12 MM. E. du Bois-Ileymond and W. Beetz on the 



Thus the partial current, when k represents the difference be- 

 tween the tensions of the electrodes, becomes 



, r „ , Hcosyte-a 

 dl = 2ttW „ * &r . 



3, cos y and ^<p must here be expressed in functions of x and 

 dx. Retaining M. Becquerel's method of notation, we then 

 obtain the determinations — 



S = vV + m% cos <y = ^-2— - s 



E/g<p = d#siny, siny: 

 partial stre: 

 */I = 27rwf>A7H.- 



m 



and thus the partial strength of the current becomes 



xdx 



(x^ + m^^^ + m^-p) 



If this expression be multiplied by a further constant quantity 

 «, as the atomic weight of the product of decomposition pre- 

 cipitated, its density, &c, we shall obtain a measure of the 

 absolute quantity of the product of decomposition which is 

 precipitated in a unit of time by the partial current upon the 

 ring of the plate from which the conical envelopes arise, but by 

 no means, as Becquerel appears to think, of the relative thick- 

 ness of the film, in which this quantity is deposited. To 

 determine this, it is clear that we must take into consideration 

 the extent of the surface upon which the deposition occurs. 

 This is readily found by differentiating the expression of the 

 basal surface of the cone as a function of the semidiameter, 

 and consequently the approximative law of the diminishing 

 thickness of the rings, when dl is divided by 2-jr.xdx. This 

 law therefore takes the form — 



u=copkmci,—- — , „ — -. 



9 V (# 2 + 7» 2 )(W+m 2 -p) 



If p be neglected in comparison with H, it becomes 



y =. wpkmct . J ; 



if, again, as in Becquerel's example, m 2 be supposed to vanish 

 in comparison with «*, and the constants be included under 

 the sign A, we get simply 



A 

 *"> 



Hence the thickness of the ring would not be, as M. Becquerel 



