when Light is radiated from Moving Molecules. 301 



So long as a is small, the mode of interference is nearly the 

 same as if t; = 0. This will be the case when A is sufficiently- 

 small, so that at first the bands are absolutely black. As A 

 increases, the distinctness of the bands will depend mainly 

 upon the relative brightnesses of the least and most illuminated 

 parts. If we call this ratio h, and denote by a the numerical 

 value of (10), we have 



A=(l-a)/(l+a), (12) 



or 



a= (1-70/(1 + A) (13) 



Now from (10) it appears that when « is equal to tt, or to 



any multiple of tt, a = 0, and the field is absolutely uniform. 



Between values of « equal to tt and 27r, 27r and Stt, and so on, 



there are revivals of distinctness, the maxima of which occur 



at values not far removed from §77, ^tt, &c. Thus, between 



2 

 TT and 27r there is to be found a value of a at least equal to 77-, 



corresponding to /i= § nearly. At this stage the bands should 

 certainly be visible. 



In order to estimate at what point the interference-bands 

 would first disappear as A increases, we must make some 

 supposition as to the largest value of h indistinguishable in 

 experiment from unity. Under favourable circumstances in 

 other respects we may perhaps assume for this purpose h = '95, 

 so that a = '025. Since a is small, a is nearly equal to tt. 

 We may take approximately sina = '0257r, ora = '9757r. In 

 fact, so long as we take h nearly equal to unity, the precise 

 value makes very Httle difference to the corresponding value 

 of a, and for the purposes of such a discussion as the present 

 we may suppose with sufficient accuracy a=7r. In this case, 



by (11), 



?^ = - (14) 



A 2t;' ^^^^ 



which gives the retardation (2A) measured in wave-lengths 

 in the neighbourhood of which the bands would first disappear. 

 This estimate diff'ers widely from that put forward by Ebert. 

 The latter is equivalent to 



^1 = -^ a^) 



According to my calculation the value of a corresponding to 

 (15) would be 54°, a would be '86, and h would be '075 ; so 

 that the bands should be hardly distinguishable from those 

 which occur when A = 0. 



