HIMALAYAS ON THE PLUMB-LINE IN INDIA. 
69 
The following applications of the test show that the values I shall now write down 
are correct : — 
,=43°-17, <p 43 = 4°-98; ?)=log-> 
,=48°-l5, (P,,=5°783; <p=iog-^ 
11-0379639 
9-5888296 
20-6267935 
19- 9291416 
0-6976519. 
11-0379639' 
9-6351413 
20- 6731052 
19-9108962 
= 4°-985. 
0-7622090. 
a,,=53°-93, ^«=6°-80; ^=log-' f 11-0379639' 
9-6808891 
— 
5°-784. 
<; 20-7188530 ;> 
19-8864756 
a 46 = 60 °- 73 , <p46=8°-21 ; <p=log ' 
0-8323774J =6°-80. 
11-0379639' 
9-7292234 
<; 20-7671873 ;> 
19-8528620 
0-9143253. 
: 8 °- 21 . 
If h be the height above the observer’s eye of the top of the prism, and hi the depth of the bottom of it 
below, then (see figure in art. 13) 
^ ^ cosi -6— cu ) 
OR sin OAR \2 / . 
'OA sin ORA 
h + r 
r 
2 sin w sin- fl 
cos I - 
= 2 sin o) tan- 
1 
since w is extremely small in the parts to which the method of the text is to be applied. 
So also 
A' ^ , 1 / 
— =2 sin w' tan - 
r 2 
Substituting for sin w and sin w' from these in the exact formula above (which applies to all cases), and 
neglecting excessively small quantities. 
Horizontal attraction of the prism on the station of the observer 
3 p IB I 1, .1, h + h' 
4 D 
2r 
or the attraction of the parts to which the method of the text applies is found by taking the sum of the heights 
(h + h'), or the whole height from the sea-level up to the surface of the attracting mass. This, it will be 
observed, is the same whatever he the height of the station of observation. In fact, the horizontal attraction 
of the mass, situated so far off as 50 miles and more, upon any station, even though in the mountains, cannot 
differ in any appreciable degree from that upon the point where the vertical line at the station cuts the sea- 
level below. 
MDCCCLV. 
