point to
another on the earth's surface would depend on the direc-
tion in w^hich it travels. Two pencils of light that travel
over paths at right angles to each other will interfere ; the
one traveling in the direction of the earth's motion will
travel 0.04 of a wave length farther than it would have
done were the earth at rest, while the other pencil at right
angles to the motion of the earth would not be affected.
The results of Professor Michelson's experiment are neg-
ative. He found very small displacements in the fringes of
his ray of light, so small that they must be accounted as
mere errors of the experiment. While we ought to expect
a displacement of 0.05 we have only such as lie between
0.004 and 0.015. Professor Michelson says:^^

"The interpretation of these results is that there is no
displacement of the interference bands. The result of the
hypothesis of a stationary ether is thus shown to be in-

" "The Relative Motion of the Earth and the Luminiferous Ether" in The
American Journal of Science, Vol. CXXII, pa^e 128.

68 THE PRINCIPLE OF RELATIVITY.

correct, and the necessary conclusion follows that the hy-
pothesis is erroneous.

'This conclusion directly contradicts the explanation
of the phenomenon of aberration which has been hitherto
generally accepted, and which presupposes that the earth
moves through the ether, the latter remaining at rest."

In another article Professor Michelson states his re-
sult thus:^^

"The luminiferous ether is entirely unaffected by the
motion of the matter which it permeates."

Professor Michelson has varied the conditions of his
experiment by trying whether deviations could be detected
through a change of level, by throwing pencils of light
upward and by repeating it at different hours of the day,
but the displacements remained insignificant. One of Pro-
fessor Michelson's articles ends thus:'^

"In any case we are driven to extraordinary conclu-
sions, and the choice lies between these three:

"i. The earth passes through the ether (or rather allows
the ether to pass through its entire mass) without appre-
ciable influence.

"2. The length of all bodies is altered (equally?) by
their motion through the ether. ^'^

"3. The earth in its motion drags with it the ether even
at distances of many thousand kilometers from its surface."

Another article by Professor Michelson on the same
subject is published in The American Journal of Science,
Vol. CXXXIV, p. 333.

What this famous experiment has to do with the prin-
ciple of relativity except in a most general way, is not yet
clear to those who have not joined the ranks of the rela-

" "Influence of Motion of the Medium on the Velocity of Light," in The
American Journal of Science, Vol. CXXXI, page 386.

""The Relative Motion of the Earth and the Ether," The American Jour-
nal of Science, Vol. CLIII, p. 478.

"This would be the case according to the theory of 11. A. Lorentz, whose
views are mainly pre.sented in the Encyclopddie der math. Wissenxchaften.

THE PRINCITLE OF RELATIVITY. 69

tivity physicists; but the relativity physicists insist very
vigorously and dogmatically that it proves, or at least
favors, their theory. Professor Michelson himself has not
joined their ranks, though he recognizes the difficulties
of the situation.

It is strange that Michelson's experiment seems to
stand in contradiction to another and older experiment
made first by Bradley, which is known as the aberration
of light. If the earth passes through the ether with its
own velocity (e) while the rays of the sun come down
upon the earth with the velocity of light (/) there ought
to be a deflection of light amounting to e/l, viz., the veloc-
ity of the earth divided by the velocity of the light in its
path from the sun towards the earth, and though this rela-
tion is very small, it has actually been observed and de-
termined to amount to a trifle over twenty seconds.

This conclusion which could be anticipated according
to the logic of mechanics seems to be contradicted by
Michelson-Morley's experiment in which the attempt is
made to measure with a ray of light the motion of the earth
while passing through the ether.

The discrepancy between the two experiments will per-
haps find a proper explanation in the proposition that if
the source of light lies outside the earth as in the case
of the rays of the sun, they will show the deflection. As
is to be expected they would come down in straight lines
like raindrops falling in an absolutely quiet air which
would be caught by a moving body as if they came down
at an angle; but if the source of light moves along with
the earth there would be no difference whichever way they
turn, first towards the east or first towards the west, or at
right angles, and the sources of the light would partake of
the acceleration of the earth so as to show no difference,
as raindrops dripping down within the car would fall down
in straight lines from its top to the floor, assuming that the

70 THE PRINCIPLE OF RELATIVITY.

doors and windows of the car are hermetically closed and
there be no draft which would deflect their perpendicular
dripping.

It almost seems as if some ether were carried along
by the earth to a considerable distance beyond its sur-
face while the other ether in outer space would remain at
rest, but it would be bold for any one but a specialist to
venture the proposition of any theory on so new a subject
of which few facts only have been ascertained. Yet most
assuredly the topic under investigation has nothing to do
with the principle of relativity, unless relativity is a mis-
nomer for the phenomena attributed to the luminiferous
ether.

The question of relativity is a philosophical problem,
but the Michelson-Morley experiment is of a purely phys-
ical nature, and so we must expect that the last word as
to its explanation should be given by physicists.

The other experiment which is assumed to verify the
principle of relativity is the one first made by Kaufifmann,
and afterwards repeated in a modified form by Bucherer.
This experiment too has little or nothing to do with rela-
tivity. On the contrary it seems to prove the existence of
something absolute for it reaches a limit of velocity.

There is at present a tendency in the world of thought,
noticeable in pragmatism and other anti-intellectual move-
ments, which seems to annihilate the very existence of
objectivity, and with it science, man's endeavor after a
purely objective cognition. Everything is relative, and the
general belief has spread that an absolutely objective de-
scription is impossible. To speak of the size of objects
seems to have lost its sense, for size has become to the
present generation merely the result of measurement, and
thus an objective determination is in some quarters looked
upon as a superstition of prescientific tradition, an inheri-
tance from the dark ages. But it is not true that there is

THE PRINCIPLE OF RELATIVITY. 7 1

no objectivity, for one of the greatest accomplishments of
Michelson was the estabHshment of a definite measure by
calculating the size of a meter in wave-lengths or red
cadmium light in a vacuum. The waves of light are ab-
solutely definite, and thus we have here a result of measure-
ment in truly objective terms. If the Kauffmann-Bucherer
experiments prove, as is claimed, that an increase of veloc-
ity means an increase of mass and that the limit which is
reached is the velocity of light, we only learn that rela-
tivity is not without bounds, and that on the contrary a
climax is reached which can not be surpassed. The high-
est velocity is the velocity of light.

The conclusion that the highest velocity is the velocity
of light seems to be contradicted by the facts of gravitation
for according to the Newtonian theory gravitation is pos-
sessed of a practically infinite velocity in that the gravity
of the sun exercises its influence upon the planets without
any perceptible difiference of time. But this is no object-
tion, for consider : The action of gravity formulated in the
well-known law of falling bodies and of their acceleration
which describes true motions is very slow in comparison
to the velocity of light. The influence which is exercised
in the strain between two gravitating bodies, say between
the moon and the earth, is not a motion at all, but a con-
dition, and this condition is the same between the two cen-
ters of the thus interrelated bodies. It is a state of tension
and there is no transference of a wave motion either from
the moon to the earth or from the earth to the moon. The
tension is simultaneous. The misconception seems to rise
from the error that there are two bodies and there is a
third item which manifests itself as a passing from the
one to the other under the name of gravitation. We must
view the whole system as one field of action in which sev-
eral bodies in motion are balanced among themselves ac-
cording to their mass. Their mutual attraction is not

yz THE PRINCIPLE OF RELATIVITY.

transferred motion but a simultaneous interaction. New-
ton retarded the general acceptance of the law of gravita-
tion, first definitely proposed by Hooke, for eighteen long
years because he could not make up his mind to believe in
an actio in distans, and when he was finally convinced, he
still expressed his misgivings how to overcome this objec-
tion, but is there any actio in distans at all? Is not the
whole system of the universe an interrelated whole and
does not a center of gravity (howsoever it may have origi-
nated) extend so far as its stress reaches? Where its
strain produces a tension, there it affects its surround-
ings. If we look upon the phenomena of gravitation in
this light we need not make the fantastical assumption
that gravity is possessed of an infinite velocity.

