392 Prof. L. Natanson on the 



with the usual signification of V 2 and 0. Write 



pJS, p/B, pJS (2) 



for the pressures, parallel to the co-ordinate axes, on the 

 element d$ of the boundary of the portion we are considering. 

 If the direction of the inwardly directed normal be denoted 

 by n, we shall have : — 



p x = l>- 2 /*(§i -* 61 )] cos (**) ~K^ + dy) ° os (wy) 



""% + ^) C0SM; ' ' (3) 



p y = "Kai + dy) cos ^ f ^~ 2 Kdy "~^ cos (?w) 



"<^ + s) cos M ; • (4) 



p° = -i\& + §W C0S M -<57 + Si) cos to) 



+ [^-2 M ^_jfl)]ooB(«). . (5) 



If now a system &p, 8?/, &e of infinitesimal virtual displace- 

 ments be imposed upon the fluid, the temperature being kept 

 constant, then the work IF fig. done by extraneous forces 

 will be 



jJdSfo&B +p y hy +p z Sz) +ffida dy dz p(XBx + YBy + Z&);(6) 



the variation of the energy T will be 



8T = \\\ dx dy dz p(u8u + v8v + wSw) ; . . . ( 7 ) 



the variation of the energy V, which in Hydrodynamics it is 

 usual * to call " intrinsic ;; energy, will be 



* See, for example, that otherwise excellent treatise ' Hydrodynamics ' 

 by Prof. Lamb, ed. 1895, pp. 11-12, 469, 507. It is not with the true 

 intrinsic energy U, but with the free energy V that we are here con- 

 cerned ; the customary use of the word " intrinsic " seems, therefore, to 

 involve a serious error. 



