Solution of a Problem in Fluaions. 329 
Arr. VII.—Solution of a Problem in Fluxtons ; by Prof. Tuxo- 
DORE STRONG. 
(Continued from p. 73 of this Volume.) 
TO PROFESSOR SILLIMAN. 
New Brunswick, Nov. 9, 1829. 
Dear Sir—I send you the following continuation of my paper. 
Yours respectfully, T. Srrone. 
; 72 
The same notation being retained; the form F= 5d (*) 
dr 
applies easily to the case in which the particle describes an ellipse, 
the centre of force being at the centre. Let a, p’, be the same as 
at the 72d page of the last Journal: then by what was there found, 
(since p=half the sum of the perpendiculars from the foci to the tan- 
gent at the place of the particle; the distance of its foot from the 
point of contact being half the difference of their pr: from the 
Ss or F 
same point) ; I have a? --ap’ — 
=a) 
cn =r*; the etiipse be- 
comes an hyperbola, the centre of force at the centre; and Fas 
—r; hence it is repulsive. Substitute in (2) for e’?, its equal 
rtdy omy 
2 
datz? 
as r. By changing (1) into a? 
change the ellipse into a parabola by ee its centre to 
an infinite distance 5 ; which makes 7 parallel to a; = =1; put 
rdy 
“Gi =V the velocity parallel to ¥ ordinates to the axis =const. and 
(2) becomes in the parabola P=" =cons. (Prin. B. 1. sec. 2. 
prop 10. and sch.) The form (1) of the Journal (for July) is easily 
adapted to the case of the particle describing a curve, when acted on 
by a force parallel to the ordinates (y) which are perpendicular to 
ec’? cosec. ina 
the abscisses (x). For (I) can be changed to ——, 
c ae” *b) =F (3); since the force acts in parallel ae 
= XVII.—No. 2. 15 
