442 



On the Radiation of Heat from the Moon. [May 27, 



connected with that previously found for Full Moon by using the devia- 

 tion produced by a vessel of hot water as a term of comparison. 



The relative amount of solar and lunar radiation thus found was 



89819 : 1, (c) 



which is quite as near that given by (b) as we could expect when we con- 

 sider the roughness of the data. 



As a further confirmation of the correctness of the two rough approxi- 

 mations to the value of the ratio existing between the sun's and the moon's 

 radiant heat already given, the subject was investigated from a purely 

 theoretical point of view. It was assumed 



(1) That the quantity of heat leaving the moon at any instant may with- 

 out much error be considered the same as that falling on it at that instant. 



(2) That the absorptive power of our atmosphere is the same for lunar 

 and solar heat. 



(3) That, as was already assumed in obtaining formula (a), the moon is 

 a smooth sphere not capable of reflecting light regularly. Then the heat 

 which leaves the moon in all directions = quantity which falls on the 

 moon =j^- 5 of the quantity which falls on the earth from the sun 



{(# — e) . cos e+ sin e} sin e . de = — 3tt. 



o 



The part which falls on the earth 

 l 



= K.| 59 ' 964 { (t - e) cos e + sin e} sin e . de 



K f • /io r K 'x , 2 + cos (1° 55') o . /locc ^l 

 = — X -I -7T . versm (1° 55)+ - 59.964 ~ ~ f sin (1° 55') J 



= — . E suppose ; 



therefore (if we may be allowed the expression) 

 sun-heat _ 13*55 X 3tt 

 moon-heat E 



= — - — (quam proxime). . . . (d) 



In the above, the proportion between the areas of surface presented by 

 the moon and earth to the sun is taken =13*55, and the angle subtended 

 by the earth at the moon =1° 55'. 



The value of the readings of the galvanometer was determined by compa- 

 rison with those obtained by using a vessel of hot water coated with shellac 

 and lampblack varnish as a source of heat. The vessel was of tin, circular, 

 and subtended the same angle at the small concave reflectors as the large 

 mirror of the telescope. It was thus found that (the radiating power of 

 the moon being supposed equal to that of the lampblack surface and the 

 earth's atmosphere not to influence the result) a deviation of 90 for full 



