IN THE FIELD ROUND A THEORETICAL HERTZIAN OSCILLATOR. 163 



('Electric Waves,' p. 150), we should have at 12 metres distance from the oscillator 

 jf = v/ = 1 '649, a factor which can very considerably nuxlify Q as a function 

 of r, if t be not equal to ar, i.e., if the disturbance have not just reached that point 

 of the field. 



Expressing Q in terms of the wave-length X, and the period 2r, we have 



fcoe^/^-^Wx] rinfcrf - '' }\ 



8 in'0 e -'>-'M L \2r \) *J . \J> (ix), 



- coe x 1^7^ J 



where v = Zirpjp, = pi X 2r. 

 Thus we may write 



where <j> is a known function. 



The next stage was to plot for a reasonable value of v, the curves $ = constant 

 for a series of values of Q at different intervals of time. In order to show the 

 decadence of the strength of the field in the neighbourhood of the oscillator, t was 

 given the 56 successive values \T, f T, JT, r, \r . . . 13f T, 14 T; or the field-changes 

 were traced for seven complete oscillations, at intervals of oscillation. This was 

 done for a sphere of 1^- wave-lengths round the oscillator, or taking the wave-length 

 to be 9 '6 metres, for a sphere of 12 metres radius round the centre of the oscillator.* 



Values of QX/(27rE/) were chosen so as to give eight systems of curves with relative 



intensities 



50, 30, 10, 1, -1, -10, -30, -50. 



In the accompany ing diagrams (Plates 1-7) the fine continuous curvest give the 50 

 intensity, the fine dotted curves the 30, the heavy continuous curves 10, and the 

 heavy dotted curves 1. The outermost circle in each case is the boundary of the 

 field explored ; the innermost circle corresponds to the boundary of the area round 

 the oscillator, within which it would hardly be legitimate to consider the oscillator a 

 double electric point. The remaining circles are those for which Q = 0, and which 

 separate positive from negative portions of the field. In the spaces Ixjtween then 

 circles the field must be considered to have alternative positive and negative intensity. 

 It must of course be borne in mind that the curves only give a meridian section of 

 the surfaces of equal intensity. 



The work of calculating, plotting, and drawing such a long series of curves was 



* HERTZ'S diagrams only extend for three-quarters of a wave-length round the oscillator. Our diagrams 

 suffice in extent to show the detachment of the loops preparatory to their outward propagation. 



t The actual selection of fine and heavy, continuous and dotted curves to represent the several intensities, 

 is due to the engraver working on the photographs of the original coloured diagrams. For special aid 

 in the preparation of the diagrams and in their reproduction by photography, we have to heartily thank 

 Messrs. E. WUENX and A. WHEEI.EU respectively. 



Y~ 2 



