M. Rudberg on the Dispersion of Light. 403 



Although the differences between the calculated and the 

 observed lengths are very small, they are not without influence 

 when we wish to pass from the lengths of undulation to the 

 indices of refraction. But the lengths of undulation in the air 

 not being themselves certainly accurate to a thousandth, and 

 the indices of refraction having a precision at least ten times 

 greater, I have taken the relation between the indices such as 

 it is derived from the supposed ratio to the lengths of undula- 

 tion, and have then compared it with observation. Calling 

 the index of refraction N, we have: 



,Wl— 1 



a I 



in which, if N' V belong to another ray : 



"n' ~ \T"/ 

 In another substance, if n, n' are the indices corresponding 

 to the same lengths I, l\ we shall have : ii = -, and also 



■^ = (-^y^ ' whence, consequently, if r = ^^^: 



IT' ~ \~n ) ' 



In which equation r ought to be constant. In taking for N 

 the indices of flint-glass. No. 13, and for n the indices of water, 

 we find, For the rays B and C : r = 2-0430 



B and D : r = 2-2928 



B and E : r = 2-3802 



B and F : r = 2-4203 



B and G : /• = 2-5476 



B and H : r = 2-G402. 

 These values are not precisely the same: the difference be- 

 tween them however has not a great influence in the present 

 case, a small variation in the indices producing a considerable 

 one in ;•; ifj for example, instead of the index of the ray C in 

 flint-glass, which = 1-G297, 1-6298 betaken, we have r = 

 2-1452 instead of 2-0430; also in taking the mean = 2-39 of 

 all these values, and calculating the indices of flint-glass ac- 

 cording to those of water, according to the formula: 



we have the second column of this table: 



