1881.] 



571 



[Chase. 



The ratio of the foregoing note may be expressed as follows : 



Combining these ratios we get 



3 tUx^ = 10 mg. 

 The repetition of the pendulum-ratio, and the simplicity of the har- 

 monic factors make these ratios so suggestive that they seem worthy of 

 further study. 



96. Universal Energy of Light. 



It may be well to state the principal facts which are embodied in notes 

 90-95, in such a way as to show more clearly the simplicity of the rela- 

 tions of the several physical velocities to the velocity of solar radiation. 



1. 





3. — = 



i/iC 



3. — 



m,., t 



X 



V 





«A ® = «o' X 



5. «s = «p (Note 92) 



6- ■y^ = Qo to- 



In these equations, w^ = velocity of equatorial rotation which Sun would 

 have if it were expanded to the locus of a particle which revolves with the cir- 

 cular-orbital velocity «„ ; by the law of conservation of areas v^ varies in- 

 versely as radius, while -y^ varies inversely as the square root of radius ; 

 •»3 = Earth's orbital velocity. 



If we assume M„ = 328470^3, we find 7i„ = 92476500 miles ; i\ — 

 185760 miles ; v. = 18.412 miles; u^ — 2986 ft.; v^= 6916.2 ft. The 

 following table shows the accordance between theoretical and observed 

 values : 



In these comparisons I have made no allowance for the photodynamic 

 projections which have caused orbital eccentricities, as it may be pre- 



* See Note 16. 



t Mean of first four estimates in Note 92. 



PROC. AMER. PHILOS. SOC. XIX. 109. 3t. PRINTED DEC. 31, 1881. 