The relation between the increase of velocity and the
increase of mass promises to throw light on the ultimate
constitution of matter, but the result of the experiment
is only the first step to a solution of this tremendous prob-
lem, concerning which at the present stage of science we
can have only vague suggestions. When the man appears
who can read the facts aright, he may be able to point out
how by a mere stress the aboriginal world-stufif which,
for all we know, may be, or even must be, the ether, pro-
duces a tension within this mysterious infinitely elastic
and incredibly thin substance, and the tension between two
centers of such contraction would, like the strain between
nodes within thin tridimensional rubber, act in all direc-
tions according to the Newtonian formula of gravitation, as
being directly proportional to the product of their amounts
of contraction, and inversely proportional to the square
of their distance between two centers. Thus the origin of
matter would be due to an unknown force which with a
velocity only inferior to the velocity of light would drive
infinitely small corpuscles around in a whirling dance with

THE PRINCIPLE OF RELATIVITY. 73

such a regulated speed that conglomerated multitudes of
such whirls would appear to us as solid masses.

Here again we would be confronted by an ultimate
limit. We would discover that objective reality, our world
of matter in motion, is built up of ultimate particles; or
perhaps better, of ultimate activities, that below the atom
there are smaller units, the hypothetical electrons, which
may be characterized as centers of force, and that they are
due to condensation which produces the phenomena of
gravitation. All further phenomena of physics and chem-
istry would have to be explained as the result of these ele-
mentary actions.

Formerly thinkers were inclined to see infinity all
around. They thought of the atomic structure not only
as infinitesimally small, but also as truly infinite; the mole-
cules being analyzable into atoms and the atoms again
into still smaller units, say into electrons or monads, and
that the monads were again compounds of monadules and
so forth — all this being argued on the poetic notion that

"Great fleas have little fleas
Upon their backs to bite 'em,
And little fleas have lesser fleas,
And so ad inHnitum."

The molecule is a kind of planetary system, with atoms
as satellites, so is the atom with its circling electrons ; why
should not the electron be of the same construction and
why should not the component parts of the electron be as-
sumed to be made after the same pattern world without
end? On the other hand our solar system is one among
uncountably many others of the Milky Way; and the
Milky Way in its turn is one universe of an enormously
larger system of many Milky Ways. This is the conclu-
sion which astronomy has deduced from actual facts. Why
then should not this^n our opinior^ enormous system^of the
many Milky Ways be only a tiny item in a still larger sys-

74 THE PRINCIPLE OF RELATIVITY.

tern, and why should we not be justified in the assumption
that we are confronted with an infinite vista into both
directions toward the infinitely small and the infinitely
great?

This notion has been brought out in the second quatrain
which reads:

"And the great fleas themselves in turn
Have greater fleas to go on,
While these again have greater still,
And greater still and so on."

A vista into infinitudes, going out into the infinitely
small and the infinitely great, now seems to become un-
tenable, and definite limits loom up, which condition, so it
seems to us, would reveal, not a bottomless and undefinable
relativity but a definite world of an objective reality with
definite interrelations and limits. If there are definite limits
in either direction we may fairly well assume that they are
in both directions. Further, if the universe is definite in
its space relation, it should also be definitely limited in
time. The world may have originated in an immeasurable
ocean of uniformities as a definite commotion and may
terminate again in a general dissolution by dissipation.
If such be the case the relativity principle would not apply
to the whole. Relativity would mean the interrelationship
of all things, but the whole as a whole would be of a
definite particularity with definite boundaries while the con-
stitution of the world would exhibit a structure of ex-
tremely tiny ultimate units of a determinably definite size,
endowed with a definite velocity and at every given point
of a definite form of motion.

While the totality of existence, the sum total of our
Milky Ways, appears to have had a beginning and may
after the lapse of immeasurable ages come again to an
end, we do not deem it excluded tha^t the same process
of world-formation may start again, as it probably was

THE PRINCIPLE OF RELATIVITY. 75

repeated long before the origin of this our present uni-
verse. While thus everything existent, even the ether it-
self in its totality, would have to be regarded as particular
and concrete with definite boundaries and as being limited
to a definite time both in its beginning and in its end, there
would after all loom up in the background of this world an
infinitude of space, an eternity of time and an unfathom-
able wealth of potentialities as to new formations which in
spite of all the light which the most advanced science will
ever shed on the world problem will keep this great All of
existence with its inexhaustible resources and its myste-
rious order an object of constant wonder and awe.

The relativity problem as such is a philosophical prob-
lem, but the relativity physicists have made a physical
problem of it, and the philosophical problem of relativity
is not a new problem, it is as old as science ; it is only the
lack of philosophical training which has led to the enun-
ciation of some baffling paradoxes which if they were true
would make objective science impossible, for they would
abolish definiteness of any kind and do away with objectiv-
ity. And strange to say, claims of this kind are upheld on the
ground of experiments which tend to establish the exist-
ence of an absolute, or as we would prefer to say, of some
ultimate, which would prove that our experience does not
float as a local tangle in an endless infinitude, but that
there is a beginning and end, and also a boundary of all
concrete reality at every definitely given moment. No mys-
ticism is needed. Infinitude and eternaHty are potential-
ities, not actualities. They are vistas of what may be, not
what is. They constitute the inexhaustible wealth of na-
ture and of life without robbing science of its validity.

There is a tendency in mankind to think of the present
moment as the climax of the past, which ushers in a new era
by being an unprecedented and unique start. Every new
generation passes through such a period of self-sufficiency

76 THE PRINCIPLE OF RELATIVITY.

and of an intoxication with their own incomparable self-
hood. The old problems seem new to them, and trying to
formulate them in an original way, they applaud their own
mistakes as something extraordinary and wonderful.
Goethe characterizes this tendency in the young graduate
who has just taken his degree of Bachelor ( See Faust,
Second Part, Act II) where this young man vents his am-
bitious conceit in these words:

"This is Youth's noblest calling and most fit!
The world was not, ere I created it;
The sun I drew from out the orient sea ;
The moon began her changeful course with me ;
The Day put on her shining robes, to greet me ;
The Earth grew green, and burst in flower to meet me,
And when I beckoned, from the primal night
The stars unveiled their splendors to my sight.
Who, save myself, to you deliverance brought
From commonplaces of restricted thought?
I, proud and free, even as dictates my mind,
Follow with joy the inward light I find.
And speed along, in mine own ecstasy,
Darkness behind, and Glory leading me!" '

It is apparent that the relativity physicists confront an
important problem, but they have not succeeded in solving
it ; they have not even as yet properly formulated the ques-
tion and their propositions are still in a state of fermen-
tation. It is difficult to say what will come of it. It is to
be hoped, however, that the movement will follow the usual
course of mental growth. The relativists will drop their
extravagant claims, they will mature the truth which they
grope after and will at last formulate it into clear state-
ments so as to justify the prophecy of Mephistopheles,
who comments upon the proud words of the young Bach-
elor thus:

"Go hence, magnificent Original !—
What grief on thee would insight cast !
Who can think wise or stupid things at all.
That were not thought already in the Past?

THE PRINCIPLE OF RELATIVITY. 77

Yet even from him we're not in special peril ;
He will, ere long, to other thoughts incline :
The must may foam absurdly in the barrel,
Nathless it turns at last to wine."

THE PRINCIPLE OF RELATIVITY AS A PHASE IN THE DEVEL-
OPMENT OF SCIENCE.

The principle of relativity made its appearance with
great pretensions, and upset not a little the scientific
world by its claim to anticiuate the traditionally classical
basis of physics, of astronomy, of mathematics, and of the
other natural sciences. It affects especially the commonly
accepted theory of the ether, and even the current views of
space and time, which have hitherto proved serviceable.
The entire realm of science was almost panic stricken for
scientists seemed to have lost the terra firina under their
feet ; they felt as if they were sinking into a bottomless abyss
and were left without a standing place in the whirl of a uni-
versal flux. Physicists of former date might take the move-
ment for a joke, and many conservative thinkers find a
good deal of humor in it, but the relativists are quite seri-
ous and are aware of the gravity of the consequences of
their subversive work.

However, the new conception sailing under the flag of
the principle of relativity which has been so noisily ad-
vanced to replace the old notions, does not prove quite satis-
factory and presents too many difficulties to be acceptable to
the average mind. It consists mainly of contradictory and
mystifying statements commonly called ''the paradoxes of
relativity," and these statements have been praised or ridi-
culed, accepted or rejected, by enthusiastic adherents or
obdurate adversaries, so that we have a state of things not
unlike the rise of a new religious creed as it sets out to
conquer the world. The names of Einstein, Lorentz, Min-
kowski, are the stars of first magnitude among the foun-
ders of the new world-conception. Their arguments, mathe-

78 THE PRINCIPLE OF RELATIVITY.

matically well excogitated and worked out with subtile
exactness, seem to carry everything before them, and we
are not prepared to say that their contentions are wrong.
Their propositions decidedly contain truths of great im-
portance, referring mainly to calculations of minute pre-
cision in complicated phenomena. Yet common sense rebels
against them and would not be convinced. Prima facie
the new doctrine seems ingeniosius quam vcrius; it is in-
geniously contrived but there is a hitch in it.

