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Mr. F. L. 0. Wadsworth on 



in fig. 1, PL VIII. ; where t is the Greissler tube which serves 

 as the source ; m a mirror, mounted on a vertical axis on 

 the movable spectroscopic arm E, ; and S the slit of the wave- 

 comparer, which separates out the radiation which is to be 

 analysed by the latter. To the lower end of the shaft which 

 carries the mirror m is fixed a drum connected with a 

 second drum a, fixed on the axis of the spectroscope by two 

 steel cords. The drum a is just one half the size of b, and 

 hence, as the arm E, revolves about the axis of the spectro- 

 scope, the mirror m revolves on its own axis with an angular 

 velocity just one half that of the arm, but in the opposite 

 direction. Hence, if the mirror is once adjusted so that the 

 direction of the reflected ray is parallel to the axis of colli- 

 mation, it will remain parallel to that axis for all positions of 

 the arm, and we have therefore a virtual rotation of the slit. 

 There will be a slight lateral displacement of the ray, which 

 can be easily investigated. 



Fio 1 



§ 



o 



For a certain position of the arm, say a b, fig. 1, the re- 

 flected ray b a will lie in the principal axis of the collimating 

 lens, which we will suppose passes through the centre of 

 rotation of the mirror m. Let 6 be the angle of deviation 

 for this position, then for any other position of the system in 

 which the deviation is 6 ± e, the reflected ray will be parallel 

 to the axis of collimation, but will be displaced laterally from 

 it a distance Ay. Finally, let a be the angle between the 

 mirror-face and the axis of collimation in the position a b, 

 then, from the construction of the apparatus, this angle for 

 any position V a will be a + e/2. From the two small triangles 

 V b H d and b V b" we get at once 



&y = b' b'' cos (a — e/2) = 2?'sin-cos (- +2a), 



