418 



Profs. John Perry and W. E. Ayrton. [May 27 r 



Discharging of the Voltameter. 

 February 14, 1878. 



Time in 



Observed value 



u' calculated 



Difference 



minutes. 



of u. 



from (7) . 



(u — ?«') . 



6 



244-0 



123*4 



120-6 



10 



156-8 



100-2 



56*6 



15 



91*4 



77 - 9 



135 



20 



62*0 



61*2 



0*8 



30 



37*8 



39*3 



— 1-5 



40 



26-6 ... 



27-0 



-0-4 



50 



20-6 



20-2 



0-4 



60 



16-4 



16:3 



o-i 



70 ■ . 



14-0 



14-1 



. , -o-i 



80 



13-0 



12-9 



o-i 



The reason why the exponentials in the equation connecting 

 currents and time when charging differ from those connecting 

 currents and time when discharging the voltameter, is as follows : — 

 If r is the resistance of the battery, galvanometer, connexions, &c, 

 but excluding the resistance of the voltameter itself, then — 



Y-v 

 u= , 



r 



where V is the electromotive force of the battery, and v that of the 

 voltameter, at any time t during the charging — 



dv du 



"dl~ ~ 1 W 



d 2 v dhi 



dP~~ r ~d$' 



which when substituted in the general differential equation, enable the 

 integration to be effected. But during the discharge after the 

 removal of the battery, if r is the resistance of the galvanometer, con- 

 nexions, &c, but excluding that of the voltameter itself, then — 



_ u v 



r'' 



dv ,dv. 



' 'di~ T W 



&c. 



Consequently the constants in the differential equation, and therefore 

 the exponentials in the equations of our curves, must be different. 

 Guided by this, we have arranged in our later experiments that r 



