Physical Aspects of Protoplasmic Streaming 



231 



Fig. 14 — continued. 



Indeed, the interference of two component waves having sHghtly 

 different frequencies is, in all probability, responsible for the major 

 change in amplitude, but it can not be the general principle govern- 

 ing the protoplasmic system. In order to explain the repeated 

 appearance of a peculiar wave form throughout several successive 

 rhythms, the example of which is shown in Figures 10, 11, and 12, 

 many subordinate components of different frequencies must be 

 attributed to the protoplasm. 



On the basis of the mathematical principle known as Fourier's 

 Theorem, any one-valued periodic curve can be analyzed into har- 

 monic curves of suitable amplitudes and phases having wave lengths 

 of 1, 1/2, 1/3, 1/4, 1/5, and successive aliquot parts of the wave 

 length of the wave to be analyzed. A given wave can be resolved 

 into only one combination of simple harmonic curves of definite 

 amplitude and phases. Theoretically, an infinite number of com- 

 ponents is generally required to represent arbitrary periodic curves, 

 but, for practical purposes, the first few components are sufficient, 

 since the Fourier series converges rapidly for most wave forms. 



The curve shown in Figure 10 is practically periodic within the 



