Properties of a Molecule in a Substance. 109 



values calculated from equation (3) putting Wi equal to 

 5'75 X 10 3G . A fair agreement between the two sets of values 

 is obtained in each case. 



A General Formula for the Coefficient of Viscosity. 



The results obtained in this paper enable us to obtain a 

 formula for the coefficient of viscosity for matter of any 

 density. Let ABC, DEF in fig. 2 represent a mass of matter 



Fig. 2. 

 ———— — ■ — ► 



li 



ABC 



in which the molecules are more or less bodily moving, in 

 planes parallel to DEF, in the direction from D to F. Let 

 the molecules in the plane DEF have unit velocity and those 

 in the plane ABC be at rest, and the velocity change 

 gradually as we pass from the plane DEF to the plane ABC. 

 If the planes are separated by unit distance, the force 

 necessary to apply to the plane DEF per cm. 2 to maintain 

 unit velocity is the coefficient of viscosity. Consider a 

 molecule moving along BE at right angles to the planes. 

 Let v x m a denote its momentum parallel to DEF at the 

 beginning of the motion, which is taken the same as that of 

 the surrounding matter, and v 2 m a its momentum when it 

 ceases to absorb momentum parallel to DEF from the sur- 

 rounding molecules, and let Z, denote the distance between 

 these two stages. The change of velocity per unit distance 

 as we pass from E to B is equal to unity, and therefore 



— I — — 2 = 1. It should be noticed that the molecule does not 



1 

 necessarily retrace its path when it ceases to absorb momen- 

 tum parallel to DEF. Let us suppose that the molecules 

 move parallel to three directions one of which is at right 

 angles to the plane DEF. Suppose n x molecules cross per 

 second from B towards E, through a plane 1 cm. 2 in area 

 parallel to the plane DEF. There is therefore a gain of 

 momentum per cm. 2 per sec. equal to « 1 (7? 1 ??? — v 2 m a ) in the 

 plane parallel to DEF, passing through the end of the 



