Interference Phenomena. 535 



which constitutes light. But an}' law connecting radiation 

 and wave-length must take in all ranges of waves, and the 

 particular law adopted gives finite values of intensity within 

 a finite range of /c even for infinitely long waves, hence the 

 result we have obtained was only to have been expected. It 

 may be said, of course, that we have assumed our wall to be 

 a perfect reflector for all wave-lengths ; but it is not necessary 

 to enter into this question any further, as, for other reasons, 

 Weber's law cannot be reconciled with experiment. H. F. 

 Weber himself really uses his law in two contradictory senses 

 and seems to have overlooked the great difference there 

 is in the distribution of energy in a spectrum according 

 as a prism or a grating is used to analyse the light. Weber 

 takes as his measure of energy the energy contained in the 

 i ' homogeneous radiation of wave-length A,." If the quantity 

 given by Weber is denoted by S, Rayleigh interprets his 

 meaning to be that the energy within a range dX is Sc/X, and 

 in the discussion of Langley's observations Weber uses his law 

 in that sense; but Weber also draws conclusions favourable to 

 his equation from the fact that Tyndall, using a prism, observed 

 the maximum heating-effect of an arc-spectrum at a particular 

 place and uses his formula as if the energy contained within 

 a range d/j, (fi being the refractive index) was Sd/u.. 



If the more natural interpretation of Weber's formula is the 

 right one, there should be no maximum of energy in a spectrum 

 formed by a prism at all, but the intensity should indefinitely 

 increase with the wave-length. For /j, and k being approxi- 

 mately connected by the relation 



/jl = {i + ck 2 , d/j, = 2cKdfc y 



the energy contained within a range dju becomes proportional 

 to 1 



~e- a2K2 dfx; 



rC 



the factor of d/m being infinite for infinite values of the wave- 

 length. This puts Weber's law out of court. We may, how- 

 ever, draw this conclusion from it : — If a is taken to be infi- 

 nitely large all radiations are of equal intensities. In that 

 case the excess of energy which we have deduced from the 

 law vanishes at every point, and the two sources may be said 

 not to interfere with each other. 



As an approximately correct law for the distribution of 

 energy in the spectrum we may take that suggested by 

 Michelson, and write for the energy &d/c, where 



