the Laics of Viscosity. 345 



The effects of external influences, represented by these 

 equations, are generally reversible. 



§ 4. Let us now endeavour to study somewhat more in 

 detail the progress, essentially irreversible, of the phenomenon 

 of relaxation. Let/> be the value towards which the pressures 

 Pxz, 'Pyy> Pzz tend by the effect o£ relaxation; the value 

 gradually approached by the pressures p yz , p zx , p xy is zero. 

 If at any point {x, y, z) o£ the fluid at a given instant t the 

 impressed distortion is zero, then there exists a pressure p at 

 -this point equal in every direction. Consider the state of the 

 fluid at (#, y, z) at the moment t, this state being determined 

 by the values e, <£, yjr, a, /3, 7, p xx , p W} p zz , p yz , p zx , p m and/? 

 of the components of the deformation and the pressures. 

 Suppose that from this instant, and during a sufficiently long 

 period, the fluid is free from the action of any external forces. 

 The pressure p (equal in every direction) ultimately reached 

 by the fluid being necessarily determinate under the given 

 (Conditions, may be represented by 



p=p(e, </>, ^, a, ft 7, p ) .... (1) 



It remains to formulate some hypothesis regarding the 

 precise form of the law of relaxation. Let T denote the 

 " time of relaxation " ; this is a constant characteristic of the 

 medium. We shall suppose that the following equations 

 represent the law of relaxation considered by itself : 



™ • (%) s =-^ ; OSOl— * • • ^ 



{ib) . (%) f — ftp, (%) 2 = -f- • (3*) 



/O \ ( d P"\ P-----P . (dPx,\ Pxy (%A 



They resemble the equations found by Maxwell in the 

 kinetic theory of gases. Similar relations are applicable to 

 various other cases of " constraint," for example to that of 

 ■electromagnetic disturbances in conducting bodies. 



§ 5. Tf to the variation {djdt) l due to the action of external 

 forces of any variable quantity we add the variation (d/dt) 2 

 which results from relaxation, we find the total variation of 

 the quantity in question. Let d/dt stand for the total variation 

 so defined. By its very nature, the pressure p cannot change 

 .except by external action ; thus 



(%) =0 and ft) -* (1 



\dt/-2 \dtJi dt v 



