Mr. Earnshaw on the Theory of the Dispersion of Light. 309 



furnishes true results the former is necessarily true ? Perhaps 

 it will be said that the undulatory theory suggested the form 

 of the assumed series. It is a sufficient answer to this, that 

 that form might have been conjectured from the mere inspec- 

 tion of the corresponding values of A and ix. After all, are 

 we sure that the form suggested is the correct one? Let any 

 one, who is inclined to think that it is, determine the coefficients 

 from the lines B, C, D, and with them calculate the indices 

 for E, F, G, H, and I entertain no doubt he will be soon will- 

 ing to resign the opinion. Again, if the method be one of 

 interpolation only, it will naturally follow that the more widely 

 the quantities are separated between which we interpolate, 

 caeteris paribus, the greater are the errors to be expected in our 

 results. Now this is so invariably found to be the case, that 

 I believe Professor Powell has allowed that the errors increase 

 with the greater dispersion of the substances employed. But 

 that which strongly inclines me to the opinion that the method 

 we are discussing is wholly unconnected with the truth of the 

 undulatory theory, or indeed of any theory, and is a method 

 of interpolation only, is the fact, that in the first applications 

 of the method the same inadvertence with regard to the values 

 of X was committed as I have before alluded to, as occurring 

 in " Researches Nos. I. II. III.," yet the results, though de- 

 duced from values of A 7iot cou?2teiianced by theory, were 

 hailed as conjirmatory of the truth of theory. 



But it is time to conclude these remarks, and therefore I 

 will only add, as a general observation, that as the index for 

 letter G is notoriously the most refractory, no method is in 

 my opinion worth attention, even though it isoere furnished 

 by theory, in which it is necessary to assume the indices for 

 both F and H in order " to tame that ray." Yet even with 

 the assumption of these, the tables for the more highly di- 

 spersive substances given in Professor Powell's book exhibit 

 errors which show that G is as untamed as ever, to say no- 

 thing of the other lines in several instances. On these grounds, 

 I cannot avoid coming to the conclusion, that the methods of 

 computation employed in compiling the tables contained in 

 the book just referred to are such as are wholly unconnected 

 with a physical theory of dispersion, and therefore their re- 

 sults, were they even coincident with experiment, add nothing 

 to the strength of M. Cauchy's theory; and, were they even 

 more discordant than they are with experiment, tend in no 

 degree to overturn it. In this opinion I may perhaps be sin- 

 gular ; but as it is just possible that a similar idea may have 

 presented itself to others who, like myself, wish to have the 

 impression, if erroneous, removed, I have ventured to make 



