or THE PLUMB-LINE IN INDIA. 
765 
Pig. 4. 
log ^1 1392 sin (3^ for the five spaces are as in the margin. The values 
of ^ belonging to each space must next be gathered out from the first, 
second, and third of the Tables of Reduction (see pages 754, 755), which 
give the values of log The natural numbers are formed into the fol- 
lowing Table, which gives the values of ^for such of the compartments (from the 18th 
1*4712930 
1*2897722 
1*1625924 
j 1*0661096 
I 2-9866678 
i No. of 
i compartment. 
1 
! 
j Values of £. gathered from the 1st, 2nd, and 3rd of 
Tables of Reduction (in par. 12) for following depths: — 
100 miles. 
300 miles. 
500 miles. 
18 
0*95149 
! 0-69152 
0-49300 
19 
0-96131 
: 0-72759 
0-53054 
! 20 
0-97029 
0-76186 
0-56876 
: 21 
0-97676 
0-79471 
0*60814 ! 
I 22 
0-98273 
0-82502 
0-64731 ' 
23 
0-98770 
0-85274 
0-68590 i 
1 24 
0-992J4 
0-87821 
0-72411 j 
25 
0-99523 
0-89932 
0-75808 1 
i 26 
0-99838 
0-92092 
0-79533 
27 
1-00081 
0-93861 
0*82803 
28 
1-00286 
0*95402 
0-85826 
29 ! 
1-00456 
0-96739 
0-88604 
30 
1*00597 
0-97892 
0-91125 
o' 
1-00714 ! 
0-98877 
0-93380 
32 
1*00814 : 
0-99738 
0-95432 
33 
1-00896 j 
1*00457 
0-97218 
to the 33rd) as are comprised in the five spaces. We must now apportion these values 
C 
ofj to the several spaces to which they appertain, take their sum, and multiply by 
1 *1392 sin ^ /3, and we shall have the Deflections produced by the mass of one mile high 
and on a base equal to a square of 200 miles each way, when diffused downwards to the 
se\eral depths of 100, 300, and 500 miles. The following Table will explain itself: — 
