Kirkwood’s Analogy in the Periods of Rotation, §c. 395 
Art. XX XVIIL.—On a new Analogy in the Periods of Rota- 
tion of the Primary Planets, discovered by Daniel Kirkwood, 
of Pottsville, Pennsylvania. 
(From the Proceedings of the American Association for the Advancement of Sci- 
ence, 2nd meeting, held at Cambridge, 1849. p. 207.) 
Mr. Sears C. Waxxer addressed the Association on the sub- 
ject of a new analogy in the periods of rotation of the primary 
planets, discovered by Daniel Kirkwood, Esq., of Pottsville, Pen 
sylvania. 
The subject of my present communication is contained in a 
letter of Mr. Daniel Kirkwood, of Pottsville, Pennsylvania, dated 
July 4th, of this year. 
The Secretary then read Mr. Kirkwood’s letter, as follows :— 
e Pottsville, Pa., July 4th, 1849. 
Sears C. Warxer, Esq., ’ : 
Sir,—Knowing the great interest you feel in astronomi- 
had little doubt of the existence of such a law in nature, an 
have been engaged, as circumstances would permit, in attempting 
its development. I have arrived at results, which, if they do 
Not justify me in announcing the solution of this important and 
nce problem, must at least be regarded as astonishing co- 
neide 
_ 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; 
n=the number of sidereal rotations performed by the former 
during one sidereal revolution round the sun ; 
