272 THE REALITIES OF MODERN SCIENCE 



however, the particles in Perrin's experiment fell until 

 the concentration at each level in the liquid became 

 such that a further decrease in the gravitational 

 p.e. of the particles would have occa- 

 .*."'- ' sioned a greater increase in osmotic 

 *.'.,." "'*' energy due to the increased concentra- 

 ... '. **/ tion. Figure 32 represents a vertical 

 .;'' ''. section of an emulsion in equilibrium. 

 Perrin, therefore, was able to obtain a 

 relation between the decrease in gravi- 

 tational energy, occasioned by a par- 

 ticle in moving from one level to a new 

 level, h cm. lower, and the correspond- 

 ing change in the energy which the 

 particle possessed as a result of its in- 

 clusion in a group of greater concen- 

 tration and hence of greater osmotic 

 pressure. 



If each particle is spherical, of radius 

 r and of density D, its mass is 4?rZ)r 3 /3. 

 The decrease in gravitational potential 

 energy of the particle considered by 

 itself is 4(7rr 3 D%)/3. Its movement 

 downward results in the movement 

 upward of a similar volume of the 

 liquid, that is, it may be considered to 

 change places with an equal volume of 

 the liquid of density d, which therefore gains in poten- 

 tial energy the amount 4(7rr 3 d%)/3. 



The corresponding increase in energy on the part of the 

 average particle is expressed as KwT, where wT is the 

 average kinetic energy of translation of a liquid mole- 



