106 PROTOPLASM 



is the cause of the other. The energy which keeps a particle 

 larger than a molecule in motion is presumed to be the kinetic 

 energy not of the particle itself but of the neighboring molecules 

 of the surrounding liquid medium ; these strike the larger particle 

 on all sides and impart to it a movement similar to the kinetic 

 motion of the molecules themselves. The movement of larger 

 colloidal particles is obviously slower than that of smaller 

 ones. The latter move so rapidly that it is impossible to follow 

 them; their motion is a trembling one of small amplitude. 

 The larger particles, which Brown saw, exhibit a dancing motion 

 of greater amplitude. When a large number of colloidal particles 

 is viewed with the ultramicroscope (or dark-field illumination), 

 the picture resembles that of the Milky Way at night with 

 the stars dancing and scintillating against a black back- 

 ground. Particles exhibit active Brownian movement only 

 when below a definite maximum size and in a medium of suffi- 

 ciently low viscosity. Particles larger than about 4 ix show no 

 motion in water. The maximum size of particles exhibiting 

 Brownian movement in water could be taken as the upper 

 limit of the colloidal state (thus including the majority of natural 

 and commercial emulsions). The viscosity of the surrounding 

 medium determines the amplitude of motion for a particle of 

 given size. As glycerin is some eight hundred times as viscous 

 as water, a particle suspended in it cannot move as freely as 

 one suspended in water. In glycerin, one or two microns is 

 the maximum size of the particle which can exhibit Brownian 

 movement. The amplitude of the Brownian movement of 

 included particles is thus an indication of the degree of viscosity 

 of a liquid. (In addition to particle size and viscosity of the 

 medium, the temperature of the latter and the density of the 

 particles are factors.) Milk is a convenient substance in which 

 to view Brownian movement. Nearly all degrees of amplitude 

 are visible. Most of the emulsion particles of butterfat are 

 in an active state of motion, but some are too large. Einstein 

 has given a mathematical expression for the mean distance that 

 a particle will move in a given time through a given (gaseous) 

 medium (based on the gas constant, the temperature, the number 

 of molecules in one gram molecule, and a factor depending upon 

 the viscosity of the medium and the size of the particle). Lange- 

 vin simplified the equation, and Perrin applied it experimentally. 



