PIERCE AND EVANS. — CAPACITY OF CARBORUNDUM. 813 



This equation by expansion becomes 



T T T 



q=CE{\- 2e'^^ + 2 (^e'^y - 2 (/«^)« + ....). (27) 



T 



If we may neglect 2 {e-^^Y in comparison with unity, equation (27) 



becomes 



r 



q=CE{l — 26'^^) approximation. (28) 



If there are w charges per second, the current-reading of a galva- 

 nometer in the charge or discharge circuit is 



I=nq, 



and the time of charge or discharge is 



pn 



where \/p is the fraction of the circumference of the commutator oc- 

 cupied by the charge segment or discharge segment, the two being 

 equal. 



With these substitutions equation (28) becomes 



I=nCE{l-2e ^"^^). (29) 



With the commutator used in these experiments \/p was .48, whence 



a48 



'nRC 



I=7iCE{l-2e "«^). (30) 



Examination of the Data of Experiment II. 



The curves of discharge current of Figures 10 and 11 with current 

 plotted against number of discharges per second are accurately de- 

 scribed by equation (30), as may be seen by reference to Tables VI. 

 and VIL, which contain a comparison of observed and calculated 

 values. 



The equations of Table VIII. were obtained as follows : Consistent 

 with the theoretical equation (30), the slope of each of the curves of 

 Figures 10 and 11 was taken at the origin. This slope is the coeffi- 

 cient of n in equation (30), and the corresponding coefficient in Table 



