the Lines of various Spectra. 47 



In order to test Corrm's theory of the connexion between 

 aluminium and hydrogen, I have measured with some care 

 the wave-lengths of the aluminium pairs as photographed by 

 Prof. Rowland. The wave-lengths of the hydrogen hues 

 were determined by myself. Cornu's theory, stated con- 

 cisely, is that for aluminium 



X = a + b Xj, 



where \ is the wave-length of a hydrogen line. According 

 to Cornu the following lines correspond : — 



Al. H. 



2373-2 4340-66 



2269-2 4101-85 



2210-15 3970-25 



2174-0 3889-15 



2150-4 3835-6 



If his theory is true, the ratios of the differences of each two 

 consecutive lines should be the same for each series. Taking 

 the first three lines of each, we find the ratio 1*76 for 

 aluminium and 1*81 for hydrogen. The other ratios agree 

 better ; but still the difference is too great. 



As noted above in the historical sketchy the law that the 

 second differences of the wave-numbers of the lines forming a 

 band is constant, is approximately true. Xo general law more 

 exact than this can, I think, be deduced with our present 

 knowledge. But there seems to be some connexion between 

 the lines forming a band and those in a series like the 

 hydrogen ones : the former may be regarded as forming the 

 " head " of this latter series. There is this true, however : 

 the bands can run in either direction, towards the red or 

 towards the ultra-violet ; while the series always turn one 

 way. But, in spite of this, it may not be without use to 

 show that the bands and the series are connected mathe- 

 matically. 



Banner's law for the distribution of the hydrogen lines, 

 stated in a slightly more general form, is : — 



- = a(l + — - — g), 772 = 0,1,2... 



A, \ C + 7/7// 7 ; 



If we substitute in this 



m = M — n, n = 0, 1, 2 . . ., 



where M is a constant many times as great as n, we have 



i = A + Bn + Cn* + &c, 



