Maxwell's Stress Theory. 493 



the six stress components. These stress formulae will enable 

 him to calculate the forces acting on the pulsating bodies. 

 But if he draws the further conclusion from this result, that 

 this stress reallv exists and really produces the forces, he will 

 be wrong. For the cause of the attractions and repulsions 

 of the pulsating bodies is not the Maxwell stress, but a stress 

 of much simpler nature, namely, the isotropic stress, or the 

 pressure, in the liquid. Still, in the limited state of his 

 knowledge, he will have exactly the same right as the elec- 

 trician to believe that the Maxwell stress is the real cause of 

 the phenomena. 



It is easy to see where the error comes in when Maxwell's 

 developments are applied to these electroidic phenomena of 

 hydrodynamics. Maxwell considers his problem as one of 

 pure statics. The stress has therefore only to produce the 

 required mechanical forces. In all points of space where no 

 such force is required, the stress is self-equilibrating. The 

 hydrodynamic phenomena on the other hand are not statical. 

 but kinetic, even if the motions be too small to be observed. 

 The stress or pressure is therefore nowhere self-equilibrating. 

 It has a double duty, first to maintain the hidden motions, 

 which constitute the field, and only secondly to produce the 

 required forces that give rise to the visible motions. 



The question whether the Maxwell stress may or may not 

 represent a real stress in the dielectric will therefore be closely 

 related to the question, whether the electric or magnetic 

 phenomena are ultimately of statical or kinetic nature. In 

 the latter case, if they depend upon hidden motions, the 

 stress will have to maintain these motions, and it cannot be 

 self-equilibrating like the Maxwell stress. Now Maxwell 

 himself considers the magnetic phenomena as kinetic, as his 

 application of the Lagrange equations to electromagnetism 

 plainly show-. And if this view be right, his explanation at 

 least of the magnetic actions at a distance will not be legitimate. 



In the meanwhile it will therefore be safest to consider 

 the Maxwell stresses as only fictitious stresses that might have 

 produced the required forces, and nor ;i< the real stresses 

 that do produce them. Other authors have also termed them 

 fictitious stresses, especially Lorentz *, who also considers the 

 stress formula? only as useful analytical formulae, but not 

 a- representing any physical reality. The reason, however, 

 why he has come to this opinion i- quite different from the 

 reason brought forward here His view is that the stress- 



• II. A. Lorentz, "Vewuch eines Theorie der elektrischen und optischen 

 Erecheinungen in bewegten Korpern," p. 28. ,: Elektronentheorie," 

 Encyklopddu der matkematuchen fVissensenaften, irol.v. 2. p. 1 <>•'!. 



