Solution of a Problem in Fluaons. 331 
I will now notice some things which readily follow from what has 
been done. Let a, p’, be the same as before; P=3.14159, etc.= 
semicircumference of a circle rad. (1); T= the time of revolution 
of the particle in an ellipse around a centre of force at the focus; 
T’=do, around a centre of force at the centre ; the arbitrary constant 
¢ 
3 being (as heretofore) so assumed as to = the area described by 
(r), the radius vector around each centre of force in the assumed 
unit of time. At the seventy-third page of the last Journal I found 
ef? 
F eT ee the force to the focus of any conic section; suppose 
: e? : 
F Xr? =const. then 7] =const.; or p’ as c’?; (Prin. B. 1. sec. 3. 
ec’? 
prop. 14.) Suppose is that F xr? =const. then ? = const. as 
before ; but in the ellipse - =PV ap’ =the area; hence ae — 
= = =const.; or T as pete (P. B. 1. prop. 15.) By (2) of 
this paper, Fas ge mbpoee 
Pap F 
=const., yeaa =PV ay’, 3p, OF ‘aaa Es == const. = 
sabia F 
= apa": T’=const..° . in different ellipses, se — = const .T’ = const. 
the circle is here considered as an ellipse; ®. prop. 10. cor. 2.) 
i if F xr? ag in different conic sections, (as een 
vz 
= =const. but = =V the velocity.".Vis as ——3 (P. prop. 16). 
2 
By (8) of the last Journal, = me Vie ne or V as Jt (PY, 
prop. 16. cor. 6.) By (7)-- (8) -+(9) I have in any conic section 
dr 
ed but by (3) of last Journal, V : V’:: ee Vi 
= ae 
11 Vr’: : p; (P. prop. 16. cor. 9-) Again, p°=9777 > hence, 
Vi Vii Saar : Ya (10); the sign eT ee of 
the ellipse, and + in the hyperbola, and r is to be neglected in the 