We have endeavored to show that the paradoxes have
merely an appearance of contradictoriness ; that they can
be explained as slightly misstated conclusions and so the
relativists could have avoided mystification. If physicists
had borne in mind that as a matter of course all determi-
nations and calculations of measurement require a refer-
ence point which remains unaltered in its relations to other
points within the field of observation and is assumed to
be stable, the problem would never have arisen. The
new cases of unstable reference points which make their
first appearance in 1727 with Bradley's investigations
would simply have demanded a corrective without in the
least upsetting the traditional view, and this will after all
be the outcome of the new movement. It is to be antici-
pated that in the long run the paradoxical features of rela-
tivism will disappear, and when the results of the new
propositions will be formulated without ado in sober con-
sistency, it will be found that they only modify the old tra-
ditional physics and astronomy under certain specially com-
plicated circumstances, particularly when the place of an
observer while making his observations possesses a motion
of its own afifecting the motions under observation.

It almost seems as if the entire proposition of the prin-
ciple of relativity might as well have been abandoned be-
cause the relativity of motion as well as of space, the field
of motion, was not unknown to earlier physicists. Is not

THE PRINCIPLE OF RELATIVITY. 79

relativity the nature of space? Denunciations to the effect
that earher physicists and astronomers had beUeved in an
absolute space are really a misconstruction of their views,
for what Newton called absolute space did not involve a
denial of the conditions about which the relativists have
troubled their minds.

As a symptom of sobering down, we mention an article
of Edward V. Huntington which appeared in the Philo-
sophical Magazine for April, 19 12, under the title "A New
Approach to the Theory of Relativity," pages 494 to 513.
After explaining experiments with synchronized clocks.
Professor Huntington says on page 507 as follows:

"These are the famous paradoxes of the theory of rela-
tivity which are often cited as proof of the assertion that
the theory of relativity is incompatible with our ordinary
ideas of time and space, but which here appear as neces-
sary consequences of perfectly natural and reasonable con-
ventions for setting clocks and laying out coordinates."

Further Professor Huntington takes away the mystery
from some other propositions of the relativity principle. He
concludes that "thus all the transformation equations used
in theorem i, are obtained by an entirely natural and ele-
mentary method."

The question then arises. Has the appearance of the
principle of relativity done nothing to promote science, or
has it even been a mistake? And we say in answer that
the principle of relativity might have approached its prob-
lem in a more conservative way simply by bearing in mind
that former physicists were perfectly aware of the fact
that whenever they made measurements they laid down
a point of reference for their calculations. This reference
point must share the motion of the phenomena observed,
or at least the difference must (for the purpose in view)
be a negligible factor. We know very well, and all scien-
tists of former jjenerations also knew, that the stabilitv of

80 THE PRINCIPLE OF RELATIVITY.

our reference point is a fiction, but without making this
fiction our calculations would sink into the bottomless.

While the geometer calculates distances on earth, he
knows very well that the reference point from which he
starts is not absolutely stable but moves around the sun
with the entire earth, including the objects and the dis-
tances to be measured. When astronomers took measure-
ments of the stars they knew very well that their own
telescopes were moving along through space with the veloc-
ity of the earth under their feet, but for the purpose in
view this movement was a negligible factor. Both physi-
cists and astronomers of former times took it as a matter
of course that we know of no point of absolute rest, that
everything is relative, and that thus there is no absolute
space in which their systems of measurement held a defi-
nite and invariable position. In this sense the principle
of relativity is not quite so new as its enthusiastic adherents
frequently claim. The contradictions and paradoxes are
merely on the surface, and there is little hope of replacing
the old orthodox mechanics which will even in the times
to come hold good for all the usual commonplace fields of
observation.

For all that, we do not mean to belittle the principle of
relativity; the new method has its advantages, and in cer-
tain spheres it will find its application. What the relativists
have accomplished may be comparable to the invention of
a micrometer which proves very useful in making minute
measurements hopelessly out of reach of the coarser in-
struments used in daily practical life. But as the microm-
eter will not abolish the usefulness of the yardstick, so
relativist considerations will not upset the commonplace
view of traditional mechanics. There is no contradiction
between the two, if only we rightly understand the philo-
sophical basis of the ordinary methods of measurement
with their indispensable fiction of laying down a reference

THE PRINCIPLE OF RELATIVITY. 8l

point and ignoring the negligible factors of changes that
take place while observations are being made, changes
that may afifect size, time and distance. The need of an
indispensable reference point, the assumption of which is
always a fiction made for the purpose in view, will be felt
no less in the more complicated considerations which have
prompted the rise of the new mechanics of the relativists.

In order to satisfy the demand of the conditions to
which relativists have devoted their special attention, we
have simply to bear in mind that the assumption of refer-
ence points is absolutely indispensable for any kind of
measurement.

We may therefore say that the relativists have pro-
posed their new theory as new in neglect of comprehending
the philosophical basis of the science of measurements. We
may grant that in the traditional treatment of kindred
problems it was perhaps ignored, yet we trust that it was
tacitly assumed.

The principle of relativity is therefore not useless, for
it is serviceable in a field where more complicated inter-
relations have to be observed; but if the relativists dig-
deeper they will find common ground with their predeces-
sors in the philosophical basis of the theory of measure-
ment. As to the ether we must consider how little we
know about its nature, and it seems premature either flatly
to deny its existence, or to affirm doubtful qualities of it.
or to make bold a priori statements as to its motions with
reference to the motions of matter. Here experiments
alone, like those made by Professor Michelson, will be
decisive. Finally whatever difficulties may still present
themselves, we may be assured that all of them will find
a satisfactory solution without upsetting the foundations
of our scientific world-conception.

82 THE PRINCIPLE OF RELATIVITY.

CONCLUSION.

The theoretical problem of the principle of relativity
has nothing to do with practical difficulties which are ques-
tions of fact. As the paradoxes disappear the theoretical
problems are solved, while the practical difficulties must
be overcome by experiment.

At the present state of our knowledge it would be fan-
tastical to suggest a solution of the physical problems con-
nected with the relativity movement, and we must leave
the discussion of them to the future, for ere we can ap-
proach a solution we must know much more about the
ultimate constituents of matter.

Who will furnish the key to the lock of the closed door
at which the relativity physicists are knocking?

The details of the physical problems and their solution
have only a slight interest for philosophy. The philosopher,
however, expects that the physicist's solutions shall be con-
sistent and that our scientific world-conception shall tol-
erate no contradictions.

If we consider the all-importance of form and the
enormous significance which the formal sciences possess, we
are inclined to regard the philosophy of relativity as a
synonym and parallel development of the philosophy of
science — the philosophy of form. But before we can
definitely say so, we would expect the relativists to work
out their philosophical substructure in a conservative way,
to rid themselves of their paradoxical propositions, give up
false pretensions to originality, recognize the past tradi-
tions of science, and rather than abandon the past, join
their cause to the legitimate progress that follows from
the tendencies, the ideals and aspirations of the established
sciences.

We do not deny the relativity of all existence through-
out and without exception, and in this sense we believe in

THE PRINCiri.E OF RELATIVITY. 83

the principle of relativity, but we still cling to the old
scientific ideal of objectivity and we can not see that the
relativity principle as frequently enunciated by the rela-
tivists is well established.

The great question before the world of thinkers is this:
Is it possible to construct a philosophy of science? The
author of this essay has answered this cjuestion in the affir-
mative, and has worked in this field for fully a quarter of
a century. He has worked out the details of a philosophy
of science, and has submitted to the world in both The
Open Court and The Monist his answers to the several
philosophical questions. These questions are: the nature
of the soul ; the origin of sentiency and of thought ; the na-
ture of reason, especially in its origin and in its relation
to language, the mechanism with which reason manifests
itself; the nature of ethics and the foundation of morality
as it is found in the laws of the objective world; the sig-
nificance of the God-conception as the authority of conduct,
as the ideal of right and wn'ong, as the standard of truth
and error, as the object of devotion, of gratitude, of rev-
erence mainly as the factor which determines good and
evil. All these questions are not beyond the scope of scien- \
tific inc{uiry and in the philosophy of science definite solu-
tions are propounded which, though based on radical prin-
ciples of unbiased thought, lead to a justification of the
historical growth of religion and science.

