56 
ARCHDEACON PRATT ON THE ATTRACTION OF THE 
and astronomical results appears from the effect it must have upon the determination 
of the earth’s ellipticity ; an effect such, that unless this quantity be fully accounted 
for, it must render the great Indian Survey comparatively useless in the delicate 
problem of the Figure of the Earth, however valuable it may be for the purposes of 
mapping the vast continent of Flindostan. 
9. The effect of a small error in the difference of latitude upon the determination 
of the ellipticity may be calculated as follows : — 
Let g be the ellipticity, a quantity known not to differ much from ; X the 
amplitude of the 
usual formula 
arc ; [Ij the latitude of the middle point of the arc. 
length of arc 1 . . . 
equatorial radius =^-2^<^+8 ^ 2^)- 
Then by the 
But sin?i.=>.— gX®+..=X^l — X=5° 23' 37'' for the arc between Kalianpur 
and Kaliana =0‘094 in parts of the radius, 
^ X "=0 00147 . 
Hence by putting 1. instead of sin X in the above formula, we shall be omitting a 
quantity of the order ^2X0 00441 cos 2|M-, which is utterly insignificant. 
length of arc 3 \ 
equatorial radius = H ' 
In the same way if L be the amplitude and M the latitude of the middle point of 
another arc. 
length of arc L 
equatorial radius ' 
:L( 1-^2 
1 — 2^ COS 2M 
length of arc X X 
length of arc L L 
1 — |2(cos 2jM/— cos 2M)|. 
Suppose the observed values of X and (/j are subject to small errors owing to moun- 
tain attraction ; to find the effect on 2 we must differentiate this expression, supposing 
the angles X, and 2 variable and the other quantities constant. 
0=f/x|l — |2(cos 2(jij — cos 2M)| 
3 
+3X2 sin 2(jtj.diJij—-K(cos 2|U/ — cos 2M)cf2, 
, _dx 2 
^ X 3(cos 2j«.— cos 2M)’ 
neglecting extremely small quantities of the higher order. 
Now in the case before us, 
X= latitude of Kaliana — latitude of Kalianpur, 
= 29° 30' 48"— 24° 7' 1 1"=5° 23' 37", 
