70 



PROFESSOR POWELL'S RESEARCHES TOWARDS ESTABLISHING 



In order to simplify the numerical calculations, it is found convenient to regard the 

 two last terms of the formula as involving factors which are respectively some power 

 of ten in the numerators, to the same amount as the number of places which would 

 be found in the values of X^ and X^ in the denominators. 



In applying the theory to the cases of particular media, we have to combine the 

 values in the above Table with those of the indices obtained from observation. These 

 I have taken from my own approximate determinations, as originally given in a sepa- 

 rate memoir, and quoted in my last paper in the Philosophical Transactions, 1837? 

 Part I. 



In the following cases therefore the logarithms of X^ are taken as above, and after 



deriving those of l—j and of ( — ) a common index 4 is added : from these we ob- 

 tain in the first instance the values ofq and /, and thence again those of jo for each ray. 

 I have not, in the present instance, thought it necessary to go through these some- 

 what laborious calculations for more than those three cases which in my former in- 

 vestigations appeared to present the greatest discrepancies with theory, viz. the oil of 

 cassia, which gave the greatest discordances ; and the two sets of observations on 

 sulphuret of carbon at the respective temperatures of 12° and 22° centigrade. 



Comparison of observed refractive indices with the results o/Mv. Kelland*s theory. 



