OR INTERNAL FRICTION OF AIR AND OTHER GASES. 255 



In the actual case the motion of the planes is rotatory instead of rectilinear, oscilla- 

 tory instead of constant, and the planes are bounded instead of infinite. 



It will be shown that the rotatory motion may be calculated on the same principles 

 as rectilinear motion ; but that the oscillatory character of the motion introduces the 

 consideration of the inertia of the air in motion, which causes the middle portions of 

 the stratum to lag behind, as is shown in fig. 8, where the curves represent the succes- 

 sive positions of a line of particles of air, which, if there were no motion, would be a 

 straight line perpendicular to the planes. 



The fact that the moving planes are bounded by a circular edge introduces another 

 difficulty, depending on the motion of the air near the edge being different from that of 

 the rest of the air. 



The lines of equal motion of the air are shown in fig. 9. 



The consideration of these two circumstances introduces certain corrections into the 

 calculations, as will be sho^vn hereafter. 



In expressing the viscosity of the gas in absolute measure, the measures of all veloci- 

 ties, 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 dimensions of _/" (a 

 pressure per unit of surface) are L~' MT"'' ; a is a length, and v is a velocity whose dimen- 

 sions are LT"', so that the dimensions of jU- are L~'MT~'. 



Thus if (Jtj be the viscosity of a gas expressed in inch-grain-second measure, and [l' the 

 same expressed in foot-pound-minute measure, then 



ft 1 foot 1 pound 1 minute ^ 



ft' 1 inch 1 grain 1 second 



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

 a fiuid 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 

 Vo is the velocity of the fluid in contact with the fixed plane, and /the tangential force 

 per unit of surface, then 



/=<rtJ„, 



where a is the coefficient of superficial friction between the fluid and the particular sur- 

 face over which it flows, and depends on the nature of the surface as well as on that of 

 the fluid. The coefficient a is of the dimensions L~" MT~'. If v, be the velocity of the 

 fluid in contact with the plane which is moving with velocity v, and if </ be the coeffi- 

 cient of superficial friction for that plane. 



The internal friction of the fluid itself is 



* Sitzungsberichte dor k. k. Akad. April 1860. 



