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weak, and in which all masses move with respect to the coordinate system with velocities which are small
compared with the velocity of light, we then obtain as a first approximation the Newtonian theory. Thus the
latter theory is obtained here without any particular assumption, whereas Newton had to introduce the
hypothesis that the force of attraction between mutually attracting material points is inversely proportional to
the square of the distance between them. If we increase the accuracy of the calculation, deviations from the
theory of Newton make their appearance, practically all of which must nevertheless escape the test of
observation owing to their smallness.
We must draw attention here to one of these deviations. According to Newton's theory, a planet moves round
the sun in an ellipse, which would permanently maintain its position with respect to the fixed stars, if we
could disregard the motion of the fixed stars themselves and the action of the other planets under
consideration. Thus, if we correct the observed motion of the planets for these two influences, and if Newton's
theory be strictly correct, we ought to obtain for the orbit of the planet an ellipse, which is fixed with reference
PART III 38
to the fixed stars. This deduction, which can be tested with great accuracy, has been confirmed for all the
planets save one, with the precision that is capable of being obtained by the delicacy of observation attainable
at the present time. The sole exception is Mercury, the planet which lies nearest the sun. Since the time of
Leverrier, it has been known that the ellipse corresponding to the orbit of Mercury, after it has been corrected
for the influences mentioned above, is not stationary with respect to the fixed stars, but that it rotates
exceedingly slowly in the plane of the orbit and in the sense of the orbital motion. The value obtained for this
rotary movement of the orbital ellipse was 43 seconds of arc per century, an amount ensured to be correct to
within a few seconds of arc. This effect can be explained by means of classical mechanics only on the
assumption of hypotheses which have little probability, and which were devised solely for this purponse.
On the basis of the general theory of relativity, it is found that the ellipse of every planet round the sun must
necessarily rotate in the manner indicated above ; that for all the planets, with the exception of Mercury, this
rotation is too small to be detected with the delicacy of observation possible at the present time ; but that in
the case of Mercury it must amount to 43 seconds of arc per century, a result which is strictly in agreement
with observation.
Apart from this one, it has hitherto been possible to make only two deductions from the theory which admit of
being tested by observation, to wit, the curvature of light rays by the gravitational field of the sun,*x and a
displacement of the spectral lines of light reaching us from large stars, as compared with the corresponding
lines for light produced in an analogous manner terrestrially (i.e. by the same kind of atom).** These two
deductions from the theory have both been confirmed.
Notes
*) First observed by Eddington and others in 1919. (Cf. Appendix III, pp. 126-129).
**) Established by Adams in 1924. (Cf. p. 132)
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 theory rather requires that the universe
should have a kind of centre in which the density of the stars is a maximum, and that as we proceed outwards
from this centre the group-density of the stars should diminish, until finally, at great distances, it is succeeded
by an infinite region of emptiness. The stellar universe ought to be a finite island in the infinite ocean of
space.*
This conception is in itself not very satisfactory. It is still less satisfactory because it leads to the result that the
light emitted by the stars and also individual stars of the stellar system are perpetually passing out into infinite [ Pobierz całość w formacie PDF ]