1904.] Train of Waves emitted ly a Hertzian Oscillator. 81 



The lines of force drawn in some of these figures need some modifica- 

 tion on account of the existence of a front of the wave-train. At any 

 instant the electromagnetic field that is propagated with the waves will 

 have reached a distance Ct from the oscillator, and therefore those parts 

 only of the curves which lie within circles of radii A(/'/2r-e/A) are 

 lines of force in the actual vibrations. Outside spheres having these 

 radii the actual field is the electrostatic field due to the fixed doublet, 

 viz. : it is the field expressed by (5) and figured in fig. A. In the 

 notation of (18) the lines of force in this field are given by the 

 equation 



QA _ 



^ e 



r 27r 



The continuations of the lines of force outside the wave-fronts at the 

 various times in question are obtained by equating this expression to 

 the values T^nj- } ijV' ~T&> % ^ ne neav y dotted, heavy 

 continuous, fine dotted and fine continuous curves in fig. A have been 

 drawn to correspond with these four pairs of values, A, being represented 

 by 1 inch(= 2-54 cm.). 



The value of v being 0*4, the following numerical values are found 

 for the various quantities : 



tan?^ e = 57r, ^ = 1-5071389, 1 = 0-239868, 

 A A A 



^ = 0-0959474, e~^= 0-908512, e~^ sin ?f = 0-906676, 

 A A 



27r^cosec 2 ^ = 6-99403. 

 A 



The circles outside which the lines of force drawn in the figures of 

 Pearson and Lee have to be replaced by other lines are given by the 

 equation 



r = A (a - 0-239868) ........... . ......... (19), 



in which a has the values -|-, J, ... . In fig. 1 of their Plate 1, r would 

 be negative ; this figure, in fact, relates to an epoch before the vibrations 

 begin, and no part of it represents lines of force that are formed. In 

 fig. 2 of their Plate 1, r would be about T ^ of a wave-length, so that 

 the circle is too small to be drawn. In fig. 3 of their Plate 1, r = 0-135 

 of a wave-length, so that the front of the waves cannot be distinguished 

 clearly from the inner circular boundary of the figure. Those parts 

 only of the lines drawn in this figure which lie between the inner 

 circular boundary and a circle of radius (0-135) A are actual lines of 

 force at the instant in question. Figs. 1, 2, and 3 of Plate 1 should, 

 therefore, be omitted. In the remaining figures of Plate 1, and in 

 figs. 9, 10 and 11 of Plate 2, parts only of the lines of force that are 

 drawn are actual lines of force at the corresponding instants during 



G '2 



