On Surface-resistance at Electrodes. 145 



been obtained, the next is got from it by the usual " rules of 

 derivation " modified from those of Arbogast to suit the case 

 where, as here, each differential coefficient is replaced by its 

 appropriate submultiple. ( Vid. De Morgan's c Calculus/ 

 p. 330.) 



5. In the ' Proceedings of the Edinb. Math. Soc* 1884-85, 

 pp. 95-100, Professor Chrystal has a note on "A Method for 

 obtaining the Differential Equation of an Algebraical Curve." 

 In the case of the cubic he gets for the non-zero side of the 

 equation a determinant of the 6th order which he says can be 

 simplified further. I find that when this simplification is 

 made, and y 2 , t/ 3 , . . . . are expressed in terms of a, /3, . . . , the 

 result agrees perfectly with the above*. 



Bishopton, Glasgow, January 9, 1886, 



XXI. Relations of Surface-resistance at Electrodes to various 

 Electrical Phenomena. By Gr. GrOKE, LL.D., F.E.S.\ 



IN some experiments described in a paper on u Evidence 

 respecting the Eeality of ' Transfer-resistance ' in Elec- 

 trolytic Cells," read before the Birmingham Philosophical 

 Society, January 21, 1886 J, I found that when a current of 

 voltaic electricity was passed from dilute nitric or sulphuric 

 acid, or strong nitric acid, into the surface of a thin platinum 

 bottle used as a cathode, the temperature of the bottle sud- 

 denly rose, notwithstanding that certain amounts of heat 

 must have been absorbed by the copious liberation of hydro- 

 gen which occurred, and by that substance assuming the 

 gaseous state, each at the surface of the bottle ; and I further 

 found that this rise of temperature was not due to heat pro- 

 duced by ordinary conduction-resistance of the bottle or of 

 the liquid, nor to resistance of any kind at the anode, and 

 that it was due to some influence other than that of chemical 

 change, at the surfaces of mutual contact of the liquid and 

 bottle ; and further, that it varied in quantity directly as the 

 amount of " resistance " to the passage of the current into 

 the surface of the bottle. I also found similar thermal effects 

 of " resistance " at the surface of the bottle, when the latter 

 was used as an anode. 



* The differential equation of the cubic appears to have "been first given 

 by Mr. Samuel Roberts in the ' Educational Times.' The question and 

 solution are reprinted in ' Math, from Educ. Times,' x. pp. 47, 48. The 

 date of the first publication of the question, which unfortunately can in no 

 case be got with certainty from the Reprint, should probably be 1868. — 

 T. M. (January 18). 



t Communicated by the Author : read before the Birmingham Philo- 

 sophical Society, January 21st, 1886. 



X See p. 130 of the present Number. 



Phil. Mag. S. 5. Yol. 21. No. 129. Feb. 1886. L 



