212 Lord Rayleigh's Investigations in Optws. 



negligible, and s 2 is the aggregate thickness of the prisms at 

 their thick ends, which we will call t ; so that the dispersion 

 (0) is given by 



0= '.Se. . (4) 



By § 2 the condition of resolution of a double line whose com- 

 ponents subtend an angle is that 6 must exceed X^-a. Hence 

 from (4), in order that a double line may be resolved whose 

 components have indices \x and //, + £//,, it is necessary that t 

 should exceed the value given by the following equation, 



^h (5) 



which expresses that the relative retardation of the extreme 

 rays due to the change of refrangibility is the same (X) as 

 that incurred without a change of refrangibility when we pass 

 from the principal direction to that corresponding to the first 

 minimum of illumination. 



That the resolving-power of a prismatic spectroscope of 

 given dispersive material is proportional to the total thickness 

 used, without regard to the number, angles, or setting of the 

 prisms, is a most important, perhaps the most important, pro- 

 position in connexion with this subject. Hitherto in descrip- 

 tions of spectroscopes far too much stress has been laid upon 

 the amount of dispersion produced by the prisms ; but this 

 element by itself tells nothing as to the power of an instru- 

 ment. It is well known that by a sufficiently close approach 

 to a grazing emergence the dispersion of a prism of given 

 thickness may be increased without limit ; but there is no cor- 

 responding gain in resolving-power. So far as resolving- 

 power is concerned, it is a matter of indifference whether 

 dispersion be effected by the prisms or by the telescope. Two 

 things only are necessary: — first, to use a thickness exceeding 

 that prescribed by (5) ; secondly, to narrow the beam until it 

 can be received by the pupil of the eye, or rather, since with 

 full aperture the eye is not a perfect instrument, until its width 

 is not more than one-third or one-fourth of the diameter of 

 the pupil. 



The value of expression (3) on which resolving-power de- 

 pends is readily calculable in all cases of practical interest. 

 For a compound prism of flint and crown, S/j, . t is replaced by 



Sfi.t-S^.t', (6) 



