IN THE FIELD ROUND A THEORETICAL HKKT/IAN OSCILLATOR. 



165 



2irr/X 



tiii cos - 



(xi). 



Now let 

 *i(r,*) = 



and 



C06 X 



3 sin 2ir [ ^- 



_i 



i . r) 



(2wr/X)co8 X 



, CM fr fe - f ) + x | 2 sin 2. (1 ^ 



/o ./% \ _, , > \ 



(2^r/X)co8 X 



(LV'Xr 



(xii), 



(xiii). 



Then ^, and <^, are constant over any spherical surface about the centre of the 

 oscillator at any time, and 



Z = <, sin 3 6 + <k, 1 

 II = <, sin cos 6, \ 



(xiv). 



The electric force can thus be considered as compounded of a force <f>., parallel to 

 the axis of the oscillator, and depending only on the distance of the point of the field 

 from its centre, and of a force <, sin 6, acting in the meridian plane perpendicular to 

 the central distance of any point and towards the oscillator axis. 



Clearly along the axis and in the equatorial plane R = 0, or the force is parallel to 

 the axis, a result already deduced by HERTZ for a simple harmonic oscillation.* At 

 very great distances we may neglect inverse squares and cubes of r, as compared 

 with first powers, and accordingly <^ vanishes as compared with ^,. In other words 

 the electric force tends at great distances to become perpendicular to the radius C L, 

 or the propagation to be purely transverse. 



At a considerable distance from the origin we may take : 



'Electric Waves, 1 pp. 142-3 



