ADAMS : RAYLEIGH-ZEISS INTERFEROMETER 273 



the central band is now particolored like the right hand band was 

 originally. The comparison band has thus apparently shifted 

 one band to the left; with further increase of concentration the 

 same sequence of events occurs, and the apparently correct 

 comparison band is shifted one additional band to the left for 

 a certain concentration difference, this difference being (on 

 our instrument) about 0.07 per cent (300 divisions) for KCl while 

 for KNO3 this concentration interval is considerably less. Now, 

 since in making readings on a series of solutions of a substance 

 we must obviously always make the final setting upon the same 

 band, we shall err if the setting is made each time upon the 

 most nearly achromatic band; and there will be one discontin- 

 uity for each such ^'concentration interval." The explanation of 

 this shift of the achromatic band is found in the relative optical 

 dispersion of solution and water, on the one hand, and of glass 

 (of the compensator plates P,, P2) and air, on the other hand; 

 for it is to be noted that in the type of instrument under con- 

 sideration the lengthening of the optical path due to replace- 

 ment of water by solution is compensated by the shortening of 

 the sa7ne path by decreasing the effective thickness of an inter- 

 posed glass plate. We shall now proceed to develop a formula 

 by the aid of which errors arising from this source can be readily 

 obviated. 



This equation may be derived by making use of the principle 

 that in general the position of the achromatic fringe is determined 

 not by the condition (as in the case of the central fringe in mono- 

 chromatic light) that the geometrical path difference shall 

 be equal to the optical path difference, but by the condition that 

 at the center of the achromatic fringe the change of phase with 

 respect to wave-length shall be a minmium.'' Accordingly if the 

 combined effect of a decrease p in optical path-length due to 

 the movement of the compensator and of an increase in path- 

 length due to the replacement of a thickness I of water by solu- 

 tion is to displace the central bright band to a point 0', this 

 displacement N-^, in terms of fringes for the wave-length X, is 

 given by 



3 See R. W. Wood, Physical Optics, 2nd Ed., 1911, p. 140. 



