Chase] •^^4: [jan. 5 and Feb. 2, 



tangential oscillations. This is the case with Sun and Jupiter. For if we 

 represe it the mass of Jupiter by 1, and Sun's mass by n, the secular peri- 

 helion distance of tiieir centres, .9391726 X 5.3028 X 214.80 r= (n + 2)r; 



and n = U»4r.87G. Bessel's value is 1047.8t!> (59.) 



The atmospheric relation of Saturn to Jupiter (51) is further shown by 



the eipiality of nebular vires vtvce. For orbital v. v. CC - ; the nebulous 



r 



mass at Jupiter's thermal radius vector,* is 1.4232', and the orbital r. v. at the 



corresponding atmospluric limit is 1.4232-^ -r- 1.4232* = 1.4232^ = 1.8007. 

 whicli is .Viexander's ratio.f The v. v. of constrained rotation varies as the 

 square of the orbital i\ v, or, in the present case, as 3.242G to 1, which 

 would require masses in the ratio of 1 to 3. 2426 to give equality of v. v. ; pro- 

 vided tlie primitive orbits were circular. "We hav^e seen, however, (6), 

 that the infra as eroidal centre is at 1.01688 X Earth's mean distance, and 

 the Jovi-Telliiric connections 1,3) suggest the probability of a similar eccen- 

 tricity in the primitive Jovi-Saturnian belt. (1.4232^x 1.01688)"= 3.3525 ; 

 1047.876 X 3.3525 = 3513.47. Bessel's ratio of Sun to Saturn is 3501.6; 



Le Venier's 3512 (60.) 



Satur.i's position at the nebular centre of planetary inertia would be 

 likely to establish permanent records of equality in still other forms of vis 

 viva. We av^cordingly find that the ratio of Neptune's to Saturn's mass 

 seems to be due to nucleal vis viva (4) when they were both at atmospheric 



(1 \ 3 

 - 1 - ; the I power of 



Neptune's, divided by Saturn's mean distance, = 5.587 ; 5.587 x 3513.- 

 47 = l'.)63 ). Newcomb's ratio of Sun to Neptune, as deduced from the 



perlurhations of Uranus is 19700 i61.) 



Tiie mi.ss ratio of Uranus to Saturn sejms to be due to atmospheric vis 

 viva \vlu;n their nucleal condensation began. For the v. v. of rotation at 



(1 \ 3" 

 — J ; the I power 'of mean distance 



($ ^- h)\9. 6.444 ; 6.444 X 3513.47 = 22641 ; Newcomb's ratio of Sun to 



Uranus is 22600 ± 100 (63.) 



Tiie mass ratio of Saturn to Earth seems to be due to equality of rota'ing 

 vis viva. For the v. v. of rotation in a contracting nucleus varies as 



Cr- 



the square of mean distance (>? ^ ©) is 90.99 ; 90.99 x 3513.47 



= riT^OO. The ratio of Sim to Earth is still a mooted question (63.) 



Th33e theoretical masses are such as to contribute to the stability of tlie 



syste n. by givin^ e(piality betwe<^n vari;)U3 forms of opposing v. v. at 



culmiiiitin j; points of o|)pi)sing disturbance. 



With the Sun expanded to Neptune's mean aphelion and rotating as a 



• Fun 1 1 n3ntal Propositions, III, IV. 

 tProc. s. P. A. xll. 39i. 



