12 ]V. F&rrel — Law of Thermal Radiation. 



of the iifth column in the preceding table with the residuals, 

 O — C, in the same column beneath. These are not satisfactory, 

 and no modified expression of Dulong and Petit's law obtained 

 by giving a different value to a in the general expression of (4) 

 gives residuals which are more satisfactory. It is evident, 

 therefore, that neither Dulong and Petit's law, nor any law of 

 the general form of (4), represents satisfactorily the law of 

 radiation, at least according to these experiments, through a 

 temperature range of 240°, though this is done through a 

 range of 160°, as we have seen, § 4, in the case of Dulong and 

 Petit's experiments. 



Applying Stefan's law, the values of y are represented with 

 the expression at the head of the sixth column with the resid- 

 uals beneath, which are also unsatisfactory. But if we use a 

 modification of Stefan's law, making the exponent e in (8) 

 equal to 4'2 instead of 4, we get with the expression at the 

 head of the last column the residuals beneath. These are very 

 satisfactory, being small in comparison with the observed 

 values of y in the third column and having a pretty regular 

 alternation of plus and minus signs throughout the whole 

 range. This comparatively simple formula, therefore, repre- 

 sents the results of Rosetti's experiments much better than his 

 own, (16), given above, as is seen by comparing the residuals 

 in the last column with those of the fourth column. 



From these comparisons it seems that some function of 

 the general form of (6), of which Stefan's law is a special case, 

 represents the law of radiation, and (8) deduced from it, the 

 law of cooling, much better than those of (1) and (4), since the 

 results of experiment are well represented by a special case of 

 the former through a range of temperature of at least 200°, 

 for the one isolated experiment at a distance of 40° below the 

 lowest of the others should not have much weight, since the 

 value of y is very small. 



12. Although neither Dulong and Petit's law, nor any ex- 

 pression deduced from the general form of (4) by giving dif- 

 ferent values to A and a, represents well Bosetti's experiments 

 through the whole range of temperature, yet by dividing these 

 into two parts we find that the part from T=329*6 to T = 489 - 6 

 is represented by the expression y=37'0 (1*0082 — 1) with 

 the residuals (O — C) below corresponding to the values of d in 

 the first line : 



<5 32-8 



72-8 



92-8 



112-8 



132-8 



152-8 



172-8 



192-8 



O-C —1-4 



-0-6 



4-0-8 



— 1-0 



—01 



— 0-5 



-1-8 



o-o 



These residuals are satisfactory through a range of 120°, from 

 <5=T2'8 to $=192 -8 the middle of which corresponds to a tem- 

 perature of about 157°, and they indicate that with a value of 



