92 
ARCHDEACON PRATT ON THE ATTRACTION OF THE 
will always be an extremely small fraction, which may be neglected ; 
“222 ’ 
deflection of plumb-line at proposed station 
deflection of plumb-line at Kaliana 
attraction at the station 222 
attraction at Kaliana X ’ 
But by art. 43. deflection at Kaliana =32' 601 ; 
.'. deflection at the station in question 
7237"-422 
X 
If we had used the second and third values of above, we should have obtained 
from the results for Kalianpur and Damargida given in art. 43., the following: — 
7277"-200 
deflection at the station in question 
X 
7143"-812 
deflection at the station in question = 
These three formulae are very nearly the same. I shall adopt the mean of them ; and 
in taking the mean I shall give the three their respective “ weiglits,” which are as the 
numbers 76, 30, 17, as the deflections in art. 43. show. This leads to the following 
formula : — 
Deflection of plumb-line, at a station the distance of which from P/> is X miles, 
7235" 
54. We may obtain X in terms of the latitude. Let L be the latitude of the place, 
and I the latitude of Kaliana; then X = 222 + (/ — L) cos 22° 30' X the number of 
miles in a degree of latitude at the centre of the Indian Arc. The value of the 
multiplier of /—L which best suits my purpose is 63'06465. As this =69 cos 23° 56', 
using this value shows that if the length of a degree in this latitude =69 miles, then 
the line Pp must run about the one-eighth of a point further from east and west than 
I have placed it, viz. W.N.W. and E.S.E. If the length of the degree be less than 
sixty-nine miles, then Vp will need a still smaller shift of position. 
Substituting the above value, we have deflection at any station of which the latitude 
is /— L degrees south of Kaliana 
7235" 114"'712 
“ 63-06465 (/— L) 4- 222 ■“ /— L + 3-5 20’ 
If we put /— L=0, 5° 23' 37", and 11° 27' 33" corresponding with the latitudes of 
Kaliana, Kalianpur, and Damargida, this formula gives for the three deflections at 
those stations 32"-590, 12"-870, and 7"’668. These so nearly accord with the values 
in art. 43, that the above formula will represent very approximately the deflection 
at any station on the whole arc. 
