Prof. P. E. Chase on Radiation and Rotation. 131 



for these three rotation-periods. For U 5 -r-n •= 101*73 solar 

 radii, and Jupiter's orbital revolution (4332*585 d.)-*-101*73 2 

 = 10-05 h. ; © 4 +-n = 19*66 solar radii, and Earth's orbital re- 

 volution (366*256 d.)+-19*66 2 = 24*205 h. ; 3> 4 -*-n = 5*442 

 Earth's radii, and Earth's rotation x 5*442 2 = 29*619 d. In 

 these accordances we have additional evidence of the equality 

 of action and reaction. 



The normal character of rotation is still further traceable, 

 even after the formation of the subordinate planets in the two 

 principal planetary belts. If we seek the point of incipient 

 condensation which would lead to such rotation-periods as 

 have been generally assigned by astronomers to the different 

 planets, we readily find that Grummere's criterions, Newton's 

 third law, and the law of equal areas lead to the formula 



n \~r) = — , in which n = Gummere's criterion, - = num- 

 ber of planetary rotations in one orbital revolution, R= radius 

 of nebular contraction, p = Sun's present radius. Taking 

 Herschel's values for T and t, we have 



■©* 



^(1). 



9 



5(2). 



9 



£ 110-4 

 9 177-6 

 © 223-1 

 S 301-8 



?5 

 ?5 



4 



102-4 

 166-4 

 2222 

 301-5 



i© 4 111*1 

 id 4 176-6 



g) 445-4 



G) 



427-1 to 719-4 



2 © 4 444-4 



% 1192-5 



\ 1829-5 

 & 3245-7 



hi 



1185-9 



1876-7 



iy 4 3258-9 



It thus appears that — 



R 



1. All the points of incipient condensation, — (1), are within 



Kirkwood's " spheres of attraction." 



2. In the pair of extra-a steroidal planets which are nearest 

 the asteroidal belt, the incipient points are near the secular 

 aphelion of the inner, and the secular perihelion of the outer 

 planet. 



3. In the pair of intra-asteroidal planets which are nearest the 

 asteroidal belt, the incipient points are near the mean aphe- 

 lion of the inner and the mean perihelion of the outer planet. 



4. The sum of the radii of nebular contraction for the two 

 principal planets of the solar system (1192*5 + 1829*5 = 3022) 

 is almost precisely equivalent to the sum of the mean perihe- 

 lion radii of the same planets ( V 2 1069*6+ h 2 1950*4 = 3020). 



K2 



