26't Prof. Powell's Observations on some Points 



Now to all who have attentively considered the nature of 

 those remarkable optical properties of bodies which are called 

 their refractive and dispersive j^owers, it will be evident that 

 we have a very j)eculiar case to consider. The problem we 

 have to solve is rather a cojnbination of two distinct problems. 

 The dispersive and refractive powers follow no proportion 

 to each other, and it is almost impossible to conceive any 

 theory, or even any empirical mathematical law, which could 

 connect the two together. For example, we have diamond 

 and water, with refractions nearly double the one of the other, 

 and dispersions nearly the same. Flint glass and oil of cassia 

 with the same refractions nearly, and dispersions as about 

 1 to 3. In a word, the absolute magnitude of the deviation 

 of any given ray, or of white light, bears no relation whatever 

 to the difference of deviation between the extreme rays of 

 the spectrum, in different media. If then we seek a theory 

 to explain the facts, it would be not only unreasonable to ex- 

 pect it to connect such obviously incongruous phaenomena, 

 but it ought most rationally to involve two distinct constants, 

 one belonging to the refractive power, the other to the re- 

 fractivc chakactek of the medium. And in conformity 

 with the general conditions of formulas of this kind, we might 

 expect that, directly or indirectly, we should have to assume 

 two quantities as given by observation, in any calculation to 

 compare theory with observation, for the spectrum of a par- 

 ticular medium. 



Now if we take the formula (1.) above stated, it is at once 

 manifest that if A a: be very small compared with /, we have 

 for all values of A very nearly, 



. /tt A a;\ 

 sm I I 



'^ ^ { = 1 (5.) 



or there is no dispersion, and the formula is reduced to 



4- = -S . H- (6.) 



Now, in any medium, if A^- be not very small compared 

 with A, we shall have different refractive indices for each 

 ray, which will differ less as X becomes greater; and if we 

 suppose A to increase indefinitely, (A.r remaining finite) the 

 above expression (6.) will be the limit to which the refractive 

 index constantly tends, and from which it does not sensibly 

 differ when A is supposed large ; that is, for some ray beyond 

 the red end of the spectrum (and such may exist though not 

 sensible to the eye) there is an absolute limit to all refraction, 



