94 
ARCHDEACON PRATT ON THE ATTRACTION OF THE 
mass in art. 43, are 27"'853, 11"’968 and 6"'909, which show how good an approxi- 
mation the formula of this article giv'es. 
58. Before proceeding to the conclusion of this paper I will gather together the 
formulee which I have arrived at. 
The deflections of the plumb-line at Kaliana, Kalianpur, and Damargida have 
been found to be as follows: — 
In the meridian 
. . 27"-853, 
ll"-968. 
6"-909 
In the prime vertical 
, . 16"-942, 
4"763, 
2"723 
Total deflections . . , 
. . 32"-601, 
12"-880, 
7"'426 
In azimuths . . . , 
. . 31° 18', 
21° 42', 
21° 31' 
The general formulae including these results and the deflections for intermediate 
stations are, — 
total deflection 
114"-712 
“■/-L + 3-520 ’ 
and the azimuth in which its acts is given by 
cos 
cos 31° 18' 
1 
— ^ sin 10(/— 
10 ^ 
L) 
deflection in meridian = ? ^ 
(/-L + 3-520)j 10(/-L) 
The formulae for altering the deflections in meridian for any change in the heights 
of the attracting mass are brought together in art. 47. Similar formulee might 
easily be calculated for the deflections in the prime vertical. If any change be made 
in the heights of the attracting mass, these formulae will show what corrections must 
be introduced into the expressions for the total deflections and their azimuths given 
above, and also into the constants in the general formulae. 
Conclusion. 
59. Before an arc can be made use of in the problem of the figure of the earth, 
we must know coi’rectly two things concerning it, — its length and its amplitude. Of 
the two arcs I have been considering, viz. from Kaliana to Kalianpur, and from Ka- 
lianpur to Damargida, the correct lengths are known from the Survey ; and, as shown 
in art. 6, these are altogether unaffected by mountain attraction. The same cannot 
be said of their amplitudes ; and till they can be obtained correctly, the arcs can 
render no service to the great problem. But the amount of deflection in the plumb- 
line caused by mountain attraction having been determined, the amplitudes obtained 
astronomically may be corrected, and the arcs may take their place — and a very im- 
portant place, owing to their length and the accuracy of the geodetic operations — in 
the investigation of the earth’s form. 
60. When the length and amplitude of an arc are known, the formula which I give 
