120 Prof. H. A. Wilson on the Diffusion of 



For the other two pairs of sides the rate of increase is 



Hence in a steady state we have 



jr(d 2 c ,d 2 c d 2 c\ dc n /1X 



To determine the distribution of the salt vapour round the 

 bead of salt we have to find a solution of this equation 

 satisfying the conditions that at the origin there is a constant 

 source of salt vapour, and that at very great distances from the 

 origin the concentration is very small. Such a solution of 



(l)iB 



Ae a <*-'> 

 ( '=~^-> ( 2 ) 



where r = ^/x 2 +y 2 + z 2 , and A and a are constants *. 



If this is put in (1) we find that u = v/2K. When x and r 

 are very small (2) gives c = A/r; so that if q is the amount 

 of salt evaporating per second we have 



dc 

 -K^477T 2 = 47rAK = y; 



or A = 2/47rK t 



Hence a JL ix-r) r 



Owing to the disturbance of the flow of the gases by the 

 bead this equation will not be exactly true close to the bead, 

 but it will hold accurately at distances large compared with 

 the radius of the bead. The shape of the region round the 

 bead which emits visible light will be bounded by a surface 

 over which c has a constant small value, say c'. If therefore 

 we observe the values of x and r at two points on this surface, 

 we have 



c' 



47rKr x 



e2K v l 



-'i) 

 i 



c > 



= g 



6 2K V 2 



-'2) 





47rKr 2 



3 



* H. A. Wilson, Proc. Camb. Phil. Soc. vol. xii. pt. o (1904). 



