188 
‘* Now let us compare this with 
2 ((y + ju)? (2+ hay + (2 + he) (y+ jay}, 
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 + ja)? (2+ he) =y 27 — @ (jy?21 + Rhy 2) 
~ 2 (yez7 fe gem +y> Zz) 
+23 (jytet + hyz* + jy%2 + ky tz) 
+ at (y oz) —iyte? + yz iy? et + ye) 
— x ( Jy=) a hy?z? 4 jyiz ae hy?z4 ae Wee L (B) 
——— = —__] 
+ ky z°) 
— 76 Grice ra iy*z” 4 pre is iy te 4 oz? 
ta Were ai ae ) 
PSEC sihe Yea |e J 
And (z+ a)" (y+ jx)" differs from this only in the signs of 
the terms containing 7. Consequently, the development of 
aly+ jay? (2+ha)*+(2+he) (y+ jay} 
differs from the series just given only by the omission of these 
terms. But this omission willnot make it agree with the ex- 
pression already found for 7 yz". 
“‘ The discrepancy first shows itselfin the numerical coeffi- 
cients of the terms 
ey 2, xyz, and xty%zs. 
In the former development (A) these coefficients are all =3. 
In the latter (B) to unity. 
«« Again, the coefficients of a®yz*, ay%z4, aty?z', ay oz, 
ay 2%, and 2*y*z* are all equal in (A) to 3, 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*z2 
and «y*z*; it must be observed that in (B) these terms have 
