﻿Intelligence and Miscellaneous Articles. 335 



To the Editors of the Philosophical Magazine. 



Gentlemen, — 

 By your courtesy I am able to reply to the matter raised by 

 Professor Lyle, whose work in Harmonic Analysis with his Wave- 

 Tracer and Analyser is well known to me. It is probably due to 

 the width of ocean which divides us that any misunderstanding 

 can have arisen. He suggests that I am not aware of Mr. 

 Wedmore's still earlier method of 1896. At that date Mr. 

 Wfdmore was a valued member of my staff ; and I had every 

 reason to know the detail of his work. The essential points of! 

 difference between Professor Lyle's process and mine appear to be 

 these. He takes one set of selected ordinates (" usually fifteen," 

 he says) to determine the analysis of the curve and to discover its 

 harmonics ; whereas I take different numbers of selected ordinates 

 for each harmonic which I wish to determine. For each harmonic, 

 with his ingenious machine which electrically reverses the sign of 

 the successive ordinates and then adds them, he is able to deter- 

 mine the amplitude directly by rocking the contacts so as to attain 

 the maximum reading, and so deduce the amplitude of the harmonic. 

 In my method this is not applicable in the slightest degree ; for in 

 the graphic and arithmetical processes one cannot rock the tem- 

 plates by which the ordinates are selected and measured, to such a 

 position as to give off-hand a maximum average value. Hence in 

 my process it is essential to determine separately the sine and 

 cosine components of each harmonic. 



In Professor Lyle's process (as also in mine) the presence of any 

 higher harmonic of an order that is any odd number of times the 

 frequency affects the result, and must if present be separately 

 evaluated and eliminated by subtraction. Hence it seems to me 

 that his process, which does not separate the sine and cosine com- 

 ponents', will be in error if there is any difference of phase between 

 the harmonic that is being determined and the higher harmonic 

 present : for the position of maximum attained by the rocking of 

 the contacts takes no account of such difference of phase. I 

 ought in justice to add that another prior worker in this field, 

 Dr. Fischer-Hinnen, whose memoir is mentioned amongst the 

 references in my paper, did determine separately the sine and 

 cosine components, though he gave no theory of the process. But, 

 indeed, the separate determination of sine and cosine components 

 is as old as Pourier. A point of novelty in Prof. Lyle's electrical 

 process w 7 as the avoidance of this very feature. A very simple 

 consideration shows that the characteristic method of Fourier's 

 analysis is the multiplication of every ordinate by the sine or 

 cosine of the angle at which it stands (or by some multiple of that 

 angle corresponding to the order of the harmonic sought), prior to 

 integrating. My process is equivalent to selecting only those 

 ordinates for which the sine or cosine needed in the multiplication 

 is either 4-1 or —1; hence the integration is effected by mere 

 addition and subtraction ; hence also it comes back to being a 

 particular case of Fourier's method. 



I am, &c, 



Jan. 27. 1912. SlLVANUS P. THOMPSON". 



