On the Laws of Viscosity. 343 



theory of viscosity, of which the accepted theory is a particular 

 €ase. 



§ 1. Let us consider an isotropic and perfectly continuous 

 fluid. Let the co-ordinates of a given point of it be a?, y, z 

 at the time t. Let J, tj, f be the components of the apparent 

 displacement impressed on the fluid in a deformation. In 

 what follows, these components will be supposed infinitely 

 small. We shall have to consider a number of variables, 

 which are enumerated below: — 



The components of the deformation or distortion: 



*H 1 + S=- • • • • a«) 



g=* ; H + sH' • • • • ^ 



The components of the velocity of displacement: 

 d£ dr) dt 



f t =u; i =v; ti = ' - ■ ■ ■ w 



The components of the velocity of deformation : 



s-= e ; ^- + ^-=a; .... (3a) 

 ox oy qz 



*?=^ ; ^ + ^=o (3c) 



The cubical dilatation and the velocity of dilatation : 



e + + ^ = A; (4) 



< ? +/+i/ = w (5) 



It may be remarked that de/dt = e ; d<p/dt=f &c. ; and 

 Anally: dA/dt = co. The quantities e, <£, ^, a, /3, 7, z«, v, 10, 

 #, /, g, a, 6, c, A, co are all infinitely small. 



§ 2. At a given instant 2 = let us impress on the fluid a 

 deformation whose components are, at the point (x, y, z), as 

 follows : 6°, 0°, ^o ; a?, /go, 7 U . Let it be assumed that at this 

 instant the properties of the medium are those of an isotropic 

 perfectly elastic solid. Let n stand for the modulus of rigidity, 



2 A2 



