A THEORY OP THE DISPERSION OP LIGHT. 



69 





and the formula becomes 



^-.-a)%+(^y' 



taking such formulas successively for the different standard rays, between any two, 

 as those for B and E, the constant p is eliminated : and combining these with a third, 

 as that for H, the coefficients q and / are determined. For brevity writing 



and similarly expressing by e, g, g^ ; A, ;?, rp- ; the corresponding quantities for the rays 

 E and H, we shall have 



(e-A) = (p;-g)^- (pj2-g2)/. 



whence we obtain, 



_ {s-.^){e-h)-{ri-e){b-e) 

 ^-(s-/3)(,,--s2)-(,,-s)(s2-/3^)' 



9 = 



{b-e) + is^-fi^)l 



Knowing the values of X from the determinations of Fraunhofer, it becomes easy in 



the above formula to introduce the values of \-j-) taking the indices as given by 



observation for the particular medium : we, thus, first determine the constants q and / 

 for the medium, and having done this, by the aid of these combined again with the 

 indices given by observation a value of/? is deduced for each ray by the formula. 



.=^.+(f)%-ay^ 



and if these values ofp for the different rays result equal, the theory is verified. 



Mr. Kelland has thus verified it to a degree of accuracy, which will probably be 

 deemed sufficient, for all the indices determined by Fraunhofer. 



The following Table contains the logarithms of the values of -^ for the standard 



rays after the determinations of Fraunhofer, without their index. 



