484 W. Mason — New Harmonic Analyser. 



Art. XXXVI. — A New Harmonic Analyzer; by Warren 



Mason. 



Since Fourier first published his "Theory AnaMique 

 de la Chaleur, ' ' there have been a number c : machines 

 called harmonic analyzers invented for the purpose of 

 evaluating his integrals mechanically. Some of these 

 have been in use for over a hundred years, so the only 

 reason for describing another one would be that it is 

 simpler to make or more accurate than other machines. 

 The instrument described in this paper has about the same 

 degree of accuracy as any except the Henrici analyzer, 

 but its main point of interest is that it can be made by 

 anyone without the use of complicated machinery. 



A periodic curve can be represented by a series of the 

 kind 

 y — A -f- A^ sin a -|- Bj cos a + ^2 ^in 2 a -|- B^ cos 2 a -f • • ♦ 



where A is a constant equal to the algebraic sum of the 

 area of the two loops forming one wave length, and A^, 

 Bi, A2, B2, etc., constants denoting the maximum heights 

 of the respective harmonics. Fourier has shown that the 

 value of any constant A« is given by the integral 



A„ — . — / y sin 71 a « a, 



TTc/O 



while the value of the constant B„ is given by 



1 f*2Tr 



B,j = — / y cos ?l a d a. 



As in the case of most harmonic analyzers, this machine 

 evaluates the above integrals by tracing an area propor- 

 tional to the value of the expression. Therefore we may 

 at once write 



K A = A,; (1) 



where A is the equivalent area referred to above, and K 

 a constant of proportionality. Substituting the integrals 

 for the above terms, we have 



K / (y/ — 2/1 ') <^^^' = ~ / 1/ sin n a d a. (2) 



X, and y in the following equations refer to the coordinates 



of the wave form with reference to axes at the origin of, 



, and along the axis of, the wave form, while x% y' , which 



