g ON THE VISCOSITY OE INTERNAL FRICTION 



planes of indefinite extent, at a distance a from one another. Suppose the 

 upper plane to be set in motion in a horizontal direction with a velocity of 

 v feet per second, and to continue in motion till the air in the different parts 

 of the stratum has taken up its final velocity, then the velocity of the air 

 will increase uniformly as we pass from the lower plane to the upper. If the 

 air in contact with the planes has the same velocity as the planes themselves, 



then the velocity will increase - feet per second for every foot we ascend. 



The friction between any two contiguous strata of air will then be equal 

 to that between either surface and the air in contact with it. Suppose that 

 this friction is equal to a tangential force / on every square foot, then 



f v 



/=/v 



where p. is the coefficient of viscosity, v the velocity of the upper plane, and 

 a the distance between them. 



If the experiment could be made with the two infinite planes as described, 

 we should find ft at once, for 



fa 



P--' 



v 



In the actual case the motion of the planes is rotatory instead of recti- 

 linear, oscillatory instead of constant, and the planes are bounded instead of 

 infinite. 



It will be shewn 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 shewn in fig. 8, where 

 the curves represent the successive 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 shewn in fig. 9. 



The consideration of these two circumstances introduces certain corrections 

 into the calculations, as will be shewn hereafter. 



In expressing the viscosity of the gas in absolute measure, the measures 



