Irreciprocal Conduction. 131 



values of x below this, one of them is the greater; for values 

 of z above this, the other is the greater. He then assumes 

 that fc, and k 2 are proportional to q x and q 2 respectively, and 

 thus proves the existence of irreciprocal conduction. 



The assumptions made, namely (1) that e x is a measure of 

 the polarization E.M.F. which opposes the passage of q t , and 

 (2) that k x is exactly proportional to g,,do not seem to be ad- 

 missible. Firstly, with regard to (1), e 1 is really propor- 

 tional to the depolarization current which exists a certain 

 time, conditioned by the time of vibration of the galvano- 

 meter &c, after the charging E.M.F. has ceased, and is not 

 proportional to the value of the polarization E.M.F. during the 

 existence of the charging E.M.F., unless the rate of depolari- 

 zation is constant, which it usually is not. Also, as will be 

 shown in a subsequent paper, the rate of depolarization with 

 unequal-sized electrodes depends on the direction of the 

 charging current. It may also be noticed that q x or q 2 &c. 

 do not necessarily bear any simple relation to the value of 

 the induced E.M.F. The quantity of electricity which passes 

 in any time dt during the existence of the induced E.M.F. is 

 proportional to the difference between the values at that time 

 of the induced E.M.F. and of the polarization ; and therefore 

 the relation between the charging E.M.F. and the quantity of 

 electricity which passes during its existence depends on the 

 rate of increase of the polarization E.M.F., which can scarcely 

 be said to be known, but is probably not constant, and may 

 even vary according to the direction of the current. The 

 validity of assumption (2) is also doubtful, for the kick (k) 

 on the galvanometer depends not only on q (the quantity of 

 electricity which passes during the existence of the induced 

 E.M.F.) but also on the magnitude of the depolarization cur- 

 rent, since the duration of the induced E.M.F. is certainly over 

 before the galvanometer-needle has moved from zero to k 

 divisions. Thus it would seem that k is only at best, in the 

 case of non-polarizable electrodes, an approximation to the 

 value of q; and therefore Christiani's numbers are not suf- 

 ficiently trustworthy to serve as foundation for an elaborate 

 theory. 



Christiani, however, assumes that k and q are exactly pro- 

 portional and plots curves * giving the relation between q and 

 the induced E.M.F. in the two directions of the current. The 

 point of intersection of the two curves is called the reciprocal 

 point; its abscissa being proportional to the induced E.M.F., 



* These curves are regular and never intersect in more than one point, 

 and with some electrolytes do not intersect within the limits of experiment. 



K2 



