422 Prof. Carl Barus on Inter ferometry 



Table is particularly drawn up to indicate the relative value 

 of the functions Z e and Z d . It will be seen that Z = Ze + Z 9 , 

 in terms of \, is a curve of regular decrease having no 

 tendency to assume maximum or minimum values within the 

 range of X, whereas ycosot passes through the usual flat 

 maximum for a = 0. The path difference, which is the 

 difference of the ordinates of these curves, thus passes 

 through zero for a definite value of e and y, and this would 

 at first sight seem to correspond to the centre of ellipses. 

 That it does not so correspond will be particularly brought 

 out in the next section. It is obvious that for a given e the 

 value of y (air-path difference) which makes the total path 

 difference zero, varies with the wave-length, hence on 

 increasing y continuously the ellipses must pass through the 

 spectrum. It is also obvious that if the grating is reversed, 

 the path difference will change sign, ccet. par., and the 

 ellipses will move in a contrary direction, for the same dis- 

 placements y of the micrometer-screw, at the mirror M or N 

 respectively. 



If e=l cm. and ^ = 3*2648 cm., the path difference will 

 be zero for the E ray. The Table shows the residual path 

 differences in the red and blue parts of the spectrum. The 

 ellipses w r ill be larger as e is smaller, the limit of enormous 

 ellipses being reached for e = or e = e f of the compensator. 



The same result may be obtained to better advantage by 

 reconstructing equation (6), and making the path difference 

 equal to zero for the normal ray. This determines 



y=efj,J cos® 



in terms of e, and the path difference is now free from y. 



7. Interferometer. — If, in equation (6), y alone is variable 

 with the order of fringe n, while a, 6, ©, l5 © 1} /3j, e, X, yu,, 

 are all constant ; i. e. if the number of fringes n cross a given 

 fixed spectrum line like the D line, when the mirror is 

 displaced over a distance y, it appears that 



^ = -^-=— .... flO) 



dn 2 cos a dn ' v ' 



where a refers to the deviation of \ e from X e normal to the 

 mirror. If a = 0, dy/dn = X/2, the limiting sensitiveness of 

 the apparatus, which appears for the case of normal rays. 



The displacement per fringe dy/d?ior dz/dn, varies with the 

 wave-length. Hence if the ellipses are nearly symmetrical 

 on both sides of the centre, i. e. } if the red and violet sides 



