MATHEMATICAL SECTION. 43 
mn’ cos ¢ 1—ecose = ’ 
— Tafa {4 aa oh ae, 
If we now put 
and also 
A =—acosz — ae cose cos7 + sin z sin ¢ 
€ cos g 
a(2—e)., : 
CA ld IRI ge ta) forse te 
cos @ 
: , ae ; 
B =—asinz — ae cose sin z — ——— coszsin ¢ 
€ cos 9 
a (2—@é d : 
$ SC) os x sin © cos ¢ + 2a sin = cost 6 
we obtain 
cig : in <” 
< =" Sae{a A, f= a 4B, Se ae } 
_we ry cose f S 
This expression contains the following integrals: 
Qn 
de’ 
= a 
R= {rep +. p,) —@ q, cose’ — a's sin aye 
c?) 
sa sin ¢’ de’ 
BAECs + p) —a@ q, cose’ — a's “sin oy}? 
cos < de’ 
dared Bes + p,) —@ q, cose’ — a's ain oy 
oO 
which must be computed for every value of © obtained by dividing 
the circumference into 7 parts. 
If we put 
a® +p. =; aq =¢ cos Q; a’ s = q sin Q, 
we get . 
{(@” + p,) —@ q, cose’ — a’ 8 sin e\-t 
= {1—q cos (e’ — a}? 
s lp 20," cos (c’ — Q) + oa.” cos 2 (c’ — Q) +--- 
