308 Mr. Earnshaw ow the Theory of the Dispersion of Light. 



investigations were commenced and conducted, we ought not 

 hastily to throw it aside. It has besides a strong claim upon 

 our indulgence arising from the fact stated by Prof. Powell, 

 " that it is certain that such a formula affords the closest ac- 

 cordance with truth throughout the whole range of low-disper- 

 sive substances; and even among many of the higher it gives 

 a very near approach to such an agreement." The following 

 remark may perhaps on this account be worthy of notice. 



The constant represented by A in equation (1.) is equal to 

 ■3- A .r, where A .r is the distance between two adjacent par- 

 ticles of the refracting medium. Now in flint glass for the 



ray B Professor Powell found — -^ =16° 10'; from which 



it follows that -. — is less than 12 ; for the ray H it is less than 

 A.r 



7 : and in oil of cassia it is less than 5. ^ is the number of 



particles of the medium which lie within a wave's length ; and 

 it has always appeared to me highly improbable that this 

 number should ever be so small as 5, 7, or 12; in fact it seems 

 more likely (from the analogy of sound) that it ought to be a 

 very high number. On this ground I feel less reluctance in 

 yieldino- to the force of the argument before stated. It is also 

 worth inquiring what effect the comparative largeness of A a; 

 (if allowed) may produce upon the convergency of the series 

 which occur in the investigations from which our formula for 

 p, is derived. 



This letter having already exceeded the limit which I pro- 

 posed to myself in setting out, it is necessary that 1 should 

 state in as few words as possible my remarks on the other 

 methods which have been made use of in the verification of 

 theor}'. The principle of them amounts to this : — A series in 

 inverse powers of A with indeterminate coefficients is assumed 

 to represent jw-. This series is then assumed to be so rapidly 

 convergent that all the terms after the first three may be 

 omitted : the coefficients of these terms are found by assuming 

 that the abridged series accurately gives the values of ju. for 

 three of the seven fixed lines ; and lastly, the remaining four 

 lines are used as a test of the truth of the undulatory theory. 

 Now I cannot refrain from asking, what has all this process 

 of assumption to do with the undulatory theory ? Surely it 

 will not be denied, that it is a common and long-used method 

 of inta-polation. Then where has such a connexion been 

 proved to exist between the undulatory theory and the prin- 

 ciples of interpolation, as to make it follow, that when the latter 



