26 



Mr. W. H. M. Christie on the 



[Mar. 1, 



of the spectrum, as compared with the height of the slit, should also be 

 taken into account, for this affects the brightness directly. Hitherto 

 advantage has not been taken of the circumstance that the height of 

 the slit is practically unlimited (except in the case of stars), and that 

 therefore it is unnecessary to magnify the spectrum in this direction. 

 Thus the advantage of the train of " half-prisms magnifying " is obvious, 

 since the breadth of the spectrum is left unaltered. In spectroscopes as 

 ordinarily constructed, the breadth of the spectrum is magnified at the 

 same time as the separation of the lines, and thus a high magnifying- 

 power is accompanied by a great decrease in the brightness, the latter 

 varying inversely as the square of the power. By using a cylindrical 

 eyepiece, however, this objection may be removed ; and there would appear 

 to be no practical difficulty in this plan, since little or no enlargement 

 of the breadth of the spectrum is required. For bright-line spectra 

 generally a Eamsden eyepiece with cylindrical lenses would answer the 

 purpose well, the height of the slit being sufficient to give a convenient 

 breadth to the spectrum without any amplification in this direction ; but 

 for viewing the solar prominences the magnifying-power should be the 

 same in both directions ; and thus with the train of " half -prisms dimi- 

 nishing," which, as will be seen, gives great purity in the spectrum with 

 a corresponding decrease in the breadth of the image of the slit, the 

 magnifyiug-power of the eyepiece must be high in the direction of 

 the breadth of the slit, and low in the perpendicular direction. An eye- 

 piece formed with a cylindrical concave or Barlow lens (within the prin- 

 cipal focus of the viewing-telescope) and an ordinary convex field-lens 

 in combination with a convex cylindrical eye-lens, would produce this 

 effect, the axes of both cylindrical lenses being parallel to the slit. 



The effect of such an eyepiece may easily be investigated. 



Let f v f 2 be the focal lengths of the concave and convex cylindrical 

 lenses, /the focal length of the convex field-lens, and F the focal length 

 of the viewing-telescope ; then, if M, M' be the magnifying-powers parallel 

 and perpendicular to the slit, 



For the rays in the perpendicular plane, suppose the concave cylindri- 

 cal lens to form an enlarged image on the field-lens, which will therefore 

 produce no effect, this image being at the principal focus of the cylin- 

 drical eye-lens. 



Then if v be the distance from the concave lens of the focus after re- 

 fraction, and m' the enlargement of the image, / and v are both negative, 

 and 



v , rd . . 1 > 



—m • .'. v = — — v-f= - — /. 



v —f m — 1 m — 1 



Also 



1 1_ = 1 . , _ -m' f 



v v-f f x ; " /l (m'-l) 2/ ' 



