HIMAJ.AYAS ON THE PLUMB-LINE IN INDIA. 
99 
This value coincides almost exactly with Colonel Everest’s determination of the 
ellipticity from a comparison of the arcs 1. and II. He makes it (see the Table 
at the end of his work). 
6/. Let us next see whether, by altering- the altitudes of the attracting mass, we 
can make the curvature of the Indian arc equal to that corresponding with the mean 
ellipticity. The above form will then give 
or 0-003324 = 0-002346-|-0-003693w — 0•001046^; ; 
.-. 3693m— 1046t;=978 
978 + 1046W 
3693 
0-265 -1-0-283M. 
As V cannot be less than 0, u cannot be less than 0-265, or somewhat more than 
to satisfy this equation. Or the heights laid down in the Tables of art. 41. must be 
so far cut down as to diminish the difference of deflection at Kaliana and Kalian pur 
by one-fourth of its amount. 
Should it be necessary to allow for the larger astronomical amplitude of the arc II. 
(noticed in art. 64.), by diminishing v by a quantity v' , then 
m = 0-265 — 0-283M'-b0-283M. 
The astronomical amplitude of arc II. is 2"-687 larger than that obtained by com- 
putation from the arc; whereas it should be l"-509* smaller than that determined 
from computation, if it bear the same relation to the difference of deflections as in 
the arc I. If then we put 
V 
2"-687-M"-509 4-196 
= =0-8294 
5-059 
w = 0-030-|-0-283m, 
and a reduction of the difference of deflections at Kaliana and Kalianpur by some- 
thing more than ^(jth part, the difference in arc II. remaining unaltered, will bring 
the ellipticity out There is, however, no reason for supposing either that the 
curvature of the Indian arc is precisely equal to the mean curvature of the whole qua- 
drant; nor that the heights of the attracting masses have been made so much too 
great. 
68. If these heights have been rightly assigned in this paper, that is, if m=0 and 
v=Q, then the ellipticity of the Indian arc 
=0002346=j5^, 
which shows that the arc is more curved than it would be if it had the mean ellip- 
ticity. 
* 15"-885 : 5"-059 : : 4"-738 : l"-509, the quantity used in the text. 
