72 Mr Weatherburn, On the Hydrodynamics of Relativity 



On the Hydrodynamics of Relativity. By C. E. Weather- 

 burn, M.A. (Camb.), D.Sc. (Sydney), Ormond College, Parkville, 

 Melbourne. 



{Received 15 December 1916 : read 5 February 1917.] 



I. The Equations of Motion. 



I 1. Relativistic equations for the adiabatic motion of a 

 frictionless fluid have been found by Lamia* and Lauef in the 

 form 



dt^ ■' dx^ ■^ dy^ dz^ ' y dx 



^ 7\ 7) f) ^ 7) P 



— (kv) + 11;^ (kv) + V ;^- (kv) + iv X- (kv) + - ^ = Fy...(l); 



where m, y, w are the components of velocity at the point {x, y, z) 

 relative to a definite system of reference 8 ; X, Y, Z those of the 

 impressed force per unit of normal rest-mass ; and 



ry= ^ (2), 



Vc^ — {u^ •\-v^ + id^) 



c being the constant velocity of light. The significance of the 

 symbols P and k is as follows. 



Since the motion is adiabatic the rest-mass of an element of 

 fluid is determined by one variable only, say the pressure p. 



If we choose some definite pressure p^ as the normal or 

 standard pressure, the element has a definite constant normal 

 rest-mass hm^. If the element occupies a volume hV relative to 

 the system of reference 8, the density k relative to that system is ^| 

 defined by 



, _8mo 



* Ann. der Physik, Vol. 37, p. 772 (1912). 



•|- Das Relativitdtsprinzip, § 36 (2nd ed. 1913). For a more general discussion of 

 the mechanics of deformable bodies from the standpoint of Relativity, cf. Herglotz, 

 Ann. der Physik, Vol. 36, p. 493 (1911); also a paper by Igndtowsky, FIn/s. Zeit., 

 Vol. 12, p. 441 (1911). 



I 



