4 JD. Kirkwood on certain Harmonies of the Solar System. 
of the orbital motion. It must also be manifest that the rotation- 
period at the epoch of solidification will depend upon the ratio 
of actoSE. Now, it ma : 
be impossible to determine 
in any particular case what 
was the diameter of a gas- 
eous planet at the com- 
mencement of the accele- 
ration of the rotary veloc- 
ity. We may assume, how- 
ever, with a high degree 
of probability, that its ra- 
tio to the diameter of the 
planet’s sphere of attrac- 
tion was the same or nearly 
the same in each instance; 
or that 
B:A’:2 D2 Ds (1h) 
where D, D’ are the diam- 
eters of the spheres of at- 
traction, and A, A’, the di- 
ameters of the planets im- 
mediately before passing 
the limit of equality be- 
tween the periods of rota- 
tion and revolution. 
- The law of rotation as 
originally announced is as 
follow: 
s 
$i-— 
“Tet P be the point of equal attraction between any planet 
and the one next interior, the two being in conjuction: P’ that 
between the same and the one next exterior. 
Let also D= the sum of the distances of the points P, P’ from 
the orbit of the planet; which I shall call the diameter of the 
sphere of the planet’s attraction ; 
_, D’= the diameter of any other planet’s sphere of attraction 
found in like manner; 
__ n= the number of sidereal rotations performed by the former 
during one sidereal revolution round the sun; 
__ n'== the number performed by the other; then it will be found 
SUR, 3 n? : ni2 > D8 ; —/3 7* (2) 
, now, T, T’= the periodic times of two planets ; 
14 t= their ion 
d, d'= thei 
10n 5 
» held at Cambridge, 1849, 
