176 BARUS— ADJUSTMENT FOR PLANE GRATING [April 24, 



(greater 6) the normal ray and the A found in the first instance is 

 too large as compared with the true value for the normal ray. 



The datum .07 cm. may be taken as the excess of 2x, corre- 

 sponding to the excess of angle for a grating one half as wide and 

 observed on both sides (2x), as was actually the case. Finally, 

 since the whole of the grating is not in focus at once a correction 

 less than .07 cm. for 2x must clearly be in question. This is quite 

 below the difference of several millimeters brought out in §§ 4 and 6. 



To make this point additionally sure and avoid the assumption 

 of the last paragraph, we will compute the conjugate focus of the 

 central ray (different angles 6) on the b' focal plane parallel to the 

 grating and to x and on the b" focal plane parallel to x. The com- 

 putation is simpler if the central ray is thus focused, than if the 

 extreme rays are focused on the x plane. The distance apart will be 



8s'=g — b' cos (^-h^')(tan (^ + ^') — tan ^), 

 8^" = g — b" cos (^ — r)(tan^ — tan ($ — 6")). 



Inserting the results for 6, 6^', ^/', b', b", g, 



83' = .06, -83"=— .04. 



Both the b foci thus correspond to large angles. Their mean, 

 however, may be considered as vanishing on the intermediate x 

 plane. 



Thus it is clear that the effect of focusing is without influence 

 on the diffraction angle and much within the limits of observation. 

 It is therefore probable that the residual discrepancy in the three 

 methods is referable to a lateral motion of the slit itself due to 

 insufficient symmetry of the slides A A and BB in the above adjust- 

 ment. This agrees, moreover, with the residual shift observed in 

 the case of parallel rays in § 8. 



Brown University, 

 Providence, R. I. 



