Dr. E. J. Mills on Cumulative Resolution. 493 



In many cases of chemical action the diapolyte is capable of 

 forming but one cumulate only ; but in others a succession of 

 cumulates occurs, each cumulate becoming in turn a diapolyte. 

 Observing that the first cumulate is affected by v, we have to 

 operate with 



v |/i[A (a _ a) B (/3 _ 4) C (y _ c) . . .] — (n— w)A a B 6 C c } , 



which leads to the second cumulate; &c. &c. Proceeding thus 

 we obtain the following series of cumulates : — 



3= [A a B,C y ...]; 



T) —v [A (a _ a) B (j8 _ 3) C (y _ c) ...]; 



jT) —V [A( a _ 2a ) B (j3 _ 2 i) C( y _ 2c ) . . .] j 

 V) =V [A (a _ 3a ) B( j 3_ 3 j) C( y _ 3c ) . . .] ; 



&c. &c. 



While these differ in composition by a uniform amount, 

 their operator v proceeds by powers ; and the curve represent- 

 ing the relation of v to their difference is a logarithmic curve. 

 I have not yet met with an instance in which the series even- 

 tually vanishes. 



It may appear at first sight unreasonable to suppose that 

 bodies of indefinitely high symbolic value, and consequently 

 of indefinitely low specific heat, can possibly exist. We are, 

 however, as yet ignorant of the exact connexion between the 

 specific heat of such bodies and their chemical formulae; and a 

 great deal of the evidence we possess points to the conclusion 

 that in their case the ordinary law breaks down. The con- 

 ception, moreover, of a purely expanding series is familiar to 

 chemists*. It may be that many or all of the cumulates, at 

 the instant after their formation, undergo katamerization f ; if 

 so, they can then possess specific heat on the ordinary terms. 

 It is sufficient if some portion of a cumulate is left to undergo 

 the continuous inflictions of the resolving power. In any 

 event the " composition," or symbolic coefficients, of the cumu- 

 late would remain undisturbed ; and the entire process can 

 therefore be followed by practical analytical operations. I 

 will now consider some typical cases of cumulative resolution. 



2. Ammonic Carbonates. — The obscurity surrounding the 

 formation of these salts has been gradually increasing ; and 

 the latest experimental researches, while solving some parti- 

 cular problems in connexion with them, have left the more 

 general ones for the most part untouched. 



The formulae of the different amnionic carbonates (omitting 



* The paraffin series, C« H2/1+2, is an instance, though here the con- 

 ception is an erroneous one. 



t Katamer, the reverse of a polymer. 



