236 ENERGY OF CURRENTS. 



CHAPTER III. 

 ENERGY OF CURRENTS. 



243. DISENGAGEMENT OF HEAT. When a system of electrified 

 conductors undergoes any modification whatever, without the inter- 

 vention of any external force, the electrical energy in the second state 

 is necessarily less than in the first. The energy lost during the trans- 

 formation may be utilised in an equivalent form, such as a mechanical 

 work, the raising of a weight, increase of the vis viva of the system, 

 a change of physical state, or finally a disengagement of heat. 



For any infinitely small transformation of the system in 

 question, the loss of energy is equal to the sum of the products 

 of each of the electrical masses, into the difference of the values 

 of potentials at the points in which they were placed before and 

 after the transformation. 



Let us consider two points A and B kept respectively at the 

 potentials V : and V 2 , and on equipotential surfaces which are 

 traversed at A and B by two corresponding portions S x and S 2 that 

 is to say, cut by the same tube of flow. The quantity of electricity 

 which traverses the two surfaces is the same ; the energy lost by the 

 current in this interval in unit time, is equal to the product of the 

 mass of electricity which issues that is to say, of the strength of 

 the current I by the difference of potentials V l - V 2 , if the current 

 goes from A to B that is to say, by the electromotive force between 

 these points. Hence, as a measure of the energy lost, we have 



W = I(V 1 -V 2 ) = IE. 



We shall assume as an experimental fact, that no part of this 

 energy is employed in changing the vis viva of the electrical masses. 

 The fact is obvious if the surfaces Sj and S 2 are equal, for then the 

 velocities are the same on entering and on leaving the tube. For 

 the general case, we have already observed that the flow is parallel 

 to the force at each point, and that therefore no effect attributable to 



