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



only to the mean annual temperatures. We shall also have to examine what relations 

 may exist between the periodical changes in these temperatures; an examination for which 

 the researches of Professor Dove have furnished us with far better materials than we 

 previously possessed. After thus estimating the entire effect of solar heat on the temperature 

 of our own globe, we shall be prepared to make also some approximate estimate of the influence 

 which it may exercise on the other planets according to the conditions under which they 

 may be placed. 



The Theorie de la Chaleur, the work of Poisson's in which the investigations alluded 

 to are given, is as admirable for the physical as for the mathematical analysis of the 

 problems there investigated; but it is so elaborate (in some cases perhaps uselessly so for any 

 practical purpose) as to render it extremely difficult for reference to particular portions 

 which may bear upon particular problems. I have therefore thought it worth while to give 

 in regular sequence the formulae which bear directly on the questions of this paper, though 

 in doing so I am led to make such citations at greater length than I might otherwise 

 deem admissible in a communication of this kind. 



17. Poisson first determines the law of temperature within the Earth on the supposition 

 of the temperature of surrounding space being everywhere equal to zero ; and then extends 

 the solution of the problem to the case in which the external temperature at any point of the 

 Earth's surface is supposed to depend on the latitude of the place, and also to be a periodical 

 function of the time, so that, denoting this temperature by £, we have 

 £ = B + A cos (m t + e) + A' cos (m' t + e) + &c, 

 where the coefficients depend on the latitude*. If u be that part of the terrestrial tempe- 

 rature which depends on £, we then have 



b -2Vs a? /m 



u = B + -Ae a 2 cos(mt + e-- V - - S) 



D 



b 

 + A 



+ &c. 

 where D and I are determined by the equations, 



D cos t m b + , 



a 



n • S ^^ 

 D sin 6 — ; 



a 

 and generally D { and S { are determined by 



r> s * . vSfcr 



D cos S t = + 



D t sin I, = X. ' "* 



X fjm' „ / f j 



A'e~ 7 ' T cos(m'* + e'-- V--8) 

 a 2 'J 



(7), 



(8), 



(9)- 



" Theorie de la Chaleur, p. 430. 



