266 Prof. Powell's Observations on some Points 



and for any other ray of the spectrum, 



±-=^,-pJ^ + ?,6^ (9.) 



Then eliminating H, we have 



= (/.-^,) - ip-p,) fl' + (?-<?,) 9" (10.) 



and 



-(H'-H'j) _ M_ (P-Pi 



= $4_ (£_J^)62 (11.) 



or for abridgement 



-vi=b^-rr- (12.) 



whence by solving the quadratic we obtain 



6'^ = ^+V^-m+ -J (13.) 



in which 



= 10 , ij- (14.) 



120 V X* A*/ 



If then we take the two values /x and /x^ from observation, 

 we readily find 9, and thence again obtain the value of H, by 

 substituting in either of the expressions (8.) (9.). Then, in 

 the same expression for every other ray of the spectrum, sub- 

 stituting 9, we shall find H ; which, if the formula be correct, 

 ought to result the same for every ray. 



This process then, if it be considered allowable, affords 

 this material advantage, that it requires only the assumption 

 of ivao values as given by observation for each medium, which 

 we have just seen is exactly the improvement required in 

 theory. Now though I have not as yet tried the result of 

 calculation precisely in the way above stated, yet it is evi- 

 dent that all the calculations I made in my two first papers 

 in the Phil. Trans., including all the results of Fraunhofer 

 and Rudberg, were conducted on an hypothesis which is in 

 principle identically the same: and in all those it is univer- 

 sally allowed the coincidences are as close as could be de- 

 sired : so that it is evident that this supposition cannot be 

 very far from the truth ; calculation grounded upon it has not 

 yet been applied to more highly dispersive media. But it 

 becomes extremely important to see whether it may be so ap- 

 plicable ; whether it may apply even as well as the methods 

 proposed on the less restricted hypotheses, such as I have em- 



