with a fluid concave lens. 223 



substituting these proportional values for the above letters, 

 our expression becomes 



_ f m (g»' -g«)-n{a»-a>) ) 



^ \ma' {a"' — a") — n a'" (a" — a') ) 

 <* In like manner, if a', a", a"' be taken to denote the refrac- 

 tive indices of the red, green, and violet ray in the correcting 

 lens, then we shall find 



J' + r'-f — v' 

 which latter may therefore be substituted for m and n. 



" The formula then becomes 



f («» - a') (a'" - a") - («'" - a") (a" - a') 1 



-* / ( (a" — a') (a'" — a") a' — (a"' — a") (a" — a') a'" J 



an expression for the distance in terms of the indices and focus 

 only. 



" In plate glass, according to Fraunhofer, a! = .515, 

 a" = .525, and a'" — 535. Which value being substituted, give 

 f K --0--(«'»^0 ^ 



a — J \ .981 (a" — a') — - 1.0J9 (a'" — a") J 

 In flint glass, from the same authority, of = .602, a" = .620, 

 a"' = .640. Which numbers being substituted, give d = .734/T 

 An impracticable distance in this case, because the dispersive 

 power of flint glass is not great enough to correct the plate 

 lens when so far removed. 



If these indices had been .602, .621, and .640, then we 

 should find d = 0, or the lenses ought then to be in contact. 

 A change therefore of .001 in the index of the green ray 

 changes the distances of the lenses from nothing to nearly 

 three-fourths of the whole focus of the plate ; consequently, 

 the determination of the proper distance to combine the three 

 colours, when the media are such as to admit of it, depends 

 upon the most delicate determination of the indices of the red, 

 green, and violet rays ; but these being so determined, and the 

 dispersive power of the medium being great enough, the most 

 complete union may be effected. 



Whether the sulphuret of carbon fall within this limit or 

 not, I am not at present able to say. I have attempted to find 

 the indices of the different colours by means of a prism ; but it 

 is extremely difficult to determine the limits of the different 

 shades, and perhaps after all the best way is by actual' experi- 



