610] 
427 
610. 
ON THE ANALYTICAL FORMS CALLED TREES, WITH APPLI 
CATION TO THE THEORY OF CHEMICAL COMBINATIONS. 
[From the Report of the British Association for the Advancement of Science, (1875), 
pp. 257—305.] 
I have in two papers “ On the Analytical forms called Trees,” Phil. Mag. vol. 
xiii. (1857), pp. 172—176, [203], and ditto, vol. xx. (1859), pp. 374—378, [247], con 
sidered this theory; and in a paper “ On the Mathematical Theory of Isomers,” ditto, 
vol. XLvil. (1874), p. 444, [586], pointed out its connexion with modern chemical theory. 
In particular, as regards the paraffins C n H M+2 , we have n atoms of carbon connected 
by n — 1 bands, under the restriction that from each carbon-atom there proceed at 
most 4 bands (or, in the language of the papers first referred to, we have n knots 
connected by n — 1 branches), in the form of a tree; for instance, n = 5, such forms 
(and the only such forms) are 
And if, under the foregoing restriction of only 4 bands from a carbon-atom, we 
connect with each carbon-atom the greatest possible number of hydrogen-atoms, as 
shown in the diagrams by the affixed numerals, we see that the number of hydrogen- 
atoms is 12 (=2.5 + 2); and we have thus the representations of three different 
paraffins, C 5 H 12 . It should be observed that the tree-symbol of the paraffin is 
54—2