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                        eq. 09: file eq09.gif


which corresponds to the theorem of addition for velocities in one
direction according to the theory of relativity. The question now
arises as to which of these two theorems is the better in accord with
experience. On this point we axe enlightened by a most important
experiment which the brilliant physicist Fizeau performed more than
half a century ago, and which has been repeated since then by some of
the best experimental physicists, so that there can be no doubt about
its result. The experiment is concerned with the following question.
Light travels in a motionless liquid with a particular velocity w. How
quickly does it travel in the direction of the arrow in the tube T
(see the accompanying diagram, Fig. 3) when the liquid above
mentioned is flowing through the tube with a velocity v ?

In accordance with the principle of relativity we shall certainly have
to take for granted that the propagation of light always takes place
with the same velocity w with respect to the liquid, whether the
latter is in motion with reference to other bodies or not. The

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temperature of the table, it is possible quite naturally to maintain
the point of view that the marble slab is a " Euclidean continuum."
This can be done in a satisfactory manner by making a more subtle
stipulation about the measurement or the comparison of lengths.

But if rods of every kind (i.e. of every material) were to behave in
the same way as regards the influence of temperature when they are on
the variably heated marble slab, and if we had no other means of
detecting the effect of temperature than the geometrical behaviour of
our rods in experiments analogous to the one described above, then our
best plan would be to assign the distance one to two points on the
slab, provided that the ends of one of our rods could be made to
coincide with these two points ; for how else should we define the
distance without our proceeding being in the highest measure grossly
arbitrary ? The method of Cartesian coordinates must then be
discarded, and replaced by another which does not assume the validity
of Euclidean geometry for rigid bodies.*  The reader will notice
that the situation depicted here corresponds to the one brought about
by the general postitlate of relativity (Section 23).

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PART III

CONSIDERATIONS ON THE UNIVERSE AS A WHOLE


COSMOLOGICAL DIFFICULTIES OF NEWTON'S THEORY


Part from the difficulty discussed in Section 21, there is a second
fundamental difficulty attending classical celestial mechanics, which,
to the best of my knowledge, was first discussed in detail by the
astronomer Seeliger. If we ponder over the question as to how the
universe, considered as a whole, is to be regarded, the first answer
that suggests itself to us is surely this: As regards space (and time)
the universe is infinite. There are stars everywhere, so that the
density of matter, although very variable in detail, is nevertheless
on the average everywhere the same. In other words: However far we
might travel through space, we should find everywhere an attenuated
swarm of fixed stars of approrimately the same kind and density.

This view is not in harmony with the theory of Newton. The latter