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Mr. E. Buckingham on the 



treated as always equal, within an infinitesimal amount, in 

 spite of the fact that they are not constant in time. 



The width d\ may be as small as we please, so that the 

 change of p x may be assigned definitely to the particular 

 wave-length X. There is no occasion for the formation of 

 any new waves ; the change in energy is a change in the 

 amplitude of waves already present, which occurs in connexion 

 with the change of period upon reflexion from the moving- 

 surface. In a short time, reflexion from the moving mirror 

 would introduce inhomogeneity into the radiation, which 

 would not have time to be all equally affected by reflexion 

 at M ; but in a long time the radiation again becomes homo- 

 geneous to the same degree as at first, and equation (12) is 

 satisfied for each wave-length. 



7. Hitherto we have considered only a small interval of 

 wave-lengths, but suppose that the strip in question is 

 merely a part of a continuous distribution of diffuse radiation 

 which may be represented by a curve such as is shown in 

 figure 2. If we take full advantage of the principle of the 



Fig. 2. 



independence of the separate elements composing the whole 

 spectrum, we must admit that the reasoning given above for 

 an isolated strip is applicable without change to every wave- 

 length of the spectrum, no matter what may be the form of 

 the energy curve p^ =/(\). "We then have the proposition 

 that when any completely diffuse radiation is compressed 

 infinitely slowly within a perfectly reflecting enclosure, the 

 energy curve is changed in such a way that the abscissa of 

 every point is multipled by some fraction /, while the 

 ordinate is multiplied by f~°, so that the area under the curve, 

 or the integral density of the energy present, is multiplied 

 by /~ 4 . This is true for any continuous or discontinuous 

 spectral distribution and not merely for black radiation. 



