174 PHENOMENA DEPENDENT ON MOLECULAR PATHS 74 



The following illustration gives an insight into the mean- 

 ing of this coefficient of viscosity. Let a fluid, whose depth 

 is equal to the unit of length, move over a horizontal plane, 

 and let its motion have become stationary and be of such 

 character that all the particles in the same horizontal plane 

 have the same velocity. A necessary consequence of this is 

 that the velocity is given by a linear function of the height 

 above the base. For in this state of motion each layer 

 experiences on its two sides equal and oppositely directed 

 friction, so that no change can occur in the velocity of a 

 layer. If we further assume that the lowest layer sticks 

 fast to the base, and that, on the contrary, the highest layer 

 has such a velocity that it moves over unit length in unit 

 time, so that the speed in each layer is numerically equal to 

 the height, then the friction on unit area which is exerted 

 between any two neighbouring layers of this fluid is equal 

 to its coefficient of viscosity. 



The measurement of the internal friction of a medium 

 consists in the determination of the value of this coefficient ; 

 it is a constant magnitude if Newton's assumption that 

 the friction is proportional to the relative velocity is really 

 true. Newton's theory will therefore be proved to be 

 true if different measures of the internal friction, especially 

 if made by different methods, give the same value for this 

 constant. 



Such an agreement of measures has really been found, 

 both for liquids and for gases, as will be described later 

 in fuller detail. In gases a perfect agreement with experi- 

 ment has also been found for those properties which, on the 

 kinetic theory of gases, are connected with the coefficient 

 of viscosity. 



75. Formula for the Coefficient of Viscosity of 



a G-as 



To establish the properties of the viscosity-coefficient of 

 a gas on our theory it suffices to carry out in greater particu- 

 larity, in the sense of our theory, the analysis of the process, 



