AECHDEACON PEATT ON THE ENDIAN AEG OE MEEIDIAN. 
581 
that required by the fluid-law, and showed that the eflect might be very sensible and 
important. The results of the calculation were embodied in the following Table : — 
Table of Deflectioxs, caused by an excess or defect of matter throughout a semi-cubic 
space of 4 millions of cubic miles, — the mean density of the excess or defect being 
Y^th part of the density of the earth at the depth of the centre of the cubic space. 
Depth of the centre 
of the 
semi -cubic Space. 
Distance, measured along the chord, from the station to the point 
where the radius of the earth di-awn through the middle 
point of the semi-cubic space meets the earth’s surface. 
379 miles. 
581 miles. 
781 miles. 
980 miles. 
1173 miles. 
50 miles 
1-940 
0-835 
0-457 
0-248 
0-118 
1.50 miles 
1-621 
0-803 
0-456 
0-252 
0-120 
250 miles 
1-383 
0-782 
0-483 
0-272 
0-131 
350 miles 
1-067 
0-749 
0-490 
0-286 
0-142 
450 miles 
0-663 
0-713 
0-425 
0-277 
0-145 
(3) In my third paper * I calculated the effect on the plumb-line of the deficiency of 
attracting matter in the Ocean. I assumed the following law, as giving an average 
representation of the mass of Avater ; viz. that the depths at the middle of the Bay of 
Bengal and of the Arabian Sea in the latitude of Cape Comorin, and at the mid-point 
between Madagascar and Australia, are severally f, 1 and 3 miles, and that the bottom 
slopes from the shores to these points, or to lines joining the first two with the third, or 
to other lines drawn northwards from those two points. 
The meridian deflections toward the north at the three stations were made to be 6"T8, 
9"-00, and 10"-44, causing an increase in the amplitudes equal to 2"-81 and l"-44. 
On combining these with the effect of the mountains, the deflections are 34"T6, 
21"'05, and 17"‘23, and therefore the true amplitudes 13"T1 and 3"-82 greater than 
the observed or astronomical amplitudes. 
These are the main results of my calculations. 
3. In the Great Trigonometrical Survey of India, which has been conducted with so 
much care and ability, the amplitudes of the two arcs in question, calculated geodeti- 
cally on the supposition of the Indian Arc being curved like the mean arc, came out, 
the first 5"-236 in excess, and the second 3"-791 in defect, of the amplitudes observed 
astronomically. Neither the attraction of the mountains, nor that of the ocean com- 
bined with it, as appears from the last paragraph, would account for these, and especi- 
ally for the negative sign. The other cause treated of (a variation in the density of the 
crust) being purely hypothetical and, if existent, yet altogether unknown in position and 
extent, it seemed hopeless to look for any precise explanation of the deviations of the 
plumb-line from that quarter, although the sufficiency of the cause to produce a sensible 
deflection was demonstrated. 
I therefore attempted in each paper to explain the difference by attributing it to the 
* PEilosophical Transactions, 1859, p. 779. 
4 K 2 
