236 The Structure of Protoplasm 



another. Furthermore, all components do not necessarily remain 

 constant in frequency and amplitude, but can change spontaneously. 



In Figure 7 the waxing and waning periods of the curve are 

 repeated without the details of the waves. The envelope, or imaginary 

 margin of the curve, is not periodic. Such is also the case in Figure 8. 

 If there are only two constant component waves, whose periods differ 

 slightly from each other, the envelope of the resultant wave is 

 periodic, no matter whether the frequencies of the two components 

 are commensurable or not. Furthermore, the resultant waves at 

 the waning periods do not exhibit such irregular and ragged pattern 

 as revealed by the curves shown in Figures 7 and 8. 



It is probably true that the major change in amplitude is due 

 to the same principle as that of beats, as stated in section VIII. But 

 actually, there must exist more subordinate components which 

 would explain the irregular pattern of the waning periods insofar 

 as they diverge from the regular beat wave pattern. The wave pat- 

 terns of Figure 7 are, therefore, a compound rhythm consisting of 

 two main components having slightly different frequencies and many 

 subordinate components of small wave lengths. All these compon- 

 ents may be variable to a certain extent. The situation in Figure 8 

 is also similar to that of Figure 7. 



The general situation of the intraplasmic force is really not 

 simple. It is a necessary conclusion of the analytical study of the 

 dynamoplasmogram that there must exist components having not 

 only slightly different frequencies, but also very divergent ones, 

 namely, frequencies twice, three times, and perhaps, even larger than 

 that of the lowest (fundamental) frequency. The course of reasoning 

 is rather abstract, yet without the concept of polyrhythm, it will be 

 impossible to explain the various types of dynamoplasmogram pat- 

 terns. As stated in this section, the components are unstable; they 

 may not remain constant during a period of time. But the com- 

 ponents, even though they are variable, must have an identity of 

 their own. One and the same plasmodium must produce many fre- 

 quencies of rhythm simultaneously. 



The next important question with which we are confronted is 

 naturally the origin of the different components. The concept of 

 polyrhythm must be harmonized with the actual mechanism and 

 structure of protoplasm. 



Mechanical engineers often study the vibration of machines by 

 separating it into a series of components by analytical methods. 

 Since each part of a machine has its own frequency of vibration, the 



