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XII. A New Automatic Motion for the Spectroscope. 

 By Walter Baily *. 



[Plate I.] 



IN this paper I propose to describe a new mechanism 

 for moving the prisms of the spectroscope, a model 

 of which was exhibited in the Loan Collection of Scientific 

 Apparatus, No. 157a. 



The instrument is founded on the following proposition : — 

 If a series of curves whose equations are 



„F(f). ,.rg),...„.(^), 



be described on each of two disks, and one disk be turned 

 over on the other so that the origins coincide, and the initial 

 lines are inclined at an angle (j>, the curves will intersect in 



pairs (viz. the curve \ r = Ff— j > of one disk with the curve 



^ r = F( j ^ of the other disk) at points lying on lines 



from the origin which divide the angle (f> into n equal angles. 

 For if 6 be the an^le measured from the initial line of one of 



6 — (9 



the disks, we have at an intersection — = ; whence 



, m n — m 



= m - , and the series of values of is 

 n 



t 2i,...{n-l)t 



■■ n n ^ n 



^nd therefore the angle </> is divided into n equal angles. All 

 these intersections are equidistant from the origin ; for 



\7nJ \m n/ \nj 



■ Putting m = 0, we have the intersection of j ^ = ^(a) f? 



which is the initial line of one disk, with ihe curve < r=:F/-j V 



of the other disk ; here also r = F( — J. 



In fig. 1, K is the common origin, through which passes 

 an axle perpendicular to the disks. One disk is fixed, and 

 K is its initial line ; and A A^, B B', C C', D D^ are slits 



* Communicated by the Author, having been read before the Priestley 

 Olub, Leeds. 



