W. Ferret — Law of Thermal Radiation. 23 



making H 100 — H = 0*912, the agreement would be much better. 

 Stefan's law, therefore, can be used without material error 

 down at ordinary temperatures, for a range even of 100°, by 

 using a value of m a little greater than that above. 



22. If in (2) we put E equal to the value of H— H where 

 3=1, that is, for the rate with which each unit of surface loses 

 heat by radiation in excess of what it receives when the differ- 

 ence between the temperature of the body and that of the 

 inclosure is 1° C, we get 



(31) E = ma T °(fl-]). 



This value of E is called by English physicists the emissivity of 

 the body at the temperature of the inclosure r , though this 

 term is often used in the sense of radiativity, or absolute radi- 

 ating power, without regard to heat received from an inclosure. 

 It is seen that, if (2) expresses the true law the emissivity 

 increases as a T °, whatever the value of a may be. With the 

 value of m and a in (29) we get, where the temperature of the 

 inclosure r=50°, 



E = 0*652Xl*0088 50 X 0*0088 = 0-00889. 



At the temperature of r =0, we get E=000574. 



In like manner we get from (7) by putting T — T =l and 

 developing 



(32) E=—eqr 1 - 



Hence, if the form of (7) expresses the true law, the emissivity 

 is as the e—1 power of ^ =T /273, or as the e— 1 power of 

 the absolute temperature, which, by Stefan's law, is the third 

 power. With the values of m and e used in (26) this gives for 

 the temperature T =50°, 



^ 0-3951 /323\ 2-833 



E= X3-833XI — =0-893. 



273 \273/ 



At the temperature r =0, we get E= 0*00555. 

 With the values of m and e in (30) we get for r =50°, 



^ 0-3673 /323\ 3 



E = — X4X(— ) =0-892. 



273 \273/ 



At the temperature of r =0, this gives E = 0*00538. 



Again, for the more general expression of (18), in which e 

 varies with T, the value of E may be deduced from (27) with- 

 out any sensible error, by using in the first member small finite 

 variations SB. and ST instead of dB. and dT. If dT=l° C, 

 then <?H becomes E, and we get 



T e -V TWT\ 



(33) K = w ^ i + cr + c-^-| 



