Barus — Use of the Grating in Interferometry. 1G9 



inasmuch as the compensation takes successively, at each color, 

 in the same way. Although the equations hold only for the 

 center and the symmetrically oblique rays belonging to the rings 

 have not been given consideration, an approximate computa- 

 tion of the motion of the ring centers may nevertheless be 

 attempted. The relations numbers 1, 3, 9, and 10, which are 

 more important, may be taken. Here is n in the order of the 

 fringe, D the grating space, 2x the difference of air path, 



2efji/ cos 6 + 2x = nk; 



this with 



sin i — sin 6' = \/ D, sin 0' =■ /jl sin 6, dfi/ dX = — -015 fi/X, 



an experimental interpolation equation for the given glass, 

 will on differentiation yield ch/dn, ds/de, dz/dX, etc. From 

 these qualitative interpretation of the above and the following 

 data is obtainable ; but quantitatively they are too crude, 

 because they ignore the essential feature of oblique reflection 

 from 31 and JV. For the radial motion, if dz/dn is the 

 displacement of grating normal to itself per fringe, 



dz _ X cos 



dn ~ 4 



is near the truth. 



Omitting these equations, an example of the displacement 

 and radial motion in a given experiment may be adduced ; 

 the former were fully 16 times less sensitive per fringe than 

 the latter. The displacement is thus a coarse adjustment in 

 comparison with the usual radial motion of the fringes and 

 this is the distinct advantage of the present method for many 

 purposes. It is like a scale division, into smaller and larger parts, 

 where the enumeration of small parts alone would be confusing 

 or impossible. The ratio of the micrometer value of displace- 

 ment and radial motion per fringe may be given any value 

 since dz/dXcc \xe. Thus e = -42'™ would correspond (for the 

 same //.) to 10 radial fringes for one displacement fi-inge. 

 Again if e = •04'^" the two micrometers would be equally 

 sensitive. Or for e = •01'=™ (microscope cover glass), the 

 lateral displacement is actually four times more sensitive than 

 the radial motion. 



The sodium lines here make admirable cross hairs and the 

 ocular itself need have none. The conditions are the same in 

 the second order, and the coarser rings and spectrum lines are 

 often easier to count. 



4. Compensator — It is not necessary, however, to use thin 

 glass, for if a compensator is provided, i.e., if the grating is 

 on the common plane between two thicknesses of identical 



