118 



Rev. Prof. Powell on the Formula 



as before, with the approximate results of my former compu- 

 tation, performed by methods which will now be wholly su- 

 perseded. 



The preceding method enables us to calculate the indices 

 for C, D, E and G, supposing those for B, F, and H assumed. 

 It may, however, be desirable, for rendering the comparison 

 of any case with theory complete and satisfactory, to possess 

 the means of calculating likewise the indices for B, F, or H, 

 assuming three others, or generally any index. For this pur- 

 pose we must have recourse to the more general form (21.). 

 This will not, in fact, be found more complex or difficult in 

 practice, notwithstanding the simplification obtained by intro- 

 ducing the particular relation subsisting between Xp Tj^ and Tj^ 

 on which the process above given depends. I shall therefore 

 here add such a statement of the more general method as may 

 be necessary for the object in view, and likewise furnish those 

 constants which are independent of the particular medium, 

 and necessary for the computation. 



The formula (21.) may be expressed, for brevity, thus: 



= (f^D-^s) ^ - W-f^s) ^ + (/^h-^b) "'' 

 and the coefficients k I m which are independent of the me- 

 dium are readily found from Fraunhofer's values of t^ t^ t^ t^^. 

 From these values we have directly 



Tb^ = 15-489 Tp- = 21-135 



T-2 = 31-075 V = 'K>.666, 



and by means of these we obtain for the coefficients in (21.) 

 the following values : 



