10 MM. E. du Bois-Reymond and W. Beetz on the 



rent in non-prismatic conductors is concerned, to ascertain 

 the true course of the electricity under the present circum- 

 stances. Although M. Smaasen has already extended the 

 fundamental equation of the dynamic equilibrium of electricity 

 to the three dimensions, nevertheless we have no instance of 

 one of these, however simple, being susceptible of mathematical 

 treatment. But in this case, by means of mere inspection, we 

 may ascertain with tolerable certainty, the probable manner 

 in which the curves of the current are arranged. Let us first 

 determine the terms of the phenomenon. 



Imagine an indefinite flat plate XX', the resistance of which 

 vanishes in comparison with that of a uniform layer of a liquid 



conductor covering it everywhere of equal thickness. The 

 other electrode in the form of a hemisphere dips into this to 

 such an extent, that the surface^ 7 of the layer passes through 

 its centre O. We have no concern with what takes place in 

 the immediate vicinity of the centre O' of the plate, perpen- 

 dicularly beneath that of the electrode; for we cannot make any 

 observations here, because those rings which are fit for inves- 

 tigation do not commence until some distance from the centre. 

 It is thus easily seen that the curves of the current, which pass 

 to the more distant points of the plate, must proceed almost 

 rectilinearly for a very long time; they then curve inwards 

 towards the plate, so as to reach it at right angles. Moreover, 

 if we conceive two curves formed by the current lying near 

 each other, in a plane falling perpendicularly upon the plate 

 through the point from which the current issues, we also 

 see, that in the rectilinear portion of their course they will 

 remain very near each other ; but that they tend to separate 

 from each other, when, having arrived near the point at which 

 they reach the plate, they curve inwards towards it (Ors, 

 O/V). 



The curves formed by the current at every point of the 

 conductor through which it has passed, indicate the direction 

 of the motion of the electricity ; but the consideration of their 

 mere length is by no means sufficient to determine the inten- 

 sity of the current, i. e. the resistance divided by the elec- 

 tromotive force, for each spot of the conductor. M. Bee- 



