98 Dr Searle, Experiments with a plane diffraction grating 



When ^ = 0, and therefore i/j = 0, 



sin o) — cos €2, oi —■ 19° 36' 49". 



Thus the maximum change in a> is only 1° 6' 29". 



§ 12. Practical exatnple. The following results were obtained 

 by Dr J. A. Wilcken, using a grating having 14,468 lines per inch, 

 ' and, hence, an interval d = 1-7556 x 10"* cm. 



The adjustments described in § 9 were either effected or tested. The plane 

 of the grating was not quite parallel to the grating shaft, but as both images 

 of the first order were observ^ed, the mean results will be hardly affected. The 

 calculated values of yjr were found on the assumption that the axis of the 

 collimator is perpendicular to the transverse axis of the grating. Sodium light 

 of mean wave length X = 5-893 x 10~^ cm. was used. Then, since the images 

 were of the first order throughout, 

 _ X _ 5-893 X 10- 5 

 ^^~ d~ 1-7556 X 10-* 

 Thus e, = cos-i mg -= 70° 23' 11", and m^^ = 0-11268. 



Each of the observed values of yp' given in the table is the mean of four. 

 Each of the first order images was observed, and for each image two values 

 of d, one on either side of zero, were taken. The grating circle, which was 

 printed on card, was a little eccentric relative to the shaft (it was a "home- 

 made" affair), and, consequently, although the settings were made to integral 

 degrees by one index, the other index did not always read integral degrees. 

 Some of the mean values of 6 are, therefore, not integral degrees. The 

 calculated values of -^ are those found from equation (20), which for con- 

 venience is written 



sin t//' = ?i2 = J sin 26 - sin 6 [(cos 6 + m^) (cos 6 - m^)]^. 

 For the sake of interest, the calculated values of w, /,- and I^ have been 

 added. The last line in the table gives the critical values as found by calcu- 

 lation. 



= 0-33568 = sin 19° 36' 49' 



The agreement between the observed and calculated values of ■^ is satis- 

 factory. 



