in the Theory of the Dispersion of Light. 



263 



of a number of like terms, for the same value of /i and A, 

 such as, r 



(2.) 



.= <+ H/ 



+ H, 



+ &c. 



The summation being extended to all the values of Ax 

 which it may be necessary to include. 



My first and approximate attempt at calculation was ef- 

 fected by taking a single term of such a series, with some con- 

 stant coefficient, which might be a sort of mean among all the 

 similar terms, and which (on extracting the root) would be, 



^^ (3) 



V A / 



The peculiar function involved is easily expanded into a 

 series; and in this way the exact formula (1.) may be ex- 

 pressed by, 



Supposing 3 terms sufficient, this is the formula of Mr. 

 Kelland : in which the coefficients can only be found by as- 

 suming 3 indices from observation. An objection has also been 

 urged by Professor Lloyd, that, on pursuing the investigation, 

 from the relations which subsist between these constants, values 

 of them are given by calculation which are at variance with 

 those derived from observation. I have also remarked in re- 

 ferring to this point at the end of my paper (Phil. Trans- 

 1838, part i.) that to propose as a sufficient theory one which 

 requires so large an assumption of data from observation, ap- 

 pears hardly consistent with the just demands of what ought 

 tc constitute a legitimate mathematical explanation of the law 

 of experimental results. 



(. /TT, 



