396 Proceed in gs of the Roi/al Societ// of Victoria. 



alternate current waves Ijy the wave tracer and analyzer^ 

 designed by the author. In the simplest case, when ;/=l, the 

 wave tracer <,dves the first component of the periodic quantity 

 operated on, which in the case of alternating electric currents is 

 the full wave. By the movement of two pairs of brushes /i can 

 be made 3, or 5, or 7, in which cases the analyzer will give the 

 3rd, 5th, or 7th components of the wave respectively. 



Now, in practical investigations with this apparatus on alter- 

 nating current waves whose harmonic expressions were required, 

 it was found much better to obtain by its means only the full 

 wave trace, and then by an arithmetical process identical with 

 the action of the analyzer and indicated by equation II. above, 

 to obtain the 3rd and higher components of the wave, and thence 

 to deduce its harmonics. 



This method of harmonic analysis was drawn attention to in 

 the paper already quoted, and though based on a different 

 formula to that of Wedmore,"^ is practically similar to his. It is 

 more suitable, however, for waves containing only odd harmonics, 

 and as I have had considerable experience in its use during the 

 last two years and have found it both expeditious and accurate, 

 it is possible that a short account may be of value to those 

 interested in alternating current work. 



4. In wave graphs it is more convenient to use angular abs- 

 cissae X where 



X = iiit=^ 27r//T. 

 Making this substitution in the equation y = f{t) it becomes 

 y=g{x) say, where 



g{x)=g{x + -2Tr), 

 and \i f{t) is an odd periodic function as in the case of alternate 

 current waves which we are now considering, 



g{x) = - g{'^ + ^) =g{x + 27r). 

 Substituting ^ (at) ior/\t) in equation II. it becomes 



nCn = ^{x) -o{x + TTJft) +^ix + 2 TTJn) - . . . 

 +g{x + n-l TTJn), 

 from which we conclude that, if 



1 Lyle : "Preliminary Account of a Wave Tracer and Analyzer." Phil. Mag., Nov. 

 1903. 



2 Wedniore: Journal Inst. Elect. Engineers, vol. xxv., p. 224 (18%). 



