W. Ferret — Law of Thermal Radiation. 7 



are represented by the expressions at the heads of the last two 

 columns of the preceding table with the residuals beneath. 

 These expressions are deduced from (4) and (8) by putting 

 a=l*00S2 in the former, and e=4*2 in the latter, and hence 

 they are modifications of Dulong and Petit's and Stefan's laws 

 respectively. The residuals are as satisfactory as in the other 

 case. 



6. The value of A in (4) or (8), if it were a true expression, 

 is the rate with which a body would cool in empty space at 

 the temperature r or T , according to the respective laws, and 

 yet it is seen how different are the values in the preceding 

 case, as seen from the numerical coefficients in the two cases, 

 the one, 1*592, being more than twice as large as the other, 

 0*730, and yet the two expressions with these very different 

 numerical values of A satisfy the rates of cooling equally well 

 through a range from 80° to 240° C But the rate of cooling 

 at any given temperature, it is seen, depends upon the differ- 

 ence between the two values of a function of the temperature, 

 and not upon the absolute values of these functions, and it so 

 happens that these differences in the two forms of function, 

 with very different values of A, however, satisfy observation 

 equally well through a considerable range of temperature, 

 although the absolute values of the functions are so different. 

 Little reliance, therefore, can be placed in values of A which 

 best satisfy the observed rates of cooling, as being the actual 

 rate with which the body would cool in empty space. And 

 this is especially the case where the observed rates are through 

 a short range of temperature and not far above the tempera- 

 ture of the inclosure ; for then the values of A and of a in the 

 one case, and of A and of e in the other, are somewhat comple- 

 mentary, so that in increasing the one and decreasing the other, 

 and vice versa, the differences, or values of R, may remain 

 very nearly the same through a considerable range of tem- 

 perature. 



Not only are very different values of A obtained from the 

 two different forms of expression (4) and (8) but likewise from 

 the same general form of expression by giving different values 

 to a in the one case, or to e in the other ; for these values, 

 especially where the range of temperature is small, may differ 

 considerably, and yet the expressions with proper, though very 

 different, values of A satisfy the observed rates of cooling 

 equally well. For instance, in the preceding case of the rates 

 of cooling observed by Dulong and Petit, although the range 

 is 160°, if the value of a is taken a little greater or less than 

 1*0082 in the one case, or e a little greater or less than 4*2 in the 

 other, the residuals are very nearly as satisfactory. There is, 

 therefore, a great uncertainty in the value of A which satisfie s 



