350 



Prof. L. Natanson on 



hypothesis consists in supposing that the law of Hooke extends 

 to the case of fluids, but has to be applied not to the com- 

 ponents of apparent deformation, but to those of actual 

 deformation. Assuming this hypothesis, we have 



p xx -p =-2ne* -(£ — §n)A*; 

 Pw~Po= -2n0*- (&-§n)A* ; 

 Pzz-&= -2m|r*- (&-fn)A* ; 



p y z=— na*; 



Pzz=—nfi*; 



p x y——ny*' ) 



(6 a) 

 (66) 

 (6 c) 

 (7a) 

 (76) 

 (7c) 



In the equations (6),jt? is the pressure which corresponds 

 to zero deformation. 



We shall thirdly assume that the limit towards which the 

 relaxation tends is attained when the quantities e*, <£*, yjr* 

 become reduced to J A* and the quantities as*, /3*, 7* to zero; 

 at the same time, the pressures p xx , p yy , p zz assume a definite 

 value which we shall call p, and the pressures p yzy p zx , and 

 pxy vanish. Let us suppose that this state of final equilibrium 

 has been reached ; we have, by equations (6), 



P—Po— -&A" : 



Therefore 



d -l=-k 

 dt 



dt 



(S> 



(9) 



and by equation (5) we may write 

 dp , dA 



dt 



= —k—r- = — ko). 



dt 



(10) 



The equation so obtained assumes the particular form, that 

 namely which corresponds to the relation h = k. This is 

 easily explained. In order to define the pressure denoted 

 by p, we had to assume, in the course of our reasoning, not 

 only equality of the pressures in the final state of equilibrium 

 (as in § 4), but, over and above this, perfect uniformity of the 

 deformation in this state of equilibrium. Now this latter 

 hypothesis involves the equality of h and k, as has been said 

 in § 5. 



§ 8. Adding, term by term, equations (1), § 3, and (2), § 4 ; 

 and adding similarly equations (2), § 3, and (3), § 4, we have 



