DISPERSION. 47 



of the two prisms were made to correct each other by varying 

 the angle, so that the ray emerged colourless, their refractions 

 were no longer equal, and the ray emerged inclined to its 

 original direction. This important discovery led to the con- 

 struction of the achromatic telescope. 



(58) It is easy to determine the condition of achromatism, 

 when a ray of light passes nearly perpendicularly through 

 two prisms, whose refracting angles are small. 



The dispersions produced by the two prisms are (ju 2 -jui) A, 

 and (pi- pi) A x , respectively (55) ; and, therefore, when the 

 total dispersion is nothing, we must have 



fa - /ii) A + fa'- p^A.'= 0, or4' = - &ZH. 



A p 2 - pi 



The negative sign, in the second member, indicates that 

 the angles of the two prisms must be turned in opposite 

 ways. 



(59) In order to ascertain the relative dispersive powers 

 of different substances, they must be separately compared with 

 some standard substance, such, e. g., as water. For this 

 purpose a vessel must be constructed, whose opposite sides, 

 formed of parallel glass, are moveable on hinges, and may be 

 inclined to one another at any angle. It is closed on the other 

 two sides by metallic cheeks, to which the moveable sides are 

 accurately fitted. The vessel being filled with water, it is 

 evident that the transmitted ray will be refracted in the sam& 

 manner as by the inclosed water prism, the parallel plates of 

 glass producing no change in the direction of the refracted 

 ray. The substance whose dispersive power is sought being 

 formed into a thin prism, a beam of light is to be transmitted 

 nearly perpendicularly through the two prisms, with their re- 

 fracting angles turned in opposite directions ; and the angle 



