204 CLAUSIUS ON THE WORK PERFORMED 



tion ; and as the same conclusion applies to every point of the 

 conductor, it follows further, that there can be no free electricity 

 within it, and hence, that during a stationary current, just as in 

 a state of equilibrium, the free electricity is distributed solely 

 over the surface of the conductor. 



According as the hypothesis of two, or only of one electricity 

 is admitted, the circumstance, that the electricity passing along 

 the interior of a conductor exercises no attraction or repulsion, 

 must receive a different interpretation. By the first hypothesis, 

 we must assume that each element of space within the con- 

 ductor contains an equal amount of both electricities, which 

 flow with equal strength of current in opposite directions. The 

 second hypothesis involves the supposition, that an element of 

 space, when it contains a certain normal quantity of electricity, 

 exercises no action on another particle of electricity, inasmuch 

 as the electrical repulsion is compensated by some other force ; 

 and further, that an actual attraction or repulsion then only 

 occurs when the element of space contains too much or too 

 little electricity ; by this hypothesis, therefore, we must assume, 

 that during a stationary current each element of space within 

 the conductor contains the normal quantity of electricity. 



This is not the place to discuss the probability of either the 

 one or the other hypothesis, for as far as the validity of the 

 following conclusions are concerned, it is a matter of perfect 

 indifference to which of the two we attach ourselves ; our choice, 

 therefore, may be governed entirely by convenience. In my 

 former memoir on machine electricity, I adopted, for convenience 

 of illustration, the first hypothesis ; for a similar reason I will 

 here employ the second. In order to translate all conclusions 

 hereafter to be given so as to be in accordance with the first 

 hypothesis, we have merely, wherever one current conveying the 

 quantity of electricity Q in one direction occurs, to substitute two 

 currents conveying the quantities of electricity IQl and — ^Q in 

 opposite directions, and then to apply to both currents the same 

 conclusions which here have reference to one current only. 



We proceed now to determine the quantity of work produced 

 by the force acting within the conductor during the motion of 

 the electricity. 



For this purpose, let us consider any element of electricity 



