Wave-length of Light. 253 



becomes the ordinary formula 



* l • A. 



a= — ssm<p, 

 n T] 



which applies to the two methods of normal incidence ; one 

 in which the grating is kept accurately perpendicular to the 

 collimator, the other in which it is kept perpendicular to the 

 observing-telescope. 



Next is the method used by Angstrom, in which i is not 

 reduced exactly to 0°, but measured and retained in the 

 formula, the grating in this case being kept nearly perpen- 

 dicular to the collimator. In this method a reading on the 

 slit is necessary ; and if a and a' are the readings on the circle, 

 and M that on the slit, the working formulae are: 



— M = S and — ^ — =<£; 



Z 2 



then, if i is, as before, the angle of incidence, 

 . 1 



s sin <£cos (i + h\ 



sin i= sin (i + S) cos <f> } 



, COS0 jj 



tanz = - —, o. 



1— cos d> 



value. Putting the general formula in the form 



-v 1 a ■ 4> /• <t>' 



\= - 2s sm v cos f i — 7T 



n 2 \ 2 



the deviation represented by the angular term will evidently 



be a minimum when i= ±-. If, then, one observes in the 

 2 



position of minimum deviation, 



X=i2*ain*. 



n 2 



In the fifth method, collimator and observing-telescope are 

 kept at a fixed angle with each other and the grating is turned. 

 In this case, if <f> is the angle of deviation, and the angle 

 between the telescopes, 



\= - 2s sin <f> cos -; • 



n 2 



These methods are general, and the choice between them is 

 simply a question of the convenient application of the appa- 

 ratus at hand. Probably the first and second methods are 



