Note on Mr. Earnshaw's paper, Phil. Mag. April 1842. 123 



form and exact method derived from a formula similar indeed 

 to that referred to by Mr. Earnshaw, but in which the very 

 imperfections pointed out by him are expressly corrected* 



As to the discrepancies between observation and theory in 

 the higher cases of dispersion, I do not consider them as 

 nearly so serious as Mr. Earnshaw appears to do ; and this 

 mainly from the experience I have had in ascertaining the 

 experimental numbers, and the degree of accuracy to which 

 they can be relied on, — for which 1 would refer to my Report 

 presented to the British Association on refractive indices. 



Thus much however is clear : the formula even in the ex- 

 treme cases agrees as well as I think can be expected with 

 observation, provided one of the constants receive a certain em- 

 pirical change in its value, constant for each medium. 



It will therefore be the next step for theory to investigate 

 whether such a change can be justified; but all this I have 

 stated at large in my work, at the conclusion. 



Mr. Earnshaw enters also upon the question of the logic of 

 the case, and the sitfficiency of what is merely an interpola- 

 tion ; three indices being assumed. This point again I had, 

 I thought, fully discussed (p. 84 et seq.); at all events, the 

 formula, in whatever manner calculation be applied to it, is 

 surely a direct deduction from theory. In particular, the very 

 simple form in which I have used it, is that deduced by Sir 

 W. R. Hamilton by a highly elegant analysis directly from 

 the principles of M.Cauchy, and to that pre-eminently gifted 

 mathematician it appeared a sufficient basis for calculation, as 

 was evinced by his own use of it, to which I have referred, 

 Art. 261. 



Upon the whole, I will merely add an expression of my 

 satisfaction that the subject has been taken up by Mr. Earn- 

 shaw, and my hope that in his hands some formula will even- 

 tually be elicited which may be found applicable to the results 

 of observation to such an extent as to clear up the discre- 

 pancies which hang over the existing investigations ; in which 

 I am well satisfied to have made a first approximation, if it 

 lead to more accurate results from the reseaixhes which I 

 may thus have excited more able analysts to undertake. 



I am, Gentlemen, 



Your most obedient Servant, 



Oxford, July 8, 1842. - BaDEN PoWELL. 



