40 
V. H. Blackman 
ones in question are ultra-microscopic, and we may assume their 
diameter to be i/ioth that of Perrin’s gamboge particles—an 
assumption which does not seem to err on the side of smallness. 
The relative density may be assumed to be the same as the gamboge 
particles (0-207), though that of the protein drops of the cell would 
probably be less. As the volume of the particles is only i/ioooth 
that of the gamboge ones, it would require a cell 30 millimetres high 
to obtain a difference of concentration of 50 per cent, between the 
top and bottom. Taking a meristematic cell of the root as 30 ju, across, 
it is easy to calculate that for ultra-microscopic particles of the size 
suggested the drop in concentration between the top and bottom of 
the cell would be only 7 parts in 10,000, or 0*07 per cent.; if the cell 
is taken as 50/x broad it is still only 11 parts in 10,000, or o-ii per 
cent. 1 There is thus no reason to believe that the differences of con¬ 
centration of particles in the cell produced under the action of gravity 
would be other than negligible in amount, and in fact so small that 
the term “creaming” can hardly be applied. It seems inconceivable 
that such small differences in concentration could produce the marked 
electrical effects required by Professor Small’s theory. 
(2) There is another great difficulty which the theory presents, 
namely, that of the factor of time. It is easy to show that even the 
very small movement—which, as pointed out above, is all that can 
be expected of the cell particles—would take place so slowly that 
it could not be a link in the chain of processes which controls the 
rapid geotropic reaction of the stem and root. Perrin, working with 
the large colloidal particles of radius 0*21 /x, allowed three hours for 
the completion of the process. With decrease in size of the particles 
or increase in viscosity of the medium, however, the time taken to 
reach equilibrium increases. In another of Perrin’s experiments 
with rather larger particles (0-38/x radius) and a highly viscous 
medium (viscosity 125 times that of water) the time taken to reach 
equilibrium was “several days.” One can calculate from this that 
particles no smaller than of 0*034 M radius moving in a watery 
medium would also take days to reach equilibrium. As by the 
author’s hypothesis the particles are ultra-microscopic and so must 
be of this order of size and probably smaller, and the cell medium 
in which they move is more viscous than water and possibly highly 
viscous, the time taken to settle down or rise up under the action of 
gravity must also be of the order of days. 
1 Even if the diameter of the ultra-microscopic, particles of the protoplasm 
be taken as only i/5th of that of the gamboge particles, the difference in 
concentration in cells 30^ and 50 n broad would be only o-6 per cent, and 
0*9 per cent, respectively. 
