354 
AECHDEACON PEATT ON THE CONSTITUTION 
of each of these towards the point of division equals the mass of each divided by the 
product of the distances of its extremities from the station. Hence the deficiency of 
vertical attraction of the sea on the station in question 
= - 3 f 0-637 
4 c 
zdudz 
-l-9y 
Q z z +{u + ay 8c 
f U ! /A+(w + «) 2 \ 7 
J. 
Suppose matter equal in amount to the deficiency in the ocean is spread down uniformly 
through a depth m . z. Then 
Resultant Vertical Attraction = 
1-9 g 
8c 
I , w¥+(# + fl ) 2 
- log e 
m ° e 
(' u + a ) 
2 
( 1+ » 
lo 
z^+ju + a)- 
(w + «) 2 
du 
\'9g C u (m— 1); 
■ 9 du 
1'9</ H 2 
8c x t«w nearl y. = ± irnw( m - 1 )y 
u l 
{u + af 
du 
U + a , 
. l 
« 1 
h U + a/ 
This formula I will apply to find the effect of the sea upon our stations. I will sup- 
pose that the bottom shelves down at the same angle on an average on the east and the 
west coasts, so as to make H-=-U = l 4-600, but that on the east coast U=600, and on 
the west 900 miles. 
The distances of the five stations from the east coast are about 0, 180, 330, 560, 840 
miles; and from the west coast about 0, 190, 300, 480, 700 miles. The distances of 
Alleppy and Mangalore from the east coast are about 120 and 350 miles ; and of Madras 
and Cocanada from the west coast about 350 and 560. For these the formula gives as 
follows : — 
Table VI. 
East Coast, 
West Coast, 
Totals, 
Stations. 
m— 50. 
W— 100. 
»i=5 0. 
«i=100. 
m=50. 
m— 100. 
Punnae 
0 0000050 g 
0-0000100 q 
00000077 g 
00000154 g 
00000127 g 
000(10254 g 
Bangalore 
0-0000018,, 
0-0000036 „ 
0-0000032 „ 
0-0000064 „ 
0-0000050 „ 
0-0000109,, 
Damargida 
0 0000010 „ 
0-0000020 „ 
0-0000024 „ 
0-0000048 „ 
0 0000034 „ 
0-0000068 „ 
Kalianpur 
0-0000006 „ 
0 0000012 „ 
0-0000016 „ 
0 0000032 „ 
0 0000022 „ 
0 0000044 „ 
Kaliana 
0 0000003 „ 
0-0000006 „ 
0 0000012 „ 
0-0000024 „ 
0-0000015 „ 
0-0000030 „ 
Punnae 
0 0000050 „ 
00000100,, 
0-0000100 „ 
0-0000200 „ 
0-0000127,, 
0 0000254 „ 
Alleppy 
00000022 „ 
0 0000044 „ 
0 0000044 „ 
0-0000088 „ 
0 0000099 „ 
O 0000198 „ 
Mangalore 
0-0000010,, 
0-0000020 „ 
0-0000020 ., 
0 0000040 „ 
0-0000087 „ 
0 0000174 „ 
Madras 
0-0000050 „ 
00000100,, 
0 0000100,, 
0-0000200 „ 
0 0000072 „ 
0-0000144 „ 
Cocanada 
0-0000050 „ 
0 0000100 „ 
0-0000100,, 
0 0000200 „ 
0-0000066 „ 
0-0000132 „ 
22. I will now take the case of an Island, and suppose it to be in the form of a 
cylinder of radius a in a sea of uniform depth h. Then by formula (1) we easily obtain 
the following result : — 
Resultant Vertical Attraction at the middle of the Island 
4c [ m m K 1 v 1 J 
_a+(l+m)h- ^ 8 +il±gg; + ljH; (ffi+/i _y a q^r ) l 
m m ' J 
— 4c\ — \/ d 1 hr) 
1 +m 
m 
2Kfi Yh)mb uhein S ^rge. 
