260 



SCIENCE 



[N. S. Vol. LI. No. 1315 



just said, arrived a't certain mathematical laws 

 for a gravitational field, laws wMdhi reduced 

 to Newton's form in most cases where observa- 

 tions are possible, but wbicb led to different 

 conclusions in a few cases, knowledge concern- 

 ing which we might obtain by careful observa- 

 tions. I shall mention a few deductions from 

 Einsitein's formulse. 



1. If a heavy particle is put at the center of 

 a circle, and, if the length of the circumference 

 and the length of the diameter are measured, 

 it will be found that their ratio is not '^ 

 (3.14159). In other words the geometrical 

 properties of space in such a gravitational 

 field are not those discussed by Euclid; the 

 space is, then, non-Euclidean. There is no 

 way by which this deduction can be verified, 

 the difference between the predicted ratio and 

 T is too minute for us to hope to make our 

 measurements with sufficient exactness to de- 

 termine the difference. 



2. All the lines in tlhe solar spectrum should 

 with reference to lines obtained by terrestrial 

 sources be displaced slightly towards longer 

 wave-lengths. The amount of displacement 

 predicted for lines in the blue end of the 

 spectrum is about one hundredth of an Ang- 

 strom unit, a quantity well within experimen- 

 tal limits. Unfortunately, as far as the testing 

 of this prediction is concerned, there are sev- 

 eral physical causes which are also operating 

 to cause displacement of the speotrum-lines ; 

 and so at present a decision can not be rend- 

 ered as to the verificajtion. St. John and other 

 workers at the Mount Wilson Observatory have 

 the question under investigation. 



3. According to Newton's law an isolated 

 planet in its motion around a central sun 

 would describe, period after i)eriod, the same 

 elliptical orbit; whereas Einstein's laws lead to 

 the prediction that the successive orlsits tra- 

 versed would not be idenitically the same. 

 Each revolution would s'tart 'the planet off on 

 an orbit very approximately elliptical, but 

 with the major axis of the ellipse rotated 

 slightly in the plane of the oAit. When calcu- 

 lations were made for the various planets in 

 our solar system, it was found that the only 

 one which was of interest from the standpoint 



of verification of Einstein's formulse was Mer- 

 cury. It has been known for a long time that 

 there was actually such a change as just de- 

 scribed in the orbit of Mercury, amounting to 

 574" of arc x>er century; and it has been shown 

 that of this a rotation of 533" was due to the 

 direct action of other planets, thus leaving an 

 unexplained rotation of 42" per century. Ein- 

 stein's formulse predicted a rotation of 43", a 

 striking agreement. 



4. In accordance with Einstein's formulse a 

 ray of light passing close to a heavy piece of 

 maitter, the sun, for instance, should experi- 

 enlce a sensible deflection in towards the sun. 

 This might be expected from " general " con- 

 siderations. A light ray is, of course, an il- 

 lustration of energy in motion; energy and 

 mass are generally considered to be identical 

 in the sense that an amount of enei-gy E has 

 the mass E/c^ where c is the velocity of light ; 

 and consequently a ray of light might fall 

 within the province of gravitation and the 

 amount of deflection to be expected could be 

 calculated by the ordinary formula for gravi- 

 tation. Au'Other point of view is to consider 

 again the observer inside the compartment 

 falling with the acceleration of the gravita- 

 tional field. To him the path of a projectile 

 and a ray of light would both appear straight ; 

 so that, if the projectile had a velocity equal 

 to that of light, it and the light wave would 

 travel side by side. To an observer outside the 

 compartment, e. g., to one on the earth, both 

 would then appear to have the same deflection 

 owing to the sun. But how much would the 

 path of the projectile be bent? What would 

 be the shape of its parabola ? One might apply 

 Newton's law; but, according to Einstein's 

 formulse, Newton's law should be used only for 

 small velocities. In the case of a ray passing 

 close to the sun it was decided that according 

 to Einstein's formula there should be a de- 

 flection of 1".75 whereas Newton's law of 

 gravitation predicted half this amount. Care- 

 ful plans were made by various astronomers, 

 to investigate this question at the solar eclipse 

 last May, and tlie result announced by Dyson, 

 Eddington and Crommelin, the leaders of as- 

 tronomy in England, was that there was a de- 



