8 



Tlie "■nitinir mav be fixed so that its iilane is iionnil to tlie collimator ; or it 

 may lie normal to the telescope ; or it may V>e normal to neitiier. These arraiit^c- 

 ruenls give rise to several different methods of raakinir and redncin^ ohservatiinis 

 each of which seems to possess some advantatjes peculiar to itself. But it 

 hecomes necessary to choose from among these that which, under the circum- 

 stances, proves to be the luost desirable and, in order to present more clearly the 

 reasons which led to the selection maile in the present instance, it may he 

 desirable to present a brief discussion of the principal methods which may be 

 adopted. For this pMr[)ose, — let 



li =^ Anü;le between the telescope and the uornul to the grating. 

 1^ = Angle between the collimator and the normal to the grating, 

 s = The grating space. 



Then, in general, we have. 



), = s (sin ft ± sin d>) 



the spectrum being of the first order. 



1st. Suppose <^ = that is, the collimator is normal to the grating. The 

 formula reduces to 



/ = .s' sin 

 and the operation consists in measuring the angle which is best done by setting 

 on the line, first one side of tlie normal and then on the otlier, and taking half 

 of the angle passed over. 



2nd. Suppose = 0— or tlie grating is kept constantly at right angles to 

 the telescope. The resulting formula and jirocess of measurement will be similar 

 to the preceding. 



3rd. The telescope and collimator may be kept at a constant angle with 

 each other ami the grating moved. The observations and reductions are easily 



m; 



ade in the following manner. 



Let a = angle between telescope and collimator. 



I = twice the angle through which the grating must be turned 

 in order to bring the line and the image of the slit upon 

 the cross wires of the telescope. 



I) and i;6 := as before. — 



tlien f' = - - 

 . h — a 



and the general formnla reduces to 



/ = 2 s sm - cos - 



