1879.] Double Refraction and Dispersion in Iceland Spar. 205 



quired to bring theory and experiment into agreement. The results 

 arising from a want of achromatism in the lenses have been considered 

 at some length. 



I have also endeavoured to show that, between the limits of the 

 lines C and g, the relation between the refractive index and the wave- 

 length may be expressed by means of the formulas 



"=' + + + • • • 



Taking the three hydrogen rays, travelling in any the same direc- 

 tion, we have three equations, neglecting ^1, &c, 



A/* 



- • 



K=P+h ■ ■ ■ ■ ■ ■ (2). 



»=f+A • • ( 3 )- 



A 3 



The values of p found by combining these equations, two and two, 

 differ on the average by about '00006, and these differences are some- 

 times positive, sometimes negative. 



Taking the mean of the values of p and the value of p Y deduced 

 from equation 1, I find the values deduced for [i% and ^ rarely differ 

 from the observed values by as much as '00006, the mean only being 

 '000032. This is considerably less in amount than the differences found 

 by Dr. Hopkinson ("Proceedings of the Royal Society," vol. xxvi, 

 p. 292) between the values of /a, as given by experiment on four kinds 

 of glass, and deduced from three terms of a similar formula, 



. b { c 



I had hoped that, in the case of Iceland spar, it might be found 

 that the quantity p obeyed Huyghens' construction accurately. 



This has proved not to be the case ; the differences are, on the 

 whole, greater than those for the line g, and of the same sign. 



