4*4 Mf. Babbage’s essay towards 
equal to p fcpx , we find 
-I r 
<p J n p OC = CtX 
and by taking p on both sides, it becomes 
j n pX=pxdC 
give/ some particular value and determine 
problem. 
Problem XIV. 
Given the equation 
a, Q oc = y a: 
Assume 
4/ X = p f pfoc 
<p as in the last 
hence 4'«4 / $a? = (p fpfap fpjfioc 
i i 
make/ = a\ then the equation becomes 
i 
<p f(p<p f (p U fi OC — p /* (p a (3x = <yx 
and by taking p on both sides 
f a (poi(sx==<p'yx 
this is an equation of the first order relative to <p. 
The equation ^ ^ . ( n ) 4> (iy — yy might be solved in 
the same manner, but they are both reducible by a simple 
transformation to the form 
Vy — Fy 
Problem XIV. 
Another method of solving the equation 
4 /* x = a? 
Assume 4 , a? = <p/ <p a?, then 4 /- a? = <p /* <p a?, and we have 
(p 1 / 2 <p a? = a?. 
Lety = (pa?, then a? = (p ‘y and the equation becomes 
<P f*y = $ y 
