400 Proceedmgs of the Royal Society of Victoria. 



is advisable to obtain four values of a from the first four ordin- 

 ates on the rising side of the wave and four from the last four 

 ordinates on the falling side, and take the mean of the eight. In 

 this way we can to a great extent eliminate any error that might 

 arise due to a harmonic even as low as the seventh not having 

 been i-emoved. 



In a similar way the phases of H,, H., etc., can be determined, 

 but it must be remembered that if, for instance, 



Hg = /^asin3(a)/ - j3), 

 and if /?q, h-^, . . l\ are the ordinates of Hg corresponding to 

 the abscissae x^., JCj, . . .Vj, then 



sin.3(A-o-/3) = <^o/^''3 etc. 

 similarly, if 



H5=/zsSin5(oj/ - y) 

 with ordinates ^„, (Tj, r^, 



then sin5(A:o - y) = ro/>^,5. 



7. The wave to be analyzed may be given in either of two 

 ways. We may have the complete trace of it obtained by the 

 author's wave tracer by the photographic method, or by any 

 form of oscillograph that gives a trace of the wave form ; or we 

 may have the values of a definite number only of ordinates per 

 half wave, such as would be obtained by the author's wave 

 tracer by the galvanometer and scale method. 



From the wave trace the complete harmonic expression can 

 theoretically be obtained, but the impossibility of accurately 

 measuring on the photograph, without elaborate apparatus, the 

 different ordinates required leads to great inaccuracy in tlie 

 result. 



From a given number of e.s. ordinates only an approximate 

 analysis can be obtained, more approximate, of course, as the 

 number of ordinates is greater. When, however, each individual 

 ordinate has been obtained with the accuracy of which the galva- 

 nometer and scale method is susceptible, the analysis obtained 

 from fifteen such ordinates is much more reliable, as far as the 

 harmonics up to the 9th are concerned, than that determined 

 from any photographic trace. 



I will therefore illustrate the method by applying it in full 

 detail to the analysis of the wave whose 15 e.s. ordinates are 



