W. Ferret — Law of Thermal Radiation. 13 



«=1*0082 instead of 1*0077 as required by Dulong and Petit's 

 law, the experiments are well represented through this range. 

 This comports exactly with what has been found in the case of 

 Dulong and Petit's experiments, in which the value a= 1*0082 

 was required for the temperature range of 160° from 80° to 

 240°, the mean of which corresponds to the temperature of 

 160°, which is nearly the same as the 157° above. The first 

 residual, corresponding to <5=32*8, being negative, indicates 

 that for lower temperatures the value of a must be still 

 greater. 



13. If we now take the range of observed values of y from 

 o = 192 '8° to = 272*8°, the mean temperature of this range 

 being about 257°, we find that they are represented by the 

 expression y= 51*87 (l*00692 t5 -l) with the residuals, O-C : 



6 



192-8° 



212-8 



232-8 



252-8 



272-8 



O-C 



o-o 



-1-0 



+ 1-0 



-0-9 



+ 0-3 



These residuals are satisfactory for the short range of 80°, and 

 indicate that for this range of higher temperatures the value of 

 a required is approximately 1*0069, though as has been explained 

 this value, determined from so short a range, is somewhat 

 uncertain. It is evident, however, that a value of a much less 

 than that of Dulong and Petit's law, is required for these 

 higher temperatures, and especially smaller than 1*0082 re- 

 quired for the first division of the experiments comprising the 

 lower temperatures. 



"We have now seen that the general expression of (4) appar- 

 ently holds in the special case of a= 1*0082 through a tempera- 

 ture range of about 160° with a mean temperature of 160°, 

 and that there are no values of A and a in the general expres- 

 sion of (4) that will satisfy experiment and observation through 

 any long range of temperature, but that for temperatures con- 

 siderably above 160° the values of a required are less than 

 1*0082, while for lower temperatures values which are greater 

 are required. The value of a= 1*0077 most probably holds 

 through a considerable range with a mean of about 200°. 



14. It is well known that for high temperatures Dulong and 

 Petit's law gives an increase in the intensity of radiation with 

 increase of temperature very much too great, and that here a 

 value of a less than 1*0077 is required, and one which decreases 

 with increase of temperature. And that the value of a must 

 be much greater than 1*0077, and even than 1*0082 at ordinary 

 temperatures was shown by Provostaye and Desains by means 

 of the thermopile.* For temperatures below 160° they found 

 that the deviations of the galvanometer needle could be repre- 

 sented by the general expression of (4) by putting $=1*009. 



* Daguin. Traite de Physique, vol. ii, p. 90. 



