HIMALAYAS ON THE PLUMB-LINE IN INDIA. 
59 
Putting these values in the above expression, attraction of element at P on A in 
direction AT 
attraction of prism QR on A in direction AT 
~ fl6^ii«; {constant — sin from -4/ = 0 to -4/=^ ; 
sin 1 0— sin 0—c^ 
'ah sin co 
M 1 , 
=^COS2«U' 
M 
1 — cos W 1 ^ 
■ — ^ tan t; 6 
sin CO 2 
~'ah 2 ^ ^ ^ ^ 
14. Corollary. The above formula will reduce itself to the following in the cases 
to which we have to apply it. 
M 1 
Attraction of prism on A in direction AT=— ^cos- 
For in these cases AQ is the circumference, and O the centre, of the earth ; QR the 
height of any point of the surface above the sea-level at A. 
Now 
attraction of prism 
1 , 
cos - 9 
= cos cy — sin cy . tan 
M 1 . 1 1 f • . 1 ^ 
= -^ cos 2 n ^ 9 2 ^ I ^ I 2 ^ 
M 1 - 
=-0 cos t; — 7 ^ CO tan 
neglecting the square and higher powers of cy. But cy is never greater than 2° 
(=0*03488 in arcs), and when it has this maximum value, 6 is less than 2°; and as 0 
increases, cy decreases in a higher degree. Hence the second term within the brackets 
is of insensible importance, and the corollary as enunciated is true. 
15. In order to calculate the attraction of the superficial crust of the earth upon 
the point A on its surface, I shall suppose a number of vertical planes to be drawn 
through A making any angles with each other, and thus dividing the surface through 
A, parallel to the sea-level, into a number of lunes all meeting again in a point in the 
antipodes of A. About A as centre suppose a number of concentric circles drawn on 
this surface ; the law of the distances of these circles will be determined hereafter. In 
this way the whole surface will be divided into a number of four-sided compartments, 
two of the sides in every compartment converging to A, and the other two being 
parts of circles concentric in A. 
