10 Michelson and Stratton — New Harmonic Analyzer. 



amplitude d (fig. 1) is proportional to f(na\ the machine gives 

 %f{na) cos n0=z2f(x) cos -dx 



o ° 7T 



which is proportional to a k if 7c= 



m 



Hence to obtain the 



integral, the lower ends of the vertical rods R (Plate I) are 

 moved along the levers B to distances proportional to the ordi- 

 nates of the curve y=f{na). 



The curve thus obtained for a k is a continuous function of 

 Jc which approximates to the value of the integral as the num- 

 ber of elements increases. To obtain the values corresponding 

 to the coefficients of the Fourier series, the angle d=n, or the 

 corresponding distance on the curve, is divided into m equal 

 parts. The required coefficients are then proportional to the 

 ordinates erected at these divisions. 



Figure 11 gives the approximate value of I cp{x) cos lex 



dx 



when <p(x) = constant from to a, and is zero for all other 



values. The exact integral is — - — . The accuracy of the 



approximation is shown by the following table, which gives 

 the observed and the calculated values of the first twenty coef- 

 ficients for a =4*0. 





/ cos Jc 



x dx 





n. 



obs. 



calc. 



A 







]00-0 



100-0 



o-o 



1 



65-0 



64-0 



1-0 



2 



00 



o-o 



00 



3 



—20-0 



—2 1 -0 



1-0 



4 



o-o 







o-o 



5 



12-5 



13-0 



—0-5 



6 



—1-5 



O'O 



— 1-5 



7 



—9-0 



— 9-0 







8 



o-o 



O'O 



o-o 



9 



6 



7-0 



— 1-0 



10 



00 



o-o 



—2-0 



11 



—6-0 



—6-0 



o-o 



12 



o-o 



o-o 



—0.0 



13 



4-0 



5 



— 1-0 



14 



—2-0 



0.0 



—2-0 



15 



. —4-0 



4-5 



0-5 



16 



0'5 



o-o 



05 



17 



8*5 



4-0 



—05 



18 



—1-0 



o-o 



—1-0 



19 



—35 



—3-0 



0-5 



20 



o-o 



o-o 



00 



