190 Lord Ray leigh on Achromatic 



have different breadths. If, then, the bars of all colours coin- 

 cide at one part of the mixture of light, they will not coincide 

 at any other part ; but at equal distances on both sides from 

 that place of coincidence they will be equally far from a state 

 of coincidence. If, then, we can find where the bars of all 

 colours coincide, that point is the centre of the fringes. 



" It appears, then, that the centre of the fringes is not 

 necessarily the point where the two pencils of light have 

 described equal paths, but is determined by considerations of 

 a perfectly different kind. . . . The distinction is important 

 in this and other experiments." 



The effect in question depends upon the dispersive power 

 of the prism. If v be the linear shifting due to the prism of 

 the originally central band, v must be regarded as a function 

 of X. Measured from the original centre, the position of the 

 nth. bar is now 



v + nXD/b. 



The coincidence of the various bright bands occurs when this 

 quantity is as independent as possible of X; that is, when n is 

 the nearest integer to 



b dv /1Q s 



n= ~I)dk; ( 18 > 



or, as Airy expresses it, in terms of the width of a band (A), 

 n=-dv/dA (19) 



The apparent displacement of the white band is thus not v 

 simply, but 



v-Adv/dA (20) 



The signs of dv and dA being opposite, the abnormal displace- 

 ment is in addition to the normal effect of the prism. But, 

 since dv/dA, or dv/dX, is not constant, the achromatism of the 

 white band is less perfect than when no prism is used. 



If a grating were substituted for a prism, v would vary as 

 A ; and the displacement (20) would vanish. 



More recently the matter has engaged the attention of 

 Cornu*, who thus formulates the general principle: — " Dans 

 un systeme de franges aV interference produites a Vaide oVune 

 lumiere hdterogene ayant un spectre continu, il existe toujours 

 une /range achromatique qui joue le role de frange centrale et 

 qui se trouve au point de champ ou les radiations les plus in- 

 tense s present ent une difference de phase maximum ou minimum" 



In Fresnel's experiment, if the retardation of phase due to 

 an interposed plate, or to any other cause, be F(X), the whole 



* Joum. d. Physique, i. p. 293 (1882). 



