BY A STATIONARY ELECTRIC CURRENT. 20? 



The work produced within the same must be accompanied by 

 just as great an increase of vis viva. In our case, inasmuch as 

 we have agreed to disregard all extraneous actions, such as, for 

 instance, electrolytic action, the work produced is fully ex- 

 pressed by the equation (I) or (I«). Strictly speaking, in con- 

 sidering the vis viva, we should regard not only the material 

 mass of the conductor, but the electricity also. In other words, 

 the particles of electricity may be accelerated or retarded on 

 their way through the space in question ; for although the con- 

 dition of being stationary implies that the velocity at any par- 

 ticular place must be constant, yet it does not follow that in 

 different places it must be equal. For instance, if the current 

 pass through a conductor with different transverse sections, the 

 electricity may move more quickly through the narrow than 

 through the wider places; just as the water of a river moves with 

 greater velocity through places where the river-bed is con- 

 tracted than through others. Nevertheless, as it is not yet 

 certain whether electricity possesses inertia or not, and hence 

 whether or not we may ascribe vis viva to the moved electricity, 

 and as, even if this were assumed, we have here but to consider 

 the changes in vis viva, and not its total value, we may, for the 

 present at any rate, disregard this possibility *. We have there- 

 fore to consider the vis viva of the material mass alone ; and as 

 by hypothesis no perceptible exterior motion is produced, the 

 increase or decrease of the quantity of heat alone remains. This 

 may be briefly expressed thus : — The whole work is employed 

 in overcoming the resistance opposed by the conductor, and 

 this, just as when friction is overcome, necessarily engenders a 

 quantity of heat equivalent to the work consumed. 



Let A be the equivalent of heat for the unit of work, and H 

 the heat generated in the enclosed space during the unit of 



* I may here remark, that, in assuming the correctness of Ohm's Jaw, the 



dV 

 same is tacitly admitted. For if the equation (1), i=:A; -r^, be true, the mag- 

 nitude and direction of the velocity of the electricity at any given point depends 

 only on the acting force at that point; and hence the inertia of the elec- 

 tricity must either be null, or at any rate so small, that the force necessary to 

 produce such changes of velocity as occur in the conductor may be neglected, 

 in presence of the force necessary to overcome the resistance opposed by the 

 conductor. 



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