86 
Dr. Young’s remarks on the reduction 
to y, as x' to M, or - = whence — — = ; conse- 
quently in the present case we have - X J* = ^ ; and M = j : 
and if we make x = 1 in the value of p , we shall obtain M in 
terms of the radius of the earth, considered as unity. When 
y is invariable, and n infinite, the density being uniform, p 
becomes •§•, and the mean density will always be expressed 
by 3 p y since the attractive force is simply as the mean den- 
sity : and if we divide 3 p by y, we shall have the relation of 
the mean density to the superficial density. The results of 
this calculation, for different values of n, are arranged in the 
table, which will be found sufficiently accurate for the pur- 
poses of the investigation, though not always correct to the 
last place of figures. 
n p 
p 
Ip, mean density 
y 
IP , comp. den. 
y 
00 -38333 
00 
1.0000=1: 
il.ocoo 
1.000 
1.000 
i .30290 
3-3°i 
.9087 
1.1005 
•8 55 
1.065 
i .27735 
1.803 
.8320 
1.2019 
•738 
1127 
i .25535 
1305 
.7660 
1.3054 
.646 
1.185 
i ,23688 
1.0, 55 
.7106 
1 - 407 1 
•575 
1.24 
f .22058 
.907 
.6617 
1.5m 
-51° 
1.30 
.20616 
.808 
.6185 
1.6168 
.458 
i-35 
f • 1 94 
.736 
.582 
1.72 
•419 
1.40 
1 .183 
.681 
•549 
1.82 
•377 
i-45 
i .172 
.646 
.516 
i -94 
•34 6 
1.49 
[to -1®* 
.617 
.486 
2.05 
.320 
1.52] 
[tV -iS 3 
•594 
•459 
2.16 
.298 
i-55] 
[tV -145 
-575 
•435 
2.28 
.28 
i-57] 
[jo - 1 
•5 
•3 
3-8 
.17 
1.8] 
The reciprocals of the mean density are inserted, on account 
