Manchester Memoirs, Vol. li. (1907), No. 6. 13 



of Mendeleef's intervals. This irregularity can be reduced 

 by adding the term 



-sin{(N - 2)22 - 5*}. 

 to the empirical formula, whereby the system is reduced 

 to 8 groups. The table would now require re-calculating, 

 and though some change in the group intervals would 

 result, these would not differ materially from the mean 

 intervals. As an example of the effect produced by the 

 above added term in throwing together two groups 8 

 intervals apart, take the case of groups V. and XIII. 

 Their mean group positions and the group positions of 

 the individual elements are 



Table III. 



Elements 



N 



V 



As 



Nb 



Group position 



4-68 



487 



5*57 



4-9; 



475 



Difference from mean 



-•07 



+ 0"I2 



+ - 82 



+ 0-18 



+ O'O 





Elements 



Sb 



Pr 



— 



Ta 



Bi 







Group position 



5-21 



4*5° 



— 



4*oi 



4-38 



Difference from mean 



+ 0^46 



-0-25 



— 



-074 



-°"37 



It will thus be seen that should Mendeleeff's system 

 of grouping be correct, then the groups are irregularly 

 spaced in the same way as the notes of the major or minor 

 musical scale are irregular in relation to the tempered 

 chromatic scale, in which each successive semitone has 

 5 '95 per cent, more vibrations than the next lowest one. 



