WILSON AND LEWIS. — RELATIVITY. 495 



or 



[ V-(MV) + '^'^JCv + k,) + m[(v. V)v + '^J] = 0, 



Hence the space and time components both ^■a^isll, and 



V-0uv) + ^^=O, (152) 



(9v 

 (v.V)v+^y=0. (153) 



at 



The first of these two is the continuity equation, the second is the 

 dynamical equation of hydrodynamics in the present restricted case.^'^ 

 The fact tliat we are thus led not to the general laws of hydrodynamics 

 but merely to the laws for a comparatively trivial case shows the 

 inadequacy of any attempt to distribute the vectors of extended mo- 

 mentum into a continuous field. 



Minkowski added to his great memoir on the " Grundgleichungen 

 fiir die electromagnetischen Vorgjinge " an appendix on mechanics 

 which seems to have been more hastily written. In this section he 

 bases his analysis upon two assumptions which must be considered 

 as fundamentally erroneous. The first of these is that /j. = /uq/ Vl — v^; 

 and the second that Swq is a constant. ^^ The results should be that 

 M = Mo/(l — 'P') an^l that Zrn is a constant. We have already dis- 

 cussed (§ 23) cases in which viq is not a constant. 



60. Every locus of a particle to which belongs the vector ?»oW 

 gives rise to the geometric vector fields 



?/?oP = ?»oW//? and moT = moO^P- 



By replacing the constant e by the constant Mq we might proceed 

 to reproduce identically all of the formulas which we have obtained 

 for the electromagnetic field. If a suitable unit of mass be cho- 

 sen, we should then observe that in case axes are .so taken that the 

 particle appears at rest, the space vector moP*k4 becomes identical 



62 It may well be that the introduction of additional terms sufficient to give 

 (153) a form as general as that ordinarily used in hydrod\'naniics would not 

 rcciuire serious modifications in (152). For in ordinary units the pressure of 

 light is measured by the density of electromagnetic energy, whereas the mass 

 of the light is it.s energy divided by the square of the velocity of light. Com- 

 pare also the fact that the changes in the equations (149) when electricity is 

 present is small in one case and large in the other. 



63 The second of these errors has already been pointed out by Abraham, 

 Rend. Circ. Mat. di Palermo, 30, 45. 



