HIMALAYAS ON THE PLUMB-LINE IN INDIA. 
57 
IJb— half the sum of these latitudes, 
= 26° 49'; COS 2|M<=0-59295. 
Suppose only ; then 
1 " 2 
^^“5° 23' 38" 3(0-59295- cos 2M) 
1 2 
“^54 0-59295— cos 2 M' 
This will be smallest when 2M is chosen as nearly 180° as possible. The great 
arc lately measured near North Cape is the one which will best meet this condition. 
Put therefore M = 70°, cos 2M = — 0-76604, and 
• - “‘'~58254 1-35899 39585 
“1I2’ 3^ 
Hence for an error of 5"‘236 in defect in the amplitude, the effect on the ellipticity 
5-236 £ 
will be to diminish it by nearly, or by nearly -gJ^th part of its whole value, 
under the most favourable circumstances. This is sufficient to show the g'reat im- 
portance of endeavouring- to account satisfactorily for the discrepancy brought to 
light by the Indian Survey ; and that, not by merely putting it down to mountain 
attraction, but by calculating that attraction by some independent means, with a view 
to see whether its amount actually corresponds with the observed anomaly*. 
10. To dissect and actually to calculate the attraction of the masses of which 
the Himalayas, and the regions beyond, are composed, appears, at the very 
thought of it, to be an herculean undertaking next to impossible. I am fully con- 
vinced, however, that no other method will succeed. It is upon this plan that the 
solution of the problem is conducted in this paper. It will be seen, that by selecting 
a peculiar law of dissection the calculation is very greatly simplified, and made to 
depend entirely and solely upon a knowledge of the elevations and depressions, in 
fact, the general contour of the surface. This information for some part of the mass 
is already supplied by the maps of the Trigonometrical Survey. 
11. In the following pages I propose, in the first place, to develope my method of 
calculation, and to deduce a formula by which the attraction can be determined with 
a precision corresponding to the degree of accuracy to which the contour of the 
surface is known. 
* If the effect of mountain attraction upon the northern division of the arc be what I make it, 15"-885, then 
the ellipticity as determined from this and the Russian arc would be too small by - s, if mountain attraction is 
neglected. The error in the ellipticity in comparing the whole arc between Kaliana and Damargida with the 
North Cape arc will, under the same circumstances, amount even to ig. This will appear from the sequel, 
6 
and is here mentioned only to illustrate the importance of the subject under consideration. 
