304 Interference of Light Radiated from Moving Molecules. 



vanislies when integrated. The first and second are included 

 under the well-known formula 



r e-'*'''cos2ra;dw= ^^~'''''' > 

 and we obtain 



In conformity with previous notation we may write 

 „_ / 47r^\ 

 a _exp|^ ^A^VV' 



or, if we introduce the value of ^ from (19), 



a" = exp(-.(-^|y} (23) 



The ratio of the least and greatest brightnesses is then, as before, 



h={l-a")/{l + a") (24) 



If we now assume as determining the limit of visibility 

 h=-95, we find a" = '025, and from (23) 



^=•690- (25) 



It appears therefore that the maximum admissible retarda- 

 tion is sensibly greater than that calculated (14) upon the 

 supposition that all the molecules move with the mean velocity 

 V, and as much as 4^ times greater than that (15) taken by 

 Ebert as the basis of his comparison with observation. 



Under these circumstances it would seem that there is no 

 discrepancy remaining to be explained. It is true that the 

 width of spectral lines is not wholly due to movement of the 

 molecules ; but it is possible that this is the principal cause 

 of dilatation when the flames are coloured by the spray of 

 very dilute solutions, as in Ebert's use of the method of 

 Gouy*. Again, it is true that interference-bands are often 

 observed under conditions less favourable than is supposed 

 in the above estimate of h. In Michelson's method, however, 

 the bands may be very black at small retardations ; and it 

 seems very probable that at higher retardations bands in- 

 volving even less than five per cent, of the brightness might 

 be visible. The question is one of very great interest, and I 

 hope that Herr Ebert will pursue his investigations until it is 

 thoroughly cleared up. 



March 7. 



* Ann. de Chim. xviii. p. 1 (1879) . 



