The Astrophysical journal . and consider it first atthe point A1 and then at thepoint A2, perpendicular to theradius of curvature of theconcave grating, then the twodirections will form the angle7. If we now let parallellight fall on the grating, thatis EzAk be parallel to E2A2,the rays will make an angleof incidence E1AlATI=al atthe first position of the grating;and the angle of incidence at the second position. Wethen have the following relations: ElA1N2=FA1C=a2, EIAIB=TA1F = R + aI=R + a2+y , «i=a2 + y. Applying this now to the actual conditions, the greatest differences of the su
The Astrophysical journal . and consider it first atthe point A1 and then at thepoint A2, perpendicular to theradius of curvature of theconcave grating, then the twodirections will form the angle7. If we now let parallellight fall on the grating, thatis EzAk be parallel to E2A2,the rays will make an angleof incidence E1AlATI=al atthe first position of the grating;and the angle of incidence at the second position. Wethen have the following relations: ElA1N2=FA1C=a2, EIAIB=TA1F = R + aI=R + a2+y , «i=a2 + y. Applying this now to the actual conditions, the greatest differences of the surface of the grating will be: for G^ - ; for G2, - ; whence , „ A AA£=- or 2 If we then make A ZB equal to one-half the width of the grating weobtain for GI3 2\ \ 1893; Sur diverses methodes relatives a. lobservation des proprieties appeleesanomalies focales des reseaux diffringents, ibid., 1421, 1893; Verifications nume-riques relatives aux proprieties focales des reseaux diffringents plans, ibid., 117,1032, ABSOLUTE WAVE-LENGTH FROM GRATINGS 243 and for G2, 2A a«ny2=— =- .20 0 We thus compute 7 for GT to be about §; for G2, about angle of incidence therefore may differ in an extreme casefor the whole surface of the grating by this amount, whence we maysafely draw the conclusion that the two grating surfaces depart soslightly from the plane that they may be regarded as perfectly planein practice; that is, within the accuracy of the measurements. III. INVESTIGATION OF THE TWO GRATINGS FOR IRREGULARITIESOF THE SPACE BETWEEN THE RULINGS The practical problem is to establish quantitatively the amountof the irregularity in the separation of the rulings, whether it becaused by the curvature of the surface or by the other defects men-tioned previously. It is necessary for this purpose to examine a fewrulings at a time successively over the whole ruled surface. Bell1evidently had in mind the method that I have employed, but, ashis description indicates, he do
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