of Central Forces. 373 
Therefore it is evident, that if a body be 
aéed upon by a fingle force which tends to 
a fixed point, the law of that force being 
given, the equation of the curve it defcribes 
has been determined: except in that particular 
cafe where == 1, or the force is inverfely as 
the diftance of the body from the centre; for 
then the above equations fail. 
Take s:1:: velocity in the cutve at V (v): 
velocity in a circle at the fame diftance =, 
; J 
2 ) + n+4 
then 2+ r= Se) force: attr y sy 
xr r 
2 
Art om Ant 
whence v? == = elie) therefore 
Pah gba Xe 
2m n—l a 
sro repre and w= sox pasa which value of 
m may be fubftituted for it in any of the three 
equations found above. 
P? 2S 26 
When. m==1, we have 3 cmt At ; hence, 
o 
b ; P’v’ : 1 
y taking the fluents, oat ae ty WOE, rh but 
° . P V Vv 
at V, this equation becomes eo > A’ XK 
jog. +; therefore the fluent corre@ed gives 
r 
P* vy? 
2 p* 
2 . 
aa 7 = A’ x lg. cn But we have juft 
found 
