1877.] 



Magnifying -power of the Half-prism. 



11 



2. Dispersion. 

 Taking it as variable, 



ty= ?£L tan <* + S^H U', ty= ^tan^+ ty' f 

 cot r M cot lp 



or 



^0=A' + m'^', &//=A" + m"2ty', 



where 



A' = ^ tan d> = dispersion at first surface, 

 A"= ^ tan dispersion at second surface; 



also 



ty' + Si// = 0, and 8D=ty + ty. 



Eliminating <fy' and ch//, we have 



m"S0 + m'^ = m"A' + m'A'', 



with the further relations, 



fy-m'ty' =A', | 

 m"d\p' = A". J 



3. Purity. 



Putting n' =—,= purity at first surface, 



II"=— =purity at second surface, 



m 



we have 



n' = ^ tan d>', and II" = tan f ; 



.'. m''S(p-\-m f ()\p=m'm' (II' + II"). 



Before proceeding further we must assume some relation between 

 ty, ty', which will give a fourth equation ; and here three cases 

 may be considered. 



i. fy> = 0, or the collimator fixed relatively to the prism. This gives 

 the dispersion and purity of the spectrum as seen by the eye, whatever 

 be the form of spectroscope used. 



ii. ^' = — ^' = 0, or the collimator and telescope movable relatively 

 to the prism in such a manner that the pencils for different parts of the 

 spectrum all pass through the prism in the same direction. This is the 

 condition in the ordinary form of spectroscope with automatic adjustment 

 to minimum deviation. 



iii. £D=0, or the collimator and telescope relatively fixed, whilst the 

 prism is turned so as to bring different parts of the spectrum into the 

 field of view. This can only be done when the angles of incidence and 

 emergence are unequal, as in the half -prism spectroscope. 



