46 Lord Rayleigh's Investigations in Optics. 



which determines the degree of confusion of refrangibilities 

 produced by the aberration. 



For a glass prism, /jl—/jl~ 1 differs very little from unity. If 

 the refracting angle be 60°, cos 2 <// = f , and thus 



Sjm=26 2 . . (31) 



By (8), (10), § 4, the value of B/jl for the soda-lines in the case 

 of a prism of " extra-dense glass " is 5*8 x 10 -5 . Hence, if 

 the image of one soda-line just touch the image of the other, 

 = -OO54, or the distance u must be about 100 times the width 

 of the beam where it falls upon the prism. With small instru- 

 ments, whose whole resolving-power is only a small multiple 

 of that necessary to resolve the soda-lines, it is possible to 

 work without a collimator by allowing a distance of 10 or 20 

 feet between the slit and the prisms ; but in the case of power- 

 ful instruments a pretty accurate adjustment of the collimator 

 is indispensable. 



The next thing to consider is the effect of curvature in the 

 faces of prisms. We shall neglect Z, the length of path within 

 the prism, as small in comparison with the other distances 

 concerned ; its influence is doubtless no more important than 

 when the faces are flat. From (4), 



giving by subtraction 



-"(H)-*S*(7 + 7 + T> 



Hence 



u v y \r s/ 2 IrW u) 



8 \v! vf u' 2 U 2 V 2 J 



=( ^_ c) (i _ !)_ %^i{(4_f)A + 4 + £) 



y \r sj 2 (W u/\r u 1 u) 



+ .(4_£V_l + 4 + £)} (34 



\u' v/\s v! v/ ) v 



