OF THE PLUMB-LINE IN INDIA, 
767 
19. This Table furnishes the following results: — 
Deflections, caused by the mass distributed 
downwards through a depth of ... 100 miles 
_ 200 miles 
300 miles 
400 miles 
I^'tto 500 miles 
Distance of middle point from A, along the chord. 
379 miles. 
581 miles. 
781 miles. 
980 miles. 
1173 miles. 
1-658 
1-499 
1-340 
1-183 
1-027 
0-714 
0-680 
0-652 
0-614 
0-558 
0 391 
0-384 
0-375 
0-363 
0 342 
0-212 
0-210 
0-207 
0-203 
0-196 
0-101 
0-100 
0-099 
0-098 
0-096 
Multiply these successive lines of numbers by 1, 2, 3, 4, 5, and we shall have the 
Deflections caused by masses having the same volumes as above, but all having the same 
density, \uz. that of the fli’st, e. y^th part of the density of the materials of the sur- 
face. The numbers then become — 
1-658 
0-714 
. 0-391 
0-212 
0-101 
2-998 
1-378 
0-768 
0-420 
0-200 
4-020 
1-956 
1-125 
0-621 
0-297 
4-732 
2-456 
1-452 
0-812 
0-392 
5-135 
2-790 
1-710 
0-980 
0-480 
Now subtract each line fi-om the line below it, and substitute the four lines thus formed 
for the last four above, and we have — 
Deflections, caused by a semi-cubic 
miles in each horizontal side, and 
mass, 200 
100 miles 
Distance of the middle from A, measured along the chord. 
379 miles. 
581 miles. 
781 miles. 
980 miles. 
1173 miles. 
« — — 1 ueii.siiy of ine sur- 
face, and the depth of its centre = 50 miles 
1-658 
1-340 
1 .noo 
0-714 
0-664 
0-391 
0-377 
0-357 
0-327 
0-212 
0-208 
0-201 
0-191 
0-168 
0-101 
0-099 
Ditto 
350 miles 
450 miles 
A« 7 l Q 
V / 0 
0-097 
Ditto 
(\»A AQ 
0-095 
u 00^ 
0-258 
0-088 
The several volumes, the lower down they are, will, owing to the converging of the 
vertical lines, be somewhat contracted, and the densities slightly increased in a corre- 
sponding degree. If we suppose, therefore, the spaces to be correspondingly enlarged 
in the horizontal direction the volumes will be all the same, and the densities all the 
same; riz. xioth part of the density of the surface, or of granite. But in order to 
compare them \rith the densities of those parts of the earth’s interior where they are 
situated, we should increase their densities in proportion ; and this will increase the 
deflection in a corresponding degree. The following is the usual law of density assumed 
from the fluid theory, D being the density of the surface, r = radius of the earth : 
from which 
I 
Density at depth d miles = -^D sin 
r—a 
gather the following results : — 
