pas 
218 On Kirkwood’s law of the rotation of the Primary Planets. 
- The following is the law in question, as stated by its author in 
this Journal, vol. ix, page 395 :— . 
“ Let P be the point of equal attraction between any planet and 
the one next interior, the two being in conjunction: P’, that be- 
tween 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 ; 
“m =the number of sidereal rotations performed by the former 
during one sidereal revolution round the sun ; 
"“n' = the number performed by the latter ; then é¢ will be found 
| D\2. 
that gO, BER De ee Sor n=n'(5) 
That is, the square of the number of rotations made by a planet 
during one revolution round the sun, is proportional to the cube 
n 
of the diameter of its sphere of attraction ; or — is a constant 
Dp? 
quantity for all the planets of the solar system. 
The simple question for us now to consider is whether this 
proposition is true. To test it, however, is a matter of more 
difficulty than might be anticipated. It involves the knowledge 
of the distances, masses, and the times of revolution and of rota- 
tion of all the planets of the solar system. Now there 1s some 
uncertainty with regard to the mass of each of the planets ; and 
still greater uncertainty with regard to the times of rotation of 
me of them upon their axes. Moreover, between Mars an 
Jupiter, we find a group of planets ; and the assumed law applies 
to them at a time when they are supposed to have been all united 
in one body. Of course there is an uncertainty with regard to 
all the elements of this planet, and we are left to conjecture the 
time of its rotation upon its axis. It is then difficult to bring this 
assumed law to the test of truth. Under these circumstances It 
has appeared to me the most satisfactory course, to take those ele- 
ments of the planetary system which have the strongest independ- 
ent probability, and compare them with this law ; and when we 
find discrepancies, to enquire whether it is admissible to vary the 
assumed elements so as reduce them to an entire harmony with 
the proposed law. This I have accordingly attempted, and the 
result is shown in the following table, where column first exhibits 
the planets in the order of their distances from the sun ; column 
second exhibits their mean distances, that of the earth being taken 
as unity ; column third exhibits their masses, the sun being taken 
as unity ; column fourth exhibits the diameter of the sphere of 
attraction of each of the planets computed after the manner 
= 
