in Homogerieous Solid Bodies. 503 



vol. iii., on the Determination of the Value of a certain Defi- 

 nite Integral; and the second, in vol. v., on a new Method of 

 Determining the Attraction of an ElUpsoid on a Point without 

 it. In the latter of these memoires, M. Chasles refers to a paper, 

 by himself, in the twenty-fifth cahier of the Journal de I'Ecole 

 Polytechnique, in which it is probable there are still further an- 

 ticipations, though the writer of the present article has not had 

 access to so late a volume of the latter Journal. Since, however, 

 most of his methods are veiy different from those of M. Chasles, 

 which are nearly entirely geometrical, the following article may 

 not be uninteresting to some readers.] 



If an infinite homogeneous sohd be submitted to the action 

 of certain constant sources of heat, the stationary temperature at 

 any point will vaiy according to its position; and through every 

 point there will be a surface, over the whole extent of which the 

 temperature is constant, which is therefore called an isothermal 

 surface. In this paper the case will be considered in which 

 these surfaces are finite, and consequently closed. 



It is obvious that the temperature of any point without a 

 given isothermal surface depends merely on the form and tem- 

 perature of the surface being independent of the actual sources 

 of heat by which this temperature is produced, provided there 



nation of the attraction of an ellipsoid given in the latter part of the paper. 

 He found soon afterwards that he was anticipated by the same author in an 

 enunciation of the general theorems regarding attraction; stdl later he 

 found that both an enunciation and demonstration of the same general 

 theorems had been given by Gauss, whose paper appeared shortly after 

 M. Chasles' enunciations ; and after all, he found that these theorems had 

 been discovered and pubhshed in the most complete and general manner, 

 with rich applications to the theories of electricity and magnetism, more 

 than ten years previously, by Green ! It was not until early m 1845 that 

 the author, after having inquired for it in vain for several years, m conse- 

 quence of an obscm-e allusion to it in one of Murphy's papers, was fortu- 

 nate enough to meet with a copy of the remarkable paper (" An Essay on 

 the AppUcation of Mathematical Analysis to the Theories of Electricity and 

 Magnetism," by George Green, Nottingham, 1828) in which this great 

 advance in ])hys'ical mathematics was first made. It is worth remarking, 

 that, referring to Green as the originator of the term, Murphy gives a mis- 

 taken definition of " potential." It appears highly probable that he may 

 never have had access to Green's essay at all, and that this is the explana- 

 tion of the fact (of which any other explanation is scarcely conceivable), 

 that in his Treatise on Electricity (Murphy's Electricity, Cambridge, 1833) 

 he makes no allusion whatever to Green's discoveries, and gives a theory 

 in no respect pushed beyond what had been done by Poisson. AH the 

 general theorems on attraction which Green and the other writers referred 

 to demonstrated by various purely mathematical processes, are seen as 

 axiomatic truths in approaching the subject by the way hud down in the 

 paper which is now republished. The analogy wth the conduction ot beat 

 on which these views arc founded, has not, so far as the author is aware, 

 been noticed by any other writer. 



