240 Prof. J. J. Thomson on the 
e L 1 ) 
Ap. p45 oe a i aa 
re} Oh == sin® = 
n vt) 

ST 
3 COS 
nr 

ol SOF 
sine —= 
n 
The coefficient of gp, in the expression for R, vanishes, 
since sr 
COs: —- 
n 
> =): 
ous 
sin? — 
n 
As A,.p+s Bp.p+, do not involve p, it is more convenient 
to use the symbols A, and B, for these quantities, and to 
write 

be 
ye ie S—p,A!—ZppisAs~ aDhp1sB; 
The tangential force ©, acting on the p’th particle may 
similarly be written 
0,= > Pp+sBs —adb,C + a2dp4sCz, 
where 
cos cos 
e n if n le pas Qer 
O= gal a (oot + gten7) + a, (cot + gts) tan) 
sin i sin” oA 

a 4) Gus 
C e n cbt Sr 2 lis ST) | 
a ie Oi n 2 nj? 
Sie == 
”) 
while Z,, the force at EM angles to the plane of the orbit, is 
given by the equation — 
: Ly= %pD —Zzp45Ds, 


where 
e” 1 eve ih 
— — @ ae + ; a aia . 
Bak. ie We ke ee .,(n—l)r 
= Sin? = siae = — SUE Ogee 
n n n 
and 
ne  @? it 
Ue Rae. str* 
sin 

