276 THE REALITIES OF MODERN SCIENCE 



Another series of Perrin's experiments dealt with in- 

 dividual motions. If one of the particles is observed 

 in a microscope its motion will be of the character 

 illustrated by the diagrams of Fig. 33. Its position 

 is observed and recorded every t seconds (t was 30 in 

 this instance). It is by such irregular motions that 

 the diffusion of the particles takes place. Einstein 

 had shown a relation between the coefficient of diffusion 

 and the average square of the displacements of a 

 particle. The diffusion is expressible in terms of 

 RT/N and the viscosity of the liquid if the radius of 

 the particle is known. If X 2 represents the average 

 square of the displacements along the x-axis for times 

 of value t seconds, then it was shown that 



(3) 



where the other terms have their previous meanings. 

 Perrin observed several thousand displacements and 

 obtained as his average value for N, 6.88 X10 23 . 



The most reliable determination of the number of 

 molecules in a mole, is the work of Millikan. It is 

 essentially a by-product of his determination 1 of the 

 amount of electricity represented by an electron. 

 You will remember that the electrostatic unit of quan- 

 tity was defined (on page 174) in terms of the repulsion 

 of two unit charges at unit distance, and the electro- 

 magnetic unit (on page 206) in terms of the repulsion 

 exerted on a unit magnetic pole at the center of a unit 

 arc of unit current. The practical unit of current is 

 the ampere and is nominally one tenth of the latter 

 unit. Because of its importance in the arts the ampere 

 1 To be described in Chapter XXII. 



