j)3 Mr. waring on the General 
yff-'+xf- 1 * fe *- 1 +$—' + ^’ 1 ~ l +yo n - l +^/-' + &c.(- n) 
s-bxvxpx a 2 /?~ a + jg ‘a— + «*/“* + yV~ 2 + 0*/ -1 + y l f/‘~ z 
+a i <?‘* L * + to.*- 2 - + + 6' 2 /3'‘~ z + Sec. (- n) + ctp x- 
a 3 /3 H “ 3 + / 6 3 a”“ 3 +a 3 /~ 3 + y V~ 3 + /Sy -3 + y 3 ^" -3 + « 3 /S”“ 3 + 
&c. (- ») + <*/> x a 4 /3' ! ~ 4 +/5V~ 4 + 
et 4 /-4+y4 < x B -^y- + +y 4 i (5 s -4+8c C . (-«), + &cc.--np(au+ 
bv + ct-rds + &x.) 
If « = 2 a, then will the coefficient of h z p be i. e» 
the above-mentioned coefficient will be-^>(<3 , «+^+ 
£/ + f/a'+..... + 4 Z> ? ). 
The fum of the contents of every three of the a- 
bove-mentioned values or roots, which is the coefficient 
of the fourth term of the equation required, will be 
cd s/p 1 x otfty + a. fid + ay 3 + j 6yd + Sec, (o) rra/bSyp* x 
ufiy* + uyft* + ftyod + «/3<T + &c. (a) + &e. + cfv Z/p" x 
u!3y ,! - 1 + ocylS K - z + fcyo/- 1 + a^ n ~ 2 + u^ n ~ + Sec. ) +. 
abt/yf X ai 6y~ 3 7^/iF^ Tfa- y~ 3 +py i c/‘-i+yK l (5 n - i +■ 
yp> 2 od~ 3 + oi^ 1 S a ~ i Sec. (i. 2 .n) + See ; and in general alb 
the terms (unlefs the quantity Z/p 13 contained in the 
term have this formula s/p n — p, or Z/p zn —p 2 ') will be=o ; 
let the general term be denoted by hlkS/p'^^^' x 
&F$ y + aFfiy + tfpy + aJyy- +Fyy +^ v / 5 A y^+«^J v + &<T.. 
firft let X+y.+v neither be equal to /z or 2 #, then will the 
term* 
