534 Prof. Arthur Schuster on 



which lies within the range die, and the amount of interference 

 is therefore seen to depend on the distribution of energy only 

 and not on any assumption respecting the regularity or irre- 

 gularity of vibration. 



19. We may apply our result to some special case. The 

 simplest experimental arrangement to obtain a double source 

 is that of placing a point from winch light diverges close to a 

 mirror as in Lloyd's experiment, and we may imagine the 

 radiation to be received on a screen at right angles to the 

 mirror and the energy to be measured by means of a thermo- 

 pile or bolometer. As the distribution of energy will entirely 

 depend on the law connecting radiation and wave-length, we 

 must introduce some assumption concerning the connexion. 

 The simplest law is that ascribed by Rayleigh to H. F. Weber, 

 according to which the energy contained within a region die of 

 the spectrum is Ce~ a2K2 d/c 



where C and a are constants and 27t/k means the time of 

 vibration. 



The excess of energy E of the double source over the 

 separate sources is from (5) 



/"»00 



|E=i Qe'^GO^KTdK, 



a yV 



If the source of light is a slit parallel to the mirror and x the 

 distance of any point on the screen from the mirror, the excess 

 of energy contained in a strip of width dx would be E<i#, and 

 r, which is half the retardation in time of the light reaching 

 the screen from the two sources, is proportional to x. Hence 

 changing the value of C and «, we may say that the excess 

 of energy Of the double source over the effects of the single 

 sources acting independently is 



G 

 t= e- xVa2 dx. 



Ct\/ 



IT 



The energy is seen to be greatest at the screen and to fall off 

 quickly towards the side. The excess of energy is everywhere 

 positive, or the total energy is increased by the presence of 

 the mirror. There is nothing intrinsically impossible in this 

 result. A source of sound will do more work when placed 

 close to a wall than if the wall were absent. If effects of the 

 same nature are generally not observed in the case of light, it 

 is due to the smallness of the wave-length of the radiation 



