IN THE FIELD ROUND A THEORETICAL HERTZIAN OSCILLATOR. i , 



tan(A- X ) = fe** - - : y&ti (xliv), 



\\liich serves readily for logarithmic calculation. 



The portion of the curve for which 8 is negative now lies between and '2, and we 

 must multiply it some 500 times to render tin- small negative values of S visible. 



The approximate value of Ob for any value of x is given by 



06= it,, 



and thus = '19021 for our special cam. 

 The asymptote is given by the 45 line 



or, for our special case Oe = 1 '63437. 



The curve for this wave has a far less sensible negative portion, and approaches 

 much more rapidly to its asymptote, being in our special case at a distance less 

 than 2 per cent, of the value of 8 from its asymptote when = 10. 



Thus we see that there is a marked difference between the phases of the component 

 transverse and component axial electric waves. The first appears to proceed from a 

 centre at distance Oa given by (xliii) from the centre, and the second from a distance 

 Ob equal i|o, or practically from a point so close to the centre of the oscillator as not 

 to be sensible in the case of any but very rapidly damped wave trains. The ultimate 



phase difference of the two waves = + x . 



III. Wave of Magnetic Induction. 8, = $,. 



Here we can either use the graphical method of p. 179, or the simple relation 

 8, = 8, - 2 X . 



The latter method shows us that the asymptote is 



or in our special case 



S = - 17615. 



Thus the ultimate difference of phase between the transverse component electric 

 and the magnetic waves is \ir x , and between the axial electric and magnetic waves 

 is - 2 X . 



It will be seen that this wave of magnetic induction for a damped wave differs 

 considerably from that given by HERTZ. 



The most notable difference is the finite negative value of 8, at the origin, and this 



VOL. cxcni. A. 2 B 



