The Theory of Geotropic Response 41 
Professor Small refers to Perrin’s work on Brownian movement 
(1910, loc. cit.) in which it was demonstrated that the rate of fall or 
rise of colloidal particles under the action of gravity can be calcu¬ 
lated from Stokes’ law. The conclusion, however, he draws from 
Perrin’s work that in the cell the “creaming is governed by Stokes’ 
law” (footnote, p. 52) is certainly mistaken. Once it is recognised 
that colloidal particles obey the “rarefaction law” it is obvious that 
Stokes’ law, which applies to freely falling particles, is only followed 
when the particles are far removed from their equilibrium distribu¬ 
tion. Perrin makes this point clear (loc. cit. 1910, p. 34), and in 
investigating the application of this law to the comparatively large 
particles of gamboge he used a tube several cms. long. The small 
ultra-microscopic granules within the narrow confines of a cell only 
0-05 mm. in height must always be little removed from their limiting 
distribution, as demonstrated above; they therefore cannot fall 
freely and Stokes’ law cannot apply. In order that the plasma 
particles should be under the same conditions as Perrin’s gamboge 
particles a cell at least a metre high would be required 1 . 
The considerations put forward above indicate that any re¬ 
arrangement of the cell particles which might occur under the action 
of gravity would be exceedingly small in amount, and would be 
accomplished very slowly. The geo tropic response, on the other hand, 
is a particularly rapid process. Under ordinary conditions a “pre¬ 
sentation time” as low as two minutes has been observed, and the 
“excitation time” is certainly very much less. Professor Small has 
himself described earlier a geotropic reaction appearing as a change 
in electrical conductivity of the cells of the root tip which is to be 
observed in as short a period as 20 seconds after the organ is placed 
horizontal. Bose (Trans. Bose Inst. 11, pp. 500 and 452, 1919) found 
in one case a large electric response occurring one second after the 
horizontal position was reached, and in another case the maximum 
deflection was attained in 90 seconds. It would seem impossible to 
correlate active electrical and mechanical reaction occurring in a 
few seconds or minutes with a redistribution of plasma particles so 
limited in extent and requiring days for its accomplishment. 
(3) There is also another difficulty which would seem to arise if 
1 Even if the cell particles were able to move freely, their small size would 
render their rate of rise, as calculated by Stokes’ law, very low. If we assume 
that their radius is 0-021 fi and that their relative density is the same as 
Perrin’s gamboge particles ( i.e. 0-207), and that the viscosity of the proto¬ 
plasmic medium in which they move is only twice that of water (o-oi), the 
rate of ascent would be only 1 p in 10,000 secs. = 2-8 hours. The rate would 
really be slower as the particles by their movement are doing work in pro¬ 
ducing a difference of potential in the cell. 
