88 



q the quantity of radiation or heat falling per minute on the 

 black bulb and also on the bright bulb. 



a q the quantity of radiation absorbed by the bright bulb. 



I q the quantity of radiation absorbed by the black bulb. 



e the emissive power of the black bulb. 



e' the emissive power of the bright bulb. 



t and t' the temperatures of the black and bright bulbs, respectively, 

 when they come to the stationarj^ temperature that indicates equilib- 

 rium between absorption and emission. 



T the temperature of the glass envelopes within which the ther- 

 mometers are inclosed iu a space that is an approximate vacuum. 



On the assumption of the Newtonian law of radiation, viz, that 

 the quantity of heat emitted is proportional to the excess of tem- 

 perature, we have the following relations : 



qz^ce {t —T) 

 aq—ee' {f — T) 



From these expressions we can, by elimination of 7", find the follow- 

 ing expression for q — that is to say, the quantity of solar radiation 

 per unit of time that is at that moment falling on the two thermome- 

 ters, at least in so far as this radiation is capable of being trans- 

 formed into heat by absorption into the bulbs of the thermometers : 



Marie-Davy, in the absence of exact knowledge of these coeiRcients 

 <2, c, <?, e% prefers to attempt to determine only relative measures of 

 the intensity of radiation. He therefore assumes that the expression 



is equal to 5.88 units, and the values for q thus obtained he 



e —a e ^ ' ^ 



calls actinometric degrees, since on the very clearest days in Paris 

 they accord well with the assumption that the so-called solar constant 

 of radiation is 100 actinometric degrees, and that the coefficient of 

 transmission of sunshine through the atmosphere is 0.875, 



Ferrel (1884), in his memoir on the temperature of the atmosphere 

 (p. 41), has improved upon Marie-Davy's theory, in that he has 

 applied to the conjugate thermometers the law of radiation, estab- 

 lished by Dulong and Petit in 1817, which is applicable to a much 

 larger range of temperatures than the Newtonian law adopted by 

 Marie-Davy. Ferrel's formula may be written : 



(^=4.584 k m" {m*-t'—l) 



where the notation is the same as before, except that m, is the num- 

 ber 1.0077, as determined by Dulong and Petit and A^ is a factor that 

 varies with the quality of the bright bulb, whose absolute value is 



