OHM ON Tin; OAKVANIC CIIICUIT. /Ill 



in cnmi)arisori willi llicir relative; (liHlanccH, a fiiriftion, to ho do- 

 tcriniiicd Hcparatcly for cac-li frivcii rase froni ilicir dirnciisions 

 and their mean distanc^e, inust h(! HiihHtitiited for tht; pro(hi(;t of 

 tlie inaf^nitiidcs of the two clernciitH, and wiiieli we will desig- 

 iiatc where it is employed by F. 



f). Hitherto wv. have taken no notice of (he inflnence of the 

 mutual distance of the clementM Initween which an (!(|nali/,ation 

 of their electric state takcH place, hecaii.se aH yet we have only 

 considered such elements aH alwayw retained the Hame relative 

 distance. .13ut now the question arises, whether this exchange 

 is directly effected ordy hetween adjacent elements, or if it ex- 

 tends to others more distant, and how on the one or the other 

 supposition is its ina;^iiitude modified hy the distance? Fol- 

 lowing the example of Laplace, it is customary in cases where 

 molecular actions at the least distance come into play, to em- 

 ploy a j)articular mode of representation, according to which 

 a direct mutual action hetween two elements separated by 

 others, still occurs at flnifx; distances, which action, however, 

 decreases so rapidly, tliat even at any perceptible distance, be 

 it ever so minute, it has to be considered as perfectly eva- 

 nescent. Laplace was led to this hypothesis, because the suppo- 

 sition that the direct action ordy extended to the next el(;ment 

 produt;cd equations, the individual members of which were not 

 of the same dimension relatively to the diflerentials of the vari- 

 able quantities*, — a non-imiformity which is oj)posed to the 

 spirit of the differential calculus. This apparent unavcjidablc 



* Poisson, in his M^moiro sur la Di»tribution dc la Chaleur, Journ. de 

 I'Ecole Polytcckn. call. xix. uxprcHScs hiitiMclfoii this subject tliuM : — 



" If a bur l)u divided, by Kections pcrpciiidicuinr to tlio axis, into nn infinite 

 number of infinitely Hinall elementH, and if wo connider the niutnal acliun 

 of tliree connocutive e!etneiiln, lliat iw to say, tlie (jiianlity of lieat tliut 

 the intermediate element ;it each inHtant coinninni<;ates to and abstracts from 

 the two others, in pro])ortioii to the positive or ne;^ativc excess of its tem))era- 

 turc over that of each <jf them, we may llienco easily determine the au(^m<.'ntu- 

 tion of ti^mpi.-rature of this element during an infinitely small instant; assu- 

 ming therefore this (piantity e(piul to tiie di(li;rential of its temperature taken 

 witli respect to the time, the ('(luation of the propagation of heat according to 

 the h.-nglh of the bar is formed ; hut on examining the (|uestion more; atten- 

 tively, it is seen without dilliculty that this equation would be foimded on the 

 comparison of two infinitely small non-liomogeneous (piantities, or of difl'erent 

 orderH, which would be contrary to the first ])rinciples of the dillerential (calculus. 

 This dillieully can only be made to disajipcar l)y su])[)osing, as M. I.aplace 

 first remarked, (Memoires de la I re classe de I'lnstitul, annee I80!),j that 

 the action of eacli element of the l)ar extends itself beyond the contact, and 

 that it exerts itself on all tlie clemciitH contained within a finite Hpace, an Hniall 

 as we please." 



