﻿Fixed- Arm Spectroscopes. 341 



where r is the distance between the spectroscope axis and the 

 mirror axis. If e be small this expression is a minimum for 

 a = 45°, when the angle between the incident and reflected 

 rays on m is a right angle. Under the conditions 



A?/ = — 2r sin 2 -, 

 22 



the angular error in the reading will evidently be 



A;/ 2r 



6 



where K is the focal length of the collimator. For most 

 prisms e will not exceed 6° from end to end of the spectrum, 

 and hence, if we suppose a =45°, for the position of mean de- 

 viation we have for the maximum error S = *0013?yR, or if 

 r/R^, 8=25". 



It is evident that there will be a change in the focal distance 

 S, b, C as the arm revolves, which, under the conditions just 

 assumed, would amount to about ^o ^- This was no * 

 altogether a disadvantage, for when the lenses and C are 

 either or both of them simple lenses, we can, by choosing 

 a value of r/Jl suitable to the particular prism used, very 

 nearly compensate for the optical change in focus in passing 

 from the violet to the red, or vice versa, by the mechanical 

 lengthening or shortening of the path S b C. From an 

 inspection of (1) it will be seen that the correction will 

 diminish as the ratio r/H diminishes, and will become 

 for r = 0, or for R=oo . This indicated at once two methods 

 of eliminating the error. The first and simplest is to place 

 the mirror between the prism and collimator instead of be- 

 tween tube and collimator, as indicated in dotted lines in 

 fig. 1 (PL VIII.) . The second is to make r = by placing the 

 mirror-face in the axis of rotation of the spectroscope. To 

 do this we must either place the prism considerably out of 

 centre, fig. 2 (PL VIII.) , or else we must place the mirror 

 above or below the plane of refraction (fig. 3, PL VIII.). In 

 either case a second reflector must be used to receive the 

 beam from the first reflector in and return it to the prism. 

 This second reflector may conveniently be a concave mirror 

 of a focal length sm+mc, which will at the same time serve 

 as collimator, or as objective of the observing-telescope. As 

 the motion of the mirror is in this case the same in direction 

 as that which must be imparted to the prism in order to keep 

 it in minimum deviation, the mirror may be attached directly 

 to the prism-table or to the prism itself*. Which of these 



* The back of the prism may be polished and silvered, and arranged 

 to act as the first reflector, as in fig. 2 6, PL VIII. 