The whole scope of existence as it presents itself in
human experience can become an object of scientific in-
quiry, and all scientific problems admit ultimately of a defi-
nite solution without equivocation or prevarication, yet
at the same time science is only one attitude among several
others from which the world can be confronted. The noetic
conception is the ideal of understanding the w^orld in its
pure objectivity represented in mental terms to the exclu-
sion of sentimental subjectivitv. But man is not a child

84 THE PRINCIPLE OF RELATIVITY.

of reason only. He is also endowed with sentiments, with
will and with artistic tendencies. While the scientific
world-conception is absolutely indispensable for the man
of thought who works for a constant elevation of mankind
upon a higher level, we must at the same time recognize
the rights of the large masses who naturally are non-
scientific and are swayed by sentiment, by devotion, by art,
by ethical aspirations, by a religious comprehension of life ;
and thus we see in artistic and religious conceptions ways
of treating the world problem which are by no means un-
justified and ought not to be repudiated on the ground that
they are non-scientific, sometimes unscientific, or even anti-
scientific and purely sentimental. Religious cosmogonies,
ecclesiastical ceremonies, religio- poetical fictions possess
values of their own which can not and should not be meas-
ured by the standards of scientific method. The mystic
also has his right to confront the world with his emotions
and visions. Nevertheless, even here the philosophy of
science will be capable of investigating various products
of these tendencies and has a right to evaluate their truth
or untruth by tracing the meaning of allegorical poetry
as well as the wholesomeness of ethical attitudes which they
encourage. In this way the philosophy of science as worked
out by the present writer has by no means been narrow but
has granted a free scope to all legitimate tendencies of the
human mind, and if the philosophy of science has been
properly understood, leaders of thought in the movements of
pragmatism, relativism, Bergsonianism and other modern
tendencies, would have been able to avoid at least some of
their aberrations, and could have devoted their energies to
efforts in the right direction. At any rate they would have
been better understood; instead of being classified with
philosophy, they would more properly have been regarded
as a new species of poetry, or as literary ebullitions. Such
they are ; as such they possess value. They are not philos-

THE PRINCIPLE OF RELATIVITY. 85

ophy, certainly not philosophy in the strict sense of the
word ; they are not scientific world-conceptions.

It may appear strange to class the movement which
proclaims the principle of relativity in the same category
with pragmatism and other antiscientific tendencies. We
do so because the relativists have much in common with
pragmatists, because both cancel the ideal of objectivity,
both identify truth with the subjective conception of the
real or with the observer's statement of facts. They iden-
tify size with result of measurement and think that the
traditional view of truth is an error.

We do not overlook the fact that the relativists are of
a highly intellectual type and employ scientific methods,
but their aim is after all a denial of the old ideal of science,
of the objectivity of truth, and of clearness of thought. All
this is surrendered for the sake of a purely subjective simpli-
fication of statement which recommends itself in their own
specialty. Certainly there is a great difiference between
relativists and pragmatists, but we recognize in both a
subjectivist tendency and a subjectivist aim. Neither of
them feel- the need of approximating objectivity and both
indulge in ideal constructions, both build air castles, the
former of mathematical fiction, the latter of philosophical
poetry.

All these modern anti-scientific isms may have origi-
nated through the one-sided tendencies of a misapplied
scientism or even through the lack of comprehension of the
principles and the significance of science among naturalists.
These isms emphasize therefore certain contentions which
have a nucleus of truth, by insisting on the rights of senti-
ment though they go too far w^ien attacking science itself
and claiming a superiority for unscientific sentiment over
clear and methodical thought.

There is no question that all these modern movements
try each in its own way to satisfy legitimate tendencies, but

^

86 THE PRINCIPLE OF RELATIVITY.

in doing so they have mostly gone astray ; partly they mis-
understand their own aspirations, partly they lack sufficient
depth of comprehension and width of horizon in encom-
passing the whole realm of human endeavor.

We do not expect that in this partisan scramble of var-
ious prejudices, the whole world of thinkers can be induced
to recognize the common ideal of philosophical thought,
but we hope that there will be enough minds to understand
the several movements, to appreciate them so far as their
aspirations are legitimate, and to discover their weak points
in which they stray away from the straight path that leads
forward to a truer, deeper and a broader conception of the
world.

APPENDIX.

[The theory of the relativity of time and space, which is at present upper-
most in the minds of physicists, has come into the foreground mainly through
the differences of measuring at large distances the time it takes light to
reach the observer's eye which is further complicated by the motions of his
own standpoint. This happened for the first time in the history of science in
the year 1726 when Mr. Bradley discovered that the fixed stars possessed
a definite and peculiar motion of their own which was due to the motion of
the earth around the sun and depended on the time it takes the light to reach
the earth.

This classical exposition of his experiments was published in the form of a
letter sent to the Phil. Trans. (Vol. XXXIV, p. 637) and has naturally become
quite inaccessible. There is probably only one complete file of the Trans-
actions west of the Alleghanies, the fortunate possessor of which is the
Chicago Public Library. Considering the rarity of this essay we deem it
proper to republish it and render it accessible to our readers. We do not
doubt the very way in which Mr. Bradley approaches the problem will throw
much light on the principle of relativity. In fact this essay will prove suffi-
cient to explain its far-reaching significance, the need of its invention and
the limitations of its use. A consideration of the foundaton of this principle
and the history of its origin will clear it of the mysticism with which its recent
representations have surrounded its statements. — p. c]

THE REV. JAMES BRADLEY ON THE MOTION
OF THE FIXED STARS/

A Letter from the Reverend Mr. James Bradley, Savilian Professor
of Astronomy at Oxford, and F. R. S., to Dr. Edmond Halley
Astronom. Reg. &c. giving an Account of a new discovered
Motion of the Fix'd Stars.
Sir,

You having been pleased to express your Satisfaction with what
I had an Opportunity some time ago, of telHng you in Conversation,
concerning some Observations, that were making by our late worthy
and ingenious Friend, the honorable Samuel Molyneux Esquire, and
which have since been continued and repeated by myself, in order
to determine the Parallax of the iixt Stars; I shall now beg leave
to lay before you a more particular Account of them.

Before I proceed to give you the History of the Observations
themselves, it may be proper to let you know, that they were at
first begun in hopes of verifying and confirming those, that Dr.
Hook formerly communicated to the publick, which seemed to be
attended with Circumstances that promised greater Exactness in
them, than could be expected in any other, that had been made and
published on the same Account. And as his Attempt was what
principally gave Rise to this, so his Method in making the Observa-
tions was in some Measure that which Mr. Molyneux followed : For
he made Choice of the same Star, and his Instrument was con-
structed upon almost the same Principles. But if it had not greatly
exceeded the Doctor's in Exactness, we might yet have remained
in great Uncertainty as to the Parallax of the Hxt Stars ; as you
will perceive upon the Comparison of the two Experiments.

This indeed was chiefly owing to our curious Member, Mr.
George Graham, to whom the Lovers of Astronomy are also not a little

* Reprinted from the Philosophical Transactions of 1727.

90 THE PRINCIPLE OF RELATIVITY.

indebted for several other exact and well-contrived Instruments.
The Necessity of such will scarce be disputed by those that have had
any Experience in making Astronomical Observations ; and the In-
consistency, which is to be met with among diflferent Authors in
their Attempts to determine small Angles, particularly the annual
Parallax of the fixt Stars, may be a sufficient Proof of it to others.
Their Disagreement indeed in this article is not now so much to be
wondered at, since I doubt not, but it will appear very probable,
that the Instruments commonly made use of by them, were liable
to greater Errors than many times that Parallax will amount to.

The Success then of this Experiment evidently depending very
much on the Accurateness of the Instrument that was principally
to be taken Care of: In what Manner this was done, is not my
present Purpose to tell you ; but if from the Result of the Observa-
tions which I now send you, it shall be judged necessary to com-
municate to the Curious the Manner of making them, I may here-
after perhaps give them a particular Description, not only of Mr.
Molyneux's Instrument but also of my own. which hath since been
erected for the same Purpose and upon the like Principles, though
it is somewhat different in its Construction, for a Reason you will
meet with presently.

