The bending of a ray of light thus described is much too light on the
surface of the earth to be observed. But the attraction of gravitation
exercised by the sun on its surface is, because of its great mass, more
than twenty-seven times stronger, and a ray of light that goes close by
the superficies of the sun must surely be noticeably bent. The rays of
a star that are seen at a short distance from the edge of the sun will,
going along the sun, deviate so much from the original direction that
they strike the eye of an observer as if they came in a straight line
from a point somewhat further removed than the real position of the
star from the sun. It is at that point that we think we see the star;
so here is a seeming displacement from the sun, which increases in the
measure in which the star is observed closer to the sun. The Einstein
theory teaches that the displacement is in inverse proportion to the
apparent distance of the star from the centre of the sun, and that for
a star just on its edge it will amount to 1'.75 (1.75 seconds). This is
approximately the thousandth part of the apparent diameter of the sun.
Naturally, the phenomenon can only be observed when there is a total
eclipse of the sun; then one can take photographs of neighboring stars
and through comparing the plate with a picture of the same part of
the heavens taken at a time when the sun was far removed from that
point the sought-for movement to one side may become apparent.
Thus to put the Einstein theory to the test was the principal aim of
the English expeditions sent out to observe the eclipse of May 29,
one to Prince's Island, off the coast of Guinea, and the other to
Sobral, Brazil. The first-named expedition's observers were Eddington
and Cottingham, those of the second, Crommelin and Davidson. The
conditions were especially favorable, for a very large number of
bright stars were shown on the photographic plate; the observers at
Sobral being particularly lucky in having good weather.
The total eclipse lasted five minutes, during four of which it was
perfectly clear, so that good photographs could be taken. In the
report issued regarding the results the following figures, which are
the average of the measurements made from the seven plates, are given
for the displacements of seven stars:
1''.02, 0''.92, 0''.84, 0''.58, 0''.54, 0''.36, 0''.24, whereas,
according to the theory, the displacements should have amounted to:
0''.88, 0''.80, 0''.75, 0''.40, 0''.52, 0''.33, 0''.20.
If we consider that, according to the theory the displacements must
be in inverse ratio to the distance from the centre of the sun, then
we may deduce from each observed displacement how great the sideways
movement for a star at the edge of the sun should have been. As the
most probable result, therefore, the number 1''.98 was found from
all the observations together. As the last of the displacements given
above--i.e., 0''.24 is about one-eighth of this, we may say that the
influence of the attraction of the sun upon light made itself felt
upon the ray at a distance eight times removed from its centre.
The displacements calculated according to the theory are, just because
of the way in which they are calculated, in inverse proportion to the
distance to the centre. Now that the observed deviations also accord
with the same rule, it follows that they are surely proportionate
with the calculated displacements. The proportion of the first and
the last observed sidewise movements is 4.2, and that of the two most
extreme of the calculated numbers is 4.4.
This result is of importance, because thereby the theory is excluded,
or at least made extremely improbable, that the phenomenon of
refraction is to be ascribed to, a ring of vapor surrounding the
sun for a great distance. Indeed, such a refraction should cause a
deviation in the observed direction, and, in order to produce the
displacement of one of the stars under observation itself a slight
proximity of the vapor ring should be sufficient, but we have every
reason to expect that if it were merely a question of a mass of
gas around the sun the diminishing effect accompanying a removal
from the sun should manifest itself much faster than is really the
case. We cannot speak with perfect certainty here, as all the factors
that might be of influence upon the distribution of density in a sun
atmosphere are not well enough known, but we can surely demonstrate
that in case one of the gasses with which we are acquainted were held
in equilibrium solely by the influence of attraction of the sun the
phenomenon should become much less as soon as we got somewhat further
from the edge of the sun. If the displacement of the first star, which
amounts to 1.02-seconds were to be ascribed to such a mass of gas, then
the displacement of the second must already be entirely inappreciable.
So far as the absolute extent of the displacements is concerned, it
was found somewhat too great, as has been shown by the figures given
above; it also appears from the final result to be 1.98 for the edge
of the sun--i.e., 13 per cent, greater than the theoretical value
of 1.75. It indeed seems that the discrepancies may be ascribed to
faults in observations, which supposition is supported by the fact
that the observations at Prince's Island, which, it is true, did not
turn out quite as well as those mentioned above, gave the result,
of 1.64, somewhat lower than Einstein's figure.
(The observations made with a second instrument at Sobral gave a
result of 0.93, but the observers are of the opinion that because of
the shifting of the mirror which reflected the rays no value is to
be attached to it.)