Cambridge Philosophical Society, 461 



result of a force either superadded or giving direction to the ordinary 

 chemical affinity of the bodies present ; that is, modifying the affini- 

 ties in the particles through which the current is passing, so that they 

 act with greater force in one direction than in another, and conse- 

 quently cause them to travel, by a series of successive decompositions 

 and recompositions, in opposite directions, so as to be finally disen- 

 gaged at the boundaries of the decomposing body. Various experi- 

 ments are detailed in corroboration of these views, which appear to 

 explain, in a satisfactory manner, all the prominent features of elec- 

 tro-chemical decomposition. 



10. "The Anatomy and Physiology of the Liver." By Francis 

 Kiernan,Esq.,M.R.C.S. Communicated by J. H. Green, Esq., F.ll.S. 



The Society then adjourned over the Long Vacation to the 21st of 

 November. 



PHILOSOPHICAL SOCIETY OF CAMBRIDGE. 



A Meeting of the Cambridge Philosophical Society was held on 

 Monday, November 11, the President of Queen's College (the Vice- 

 Chancellor) being in the chair. A communication was read by 

 Mr. Murphy, being a " Second Memoir on the Inverse Method of 

 Definite Integrals." 



The principal object of Mr. Murphy's present memoir is to afford 

 the means of recurring from <p (x) to/(£) when the definite integral 

 of the latter function, multiplied by t * and taken from£=0 to£=l, is 

 expressed by the former. When f(t) is any of the functions ordi- 

 narily adopted in analysis, <p (x) converges to zero as x increases in- 

 definitely. Mr. Murphy's former memoir was confined to this case. 

 In the investigation of" the properties of f (t), when (x) = 0, the 

 author proves that the former function vanishes an indefinitely great 

 number of times, and corresponds with such physical phenomena 

 as are usually called latent. He next gives the theory of recipro- 

 cal functions, namely, of such functions, L n ,\ m , (generally, but not 

 necessarily, of different species,) that the integral single or double, 

 &c, of the product may vanish between limits when n and m are 

 unequal integers : Laplace's functions are a particular instance of 

 this reciprocity. 



The author, in the last section of his memoir, has applied the the- 

 ory of reciprocal functions to the problem of recurring from (x) 

 to f (t), whatever be the form of the given function ; and also to 

 tfee expansion of any function (x) in negative powers of x, and 

 other forms which vanish when x is taken very great. 



Professor Airy gave an account of deductions founded on the 

 observations of the Aurora? Boreales of September 17 and Oc- 

 tober VI. They related principally to the elevation of the upper 

 part of the luminous arch above the earth's surface. For the former 

 he used observations made by himself at Cambridge, by Mr. Phillips 

 at York, and by an unknown observer at Manchester ; for the lat- 

 ter he relied on his own observations at Cambridge, those of Mr. 

 Phillips at York, those of Messrs. Potter, Clare and Hadleigh at 

 Manchester, those of an unknown correspondent of the Durham 



