492 Dr. E. J. Mills on Cumulative Resolution, 



nesses of metal as possible, the luminous effect of the differ- 

 ent colours, in order to base thereupon some further infer- 

 ences. It is clear that experiments in this direction will be 

 of the highest interest as regards our knowledge of optical 

 and electrical phenomena. 



The results of this investigation are as follows : — 

 The property of experiencing a diminished electrical resist- 

 ance under the influence of Luminous rays is not confined to the 

 metalloids selenium and tellurium, but belongs also to platinum, 

 gold, and silver, and in all probability to metals in general. 



The electrical current diminishes both the conductivity and 

 also the sensitiveness to light, of its conductor ; and both of 

 these, after cessation of the current, gradually acquire their 

 former values. 



LXVL On Cumulative Resolution. 

 By Edmund J. Mills, D.Sc, F.R.S.* 



1. ~FF a substance, or mixture of substances, combine with 

 J- itself n times, and each time lose a particular fraction 

 of itself according to a fixed law, it may be said to undergo 

 cumulative resolution. The body undergoing cumulative reso- 

 lution will, in the sequel, be termed the diapolyte; and it will be 

 spoken of as cumulatively resolved, or diapolyzed, with respect 

 to what it loses (the apolyte) in the manner above expressed. 



One of the most frequent forms of cumulative resolution is 

 represented by the following general equation : — 



n A a Bp C y . . . - (n — m)A a B b G c . . . 



= ^«(a-a)+)Ks -t>w(/3— b) + mb ^- J n(y—c) + mc • • • 



When n becomes exceedingly large with respect to m (in 

 which case it will be denoted by v), the right-hand side of the 

 equation becomes 



y[A( a _ ) B (/3 _ A) C (y _ c) . . .]. 



I shall apply the term cumulate to a product having this 

 general formula, and thus obtained, and designate it by the 

 special symbol ^ which will always include a numerical 



value, unless when used as an operator. 

 In the latter case an expression 



-Y X = Y 



— ^n—m 



is to be interpreted thus, — " The substance X becomes the 

 substance Y when n units of it lose (n—iri) units of apolyte 

 by way of cumulative resolution." 



* Communicated by the Author. 



