in the Theory of the Dispersion of Light. 265 



difFerent in diiferent media ; this may be called the refraction 

 constant. If we had any means of determining it by experi- 

 ment, it would be a most important step for the theory. But 

 it is evidently a datum quite independent of the dispersion. 

 This quantity corresponds to {h) in Mr. Tovey's notation, 

 and to (P) in Mr. Kelland's, who has determined it for 

 Fraunhofer's media ; as I have done for several of those I 

 have examined. (Phil. Trans. 1838, part i.) It is an index 

 not <Treatly below that for the red extremity of the visible 

 spectrum. Whether it may j^ossiblij be connected with the 

 refraction of heat may become an interesting question. 



To return to the dispersion :— according to the exact me- 

 thod we have still two more constants to determine, viz. in 

 Mr. Kelland's notation (Q) and (L) ; in Mr. Tovey's [h') and 

 (F) : these like the former must be ultimately derived from 

 observation, and they are in fact obtained from the assump- 

 tion of two more observed indices. 



But pursuing the same idea as that just adverted to, it 

 would seem reasonable that as one datum for each medium is 

 the refraction constant, so one more should supply a disper- 

 sion constant ; and, on looking at the nature of the formula, 

 it would seem that this should depend on the arc % A x. 

 Now the coefficients Q and L arise from the summation of 

 the various combinations of H, and Ax^; H^^ and A^r^^ H,,, 

 and Aa;,;,,&c. And if we recur to the simple consideration 

 of one term of the summation, which furnished my first ap- 

 proximate formula, we shall see that we here avoid this diffi- 

 culty, and in fact have only the tiso constants of refraction and 

 dispersion to derive from observation. And though it may 

 be true in reference to the physical theory that for the adop- 

 tion of that formula no legitimate ground appears, yet for the 

 reasons already adduced it may be worth while to examine 

 the application of it more closely. 



If we take the simple formula (3.), or what is the same 

 thing, on developing, (see Lond. and Edinb. Journal of Sci- 

 encet Jan. 183G) and substituting the value of X in air, 



^ = h(i-1 j(,Aa.).+ 4|;(.A.r&c.} (7.) 



writing for abridgement, TrA.r = 6, 



we shall have, for any one ray, 



-^ = /^-pfl'^ +<7fl' (8.] 



