28 , On Kirkwood’s Analogy. 
I should not desire that this should be denominated a La W. ‘Na- 
ture’s laws must be precise and complete. The relation which _ 
we are considering claims only to be approximate—an analogy. 
And in speaking of it, . shall call it by this name, Kirkwood’s 
Analogy. And where we have by hypothesis a right to expect 
analogy and not perfect accordance, the want of perfect accord- 
ance must not be considered to cast doubt upon the theory. 
sides, if Kirkwood’s Analogy were the result of a general law, _ 
would not the action of the law be modified in all probability by 
circumstances which would prevent us from perceiving any strict 
mathematical precision? The considerations which w 
strong arguments against bgpintheat of other kinds, do at peal 
to me weighty when applied to any thing so rude as the motion 
of chaotic matter. 
There is a formula known as “ Bode’s law”—an empirical for- 
mula—expressing a supposed analogy, for which no reason was 
ever assigned and which, even before it was broken by the new 
lanet Neptune, was found utterly devoid of that universality and 
precision which must characterize all laws of nature. Thoug 
was considered a remarkable coincidence, and perhaps as capa- 
ble of suggesting some law of nature, no true mathematician 
could ever have regarded it asa real raw. Moreover, Gauss 
shown long since that it did not hold for Mercury. ; 
This ‘Law of Bode” was analogous to the theory of Kepler, 
that as there were but five regular solids, there could be but five 
ponchay intervals, and therefore no planet between Jupiter and 
Kepler s theory was totally overthrown by ii discovery of 
Uranus, as the other has been by the discovery of Neptune. 
Bo 
erly given, would make the distance of Neptune beyond the orbit 
of Uranus nineteen times the distance of the Earth from the Sun, 
while it is in fact less than eleven times this distance beyond it, 
so that the fallacy of At formula must now be so evident as to 
require no demonstratior 
Discordances such as ae which, exist in the application of 
this law to the planetary system, would afford sufficient reason 
for rejecting the analogy of Kirkwood; but, with even these dis- 
cordances, the fact, that a single formula would approximately =. 
represent the truth to so great an extent, would justify us in be- 
stowing much time upon its consideration. 
[Dr. Gould then gave a brief sketch of the points of connec- 
tion between the nebular hypothesis and the new analogy,— 
ywing how the one would lead to the other. ] 
It will be remarked that in the Seda “sphere of attraction,” 
the word sphere is not used in its geometrical sense. Nor is a 
_ planet necessarily in the centre of its sphere of attraction, for 
