70 
Mr. Robertson on the Precession 
3v/ 6 2 — 
X s / C 2 — X a — 3\/ C - — X 2 XX - X == C 2 X — X " X X v/ C 2 — X 2 — 
x 2 x x 2 x = c x V c 1 — x 2 — 4X 2 x s/ c 2 — x 2 . Conse- 
is x V" c* — x 2 x x 2 x V c * — x 2 ; 
4 
2 bf 
X x C Z — X Z z 
quentlythe fluxion of 
and the fluxion of x x ^ is ~~ x x V c* — x 2 x - — ~ 
c z 4 c z 4 c z 
x x x v/ c 2 —x 2 . Hence the fluent of x x c 2 — x 2 x 
c z 4 
x x 2 x V c 2 — x 2 = the fluent of xxV^ c 2 — x 2 x the 
fluent of ■— 
» X X 2 X Vc 2 —X 2 = X - * - -~ 
c 2 c 4 
; and therefore 
by transposition, the fluent of ~~ x xV c 2 — x 2 x x 
— ~ x ' z = the fluent of x x z x V r 2 — x 2 . Again, as VI is 
equal to ^ v/.t 2 ~ x 2 , the fluxion of the area DVIF is y \/ c 2 — x a 
xy = xx \/ c 2 — x 2 , and therefore the fluent of x x 
V c — x 2 is the area DVIF ; and the fluent of x x V c 2 — x 2 x 
r £ 
£** C 7, C z 
— is the area DVIF x — • Consequently the area DVIF x — — 
, zh f x * x c - ~- . l t — the fluent of x x 2 x V c — x 2 , and there- 
c 2 4 c 
dfe T>t7TT- c 2 dfg 2 bf xxc 2 —x 2 It 
for * area DVIFx - - -£■ x -/• x = 
ent of — 7- x xx' xV c'—x', or the force of the particles 
in the area DVIF to turn the ellipse. Hence, when x becomes 
equal to c , the force of all the particles in the semi-ellipse 
DGF, to turn the ellipse, is equal to the semi-ellipse DGF x 
- x — = the semi-ellipse DGF x — x — x By article it, 
therefore, the force of all the particles in the whole ellipse', 
which tend to turn it about the centre, is the whole ellipse 
PELQxfx^xg-. 
x — - == the flu- 
