OF THE PLUMB-LINE IN INDIA. 
771 
shelves up in a pyramidal form to the ridge IJ, 2000 miles long and 210 miles from A 
and nsmg to an elevation above A of 1-6 mile; whence it shelves down again to Gh’ 
riff. 5. 
1200 miles further off, where it abruptly terminates at a height of half a mile above the 
le\el of A. That this is a fair representative of the mass with reference to its effect on 
A, will be^ seen in the course of the investigation in this, — that its area, its volume, and 
its attraction on A, as well as its principal heights, are all the same as in the case in 
nature. The following are the measures : AF or «=210 miles ; FE or c=1000 miles ; 
FK or e=1200 miles; DF or ^=160 miles; El or A=l-5 mile; GL or A'=0-5 mile. 
The area of the base of this figure =2000(1200+75)=2,550,000 square miles. The 
volume =i(A+/02000x 1200+1^x2000x150=2,650,000 cubic miles. The average 
height of the whole figure lgo o + |/,x 2000x 75 
® 2000 X 1200 + 2000 x 75 ~ ^ mile. 
It is not difficult to prove by the Integral Calculus, that the Attraction of this mass 
on A in the direction AD, its density being half the mean density of the earth. 
16/60 
+ (a + e)^-fc® — c 
+ — c a -\-e 
--(A-/01og, 
V {a-\- eY + + a + e~} 
-f -f « 
+A 
a-h 
c W ■ 
-h-eA=|^,B-l+^. 
'A+ a/'i+A^' 
b 
+7/+^ log. 
- + B 
c 
J 
A 
^1+A2 + — R 
a — b 
B 
a — b 
Also the attraction of a tabular mass on the same base and of height ]c 
0 I a/«2 4.^2_“ a-i-P “*“R3 ^ 
16760 
-H-B 
c 
-loge 
a — b 
B 
a — b 
5 I 2 
