RECENT ADVANCES IN SCIENCE 625 



readily be measurable. Given fine weather, this eclipse will 

 offer a splendid chance for testing this result of the theory, 

 and it is to be hoped that one or more expeditions will be sent 

 for the purpose of making these observations. 



Another consequence of the theory is that atomic vibrations 

 are executed more slowly in an intense field of gravitation : 

 therefore the spectral lines of the sun or of any star should 

 be displaced to the red as compared with the positions of the 

 corresponding lines obtained from a terrestrial source. The 

 displacement in the case of the sun is equivalent to the Doppler 

 displacement produced by a radial velocity of 0*63 kms. per 

 sec, and for a star whose mass and density in terms of the 

 sun are M and P the displacement would correspond to a 

 velocity 0*63 M s /a*. Attempts have been made at the 

 Mt. Wilson Solar Observatory to detect this displacement in 

 the case of the sun, but no conclusive results have yet been 

 obtained. This is not surprising in view of the number of 

 other causes which tend to produce displacements, such as 

 pressure and density effects, possible effects due to anomalous 

 dispersion and the mutual influence of spectral lines and to 

 lines originating at different levels in the sun's photosphere, 

 etc. It is not probable that much information will be obtained 

 in this direction either for or against the theory. 



A more important test is derived from the application of 

 the theory to planetary motions. The new law of gravitation 

 is equivalent to Newton's inverse square law to a first approxi- 

 mation, but a second approximation introduces some small 

 additional terms into planetary theory. The only effect which 

 is of any importance and comes within reach of verification by 

 observation is a secular motion of the planetary perihelia : 

 the theory requires that a planetary orbit should rotate in the 

 direction of motion with an angular velocity 24'rr 3 a i /c z T i (i-e i ) 

 radians per revolution of the planet, where a, T, e are the semi- 

 axis, period, and eccentricity of the orbit. This gives in the 

 case of Mercury a rotation of forty-three seconds per century, 

 which is exactly the amount of the discordance observed and 

 which has remained for so long an unsolved puzzle. The new 

 theory has thus obtained a striking success. The following 

 comparison between the observed values of the secular motions 

 of the perihelia (eda>) and of the nodes (id& ) of the inner 

 planets with the values calculated (1) from Newcomb's tables, 



4i 



