W. Ferrel — Law of Thermal Radiation. 15 



that of radiation increases in a much higher ratio, is to appar- 

 ently diminish the latter, and render a smaller value of the 

 exponent e necessary. But in all cases these experiments indi- 

 cate that there must be a gradual, though small, increase of the 

 exponent, with increase of temperature, and that at very high 

 temperatures this exponent must be greater than that of 

 Stefan's law. It is therefore reasonable to suppose that at 

 ordinary temperatures, and especially at very low tempera- 

 tures, the value of e is less than that of Stefan's law, which, we 

 have seen, seems to hold for temperatures from about 50° to 

 137°. 



It appears, therefore, that neither Stefan's law nor any other 

 of the general form of (6) with a different value of e repre- 

 sents the true law of nature through the whole range of ex- 

 periments, but that different values of e in (8) are required for 

 different ranges of temperature, and values which increase with 

 increase of temperature, to represent the observed rates of 

 cooling approximately through a given, not very great, range 

 of temperature. But the general expression of the radiation 

 (6), and that of the rate of cooling (8) derived from it, seem to 

 be much better than those of (1) and (4), since only small 

 changes in the value of e with change of temperature are 

 required, and the formulas, with any given value of e, hold 

 through a much greater range of temperature, as is seen in the 

 case of Rosetti's experiments, which are well represented 

 through a range of 210° with the value e=4t'2, (§ 10). 



16. For determining the law of radiation it is necessary to 

 have either experiments on the rate of continuous cooling of 

 a body through a long range of temperature, or to have the 

 observed rates through shorter ranges but for different temper- 

 atures of the inclosure. Yery interesting and important ex- 

 periments of the latter kind have been made by Graetz on the 

 rates of cooling of a glass bulb with mercury both in a perfect 

 vacuum, as supposed, and in an inclosure containing air of low 

 tension.* The three temperatures of the enclosures were those 

 of melting ice, boiling water, and boiling aniline, 182 - 7°. The 

 ranges of the observed rates of cooling were from 33° to 42°, 

 and these rates were observed down to about 20° above the in- 

 cisures. The results were discussed with reference to both 

 Dulong and Petit's law and Stefan's. He determined the value 

 of m in an expression similar to that of the special case of (4) 

 in which a— 1*0077, for each group of the observed rates of 

 cooling. It is seen how this may be done by means of (4) and 

 (5') from the observed rates or values of R. He obtained the 

 following three values of m, expressed here in calories per 

 minute instead of per second. 



* Wied. Ann., xi, 973, and xiv, 232, 1881. 



