228 The Structure of Protoplasm 



appearance of a characteristic wave form in successive rhythms (cf. 

 Figs. 10, 11, and 12) of the vital process. 



By studying many examples of wave trains, it seems most prob- 

 able to me that such extraordinary variability in the pattern is due 

 to nothing but the well-known physical phenomenon called inter- 

 ference. 



Interference is one of the most remarkable phenomena asso- 

 ciated with wave motion. It is well known in acoustics, optics, and 

 other fields of science. The significance of interference in vital 

 functions has, however, been scarcely considered. In order to study 

 the rhythmic character of protoplasmic force, the rhythms being 

 regarded as a combination of a series of components, it is pertinent 

 to take up the general features of compounded harmonic waves. 



A simple case is that of two superimposed harmonic waves 

 having equal wave lengths. The resultant wave is a harmonic curve 

 of the same frequency, no matter what the amplitudes and phases of 

 the component waves may be. The amplitude of the resultant depends 

 upon the amplitudes of the two component waves, and upon the 

 phase difference between them. If the components are always in the 

 same phase, the amplitude of the resultant wave is the sum of the 

 amplitudes of the components. If one of the two components is half 

 a period behind the other, the amplitude of the resultant is the 

 difference of the amplitude of the components. From this, it follows 

 that any number of harmonic curves of the same wave length may be 

 so formulated that the resultant is a single harmonic curve of the 

 original wave length. Conversely, if a harmonic curve is experi- 

 mentally obtained, it can be assumed to be the resultant of numerous 

 indeterminate harmonic components having the same wave length. 

 The resultant wave will exhibit a harmonic curve regardless of the 

 amplitudes and phases of the components. If, therefore, the pattern 

 of a dynamoplasmogram shows pronounced similarity to a simple 

 harmonic wave, this does not necessarily mean synchronous coopera- 

 tion of the intraplasmic forces; it means simply, that all the com- 

 ponent forces in one and the same plasmodium have the same 

 frequency of the motor mechanism. 



The next case is very important for our subject; it is that in 

 which the frequencies of the two component waves differ slightly. 

 Because of a difference in wave length, the phase difference between 

 the two components does not remain constant. The amplitude of the 

 resultant wave is increased when the waves are in the same phase, 

 but when the waves are in opposite phases, the amplitude of the 



