142 Intelligence and Miscellaneous Articles. 



sky, N the number of diffracting particles contained in unit volume 

 of air, a the amplitude of the incident vibration of wave-length A, 

 and p a factor constant for all values of A. 



As the greater part of my observations could not be calculated 

 by this formula, I have sought the reason for the disagreement. 



The formula — is based on the hypothesis that the number ~N of 



A 



particles contained in unit volume of air is sensibly the same for 

 all dimensions of these ; it will therefore not be verified unless this 

 hypothesis is realized. 



If we compare the particles to spherical globules of density D 

 and with different radii r, falling in a medium of density p, they 

 will take, at the end of a very short time, a constant velocity of 

 fall in the resisting medium given by the formula 



V yp 



yp 



y being a factor which depends on the nature of the medium. 

 In air we should have 



V = AVr. 



If, at the beginning, the diffracting particles, equal in number 

 for all dimensions of the same order as the A's of the incident light, 

 are uniformly distributed in the unit volume of air and left to them- 

 selves, they will take different velocities according to their dimen- 

 sions, and we may assume that, when the permanent state is 

 established, the number contained in unit volume varies, for each 

 dimension of the particles, in the inverse ratio of the velocity ; in 

 this case we should have 



Vf 



Giving to r the extreme relative values 1 and 2 which correspond 

 sensibly to the dimensions of the particles which diffract more 

 especially the extreme wave-lengths of the spectrum ; for the 



B' 

 extreme red N= — rz and for the extreme violet N'=B'. 

 Vr 



N 

 We must then, in the preceding formula, replace IN" bv — _ or 



N' V r 



by —r^, and the formula becomes 



VA 



JV D = JC 

 Vaa 4 a 4 ' 5 ' 

 In reality we might found several hypotheses on this mode of 



"NT' 



distribution ; — = might be replaced by N'/(A), the function of A 



Va 



depending on a certain power of the velocity, and consequently of 

 the dimensions of the particles. 



