1869.] 



Heat from the Moon. 



439 



In column 3 is given the mean of the deviations of all the single differ- 

 ences from the mean difference of all the readings taken with the moon on 

 and with the moon off the apparatus. 



In column 4 the arithmetic mean of all the observed deviations. 



In column 5 the calculated deviation for each night at midnight, on the 

 assumption that the deviation corresponding to full moon =100, and that 

 the moon is a smooth sphere. We have then 



Q (quantity of heat coming from the moon's surface) 



cos 0. cos (e — Q) dd 



C 



= 2 {tt — e . cos e+ sin e}*, 



where e = ir— apparent distance between the centres of the sun and moon. 



Q 



When e = (full moon), Q= — . 7r, 



when e= — (half moon), Q= ^, 

 — _ 



when e = 7r (new moon), Q=0 ; 

 .'. if full moon = 100, Q in general 



=s=100/l — |cose+ sine^ (a) 



In column 6 we have the deviation for full moon calculated from the 

 observed mean deviation for each night. 



In column 7 the supplement of the apparent distance between the cen- 

 tres of the sun and moon. 



In column 8 the approximate mean altitude of the moon. 



In column 9 the number of times the telescope was put on or off the 

 moon during the observations included in the mean result. 



In all these observations the deviations which have been measured are 

 those due to the difference between the radiation from a circle of sky con- 

 taining the moon's disk, and that from a similar circle of sky close to it 

 not containing the moon's disk. 



The annexed diagram will show approximately the rate at which the 

 moon's light increases and diminishes with its phases as deduced from for- 

 mula (a) ; and the ringed dots with the accompanying Roman figures (for 

 reference) give the quantity of the moon's heat as determined by observa- 

 tion on different nights. 



Although there is considerable discordance between some of the observed: 



* This formula is based on the assumption that the heat coming to the earth from an, 

 element (£S) of the moon's surface =K . <5S . cos 9 . cos <p, 6 and being respectively the 

 inclinations of the lines to the sun and to the earth from the normal to that point of the 

 moon's surface, and K a constant. 



