THE OCEAN ON THE PLUMB-LINE IN INDIA. 
701 
^ 4. The effect of the Ocean on the Elli^ticity of the Great Arc of Meridian in India. \ 
12. The results in the last paragraph increase the amplitudes of the two arcs Kaliana 
Kalianpur and Kalianpur— -Damargida by the quantities 2"-82 and l"-44. In former 
communications I have shown that the etfect of mountain attraction is to decrease these 
amplitudes by 14"’896 and 5"'257. The etfect, then, of the ocean is to reduce these to 
12"-88 and 4"-12. 
In my Paper of 1865 I obtain the following formula for calculating the effect of errors 
in amplitude on the ellipticity. If 15"-885(l-w) and 5"-059(l-^) be corrections to be 
added to the astronomical amplitudes of these two northern portions of the arc, then 
the ellipticity of the arc 
= 0-002346 + 0-003693zi--0-00104Gy. 
Put, therefore, 15-885(1 — w) = 12-88 and 5-059(1— 'y) = 4-12 ; 
^=0-18918 and ij=0-18561, 
enipticity= 0-00361 4= 
This is nearer to the mean value of the ellipticity than the hypothesis of deficiency of 
matter below will make it, if the deficiency extend no deeper than 300 miles below the 
surface (see my last Paper). The allowance, therefore, for the effect of the ocean brings 
back the curvature of the Indian Ai’c, as deduced by the comparison of the computed 
and observed amplitudes (the latter being corrected for the effect of mountain and ocean 
attraction), more nearly to the mean curvature, and thus far acts in the right direction. 
I may also observe, that the increase of amplitude between Damargida and Punnoe 
deduced from the last paragraph, taken in combination with the decrease which the 
mountains produce (as far as we can infer this latter amount by supposing the law of 
attraction between A and C to extend to P), is not very different from the error which 
Colonel Eveeest deduced (p. clxxvii of his volume of 1847) for that portion of the arc. 
lo. The effect of the mountain and ocean attractions is shown in the accompanying 
diagram (fig. 2). SDPrnN is the meridian line in the longitude of Cape Comorin or 
Punnoe (P), on the supposition that the ocean is of the same density as superficial rock, 
and that the mountain mass is all removed. D is 36° from P, and T)d — the depth which 
measures the deficiency of matter arising from the inferior density of sea-water = about 
1-878 miles. From d the curves dT and slope up to Punnoe and the neighbourhood 
of the south pole, so as to make the change of depth vary in arithmetical progression. 
The cm-ve dP produced through P reaches a height at M (25° from P, and where the 
axis of the Ilimmalayas crosses the meridian) = Mm = l-878 x 25 - 4 - 36 ==1-3 mile. The 
a\eiage height of the wliole mountain mass (in the Enclosed Space) is only about one 
mile; also the greatest height between Punnoe and the beginning of the Himmalayas, 
which is about half-way, does not exceed half a mile ; and about Kahana it is only one- 
fifth of a mile. Hence the curve PM decidedly lies above the general curve of Asia 
fiom Punnce towards the north pole; and the curvature of the actual meridian line is 
greater than the average curvature. Tliis is the result to which the ellipticity deduced 
