76 



DISPLACEMENT INTERFEROMETRY BY 



a single plate compensator (say C, fig. 79, 5 mm. thick) normally into the rays 

 8 5 and 2 i, preferably in the same vertical plane. When the plate is not per- 

 fect it may be necessary to adjust for coincidence of slit images. 



If, now, this plate is rotated about a horizontal axis (normal to the lines 

 8 5, 2 z) the fringes walk laterally through the broad coincident slit-images 

 in such a way as to clearly outline a moving design of the form given in figure 

 So. In other words, as a first approximation (for the case is, of course, essen- 

 tially more complicated) the achromatic fringes may be assumed to be a 

 family of confocal equilateral hyperbolas, referred to given horizontal and 

 vertical axes. When the rays 8 5 and I 2 are at the same level, the broad 

 slit-image is in a position of symmetry relative to the hyperbolas (fig. 80). 

 When this is not the case, the image is at ss or ss', with the fringes very rapidly 

 becoming horizontal. Since this design is similarly carried out with decreasing 

 coarseness from red to violet, it is clear that a single characteristic central 

 achromatic fringe results, invaluable for purposes of displacement interferome- 

 try from its smallness, and since from the breadth of slit it can be made so 



intensely luminous. When the path-difference of the rays 8 5, I 2, in figure 79 

 is changed by the micrometer or by independent compensators, the figure 80 

 shifts bodily up or down the slit-image. It is also obvious that when the 

 fringes with white light are horizontal they must appear as horizontal black 

 bands in the spectro-telescope, regardless of the width of slit used; and hence 

 these fringes also are excessively luminous, while their displacement may be 

 referred to a definite wave-length. If the interferometer is not self-adjusting 

 the axes of figure 80 are as a rule inclined, and fringes are obtained in all 

 angles of altitude needing special adjustment. The spectium fringes then 

 demand a fine slit,* but are also horizontal. The shift of achromatic fringes 

 due to micrometer displacement may therefore be at once expressed in terms 

 of the spectrum fringes rigorously in a given wave-length. 



A very interesting transformation of the design (fig. 80) will be noticed, 

 if by rotating any of the mirrors, N, m, figure 79, for instance, the two white 

 slit -images seen in the telescope are passed horizontally through each other. 

 During this motion the originally vertical, nearly linear, achromatic fringe 

 passes through the form of the area between the hyperbolas a and b, figure 80; 

 next through the area between b and c (coincidence of slit-images) ; then into 

 the area between c and d; finally again into a vertical hair-line, always retain- 

 ing its individuality among the surrounding colored fringes of similar shapes. 



* A method of avoiding this condition will be given in Chapter IX. 



