LAW OF CHANGE OF THE AVERAGE SEPARATION OF THE iV-COMPONENTS 



WITH THE WAVE-LENGTH. 



A glance through Tables i and 2 shows that for both iron and titanium the tendency is for the values 

 of AX gradually to increase as we pass to greater wave-lengths, while the values of AX/X^ remain of about 

 the same magnitude throughout. A statistical study of this apparent constancy of the averages AX/X' 

 has been made; and both the range of wave-length and the number of lines available are sufficient to 

 show clearly how the matter stands. 



The method of treatment has been to obtain the mean value of AX/X^ for the M-components for each 

 500 A from X3700 to X6700. When there are two or more pairs of -components the mean of the separa- 

 tions is taken. This is necessary for the sake of consistency if any Hues other than clear triplets or quad- 

 ruplets are to be considered, since the measurement of the widened -components given by a great many 

 lines is merely the mean separation of two or more unresolved pairs. 



The averages thus obtained are presented in Table 7. The means for the six groups of 500 A are 

 given first, then the means for the three groups of 1000 A. These latter are the means for the whole 

 number of Unes considered in the range, not the averages of the means for the 500-groups. Of course, 

 no account can be taken in this summary of the considerable number of Hnes which are described, but 

 whose w-components are not measurable. 



Table 7. Means of AX/X' (-components) for Successive Regions of Wave-length. 



The close agreement of the means shows that there is a real relation, giving an approximate constancy 

 of the values of AX/X- for different parts of the spectrum. Taking the successive means of the 500-groups, 

 the average value for iron is 2.013, for titanium 1.858. The largest deviation from the mean for any 

 group is 8.7 per cent for iron and 9.4 per cent for titanium. For neither element is there any systematic 

 change in the means for successive groups. 



The means for the groups of 1000 A show a still closer agreement, the largest deviation from the mean 

 of these groups being only 1.2 per cent for iron and 6.8 per cent for titanium. 



It will be noticed that the mean values for titanium run smaller than those for iron, although the 

 titanium measurements correspond to the larger field-strength. A number of spectra will have to be 

 examined in this way and the measurements reduced to the same field-strength before we can say what 

 significance, if any, there is in this point. It may prove to be connected with certain properties of the 

 elements concerned. 



It is not difficult to see that this constancy of the mean value of AX/X- depends on the general relation 

 of this quotient to the fundamental interval a, and that it results from the fact that the great majority 



53 



