794 Mr. S. Lees on the Analysis of 



of the secondary radiation from the two edges of the slit 

 had to be given up, exposures with slits of various width 

 showing the lines at the same distance. The only possibility 

 left was that the cathode rays were not focussed in only one^ 

 point of the target. Consequently, the bulb was placed 

 in such a position that the X-rays used were emitted at a 

 minimal angle with the surface of the target, and now both 

 the direct and the reflected lines were simple. Possibly 

 former cases of double lines may be referred to the same 

 cause. 



Physical Laboratory, 

 University of Lund, 

 Sept. 1914. 



LXXXVI. Note on the Analysis of Energy Distribution for- 

 Natural Radiation. By S. Lees, Reader in Applied 

 Thermodynamics in the Manchester School of Technology 

 and in the University of Manchester *. 



§ 1. fTVEE following remarks are suggested by a paper of 

 JL Lord Payleigh's (Phil. Mag. xxvii. p. 466, 1889).. 

 Indeed, the theorem deduced in § 4 may be regarded as 

 analogous to a theorem given by Rayleigh in his paper. 



§ 2. At any point (#, y, z) in a medium traversed by 

 natural radiation corresponding to some definite temperature, 

 we may denote the component electric forces at time t by 

 (X, Y, Z) . We shall consider any time-interval defined by 

 < t < T, and suppose that 



X = from £=— co t(W = 0, 

 X=X(*)„ *=0 „ *.=T, 

 X=0 „ *=T „ £ = oo. 



Then by Fourier's theorem, 



X(£) = - 1 1 X(V) cos p(u — t) dp du, . (i.) 



7r J P =o J«=o 



where we assume that X is finite, and only has a finite 

 number of discontinuities in the interval 0<£<T. We may 

 thus express X in the form 



Jo ' 



f (p) cos (pt +J3) dp, . . . (ii.) 



where, of course, (3 may be a function of p, and the analysis 

 is purely formal. 



* Communicated by the Author. 



