348 
ARCHDEACON PRATT ON THE CONSTITUTION 
In order to ascertain for what zones this simpler formula for R may be used, I observe 
that in the final result decimals are to be retained to the 7th place in the ratio of ver- 
tical attraction to gravity. Hence 3/3R-^720 wto must be calculated to seven places of 
decimals. The largest value j3 will have is 149°. Hence in 447R-p720nm a quantity 
as small as 0-0000001 must be retained, or a quantity in R as small as 0-000000161 mto, 
or say 0-00000016 wto, must be retained. Hence the neglected term 
or 
24 y ' (2 r- 
n 4 /h + mk\ 
+ 1 f) 01 24?\2r+ 1 ) 
22 \ 
wttt) 
must be <0-00000016 wto, 
2r + l><y^uyi-(l 
174 V nm\ 
whr)- 
When numerical values are given to the quantities involved it will be easy to find the 
least integral value of r which satisfies this condition ; that value of r shows the first 
zone for which the second form of R can be used. 
18. I purpose making, as I have already said, w=160. The several formula; now 
calculated in the last paragraph I gather together and write down here, n being put— 1G0. 
_ g$ R 
Resultant Vertical Attraction for zone= 
38400 m 
,, 2 cos <i> — cos 3c£> — cos 5$ n m(f 2 -2tt)-A 5 
R= — l+cos<p A 77 . - 7 - A--. i\ - 9 -—0-00020 v ' 
32(2?-+ I) 5 
r(r+ 1) 
tan <p = 0-04045 
^ 2r + 1 
or 
w 
hen 
K=-0 00082 ^^ 1 ) 4 + ( 2 ^ 1 ) 4 +' -5^+1) y ■ ■ ■ 
_ . h + mkr\ , 22 \~\i 
^r + 1 1S > ~ VgT [m (2 r + 1 ) 2 ) ] 
• (4) 
. ( 5 ) 
. ( 6 ) 
• (') 
§ 5. Numerical application of the formulae to find the “ Resultant Vertical Attraction ” 
of the Himalayas upon Stations of the Indian Arc of Meridian through Cape Comorin. 
19. The formulae of the last paragraph I shall now apply to find the resultant vertical 
attraction of the Himalayas at the three nearest of the stations I have entered in the 
Table in § 1, viz. Kaliana, Kalianpur, Damargida. The attraction at the rest can be 
found more simply. 1 shall take two cases of to, viz. to= 50 and to=100. 
