102 DISPLACEMENT INTERFEROMETRY BY 



rotated 180 the dispersion (Z?i D 2 ) is zero, but the illumination is neverthe- 

 less colored, because only the undeviated beam gets through the interferom- 

 eter, or strikes the second grating. This undeviated beam is usually green; 

 but it is advantageous to have several of these gratings in which the undeviated 

 beam (alteration the prism angle p) is red, yellow, blue, etc. If there is an 

 angle between the planes of dispersion of gratings I and II, the two corre- 

 ronding spectra will cross at an angle and the interferences will be found 

 within the quadrilateral resulting. 



To indicate the uses of these paired apparatus, suppose that the inter- 

 ferometer shows horizontal achromatics in the absence of gratings I (colli- 

 mator) and II (telescope). Then if II is introduced (dispersion plane hori- 

 zontal) a luminous spectrum with strong interference bands (horizontally 

 fan-like, opening from blue to red) throughout its length and breadth will be 

 seen. These extend, of course, above and below, far beyond the limits of the 

 achromatic fringes. If the fringes were not horizontal the slit would either 

 have to be fine or the telescope (with II) would have to be rotated on its axis 

 sharply into the right position. 



If both gratings I and II are used in parallel, a less luminous ellipse of green 

 light, more highly dispersed and carrying the fringes, will be seen. If I and 

 II are used in opposition a sharp image of the slit in green light carrying the 

 fringes appears. If I is used alone, the green ellipse, less extended and with 

 fringes, appears again. All admit of an indefinitely wide slit on proper rotation 

 of the spectro- telescope. 



On applying this apparatus to the linear phenomenon, one may note that 

 there are now three dispersions, D\, D%, and d, the latter symbol applying to 

 the prism within the interferometer (fig. 92, Chap. VIII). Hence the disper- 

 sions Di-\-D 2 d or ^d alone are available; in other words, the spectra corre- 

 sponding to d are necessarily reversed. The spectra due to D\ are not. Hence 

 if DI and D% are opposed, one obtains two sharp slit-images in green, but of 

 different width in view of the D+d and D d effect. At their line of coinci- 

 dence is the linear phenomenon, in green light, which on proper focussing will 

 not otherwise differ from the phenomenon with white light. If the gratings I 

 and II are in parallel, the dispersion Di+D 2 =*=d so much exceeds d that we 

 approach the case of non- re versed spectra. The fringes are parallel curved 

 arcs in green, covering a wide vertical region of the spectrum. The curved 

 lines do not admit of a very broad slit; i.e., the fringes suddenly appear, as 

 soon as the Fraunhofer b- lines (for instance) coincide ; otherwise they vanish 

 at once, precisely as in the case of non-reversed spectra of slightly unequal 

 lengths. 



78. Quartz prism. As there was a good quartz prism in the laboratory, it 

 seemed interesting to place it between the mirrors m and m' of figure 92, 

 Chapter VIII. The linear phenomenon thus obtained did not differ from the 

 usual form after a single dispersion ; but on second dispersion with the spectro- 

 telescope a much coarser laterally broadened pattern was obtained, which in 



