a Wave-Tracer and Analyser. 557 



11. On the tbrmiilii established in § 10, that 2n times the 

 «th component ot any periodic function /(/) is equal to 



a simple method of analysing periodic curves (specially 

 simple for those containing only odd harmonics) can be based 

 which is very analogous to that proposed by Wedmore*. 

 The formula on which his method depends is 



/(')+/(«+3+/0+2^)+&c. +f{t + (:n-l)l} 



= «{(•„ sin (^n(£)t — On) + Con f^iii {'^nwt - ^^h) + &c.}. 



Thus the function he gets from adding n equal spaced 

 ordinates of a full wave is periodic, of periodicity n times 

 that of the original wave, and contains only those of its 

 harmonics that are any multiples of n, while the method 

 here proposed will give components which are odd periodic 

 functions, in fact the components as I have defined them in 

 the early part of this paper. 



12. It is obvious that the wave-analyser can be applied to 

 wave-forms that contain both even and odd harmonics, and 

 that the operation in § 2 is the simplest example of its use. 



With a commutator that acts four times per period w^e 

 have a very accurate means of testing whether the wave- 

 forms of E.M.F., current, or flux that originate from a given 

 generator contain only odd harmonics. 



A careful test by this method was made of the E.M.F. 

 curve of a Parson^s generator, both when on practically open 

 circuit and when carrying a heavy inductive load. In neither 

 case was there the slightest indication that a second component 

 was present. A similar test was made of the wave-^form of 

 current from a rotary transformer supplied with direct current 

 from storage-cells, and also of the wave-form of the magnetic 

 flux produced by this current in a ring of iron wire. In these 

 cases again the second component was absent, the galvano- 

 meter remaining steady at zero independently of the position 

 of the movable brushes. This of course does not prove that 

 in wave- forms produced by other machines no second com- 

 ponent is present. 



13. Fig. 4 (PL XX III.) shows a wave-analyser made to obtain 

 the 1st, 3rd, 5th, and 7th components of E. M.F., current, or flux- 

 waves when driven direct by the generator if it is a four-pule 



* ^ee Journal ln.<t. Elect. Eugineerjj. vuL xxv. p. '2'2\ (1800). 



