CHAPTER XL 



VISCOSITY. 



275. THE main theme of this Chapter is the resistance to 

 distortion, known as viscosity or internal friction, which is 

 exhibited more or less by all real fluids, but which we have 

 hitherto neglected. 



It will be convenient, following a plan already adopted on 

 several occasions, to recall briefly the outlines of the general theory 

 of a dynamical system subject to dissipative forces which are 

 linear functions of the generalized velocities*. This will not only 

 be useful as tending to bring under one point of view most of 

 the special investigations which follow; it will sometimes indicate 

 the general character of the results to be expected in cases which 

 are as yet beyond our powers of calculation. 



We begin with the case of one degree of freedom. The equa 

 tion of motion is of the type 



aq + bq + cq Q ........................ (1). 



Here q is a generalized coordinate specifying the deviation from a 

 position of equilibrium ; a is the coefficient of inertia, and is 

 necessarily positive ; c is the coefficient of stability, and is positive 

 in the applications which we shall consider; b is a coefficient of 

 friction, and is positive. 



If we put 



T=laf, V=\vf, F=W ............... (2), 



the equation may be written 



q ..................... (3). 



* For a fuller account of the theory reference may be made to Lord Kayleigh, 

 Theory of Sound, cc. iv., v. ; Thomson and Tait, Nattiral Philosophy (2nd ed.) 

 Arts. 340-345; Eouth, Advanced Rigid Dynamics, cc. vi., vii. 



