LUNAR EMISSIVITY. 137 



that there is conduction in only one direction, hence the differential terms 

 in y and z disappear). The second term represents the loss of heat by 

 radiation from the surface; while the last term represents the change in 

 temperature at the surface. The dependent variable enters here as a 

 fourth power, and makes the solution difficult. The computations are 

 made for instantaneous eclipse, while in the actual case the shadow moves 

 slowly across the surafce. Hence the error due to neglecting conductivity 

 is partly compensated by the slow eclipse. 



By neglecting conductivity from the interior, the temperature of the 

 surface will fall more rapidly and we have a steeper temperature decadence 

 curve. The solution of the equation is very simple if we neglect conduc- 

 tion, and is 







6 = 





0t 



ds 



for I in minutes, (7=76.6X10 12 gram calories per square centimeter per 

 minute, d=2, and 5 = 0.2 (approximate values for rock material). Hence 



- T 30O 



vi + 0.0155/ 



In fig. 97 are plotted the temperature decadence curves for the radiation 

 constant o, for 0.3 a (emissivity of iron oxide) and for 0.1 0. The curves 

 show that for a full radiator the temperature would fall from 300 to 280 

 (room temperature when the bolometer would be in temperature equilib- 

 rium with the moon) in 17 minutes, for 0.3 a in 55 minutes, and for 0.1 a 

 in 140 minutes. The solution for 0.1 a and 0.3 a is, of course, only ap- 

 proximate since the emissivity varies more nearly as the fifth power instead 

 of the fourth power, as here used; and the computed temperatures should 

 be somewhat higher. The computation is also made (fig. 97), assuming 

 the temperature to be 350 . Here, for a complete radiator the temperature 

 would fall from 350 to 280 in 38 minutes, and for 0.3 a in about 130 

 minutes. By including the conductivity term these periods would be con- 

 siderably prolonged. The present solution is close enough, however, to 

 show that the temperature (300 ) decadence curve is not coincident with 

 the eclipse curve, unless the emissivity is of the order 0.3 a. Hence the 

 writer's 1 previous surmise that at the beginning of totality radiation should 

 still be appreciable is substantiated, although the observations made by 

 Langley seemed to contradict it. Very's observations 2 show that during 

 totality of the eclipse of January 17, 1889, the radiation from the umbra 

 of the eclipsed moon was about 1 per cent of the heat which was to be 



1 Phys. Rev., 23, p. 247, 1906. 



2 Very: Distribution of the Moon's Heat, p. 40. 



