( 821 ) 



direction of motion, the elocd'on behaves cis if it Imd a mass ///,, in 

 those in Avhich the aeeeleration is normal to the path, as if tiie 

 mass were m^. These quantities tn^ and //v., may Iherefore properly 

 be called the "longitudinal" and "traiiSNerse" electromagnetic masses 

 of the electron. I shall suppose that there is ix? of/u^r, no ^'■fruc" or 

 "material" mass. 



Since k and / differ fi-om unity by quantities of the order — , we 

 find for very small velocities 



m, — m^ — — — . 



This is the mass with Avhich we are concerned, if there are small 

 vibratory motions of the electrons in a system without translation. 

 If, on the contrary, motions of this kind are going on in a body 

 moving with the velocity ?/' in the direction of the axis of x, we 

 shall have to reckon with the mass m^, as given by (30), if we con- 

 sider the vibrations parallel to that axis, and with the mass />?,, if 

 we treat of those that are parallel to OY or OZ. Therefore, in 

 short terms, referring by the index ^ to a moving system and by 

 JS" to one that remains at rest, 



(^) 



= l-^—-^J^Ukl\m{:E') (31) 



y a 10 J 



§ 10. We can now proceed to examine the influence of the Earth's 

 motion on optical phenomena in a system of transparent bodies. In 

 discussing this problem we shall fix our attention on the variable 

 electric moments in the particles or "atoms" of the system. To these 

 moments we may apply what has been said in § 7. For the sake 

 of simplicity we shall suppose that, in each particle, the charge is 

 concentrated in a certain number of separate electrons, and thai the 

 "elastic" forces that act on one of these and, conjointly with the 

 electi'ic forces, determine its motion, have their origin within the 

 bounds of the same atom. 



I shall show that, if we start from any given state of motion in 

 a system without translation, we may deduce from it a corresponding 

 state that can exist in the same system after a translation has been 

 imparted to it, the kind of correspondence being as specified in 

 what follows. 



a. Let A^, A\, A'^, etc. be the centres of the i)articles in 

 the system without translation (JS") ; neglecting molecular motions 

 w^e shall take these points to remain at rest. The system of points 



