28 Mr. W. H. M. Christie on the [Mar. 1, 



Thus, there being n half -prisms in the train, 

 Breadth of spectrum-lines . . =m M . b v 



Dispersion =(m M ~ 1 + m M_2 + . . +m 2 +m+l)A 



m n -l * 



= — . A 



m — 1 



Purity of spectrum = m ~^ 



m — 1 m n b l 



Quantity of glass =(m 2 ^ +m 2 ^ + . . +m 4 +m 2 + l)Q 



m—1 



Thickness of glass =(m M - 1 +m n - 2 + . . +m 2 +m + l)i 



_m M — 1 

 m — 1 ' 



m w -i t/ 



Total brightness of spectrum.. = 5 . |(Z; 1 n + ^ 2 M )c m _1 ' . 



2. Half-prisms diminishing. 

 Breadth of spectrum-lines . . =— . 5 . 



Dispersion =/_^_+ _!_+.. + l + A 



\m n 1 m n * m? m J 



A 



# m 



m n -l 1 

 . — .A. 



m — 1 m n 



Purity of spectrum = . _ . 



m —1 b 2 



Quantity and thickness of glass the same as for " half-prisms magni- 

 fying." 



q fn n — 1 ^ 



Total brightness of spectrum.. — -i. . j(fc? + &2)c m - 1 ' 



3. TFAoZg prisms. 

 Breadth of spectrum-lines . . =b 3 . 

 Dispersion = 2p . A. 



Purity of spectrum = 2p . — . 



b 3 



Quantity of glass = 2p . m 2(rt-1) . Q. 



Thickness = 2p . m' 1 " 1 . t. 



Total brightness of spectrum.. =^ . £ + fc/)c * 

 and fc 2 are nearly equal to & x 2 and ~k 2 2 respectively. 



4. ^4 train of n half -prisms magnifying followed by a train of n AaZ/*- 

 prisms diminishing. 



Breadth of spectrum- lines . . =1. 



