* 
344 - Central Forces. 
the place of the particle, estimating the chord onr. Then, since 
d. 
‘cde =Tridz, ap = coeds (7) is easily changed to the forms 
c’2 dr2 d 4 ‘ot. 2 
= <ed(= ia) - =. —c?d (=) — Tcot.p= 
Qdr : Qdr 
¢/? 2 2 
oo 34(wainwy)-Teott=-Fa(5 ~Teotp= ap Tet 
ee dr 
V2dp V2 c/2 gts 
= pdr Suede — Tcot.L = eR Obl =aReneb 
Mos, cf? cdc ~ ce 
‘Leo: b= earned ESE phos Tcot.)=-—d (ar) 
Qdr 2dr 
c’? ' d.V? fy 
Dp +T tan.lb=- Sar + sin-beosas— 
Qdr : 
aE 
sin.beos.p > Loot = - a( 
d.V? 
Teonp== = +Ttan.L=F, (D). 
If the disturbing force acts constantly ‘in the direction of the ele- 
ments of s and is denoted by F’, and if F” denotes the attraction 
towards the first centre, then F=F”—F’cos.l, T=F’sin.l; by 
substituting these values of F and T in (D), since —F’cos-) is 
2 
7 
found on both sides of the resulting equations, they become >; — 
ce’? 7 dr? ce? 2 ‘seot.2 (72 1 e470 
$4 sas) = So ee oe 34a) ee zp) 
or a ee: dr 
< c2dp V2 dp V? ¢/2 é Re c’? 
pir pdr -R~p?R~r?Rsnp — to 
Qdr 
c/? 
pn eee F.- a¥2.  .d¥e Bde 
r? sin.? dr - ) eos. b= ~— dr t cos. dr des 
2d: : 
ees 
=F”, (E). It is evident that the formule (E) will apply whether 
the force F’ is accelerating or retarding ; for instance, they are ap- 
plicable when the particle moves in a resisting medium, in which 
case teal particle is retarded in the direction of the elements of s, and 
as FY isa retarding force its sign must be changed; also, the siga 
