CHAPTER IX. 



VISCOSITY. 



174. WE now proceed to take account of the resistance to 

 distortion, known as viscosity* or internal friction, which (Art. 2) 

 is exhibited by all actual fluids in motion, but which we have 

 hitherto neglected. The methods we shall employ are of necessity 

 the same as are applicable to the resistance to distortion, known 

 as elasticity, which is experienced in the case of solid bodies. 

 The two classes of phenomena are of course physically distinct, 

 the latter depending on the actual changes of shape produced, the 

 former on the rate of change of shape, but the mathematical 

 methods appropriate to them are to a great extent identical. 



175. Let p xx , Px,,, p x , denote the components parallel to x, y, z, 

 respectively, of the force per unit area exerted at the point P (x, y, z] 

 across a plane perpendicular to x, between the two portions of fluid 

 on opposite sides of it; and let p vx , p v&amp;gt;J , p v and p^, p^, p a have 

 similar meanings with respect to planes perpendicular to y and z 

 respectively*. It is shewn in the theory of Elastic Solids that these 

 nine quantities, which completely specify the state of stress at the 

 point P, are not all independent, but that 



We need not here reproduce the proof of these relations, as their 

 truth will appear from the expressions for p yt , &c. to be given 

 below. 



* As is usual in the theory of Elasticity we reckon a tension positive, a pressure 

 negative. Thus in the case of a fluid in equilibrium we have 



