22 W. Ferret — Law of Thermal Radiation. 



21. Although the general expression of (2) has not been 

 found to represent observation well through as great a range 

 of temperature as that of (7), yet if we put 



(29) H — H = 0-652(l-0088 (5 — 1), 



the value of a To being in the case of the examples of the pre- 

 ceding table, we get the values of H— H in the last column of 

 this table. It is seen that the values differ but little from 

 those of the other columns throughout the whole range. It is 

 seen, therefore, how nearly three very different functions, with 

 differing values of the constants, give the same results, and con- 

 sequently would represent observations equally well. In each 

 of these the value of the constant m enters as a numerical co- 

 efficient, and these are respectively, taking the expressions in 

 the preceding order, 0*438, 0-3951, and 0*652. And differences 

 of the same order have been found where these expressions 

 have been applied to results of experiment and observation. 

 We have, therefore, only a vague idea of the real value of this 

 constant. It probably falls within the range of the numbers 

 above, and is undoubtedly much smaller than the value given 

 by Pouillet, 1*146, for a lampblack surface, as deduced from 

 Dulong and Petit's experiments in accordance with their law, 

 and putting the relative radiativity of glass at 0*80. These 

 values have all been determined from the experiments of 

 Dulong and Petit with a bare glass surface at temperatures 

 from 80° to 240°. But at the temperature of 100° Lehnebach 

 found the radiativity of bare glass and that covered with lamp- 

 black the same. At lower temperatures at least there must be 

 a considerable difference, but not as much as Pouillet supposed. 



The three forms of expression from which the results of the 

 preceding table have been computed, are equally as well appli- 

 cable to any observed rates of cooling, the law in both cases 

 being the same, but the constant coefficient different, as may 

 be seen by comparing the expressions of H — H with those of 

 R in (4) and (8). So either of these can be used for all ordi- 

 nary temperatures by using the values of the constants e and a 

 used in (26) and (29), but the numerical coefficients will of 

 course be different, depending upon the thermal capacity of 

 the cooling body, as is seen from (5) and (9). 



By Stefan's law, (7) with e=4, we get, by determining the 

 value of m so as to give H 100 —H = 0*912, 



(30) H-H =0-3673(2 4 -l). 



This gives the values of H— H in the last column of the pre- 

 ceding table. The differences between these numbers and 

 those of the other columns are considerable, but if m were so 

 determined as to give the best general agreement, instead of 



