236 
and, again, the definite integral 
2 ( Y2 Samah oleae 2 ( Y2 
5 PS es a yh Y= : a : 
| \ine @ y —1) a+yPdxdy=F (Aa Ae) (nr e y? da dy: 
2) 
or, more generally, that the multiple definite integrals 
feels ... F(ays..). aty@sy... dadyda... 
M4 YY Z1 
and 
% ( Y2 [ Z2 SS 
= —-1.g—-1....).a+y8zy... 
ee L.y-1.s-1 ) . eeyPar dzdydz... 
may be reduced, respectively, to the simpler symbolic forms 
F (eDatPptP,t +++) leele he .. ceylar... dedyde... 
TY Zy 
and 
GAS Na a Seens ) [Fe ralve .. aryhsr... drdydz... 
MY" 2 
7. Again, it appears from considerations suggested in the last article, 
that the definite integral 
22 [y2 x %2 (Y2 
(2 \ ‘3 (=) aS (Pa "E) " ie i any? dacdy, 
and the definite integral 
we (y2__f(a—t A,\ (2 (¥ 
| | r(=). anyPdady -¥(=*) |r) x2 yF dady ; 
HI Y1 y-1 Ag 
or, more generally, that the definite integral of the fourth order 
he Pals le F (=) aeybsiw® dady dzdw 
H4Y1 71 Wi yw 
may be reduced to the symbolic form 
F (ePatPy gt )) . [es la | at Pe x2 yh zt we da dy dz dw, 
1 
- U4 Y14 ZW 
and the corresponding definite integral 
la | cee ee 3d: 
(ss z irs F (aS) ~& Yy Best w dx dy dadw 
to the symbolic form 
An) XS Mae | 72 We 
F( a x). { “lp | 5 x2 y8siw da dy dzdw. 
Ag. Ag ]) “EYL 210 at 
