EEV. E. HAELET OX THE i\IETHOD OF SY]\OIETEIC PEODUCTS. 
355 
That result, arranging the terms according to descending powers of f, is 
n=^x 
— 4 d^cde 
' ' 1 
— 48 d%d 
+ 4 d'dde 
+ 8 d^de 
+ 12 d^bde 
+ 164 d'^dcd 
+ 16 d'bcd- 
+ 248 d^dd 
! +16 d^dd 
- 60 d%^d 
— 20 d%^ce 
-396 d^dd 
— 16 d%^d‘ 
+ 252 d^h'c 
-120 d^ddd 
1 
- 56 d-d 
+( 
+ 2 a}^ce^ 
+ 4 a}^<P^ 
— 2 a'‘6V 
+ 12 a}^bed^ 
-32 a'^^d^e 
-32 a'W 
— 96 d}'c"d-e 
-32 d‘cd'‘ 
-20 a‘«iW 
— 12 d^b'c^e' 
+ 168 
+ 96 
+ 592 
+ 768 
+ 160 
+ 384 
+ 102 
+ 16 
- 888 
— 1632 
a}%-cd'e 
(d^bc^de 
a}%c-d^ 
a''c‘e 
a'^cW- 
a}^f/ce~ 
d^b*d-e 
a'°SV</e 
— 1328 
— 6176 
— 2944 
— 256 
— 54 
36 
640 
2392 
+ 13824 
+ 23936 
+ 
+ 
+ 
a}'‘b-c*e 
d^b'^c^d' 
cd^be'd 
cd‘‘c’ 
a''6V 
«'^6“c(7e 
d^b^d^ 
d^b^c^e 
d^dc-dr 
d^ddd 
I 
+ 6208 
+ 180 
— 1420 
— 10200 
-56800 
— 36576 
+ 170 
+ 2460 
+ 58240 
+ 89360 
d^Ird 
d^b'de 
d^dc-e 
d^dcd~ 
d^dc^d 
d^dd 
a*'5®ce 
d-dd- 
d'^h'dd 
d-dd 
I 
+ 50 a' 
— 27600 d^dcd 
— 111200 d^dd 
+ 5000 d%^H 
+ 75000 
— 26250 dd'^c 
+ 3750 dd^ 
)r 
- 4 
d^dd 
1 
832 
d^dd*e 
1 
— 212480 
d'bc'e 
1 
2361200 
d'ddde 
r 1 
— 38200000 
d%^dd 
- 8 
d'bcd' 
+ 
38640 
d^dd^dd 
— 90880 
d^bdd- 
+ 
90400 
d-ddd;' 
— 54680000 
d%'’d 
+ 24 
d^bd'd 
— 
19392 
d'‘dc-d^e 
— 166400 
d^c^d 
— 
4461600 
d-dc’’e 
+ 150000 
dd'de 
+ 280 
d'dde^ 
+ 
5376 
d'^d-cd'^ 
+ 580 
d^dd 
— 
2585600 
d'dc*d- 
+ 3975000 
dd^c-e 
— 112 
d'‘cd^d 
+ 
24128 
d'^bc^d 
+ 49620 
dW'cde- 
— 
9792000 
d-dc'''d 
+ 1650000 
dd^cd^ 
+ 64 
d^d'^e 
+ 
6016 
d''Lc^d-e 
— 4560 
dddd^e 
— 
5024000 
dW 
+ 35550000 
dd^dd 
+ 12 
d%^d 
+ 
768 
d^bc^d^ 
+ 218240 
d'^d'de- 
+ 
96000 
d'dcd 
+ 85640000 
ddd 
- 628 
d%-cdd 
+ 
7168O 
d^dde 
+ 91920 
d^ddd'e 
+ 
29000 
d'dd-e 
— 1237500 
dd^ce 
+ 128 
d%-d^e- 
— 
21760 
d'^'c^d^ 
— 7680 
d^dcd^ 
+ 
1971000 
d'ddds 
— 300000 
dd^d- 
- 520 
d%dd 
— 
1760 
d^dcd 
+ 1554720 
d^dc^de 
8000 
d'dcd-' 
— 19925000 
dd'^dd 
-1392 
d%dd-e- 
— 
2160 
d^dd'd 
— 136320 
d^ddd^ 
+ 
7258000 
d^dc^e 
— 87550000 
dd^d 
+ 256 
d^'hcd*e 
— 
66000 
d*dc-de- 
+ 1500800 
dWd'e 
+ 
4188000 
d'dc^d- 
+ 162500 
dd^e 
— 256 
d%d^ 
+ 
19120 
d^dcd^e 
+ 793600 
dWdd- 
+ 25144000 
d^dc^d 
+ 6175000 
dd'^cd 
— 8576 
d^c^dd 
— 
1 856 
d'dd'^ 
+ 2028800 
d^ddd 
+ 21952000 
d^dd 
+ 58475000 
dd^d 
+ 6528 
d^c^d^e 
— 
114640 
d'ddd 
+ 499200 
d^bd 
— 
17500 
d'^d^d 
— 812500 
dd'^'d 
-1792 
d^dd^ 
— 
40320 
d%'^dd-e 
— 13500 
d'-dde- 
— 
855000 
d'^d^cde 
— 24625000 
dd^d 
+ 316 
d^ddd 
— 
2560 
d'ddd^ 
— 206300 
d-dc'd 
— 
10000 
d°b\P 
+ 5937500 
dd'c 
+ 1708 
d^ddd 
— 
529920 
d 'dc‘de 
— 88800 
d'-dcd'e 
— 
6985000 
d'ddde 
— 625000 
dd^ 
+ 3424 
d^dcdrd 
1 
+ 
9216O 
d^-ddd 
1 
+ 4800 
d-dd^ 
1 
— 
3660000 
d'^ddd? 
1 
