Interference with Reflecting Gratings. 125 



vanish. Finally, when ND is zero, as in the original 

 unbroken grating, the size of the fringes is infinite. 



It has been stated that the use of the slit or a laterally 

 limited objective is advantageous because all the lines are 

 much sharper. Inert or harmful illumination is cut off. If 

 the slit is over the objective of the telescope only a small 

 part of the field of view shows the lines ; if placed over the 

 objective of the collimator, the fringes are of extreme clear- 

 ness throughout the spectrum. It may be ultimately of 

 advantage to use the edge near the crack g' only, together 

 with the whole of g. For if a small strip of g' at the crack 

 S is used with the whole of g, the smaller fringes are 

 weakened or wiped out. Thus the inner edge of the nearer 

 grating with successive parts of the further grating is chiefly 

 effective in the production of these interferences. 



To bring the two edges quite together was not pos- 

 sible in my work, as they were rough and the apparatus 

 improvised. 



7. Data. — Some measurements were attempted, with the 

 view only of checking the equations presently to be deduced. 

 The adjustment on an ordinary spectrometer is not firm 

 enough, and the fringes being very fine (a few minutes of 

 arc) are difficult to follow unless quite stationary. 



These observations gave both the values of de/dn, displace- 

 ment per fringe, for different angles of incidence i and of 

 diffraction 6, and dd/dn, the angular deviation per fringe at 

 the D line. In measuring the latter it was necessary to 

 count the fringes between the C and D lines and divide 

 their angular distance apart by these numbers. As e cannot 

 be measured, its successive increments Ae from the first 

 position must be used. These are presently to be associated 

 with the corresponding increments of dn/dd. The data will 

 be found in the original paper. 



8. Equations. — In fig. 4 (p. 126), L and L' represent a pair 

 of corresponding white rays, reflected into II and R' and dif- 

 fracted into D and D' at angles i and #, respectively. The 

 half gratings g and g' are separated along the crack S, and 

 g is movable parallel to itself by a micrometer screw normal 

 to g '. Let the normal distance apart of the gratings be e. The 

 incident rays L, L' strike the originally coplanar grating at 

 points N rulings apart, or ND cm. apart, if D is the grating- 

 space. In the separated grating let these points be at a 

 distance c apart. Let d be the incident wave front and h 

 the corresponding diffracted wave front, and call the angle 

 between c and d, y. 



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