508 LIVING TOEPEDOS IN BERLIN. 



term the Irreciprocity-term. According to our numbers, it seems to 

 increase with the length of the tract traversed. If the objection raised 

 against this is well founded, then it should be possible to represent 

 the phenomena in a mathematical form, even when the term is 

 assumed to be independent of the length of the tract traversed. 



First of all, the question arises, in what way the dependence of the 

 irreciprocity upon the current density is to be conceived of. This 

 question cannot be answered with certainty. The best course seems 

 to be to suppose that the irreciprocity increases with the homo- 

 dromous current density, and indeed the small difference already 

 pointed out between homodromous current strengths for longer 

 and shorter tracts, allows us to assume the irreciprocity term to be 

 proportional to this current strength without any considerable 

 error, rather than to suppose that, in accordance with the previous 

 paragraphs, it grows more slowly than it. We may proceed then 

 further in the following way. Let us imagine, in place of the 

 induction shock, that an equivalent portion of the short duration t 

 is cut out of a constant current, and that E is the electromotive 

 force of the cut-out portion. Next let 



R denote the resistance of the circuit from clay point to clay 

 point, containing the secondary coil of the inductorium 

 and the galvanometer ; 



or the specific resistance of the organ traversed longitudinally by 

 the current, irrespective of irreciprocal resistance or with a 

 homodromous current. ; 



/ the length of the long tract ; 



k that of the short tract of the organ ; 



q the cross section of the preparation 1 ; 



2i, I k the homodromous ; 



I f i, I fk the heterodromous current strength for the longer and 

 shorter tracts respectively ; 



al/q, cr^/^the resistances of the long and short tracts respectively 

 with homodromous current ; finally, 



IiC/q, I k c/q the irreciprocity terms for the long and the short 

 tract respectively, in which c is a constant. 



1 In the first communication (p. 454), in a similar consideration, we put the 

 transverse section = i . It would simplify the expressions and change nothing in 

 the result if we did the same here, but the formulas are clearer if the transverse 

 section appears in its proper place. Moreover, we neglect the circumstance that 

 in our experiments, the current did not pass through the preparation from transverse 

 section to transverse section, but from one clay point to the other applied to the 

 preparation laterally. 



