Electricity in a uniform plane conducting Surface, 387 



vol. lxvii. p. 344, 1846) the strength of the current at various 

 parts of the disk ; and that, from the expression for the differ- 

 ence of potential between the electrodes, he deduced by Ohm's 

 law the resistance of a circular disk with two small electrodes 

 anywhere upon it. In order to test experimentally the value 

 thus obtained, he seems to have devised independently the 

 arrangement now commonly known as Wheatstone's bridge ; but, 

 owing to the smallness of the resistance to be measured, he was 

 unable to obtain satisfactory results. 



Soon after the publication of KirchhofFs paper, Smaasen* 

 gave an investigation of the flow of electricity in a plane conduct- 

 ing sheet, in which he takes account, in determining the poten- 

 tial, of the electricity given off to the air, and deduces the resist- 

 ance of an infinite sheet with two small circular electrodes by 

 a process which, though longer than that employed by Kirch- 

 hoff, may be regarded as more direct. It consists in finding the 

 resistance of the space between two lines of flow at an infinitely 

 small distance apart, and then extending by integration the ex- 

 pression thus obtained so as to make it apply to the unlimited 

 sheet. In a subsequent paper f Smaasen determined by an 

 analogous process the resistance of a conducting sphere, or of an 

 unlimited conductor of three dimensions J. Smaasen's treat- 

 ment of the subject is, like KirchhofFs, based chiefly upon the 

 mode of distribution of the potential ; the only investigation we 

 are acquainted with which deals specially with lines of flow is con- 

 tained in the paper by Professor W. Robertson Smith from which 

 we have already quoted. The starting-point adopted by Pro- 

 fessor Smith is the same as that from which we have set out in 

 the following communication; and, indeed, we found, after ma- 

 king some progress in our own work, that several of our demon*- 

 strations (which we at first thought were new) had been already 

 given by him, while all the chief conclusions were, as we have 

 said above, implicitly contained in KirchhofFs original memoir. 

 Consequently, although the present paper contains a few minor 

 results which, so far as we know, have not been pointed out ex- 

 plicitly before, we do not claim for its contents any essential 

 novelty; and our only reason for venturing to publish it is that 



* Pogg. Ann. vol. lxix. p. 161. 



t Pogg. Ann. vol. lxxii. p. 435. 



% About the same time, the same subject was takeu up by Ridolfi of 

 Florence {II Cimento, An. V. 1847, May- June), whose paper, however, we 

 only know from the references of Beetz (in Dove's Repertorium, vol. viii. 

 p. 147) and Poggendorff (Pogg. Ann. vol. lxxii. p. 449). No reference to 

 this paper is given either in the Royal Society's Catalogue of Scientific 

 Papers, or in the carefully compiled " Bibliographic " of the mathematical 

 theory of the voltaic pile in Verdet's Conferences de Physique {(Euvres de 

 Verdet, vol. iv. p. 351). 



