Dr Searle, Experiments with a plane diffraction grating 107 



^^^ = F+l + (F-l)cos2<Ai' ^^^^ 



where k ■= sec cf) and sin <f) = iX/d. 



To compare theory with experiment, we may plot the value of 

 OK given by (18) against the bench reading of K. If the zero of 

 this bench is at the end nearest 0, the points will lie about a 

 straight line equally inclined to both axes. An alternative method 

 is used in § 12. 



§ 11. Experimental details. The cross- wires should be mounted 

 so that E is as nearly as possible on the axis of P. The lines joining 

 the nodal points oi L to E are made coincident and parallel to the 

 bench by the method of § 7. The axis of Q is set approximately 

 parallel to the bench; optical methods are available. The cylin- 

 drical lens A is adjusted optically. For a given direction of the wire 

 at E, there are two positions of Q, 180° apart, in which A forms 

 a sharp image of the wire on H. If the positions of these images 

 are not identical, the error can be corrected by moving A at right 

 angles to its generators across the end of Q. 



To set the lens L so that E is at its focus, a plane mirror is 

 substituted for H, Q and G are removed, the cross-wires are 

 illuminated and L and the mirror are adjusted so that E coincides 

 with its own image. The plane of G is made perpendicular to the 

 bench by the same method, the plate covering the grating serving 

 as the plane mirror. The bench on which K slides is adjusted 

 optically. First set P and Q so that a vertical image of the wire 

 is formed on K. Then slide L along the main bench and readjust 

 K. If the position of the image relative to K is unchanged, the 

 auxiliary bench is correctly placed. If a micrometer eyepiece is 

 used in place of the screen K, two images will be seen except when 

 the wire is horizontal, since sodium light has a double spectrum 

 line. Unless the wire is very fine, the images will overlap. The 

 doubling of the images causes no inconvenience. 



§ 12. Practical example. The following results were obtained 

 with a grating of 14,493 lines per inch. 



For this grating, d = 1-7526 x 10~* cm. The wave length was 5-893 x 10~^ cm. 

 The image of first order was used; thus i = 1. Hence 



sin (p =^ 0-33625, k" = sec^ </> = 1-1275, (/> - 19° 38' 55". 



A cylindrical lens of + 2-5 dioptre was used. The corrected value of OH 

 was 38-91 cm. The angle ^|^^ was varied from 0° to 180° by steps of 15°. The 

 bench readings in columns 2 and 4 arc theoretically identical, and their mean 

 is given in column 5. The values of OK calculated by ( 18) are given in column 6. 

 To facilitate comparison, the mean difference between columns 5 and 6 has 



