520 M. Mascarfc on the Achromatism of Interferences. 



correct. In one of his experiments on the topaz he only ob- 

 served a retardation of 16*6 undulations, the calculated value 

 being 21, and he adds : — 



" The difference 4*4 is too great to arise from inaccuracy 

 in my micrometric measurements ; but it is possible that the 

 dispersion by the twofold refraction, that is to say, the differ- 

 ence of energy of the twofold refraction for rays of different 

 colours, modified the superposition of the fringes produced by 

 these different rays in such a manner that errors were caused 

 in the determination of the position of the central band, and 

 that it was owing to a like source of error that the discord- 

 ance in question partly arose." 



2. The employment ofa prism produces another effect which 

 is very remarkable : at the same time that the refraction 

 changes the direction in which the fringes of different colours 

 appear it modifies their angular aperture in an unequal manner; 

 the super|)osition of systems corresponding to neighbouring 

 wave-lengths is then much more complete than in the original 

 phenomenon, and a considerable number of fringes can be 

 distinguished on either side of that which is achromatized. 



It was by observing in this manner through a prism the 

 rings produced by a layer of air between two glasses, that 

 Newton perceived more than forty of them ; the appearances 

 are then analogous to those presented by the employment of 

 a homogeneous light. 



To explain this peculiarity I shall consider, in a more gene- 

 ral manner, any phenomenon of fringes localized on a sensibly 

 plane surface S, such as ordinary interferences received on a 

 screen, Newton's rings, the bands of chromatic polarization in 

 a crystal of variable thickness, &c. I shall assume, moreover, 

 that the fringes are symmetrical with respect to a straight line 

 to which they are normal, and that the point of observation is in 

 the plane of symmetry, the eye being furnished with a prism 

 of which the principal section is parallel to the same plane. 



Taking the axis of x on the right line of symmetry, and the 

 axis of y normal to the surface S, let A be the ordinate and 

 — a the abscissa of the point P, where the eye furnished with 

 the prism is situated, x the abscissa of the point M regarded, 

 i the angle which the ray MP makes with the normal, D the 

 deviation produced by the prism, and 6 the angle which the 

 refracted ray makes with the normal. 



The difference in path A of the rays which interfere 

 at the point M should be considered in general as a function 

 of X and of i ; the deviation D is itself a function of i and of 

 the index of refraction n. Denoting the wave-length by X, 

 we may then write 



