ELECTROMOTIVE FORCES OF THE ELECTRIC ARC. 307 



the current will be defined as the E.M.F. of the apparatus, under the given set of 

 conditions and for that particular current which was initially supposed to be flowing. 



In this definition the qualification, " if the irreversible transfer of energy is 

 proportional to the square of the current and the reversible to the first power of the 

 current," predetermines that the apparatus must obey OHM'S law over whatever 

 range it may be possible to vary the current without in any way changing the state of 

 the apparatus, in order that it can be said to have a resistance at all. If, however, 

 the qualification is in any case not fulfilled, it will become necessary to consider the 

 terms in the conceivable equation between V and A other than those in which A 

 occurs to the powers or 1. 



So far nothing has been said of the signs which the two quantities resistance and 

 E.M.F. can have, as their signs are more or less a matter of convention. If we call a 

 current flowing round the circuit in the same direction as the E.M.F. of the source 

 would tend to make it flow a + current, and a transfer of energy from the source to 

 the apparatus a + transfer of energy, then their signs are determined and agree witli 

 ordinary practice, so that the resistance and the E.M.F. of the apparatus which 

 oppose the flow of the current will have -J- signs. It is to be noticed, however, that 

 this definition does not preclude in any way the possible existence of a negative 

 resistance ; for if, instead of an irreversible transfer of energy from the source to the 

 apparatus, proportional to the square of the current, there were found (the conditions 

 of the apparatus being, of course, maintained constant as before) to be a transfer in 

 the opposite direction, i.e., from the apparatus to the source, then the coefficient of A 2 

 would have to be negative, so that in this case the apparatus would possess a true 

 negative resistance. Although in what follows it will be shown that this is not the 

 case with the arc, it is as well to draw attention to the matter, as a considerable part 

 of the controversy on the negative resistance of the arc under certain conditions arose 

 from some of those who took part defining resistance as an essentially positive 

 quantity, and then trying to prove that it could not be negative in the case of 

 the arc. 



A single value of V corresponding to a single value of A is evidently not sufficient 

 to determine whether any conductor fulfils the above definition of resistance and 

 E.M.F. To determine this the current must be varied over some range, SA, and in 

 such a manner that the conditions of the conductor remain unchanged, and a series 

 of observations must be made within this range. 



The essential stipulation, that the test must not alter the body tested, is the main 

 difficulty in the experiments on the resistance and E.M.F. 's of the arc. For it is well 

 known that, corresponding with each steady value of the current, the size and 

 configuration of the vapour column and craters are different in spite of the fact that 

 the length, the nature of the electrodes, and the other conditions may be kept 

 constant, so that the arcs corresponding with any two different steady values of the 

 current, however nearly equal they may be, are really two distinct and different 



2 B 2 



