374 The Inverfe Method 
Ant 2 
found that = OM jae (+ =) * upon the pre- 
2 
fent fuppofition ; therefore A? = = fubftitute 
2 
and reduce, then p* = a Ow? sees 
1 IY, log. sf 
a J 
Re a ane 5 Pad 
, the equation of the curve. 
Vine i +75 z X bog. — 
Next, to find hae angle defcribed, or r the Nat 
of the line joining the centre of force and the 
body in refpect of the line CV for any given 
value of it. By fimilar triangles we. have 
y? : p? ::tn® :¢v?, and by divifion, 
y>_p® +p? s:'un®: iv? 
aii vast sene TO oan 
exe. ep? ye tir? pe tsun® 2X2 i22 9% 282 (eben. 
ing fuppofed = XY) ; confequently 
é beets whatever be the 
Vy — pi 
value of n. Subftitute therefore, in this. equa- 
tion, the feveral values of p found above, and 
there will arife the following equations: 
Pay cae —— x Py) 
% 
Tas a i 
Dee n— m 2 al—2 m1 
m—1 
. rP = 3 ry 
2 Nae 7 Ss z tat 
n—1 —__. Pp ayn— — 
eee oi ys oa aes 
