454 OHM ON THE GALVANIC CIRCUIT. 



C what X CO M does for A, we obtain instead of the one conditional 

 equation the two following : — 



{u) — {u') =a, 



(u) - {u") = a', 

 where a represents the electric tension between the bodies A 

 and B, and a' that between A and C. In the same manner we 

 now obtain instead of the second conditional equation the fol- 

 lowing : — 



/du\ , , /du'\ ,, „ {dif\ 



It is immediately apparent how these equations must change 

 when a greater number of bodies are combined. We shall not 

 enter further into these complications, as what has been stated 

 suffices to throw sufficient light upon the changes which have 

 in such a case to be performed on the equations. 



14. To avoid misconception, I will, at the close of these gene- 

 ral observations, once more accurately define the circle of appli- 

 cation within which our formulcC have universal validity. Our 

 whole inquiry is confined to the case where all the parts of the 

 same section possess equal electroscopic force, and the magni- 

 tude of the section vai'ies only from one body to the other. The 

 nature of the subject, however, frequently gives rise to circum- 

 stances which render one or the other of these conditions super- 

 fluous, or at least diminishes their importance. Since the know- 

 ledge of such circumstances is not without use, I will here illus- 

 trate the most prominent by an example. 



A circuit of copper, zinc, and an aqueous fluid, will whoUy 

 come under the above formula when the copper and zinc are 

 prismatic and of equal section ; when, further, the fluid is Uke- 

 wise plasmatic and of the same or of smaller section, and its 

 terminal surfaces everywhere in contact with the metals. Nay, 

 when only these last conditions are fulfilled with respect to the 

 fluid, the metals may possess equal sections or not, and touch 

 one another with their full sections, or only at some points, 

 and even their form may deviate considerably from the prisma- 

 tic form, and nevertheless the circuit must constantly obey j 

 the laws deduced from our formulae ; for the motion of the elec- 

 tricity produced with such ease in the metals, is obstructed to 

 such a considerable extent by the non-conductive nature of the 

 fluid, that it gains sufficient time to diffuse itself thoroughly 



