142 



THE STUDY OF SPEECH CURVES. 



addition. In the present case we have no further information concerning 

 the curve and as the best approximation we must use the maxima and 

 minima as we find them. 



We now propose to multiply the ordinates of the curve by e^ °-'^^' and 

 then to perform a simple harmonic analysis of the new curve, as indicated 

 by the principles of the frictional analysis (Chapter VII). We expect 

 thereby to obtain the frictional sinusoids out of which the curve was 

 originally composed. 



Since each of the ordinates is to be multipUed by the corresponding 

 value of e + '""'^", we have first to calculate this quantity for the 36 ordinates. 

 We first obtain s.log e = 0.0028 X 0.4343 = 0.00122. The 36 abscissas have 



70 

 60 

 50 

 40 

 30 



ro 



10 



eo 



70 

 60 



50 

 40 



30 



ao 



I I I I I 



1 



I I I I 



I a .3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 13 



Fig. 125. — Harmonic plot to figure 124, or fric- 

 tional harmonic plot to figure 121. 



1 2 3 4 5 6 7 B 9 10 II 12 13 14 15 16 17 18 



Fig. 126. — Plot of inharmonic components 

 from figure 125. 



the values 0, 10, 20, 30, . . . ; we have therefore only to find £^io.loge = 

 0.00122X 10 = 0.0122, and then to multiply this by 0, 1, 2, 3, . . . 35. The 

 results are given in the first column of the adjacent table. For each of 

 these values we find the numerus (from a table of logarithms). The 

 values of e"™^"' thus obtained are given in the second column. The third 

 column gives the values of y in the original curve ; the last column gives 

 the product i/.e"""^^'. These are the ordinates of the new curve (figure 

 124) from which the frictional element has been removed. 



The new ordinates are multiplied by the cosines as indicated in the 

 adjacent table. With the schedules we obtain a and h as usual. These 

 are used to give c, q, and r as before. The results give the simple harmonic 

 analysis of figure 124, or the frictional harmonic analysis of figure 121. 



