5 1 0 A P P E N D I X C
could be overcome if we recognize the equivalence of mass or inertia and gravity or weight
which has been confirmed by experiment with remarkable accuracy. All that we know of
gravitation is that in certain portions of space bodies fall or move with uniform acceleration.
Thus for an observer in an elevator falling to the earth during a small period of time there
is no gravity. Free bodies will not fall toward his floor since the floor itself is falling just as
fast. But to an observer on the earth such a free body is subject to gravity and moving with
accelerated motion. It is, therefore, always possible, if we know how events would appear
in a system that is free from gravity, to calculate how the same events would appear in a
system in which they are supposed to be under the influence of gravity. This possibility of
passing from one formulation of what has happened to the other proves that both are based
in the recognition of the same laws of nature. There are, however, mathematical difficulties
in working this out. These difficulties are overcome if we abandon Euclidean Geometry and
use instead of the usual system of co-ordinates invented by Descartes, a system of co-
ordinates first used by Gauss and an absolute differential calculus developed by Riemann,
Christofel, Rici and Levi Civita. If, in the light of this general principle of Relativity, we re-
examine the subject of gravitation, we come to a much more general though a more com-
plicated theory than that of Newton. Newton’s theory, however, is seen to be approximately
true according to the new theory, so long as we are restricted to ordinary masses and to
velocities that are small in comparison with that of light.
If the new theory of gravitation be true there are three facts which are then explained and
which can not be explained on the Newtonian theory: first, a certain anomaly in the motion
of he planet Mars [Mercury!]; second, the bending of light rays that pass near the surface
of the Sun, and third, a certain displacement of lines in the spectrum of light coming from
the Sun. The last has not yet been satisfactorily determined. Professor Einstein brought re-
peated applause from his audience by his generous reference to the British scientists who
in spite of the war, fitted out two costly expeditions to test the truth of his theory.
In the concluding portion of his lecture, Professor Einstein dealt briefly with the consid-
erations which lead him to reject the idea of a universe containing a finite amount of matter
in an infinite space. An infinite amount of matter seems to be incompatible with the known
behavior of bodies. We are, therefore, forced to conclude that space is finite.
The general significance of the theory of Relativity he held to consist in the fact that it
shows us the folly of beginning with Euclidean space and then asking how gravity acts in
such a world. Instead, we should begin with the study of the way bodies actually behave
and formulate the nature of space accordingly.
IV. THE ETHER
AND
RADIATION.
The fourth lecture dealt with the ether and the theory of radiation.
The progress of modern electrical theory has enabled us to explain electro-magnetic and
optical phenomena by means of the equations of certain fields which hold in a vacuum and
do not need any material carrier. The definiteness and simplicity of the resulting laws and