1881.1 OOJ [Chase. 



of incipient subsidence, or secular perihelion (.477), bears to Earth's semi- 

 axis major. If sucli is tlie case, it furnishes another instance, lil<;e tlie 

 inner moon of Mars, of the establisliment of a nucleolus, by subsidence 



within a condensing nucleus. If we take Encke's mass, aqrk^-[> ^°<1 

 Herschel's time, t = 24'' 5", the proportion 



•«'-^^(f-X^(f).. 



gives r^ = . 379 i\^. 



Herschel gives .396; Newcomb, .378; Searle, .34; Chambers, .374. 



Mars, the outermost of the dense belt of planets, furnishes clear evidence 

 of the dependence of nascent velocity upon photodynamic influence. If we 

 designate the centripetal photodynamic acceleration at Earth's semi-axis 

 major by (p^, and the action at the mean secular aphelion of Mars by 

 , we find 



Substituting Hall's values for m , (0000^00). ^^^ t . (34'' 37™ 22^7), we 

 get r^ = .546ra 



Herschel gives .517 ; IS'ewcomb, .531 ; Searle, .52 ; Chambers, .621. 



23. Fourier's Theorem. 



In the activities of the luminiferous sether we may reasonably look for 

 abundant evidences of the truth of Fourier's theorem : "Every periodic 

 vibratory motion can always, and always in one manner, be regarded as 

 the sum of a certain number of pendulum vibrations."* In Note 5, I gave 

 an estimate of the mass at the centre of condensation, which was based 

 upon this theorem. The same value may also be obtained as follows : If 

 we consider simple lines of force, in homogeneous nebular condensation, 

 we find the centre of gravity coincident with the linear centre, and the 

 centre of oscillation at two-thirds of tlie distance from a point of suspen- 

 sion, or principal inertia, to a point of oscillation, or inferior inertia. If 

 we consider radial action frona or towards a centre, we know that the 

 oscillations of a conical pendulum are synchronous with those of a linear 

 pendulum of four times tlie length. We know, moreover, that centripetal 

 acceleration varies as the fourth power of the velocity of circular orbital 

 revolution. In the conversion of tendencies to nucleal rotation into ten- 

 dencies to orbital revolution, the oscillating particles are, therefore, sub- 

 jected to central influences which may be represented by (3 X 3 X 4)* = 

 331776, which is the ratio of the mass at the centre of nucleation to the 

 mass at the centre of condensation, as estimated in Note 5. It differs by 

 less than 2V of one per cent, from the value found in Note 16, and by less 

 than yij of one per cent, from the value found in Note 17. 



* Prof. Mayer's statement of the theorem, iu Am. Jour. Sci. [3] , viii, 85. 



