Evaluating the Surface- lemperature of the Planets. 161 



polar coordinates and omitting as before the time-factor, we 

 have 



| = A J (^)f . . . + (A w cos ra0 + B n sin %0)J„(£r) -!-..., 



n being integral. 



Thus mean -x/r over circle of radius r = A J (kr). At the 

 centre of the circle, y r=0 = A ; so that mean yjr over circle 

 r = y}r x Jo(^')> an d vanishes as before when J (kr) = 0. 



A similar method applies in three dimensions. Thus 

 (' Theory of Sound,' § 330) we have in general 



yfr= —2ik So — i — + terms in spherical harmonics of orders 



1, 2, &c, vanishing when integrated over a sphere and also 

 vanishing when r = Q. Hence 



Mean -\jr over sphere r=Y r=Q X i 



Accordingly mean -ty vanishes if Jcr = ?i7r, or r=^??A. If 



Mean ^ over *±wr|r r=0 x ^+tv * 



For an example, reference may be made to the case of plane 

 waves treated in § 331. v 



X. A General Method for Evaluating tlie Surface -Tem- 

 perature of the Planets ; with special reference to the 

 Temperature of Mars. By Prof. Percival Lowell *. 



THE surface-temperature of the several planets is a subject 

 of fundamental importance to an understanding of their 

 physical conditions. To attack the problem critically is 

 therefore of interest, the more so that it has not hitherto been 

 done. 



Heat hitlierto deduced from Distance only. — For example, up 

 to the present time the chief obstacle to crediting Mars with 

 the possibility of life has lain in accounting for sufficient 

 heat on the surface of the planet. Yet so far the determi- 

 nation of this heat has been limited to simple consideration 

 of distance from the sun. Thus Prof. Young, who feels the 

 difficulty acutely, says in his' General Astronomy ' (ed. 1898, 

 p. 363), " We know that on account of the planet's distance 

 from the Sun the intensity of solar radiation upon its surface 

 must be less than here in the ratio of l 2 to 1*521 2 "; while for 



* Communicated by the Author. 

 Phil. Mag. S. 6. Vol. 14. No. 79. July 1907. M 



