HIMALAYAS ON THE PLUMB-LINE IN INDIA. 
67 
The formula (8.) then gives the following successive values : — 
Distance from A of the 
nearer ends of the 
compartments. 
Length of the compartments. 
Distance from A of 
the middle points of 
the compartments. 
1. 
a 1= 6-75 
a 1= 
= 0*075 
0*787 
2. 
a 0— 0*825 
<P 2= 
= 0*0825 
0*866 
3. 
a 3= 0*907 
= 0*0907 
0*949 
4. 
a 4= 0*998 
= 0*0998 
1*048 
5. 
a 5= 1 098 
P5 = 
= 0*1098 
1*153 
6. 
a 1*208 
^5 6 = 
= 0*1208 
1*268 
7. 
1-329 
^ 7 = 
= 0*1329 
1*395 
8. 
a 8= 1*461 
•P g — 
= 0*1461 
1*534 
9. 
a g= 1*607 
<P 9 = 
= 0*1607 
1*687 
10. 
1-768 
= 0*1768 
1*856 
11. 
1*945 
<Pn = 
= 0*1945 
2-042 
12. 
aj2= 2*140 
= 0*2140 
2*247 
13. 
2*353 
(Pj3 = 
= 0*2353 
2*472 
14. 
aj4= 2*589 
'Pl 4 = 
= 0*2589 
2*719 
15. 
2*848 
= 0*2848 
2*990 
16. 
ajg= 3*133 
= 0*3133 
3*289 
17. 
3*446 
= 0*3446 
3*616 
18. 
ai8= 3*790 
fis= 
= 0*3790 
3*980 
19. 
“l 9 = 4*170 
^19~ 
= 0*4170 
4*378 
20. 
4*586 
= 0*4586 
4*813 
21. 
a2i= 5*046 
^ 21 " 
= 0*5046 
5*298 
22. 
a2o= 5*550 
'^22 = 
= 0*5550 
5*828 
23. 
a., 3= 6*106 
^23 ~ 
= 0*6106 
6*408 
24. 
6*716 
^24 = 
= 0*6716 
7*054 
25. 
a, 5 = 7*388 
^•25~ 
= 0*7388 
7*707 
26. 
^ 26 = 8-127 
’P 26 = 
= 0*8127 
8*533 
27. 
£* 27 = 8*939 
^ 27 “ 
= 0*8939 
9*386 
28. 
29. 
a 28 = 9*833 
a.,9=10*8l6 
^ 28 “ 
^29 = 
= 0*9833 
= 1*089 
10*324 
11*360 
30. 
^ 30 = 11*905 
= 1*202 
12*506 
31. 
13*107 
'P 31 = 
= 1*326 
13*770 
32. 
a.,„= 14*433 
^ 32 “ 
= 1*462 
15*211 
33. 
«33=15*99 
P. 33 ” 
= 1*620 
16*80 
34. 
a.„= 17*61 
P34” 
= 1*800 
18*51 
35. 
^ 35 = 19*41 
P 35 = 
= 1*992 
20*40 
36. 
^36=21*40 
= 2*211 
22*50 
37. 
a 37 = 23*61 
^7- 
= 2*456 
24*83 
38. 
a38= 26*06 
'P38” 
= 2*734 
27*43 
39. 
a. 39 = 28*79 
P39" 
= 3*054 
30*31 
40. 
a^=31*84 
P40- 
= 3*419 
33*55 
41. 
= 35*26 
P 41 = 
= 3*600 
37*06 
42. 
a^= 38*86 
P42" 
= 4*314 
41*01 
When part of the attracting mass is near, and therefore w is not so small that it may be neglected (as in 
art. 14.) — which will be the case in carrying the survey into the mountainous regions — a different formula 
must be used for calculating the deflection of the plumb-line caused by the nearer parts of the attracting mass. 
Let, as before, the mass be divided by lunes, which for the parts now under consideration must be narrow ; 
let w and be the angles which the highest and lowest points of a small vertical prism, reaching from any 
point of the surface down to the sea- level, makes with the horizontal line at the eye of the observer. Let 9 be 
the horizontal distance from the observer of the middle line of the prism, in degrees ; /3 the width of the lune, 
in degrees ; I the length of the compartment on which the prism stands, in miles ; r the radius of the earth, in 
miles. Then the Lemma in art. 13. leads to the following exact formula : — 