Mr. Molyneux's Apparatus was compleated and fitted for ob-
serving about the End of November 1725, and on the third Day
of December following, the bright Star at the Head of Draco
(marked v by Bayer) was for the first Time observed, as it passed
near the Zenith, and its Situation carefully taken with the Instru-
ment. The like Observations were made on the 5th, 11th and 12th
Days of the same Month, and there appearing no material Difference
in the Place of the Star, a farther Repetition of them at this Season
seemed needless, it being a Part of the Year, wherein no sensible
Alteration of Parallax in this Star could be expected. It was chiefly
therefore Curiosity that tempted me (being then at Kezv, where the
Instrument was fixed) to prepare for observing the Star on Decem-
ber 17th, when having adjusted the Instrument as usual, I per-
ceived that it passed a little more Southerly this Day than when it
was observed before. Not suspecting any other Cause of this Ap-
pearance, we first concluded, that it was owing to the Uncertainty
of the Observations, and that either this or the foregoing were not
so exact as we had before supposed ; for which Reason we purposed
to repeat the Observation again, in order to determine from whence
this Difference proceeded ; and upon doing it on December 20th, I

THE PRINCIPLE OF RELATIVITY. 9I

found that the Star passed still more Southerly than in the former
Observations. This sensible Alteration the more surprized us, in
that it was the contrary way from what it would have been, had it
proceeded from an annual Parallax of the Star: But being now
pretty well satisfied, that it could not be entirely owing to the want
of Exactness in the Observations ; and having no Notion of anything
else, that could cause such an apparent Motion as this in the Star ;
we began to think that some Change in the Materials, &c. of the
Instrument itself, might have occasioned it. Under these Apprehen-
sions we remained some time, but being at length fully convinced,
by several Trials, of the great Exactness of the Instrument, and
finding by the gradual Increase of the Star's Distance from the Pole,
that there must be some regular Cause that produced it; we took
care to examine nicely, at the Time of each Observation, how much
it was: and about the Beginning of March 1725, the Star was found
to be 20" more Southerly than at the Time of the first Observation.
It now indeed seemed to have arrived at its utmost Limit Southward,
because in several Trials made about this Time, no sensible Differ-
ence was observed in its Situation. By the Middle of April, it
appeared to be returning back again towards the North : and about
the beginning of June, it passed at the same Distance from the
Zenith as it had done in December when it was first observed.

From the quick Alteration of this Star's Declination about this
Time (it increasing a Second in three Days) it was concluded, that
it would now proceed Northward, as it before had done Southward
of its present Situation ; and it happened as was conjectured : for
the Star continued to move Northward till September following,
when it again became stationary, being then near 20" more Northerly
than in June, and no less than 39" more Northerly than it was in
March. From September the Star returned towards the South, till
it arrived in December to the same Situation it was in at that time
twelve Months, allowing for the Diflference of Declination on account
of the Precession of the Equinox.

This was a sufficient Proof, that the Instrument had not been
the Cause of this apparent Motion of the Star, and to find one
adequate to such an Eflfect seemed a Difficulty. A Nutation of the
Earth's Axis was one of the first things that oflfered itself upon this
Occasion, but it was soon found to be insufficient ; for though it
might have accounted for the change of Declination in v Draconis
yet it would not at the same time agree with the Phaenomena in
other Stars ; particularly in a small one almost opposite in right

92 THE PRINCIPLE OF RELATIVITY.

Ascension to v Draconis, at about the same Distance from the North
Pole of the Equator: For, though this Star seemed to move the
same way, as a Nutation of the Earth's Axis would have made it,
yet it changing its Declination but about half as much as v Draconis
in the same time (as appeared upon comparing the Observations of
both made upon the same Days, at different Seasons of the Year)
this plainly proved, that the apparent Motion of the Stars was not
occasioned by a real Nutation, since if that had been the Cause, the
Alteration in both Stars would have been near equal.

The great Regularity of the Observations left no room to doubt,
but that there was some regular Cause that produced this unex-
pected Motion, which did not depend on the Uncertainty or Variety
of the Seasons of the Year. Upon comparing the Observations
with each other, it was discovered that in both the fore-mentioned
Stars, the apparent Difference of Declination from the Maxima, was
always nearly proportional to the versed Sine of the Sun's Distance
from the Equinoctial Points. This was an Inducement to think,
that the Cause, whatever it was, had some Relation to the Sun's
Situation with respect to those Points. But not being able to frame any
Hypothesis at that Time sufficient to solve all the Phaenomena, and
being very desirous to search a little farther into this Matter ; I began
to think of erecting an Instrument for myself at Wansted, that
having it always at Hand, I might with the more Ease and Certainty,
enquire into the Laws of this new Motion. The Consideration like-
wise of being able by another Instrument, to confirm the Truth of
the Observations hitherto made with Mr. Molyneux's, was no small
Inducement to me ; but the Chief of all was, the Opportunity I should
thereby have of trying, in what Manner other Stars were affected
by the same Cause, whatever it was. For Mr. Molyneux's Instru-
ment being originally designed for observing v Draconis (in order
as I said before, to try whether it had any sensible Parallax) was
so contrived, as to be capable of but little Alteration in its Direc-
tion, not above seven or eight Minutes of a Degree; and there
being few stars within half that Distance from the Zenith of Kew,
bright enough to be well observed, he could not, with his Instru-
ment, thoroughly examine how this Cause affected Stars differently
situated with respect to the equinoctial and solstitial Points of the
Ecliptick.

These Considerations determined me; and by the Contrivance
and Direction of the same ingenious Person, Mr. Graham, my In-
strument was fixed up August 19, 1727. As I had no convenient

THE PRINCIPLE OF RELATIVITY. 93

Place where I could made use of so long a Telescope as Mr. Moly-
neux's, I contented myself with one of but little more than half the
Length of his (viz. of about 12^ Feet, his being 24|) judging from
the Experience which I had already had, that this Radius would be
long enough to adjust the Instrument to a sufficient Degree of
Exactness, and I have no reason since to change my Opinion : for
from all the Trials I have yet made. I am very well satisfied, that
when it is carefully rectified, its Situation may be securely depended
upon to half a Second. As the Place where my Instrument was to
be hung, in some Measure determined its Radius, so did it also the
Length of the Arch, or Limb, on which the Divisions were made to
adjust it: For the Arch could not conveniently be extended farther,
than to reach to about 6^° on each Side my Zenith. This indeed
was sufficient, since it gave me an Opportunity of making Choice
of several Stars, very different both in Magnitude and Situation ;
there being more than two hundred inserted in the British Catalogue,
that may be observed with it. I needed not to have extended the
Limb so far, but that I was willing to take in Capella, the only star
of the first Magnitude that comes so near my Zenith.

My instrument being fixed, I immediately began to observe
such Stars as I judged most proper to give me light into the Cause
of the Motion already mentioned. There was Variety enough of
small ones ; and not less than twelve, that I could observe through
all the Seasons of the Year ; they being bright enough to be seen
in the Day-time, when nearest the Sun. I had not been long ob-
serving, before I perceived, that the Notion we had before enter-
tained of the Stars being farthest North and South, when the Sun
was about the Equinoxes, was only true of those that were near the
solstitial Colure: And after I had continued my Observations a few
Months, I discovered, what I then apprehended to be a general
Law, observed by all the Stars, viz. That each of them became sta-
tionary, or was farthest North or South, when they passed over my
Zenith at six of the Clock, either in the Morning or Evening. I
perceived likewise, that whatever Situation the Stars were in with
respect to the cardinal Points of the Ecliptick, the apparent motion
of every one tended the same Way, when they passed my instrument
about the same Hour of the Day or Night ; for they all moved
Southward, while they passed in the Day, and Northward in the
Night ; so that each was farthest North, when it came about Six
of the Clock in the Evening, and farther South, when it came about
Six in the Morning.

