670 Mr W. HOPKINS, ON THE EXTERNAL TEMPERATURE OF THE EARTH, 



and, therefore, 



7r 2 2 2 



trh cos 9 = h \ 1 + — cos 9 + - . cos 2.9 cos 40 + cos 69 - &c.l. 



c 2 3 3.5 5.7 J 



Neglecting the differences between the true and mean values of the angular motion ^of 



the Earth round the Sun, and that of the Moon round the Earth, we shall have, at any 



time t, 



9 = n(t- t), 



where r denotes the time of the Sun's crossing the lunar meridian of the proposed place 

 at the Moon's equator, and n denotes the mean angular velocity with which the Sun separates 

 from that meridian. Preserving the unit of time, one year, which Poisson has taken, we 

 shall have for the length of the mean solar day at the proposed place on the Moon (since it 

 equals the Moon's mean synodic period) 



Moon's mean synodic period 1 



Earth's mean period 12,37 



and consequently we have 



Hence if we put 



n 



2tt = 



12 . 37 

 n = 2tt . (12,37). 



v/7r(l2,37V 



to = *, 



a 



the expression for the temperature of the Moon at her equator, and at a depth a; beneath 



her surface, will be 



7T 



+ h.— ;— e'^cos \n(t — t) - xw - $\, 

 D 2 ' 



+ h.— ;-e- xm ^ cos {2n(t - t) -m#\/l -$'], 

 D 3 



- h -Trr'T L l e ~ XWs/J cos {*»(«- t) - xtoy/t - f } , 



J J -o , O 



+ &c , 



where 



and, therefore, 



b + a) \A = Z> (i) cos $ {t) , 

 to\A= D (t, sin^», 



D m m V b 2 + sbay/i + 2tV. 



It will be observed that the temperature here denoted by P is what is properly termed 

 the temperature of stellar space, or, more accurately, that temperature which the portion of 

 space occupied by the solar system would derive from the stars alone. It must not be 



* Theorie de la Chaleur, Art. 222. 



