Dr Searle, Experiments with a plane diffraction grating 95 



Since e^ = ^tt, cos eg = Wg = iX/d. From the values of the 

 interval d and the wave length A, cos eg is found and then the 

 values of ip corresponding to the mean values of 6 are calculated 

 by (20). These values are compared with the mean values of j/f 

 given by the goniometer readings. 



§ 10. Distortion of the image. As 6, and consequently i/r, increases, 

 the observer sees that the angle between the images of the col- 

 limator wires undergoes great changes. When ^ = 0, the images 

 are at right angles, but the angle diminishes rapidly as 6 reaches 

 its critical value. The theory shows that they are actually tan- 

 gential one to the other when 6 has its critical value, but, as no 

 light is transmitted in the critical position, the phenomenon cannot 

 be observed. If the collimator wires are stretched across a small 

 circular opening, the image of the edge is distorted into an oval, 

 which is practically an ellipse having the images of the wires as 

 conjugate diameters. When, however, 6 approaches its critical 

 value, the oval begins to deviate from an ellipse. 



In Fig. 5 let OX, OY or OT, OZ, OL, ON meet a sphere described 

 about as centre in X, T, Z, L, N. Let OJ be the diffracted ray 

 corresponding to the incident ray OX; 

 the ray OX corresponds to the line of 

 collimation of the collimator and OJ to 

 that of the goniometer, when the image 

 of C is brought to the intersection of the 

 goniometer wires. Let OP^ be a ray nearly 

 parallel to OX and let OP^ be the corre- 

 sponding diffracted ray. Let the great 

 circles through Z and P^, J, Pg cut the 

 great circle TXS in H, K, M. Let *S be _ 



the pole of ZJK and let the great circle Fio- 5 



SJ meet ZP.^M in Q. Then ZJQ = ^tt. 



If the goniometer is mounted as described in § 8, and if its line 

 of collimation coincides with OJ, its horizontal cross-wire will 

 correspond to SJQ and its "vertical" wire to ZJK. The rays 

 parallel to OP2 will come to a focus in the focal plane of the gonio- 

 meter at D', whose coordinates referred to the horizontal and 

 vertical wires through D (Fig. 4) are/ x angle QOJ and/ x angle 

 P^OQ, where/ is the focal length of the lens. 



If points on a curve CC in the focal plane of the collimator 

 give rise to diffracted rays whose directions are shown by points 

 on the curve JPg o^ ^^^ sphere, and if the image of CC in the 

 focal plane of the goniometer is DD' , the angle between the 

 "vertical" cross- wire and the tangent to DD' at D is equal to /, 

 the angle between the great circle JZ and the tangent at J to the 

 curve JPg. 



