28 W. Ferrel — Law of Thermal Radiation. 



above refers to the sun's heat-radiation as it reaches the earth's 

 surface, as seems to be the case, then the numerical coefficient 

 in the conditions above should be increased at least one-third 

 for the loss in passing through the atmosphere, the effect of 

 which would be to increase considerably the preceding com- 

 puted temperatures. 



26. The condition which determines the temperature at 

 which a body in space at the distance of the earth from the 

 sun would stand from the effect of the sun's thermal radia- 

 tion, is 



(37) H=£-A 



a 



in which H, as in the case of (34), is a function of the tempera- 

 ture of the form of (1), (6), etc., according to the assumed law, 

 and in which d and a are the relative radiativities and absorp- 

 tivities of the body with reference to lampblack, supposed to 

 be a perfect absorber. In a lampblack surface, as that of a 

 black-bulb thermometer, or any one in which there is no selec- 

 tive absorption and radiation, but all the wave-lengths are 

 radiated in the same proportions as those of a lampblack sur- 

 face, we have d/a=l in the resultant of the radiations and 

 absorptions of all wave-lengths. 

 By means of (1) we get from (37) 



(38) ma T =i— A 



<x 



as the condition for determining the temperature r of the 

 body. But here, as in the preceding case with regard to the 

 sun's temperature, the uncertainty in the true value of m 

 comes in, but not so much that of the other part of the law, 

 since we have here to deal with temperatures differing but 

 little from those of the experiments upon which the law is 

 based, and so have to extend the law through a small range 

 only of temperature. Dulong and Petit's value of a has been 

 shown to be too small and Pouillet's value of m too large for 

 ordinary temperatures of the earth's surface. Taking, there- 

 fore, the value of a= 1*0082 as given at the head of the last 

 column but one of the table of § 4, which has been found best to 

 satisfy the results of experiment as corrected by Stefan, and the 

 value of m=0'7188 in §7, and putting A=2*2, as heretofore, 

 the preceding equation, (38), gives in any case in which 8/a=l, 

 r= — 33° as the temperature at which the body would stand, as 

 determined from the preceding condition with the assumed 

 value of the constants, and as the mean temperature of the 

 earth and moon if their surfaces satisfied the conditions above 

 with regard to radiation and absorption. 



