REFRACTION AND DISPERSION OF THE HALOGENS, HALOGEN ACIDS, ETC. 25 



The refractivity can be expressed by the formula 



i\D 5-6685 x 10". 



' 



Thr calculated values are shown in column 3 and the differences in column 4. 



ERRORS OF EXPERIMENT. 



Refraction. In the determination of the refractivities for the green, mercury line 

 the principal source of error is the impurity of the gas, and, in the case of vapours 

 which absorb light, such as the halogens and sulphur, the limitation of the number of 

 bands which can be read before the light fails. 



It will be seen that experiments of a series generally agreed to 1 part in 500, and 

 the mean is probably within 1 in a 1000 of the truth. In iodine and ozone, however, 

 the errors may amount to 1 or 2 per cent. 



Dispersion. It will be observed that the values of the refractivities for the other 

 seven wave-lengths are relative to that found for the green mercury line. 



The degree of accuracy attainable depends on the number of bands read and the 

 dispersive power of the gas. As an example take nitric oxide. 



Here O-l]*.^ = '00029306, Gu-l]A = 4o = "00029776. 



The dispersive power is 297 .^~^ 3<)6 = 2 * 6 ; and if 400 green bands are counted, 

 the number which represents the effect of dispersion is 1 2 a i , 8 7 Q 7 u a = 6'3 bands. We 

 consider that 1/15 of a band can be read; so that the value of the dispersive power 

 should be correct to 1 part in 95. It may be assumed that by determining the 

 constants from eight independent values of the refractivity instead of two the 

 accuracy is at least doubled, and the error should not exceed 1/200 of the effect 

 itself. 



This claim is supported by the experimental results. Thus, in the six experiments 

 from which the dispersion of HC1 was determined, the values of (/*&& /u^oo) * 10 8 were 

 816, 815, 813, 818, 805. 



In eight experiments on HBr they were 1370, 1388, 1393, 1356, 1372, 1376, 1368, 

 1363. 



CALCULATION OF THE CONSTANTS. 



The calculation of the constants N and n of the formula /* 1 = N/( a 2 ) by the 

 method of least squares is very laborious if carried out in the ordinary manner. The 

 following modification was, therefore, adopted. Using subscripts to denote the eight 

 refractive indices and their frequencies we have eight equations of the fonn 



_1_ -n : ' 



M,-l " N 



.. VOL. CCXIII. - A. E 



