306 Mr. Earnshaw on the Theory of the Dispersion of Light. 



H and A being constant for the same medium, and the values 

 of K to be used being those which belong to air. 



Both these formulae are of the form -^ — ., but though from 



sm 6 ° 



this circumstance they might be supposed to be similar, they 



do in fact materially differ ; for in the former it is the arc d 



which for different rays is proportional to -, while in the 



A 



latter it is the sin 9 which is proportional to — ; a distinction 



which will be considered very important, when it is remem- 

 bered that the results are expected to be accurate in the third 

 place of decimals, and to approximate to the figure in the 

 fourth place, and that the values of 9 are by no means small. 

 Let us consider the case of flint glass, No. 13: the values of 

 9 in "Research No, I." range from 16° 10' for letter B, to 

 27° 39' for H. In the formula (2.) I find the corresponding 

 values to be IS'^ 21 i' and 27° 22'; consequently the range of 

 9 in the latter case is greater than in the former by above half 

 a degree ; an excess, which, being nearly the 30th part of the 

 value of 9 for B, and about the 20th part of the whole range 

 of 9, must be expected to produce some manifest discrepancy 

 of results. 



As no applications of the formula (2.) have ever, to my 

 knowledge, been made public, I have appended the following 

 tables, which are computed by it. The second and third 

 columns contain the indices of refraction by experiment and 

 by theory, and the last shows the error of theory. In the 

 first table H = 1-6083, and for line B, 9 = 15°21i'; in the 

 second table, the corresponding quantities are H = I'SS^S 

 and 9 = 22° 43'. 



The constants H A were in both these cases determined by 

 assuming the indices for B and H to be the same by theory 

 as experiment. 



