1881.] •'5* '[Chase. 



Let us take for ma the value given by Note 17 ; for Wg, Hill's estimate, 

 ^^Q^Q ; for ta , 23" 21"' = 84060 sec. Then 



427840 ^ r^'—\2j^ '-"•'' 



43082 1 /gt\ 



331799 ^ r^ ~ \ 2 /« ^^'■^ 



Introducing Stockwell's value, pg =; .672241, together with (2) and (3), 

 into (1), we have 



(43082 J_\2 _/-A20dO_ 1\^ 



331799 ^ r^) ^ -672241 _ ^43r.84Q X ,..^ 



Hence we find : 



Vp = .9606 r^ . 



Herschel gives .983 ; Newcomb and Holden, .967 ; Newcomb, in John- 

 son's Cyclopaedia, .9602 ; Searle, .96 ; Chambers, .948. 



19. Centres of Density and Nebulosity. 



Earth's nascent relation to the maximum value of Sun's v gr introduces, 

 as we have seen, the factor of gravitating subsidence to a spheroidal nu- 

 cleus, (1 -|- ey. Jupiter's relation to the same value, indicates the forma- 

 tion of a secondary nucleus, at the centre of primitive nebulosity ; for Sun's 

 superficial V gr, 270.68, is accelerated, in Jupiter's nascent velocity, in 

 the ratio which is due to solar condensation to Jupiter's secular perihelion, 

 or rupturing atmospheric locus, which is .9397 of its semi-axis major, the 

 greatest eccentricity being .0603. We have, therefore : 



(■|-)^ = {V~gr)^ H- .9397 == 288.076 miles. 

 Professor Hall's estimate of t is 9" 55" 26^5 = 35726.5 seconds. 



This gives gr^ =:r 388.076 ^ ^ = .016127 m. = 2.654 g^; r^ = (— j 



/ 331799 \ ^ ^ 



= ll047T8"79 ^2.654)r- r^ ^ 10.924 ^ 



Herschel gives 10.977 ; Newcomb, 10.85 ; Searle, 10.93 ; Chambers, 

 10.75. 



20. Central Nebulous Rupture and Subsidence. 



The co-ordinate influence which is shown in the nascent velocities of 

 Earth and Venus (Note 18). has an analogue in Jupiter and Saturn. If we 

 represent Jupiter's atmospheric rupturing locus by p , and Saturn's locus 

 of incipient subsidence, or secular aphelion, by p^, we find : 



Ps -py- -■ (Vg^)o '■ KjJs 

 10.343 : 4.8863 : : 270.68 : 127.81. 

 Prof Hall's estimate of t^ is lO"* 14>» 23^4 = 3683,4 seconds. Dividing 



127.81 miles by J., we get g^ = .0069344 m. — 1.141 g^ ; r\ = 



(Sri -"«)'^- '3 = ">"••■ 



Herschel gives 9.87 ; Newcomb, 8.86 ; Searle, 9,01 ; Chambers, 9.07. 



