THE OCEAN ON THE PLUMB-LINE IN INDIA. 
781 
stations of the two higher portions of the Great Arc : P is Punnoe, the station close to 
Cape Comorin. Draw EPF east and west, meeting Africa in E and the Malay Peninsula 
in F. I call the depths at the middle points, viz. at a and h, of these lines at the open- 
ing of the Arabian Sea and Bay of Bengal into the Indian Ocean, a and h : and I 
assume that the bottom slopes up gradually from these points in lines due north to 
m and n, near Karachi and the Sandheads of Calcutta ; and that the bottom shelves 
doy.m to these lines from every part of the shore. Thus to find the depth at any point 
H, we must draw KKJc at right angles to am ; first find the depth at h in terms of «, 
from the measured ratio of mh to ma ; then find the depth at H in terms of that at h, 
and so in terms of «, from the measured ratio of 'Rk to Jik. In this way the depth at 
aU points in the Ai-abian Sea and the Bay of Bengal may be found in terms of a and h. 
I next assume that at a point D, 36° south of Cape Comorin and nearly midway between 
Madagascar and Australia, the depth is D ; and that the bottom slopes down gradually 
to D from all sides— from the bottom at FP and PE, from the shores on the east and 
west, and from the neighbourhood of the south pole. It will soon be seen that any 
imcertainty regarding the depth down towards the south pole is comparatively unim- 
portant. From this description it will be seen that the depth along any line PI may 
be found as follows : — The bottom slopes down to L from both shores : the depth at L 
IS known in terms of « and D from the ratio of «L to LD. Again, the depths along a 
line CMKQ are found thus. The depth at M is found in terms of a from the slope of P«. 
From M to N the bottom slopes to a depth which is found in terms of D by the relative 
distance of N from Madagascar, the nearest shore, and D. By this contrivance the 
depths of aU parts of the ocean under examination can be found in terms of one or more 
of the arbitrary depths a, h, D : and by rightly choosing these quantities I think we shall 
have a very good average representation of the volume and general form of the ocean, 
as far as its effect on the stations in India require a knowledge of it. The effect of the 
ocean to the right of the eastern peninsula and archipelago I have omitted, as it would 
be about the same for all the stations. 
§ 3. Calculation of the attractions and defiections. 
5. The method^ of calculating the attraction is precisely the same as that adopted in 
my Paper of 1855 for the Mountains. Thus for the station P. Through P imagine 
great circles drawn (not given in the diagram to prevent confusion) at 30° apart. These 
^vi]l diAde the surface into lunes reaching to the antipodes. The lines drawn in the 
diagram are the middle or dividing lines of these lunes, along which the attraction acts. 
Around P describe a ch’cle with radius =5°; and beyond this other circles with the radii 
noted m the Table in page 782. The property of this law of dissection is, that the 
attractions of the masses of the several compartments into which this process divides the 
surface, are proportional to their average depths; or if d,d^d^...he the depths, the 
attractions of the masses on P are as d,d^d^... The attraction of each mass^' 
X depth. Now the density of sea water =1‘028 x dens, of distilled water. 
* See p. 64 of Paper of 1855. 
