A SWARM OF METEORITES, AND ON THEORIES OP COSMOGONY. 
11 
-g {wIp) ^ or ^ e^jx^. It follows, therefore, that Ritter takes the surface 
value of 1 /= log^ 2'062. But he intends the central density to be 100 times the 
surface density ; hence, to take the same solution, we must have e’’ equal to 100 
times 2'062. Therefore, his value of t] would be 
77 = log, 100 + log, 2-062, 
or 
77 = 5-3288465. 
Now, as I want to make a comparison between my solution and his, I start with 
this value of 77 . The only object attained by the choice of this particular value h 
that the two solutions become easily comparable. It will be seen below that the 
value of 77 does not make the central density exactly 100 times the surface density, 
but only satisfies that condition approximately. In Ritter’s graphical treatment of 
the problem this value 100 is the exact datum, whereas in my method we start with 
an exact value of 77 , and proceed to find the ratio of central to surface density. 
With this value of 77 (whence log^Q e’’= 2-3142888) I find the following series 
for y ;— 
34-3667 , 354-321 4638-79 , 67,532-0 1,044,280 
y = 0-3288465 --^ ^- — - 
t/O t/y tA/ lA/ 
, 16,789,000 2-77 x 108 , 4-4x103 
d“ ^12 -^14 ' 16 • • • ; • • (16) 
tO lA/ tO 
and, by differentiation, the series for dyjdx is obvious. 
This series will be very accurate from 37 = 00 to about cc = 8. Thus, when rja = "1, 
or a: = 10, we have 
7 /= 5-016558, =+ -0568910, 
and even the far less convergent series for d-yjdx^ gives — ’0150891, agreeing with 
— eyjx^ to the last place of decimals. When rja = -125, or ai = 8 , we have"^ 
wRence, 
y = 4-86392.5, 
dy 
dx 
-101168, 
d-i! 
J=- -031024, 
with y correct to four, and proliably to five, places of decimals, and dyjdx probably 
correct to four places of decimals. This is amply sufficient for our purpose. Indeed, 
accuracy of this order would be altogether pedantic, were it not that the errors 
accumulate. 
* Even when a; = 5, I find from tliis series y — 4-342, "vvdiicli lies -ymry near to 1 / = 4 .332, fonnd 'bclo-^v. 
But the series for dyjdx is useless. 
C 2 
