760 AECHDEACOX PKATT OIS’ THE DEFLECTIOX 
its being true in nature. The existence of the mountain-mass is a fact indisputable 
Not so the compensating cause, which is simply conjectural as to its ex^tence, an 
altogether uncertain as to its extent, if it exist. We have no certam and mdepen ent 
method of determining this ; nor of ascertaining, even if the hypothesis be vahd, how 
far down the attenuation extends, or what law it foUows. _ ^ 
14. I will now determine the effect of these several results upon the Ellipticity of the 
Indian Arc. 
The corrections to be applied to the astronomical amplitudes of the two arcs Kaliana 
— Kalianpur and Kalianpur=~~Damargida, are determined by taking the differences o 
the numbers in each line of the Deflections above given. Hence we get— 
. - T . Kalianato Kalianpur to 
Corrections to be added to the astronomical amplitudes, m Kalianpur. Damargida. 
consequence of the attraction of the mass of the Himma- 
layas and of the region beyond 
Ditto, from the same cause, modified by the supposed atte- 
nuation below, extending down to a depth of 100 miles 1-602 ^ _ 
, . . 300 miles 6-503 0-44a 
500 miles 8-487 2-305 
Ditto! !.’!!!!!!!---• lOOO miles 12-118 3-091 
Putting the arbitrary expressions 15"-885 (i—u) and 5"-059 (1— -y), taken from par. 8, 
for these pairs of corrections in succession, we find the foUonnng corresponding la ues 
of u and v 
— 0-0028 and -0-0391 
+ 0-8992 +0-9998 
0-6906 0-9120 
0-4657 0-5444 
0-2371 0-3890 
By substituting these, in succession, in the formula (2) of par. 8 for e, the ellipticit), 
we have the following values 
g=:0-002377 or — , when no Deficiency of Matter exists. 
421 
0-004621 or — , when Deficiency of Matter extends do-^m 100 miles. 
216 
0-003573 or when Deficiency of Matter extends do-«m 300 miles. 
280 
0-003497 or — , when Deficiency of Matter extends dovm 500 miles. 
286 
0-002815 or — , when Deficiency of Matter extends do^vn 1000 miles. 
355 
The value of the semi-axis major may similarly be found. These values of the eUip- 
ticity differ in every instance from the mean value, They seem, however, to point 
