the Laws of Viscosity. 349 



ponents is the fact that they are affected by the phenomenon 

 of relaxation, whereas the apparent components have no con- 

 nexion with this phenomenon; this difference is an immediate 

 consequence of our definitions. 



In order to find, by the aid of these new variables, the 

 analytical expression of what takes place in the interior of an 

 element of the fluid, let us formulate three new hypotheses .; 

 these will constitute, in our new course of thought, the exact 

 analogue of the suppositions made formerly and enunciated 

 above, §§2, 3, 4, and 5. We shall in the first place suppose 

 that the quantities e*, <£*, ^*, a * ? /3* ? y* vary for two 

 reasons. They come within the action of external forces, and 

 their variation on this account may be expressed by the manner 

 in which the apparent deformation is changing. They further 

 vary on account of relaxation ; by the effect of this, e*, <£*, 

 and yjr* tend towards a common limit which is JA*, whereas 

 a*, /3*, and 7* converge towards zero. Thus, denoting by T 

 the same characteristic period as that considered in § 4, we 

 have 



de* de e*— lA* , Q . 



iu = dt- — t— {da) 



dT"dt ~T ' • • • • ( 3 ^) 



dt " dt T ' • • • • (oc,) 



da* da a* 



!*=*-'?> ' * (4a) 



d/3* = d(3_/3* 



dt ' dt T' ^ J 



dy* _ dy _ y* 



dt ~ dt T 



By equations (3) we have 



(/A* ^A 



(4 c) 



u d t (*) 



We shall suppose, in the second place, that the inequalities 

 of pressure are always connected with the components of the 

 true deformation by the simple law of proportionality. For 

 elastic solids in the ideal theory the notion of true deformation 

 becomes identical with that of apparent deformation ; but we 

 know that such is not the case for fluids. Thus our actual 



