The Theory of Electrolytic Dissociation. 279 



small as we please. Let ns then make them so small that 

 the duration t shall be but a small part o£ the duration 1/8 r. 

 Then we are at liberty to substitute a single u fw with one 

 definite wave-frequency, for the entire of the little group of 

 u f w's of different wave-frequencies that furnish the rays 

 that fall within any one of the foregoing degrees. To see 

 this it is only necessary to proceed by successive steps which 

 are so exactlv analogous to those adopted in § 17, that it is 

 unnecessary to repeat the procedure here. We therebv learn 

 that— 



Theorem XIII. 



When ice have to consider in any problem what happens 

 within a limited time, it is permissible to divide the wave- 

 frequencies (or the corresponding wave-lengths) of the light 

 with which we are concerned, into little (/roups and to substitute 

 light of a single wave-frequency for each of these. 



It is important to bear in mind that this substitution can 

 be effected whatever be the intensities, phases, and states of 

 polarization of the individual undulations of the little group, 

 inasmuch as it depends upon our pairing each member of 

 the group with a supposed one which we are at liberty to 

 conceive of as in the opposite phase, in the same state of 

 polarization, and of the same intensity as that member of the 

 group with which it is paired ; and this can be effected 

 however unrelated in these respects that member of the group 

 may be to its colleagues. 



22. The foregoing theorems (with perhaps a few additions 

 such as the theorem which explains how to resolve a beam or 

 pencil of light into its component u f w's) would be a suffi- 

 cient foundation on which to proceed with the chamber study 

 of optical phenomena by the new analysis. It will, however, 

 be convenient to continue the study in conjunction with ex- 

 periments which will afford assistance ; and accordingly we 

 intend next to inquire how to exhibit in optical instruments 

 the resolution of light into its component u f w's, and how to 

 employ this resolution as our guide in making and in inter- 

 preting experiments. 



[To be continued.] 



XXV. The Theory of Electrolytic Dissociation. By W. C. 

 D. WHETHAM, ALA., F.R.S., Fellow of Trinity ' College. 

 Cambridqe *. 



THE theory of the ionic dissociation of electrolytes, chiefly 

 due to Arrhenius, was successful in explaining the 

 electrical properties of aqueous solutions, and in co-ordinating 



* Communicated by the Author. 



