W. Ferret — Law of Thermal Radiation. 19 



These values of R compared with the corrected observed 

 values of R in the fifth column of the table in § 4 leaves the 

 residuals, O — C, in the third column of the preceding table. 

 Hence the expression of (19) with the assumed constants, 

 represents the experiments of Dulong and Petit, with the pre- 

 ceding residuals, which are very satisfactory. 



With the values of A, e and T above, and the known values 

 of r, c and a given in § 5, (20 ; ) gives «^=0*4:086, which is con- 

 siderably larger than the value 0-3296 in § 7. With this value 

 and the value of e given by (21) we get from (18) 



(22) H 100 -H =0'8958 



This differs but little from the value of (13), § 7, obtained from 

 (7) with the constant value of 6=4*2. 

 If instead of (21) we put 



(23) 6 = 3-0 + 0-00032 r 



we get from (19) with the value of A=25'0 and T =23-8 / , the 

 values of R in the fifth column of the preceding table corre- 

 sponding to the values of T in the fourth column. These 

 compared with the values of y in the table of § 10, give the 

 residuals, O — C, in the sixth column. These are quite satisfac- 

 tory considering the large temperature range of 240°. 

 If in (19) we put A= 1-122, T =20°, and 



(24) 6=3-0 + 0-00034 r 



we get the values of R in the last column but one of the pre- 

 ceding table, which compared with the differences of the rates 

 of cooling between a bare and silvered thermometer given in 

 § 8, give the residuals in the last column. The preceding 

 values of H, § 17, obtained from Graetz's experiments should 

 be represented by (6) with proper values of m and 6, or with 

 the values of H and e for given temperatures it should give m 

 a constant for each of these temperatures. With the preced- 

 ing values of H for the temperatures of 42°, 142°, and 216° 

 and with the value of 



(25) e.-=3-0 + 0-0004 r 



we get respectively the following three values of 



m=0-3792, m = 0-3804, m = 0-3795 



The numerical coefficient of r was assumed so as to make the 

 first and last very nearly the same, but the very near agree- 

 ment of the other with these depends upon the accuracy of 

 (6) with the assumed value, of e above. 



The difference between the numerical coefficients of r in the 

 expressions of (21) and (23) indicate that the exponent e for 

 glass increases a little more with increase of temperature than 



