THE SOURCES OF ENERGY 



35 



Velten l concluded that the streaming plasma always followed the path 

 of least resistance, whereas Hormann (I.e., p. 17) states that in elongated 

 cells the current always follows the path of absolutely greatest resistance. 

 Hermann's remarks, however, would apply only if the friction were between 

 a membrane and a fluid which did not wet it. In the plant-cell, the 

 resistance to streaming is dependent solely upon (i) the viscosity of the 

 streaming layers, which is unaffected by the direction of the streaming move- 

 ment, and (2) upon the path followed. That the total resistance to a complete 

 circuit around the long axis of a cell will be greater than around its short 

 axis is self-evident, but the path of least resistance is that in which the 

 passage across a certain space requires the least expenditure of energy. 

 Now every bend or turn in the stream which is sufficiently sharp to pro- 

 duce eddy currents increases the resistance to flow, and hence, other things 

 being equal, the path of least resistance will be that in which the current 

 flows along a straight, or uniformly curved, path. A path parallel to the 

 long axis of the cell will naturally be assumed when the cell is rectangular 

 or flattened, and a spiral path fulfils the above conditions best when the 

 cell is an elongated cylinder, as in Chara and Nitella. That the spiral 

 direction of streaming in the latter case may be of biological utility is 

 quite possible, just as may also be the spiral twisting of the cortical cells 

 themselves, but teleological explanations afford no indication of causal 

 relationship. 



With regard to streaming in threads, it is important to remember that 

 in thin ones the entire mass may appear to stream in a particular direction, 

 whereas in thick ones showing streaming in opposite directions, the central 

 portion is usually at rest. 



SECTION 13. The Sources of Energy. 



The direct agencies in producing streaming are probably physical in 

 character, although the energy is without doubt ultimately derived from 

 the chemical changes occurring in the protoplasm. Although we cannot 

 at present refer the phenomenon to its immediate causes, this is no reason 

 for evading the question by referring streaming to the domain of vital 

 phenomena. All ' vital ' phenomena are simply manifestations of the same 

 elemental properties of matter, and of the same transformations of energy, 

 with which the sciences of Chemistry and Physics make us familiar. The 

 only difference is that in the case of organized structures these forces and 

 properties often enter into complicated and interacting combinations, the 

 precise nature of which is at present obscure. The physiologist must, how- 

 ever, hold in view the possibility that all 'vital' entities may ultimately be 

 found reducible to simpler physical and chemical ones. 



1 Flora, 1873, p. 85. 

 U 2 



