2O8 RALPH S. LILLIE. 



peripheral and the central regions of the protoplasm ; this may 

 be amply sufficient to account for the striking change in the con- 

 figuration of the cytoplasmic colloids. 1 The peripheral layer 

 would become positive relatively to the central region under the 

 conditions existing in such a system as a cell with a surface 

 polarization of the kind indicated. If we can draw safe infer- 

 ences from the cytological facts the astral centers do in fact show 

 the properties of negative regions. 2 I hope however to consider 

 the physiology of cell-division from the above point of view more 

 fully in a later paper. 3 



1 It may be desirable to give here the estimate on which this statement is based. If 

 we assume that the surface potential difference due to the physiological polarization has 

 the same value as the potential difference of the demarcation current of muscle (ca. 0.08 

 volt) and that the fall of potential or negative variation during cleavage is equal to that 

 of the action current (fa. 0.05 volt), we infer that in the resting cell there is a potential 

 difference between exterior and interior equal to ca. 0.08 volt. This gradient, being due 

 mainly to the unequal permeability of the plasma-membrane to the two ions, exists 

 almost entirely between the inner and outer surfaces of the plasma-membrane ; the 

 interior of the cell (cytoplasm) would thus have an almost uniform negative potential 

 of about this value with little if any fall between its central and peripheral regions. 

 If now, in consequence of a sudden increase in permeability, the potential difference 

 across the plasma-membrane decreases by 0.05 volt, a gradient will temporarily exist 

 between peripheral and central regions of the protoplasm equal to this value, the most 

 negative region being that most remote from the periphery. A gradient of 0.05 volt 

 between the center and the periphery of a sea-urchin egg, diameter 0.072 mm., is a 

 gradient of 0.05 volt in 0.036 mm., i. e., i volt in 0.072 cm. or about 14 volts per 

 centimeter. The assumed potential differences may be too high, though they are typi- 

 cal of the directly observed values in muscle cells. The change in permeability is also 

 probably rather gradual than sudden. At least these considerations show that a strong 

 electrical field may arise between central and peripheral regions of the cell under 

 the conditions assumed. Of course no such potential difference could be main- 

 tained without the performance of electrical work on the part of the cell (assum- 

 ing the free movements of ions within the cytoplasm); but its existence for only a few 

 seconds might well produce the observed effects. This note, however, aims merely 

 at justifying the above statement in the text, not at a complete discussion. 



2 Cf. my paper in American Journal of Physiology, 1905, XV., p. 46. 



3 In my first paper dealing with the theory of cell-division (BIOLOGICAL BULLETIN, 4, 

 1903, p. 175) the system of astral radiations was recognized as evidence of an electrical 

 potential difference between peripheral and central regions of the dividing cell, and 

 the form change was ascribed to a capillary electric change of surface-tension. The 

 tentative hypothesis then presented to account for the general course of the process 

 was, however, quite different from that outlined above, and, with the exception of 

 certain details, will have to be abandoned. 



