344 
A TENTH MEMOIR ON QUANTICS. 
[693 
R.G.F. of quintic = 
Deg-orders. 
1 .1 - b 5 
0.0-10.10 
+ d .1 — ag- 
3.3-12. 8 
+ e . 1 — b 2 
3.5- 7. 9 
+/ .1-6 
3.9- 5.11 
+ h . 1 — ag 2 
4.4-13. 9 
-4-i . 1 — b 2 g 
4.6-12.10 
+j .1 -ag* 
5.1-14. 6 
4- k . 1 — b 2 
5.3- 9. 7 
4- l . 1 —bg 
5.7-11. 9 
+ m . 1 - ag 2 
6.2-15. 7 
+ n . 1 — b-g 
6.4-14. 8 
+ o . 1 — b 3 
7.1-13. 7 
+ p . 1 -b-g 
7.5-15. 9 
+ r . 1 — b-g 
8.2-16. 6 
+ dj . 1 — ag 2 
8.4-17. 9 
+ s . 1 — abg 
9.3-16.10 
+ hj . 1 - ag 2 
9.5-18.10 
+f -l-ctg 2 
10.2-19. 7 
+jlc . 1 -b 2 g 
10.4-18. 8 
4-t . 1 — b 3 
11.1-17. 7 
+jm. 1 — ag 2 
11.3-20. 8 
+jo . 1 - bg 
12.2-18. 4 
+ v . 1 — b 5 
13.1-23.11 
+ js .1 -bg 
14.4-20. 6 
+jt .1 -g 
16.2-20. 2 
+ w . 1 — a 
18.0-19. 5 
Y—a.l—b.Y—c.Y—g.Y—q.Y—u, 
where observe that each negative term of the numerator is equal to a positive term 
multiplied by a power or product of terms a, b, g, contained in the denominator: 
this is the condition above referred to. The expansion thus consists only of terms 
each with the coefficient +1 ; for instance, a part of the function is 
s (1 — abg) s 1 — abg 
\ — a.\ — b.\—c.Y—g.\ — q.\—u’ \—c.\—q.Y—u'Y—a.Y—b.Y—g ,