398 Kirkwood’s Analogy in the Periods of Rotation, §c. 
The following is a very brief history of the astronomical dis- 
covery communicated to the American -Association for the Ad- 
vancement of Science, at its session in Cambridge, Mass., in Au- 
gust, 1849, by Sears C. Walker, Esq. . 
My dirst notions in regard to the existence of an unknown law 
regulating the revolutions of the planets on their axes, date some 
time previous to the commencement of 1839. No investigation 
of the subject, however, was undertaken until the spring or sum- 
mer of that year, when, in reading Young’s Mechanics, I was 
struck by the remarks at the 204th page in support of the con- 
' jecture that both the progressive and rotary motions of the heav- 
enly bodies were originally communicated by the same impulse. 
While reflecting upon the subject it occurred to my mind that an 
examination of this theory, in case it were founded in truth, might 
possibly develop that harmony, of which I had for some time en- 
tertained a vague conception. Having determined to give the 
subject my earnest attention, I commenced by calculating the 
distance from the centre of each planet to the point at which, ac- 
cording to the known laws of dynamics, the projectile force must 
have been impressed.* These distances I compared with each 
other in a great variety of ways. Failing thus, however, to de- 
tect any relationship between the different members of the sys- 
tem, I abandoned this hypothesis as hopeless. 
After this, my leisure hours were spent for several years, with, 
no better success, in comparing the masses, volumes, densities, dis- 
tances, é&c. At length, as the only remaining source of hope, I 
took up the nebular hypothesis of Laplace. This was in 1846. 
Here I soon found that a proper discussion of the questions which 
presented themselves required an analysis beyond my reach, and 
that consequently there was little prospect of attaining my object 
by any direct process of mathematical reasoning. Still, however, 
I could not persuade myself utterly to abandon my laborious 
though hitherto unavailing pursuit. 
ad not been long engaged in my researches on the nebular 
hypothesis when the diameter of the sphere of attraction present- 
ed itself to my mind as a probable element of the law sought. 
Further consideration of the subject led to the conjecture that 
the ratio of the angular velocity of translation to that of rotation, 
or, which is the same thing, the number of a planet’s days in its 
year, might be another element. Finally, on the 12th of August, 
1848, I obtained the simple analogy announced a few months 
since in my letter to Mr. S. C. Walker. My delight as I applied 
it to the different planets in succession and found its wonderful 
agreement with the known elements of the system, may wel 
imagined. 
* In these calculations I was, of course, under the necessity of making certain as- 
sumptions in regard to the variation of density from centre to surface. 
ee 
