406] 
ON THE CURVES WHICH SATISFY GIVEN CONDITIONS. 
261 
[11111] = + 6o 
- 20 
+ i5 
- 30 
+ 5 
+ 30 
- 10 
- 30 
+ 10 
- 15 
+ 10 
(14) (13) (12) (11) 
(14)(13)(111) 
(14)(22)(11)(11) 
(14) (112) (11) 
(14) (1111) 
(23)(12)(11)(11) 
(23)(111)(11) 
(113)(12)(11) 
(113)(111) 
(122) (11) (11) 
(1112)(11) 
(11111). 
To form the symbolic parts, we follow each branch of the tree to each point of 
its course: thus from the branch 113 we have 
(113) belonging to [113], 
(113) (111) „ [11111], 
(113) (12) „ [1112], 
(113) (12) (11) „ [Hill]; 
viz. (113) belongs to [113]; (113)(111), read 11 (3 replaced by) 111, belongs to [11111]; 
(113) (12), read 11 (3 replaced by) 12, belongs to 1112; (113) (12) (11), read 11 (3 
replaced by) 1 (2 replaced by) 11, belongs to [11111]. 
And observe that where (as, for example, with the symbol 122) there are branches 
derived from two or more figures, we pursue each such branch separately, and also 
all or any of them simultaneously to every point in the course of such branch or 
branches; thus for the branch 122 we have 
(122) 
(122)(ll)j 
(122)(11)J 
(122)(11)(11) 
(same twice) 
belonging to [122], 
[H12], 
[11111]. 
Similarly for the branch 23 we have 
(23) belonging to [23], 
(23)(111) 
» 
[1112], 
(23)(12) 
[122], 
(23) (12) (11) (same as infra) 
» 
[1112], 
(23)(11)(111) 
[11111], 
(23) (11) (12) (same as supra) 
?> 
[1112], 
(23)(11)(12)(11) 
[11111].