IN THE FIELD ROUND A THEORETICAL HKUT/IAN OSCILLATOR. 



Now let 8, give the phase of the- sine term in (xxxvi), or : 



X - 2irr fi 

 6 - T" "* 



Comparing with (xxiv), we see & = & + 2 \> or : 



8, = 8, - 2 X . 



Thus the phase of the wave of magnet if^ induction always differs hy a constant 

 from that of the wave of axial comjxnient electric fonv. 



Since dfti/dr = dft.,/ilr, the velocity of the wave of magnetic induction equals that 

 of the wave of axial component electric force, and is given hy the V, of (xxvi), or 

 the diagram of p. 169. 



(11.) In our diagram (p. 184) we have plotted 8, from the calculated curve for 8 t , 

 hut it is interesting to note the following graphical construction for finding it 

 directly. Let = 27rr/X as before. 



Let Ox be the axis of , Oy of 8,, then 8, = 4 &. Take Ob = cos* x , 

 Oa = (27rr c /A) = ,, and let the vertical through a meet the horizontal through 

 /> in c. Let On equal , then an = > and an/ca = ({ io)/co8* x = tan (/?, 3 X ), 

 or the / acn = /J, 3 X . 



Take cz, so that ^ zca = 3\, then y8, = ^ zen. If a circle be descril>ed round c 

 with radius cz = I, the arc zm corresponding to the angle zcn is the required length 

 ,. Subtract this arc (rectified, say, by RANKINE'S rule) from the corresponding 

 ordinate ne of the 45 line through the origin (8 = C), and we find the true value of 

 8, = np. This construction was actually gone through and compared \\itli the 

 calculated values for verification. 



9 



zm. 



x 



N.B. The angle x has been much exaggerated for diagrammatic purposes. 



(12.) Before we refer the reader to our diagram giving the phases of the various 

 waves, and descrite how they were obtained, it seems well to consider the combined 

 wave of total transverse electrical force in the equatorial plane. The resultant electrical 

 force in this plane may be considered, as we have already seen, to consist of two parts, 

 I laving different wave-speeds ; but, possibly, if a receiver were sufficiently small, it 

 might not l>e possible to differentiate them, and HKMTX'.S theoretical view of their 



2 A 2 



