LIVING TOEPEDOS IN BERLIN. 509 



Then we have 



m T Et 



= R+ ^' *~R+*!' 

 2 2 



^ = TZ T~S i>k = ~n F7* W 



The irreciprocal resistance is made here dependent upon the 

 dimensions of the tracts traversed by the current, only in so far 

 as the homodromous current density, which is taken to be pro- 

 portional to the irreciprocity term, depends upon those dimensions. 

 Now according to our observations, irrespectively of the opposite 

 signs of / and 1, , we must have 



i. e. we must have 



,, (T iC ^ (T ,0 



R + + -- > R + + JL 

 q 2 2 t 



2 2 



or (qR + t(r)Ii>(qR + l<T)I k . (d) 



This is impossible, since for R = o, or a mean value of R, the left 

 side, factor for factor, is the smaller, and since, if all resistances are 

 made to disappear in comparison with R, at the most, equality of 

 both sides will be obtained. Consequently we do not succeed, when 

 the irreciprocity term is assumed to be independent of the length 

 of the tract traversed. 



On the other hand, if in (a) we substitute 



for (Icr + Ii c)/q and for (&<r + I k c)/q 



i. e. if we treat the irreciprocal resistance as an increase of the 

 specific resistance proportional to the current density when the 

 current is a homodromous current, then we get instead of (b) the 

 inequality 



(gR + # a) ll t > (qR + Jcr) kl k . (c) 



