96 Dr. A. Schuster on an easy Method for 



the adjustment without much loss of time and with simple ap- 

 paratus. 



The adjustment, as the following consideration will show, 

 can be made on each line of the spectrum without any appa- 

 ratus whatever. The only requirement is that the prism should 

 be movable. 



Suppose the rays which fall on the prism to be either con- 

 vergent or divergent ; then, after their passage through the 

 prism they will seem either to converge to or diverge from a 

 point, which is the secondary focus : as the prism is turned, so 

 as to change the first angle of incidence, the secondary focus 

 will change. If the rays are strictly parallel, then, whatever 

 be the position of the prism, the focus will not be altered. 

 This, then, is a delicate test for ascertaining whether rays 

 proceeding from the collimator are parallel or not. It remains 

 to be shown how it can be converted into a rapid method to 

 put the collimator into the right adjustment. 



The three fundamental equations for the passage of a ray 

 of light through a prism, 



sini=nsinr, (1) 



sin i' = n sin/, . (2) 



r + r f = a, (3) 



give 



di' cos i cos r' . . x 



= (4) 



di cos i cos r 



In these equations i and i l are the angles which the ray 

 makes with the first and second surfaces respectively on en- 

 tering and leaving the prism ; r and / the two corresponding 

 angles of refraction, and a the angle of the prism. The right- 

 hand side of equation (4) will, as a little reflection will show, 



steadily decrease when i is increased from to ^. This shows 



that the greater the first angle of incidence the more nearly 

 parallel are the rays. The following system of consecutive 

 approximation will therefore give the desired result. 



Suppose the collimator is out of adjustment: move the 

 telescope slightly out of position of minimum deviation ; then 

 two positions of the prism exist which will bring the desired 

 ray into the middle of the field. Call the position in which 

 the first angle of incidence is greatest A, the other B. 



1. Put the prism into the position A, and focus the telescope 



