500 Dr. E. J. Mills on Cumulative Resolution. 



Hence T) = j/C 6 H 10 5 ; jT) = v 6 C 6 . Water and carbon are 

 the extremes of composition for this series. 



For poly glyceric alcohols, according to the same authority*, 



wC 3 H 8 3 — (n— 1) H 2 = C 3n H 6ra+2 2re -t-i. 



Hence T) = ^3 H 6 2 or glycide ; T) = v 3 C 3 H 2 . H 2 and 

 C 3 H 2 represent the two extremes of this series. 



Caramels. — By a similar process, applied to cannose, the 

 series of caramels is formed, 



7lC 12 H 22 U — (n — 1) H 2 = C 12 « H 20ra+ 2 Oion+l- 



Of its members, T) = vC 12 H 20 O 10 , ^) = v 2 C 12 H 18 9 (carame- 

 lane), T) = y 6 C 12 H 10 5 , and V) = v 7 C 12 H 8 4 (caramelene) 

 are known. Caramelin seems to be exactly intermediate be- 

 tween T) and T). 



11. Etherification. — In the case of the fatty alcohols, it 

 is usual to form ethers by what, in effect, is a dehydrating 

 process. This is accurately represented by the equation 



2C ra H 2ra -|-2 — H 2 = C 2ra H 4n+2 0, 



whence T) = vC 2 H 4 . In conformity with this result, we find 

 that the action of oil of vitriol on fatty alcohols, when pushed 

 to an extreme, yields olefines, but not methylene. Here also 

 we find striking evidence of the correctness of the theory of 

 cumulates as enunciated in (1). 



12. Conclusion. — The process of cumulative resolution, of 

 which a brief sketch has been given in the foregoing sections, 

 is one of very general prevalence in chemical operations. In 

 the particular form of it there illustrated, the transition from 

 one compound to a successor in multiple proportion is effected 

 in hyperbolic paths, whose successive points at infinity lie on 

 a logarithmic curve. Such points at infinity are actually 

 realized as conditions of unstable equilibrium, under which a 

 new ordinal compound commences to take its rise. 



Having regard to the fact that the same theory that applies 

 to plants is also found to regulate the deportment of ordinary 

 reagents and mineral substances, we must so far regard the 

 latter as living beings. 



Anderson's College, Glasgow. 



• Fownes's < Manual of Chemistry ' (1868), p. 666. 



