Physical Aspects of Protoplasmic Streaming 237 



analytical method is a very helpful means of learning from what 

 part of the machine the vibrations come. 



In the case of protoplasm, we do not know in what parts of the 

 Plasmodium the components having different frequencies originate. 

 Each component postulated for the motive force represents simply 

 the resultant of a group of waves having that frequency of different 

 amplitudes and phases generated in any locus of the Plasmodium. 

 Components having different frequencies may come from different 

 loci of one and the same plasmodium. It is, however, surprising that 

 components having not only slightly different frequencies, but very 

 divergent ones are operative in the same protoplasmic system. 



A single string, when it vibrates, produces a series of "over- 

 tones" simultaneously, the frequencies of which are 2X, 3X, 4X, and 

 successive aliquot parts of the fundamental vibration. Whether 

 divergent frequencies of components of the protoplasmic force have 

 structurally or physiologically a common origin, just as in the 

 case of a series of overtones from the vibration of one and the same 

 string, or whether divergency of rhythm is attributable to struc- 

 tural heterogeneity of the protoplasm, is a problem for the future. 



X. ANALOGY AS A MEANS OF ILLUSTRATION 



An attempt to compare a complex mechanism, such as a Plas- 

 modium, which is composed of many unknown factors, with a simpli- 

 fied model may seem to be misleading. Nevertheless, an illustration 

 by means of a model will be helpful, insofar as it is concerned with 

 an explanation of the physical principle which governs the complex 

 living system, just as it governs the simple non-living model. 



The first problem in construction for this analogy is to make a 

 model which, in gross form, resembles the plasmodium with its two 

 parts connected by a single strand of protoplasm. Figure 18 shows 

 a double chamber containing two water reservoirs connected by a 

 single tube. These two reservoirs are comparable to the two blobs of 

 protoplasm in the double chamber (cf . Fig. 5) . The bottom of each 

 of these two reservoirs can be moved up and down by means of a 

 pin-and-slot device. As there is a difference h between the two water 

 levels in reservoir a and b, the water has a tendency to flow from a 

 through the tube to b. The motive force of the movement of the 

 water through this connecting tube is expressed in terms of the 

 dijference in pressure (difference h in level) between the two 

 reservoirs, and not the absolute pressure H at the height of the 



