of Maxwell's Electrical Theory. 18? 



no difficulty on the mere ground of requisite density in ex- 

 plaining the justifiability of ignoring the equation of equili- 

 brium. And we see that in all material transparent bodies 

 we are fully warranted. 



I have not, however, been able to satisfy myself that in the 

 present case the aether density is stable, i. e. that it will not 

 gather itself up round nuclei. If it did so, its density not in 

 the neighbourhood of these nuclei might be too small to enable 

 us to ignore the equation of equilibrium. 



16. Case III. seems the most satisfactory one. Suppose 

 the aether absolutely rigid and motionless except in a thin 

 skin coating every atom of matter. Suppose in this skin it 

 has exactly the same freedom as in case I. This is equivalent 

 to supposing that in the aether the terms of I depending only 

 on "^ vary infinitely rapidly with all variations of ^ except in 

 the skin, where they are zero. In this case the atoms of 

 matter will be unimpeded in their motion through the aether, 

 the equation of equilibrium can be rigorously ignored for the 

 aether, the electrical equations for the aether reduce to Max- 

 well's form, and the investigation in § 64 of f Electromag.' 

 concerning convection currents is made satisfactory. 



These assumptions sound highly artificial, so it is well to 

 remark that the mathematical results of a theory apparently 

 different in fundamental assumptions are identical. This 

 theory may be stated in the following different forms : — ■ 



(1) The aether is immovable and freely penetrates all atoms 

 offering no resistance to their motion. 



(2) The theory of ( Electromag.' is true of matter, but 

 Maxwell's theory is true of free aether. 



(3) For matter the theory of ' Electromag/ is true. For 

 space where there is no matter we have in place of the funda* 

 mental assumptions of §§ 23 to 31 the following : — For such 

 space the undashed letters have no meaning. The Lagrangian 

 function is the volume-integral of 



27rK- 1 D' 2 - i * H' 2 /87r. 

 k' = 0. S v'D' = 0. Y v'H = 4irC = ^D'/d *. 



In addition certain assumptions must be made with regard to 

 the bounding surface of matter. They are most readily ex- 

 pressed by saying that for a thin skin bounding the matter 

 the assumptions of i Electromag/ are true, and that for this 

 region the Lagrangian function per unit volume of the 

 standard position is 27rK~ 1 D 2 — //, H 2 /87t, the outer surface of 

 the skin being motionless and the inner surface moving con- 

 tinuously with the matter. 



I have given these three forms to indicate that the theory 



02 



