April A,, 1889] 



NATURE 



547 



Near 3 Ursae Majoris 



„ c ., 



Meteor- Shower i. 

 R.A. Decl. 



.. 164 ... 58 N, 



.. 206 ... 57 N. 



249 ... 51 N. 



April 9-12. 

 Slow ; bright. 

 April 9-12. 



THE FORCES OF ELECTRIC OSCILLATIONS 

 TREATED ACCORDING TO MAXWELL'S 

 THEOR Y. BY DR. H. HER TZ> 

 III. 

 The Interference Experiments. 



IN order to ascertain the velocity of propagation of electric 

 force in the equatorial plane, we brought it into interference 

 with another wave advancing with corresponding constant velo- 

 city in a wire. The result was, that the successive interferences 

 did not occur at equal distances, but followed more rapidly in 

 the neighbourhood of the oscillator than at greater distances. 



This behaviour was explained by the supposition that the total 

 force could be decomposed into two parts, of which the one, 

 the electrodynamic, travelled with the velocity of light, while 

 the other, the electrostatic, travelled with a greater, perhaps an 

 infinite, velocity. 



According to our theory now, however, the force in question 

 in the equatorial plane is — 



7 = E/ ^ ^ _ sin (mr -nt) _ cos {mr-nt) ^P i"'^ zJ'J) \ , 

 " ~ \ mr m'^r* m^r^ / 



and this expression in no way splits up into two simple waves 

 travelling with different velocities. If, then, the present theory is 

 correct, the earlier explanation can only be an approximation 

 to the truth. 



We will investigate whether the present theory leads to a 

 general explanation of the phenomenon. 



First, we can write Z = B sin («/ - SJ, where the amplitude 



1^ 



y(i-»»v + «v*), 



and the phase Sj is determined by the equation — 

 sin mr cos mr _ sin mr 

 tr nih-' tii'^r^ 



RKii 



tan 5, 



cos mr 



sm mr 

 nrr' 



ch, after transformation, gives — 

 8, = mr - tan"^ 



In Fig. 5, the quantity Sj is represented as a function of mr 

 by the curve labelled S^. The length ab corresponds in the 



figure to the value of v, both for ordinates and abscissae. If one 

 considers, not mr, but r, as the variable abscissa, the length ab 

 corresponds to the half wave-length. 



In order to immediately attach the experiments which we wish 

 to discuss, the abscissa axis is further divided into metres be- 

 neath the diagram. From the result of direct measurement 



' Translated and conrtnunicated by Dr. Oliver Lodge. 

 p. 452- 



Continued from 



{Wie({. Ann., xxxiv. p. 609, 1888), \ was equal to 4'8 metres, 

 and thus the scale-length of a metre is determined. The zero of 

 the scale is, however, not at the oscillator, but at a distance of 

 o*45 metre from it ; for in this way the scale corresponds to the 

 actual division of the base-line on which the position of the 

 interferences was determined. One sees from the figure that 

 the phase does not in general spread from the source, but its 

 course is such that the waves arise at a distance of about ^\ from 

 it, and give off thence a part to the conductor and a part out 

 into space. At great distances, the phase is sir.aller by the 

 value IT than it would be if the waves had spread out with 

 constant velocity from the source : the waves therefore behave, 

 at great distances, as if they had traversed the first half wave- 

 length with infinite speed. 



The action, 'w, of the wire-waves at a definite position of the 

 secondary conductor can now in any case be represented by the 

 form 70 = C sin {nt - 5.^) ; wherein the abbreviation — 



5, = w,r -f 5 = ■^^ + 5 



is used. A^ denotes the half wave-length of the waves in the wire, 

 which in our experiment was 2-8 metres ; 5, the phase of its 

 action at the point r = o, which we can arbitrarily change by 

 adjustment of the length of the wire. 



By this means we could change the amplitude, C, and give it 

 such a magnitude that the action of the wave in the wire was 

 approximately equal to that of the direct action. The phase of 

 the interference depends, then, only on the difference of the 

 phases 5i and 3.^. With the particular adjustment of the second- 

 ary circle to which our expression for w refers, both actions 

 correspond (the interference has the sign -i- ) if Sj - 5^ is equal 

 to zero, or a whole multiple of 27r ; the actions disagree (the 

 interference has the sign - ) if 5i - 83 is equal to ir, or any whole 

 multiple of it. No interference occurs (the interference has the 

 sign o) if Si - 5., is a whole multiple of ^ir. 



We will now so determine S that at the zero of the metre - 

 divisions the phase of the interference has a definite value, 5„, 

 so that Si = Sj + So. 



The straight line i of our figure shall then represent the 

 value of S2 + So as a function of the distance. The line is 

 specially drawn with such a slant that for an increase of abscissa 

 by Ai = 2 '8 metres the ordinate increases by the value w, and 

 is so arranged that it cuts the curve 5i in a point whose abscissa 

 is the zero of the metre-divisions. 



The lines 2, 3, 4, &c., represent further the course of the 

 values S2 -f Sft - ^ir, S.^ -f So - ir, S.^ + So - fir, &c. These 

 lines are parallel to the line i, and so drawn that they cut one 

 and the same ordinate at distances of \ir, and one and the same 

 abscissa at distances of I "4 metre. 



Project now the section of these straight lines with the curve Sj 

 on the axis of abscissas below, and one gets immediately those dis- 

 tances for which 5i = S.^ -I- So -t- ^ir, 83 4- So -H ir.Sj -f Sq + ^t, 

 &c., for which, therefore, the phase of the interference increases 

 from the origin by iw, tt, ^r. 



One obtains immediately from the figures the following : — 



If the interference at the zero of the base-line possesses the 

 sign -f-( -), it vanishes for the first time at a distance of about 

 I metre ; it attains the sign -{ + ) at about 2*3 metres, vanishes 

 again at 4*8 metres, and reverts back to the sign -|- ( - ) at about 

 76 metres ; it is again o at 14 metres, and from thence onward 

 the signs recur at fairly regular intervals. If at the zero of the 

 base-line the interference was zero, it will be zero again at about 

 2*3, 76, and 14 metres, while it has a prominently positive or 

 negative character at about I metre, 4'8 metres, 11 metres 

 distance from the zero. For mean phases mean values serve. 



If one compares with this result of theory the result of experi- 

 ment, especially those interferences which occurred with arrange- 

 ments of ICO, 250, 400, 550 centimetres of wire ( IVied. Ann., 

 xxxiv. p. 563), one will find a correspondence as complete as 

 can be at all expected. 



I do not succeed quite so well in calculating back to the 

 interferences of the second kind (/.f., p. 565). To get these 

 we used an arrangement of secondary circle by which the 

 integral force of induction through the closed circuit came 

 prominently into account. If we regard the dimensions of the 

 latter as vanishingly small, the integral is proportional to the 

 rate of change of the magnetic field normal to the plane of the 

 circle, and hence to the expression — 



'^^ = AE/m-'n'^- i - 

 (/t l 



