^l^ ,\«:'Pirof. Grove on the Application of 



nic School. I am confirmed in this conjecture from the man- 

 ner in which that clistinf;uished analyst treats cases of the kind 

 here discussed in his Theorie de la Ckalenr'. thus, in reference 

 to the isolated case of the general series above, when A = 1, 

 he says, " Elle est de I'espece des series periodiques qui ne 

 sont ni convergentes ni divergentes, inais qu'on pent nean- 

 moins employer en les conslderant comnie les limites de series 

 convergentes, c'est-a-dire en muitipliant leurs termes par les 

 puissances ascendantes d'une quantite infiniment peu differ- 

 ente de I'unite." — Theorie de la Chaleur, p. 119. And again, 

 " L'integrale d'une quantite periodique qui s'etend a I'infini, 

 doit toujours etre consideree comir.e la limite d'une autre in- 

 tegral dont les elemens decroissent a mesure que la variable 

 augiDcnte, et sont nuls quand la variable est infinie; observa- 

 tion semblable a celle que nous avons deja fait relativement 

 aux series infinies de quantites periodiques." — Ib.^ p. 207. 

 And this is the erroneous principle to which the mistakes ani- 

 madverted upon in Mr. Moon's paper are all to be traced, 

 and which will be found to affect the accuracy of many other 

 received results in the doctrine of series and of definite inte- 

 grals. 



It may perhaps seem that the principle here deprecated, and 

 which consists in i)ringing an isolated and independent case 

 under the control of a law which governs a continuous series 

 of cases, with the view of effecting a particular purpose, — it 

 may perhaps seem that this principle is virtually sanctioned by 

 myself at p. 363 of the present paper, where 1 give to the in- 

 finite exponent in the expression for S the peculiar form k. oo ' 

 — to the exclusion of other forms for infinity that may appear 

 to be equally admissible — merely, it may seem, to effect a par- 

 ticular purpose. But it is not so. Any form for the exponent 

 in question, other than that I have given to it, would be erro- 

 neous; as I shall show in a subsequent number of this Jour- 

 nal, if I be indulged with a brief space for that purpose. 



JhXXI. Oil the Application of Voltaic Ignition to Lighting 

 Mines. % W. R. Grove, Esq.y M.A., F.R.S., Professor 

 of Experimental Philosophy in the London Institution. 



To Richard Phillips, Esq., F.R.S., ^c. 

 Dear Sir, 



IN the Comptes Rendus of the Paris Academy of Sciences 

 for the 1st and 15th of September last, are conmiunications 

 by M. Boussingault and M. De la Rive, on the employment 

 of the voltaic disruptive discharge for the illumination of mines. 



