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



and any other homologous series. Eventually, then, all ho- 

 mologous series tend to become the same. 



The complexity of any member of such series as the above 

 clearly depends on the value of n and on the ratio r of C to H ; 

 and these are its only variables. We have, in the series of fatty 

 alcohols, 



r= 



2n + 2> 



a hyperbolic relation between r and n. A similar relation 

 holds good in all homologous series, excepting that of the ole- 

 fines, where r= '5, and the complexity (determined by n alone) 

 is altogether linear. But, this series omitted, it obviously fol- 

 lows that the physical properties of homologous bodies cannot be 

 a linear function of their symbolic value. Kopp's law, there- 

 fore, has no chance of demonstration except in the case of the 

 olefines. 



The following equation includes the results of Thorpe and 

 Young*, 



V-^» il2n + 2 — «0-tl 2 = \J n —a ^2n-2a+2- 



On the whole, it appears that the olefines, not the paraffins, 

 constitute the basis of carbon combinations, to which they are 

 in fact asymptotic. 



8. Plant-products. Celluloids. — When a living plant 

 takes up carbonic dioxide and water it loses oxygen, and forms 

 cellulose, cannose, glucose, glucosides, and other products. 

 If we take the equation 



[(n + l)C0 2 + nH 2 0]-(n + l)0 2 = C n+1 H 2n O n , 

 and give successive integral values to n, we obtain the ratios 

 of cellulose, starch, dextrin, or glucosan (?i = 5),hydric kinate 

 (?i= 6), cannose (n= 11), and glucose (n = oc). The ratios in 

 the cumulate V) are CH 2 0. These confirm Debus's lawf, 



that 7Y = 1 is a maximum value in the case of alcohols. 



Acid Bodies. — The composition of vegetable-acid bodies 

 cannot be represented by a lower formula than CH 2 0, nor, 

 according to Debus'sj law, by a higher one than C M H x +b O n +b, 

 if b stand for the " basicity." In systematic works the general 

 type of the formulas of these bodies is C n H 2n _ 2p O m , which 

 has the advantage of keeping the coefficient of H necessarily 

 even. The maximum formula is most simply constructed thus, 



[nC0 2 + (?i— p)H 2 0] — Op** = C n H 2 „_ 2/ > 3Jl _( 2 /,+*), 



* Proc. Roy. Soc. vol. xx. p. 488. 

 t Cliem. Soc. Journ. vol. xix. p. 256. 



