ee: ied 
of Central Forces. 417 
2 
= — If therefore 22> = 2V?yx 1—m = 
2V* —c’, the ‘curve will be a cycloid. Or if 
the value of x, in this cycloid, be taken to the 
correfponding value of x in the curve defcribed, 
ae.°7) v 2x 1—m to 4, the curve may be 
eafily conftructed. 
Cor. 4. It was found above that = ye ae 
Att 
——— 
—_ 
M1 XK" 
, and at the vertex of the curve A em 
3? 2 
o, therefore the correct fluent becomes — ha: J 32> 
gt! nda 3 ytd 
n—1 di y— 
Atti x 
, @ being the value of y 
x ; tig : 2 
when y =o. If therefore n= 0, then eee: 5 
drt aT b 
; by reduction x —= ———= 
eK Vad 
tL 
2 
=——; hence x = ——— x d—}| 
Vv d—y V¥2A 4 
b 
ViA 
x 
x eae , Making x om By when y=d. 
~The curve therefore is a parabola, whofe axis 
is perpendicular to the plane, latus retum = 
2 
7a and force = A, meafured by the velocity 
2 
generated in the time (1). 
Eff NOTE. 
