188 4 
‘«* Now let us compare this with 
3 {(y +juy? (2+ hay? + (+ he) (yt jx)"}, 
to which the analogy of example (2) in my former Paper, 
p- 163, might lead us to expect to find it equal. 
** Developing by the binomial theorem, we have 
(y+ joy? (2+ ha ay et —a (jy shy zt) 
~ 2 (y? ord 2 ufZt +y) Zz) 
+23 (jyte? + kysz? +jy%z? + ky z+) 
+24 (y 82) —iytz? + ytz3 iy? zt t+ yz’) 
—-2° ( ym af hy®z* a ys ay hye ae jyZ b (B) 
co 
+ hy z*) 
— (yiz) a iy *z* ae yz = iy tz 4 yz 
2 ty *z® + yp z7 ) 
Ea ical lus nay J 
And (z+ a)" (y+ja) differs from this only in the signs of 
the terms containing 7. Consequently, the development of 
4 {y+ jay (2+ha)? 4+ (e+hey (yt+jzy} 
differs from the series just given only by the omission of these 
terms. But this omission will not make it agree with the ex- 
pression already found for 7 yz". 
«‘ The discrepancy first shows itselfin the numerical coeffi- 
cients of the terms 
sy%2, sy%z*, and sty%z°. 
In the former development (A) these coefficients are all =4. 
In the latter (B) to unity. 
‘* Again, the coefficients of a°y*z*, ay%z4, a8y?z*, 2y*z”, 
asy®z*, and 2*y*z* are all equal in (A) to }, in (B) to unity. 
It is needless to proceed further in the comparison of the two 
developments. 
«¢ As regards the first instance of disagreement, viz. that 
between the coefficients in the two series of the terms 2°y“z= 
and a*y?z*; it must be observed that in (B) these terms have 
