EINSTEIN'S LAW OF GRAVITATION 243 



we might obtain by careful observations. I shall mention 

 a few deductions from Einstein's formulae. 



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 v (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-Euclid- 

 ean. There is no way by which this deduction can be veri- 

 fied, the difference between the predicted ratio and ir is too 

 minute for us to hope to make our measurements with 

 sufficient exactness to determine the difference. % 



2. All the lines in the solar spectrum should with refer- 

 ence to lines obtained by terrestrial sources be displaced 

 slightly towards longer wave-lengths. The amount of dis- 

 placement predicted for lines in the blue end of the spec- 

 trum is about one-hundredth of an Angstrom unit, a 

 quantity well within experimental limits. Unfortunately, 

 as far as the testing of this prediction is concerned, there 

 are several physical causes which are also operating to 

 cause displacement of the spectrum-lines ; and so at pres- 

 ent a decision cannot be rendered as to the verification. 

 St. John and other workers at the Mount Wilson Obser- 

 vatory 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 

 period, the same elliptical orbit; whereas Einstein's laws 

 lead to the prediction that the successive orbits traversed 

 would not be identically the same. Each revolution would 

 start the planet off on an orbit very approximately ellipti- 

 cal, but with the major axis of the ellipse rotated slightly 

 in the plane of the orbit. When calculations were made 

 for the various planets in our solar system, it was found 

 that the only one which was of interest from the stand- 

 point of verification of Einstein's formulae was Mercury. 

 It has been known for a long time that there was actually 

 such a change as just described in the orbit of Mercury, 



