The Inverse Method of Central Forces. 103 
1 1 
flexure, viz. y = —3— x y= x 1; which will 
Cry 
be greater or less than r, according as ” is greater 
or less than g; ¢ being less than unity. Substitute 
this value of y in the above equation, and, at the 
same time, suppose y = #; then the point of con- 
trary flexure will be at an apse: therefore a simi- 
lar and equal curve will be described on the other 
side the apse that was described before : but this 
is impossible, as the curve is now convex towards 
the centre of force; wherefore the body, upon this 
supposition, can never arrive at an apse, but will 
continually approach nearer and nearer to a circle 
described at the distance y determined above; 
which circle wil] therefore be an asymptote to the 
orbit, or spiral described. By substitution 
Ls ped 
jess Mm b ier I” a—t1 
¢f-* xX Van — my 
n—1 <2uS 
ir eeeg perpen: ~ ot Kor tak 
ltt 
M—iakc. Pyar 
m P? oo 
,or= 
Sai sa | Soo 
(»— i+cx if ete! 
q74 qg—1 
Hele 
m P* c-* 
Sel g ba eM ha a 
(mmate. =) x Bi 
quart 
