362 The Followers of Maxwell. 



perpendicular to the radius from the centre, where $1 depends at 

 any instant only on the distance from the vibrator, and 

 denotes the angle which the radius makes with the axis of the 

 oscillator. At points on the axis, and in the equatorial plane, 

 the electric force is parallel to the axis. At a great distance 

 from the oscillator, 2 is small compared with 0,, so the wave is 

 purely transverse. The magnetic force is directed along circles 

 whose centres are on the axis of the radiator ; and its magnitude 

 may be represented in the form 3 sin 9, where 3 depends 

 only on r and t ; at great distances from the radiator, c< 3 is 

 approximately equal to 0,. 



If the activity of the oscillator be supposed to be continually 

 maintained, so that there is no damping, we may replace p { by 

 zero, and may proceed as in the case of the magnetic oscillator* 

 to determine the amount of energy radiated. The mean out- 

 ward flow of energy per unit time is found to be Jc 3 ^ 2 (27T/X) 4 ; 

 from which it is seen that the rate of loss of energy by radiation 

 increases greatly as the wave-length decreases. 



The action of an electrical vibrator may be studied by the 

 aid of mechanical models. In one of these, devised by Larmor,f 

 the aether is represented by an incompressible elastic solid, in 

 which are two cavities, corresponding to the conductors of the 

 vibrator, filled with incompressible fluid of negligible inertia. 

 The electric force is represented by the displacement of the 

 solid. For such rapid alternations as are here considered, 

 the metallic poles behave as perfect conductors; and the 

 tangential components of electric force at their surfaces' are 

 zero. This condition may be satisfied in the model by suppos- 

 ing the lining of each cavity to be of flexible sheet-metal, so as 

 to be incapable of tangential displacement ; the normal displace- 

 ment of the lining then corresponds to the surface-density of 

 electric charge on the conductor. 



In order to obtain oscillations in the solid resembling those 

 of an electric vibrator, we may suppose that the two cavities 

 * Cf. p. 346. 



7 Proc. Camb. Phil. Soc. vii (1891), p. 165. 



