W. Ferret — Law of Thermal Radiation. 17 



But, in accordance with what has been stated in the pre- 

 ceding case with regard to the values of m, these belong prop- 

 erly to the middle temperatures of the groups, and we get 

 from the preceding expression of H for the several temj>era- 

 tures of the middle of each group, making the minute the unit 

 of time: 



H 42 = 0'6415 H U2 =1-8810 H 2]6 = 3-7224 



In order now to determine the value of e in the general ex- 

 pression of (6) which will satisfy any two successive values of 

 H, and so be true for a point very nearly the mean of the two, 

 we have to satisfy the following conditions : 



log H 142 -log H 42 =e(\og T 142 -log T 42 ) 

 log H 216 - log H 142 =e(log T„.-log T 142 ) 

 From these conditions with the preceding values of H for the 

 several temperatures we get 



e=3 , 90 at the temperature of 92° 

 g=4-16 " " 179 



These results accord very well with those previously ob- 

 tained by other methods and from other experiments, and in- 

 dicate that the valne of e increases with increase of temperature 

 and that Stefan's law, in which 6=4, holds through a considerable 

 range of temperature of which the mean is about 125°. We 

 have seen in § 9 that this same value of e satisfies other experi- 

 ments from 75° to 137°, the mean of which is 106°, while for the 

 higher temperature of about 160° the value of e=4z'2 is re- 

 quired. While it cannot be claimed that these results are very 

 accurate, and so a very nice agreement in the con^arisons can 

 not be expected, yet taken altogether they indicate very clearly 

 that the value of e must be considerably less for low than for 

 high temperatures. 



18. So far, in the general expressions (6) and (8) we have 

 regarded the exponent e as constant, and have found that a 

 constant value of e may be found which will make (8) repre- 

 sent observation through a considerable range of temperature, 

 though the value required is a little greater for high than for 

 low temperatures. It is evident, therefore, that the value of 

 this exponent must gradually increase with increase of tem- 

 perature. We will therefore assume that within the range of 

 experiment 



(17) e=e + cr 



in which e is the value of e where r=0. With a varying 

 value of e we must change the last form of the expression of 

 (7) to 



/T e \ T e 



(18) H-H ^Af^-l) in which A=m P>_ 



Am. Jour. Sci.— Third Series, Vol. XXXVIII, No. 223.— July, 1889. 

 2 



