372 | The Inverfe Method 
If a body defcend directly towards the centre 
1 
by an accelerating force = - », ah ea the 
velocity it has acquired when at the diftance y 
from that centre, then it is well known that 
Att 
“% —j=uu. Take the fluents; then 
«a4 
; 2 in 
a—1 xX jy" 2 ae x or “ 
requires no correction if the body defcend from 
an infinite height; for in that cafe both fides 
of the equation vanifh at the fame time. At 
the point V, therefore, or at the diftance r from 
the centre, the {quare of the velocity acquired 
by defcending from an infinite height = 
n--3 n-f-s 
2 & . Let therefore in general am Ane 
m——i K r?—* n—~1 Xr"! 
= v?, where m may be either greater, equal to, 
or lefs than unity. Hence by fubftitution and 
reduction, we have 
V aaxPy es = 
ie bi aha ye * ™m {* 1 
i Seaegees 
n—t1 x 1 
= fi Serie 
2. p= 2 hea) a3 
gg oe 
ms 1—m x Psy . - 
3 P= : m 2A 
ct tle 
— yo There- 
