Motion in Stellar Systems, 201 



pagate waves with the velocity gt ; h = height of fall in time t, 

 or of projection with velocity gt, or of alternate fall and rise 

 in perpetual elastic rebound with maximum velocity gt. At 

 Sun's surface, where g is a maximum for our system, and 

 where the collisions of subsiding particles have changed free 

 revolution into constrained rotation, gt = the velocity of light. 

 Therefore, if we designate the velocity of light by v k , and 

 remember that in an expanding or contracting rotating nucleus 



g oc -%, while t varies as r 2 , the modulus velocity of sethereal 



oscillation, of nucleal rotation, and of limiting gravitating 

 acceleration, in the solar system has been, is, and will continue 

 to be v\. Hence we derive the universal equation 



9= 



v K m 

 1 



,2 > 



which holds for all masses and distances, provided m and r are 

 expressed in terms of Sun's mass and semidiameter. 



Laplace (Bowditch's translation, III. vii. § 47 [2128 2 ]) 

 shows that the solar " atmosphere can extend no further than 

 to the orbit of a planet whose periodical revolution is per- 

 formed in the same time as the sun's rotatory motion about 

 its axis." Faye (Comptes Rendus, April 21, 1884, p. 949) 

 traces the indication of this limit to Kant. I designate it 

 therefore by p K , Sun's semidiameter being p and Jj = p K -r-p . 

 It may be deduced from v x as follows: — 



Let t k = time required by a luminous wave to pass from 

 Sun to Earth; v = limiting velocity of planetary revolution 

 at Sun's surface = \/<yoPo> v r = velocity of solar equatorial 

 rotation. Then, if we take Eyren's estimate of the constant 

 of aberration (' The Observatory,' vi. p. 365), 



* x =20"-492 x 31558149 s -r-12936000"=498 s -99; L f =v +v r ; 

 7rL f =^; ttL 3 =^ ; ^=214-45 /9o -5-498-99 = -42977 / o ; 



Vq V r 



v =2?rx 214-45* p -5-31558149«'000625255p ; 



^=687-351 ; L = (687-351^7r) l = 36-301. 



v 



Bode's law, notwithstanding its failure in the case of Nep- 

 tune, may perhaps be a partial expression of a more extensive 

 and more general law. Indeed, within the solar system, 

 planetary or belt-positions are nearly represented by the series 

 4, 7, 10, 16, 28, 52, 100, 196, 292, in which there are two 



