348 Prof. L. Natanson on 



equation. Now equation (1) appears to be capable of an 

 immediate generalization. From the definition of the pressure 

 p it is evident that the differential coefficient dp J at must 

 necessarily be expressed by a function which is an invariant 

 for all orthogonal transformations. The quantity co, in fact, 

 belongs to this series of invariants. Let 



fy^-to + itf+f + tf+^ + V + ^+ja*), # (3) 



where i andj denote two new constants. Now dpjdt still 

 possesses the properties of an invariant, but the law of 

 variation of pressure ceases to be the same for an increasing 

 as for a decreasing pressure; we have a sort of hysteresis 

 phenomenon. 



It would not be difficult to push the attempt at generalization 

 still further. However, the choice of a particular form for 

 dpjdt has — as will be evident from the sequel — no serious 

 influence on the progress of our calculations. This is why 

 we shall confine ourselves, in the present study, to the simple 

 hypothesis explained above, in § 5. 



§ 7. The quantities 



?> V, f; €, (/>, -f; a, £,7; A; u, v,w; e-,f 9 g; a,b,c; co (1) 



which have up till now entered into our discussion relate to 

 the apparent deformation of a fluid, i. e., to one which our 

 senses enable us to perceive. For this reason, we shall apply 

 the term apparent to these quantities. A reference to § 3 

 will explain the function of these quantities : they serve to 

 define the influence exerted by external forces on the 

 inequalities of pressure. 



We shall now introduce analogous (but essentially different) 

 variables whose consideration naturally presents itself in the 

 study of the phenomenon of relaxation. By the action of this 

 phenomenon, the true state of a material element is, in general, 

 very different from the apparent state which we attribute to 

 it in making use of the testimony of our senses. Let 



£*, 7)*, £*; e* (/>* yfr*; a* 0* 7*; A*; u* tf* «?*; 



e*, /*,$*; a*,b*,c*; »*'.., (2) 



be quantities which define the true state of an element in the 

 same way in which the quantities (1) define its apparent 

 state ; we shall say that they are the true (or absolute) com- 

 ponents of the deformation. Their mutual relations are the 

 same as those to which the apparent variables are subject. 

 But what sharply distinguishes them from the apparent com- 



