( 672 ) 



Now, if the ])late is kept at a ('((iistaiit tei)i|teratnre, the radiation 

 will ulsu be stali(»)iaiy and i>/ iiiav l)c replaced by its mean value 



ï>/ = 





diiriii^j,' iIk' time if. Sid)stitiiting tli(,' \aiiie (9j, \\ (> Lid intej^rals of 

 two diirereiit kinds, some eoiitainiiig tlie square of a sine, and others 

 tlie product of two sines. The integrals of the second kind will 

 disappear, and 



ƒ 



5 



inn:t 1 



sin^ (It = — x% 



{> 2 



so that 



\ MJ = 00 



t>..' = — :^ a J (11) 



As l(t the frcipieucy of tlie terms in (9), it is given l»y 



7/trr 



" = 1F-' <!-' 



it will therefore increase by ecpial dilferences -, if we 'j:i\o to //Mts 



successive values. 



Bv choosing for »> a value sulTlicieiitly large, we may make this 



stei) ~ as small as we like, so that ultimate! v, even between two values 



of tlie frequency // and // -f- dn, widch are in a j>hysical sense 

 iidiidtely near each other, there will be a certaiiU number of values 

 of (12) and of corresponding terms in the series (11). The number 



of these terms will be - <(n, lieiu-e. ü we suppose fi,,,. or 



JT 



(l-) 



'J r 



fim = -r; I ■'"" "f • ^., dt 



{) 

 to have the same value for each term of this groiq), iIk- corivspondinu' 

 pari of (11) will be 



-— a,n^ (hi. 



2jr 



Substituting this for b:,* in (8), we get for the radiation across 

 io', due to the rays Avith frequencies between n and ;/ -}- (hi, 



cO- , ... 



2nr 



