On the Generality of a New Theorem. 139 



As Crookes and others have already pointed out, since many 

 gases yield different spectra under the influence of varying 

 electrical conditions, it is evident that the fact of the existence 

 of two well-marked spectra of argon gives not the slightest 

 presumption in favour of the hypothesis that the new gas is a 

 mixture. In order to discover whether argon possesses a dual 

 nature, the gas must be split up in such a way that its com- 

 ponents give different spectra under like electrical conditions; 

 then alone would the evidence of the spectroscope be of weight 

 in proving the dissimilarity of the several parts. 



The results of this work are thus far only those which were 

 to have been expected from a high tension galvanic battery, 

 reasoning from the work of other investigators with the 

 Toepler-Holtz machine. The battery, however, gives a 

 current so admirably constant and so easily regulated as to its 

 tension, that we hope to be able to use it as a means of 

 determining whether the oscillatory discharge produces its 

 effect simply by increasing the temperature, or because of 

 some inherent property in the manner of the discharge. 



It is our intention to extend the investigation by the syste- 

 matic photographic study of the action of the varying 

 discharge upon all the elementary gases in the purest con- 

 dition, as well as upon mixtures, under widely varying 

 conditions of temperature and pressure. 



Harvard University, Cambridge, Mass. U.S. 



XXI. On the Generality of a New Theorem. 



To the Editors of the Philosophical Magazine. 

 Gentlemen, 



A CORRESPONDENT writing to me on the 14th of 

 last December pointed out to me that the first of my 

 propositions in the paper on " Microscopic Vision " in the 

 October number of the Philosophical Magazine, p. 335, viz.: — 

 However complex the contents of the objective field, 

 and whether it or parts of it be self-luminous or illumi- 

 nated in any way however special, the light which 

 emanates from it may be resolved into undulations each 

 of which consists of uniform plane waves 

 (in which mention is made of only one kind of motion, viz. 

 light), may be further generalized into the following : — 



" The most general motion of given period within any 

 space may be analysed into trains of " uniform " plane 

 waves." 