94 THE PRINCIPLE OF RELATIVITY.

Though I have since discovered, that the Maxima in most of
these Stars do not happen exactly when they come to my Instrument
at those Hours, yet not being able at that time to prove the con-
trary, and supposing that they did, I endeavoured to find out what
Proportion the greatest Alterations of Declination in different Stars
bore to each other ; it being very evident, that they did not all change
their Declination equally. I have before taken notice, that it ap-
peared from Mr. Molyneux's Observations, that v Draconis altered
its Declination about twice as much as the fore-mentioned small
Star almost opposite to it ; but examining the matter more particu-
larly, I found that the greatest Alteration of Declination in these
Stars, was at the Sine of the Latitude of each respectively. This
made me suspect that there might be the like Proportion between
the Maxima of other Stars ; but finding, that the observations of
some of them would not perfectly correspond with such an Hypoth-
esis, and not knowing, whether the small Difference I met with,
might not be owing to the Uncertainty and Error of the Observa-
tions, I deferred the farther examination into the Truth of this
Hypothesis, till I should be furnished with a Series of Observations
made in all Parts of the Year ; which might enable me, not only to
determine what Errors the Observations are liable to, or how far
they may safely be depended upon ; but also to judge, whether there
b.ad been any sensible Change in the Parts of the Instrument itself.

Upon these Considerations, I laid aside all Thoughts at that
Time about the Cause of the fore-mentioned Phaenomena, hoping
that I should the easier discover it, when I was better provided with
proper Means to determine more precisely what they were.

When the Year was compleated, I began to examine and com-
pare my Observations, and having pretty well satisfied myself as to
the general Laws of the Phaenomena, I then endeavoured to find
out the Cause, of them. I was already convinced, that the apparent
Motion of the Stars, was not owing to a Nutation of the Earth's
Axis. The next Thing that offered itself, was an Alteration in the
Direction of the Plumb-line, with which the Instrument was con-
stantly rectified ; but this upon Trial proved insufiicient. Then I
considered what Refraction might do, but here also nothing satis-
factory occurred. At last I conjectured, that all the Phaenomena
hitherto mentioned, proceeded from the progressive Motion of Light
and the Earth's annual Motion in its Orbit. For I perceived, that,
if Light was propagated in Time, the apparent Place of a fixt Ob-
ject would not be the same when the Eye is at Rest, as when it is

THE PRINCIPLE OF RELATIVITY.

95

moving in any other Direction, than that of the Line passing through
the Eye and Object ; and that, when the Eye is moving in different
Directions, the apparent Place of the Object would be different.

I considered this Matter in the following Manner. I imagined
CA to be a Ray of Light, falling perpendicularly upon the Line BD ;
then if the Eye is at rest at A, the Object must appear in the Direc-
tion AC, whether Light be propagated in Time or in an Instant.
But if the Eye is moving from B towards A, and Light is propa-
gated in Time, with a Velocity that is to the Velocity of the Eye,
as CA to BA ; then Light moving from C to A, whilst the Eye
moves from B to A, that Particle of it, by which the Object will be
discerned, when the Eye in its Motion comes to A, is at C when
the Eye is at B. Joining the Points B, C, I supposed the Line CB,

to be a Tube (inclined to the Line BD in the Angle DBC) of such
a Diameter, as to admit of but one Particle of Light ; then it was
easy to conceive, that the Particle of Light at C (by which the ob-
ject must be seen when the Eye, as it moves along, arrives at A)
would pass through the Tube BC, if it is inclined to BD in the Angle
DBC, and accompanies the Eye in its Motion from B to A ; and that
it could not come to the Eye, placed behind such a Tube, if it had
any other Inclination to the Line BD. If instead of supposing CB
so small a Tube, we imagine it to be the Axis of a larger ; then for
the same Reason, the Particle of Light at C, could not pass through
that Axis, unless it is inclined to BD, in the Angle CBD. In like
manner, if the Eye moved the contrary way, from D towards A,
with the same Velocitv ; then the Tube must be inclined in the Ansfle

g6 THE PRINCIPLE OF RELATIVITY.

BDC. Although therefore the true or real Place of an Object is
perpendicular to the Line in which the Eye is moving, yet the vis-
ible Place w^ill not be so, since that, no doubt, must be in the Direc-
tion of the Tube ; but the Difference between the true and apparent
Place will be (cceteris paribus) greater or less, according to the
different Proportion between the Velocity of Light and that of the
Eye. So that if we could suppose that Light was propagated in
an instant, then there would be no Difference between the real and
visible Place of an Object, although the Eye were in Motion, for
in that case, AC being infinite with Respect to AB, the Angle x\CB
(the Difference between the true and visible Place) vanishes. But
if Light be propagated in Time (which I presume will readily be
allowed by most of the Philosophers of this Age) then it is evident
from the foregoing Considerations, that there will be always a
Difference between the real and visible Place of an Object, unless )
the Eye is moving either directly towards or from the Object. And
in all Cases, the Sine of the Difference between the real and visible
Place of the Object, will be to the Sine of the visible Inclination
of the Object to the Line in which the Eye is moving, as the Veloc-
ity of the Eye to the Velocity of Light.

If Light moved but 1000 times faster than the Eye, and an Ob-
ject (supposed to be at an infinite Distance) was really placed perpen-
dicularly over the Plain in which the Eye is moving, it follows from
what hath been already said, that the apparent Place of such an
Object will be always inclined to that Plain, in an Angle of 89° 56'^ ;
so that it will constantly appear 3'^ from its true Place, and seem
so much less inclined to the Plain, that way towards which the Eye
tends. That is, if AC is to AB (or AD) as 1000 to one, the Angle
ABC will be 89° 56'i, and ACB = 3'i, and BCD = 2ACB = 7'.
So that according to this Supposition, the visible or apparent Place
of the Object will be altered 7', if the Direction of the Eye's Motion
is at one time contrary to what it is at another.

If the Earth revolve round the Sun annually, and the Velocity
of Light were to the Velocity of the Earth's Motion in its Orbit
(which I will at present suppose to be a Circle) as 1000 to one ; then
tis easy to conceive, that a Star really placed in the very Pole of the
Ecliptick, would, to an Eye carried along with the Earth, seem to
change its Place continually, and (neglecting the small Difference
on the Account of the Earth's diurnal Revolution on its Axis) would
seem to describe a Circle round that Pole, every Way distant there-
from 3'|. So that its Longitude would be varied through all the

THE PRINCIPLE OF RELATIVITY. 97

Points of the Ecliptick every Year ; but its Latitude would always
remain the same. Its right Ascension would also change, and its
Declination, according to the different Situation of the Sun in respect
to the equinoctial Points ; and its apparent Distance from the North
Pole of the Equator would be 7' less at the Autumnal, than at the
vernal Equinox.

The greatest Alteration of the Place of a Star in the Pole of
the Ecliptick (or which in Effect amounts to the same, the Propor-
tion between the Velocity of Light and the Earth's Motion in its
Orbit) being known ; it will not be difficult to find what would be
the Difference upon this Account, the Difference between the true
and apparent Place of any other Star at any time ; and on the con-
trary, the Difference between the true and apparent Place being
given ; the Proportion between the Velocity of Light and the Earth's
Motion in its Orbit may be found.

As I only observed the apparent Difference of Declination of
the Stars, I shall not now take any farther Notice in what manner
such a Cause as I have here supposed would occasion an Alteration
in their apparent Places in other Respects ; but, supposing the Earth
to move equally in a Circle, it may be gathered from what hath been
already said, that a Star which is neither in the Pole nor Plain of
the Ecliptick, will seem to describe about its true Place a Figure,
insensibly different from an Ellipse, whose Transverse Axis is at
Right-angle to the Circle of Longitude passing through the Star's
true Place, and equal to the Diameter of the little Circle described
by a Star (as was before supposed) in the Pole of the Ecliptick;
and whose Conjugate Axis is to its Transverse Axis, as the Sine
of the Star's latitude to the Radius. And allowing that a Star by its
apparent Motion does exactly describe such an Ellipse, it will be
found, that if A be the Angle of Position (or the Angle at the Star
made by two great Circles drawn from it, thro' the Poles of the
Ecliptick and Equator) and B be another Angle, whose Tangent is
to the Tangent of A as Radius to the Sine of the Latitude of the
Star ; then B will be equal to the Difference of Longitude between
the Sun and the Star, when the true and apparent Declination of
the Star are the same. And if the Sun's Longitude in the Ecliptick
be reckoned from that Point, wherein it is when this happens ; then
the Difference between the true and apparent Declination of the
Star (on account of the Cause I am now considering) will be always,
as the Sine of the Sun's Longitude from thence. It will likewise
be found, that the greatest Difference of Declination that can be

98 THE PRINCIPLE OF RELATIVITY.

between the true and apparent Place of the Star, will be to the Semi-
Transverse Axis of the Ellipse (or to the Semi-diameter of the
little Circle described by a Star in the Pole of the Ecliptick) as the
Sine of A to the Sine of B.

