544 
[621 
621. 
ON THE NUMBER OF THE UNIVALENT RADICALS C„H W . 
[From the Philosophical Magazine, series 5, vol. m. (1877), pp. 34, 35.] 
I have just remarked that the determination is contained in my paper “On the 
Analytical Forms called Trees, &c.,” British Association Report, 1875, [610]; in fact, in 
the form C n H 2n -H, there is one carbon atom distinguished from the others by its being 
combined with (instead of 4, only) 3 other atoms; viz. these are 3 carbon atoms, 2 
carbon atoms and 1 hydrogen atom, or else 1 carbon atom and 2 hydrogen atoms 
(CH., methyl, is an exception; but here the number is =1). The number of carbon 
atoms thus combined with the first-mentioned atom is the number of main branches, 
which is thus = 3, 2, or 1; hence we have, number of radicals C il H 2n+1 is = 
No. of carbon root-trees C n with one main branch, 
+ No. of „ „ with two main branches, 
+ No. of „ „ with three main branches; 
and the three terms for the values n = 1 to 13 are given in Table VII. (pp. 454, 455 
of this volume) of the paper referred to. 
Thus, if n = 5, an extract from the Table (p. 454 of this volume), is 
Index x, or 
number of 
knots 
Index t, or num 
ber of main 
branches 
Altitude 
0 
1 
2 
3 
4 
5 
1 
1 
2 
1 
4 
2 
2 
1 
3 
3 
1 
1 
4 
1 
1 
Total ... 
1 
4 
3 
1 
9