34 On the Number of the Univalent Radicals C„ H 2n +i. 



When used for vacuum-tubes this coil gives illumination 

 of extreme brilliancy and very long duration : with 20 to 30 

 cells and a slow-working mercury break, giving, say, 80 sparks 

 per minute, the striae last long enough for their forward and 

 backward motion to be perceived directly by the unassisted 

 eye. The appearance of the striae when observed in a re- 

 volving mirror (as described in the Proceedings of the Royal 

 Society, vol. xxv. p. 73) was unprecedentedly vivid, and this 

 even when only two or three cells were employed. 



Ill* On the Number o the Univalent Radicals G n H2»+i. 

 By K, Cayley, Esq* 



I HAVE just remarked that the determination is contained 

 in my paper " On the Analytical Forms called Trees " 

 &c, British-Association Report, 1875 ; in fact, in the form 

 Cj»H 2w+ i 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 3 , 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 n R 2n +i is = 

 No. of carbon roofctrees C„ with one main branch, 

 + No. of „ „ with two main branches, 



+ No* of j, ,j with three main branches; 



and the three terms for the values n=l to 13 are given in 

 Table VII. (pp. 296, 297) of the paper referred to. 

 Thus ?i = 5 (an extract from the Table) is 



Index x } or 



number of 



knots. 



Index t, or num- 

 ber of main 

 branches. 



Altitude. 









1 



2 



3 



4 





5 



1 



2 

 3 

 4 





1 



1 



2 

 1 



2 

 1 



1 



4 

 3 



1 

 1 





Total ... 





1 



4 



3 



1 



9 



and the number of the radicals C 5 H n (isomeric amyls) is 

 * Communicated by the Author. 



