26 On Kirkwood’s Analogy. 
Perhaps this is the very condition required to ‘ maintain p=p'y 
and consequently v=v’. In this case we may conclude sil Pp Ss 
had exceeded p’ immediately after the breaking of the ring, and ~_ 
only arrived at a state of equality by the loss of oe from + 
Prof. Peirce remarked that Kirkwood’s analogy was the ani a 
discovery of the kind since Kepler’s time, that approached near __ 
to the character of his three physical laws. e’s law, so. call- 
ed, was at best only an imperfect analogy. Kirkwood’s analogy 
was more comprehensive and more in harmony with the known 
elements of the system. ‘The diameter of the sphere of attrac- 
tion, a fundamental element in this analogy, now for the first . 
time gave an appearance of reality to Laplace’s nebular hypothe- 
sis, which it never had before. The positive testimony in its 
favor would now outweigh the former negative evidence in the 
case, however strong it may have been. It follows at least from 
Kirkwood’s analogy, that the planets were dependent upon each 
other, and therefore connected together in their origin, whatever 
may have been the form of the connection, whether that of the 
nebular hypothesis, or some other not yet imagined. 
Arr. IV.—On Kirkwood’s Analogy ; by Dr. B. A. Gouxp, Jr. 
(From the Proceedings of the American Association, 2nd meeting, held at Cambridge, 
3.) 
Tue subject which Mr. Walker brought to the notice of this 
Section on Saturday, is one of far more than ordinary interest. 
Besides the elegant es ig of Mr. Kirkwood’s formula, his 
theory must, if it be confirmed, materially influence our views of 
cosmogony and of rhe theory of the Universe. I have devoted . 
all of the time which my duties have allowed since Mr. Walker _ 
made his communication, to the numerical examination of the — 
Analogy to which he referred and which prompted his beautiful 
investigations. I will state the results, though not in the fullness 
ea which they deserve, and with which I at first hoped to be able to 
give them; for although the subject is large, and one which we 
cannot expect to exhaust for many years, yet the time of the Sec- 
tion is so precious at this late hour, that I shall limit myself to as 
brief a ee as possible. 
rk wood’s eae as regards the rotation of the plas 
¢: bate in support of the nebular hypothesis. ‘The 
“minds of many have been wavering of late with regard to this 
hypothesis ; Gheif doubts have been strengthened by the unquali- 
fied assertions that all nebulas are resolvable ; but this analogy of 
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