72 PROFESSOR POWELL'S RESEARCHES, ETC. 



ticular, is thus resolved into an assemblage of small lines. Thus some uncertainty 

 may be fairly admitted to exist in the data ; at any rate enough to render farther 

 examination desirable before we can pronounce on the insufficiency of the theory. 



General Remarks on the Formula. 



If the accordances be allowed to come sufficiently within the limits of error, it may 

 not be improper to add a remark with respect to the entire nature of the formula, 

 and the light in which, (in its present state,) the theory of dispersion must be re- 

 garded. 



The relation here expressed between the index and the wave-length involves three 

 constants dependent on the medium ; which must be in some way derived from ex- 

 perimental data : and which are here directly deduced by assuming some three, at 

 least, of the observed refractive indices for the medium. 



The whole process then seems equivalent to assuming these three indices, and then 

 interpolating the intermediate values. This, though under a different form, is also 

 palpably the case with the method adopted in my former paper. 



Now it maybe contended that this actually carries us but a very little way towards 

 a real or satisfactory explanation, and that a complete theory ought to assign also an 

 independent relation between the constants. 



The consideration of this point has been included in the valuable researches lately 

 made by Professor Lloyd of Dublin, given in a paper read before the Royal Irish 

 Academy, and noticed in the reports of that body, (Nos. 2 and 3.). But I have been 

 informed by the author that, in pursuing that research, he has found theory, as yet, 

 incapable of furnishing the relation in question. 



It seems, therefore, that in the present state of our knowledge we must be con- 

 tent to regard the constafits of the formula as unexplained by theory. But the pro- 

 cess by which we here obtain them, (viz. by assuming three indices from observation,) 

 may be viewed as simply auxiliary. The main calculation may be regarded as in- 

 dependent, and considered to involve two of these constants only as j/'they had been 

 adopted empirically; whence we proceed to verify the formula by the coincidences 

 of the values of the third, viz. p. But even with this deficiency, it seems to me 

 not an unimportant step to be able, with two empirical constants, dependent on the 

 medium, but independent of the ray, to assign a third quantity, which expresses for 

 each ray a relation between the wave-length and the refractive index, with so near 

 an approximation to the truth, even in the most extreme case as yet known. 



Oxford, January 7, 1838. 



