Researches on the Discharge of the Electric Organ. l5 



discussion liorc. llic discliarge of any single plate cannot of course 

 occur before a stimulus is given, so that the freedom of deviation 

 from the modal value can never be symmetrical. There must exist 

 a certain instant before which the chscharge can never occur. We 

 shall caU this instant the origin of the discharge. This origin may 

 be at the instant of stimulation or it may be later. 



T(j adapt the present case to that of Gauss's it is assumed that 

 the equivalent elementary interval with respect to the deviation is 

 proportional to the interval between the origin and that instant. 



Denoting tlie latent [)eriod <>f a single plate l)y .r, the al>ove 

 assumption gives 



i. e. Jlog.r = A-, 



where /;■ is a proi)ortional constant. Tins nieaiis that, when the 

 logarithm of x is taken as the measure of the abscissa, the case 

 becomes identical with that of Gauss's. 



The well known curve of probal»ility is expressed by 



7/ = ^f -&-'T-, (1) 



w'here tlie origin of x is at the maximum of y. Transforming the 

 origin to — .t,i. then 



is ol)tained. Substituting the logarithm of x and of x^ instead of 

 them, the above reduces to 



y = Ae " .Co \~') 



Since the total electromotive force at any instant must be pro- 

 portional to the number of plates simultaneously discharged at that 

 instant, then, wlien y is taken as the electromotive force at a point 

 on the discharge curve and x as the time-interval measured from 

 the origin of the discharge to that point, the curve expressed by 

 the above formula ought to represent the rlischarge curve obtained 

 by the oscillogragh. 



