206 Mr. S. P. Langley's Experimental Determination of 



determined, are wholly untrustworthy, as will appear more 

 fully later. 



Bedtenbacher proposes the formula 



1 c 



— 2 =a + b\ 2 +T^ 

 n* X 



for expressing the same relation. Using the same lines as 

 before for determining the unknown constants, we have for 

 the Hilger prism, 



- 2 =0'412297^0'00093711X 2 ^ ' 00 , 3 2 922 ° ; 

 n 2 A 2 



a formula which also satisfies the observations in the visible 

 spectrum, but fails when extended to the invisible. The 

 curve representing it has a minimum point, corresponding to 



?i = l'5647 for a value of A found from the equation X 4 =y; or 



in the special case of the formula above, where j is positive, 



\= 1'430 ; so that for every value of n greater than T5647 

 there are two real values of A. This formula therefore is even 

 less satisfactory than that of Cauchy. 



Briot gives a formula which has been asserted by other 

 investigators* to represent satisfactorily the results of obser- 

 vation throughout the whole spectrum, namely 



From four equations like this, using values of n and X cor- 

 responding to the Fraunhofer lines A, C, F, and H, the values 

 of the constants were determined! as follows: — 



a=O41028, b= -0-0013495, c= -0*000003379, 

 £=+0-0022329. 



With the aid of these constants the wave-lengths corre- 

 sponding to given refractive indices were computed, and a 

 curve representing the formula was plotted. This curve, as 

 well as those representing Cauchy's and Redtenbacher's 

 formulae, is shown in Plate VIII., where we may obtain by 

 simple inspection the actual errors of all the formulae in 

 question ; or we may take them from the following table, 



* Mouton, Comptes Rendiis, vol. lxxxix. p. 291, and vol. lxxxiii. p. 1190. 



t This formula has the practical inconvenience of leading to cubic 

 equations, either in n 2 or X 2 , the solution of which is so tedious as to 

 forbid its use where many places are to be independently found. I have 

 been aided in the present lengthy numerical computations by Professor 

 M. 15. Goff. 



