THE OCEAN ON THE PLUMB-LINE IN INDIA. 
793 
of the ocean on the point half-way, which I have called “ Near-Goa,” as well as upon 
Punnce and Karachi, the two extremities, with a view to obtain the approximate law of 
the force along this line. The formulae of par. 9 show that the chief part of the effect 
arises from the portions of the sea which depend on D, down in the south at a consider- 
able distance from Hindostan. The law, therefore, along the above line may be obtained 
approximately by assuming a formula irr powers of X, or the difference of latitude of any 
point on the line and Pmrnce. The value of this difference is 8°-5 at “Near-Goa,” and 
1/ at Karachi. The east and west parts of the force I ireglect, as not modifying the 
force- northwards at all materially. In this way I obtain— 
Deflection = 1 9"- 71 ~ 0"-585^+ 0"-00084xh 
This, as may be seen by sirbstitution, gives the deflections of par. 11 at the three sta- 
tions, Punnce, Near-Goa, and Karachi. It is easily seen, by the resolution of forces, that 
the ratio of the force prodircing this deflection to gravity equals the tangent of this 
deflection. Hence, calling the force W, 
W 
y=0-000095556839 — 0-000002836162x-f0-000000004072?i^ 
X being expressed in degrees and parts of a degree. 
15. We shaU soon require the integral of this force multiplied by the element of its 
direction, taken between x=0 and ?.=17. I will therefore calculate it at once. 
J^(ft=0-000095556839x-0-00000141808U’+0'000000001867x= 
= 0 •0012215 in parts of a degree 
= 448-25 feet. 
This, it will be soon seen, is the rise of the sea-lerel at Karachi abore that at Cape 
Comorin in consequence of the deficiency of attraction of the ocean, on the hypothesis 
as to depths which I have assumed. 
16. I will now consider the force arising from mountain attraction. It has been 
proved (m my Paper of 1855) that the Himmalayan Mass attracts points between A and 
C (in the diagram, fig. 1) as if it were a dense prism of great length and small transverse 
dimensions running about W.N.W and E.S.E., and cutting the meridian of the Great 
Ar-c at about 3° 30' north of Kaliana. The law of attraction for places between Kaliana 
and Damargida varies as the distance from this line inversely. For distances from 
this line greater than Damargida this law needs modification, for the following reason. 
A prism attracts a point opposite its middle with a force varying inversely as the 
product of the distances of the point from the middle and from either of the extremities. 
Hence when the point is not far from the prism in comparison with the prism’s length, 
the force will vary nearly as the inverse distance ; but when at a considerable distance, 
it will vary more nearly as the inverse square. 
The point where the line joining Punnce and Karachi cuts the 20° parallel of longi- 
tude is about equally distant with Damargida from the above fixed line (or axis) of the 
Himmalayas. I shall therefore take the deflection there to be the same as at Damargida, 
MDCCCLIX. 5 
