294 Mr. J. W. L. Glaisher on a Class of Definite Integrals. 



As to the theoretical interpretation of the experiments, it 

 seems to me that three views chiefly are worthy of being taken 

 into consideration, viz, : — 



(1) The assumption which suggested the investigation, that 

 light actually decomposes chlorine molecules into chlorine atoms. 



(2) One might assume that highly refrangible light, in acting 

 upon chlorine, was doing a peculiar unknown kind of work, 

 which in its turn was changed into heat and thus caused the 

 expansion. 



(3) One might say that the distinction made since the time 

 of Seebeck and Melloni, between heating and non-heating but 

 chemically active rays, had no sufficient foundation in fact, and 

 look upon the phenomenon above detailed as a direct proof of 

 the existence of bodies which are heated more strongly by violet 

 than by red light. It is true, indeed, that that distinction is 

 founded almost entirely upon the behaviour of rays towards a 

 thermopile covered with lampblack, and therefore, strictly speak- 

 ing, applies solely to lampblack as light-absorber. If, for in- 

 stance, red light did not happen to heat this particular sub- 

 stance, we should perhaps not know those rays to be thermically 

 active. 



Of the above assumptions, the second appears to me the least 

 plausible ; while the first, on the other hand, is no little sup- 

 ported by the coincidence of the rays which make chlorine 

 expand with those which are known to render it chemically 

 active. 



I have projected additional experiments for the further elu- 

 cidation of the subject ; but as I have no electric lamp, and 

 hence the possibility of their being carried out depends entirely 

 on the state of the weather, I considered it best, in the mean 

 time, to publish my present observations as they are. 



Bromine, according to a few preliminary experiments, behaves 

 like chlorine ; other substances than these two have not as yet 

 been tried. 

 Bonn, September 1, 1871. 



XXXII. On a Class of Definite Integrals. 

 By J. W. L. Glaisher, B.A., F.R.A.S., F.C.P.S.* 



THE Theory of Definite Integrals, strictly speaking, is con- 

 fined within a very small compass ; in fact it can scarcely 

 be said that there exists a Theory of Definite Integrals in the 

 same sense as we speak of the Theory of Equations, the Theory 

 of Curves, &c. : the integrals are evaluated, but their properties 

 are not, as a rule, studied. The majority of works having the 

 * Communicated by the Author. 



