144 



THE STUDY OF SPEKCH CURVES. 

 Table of Results of Frictional Analysis of Figure 121. 



To calculate the inharmonics we may follow the rule given above 

 (p. 81) as a first suggestion. We find minima at 2.2, 2.6, 0.4, and 1.3, 

 which we divide in the usual way. For the first group we have 



( 1X1S.4)+(2X24.6)+(3X54.9) + (4X68.5)+(5X18.2)+(6X17.2)+(7X5.7)+(8X2.4) + (9X1.0 ) 



18.4+24.G+54.9+6S..5+18.2-f 17.2+5.7 + 2.4+1.0 



= 3.0, 



indicating a component with wave-length 360mm. h- 3.6= 100.0mm. 

 For the other groups we find in like manner 10.4, 12.8, 15.7, and (since 

 the series is cut off at a rise) 18.0. Taking j of the maximum as the 



amplitude of each com- 

 =- ponent we have 91.4, 

 3.6, 7.6, 2.1, and 3.2 as 

 the set of amplitudes. 



Two modifications 

 suggest themselves. As 

 indicated by figure 76, 

 the harmonic elements 

 that are produced by 

 an inharmonic fall off 

 steadily according to a 

 definite law. We can 

 not attempt to apply 

 the law here, but we see 

 at once that the series 



Fig. 127.— Actual components of figure 121. of amplitudes fails tO 



fall from beyond 18.2 as it must do if only the inharmonic 3.69 is present; 

 there must be another tone at or near the 6th harmonic with the ampU- 

 tude 17.2 for the 6th partial. We can therefore treat 18.2 as a minimum 

 and divide it in the ratio of its neighbors. We then have the com- 

 ponent 6.3 with the wave-length 57.2mm. and the assumed amplitude 

 22.9mm. We also observe that the amphtude falls from 54.9 to 24.6, 



