340 
ARCHDEACON PRATT ON THE CONSTITUTION 
by laying down the heights on a plan, I come to the conclusion that the mass of the 
Himalayas may, for the purpose of this problem, be represented as a vast tableland, 
15,000 feet or 2*48091 miles above the sea-level. If a number of zones are drawn around 
the three stations Kaliana, Kalianpur, and Damargida, their width being about 50 miles 
(49*45 exactly, as will be seen further on), then the tableland will begin on the 2nd 
zone from Kaliana, the 8th from Kalianpur, and the 17th from Damargida; and the 
horizontal extent of the tableland lying on these and the following zones, as determined 
from the plan, is shown by the values of (3 in the following Table IV. In some cases 
/ 3 is made up of two or even of three portions added together, when the zones cross the 
tableland in two or more places, owing to its irregular outline. 
Table IV. 
Kaliana. 
Kalianpur. 
Damargida. 
Zones. 
js. 
Zones. 
( 5 . 
Zones. 
A 
2 
74 
8 
45 
17 
22 
3 
1 10 
9 
62 
18 
41 
4 
1 27 
10 
79 
19 
50 
5 
137 
11 
88 
20 
62 
6 
144 
J2 
92 
21 
68 
7 
149 
13 
97 
22 
73 
8 
113 
14 
76 
23 
58 
9 
88 
15 
58 
24 
46 
10 
79 
16 
47 
25 
32 
11 
66 
17 
46 
26 
9 
1 2 
56 
18 
35 
27 
12 
13 
• 109 
19 
76 
28 
12 
14 
87 
20 
46 
29 
12 
15 
79 
21 
6 
n; 
61 
22 
6 
17 
37 
§ 3. Formulas for the Vertical Attraction of a Spherical Cap of matter on the earth's 
surface on the mid points of its upper and lower surfaces , and of its divisions into 
a Central Portion and Zones. 
8. By a spherical cap is meant such a part of 
a spherical shell as would be generated by the 
revolution of the figure APQB round the vertical 
A B. 
A is the station attracted. The chord A P =u 
miles ; the thickness of each cap, above and below 
the station-level, is t miles. Let c and r be the 
distances of the attracted point A and of any par- 
ticle of the cap from O ; D the angle between c 
and r; z = c — r; u=c chord $; v=c vers $, which 
=w 2 -p2c. 
First. Suppose the cap immediately below the 
station-level. The attraction of an elementary ring 
c 
