with Formula: for ascertaining its power. 259 



obstacles, then in time any amount of work would be per- 

 formed provided the current remained constant. A current 

 can easily be conceived so feeble as to take millions of years 

 to reduce a pound of copper. If the entire circuit of single 

 atoms be increased at every part, in fact if the mathematical 

 voltaic circle be increased to the size of a tunnel, then (W), the 

 amount of work performed in a given time, would be equal to the 

 intensity of the battery, minus the resistance of our working 

 apparatus, multiplied by the number of parts of the tunnel 



(A) thus: W=T^nr!.xA. 



This equation, however, gives us the total amount of che- 

 mical actions in the whole series of batteries and decomposi- 

 tion troughs, or, in other words, the sum of the actions evinced 

 in each; we generally, however, are desirous of estimating 

 the amount done in one particular cell, in which case we di- 

 vide our equation by the number of cells and troughs (n) thus : 



n 

 Sometimes this equation is rendered extremely complex by 

 an increase of the circuit at one side but not at another ; in 

 fact, the tunnel is cut away on one side, and this is a case that 

 is perpetually occurring in practice. In this case it is not 

 impossible but that the force is only derived from those parts 

 of the circuit which are complete : in that case the equation 



T— R x A p * 



would be W" = " , p standing for the incomplete 



parts. In this view of the question we are supported by the 

 analogy of water running through a pipe of given dimensions 

 from a cistern ; for however 

 large this cistern be, pro- 

 vided there be no more 

 pressure, the water running 

 through the pipe would be 

 the same. So far as the 

 voltaic fluid is concerned I 

 feel certain, from numerous 

 observations, that beyond a 

 certain point the increase of a battery does not cause a greater 

 amount of electricity to pass through a given resistance ; and, 

 perhaps, in those cases, where the enlargement of a battery in- 

 creases the voltaic force, the battery in the former instance 

 was deficient in size in relation to the size of the resisting 

 part R, the tunnel, in fact, having been defective originally in 

 that part. It is possible that the expression for this con- 

 dition might be altered ; for R, the resistance to the single 



S2 



