Experiments with Alternating Currents. 243 



In the case of intermittent contact no current will go 

 through the galvanometer when 



(1-r) sin^= - j s'mpt- — sin^p*— yj j, 



A ; ~2\ 30 sin^ /* 

 Let pi = + BO, when S0 is infinitesimally small r= — go , 

 » =-W, „ „ „ „ y=+oo; 



nothing corresponding to these results can be obtained in 

 practice. 



In the above equation the contact is supposed to be of 

 infinitesimal duration ; as a matter of fact this is not the case : 

 let r= time of contact, then a more correct equation would be 



30 C t+T . 



sin pt dt 



However, this equation, integrated, would also give rise to 

 expectations of discontinuity in r, when 



T T T 



*= — 2> 7r ""2' 27r "~2' 



It will be interesting to find what would be the theoretical 

 readings for various values of pt. 



I. Let jo* =30°, 



n ^ 1 f-, 1 sinl5° ) _ Q _ 



f=*4914 ; Reading =491. 



II. Let pt= 60°, 



(1— r) = *495, ^ = '505. Reading = 505 approx. 



III. Let ^ = 90°, 



(l-r) = -4882, r=-5118. Reading = 5 12 „ 



IV. Let ^=120°, 



(l-r)=-4814, r=-5186. Reading=519 „ 



V. Let pt= 150°, 



(l-r) = -4678, r=-5322. Reading = 532 „ 



VI. Letp*=180°, 



r changes from ■+• cc to — oo . 



