A SWARM OF METEORITES, AND ON THEORIES OF COSMOGONY. 41 
in order to distinguish them, let them be accented, so that, for example, we write 
a, /3"^, p, &c., in (43), (44), and (45), in place of a, p. 
Now Table III. shows that, when a' = 2a, M' = M = 2M nearly. Hence, 
M'la = Mja nearly. But, at radius 2a in Table III., v^/vq^ = '298 = ’3, and this 
is what we now write or ja', whilst Vq — fi-pMja. 
But /3^ = f very nearly; hence, = '3, or /B''^ = ’36. 
Thus, 3/y8'2 = 8-333. 
Then, substituting 2a for a, and noticing that in Table III., tv/^p = -163, when 
r = 2a, the first law of density (44) becomes 
163 
g-¥a-2aM _ 
fl - 4 + 
\ ^7 J 
(46) 
Again, since M' = 2M, and a! — 2a, p — ^p, = 4 X = 4 X ’163 by Table III., 
nP xP 
and = -65 = 4 nearly. 
\p ® 
Thus, according to the second assumption, we have by (45) 
Wn 
2a 
3/(r) = (t - + log ( —) , and, since — = 2-78, 
^5’^ = 2-78 ( 1 
3/(r) 
r 
2-78 
+ 2-78 log Ut . 
+ log f£T; 
I3~(L - ia-lr-) l+iajr ' 1 - ia-jr 
and the law of density is 
10 
3P 
= -163 
Q--6f(r)ir- _ g-3/(r)/|3'»(l-4a=/r^) 
(47) 
The values computed from these alternative formulas (46) and (47) will be compar¬ 
able with those in Table III. 
In Table III. we have the value of ivj^p computed at distances rja = 2-208, 2-463, 
2-786. The follov/ing short table gives the result extracted from Table III. for 
comparison with the values computed from (46) and (47) :— 
rja = 
2-0, 
2-208, 
2-463, 
2-786. 
Convective equilib., — = 
sP 
•163, 
•092, 
•033, 
0. 
w 
First hypoth. (46), — = 
3P 
-163, 
•074, 
•033, 
•015. 
w 
Second hypoth. (47), p- = 
3P 
•163, 
•071, 
•029, 
•on. 
M DCCCLXXXl X.-A. 
G 
