534 Royal Society : — 



the difference being that, in the double reflection, there is a ver- 

 tical inversion of the spectrum, which, however, produces no dis- 

 cernible effect in either the spectrum or curvature of the lines ; 

 and as the spectroscope constructed with the double reflecting 

 prism is known to produce, with double dispersion, double cur- 

 vature, we here have an additional proof, if such were required, that 

 the single reflecting mirror does the same. 



The remedy, or means of producing straight spectral lines, 

 which I have alluded to, is simply that of constructing the " slit " 

 with curved instead of rectilinear edges. There is but little 

 practical difficulty incurred in construction, and no apparent objec- 

 tion to its use. It may be objected that for each variation of prism- 

 power in use there should be a special slit. It is, however, only in 

 spectroscopes arranged for high dispersion that the curvature be- 

 comes objectionable ; in such there is seldom a change required, 

 and a single slit of medium balancing-power would probably remove 

 all practical difficulty, or objectionable curvature of the lines. I 

 have found by trial that, when two compound prisms were in use, 

 giving a dispersion from A to H of nearly 14°, the spectral lines 

 were straight in a field of one degree, when the radius of curvature 

 of the slit was made 1*25 inch. 



[Note on the above Paper. 



If a ray of light be refracted in any manner through any number 

 of prisms arranged as in a spectroscope, undergoing, it may be, any 

 number of intermediate reflections at surfaces parallel to the com- 

 mon direction of the edges of the prisms — or, more generally, if a 

 ray be thus refracted or reflected at the surfaces of any number of 

 media bounded by cylindrical surfaces in the most general sense 

 (including, of course, plane as a particular case), the generating 

 lines of which are parallel, and for brevity's sake will be supposed 

 vertical, and if a be the altitude of the ray in air, a, a", . . . . , its 

 altitudes in the media of which the refractive indices are /*', /x", . . ., 

 then 



(1) The successive altitudes will be determined by the equations 



sin a=//, sin a'=/x", sin a" = . . . . , 



just as if the ray passed through a set of parallel plates. 



(2) The course of the horizontal projection of the ray will be the 



same as would be that of an actual ray passing through a set of 



,. - » j. . j. u! cos a! ix" cos a," . , ■, ,, , 



media of refractive indices c , £- , .... instead ot u , 



cos a cos a 



li", .... As a'<a, the fictitious index is greater than the actual, 

 and therefore the deviation of the projection is increased by ob- 

 liquity. 



These two propositions, belonging to common optics, place the 

 justice of Mr. Grubb's conclusions in a clear light.— April 30, G-. 

 Q-. Stokes.] 



