14 W. Ferrel — Law of Thermal Radiation. 



The value, also, obtained by "Winkelmann for temperatures 

 between 0° and 100° is a— 1-0089 * 



Heat radiation should vanish down at the temperature of 

 absolute zero, and hence Dulong and Petit's law cannot hold 

 down at very low temperatures, since it does not make the 

 radiation vanish there, though it reduces it to about one- eighth 

 of what it is at 0° C. For the same reason no special case of 

 the general expression (1) can hold at any low temperature. 

 A value of a gradually increasing and approximating to infinity 

 as the zero point is reached would be required. This being 

 the case it is reasonable to suppose that the increase in the 

 value of a may commence at very high temperatures and con- 

 tinue on down, though this is a consideration of no great 

 weight. 



From what has been shown, therefore, it is evident that 

 Dulong and Petit's law holds through only a comparatively 

 short range of temperature, and the same is true of any func- 

 tion of the same general form, but by giving different values 

 to a in the expression of (4), smaller at high temperatures and 

 much greater for low temperatures, an expression may be had 

 which represents the difference of radiation between the body 

 and the inclosure, and so the rate of cooling, approximately 

 through a considerable range of temperature. 



15. "We have seen, § 9, that the observed rates of cooling 

 seem to confirm Stefan's law for a range of temperature from 

 about 50° to 137°, while for higher temperatures, according to 

 Rosetti's experiments, an exponent of 4*2 instead of 4 is 

 required in the general expression of (8). And according to 

 Schleiermacher's experiments! still higher values of the ex- 

 ponent e are required for very high temperatures to represent 

 approximately the experiments through any given not very 

 great range of temperature. These experiments, however, 

 indicate that different values of the exponent are required for 

 the different kinds of radiating wire, as is to be expected, since 

 the radiations of different qualities with regard to wave-length 

 are not in the same proportion in the different wires, or the 

 same as that of a glass or lampblack surface. For the bright 

 platinum wires of apparatus I and II, Stefan's law is satisfied at 

 temperatures from 150° to 300°, while in apparatus III with a 

 dark, though rot coated with lampblack, wire, his law is not 

 satisfied until a temperature of about 400° is reached. This 

 probably arises from the want of a perfect vacuum in the tube 

 through which the heated wire passed, for it is well known 

 that it is almost impossible to have such a vacuum as to render 

 the conduction insensible, and the effect of any conduction, 

 which increases nearly in proportion to the temperature, while 

 * Pogg. Ann., clix, 177, 1876. \ Wied. Ann., xxvi, 287. 



