504 Lieut. Col . Lambton’s abstract of the results deduced 
these Indian measurements may rest on their own ground, I 
shall examine whether the increments to a succession of con- 
tiguous degrees as deduced from the present data, be con- 
sistent with the elliptic hypothesis, beginning with the degree 
in latitude g° 34' 44", as determined by observation. To effect 
this let m^ 2 \ &c. be the measures of complete 
contiguous degrees on the meridian in latitudes /(*), fl 2 K 
l( 3 \ See. Then, if a meridian of the earth be an ellipse, we 
know from equation 2, that the compression will be expressed 
?n ( 2 ) — m (3) — 
by 
3 (Sin. 2 F — Sin. 2 ^ 1 ) 
or 
3 (Sin. 2 sin. 2 /^ , l 
or 
— ~r — — — 7-7- ; let the length of the diameters be what 
Sin. 2 ^ 1 ! & 
1 (Sin 
they will. So that we shall have 
m 
^-*(0 
3 m 
(Sin. 2 
t'h 
or 
3m^\sin. 2 / - Sin. 2 /' 1 ) 

3 7n (,) (Sin. 2 A 2) — Sin. 2 ^ 1 ) 
(3} (i) 
.WA 9 
3 wi^(Sin 
. ; and by reduction m 
.*/ 3)_ Sin .^(0 J 
( 3 ) 
= 
=(m^— m { 
!0) Sin -’ 
9 Sin.* 
/(3) _ sin. 
(W— Sin. 
*/( J ) 
«j(0 
and 
+ 
(0 
m 
+ 
( 
m ^ 
+ 
( m (2) _ 
to m^= 
: m ^ 
+ 
( — 
Sin. — Sin. 2 
Sin.*/( 2 )— Sin. 2 