If the Star hath North Latitude, the Time, when its true and
apparent Declination are the same, is before the Sun comes in Con-
junction with or Opposition to it, if its Longitude be in the first or
last Quadrant (viz. in the ascending Semi-circle) of the Ecliptick;
and after them, if in the descending Semi-circle ; and it will appear
nearest to the North Pole of the Equator, at the Time of that
Maximum (or when the greatest Diflference between the true and
apparent Declination happens) which precedes the Sun's Conjunc-
tion with the Star.

These Particulars being sufficient for my present Purpose, I
shall not detain you with the Recital of any more, or with any farther
Explication of these. It may be time enough to enlarge more upon
this Head, when I give a Description of the Instruments &c. if that
be judged necessary to be done; and when I shall find, what I now
advance, to be allowed of (as I flatter myself it will) as something
more than a bare Hypothesis. I have purposely omitted some mat-
ters of no great Moment, and considerd the Earth as moving in a
Circle, and not an Ellipse, to avoid too perplexed a Calculus, which
after all the Trouble of it would not sensibly differ from that which
I make use of, especially in those Consequences which I shall at
present draw from the foregoing Hypothesis.

This being premised, I shall not proceed to determine from the
observations, what the real Proportion is between the Velocity of
Light and the Velocity of the Earth's annual Motion in its Orbit;
upon Supposition that the Phaenomena before mentioned do depend
upon the Causes I have here assigned. But I must first let you know,
that in all the Observations hereafter mentioned, I have made an
Allowance for the Change of the Star's Declination on Account of
the Precession of the Equinox, upon Supposition that the Alteration
from this Cause is proportional to the Time, and regular through all
the Parts of the Year. I have deduced the real annual Alteration
of Declination of each Star from the Observations themselves ; and
I the rather choose to depend upon them in this Article, because all
which I have yet made, concur to prove, that the Stars near the
Equinoctial Colure, change their Declination at this time 1"^ or 2"
in a Year more than they would do if the Precession was only 50",
as is now generally supposed. I have likewise met with some small

THE PRINCIPLE OF RELATIVITY. 99

V^arieties in the Declination of other Stars in different Years, which
do not seem to proceed from the same Cause, particularly in those
that are near the solstitial Colure, which on the contrary have altered
their Declination less than they ought, if the Precession was 50".
But whether these small Alterations proceed from a regular Cause,
or are occasioned by any Change in the Materials &c. of my Instru-
ment, I am not yet able fully to determine. However, I thought it
might not be amiss just to mention to you how I have endeavoured
to allow for them, though the Result would have been nearly the
same, if I had not considered them at all. What that is, I will shew,
first from the Observations of v Draconis, which was found to be
39" more Southerly in the Beginning of March, than in September.

From what hath been premised, it will appear that the greatest
Alteration of the apparent Declination of v Draconis, on account of
the successive Propagation of Light, would be to the Diameter of
the little Circle which a Star (as was before remarked) would seem
to describe about the Pole of the Ecliptick as 39" to 40", 4. The
half of this is the Angle ACB (as represented in the Fig.) This
therefore being 20", 2, AC will be to AB, that is, the Velocity of
Light to the Velocity of the Eye (which in this Case may be sup-
posed the same as the Velocity of the Earth's annual Motion in its
Orbit) as 10210 to One, from whence it would follow, that Light
moves, or is propagated as far as from the Sun to the Earth in 8' and
12".

It is well known, that Mr. Romer, who first attempted to
account for an apparent Inequality in the Times of the Eclipses of
Jupiter's Satellites, by the Hypothesis of the progressive Motion
of Light, supposed that it spent about 11 Minutes of Time in its
Passage from the Sun to us : but it hath since been concluded by
others from the like Eclipses, that it is propagated as far in about
7 Minutes. The Velocity of Light therefore deduced from the fore-
going Hypothesis, is as it were a Mean betwixt what had at different
times been determined from the Eclipses of Jupiter's Satellites.

These different Methods of finding the Velocity of Lig'ht
thus agreeing in the Result, we may reasonably conclude, not only
that these Phaenomena are owing to the Causes to which they have
been ascribed; but also, that Light is propagated (in the same
Medium) with the same Velocity after it hath been reflected as
before ; for this will be the Consequence, if we allow that the Light
of the Sun is propagated with the same Velocity, before it is re-
flected, as the Light of the fixt Stars. And I imagine this will

TOO THE PRINCIPLE OF RELATIVITY.

scarce be questioned, if it can be made appear that the Velocity
of the Light of all the Hxt Stars is equal, and that their Light moves
or is propagated through equal Spaces in equal Times, at all Dis-
tances from them: both which points (as I apprehend) are suffi-
ciently proved from the apparent alteration of the Declination of
Stars of dififerent Lustre ; for that is not sensibly different in such
Stars as seem near together, though they appear of very different
Magnitudes. And whatever their Situations are (if I proceed ac-
cording to the foregoing Hypothesis) I find the same Velocity of
Light from my Observations of small Stars of the fifth or sixth, as
from those of the second and third Magnitude, which in all Proba-
bility are placed at very different Distances from us. The small
Star, for Example, before spoken of, that is almost opposite to j»
Draconis (being the 35th Camelopard. Hevelii in Mr. Flamsteed's
Catalogue) was 19" more Northerly about the Beginning of March
than in September. Whence I conclude, according to my Hypothesis,
that the Diameter of the little Circle described by a Star in the
Pole of the Ecliptick would be 40", 2.

The last Star of the great Bear's tail of the 2d Magnitude
(marked -q by Bayer) was 36" more Southerly about the Middle of
January than in July. Hence the Maximum, or greatest Altera-
tion of Declination of a Star in the Pole of the Ecliptick would
be 40", 4, exactly the same as was before found from the Observa-
tions of V Draconis.

The Star of the 5th magnitude in the Head of Perseus marked
T by Bayer, was 25" more Northerly about the End of December
than on the 29th of July following. Hence the Maximum would
be 41". This Star is not bright enough to be seen as it passes over
my Zenith about the End of June, when it should be according to
the Hypothesis farthest South. But because I can more certainly
depend upon the greatest Alteration of Declination of those Stars,
which I have frequently observed about the Times when they be-
come stationary, with respect to the Motion I am now considering;
I will set down a few more Instances of such, from which you may
be able to judge how near it may be possible from these Observa-
tions, to determine with what Velocity Light is propagated.

a Persei Bayero was 23" more Northerly at the beginning of
January than in July. Hence the Maximum would be 40", 2. a
Cassiopece was 34" more Northerly about the End of December than
in June. Hence the Maximum would be 40", 8. ft Draconis was 39"
more Northerly in the beginning of September than in March ;

THE PRINCIPLE OF RELATIVITY. lOI

hence the Maximum would be 40", 2. Capella Vv^as about 16" more
Southerly in August than in Feb.; hence the Maximum would be
about 40". But this Star being farther from my Zenith than those
I have before made use of, I cannot so well depend upon my Ob-
servations of it, as of the others ; because I meet with some small
Alterations of its Declination that do not seem to proceed from the
Cause I am now considering.

I have compared the Observations of several other Stars, and
they all conspire to prove that the Maximum is about 40" or 41".
I will therefore suppose that it is 40"^ or (which amounts to the
same) that Light moves, or is propagated as far as from the Sun
to us in 8' 13". The near Agreement which I met with among
my Observations induces me to think, that the Maximum (as I have
here fixed it) cannot diflFer so much as a Second from the Truth,
and therefore it is probable that the Time which Light spends in
passing from the Sun to us, may be determined by these Obser-
vations within 5" or 10" ; which is such a degree of exactness as
we can never hope to attain from the Eclipses of Jupiter's Satel-
lites.

Having thus found the Maximum, or what the greatest Alter-
nation of Declination would be in a Star placed in the Pole of the
Ecliptick, I will now deduce from it (according to the foregoing
Hypothesis) the Alteration of Declination in one or two Stars, at
such times as they were actually observed, in order to see how the
Hypothesis will correspond with the Phmiomena through all the
Parts of the Year.

It would be too tedious to set down the whole Series of my
Observations ; I will therefore make Choice only of such as are
most proper for my present Purpose, and will begin with those of
V Draconis.

