of gen Forces. il 366 
It y be infinite, thane en P ear 
ae ee “a “| 
, Pp? = “m P® —.” . n 
a Vem P + VF ‘The body will 
oF Vim 
- therefore go off to an infinite diftance in 
a finite number of revolutions. 
But if y==o, the value of the ‘fenttians 
Vin P —PXV re mP oe 
Vin—1 y° ab 7?  P? ob M gee Te) 
nothing, wherefore .the body will make an 
infinite number of revolutions in defcending to 
the centre. From the above equations the 
trajectory may be conftructed. 
Next, if m==1, the equation of the trajectory 
being pale xy, the curve in io ig the body 
P. 
moves is the log. fpiral. But 2=+ ys ; 
x xa, therefore z= ts x log. when 
y a Pe rT 
the sehen afcends, and z= <A oan x lope? = 
é ge ew a een 
1 it defcends; wherefore, = body can 
neither defcend to the centre, nor go off to an 
infinite diftance in a finite number of revolu- 
tions. If P=r, or the body be projected at 
right angles to the line drawn from the centre, 
it is evident that it will defcribe a circle. 
Bbb ’ In 
