628 PROFESSOR FREDERICK GUTHRIE 
existence of yet undiscovered ones, confers an unique importance on the study of 
the olefines; for the latter bodies stand in much the same relation to many such 
Series as does the ‘‘common difference ” to an arithmetical one. 
A common difference, whose successive chemical additions to any one term of 
such a series would yield, theoretically, every higher successive term, is methylen 
C, He. 
According to some chemists, methylen has been obtained ; according to others, 
its existence is possible, although never obtained; while, in the eyes of a third 
class, its existence is an impossibility. Up to the present time it is perhaps 
safe to assume that this hydrocarbon has not been prepared in the pure state. 
Although, if we had only one term of such a series from which to start, the 
existence of methylen would be necessary and sufficient for the theoretical solu- 
tion of the problem of the successive syntheses of the following terms in the 
manner above indicated, any multiple of methylen would furnish the means of 
forming successive terms, situated from one another at intervals of the magnitude 
of the hydrocarbon employed. 
In general terms,—If C,, H,, Q be the formula of the starting term, where Q 
denotes the whole of whatever constituents are present besides C,, H,, then, by 
means of methylen, we may get, in succession, 
OHeig of, ynliioden we robin) 
ey a rt aaa OE BN 
real tae eats URIS SV aa al pe 
Gap Ca Hu, ele ul oldiuiooatad rg) 
Bed. Gt Be eens se Se ee 
we. 
But if the difference be ethylen, we can only form every alternate term — 
Gr Hi AOds cnatinaey Gio kee a 
ct i Crts Ant, Q. = fs Bu 7 (3) 
tt Cntg Hts Bey iica hee eeeticiae (), 
&c. 
With propylen, every third term; and so on. 
Further, it is clear that, supposing we have ethylen as the common dif- 
ference, we can fill up the entire series provided we have two starting points 
which differ by methylen— 
C,H C,H, Q (1) C,H, Crto Ht @ (2) 
COME Crt, Hnty (3) CH Cn+¢ Hm+, (4) 
t 4 Cntg Hats Q (5) ams Cnts Hints (8) 
c c. 
in which the two series, derived from the two initial terms, are supplementary 
of one another. 
Again, if we had only propylen at our disposal as a difference, we could still 
complete the series provided we had éhree consecutive starting terms. And so, 
mutatis mutandis, for the other limitations. 
