62 
ARCHDEACON PRATT ON THE ATTRACTION OF THE 
only one-sixteenth part greater than its smallest value, when dz=a-\-ip. 1 shall there- 
fore take this middle value instead of the variable value, and the expression (1.) be- 
comes integrable. Suppose h is the mean value of h from d=ci to 6=o(.-\-<p ; then 
Attraction of whole mass standing on the compartment BB'C'C 
( 2 .) 
By this approximation the attraction of the nearer and narrower part of the mass 
is made a little too small, and that of the further and wider part a little too large. 
These errors tend to counterbalance each other; and the residual error, if any, will 
be very trifling. In some of the compartments the compensation may be exact ; in 
others, in excess ; in others, in defect — according to the variations of k. So that 
taking all the masses on the lune, the probabilities are that the compensation on the 
whole will be perfect, and that no error will be incurred. 
si. 
cos^ - fl 
18. That the extreme values of — ^ do not differ more than one-fifteenth and 
sin -6 
one-sixteenth from its middle value appears as follows : — 
According to the law of dissection, which I shall soon adopt. 
9 = — a, when a is very small ; 
^=~cc, when a is about 38° ; 
(p=^a, when a is about 52° 30' ; 
a, when a is about 65°; 
ip=^a, when os is about 76° ; 
<p=^cc, when a is about 84°; 
<p=^a, when a is about 130°; 
and p has intermediate values for intermediate values of os, and of course the smaller 
the ratio which (p bears to os, the less will be the error in our approximation. Now 
out of 49 cases in which we have to use the formula (2.), 
