177, 178.] GENERAL EQUATIONS. 219 



du dv dw\ _ du 



The quantity ft is called the coefficient of viscosity. Its 

 physical meaning is as follows. If we conceive the fluid to be 

 moving in a series of horizontal planes, the velocity being in 

 direction everywhere the same, and in magnitude proportional to 

 the distance from some fixed horizontal plane, each stratum of fluid 

 will then exert on the one above it a tangential retarding force 

 whose amount per unit area is ft times the upward rate of variation 

 of the velocity. 



If [J/], [Z], [T] denote the units of mass, length, and time, 

 the dimensions of the ps are [ML~ l T~ 2 ], and those of a, b, c, &c. 

 are [T 1 ], so that the dimensions of /JL are [ML~ l T 1 ]. 



The effect of viscosity in modifying the motion of a fluid de 

 pends however, as will appear from the examples given below, not 



so much on the value of ft as on that of , = ft , say. The quantity 



ft is called by Maxwell the kinematic coefficient of viscosity. Its 

 dimensions are [L? T 1 ]. 



It is beyond our province to discuss the various experiments 

 which have been instituted with a view to determining the values 

 of ft, or of ft , for different substances. We may state, however, 

 that ft is found in gases to be independent of the density, and to 

 increase with the temperature, its value being, according to Max 

 well, proportional to the temperature measured from the zero of 

 the air-thermometer, e.g. Maxwell finds for air 



^ = 0001878(1 + -003660), 



the units of length, mass, and time being the centimeter, gramme, 

 and second, and the temperature 6 being expressed in the centi 

 grade scale. 



The value of ft for water is, according to the experiments of 

 Helmholtz and Piotrowski, 



ft = -014001 



