Bop  ¥ S asiminaiion of K ——e Analogy. 19 bs | 
Sa boidal stine on each of the adjacent lateral angles of the prism, and 
not as is‘usual, on the alternate angles. It is permeated in ever 
part: by. acicular: rutile. ‘This rutile, in one or two instances, has 
% shot through:similar cavities in other crystals, its delicate hair-like 
needles remaining unbroken while their opposite extremities are 
deeply imbedded in the quartz. In one of these cavities the depth 
_Is more than twice that of the transverse diameter, but the same 
___, Step-like succession of layers is observed as in the large one, di- 
i. minishing i in their descending order, until they nearly ri 
ina point towards the centre “of the crystal. Compared with t 
‘large cavity, there is greater evenness of outline in these little 
Hidgee ws a nearer approach to parallelism between them. 
ie, a of Kirkwood’s Analogy; by Sears 
C. Wak 
(From the Proceedings of the American oe 2nd meeting, held at Cambridge, 
1849, p. 212.) 
In order that Kirkwood’s Analogy should apply to all the plan- 
ets of the Solar System, including the interpolated planet between 
ts and Jupiter, four fundamental conditions must prevail for 
each planet considered as the middle of a consecutive series of 
five; namely: 
__ (a,+6,)e,+(a’—b')e’ 
Ry c+ 
I. ......m=[(a —a,—),)c,]? 
Til. .....m=[(a/—a —b’)c’]? 
2 2 
SES 6=—.* 
Where 
G,, @,, a, a’, a’ =the five mean distances of*the pla 
m=the mass in parts of the sun’s a aia 
accente 
T’=the sidereal year, in amet mean solar days. 
oe 6=the sidereal rotation in the 
es k=Gauss’s ssenclation constant: "from Kepler’s third 
x=a similar rotation constant from Kirkwood’s 
hatogy-. 
r,=the inner radius pe = sphere of attraction for 
the third plan 
r’ =the outer radius of the sphere of attraction for 
the third plan 
r,,=the outer radius of the sphere of attraction fai 
=the inner radius of on sphere of attraction for 
the fourth planet. = 
