36 



PROFESSORS G. D. LIVEING AND J. DEWAR 



An inspection of the map shows in several places an arrangement of the lines which 

 suggests an harmonic relation of some sort between them : groups of lines where the 

 successive lines are set at gradually increasing distances and have a gradually 

 diminishing intensity. Such a group may be seen between the wave-lengths 3431 '8 

 and 3450*7, another beginning at X 3368 '8. 



In many cases we find that the distances between the lines of the group are in 

 arithmetic progression, so that the wave-lengths of the group may be represented by 

 a general formula an z + bn + c, the different lines of the group being deduced from 

 this expression by giving n successive integral values. 



Taking the series of strong lines of the spectrum between X 3669'8 and X 3547'7, 

 we find the second differences of wave-length approximately constant, and equal to 

 0'443. Comparing then the observed wave-lengths with a series calculated to have 

 their differences in arithmetic progression with a common difference, 0'443, we find 



In many other groups a similar relation between the wave-lengths may be observed. 



GROUP with second differences of wave-length equal to '3. 



