232 The Structure oj Protoplasm 



limit of the time scheme under consideration. Therefore, this curve 

 can be analyzed into its Fourier components. The characteristic 

 wave form of this figure enables one to predict that both odd and 

 even harmonics are present. Figure 15 shows the analysis of the 

 experimental curve of Figure 10 into its first four components. This 

 analysis was done by means of a graphical method developed by 

 Wedmore (1895). The amplitudes of the 1st, 2nd, 3rd, and 4th 

 component, having the period of ca. 84, 42, 28, and 21 seconds are 

 respectively 11.75, 1.95, 1.45, and 0.70 cm. of water. When these four 



Fig. 15. 



components combine, they produce the resultant shown in the thick 

 line, which is almost the same as the dynamoplasmogram pattern of 

 Figure 10. 



In Figures 11 and 12, very similar wave forms are repeated, but 

 the amplitudes do not remain constant during the experiments. 

 These curves are non-periodic within the range under consideration. 

 Although there is no general method of analysis for non-periodic 

 curves, "much information may be obtained from such curves by 

 making skillfully assumed analyses" (Miller, 1916, 141) . The gradual 

 decrease of amplitude is assumed to be due to an interference effect 

 between two components, the frequencies of which are nearly in 

 unison; it is not due to the gradual "exhaustion" of the protoplasm. 

 The amplitude will increase again after a certain period of time. 



By varying the amplitudes and wave lengths of the components 

 and shifting them arbitrarily along the axis, very similar resultant 

 waves can be reproduced from three components. Figure 16 shows 

 the redrafting of Figure 11. The resemblance of both the experi- 

 mental curve (Fig. 11) and the resultant of the artificially combined 

 harmonic curves (Fig. 16) is striking. The serial ratio of the wave 



