HIMALAYAS ON THE PLUMB-LINE IN INDIA. 
<J3 
55. It may easily be shown from the results of the foregoing articles, that the 
formula above amounts to supposing, that the Himalayas and the regions beyond 
attract the three stations and all intermediate stations on the arc between Kaliana 
and Darnargida, as a bar of matter would, running about W.N.W. and E.S.E. at a 
distance of 222 miles from Kaliana, the length of the bar being infinite, its transverse 
section small, and its density such that the mass of the Himalayas and attracting 
regions beyond shall equal the mass of 1284 miles of its length. 
56. In order to deduce from this formula for the total deflection the deflection in 
the meridian, which is the part of most importance, we ought to know the azimuth 
of the vertical plane in which the total deflection takes place. This is not the same 
for the three stations A, B, and C. By article 43. it appears that the azimuths at 
those three stations are 31° 18', 21° 42', and 21° 31'. After various trials I find that 
the following formula represents the law with sufficient exactness. If & be the azi- 
muth (measured from the north), then 
. cos 31° 18' 
COS . 
1 — sin 1 0(/ — L) 
When /-L=0, 5° 23' 37", and 11° 27' 33", this gives ^=31° 18', 21° 35' and 19° 58'. 
This last differs by 1° 33' from the value in art. 43 ; but the second only by . These 
are sufficiently near the truth, as the cosine in the extreme case will differ from the 
truth by only about part. The formula for the azimuth departs most from 
the truth when /— L=9°, that is, at a point about half a degree south of the middle 
point between Kalianpur and Darnargida. But the form of the function is so chosen, 
that it does not vary much along the whole arc between those stations ; and the 
above-mentioned departure amounts to only one-seventieth part of the proper value. 
Between Kaliana and Kalianpur I think the formula will represent the azimuth very 
exactly; and although below that not with the same exactness, yet to a degree 
of approximation whieh will introduce no error of importance in the value of the 
deflection in the meridian. 
57 . We may show this by combining this formula with that deduced for the total 
defleetion in art. 54. Thus 
Defleetion in the meridian at any place of which the latitude is I— total deflection 
X cos^ 
114"-712 
~/-L-t-3-520^ 
cos 31° 18' 
T^sin 10(/-L) 
9&"-016 
(^— L-t-3-520)|l — ^sin 10(^— L) j 
When /— L=0, 5° 23' 37", and 11° 27' 33", this gives for the meridian deflections 
27"‘845, 1 1"‘965, and 7"‘207. These quantities, as calculated from the attracting 
MDCCCLV. o 
