THEORY OF RELATIVITY 
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theory. Only three of these tests have so far been suggested by 
Einstein as possible; the fact being that Newton’s law is a very 
close approximation to Einstein’s law, the latter being capable 
of degeneration into the former. 
Tests. 
First: To account for the inconsistence of the observed ad- 
vance of the perihelion of Mercury with the theoretical value 
based on Newton’s law of gravitation. 
That theoretical astronomers did not know what to do next 
concerning the discrepancy after trying various schemes follows 
from the words of Simon Newcomb in his ‘Astronomical Con- 
stants’ : -Tn case where our ignorance is complete all hypotheses 
which do not violate known facts are admissible.” But there 
was no hypothesis that could make goood. 
According to observation the line of apsides of the orbit of 
Mercury revolves in the direction of motion of the planet about 
the Sun through an angle of 574 seconds of arc in a century. The 
angle calculated from the perturbations of the planets accounted 
only for about 531" leaving a remainder of 43" that could not be 
accounted for. 
Einstein’s calculations based on his theory of gravitation 
showed that the Sun’s gravitational field at Mercury produced 
the additional 43" per century required. The effect of the Sun’s 
field on the other planets according to the same law is quite small, 
on account of their distance from the Sun, amounting to about 
8" in the case of Venus, about 4" in the case of the Earth and 
still smaller amounts in case of the remaining planets. The 
striking feature of the calculation is the absence of any adjust- 
able constants in the formula used. The only constants appear- 
ing are the period of the planet, T, the semi-major axis of the 
orbit, a, and the eccentricity, e. 
Second : The curvature of rays of light coming from fixed stars 
and passing near the Sun, due to the gravitational field of the 
latter. 
In the first place it follows from the general theory that light 
travels slower in a gravitational field than in a region devoid of 
such a field, moreover its path is not a straight line the equation 
of the geodesic being : 
8 j ds±o 
or the geodesic in a field of force is curved ; the amount of curva- 
