24 W. Ferrel — Law of Thermal Radiation. 



This with the values of m in § 20 used in computing the first 

 column of values of H— H in the table and the values of e and 

 c in (23), we get for r=50° or T=323°, 



323-oie / 323 ] 323 \ 



E = 0*438. K , ( 3-0 + "00032 T + -00032 -S. ) = 0-00890. 



273 s \ 0-4343 / 



At the temperature r=0, we get E = 0-00560. There is a very 

 nice agreement in these results from these several different 

 forms of expression at the temperature of 50°, but it is not 

 quite so satisfactory at 0°, which was to be expected, since this 

 is one of the limits of the range to which the several forms are 

 applicable. The values of E above at 0° do not differ much 

 from those of Winkelmann* and Kundt and Warburg, f which, 

 reduced to our unit of time, are respectively '00528 and 

 0-00558. 



In § 7 we have found from Dulong and Petit's experiments 

 by their law #2=0*7188. With this value and Dulong and 

 Petit's value of «= 1*0077 we get from (31), applied as in a 

 preceding example, E=0 - 00589 at the temperature of 0°, but 

 E=0-02202 at the temperature of 160°. Also with the value 

 of m=0'3296, as obtained from Dulong and Petit's experi- 

 ments by Stefan's law, with the exponent e=4*2, we get from 

 (32), E=0-00507 at the temperature of 0°, but E=0-02218 at 

 the temperature of 160°. These values of E from these two 

 different formulae agree very closely at the temperature of 160°, 

 but not at the temperature of 0°. This is because these for- 

 mulae are derived from expressions which represent experiment 

 and observation through a temperature range of which the 

 mean is 160°, but it is not claimed that these expressions hold 

 down to the temperature of 0° ; in fact it has been shown that 

 they do not. The values of E, therefore, from (31) and (32) 

 which have been deduced from these expressions, can be cor- 

 rect only within the limits of the range for which they hold, 

 and not down at 0°. 



From (33), with the value of e in (21) and the value of 

 m= 0-4086, which are the values deduced from Dulong and 

 Petit's experiments, we get, in the manner of the preceding 

 example, E=0-00574 at the temperature of 0°, butE = 0*02211 

 at the temperature of 160°. As these values are deduced from 

 a formula which is supposed to be applicable to all tempera- 

 tures within the range of experiment they should be more ac- 

 curate, at least at the temperature of 0°, than the preceding 

 results. The preceding value of E at 160° is very nearly the 

 same as the other two values from expressions less general, but 

 adapted to this range of temperature, and is a mean of the 

 two. The preceding value of E at 0° falls between the two 



* Pogg. Ann., clvii, 497. f Pogg. Ann., clvi, 208. 



