1904.] Train of Waves emitted by a Hertzian Oscillator. 79 



This is the case discussed by Hertz, but his discussion has no very 

 definite reference to the front of the waves. The field due to the 

 initially existing doublet is the well-known electrostatic field of a 

 doublet, the lines of electric force being identical with the lines of 

 magnetic force due to a magnet or to an uniformly magnetised sphere, 

 or with the lines of flow of incompressible fluid through which a 

 sphere is moving. These lines have been traced often,* a few of 

 them are traced in fig. A. 



FIG. A. 



Hertz t has figured the lines of force within a distance of f X of the 

 oscillator at a number of instants during the progress of a vibration. 

 It would be easy to determine the modifications that ought to be made 

 in his figures on account of the existence of a front to the advancing 

 wave-train and of the existence outside that front of an electrostatic 

 field. The moment of the doublet which gives rise to this field is the 

 maximum moment of the vibrating doublet. At any instant during 

 the vibration the electromagnetic field of the vibrator will be 

 established within a distance from the doublet equal to the distance 

 which light would travel in the time that has elapsed since the 

 commencement of the vibrations. After one-eighth of a period, for 

 instance, this field will be confined to the region within a sphere of 

 radius % A, and outside this sphere the field is the above-described 

 electrostatic field. It follows that, to obtain the lines of force during 

 the first three-quarters of a period, a circle of suitable radius should be 



* See, e.g., J. J. Thomson, ' Elements of Electricity ^and Magnetism,' p. 223, 

 Lamb, ' Hydrodynamics,' p. 137. 



f ' Electric Waves,' pp. 144, 145. The figures are reproduced by M. Brillouin, 

 loc. cit., pp. 292, 293 ; and by A. G-ray, ' Magnetism and Electricity/ vol. 1 

 (London, 1898), pp. 406408. 



VOL. LXXIV. G 



