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LI II. Remarks upon the Law of Complete Radiation. 

 By Lord Rayleigh, FM.S.* 



BY complete radiation I mean the radiation from an ideally 

 black body, which according to Stewart f and Kirchhoff 

 is a definite function of the absolute temperature and the 

 wave-length X. Arguments of (in my opinion J) considerable 

 weight have been brought forward by Boltzmann and W. Wien 

 leading to the conclusion that the function is of the form 



5 <f>{0X)dX, (1) 



expressive of the energy in that part of the spectrum which 

 lies between X and X + r/A. A further specialization by 

 determining the form of the function <fi was attempted later §. 

 Wien concludes that the actual law is 



Cl \- 5 e~ c ^ dX, (2) 



in which c\ and c 2 are constants, but viewed from the theoretical 

 side the result appears to me to be little more than a con- 

 jecture. It is, however, supported upon general thermo- 

 dynamic grounds by Planck ||. 



Upon the experimental side, Wien's law (2) has met with 

 important confirmation. Paschen finds that his observations 

 are well represented, if he takes 



c 2 = 14,455, 



6 being measured in centigrade degrees and X in thousandths 

 of a millimetre (fi). Nevertheless, the law seems rather 

 difficult of acceptance, especially the implication that as the 

 temperature is raised, the radiation of given wave-leno-th 

 approaches a limit. It is true that for visible rays the limit 

 is out of range. But if we take X = 60/z, as (according to 

 the remarkable researches of Rubens) for the rays selected by 

 reflexion at surfaces of Sylvin, we see that for temperatures 

 over 1000° (absolute) there would be but little further increase 

 of radiation. 



The question is one to be settled by experiment ; but in the 

 meantime I venture to suggest a modification of (2), which 

 appears to me more probable a priori. Speculation upon this 

 subject is hampered by the difficulties which attend the 

 Boltzmann - Maxwell doctrine of the partition of energy. 

 According to this doctrine every mode of vibration should be 



* Communicated by the Author. 



t Stewart's work appears to be insufficiently recognized upon the 

 Continent. 



X Phil. Mag. vol. xlv. p. 622 (1898). 



$ Wied. Ann. vol. lviii. p. 662 (1896). 



|| Wied. Ann. vol. i. p. 74 (1900). 



2 P 2 



