On a Simple Form of Harmonic Analyser. 367 



true. It may be that energy passes from the potential into 

 the kinetic form in the aether itself, and not merely on the 

 surface of the molecules. Kinetic energy may consist of the 

 motion of the whole system of energy-cells. This would lead 

 us very near the theory which regards the molecule as being 

 nothing but the mathematical centre from which forces pro- 

 ceed, or perhaps, from another point of view, as having infinite 

 extension. 



XXXV. On a Simple Form of Harmonic Analyser. By 

 George Udny Yule, Demonstrator in Applied Mathematics, 

 University College, London *. 



" The subject of the decomposition of an arbitrary 

 function into the sum of functions of special types has 

 many fascinations. No student of mathematical physic?, 

 if he possess any soul at all, can fail to recognize the poetry 

 that pervades this branch of mathematics."— Oliver 

 Heaviside. 



§ 1. A BOUT a year ago several instruments for deter- 

 X\. mining the coefficients of a Fourier Series 

 expressing the equation to a given curve were described 

 before this .Society by Professor Henrici f- One of them, 

 Professor Henrici's shifting- table analyser, used a planimeter 

 as the integrator; an arrangement that seemed to me very 

 noteworthy from the point of view of simplicity and cheap- 

 ness. The analyser I am going to describe also uses a 

 planimeter : consequently it can also only give the value of 

 one coefficient at a time. 



§ 2. Let P Q R be the curve to be analysed. Let the base 

 PR range from a=—l to #= -t I, and the equation to the 

 curve in terms of a Fourier Series be 



?/ = iA o - r -A 1 cos0 + A 3 cos2#+ . . . 



+ LVsin0-f B 2 sin 2(9+ . . ., 



= TTX/I 



where 



and ^A is the mean ordinate of the curve. The values of the 

 other coefficients are given by 



* Communicated by the Physical Society : read March 8, 1895. 

 t Phil. Mag-, xxxviii., July 1894 ; also Catalogue of the Mathematical 

 Exhibition at Munich (1892-93). 



