1880.] "*1jO IChase. 



Astronomical Approximations. II, III. By Pliny Earle CJiase, LL.D., 

 Professor of Philosophy in Ilaverford College. 



(Read before the American Philosophical Society, Jan. 2, 1880.) 



II. Velocity of Light, and Kirkwooti" s Analogy. 



The cosmical undulations should produce effects at every centre of in- 

 ertial reaction, which would furnish data for approximate determinations 

 of the velocity of light. We have seen that the favorable central position 

 of the Earth, in the belt of greatest condensation, leads to a simple equation 

 for Sun's apparent diameter and, therefore, for finding the quotient of 

 Earth's distance from Sun by Sun's semi-diameter. The accuracy of the 

 result is confirmed by other inferences which may be drawn from the 

 same data. 



Kirkwood's Analogy may be formulated thus : 



( Pn Y X C ) = a constant (1.) 



Let P o denote Sun's semi-diameter ; p v p. 2) etc., the mean vector-radii of 

 the several planets (Mercuryj, Venus.,, etc.); !>■, mass; t, time of rotation 

 synchronous with revolution at Laplace's limit ; V number of rotations in 



^o orbital revolutions synchronous with primitive solar rotation ; v , velocity 



/ 



of light; v n , velocity of revolution (\/gr) at the surface of planet n ; r, 



planetary radius ; the subscript figures being applicable to ,"•> t, '■', v, and 



r. The actions and reactions of light-waves, between the nucleal centre 



(Sun) and the principal centre of primitive condensation (Earth), lead to 



the equation, similar to Kirkwood's : 



(&*($-(%&»<&$ « 



For Earth, p n — p 3 = 2U.~,4p ; » n = v s = 366.256V v n = v 3 = .0012- 



Substituting, and taking the 



(3.) 



If we designate density by *, . mass varies as r 3 ^, or a« the square of 



A Therefore ?» = (% + $) = (^L ■+■ 5074 sec.Y = 3.9175. 

 « d \ffo 9s/ V 214.54^ / 



PROC. AMER. PHILOS. SOC. XVIII. 105. 3c. PRINTED FEB. 28, 1880. 



