550 Prof. T. R. Lyle : F reUmi nary Account of 



■which is the snm o£ the wth, 3nth, 5/ith, &c., hiirmoiiics 

 contained in the original function. 



1. In order to either plot or photograph the wave-form of 

 an alternate current, I send the latter through the primary of 

 an air- circuit transformer whose secondary has few turns. 



In the secondary circuit is a commutator (attached to the 

 spindle of the generating alternator or of a synchronous 

 motor) which commutates twice per period, and from the 

 commutator the circuit is completed through a high resistance 

 and a delicate Ayrton-Mather dead-beat galvanometer. Two 

 of the four brushes of the commutator are attached to a 

 divided circle which can be rotated by means of a tangent- 

 screw, so that commutation can be effected at any point or 

 instant of the phase of the }»rimary alternate current-wave. 

 For each position of the movable brushes the galvanometer 

 will show a steady deflexion which is proportional to the 

 instantaneous value of the primary or original current at the 

 instants of commutation. 



' 2. For if i) be t,he current through the primary of the air- 

 transformer, M the mutual inductance of its coils, and r the 

 large resistance in its secondary circuit, then the secondary 

 current will be - . , 



T at' 



This is Ipgitimate, as the time constant of the secondary is 



made so small as to be inappreciable not only relative to the 



time constant of the primary, but in itself. 



T 

 If now commutation be effected at times ^, ^+ — ^-f T, &c.' 



where T is the period, the quantity Q of electricity that flows 

 through the galvanometer during one complete period will 

 be given by 



T 



Q= f Jc- J rfO 



= C,^T_C,-CWT+fUT 



= -40,; 



for, as only odd harmonics appear in alternate current-waves 

 (see § 12), C;^T=_-C^; therefore 



