100 ATTRACTION OF THE HIMALAYAS ON THE PLUMB-LINE IN INDIA. 
The degree of increased curvature may be judged of from this. The height of the 
middle point of an arc of which the amplitude is X, above the chord of the arc, 
=laA={l-sQ+? cos 2^)1 
(M being the latitude of the middle point, and X sufficiently small to allow to be 
neglected. In the arc between Kaliana and Damargida (which is about 800 miles 
long), X=0’2, cos 2|a-=0‘67473, and a=4000 miles. Hence height of middle point 
above the chord =20(1 — 1*5 12s) miles. 
For the mean ellipticity, this =19'8992 miles. 
For the ellipticity 126 - 2 ’ =19*9290 miles. 
For the ellipticity — this =19*8460 miles. 
The ellipticity, therefore, which results from taking account of mountain attraction 
raises the middle point of the arc by 0*0298 of a mile, or 157 feet ; whereas the ellip- 
ticity when mountain attraction is neglected depresses the arc through 0*0532 of a 
mile, or 281 feet. These quantities are nearly in the ratio of 5 : 9. Hence the con- 
sideration given to mountain attraction in this paper brings the curvature of the 
Indian arc nearer to the mean curvature than the neglect of mountain attraction 
does in the ratio of 5 ; 9 *. This is, as far as it goes, in favour of these calculations. 
69. The conclusion, then, to which I come is, that there is no way of reconciling 
the difference between the error in latitude deduced in Colonel Everest’s work and 
the amount I have assigned to deflection of the plumh-line arising from attraction — 
and which, after careful re-examination, I am decidedly of opinion is not far from the 
truth, either in defect or in excess — but by supposing, that the ellipticity which 
Colonel Everest uses in his calculations, although correct as a mean of the whole 
quadrant, is too large for the Indian arc. This hypothesis appears to account for the 
difference most satisfactorily. The whole subject, however, deserves careful exami- 
nation ; as no anomaly should, if possible, remain unexplained in a work conducted 
with such care, labour, and ability, as the measurement of the Indian arc has exhi- 
bited. 
* An increased curvature is, moreover, more in accordance with what might be expected, as the effect of the 
upheaving of the enormous mass of the Himalayas and neighbouring regions, than a diminished curvature. 
Deep River ^ Cape of Good Hope, 
July 12, 1854. 