This Star appeared farthest North about September 7th, 1727,
as it ought to have done according to my Hypothesis. The follow-
ing Table shews how much more Southerly the star was found to be
by Observation in several Parts of the Year, and how much more
Southerly it ought to be according to the Hypothesis.

Hence it appears, that the Hypothesis corresponds with the Ob-
servations of this Star through all Parts of the Year ; for the small
Differences between them seem to arise from the Uncertainty of
the Observations, which is occasioned (as I imagine) chiefly by
the tremulous or undulating Motion of the Air, and of the Vapours
in it ; which causes the Stars sometimes to dance to and fro, so

102

THE PRINCIPLE OF RELATIVITY.

b

d* <»

th

(I. to

o z

o J2

° Z

o K

W 2 o

W 15 S

w IS 2

« ^ S

^ 2 %

gig

^2 H

g 2 g

u H :?

S H O

M H 5

u H O

iffer:

CLINA
iBSERA

iffer:

CLINA
E HYP

iffer:

CLINA
E HYP

0 w o

0 S W

Q W O

0 S W

" "" s

« 0 H

" ° s

« 0 H

1727 D.

K «
H

g S

1728 D.

B «

g S

Oct. 20

4i

4i

Mar. 24

37

38

Nov. 17

Hi

12

April 6

36

36i

Dec. 6

17i

18i

May 6

28i

29i

Dec. 28

25

26

June 5

18i

20

1728

June 15

17i

17

Jan. 24

34

34

July 3

Hi

111

Feb. 10

38

37

Aug. 2

4

4

Mar. 7

39

39

Sept. 6

0

0

much that it is difficult to judge when they are exactly on the
Middle of the Wire that is fixed in the common Focus of the
Glasses of the Telescope.

I must confess to you, that the Agreement of the Observations
with each other, as well as with the Hypothesis, is much greater
than I expected to find, before I had compared them ; and it may
possibly be thought to be too great, by those who have been used
to Astronomical Observations, and know how difficult it is to make
such as are in all respects exact. But if it would be any Satisfaction
to such Persons (till I have an Opportunity of describing my In-
strument and the manner of using it) I could assure them, that in
above 70 Observations which I made of this Star in a Year, there
is but one (and that is noted as very dubious on account of Clouds)
which differs from the foregoing Hypothesis more than 2", and this
does not differ 3".

This therefore being the Fact, I cannot but think it very prob-
able, that the Phcenomena proceed from the Cause I have assigned,
since the foregoing Observations make it sufficiently evident, that
the Effect of the real Cause, whatever it is, varies in this Star, in
the same Proportion that it ought according to the Hypothesis.

But least v Draconis may be thought not so proper to shew the
proportion, in which the apparent alteration of Declination is in-
creased or diminished, as those Stars which lie near the Equinoctial
Colure: I will give you also the Comparison between the Hypoth-

THE PRINCIPLE OF RELATIVITY.

103

esis and the Observations of r) UrscB Majoris, that which was far-
thest South about the 17th Day of January 1728, agreable to the
Hypothesis. The following Table shews how much more Northerly
it was found by Observation in several Parts of the Year, and also
what the Difference should have been according to the Hypothesis.

(14

t^ CO

(i<

to so

0 z

0 s

0 z

0 55

g g 2
a 2 5

« 25 S

g2g

NCE
ION
ITIO

w z S
^ 2g

S ^ >

S^2

S^>

§52

IFFEl
CLIN
iBSEI

W J5 ><

£ 3 W
Sua

IFFEl
CLIN
BSEE

w ^ >:

£5S

Q W 0

Q w S

Q W 0

Q W S

« ° >

« 0 S

" ° >

W « H

1727 d.

H «

1728 d.

Sept. 14

29i

281

April 16

18i

18

Sept. 24

24i

25i

May 5

24i

23i

Oct. 16

19i

19i

June 5

32

31i

Nov. 11

Hi

lOi

June 25

35

34i

Dec. 14

4

3

July 17

36

36

1728

Aug. 2

35

35i

Feb. 17

2

3

Sept. 20

26i

26i

Mar. 21

Hi

lOi

I find upon Examination, that the Hypothesis agrees altogether
as exactly with the Observations of this Star, as the former; for in
about 50 that were made of it in a Year, I do not meet with a
Difference of so much as 2", except in one, which is mark'd as doubt-
ful on Account of the Undulation of the Air &c. And this does not
differ 3" from the Hypothesis.

The agreement between the Hypothesis and the Observations
of this Star is the more to be reguarded, since it proves that the
Alteration of Declination, on account of the Precession of the Equi-
nox, is (as I before supposed) regular thro' all Parts of the Years;
so far at least, as not to occasion a Difference great enough to be
discovered with this Instrument. It likewise proves the other part
of my former Supposition, viz. that the annual Alteration of Decli-
nation in Stars near the Equinoctial Colure, is at this Time greater
than a Precession of 50" would occasion : for this Star was 20" more
Southerly in September 1728, than in September 1727, that is, about
2" more than it would have been, if the Precession was but 50".
But I may hereafter, perhaps, be better able to determine this Point,

I04 THE PRINCIPLE OF RELATIVITY.

from my Observations of those Stars that He near the Equinoctial
Colure, at about the same Distance from the North Pole of the
Equator, and nearly opposite in right Ascension.

I think it needless to give you the Comparison between the
Hypothesis and the Observations of any more Stars ; since the Agree-
ment in the foregoing is a kind of Demonstration (whether it be
allowed that I have discovered the real Cause of the PhcBnomena or
not;) that the Hypothesis gives at least the true Law of the Varia-
tion of Declination in different Stars, with Respect to their differ-
ent Situations and Aspects with the Sun. And if this is the Case,
it must be granted, that the Parallax of the fixt Stars is much
smaller, than hath been hitherto supposed by those who have pre-
tended to deduce it from their Observations. I believe, that I may
venture to say, that in either of the two Stars, last mentioned, it
does not amount to 2". I am of Opinion, that if it were 1", I should
have perceived it, in the great number of Observations that I made
especially of v Draconis; which agreeing with the Hypothesis (with-
out allowing anything for Parallax) nearly as well when the Sun
was in Conjunction with, as in Opposition to, this Star, it seems
very probable that the Parallax of it is not so great as one single
Second ; and Consequently that it is above 400000 times farther from
us than the Sun.

There appearing therefore after all, no sensible Parallax in the
fixt Stars, the Anti-Copernicans have still room on that Account,
to object against the Motion of the Earth; and they may have (if
they please) a much greater objection against the Hypothesis, by
which I have endeavoured to solve the fore-mentioned Phcenomena ;
by denying the progressive Motion of Light, as well as that of the
Earth.

But as I do not apprehend, that either of these Postulates will
be denied me by the Generality of the Astronomers and Philosophers
of the present Age; so I shall not doubt of obtaining their Assent
to the Consequences which I have deduced from them; if they are
such as have the Approbation of so great a Judge of them as Your-
self. I am

Sir, Your most Obedient
Humble Servant

J. Bradley.
POSTSCRIPT.

As to the Observations of Dr. Hook, I must own to you, that
before Mr. Molyneux's Instrument was erected, I had no small

THE PRINCIPLE OF RELATIVITY. IO5

opinion of their Correctness ; the Length of his Telescope and the
Care he pretends to have taken in making them exact, having been
strong Inducements with me to think them so. And Since I have
been convinced both from Mr. Molyneux's Observations and my
own, that the Doctor's are really very far from being either exact
or agreeable to the Phcenomena; I am greatly at a loss how to ac-
count for it. I cannot well conceive that an Instrument of the
Length of 36 Feet, constructed in the Manner he describes his,
could have been liable to an Error of near 30" (which was doubtless
the Case) if rectified with so much Care as he represents.

The Observations of Mr. Flamsteed of the different Distances
of the Pole Star from the Pole at different Times of the Year,
which were through Mistake looked upon by some as a Proof of the
annual Parallax of it, seem to have been made with much greater
Care than those of Dr. Hook. For though they do not all exactly
correspond with each other, yet from the whole Mr. Flamsteed con-
cluded that the Star was 35" 40" or 45" nearer the Pole in December
than in May or July: and according to my Hypothesis it ought to
appear 40" nearer in December than in June. The Agreement there-
fore of the Observations with the Hypothesis is greater than could
reasonably be expected, considering the Radius of the Instrument,
and the Manner in which it was constructed.

/ .

,\

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