OP AIR AND OTHER GASES. 9 



of all velocities, forces, &c. must be taken according to some consistent system 

 of measurement. 



If L, M, T represent the units of length, mass, and time, then the dimen- 

 sions of / (a pressure per unit of surface) are L~ 1 MT~*; a is a length, and v 

 is a velocity whose dimensions are LT~\ so that the dimensions of /A are 



L- I MT~\ 



Thus if /x be the viscosity of a gas expressed in inch-grain-second measure, 

 and p.' the same expressed in foot-pound-minute measure, then 



p. 1 inch 1 pound 1 second _ 

 (if ' 1 foot ' 1 gram ' 1 minute 



According to the experiments of MM. Helmholtz and Pietrowski*, the 

 velocity of a fluid in contact with a surface is not always equal to that of 

 the surface itself, but a certain amount of actual slipping takes place in certain 

 cases between the surface and the fluid in immediate contact with it. In the 

 case which we have been considering, if v a is the velocity of the fluid in 

 contact with the fixed plane, and f the tangential force per unit of surface, then 



f=<rv,, 



where tr is the coefficient of superficial friction between the fluid and the par- 

 ticular surface over which it flows, and depends on the nature of the surface as 

 well as on that of the fluid. The coefficient cr is of the dimensions L~"MT~ l . 

 If v, be the velocity of the fluid in contact with the plane which is moving 

 with velocity v, and if a-' be the coefficient of superficial friction for that plane, 



f=<r'(v-v l ). 

 The internal friction of the fluid itself is 



//! , l , a ' 



Hence v=f (- + -,+ 



\<r <r 



If we make -=/3, and , = {?, then 



* SUzungsberichte der k. k. Akad. AprU 1860. 

 VOL. II. 



