0. Barus — Resolution of Interference Fringes. 309 



seen being just short of darkness to obtain the sharpest effects, 

 though the results are perfectly distinct, if more washed, for 

 wider slits. 



What one would expect to see as the spectroscope S ' G is 

 moved across the field from left to right is the usual form of 

 channeled spectrum, with the fringes moving horizontally from 

 end to end of it. What actually appears, how T ever, is a succes- 

 sion of intercepts between an upper and a lower horizontal, of 

 broad concentrically circular or oval absorption bands, all of 

 a very large radius, the displacement being on the plan shown 

 in fig. 2, or the reverse. In other words, the spectroscope 

 reveals the similarly intercepted arcs of large absorption bands. 

 The arcs if essentially horizontal move up and down, if essen- 

 tially vertical right and left. They are never quite vertical, 

 and they become thinner and more crowded toward the ends 

 of the spectrum. The groups 1, 2, 3, appear in succession. 



The phenomenon is exceptionally sensitive to changes in the 

 approximate verticality of the slit, so that if the spectroscope is 

 slightly rotated on its axis, all the groups may reappear in 

 turn. 



2. Explanation. — To interpret this phenomenon it is con- 

 venient to plot the order n of a given fringe in terms of its 

 distance x from the center of fringes, where n = (c / r ( X / 2) ) x, 

 r being the virtual distance of the fringes on the screen, here 

 the slit of the spectroscope, from the virtual position of the 

 two slit images for the wave length \. There will be dark 

 bands for a given color A,, as fig. 3 shows, whenever n = 1, 3, 

 5, etc. The two lines drawn show the limits of the spectrum 

 for any distance of fringe x and the heavy horizontal lines the 

 number of dark bands to be expected. Thus for the value 

 of x corresponding to vr, there will be three black bands in 

 the spectrum, their color distribution depending upon their 

 position between v and r. As the slit moves from right to 

 left from the positive to the negative values of x, bands will 

 enter the red end and leave the violet end, for a positive value 

 of x and do just the reverse for a negative value of x. 



The question now arises as to what will happen if the fine 

 slit is not quite parallel to the fine interference fringes, crowded 

 together as they are in a vertical band about half an inch in 

 breadth. The oblique but fine slit in such a case corresponds 

 to a succession of values of x depending upon the obliquity 

 and length of the slit, and the diagram, fig. 3, therefore, shows 

 the case for only one point in the length of the slit. It is thus 

 necessary to introduce the third dimension corresponding to 

 the breadth of spectrum, at right angles to the plane of fig. 3, 

 which plane may be supposed to correspond to the bottom 

 point of the slit. If the horizontal projection of the oblique 



