1288 



l/i (ll,^ (/*, = (loj^, when we rejueseiit the distance of an element 

 (/(I) to tio)^ by /", : 



yd^ a rr ,d<f{i--é"-{^-^r 1 



•7- jj ^ ö7 



td kl'.I.J di' 2?'' 7\ 



dvidvi . (17) 



If /i' were constant, we .should of course lind 7'/'" = o and //• := o. 

 if, however, in a detinite region //' is greater than in the snrronnd- 

 ing volnnie elements, then in a line parallel to the ^-axis and passing 

 throngh the centre of (his legion 7-//; will be negative, and in a 

 line parallel lo Ihe C-axis positive. The imaginary agent and w; have 

 then opposite signs, so that here also the condensed gronp will be 

 elongated in a dii'iction forming an angle of 45° with the original axes. 



§ H. The ((p/)/ic(ttioii of the virial relation. In order to calcnlate 

 the stress tensor from the valne fonnd for /r,, we shall make use 

 of the virial equation. We shall, however, have to demonstrate 

 befoi-ehand Ihe applicability of this ecpiation for the case under 

 consideration. Let us for this purpose consider a definite volume in 

 the space in which Ihe flowing gas is found. We shall assign to 

 it the shape of a rectangidar parallelepiped and choose the coordinate 

 axes parallel to the sides. As we think ihe state stationaty. the 

 expression ^ m x x, in which the summation extends o\ er all the 

 molecules in the volume will be constant. The fact that through the 

 boundary planes molecules enter and leave the (considered space, 

 does not affect this. We conclude from this that: 



/ /' . • 



- (^ rn X x) = <d — :E m ^ f 2 .r A' -f O in (x^—x,) I x' t' (x) dx . (1 8) 

 dt , J ' 



• 

 In this A' is the .t-component of the force acting on a molecule, 



,/', and ,/j are the abscissae of the boundary planes of the parallel- 

 epiped normal to the .r-axis, and is the area of these planes, 

 /'{x) il-r denotes the number of molecules per ccm*., of which the 

 , /-component of the velocity lies between x and x -\- dx. The latter 

 term refers lo the change in the value of 2mxx, which results 

 from Ihe molecules entering and leaving through the planes x^ = c 

 and .1', = r. The molecules entering and leaving through other 

 boundary planes will yield on an average a contribution zero to 



d 



- i' )n X X. Let us put : 

 dt ' 



