16 W. Ferret — Law of Thermal Radiation. 



m = , '7ol8 for temperature of inclosure 0° 

 >«=:0-8286 " " 100 



»i=0"8118 " " 182-7 



If Dulong and Petit's law were correct throughout the whole 

 range of the experiments these values, of course, would be 

 equal, since m in (4) is a constant where the law holds. But 

 these values of m must be referred, not to the temperatures of 

 the enclosures, but to the mean or middle temperatures of the 

 range of each group, since they are determined from the ob- 

 served rates of cooling within these ranges and are such values 

 as best satisfy the observations. The middle temperatures of 

 the groups are respectively 42°, 142° and 216°. With these 

 values of m for the several temperatures, we get from (1) with 

 a= 1-0077, 



H 42 = l-038 H 142 = 2-464 H 216 =4-261 



If we now wish to determine the value of a in the general 

 expression of (1) which will satisfy any two of these consecu- 

 tive values of H, and so give a law which will hold approxi- 

 mately through the whole intervening range and accurately for 

 the middle point, or nearly, of this range, we must have 

 values wmich satisfy the following conditions : 



logH 142 -logH 42 = 100log« 



lo g H 216 - lo g H !« = ^ lo g a 



From these conditions we determine the values 



a= 1-0087 at a temperature of 92° 

 «= 1-0073 at a temperature of 179 



From these results it is seen again that the value of a de- 

 creases with increase of temperature, very much in accordance 

 with what has been shown from other experiments and by 

 different methods, except that the last value of a above is 

 rather too small. We have seen, § 4, that a value of a= 1-0082 

 satisfies very well Dulong and Petit's experiments for a con- 

 siderable range on each side of the mean temperature of 160°, 

 and that the same value, § 12, satisfies it fairly well through a 

 range of at least 120°, of which the mean temperature, 157°, 

 is nearly the same ; but that Rosetti's experiments through a 

 range of 80° of which the mean temperature is 257°, requires 

 a value of a— 1 ■00692. 



17. Graetz also discussed his results by Stefan's law, and 

 with the following form of the expression of this law, H = <rT 4 , 

 he obtained, where the second is the unit of time : 



6— 1-086 . 10 -12 for the group with inclosure of 0° 

 0= 1-05 7 . 10- 1 - " " " 100 



<f = 1-085 . 10- 1 - " " " 182-7 



