RADIATION AND TEMPERATURE. 24-9 



Wien's formula for radiation in the small range dX is 



x ~ X 6 

 Planck's modification is 



x = -f 

 1 ew-l 



where C l and 2 are constants. These last formulae must for the present 

 be regarded as of less weight than those for A TO and E m , as they are 

 obtained by the aid of special molecular hypotheses. 



Since the enunciation of Stefan's law and the foundation of the 

 thermodynamics of radiation, much work has been done to test the 

 formulae obtained by the theory.* Lummer and Pringsheim used as 

 radiating source a constant-temperature enclosure with a small hole in 

 the side, the enclosure being of different materials according to the 

 temperature. The radiation emerging from the hole was practically the 

 full radiation for the temperature of the enclosure. For imagine that a 

 stopper at the temperature of the enclosure is put into the hole, the full 

 radiation strikes on the stopper ; but it only exceeds that passing out 

 through the hole by the amount emitted by the stopper and reflected by 

 the sides of the enclosure back to the stopper again, and this is 

 negligible if the hole is small enough. 



The issuing radiation was measured by a bolometer, and the fourth- 

 power law was very exactly verified. Using a fluorspar prism, the 

 radiation was dispersed, and a bolometer travelling along the spectrum 

 gave the position of maximum energy and the amount of that energy. 

 The formulas X m O = constant and E m = constant x # 5 were verified. 



In subsequent work f Planck's formula has been shown to accord 

 very closely with observations on the energy in different parts of the 

 spectrum more closely than that of Wien. But it should be noted that 

 C 2 is in Wien's formula 5X m d, where A OT is the wave-length for which E 

 is a maximum and in Planck's very nearly the same. Hence we have 



&\rn 



practically e~*~ in the denominator, and this is great compared with 1, 

 so long as A. is less than X m . The two formulas nearly agree, therefore, on 

 the shorter wave-length side of the maximum. 



The confirmation of these formulae justifies their use to determine 

 the temperature of bodies emitting full radiation. Thus Lummer and 

 Pringsheim J have determined the temperature of a uniform-temperature 

 enclosure (1) by measuring the total radiation emitted, (2) by measuring 

 the wave-length of maximum energy, (3) by comparing the brightness of 

 a given part of the spectrum with the brightness of the same part of a 

 spectrum emitted by a surface at a lower known temperature and using 

 Planck's formula. All three methods gave the temperature as 2325 

 absolute within 20. The constants in the formula had been previously 

 determined. 



* An account of the subject will be found in the CongrJs International d< 

 Physique, ii. p. 41, by Lummer, who has been one of the chief workers. 

 + Paschen, Ann. d. Physik, 4-2, Feb. 1901, pp. 277-298. 

 t Berichtc der Deut. Phys. Oes., 1903, p. 3. 



