AND THE OTHER PLANETS OF THE SOLAR SYSTEM. 647 



The temperature £ is that external temperature which, if it actually existed, would, by 

 hypothesis, produce the same effect on the Earth's internal temperature as those external 

 causes which really exist. The expression for £, therefore, at any point of the Earth's surface, 

 depends on 



(1) The exchange of radiating heat between the proposed point and any external 

 bodies, such as the stars, or the component particles of the atmosphere; 



(2) The heat communicated to or abstracted from the Earth at the proposed point 

 by the atmospheric particles immediately in contact with it, such transference of heat taking 

 place by conduction ; 



(3) The heat emanating from the Sun, and arriving at the proposed point after 

 suffering a certain degree of absorption, whether in passing through the atmosphere, or through 

 planetary space. 



Thus the quantity of heat which passes through an element w of the Earth's surface at 

 the point proposed (P) in time It, may be represented by 



P . (U - £) U)6t, 



where p is a constant which measures the emissive power of the Earth's surface at P. Also 

 if £ be the temperature of surrounding space which would produce the same effect as (l), 

 this effect may be represented by 



X (m - £) wSt ; 

 and similarly the effect of (2) may be expressed by 



X,(« - tj)u>8t. 



Again, let a denote the quantity of heat which proceeds from the Sun, and would, inde- 

 pendently of the absorption above mentioned, fall on a unit of the Earth's surface. Then k<j 

 may represent that part of this quantity which actually reaches the Earth's surface and 

 enters it at P : and if 9 be the angle of incidence at P, the quantity of solar heat which 

 passes through w in time St will be equal to 



Ka cos 9 , w$t. 

 Hence, we obtain 



P (» ~ D = X (» ~ D + \ (u - rj) - K a cos 9, 

 and since we must here have 



p*A-+X,, 

 we have 



Y A m X ks cos 9 



5 " xTx; e + xTx, * + T7x7 " 



In the sequel, Poisson assumes that the effect of the atmospheric particles in immediate 

 contact with the Earth is much less than that produced by the inter-radiation between the 

 Vol. IX. Pakt IV. 83 



