252 Mr. W. Sutherland on the 



2. A Special Series in the Magnesium Spectrum, confirming 

 the existence of Optical Harmonics. 

 The main lines in the Mg spectrum can be well represented 

 as two sets of triplets having the following equations of the 

 Rydberg type as given in (2) , but with B treated as a some- 

 what variable parameter, namely, 



3973(n 1A , l)on 



n= 39770 £_ 104320_ 

 39790 J + -26) 2 



39730") in70 - n 

 n=39770>- 1Q725 ° . 



39790 J (m-h-8) 2 



But amongst the subordinate lines of the Mg spectrum 

 there is an exceptional series to which Bydberg drew 

 attention, as his type of equation fails to apply to it, and he 

 is constrained to use a cumbersome expression for its repre- 

 sentation (Wied. Ann. I. 1893). The wave-lengths X and the 

 wave-numbers n of these are 



X... 5528-75 4703-33 4352-18 4167*81 4058-85 3987-08 

 n... 18087-27 21261-53 22976*99 23993-41 24639-95 25081*01 



If we assume that the values of n come under our formula 

 »=39730- 10725 ° 



[m + n)-> 



and calculate the values of m+^ we get 



2-226 2-410 2-530 2*6106 2-666 2*706 



which, when subtracted from the integer 3, give the re- 

 mainders 



•774 -590 -470 -3894 -334 -294 



and these, when multiplied respectively by the successive 

 integers from 3 to 8, give the products 



2-322 2-360 2*350 2-3364 2'338 2*352 ... (A) 



of which the mean value is 2 343, and therefore the values 

 of m + /jl are nearly of the form 3 — 2-343/s where s has the 

 integral values from 3 to 8. This formula gives for m + fu, 

 2*219 2*4143 2*5314 2*6095 2*6653 2*707, 



the maximum departure of which from the original values 

 given above amounts to 32 parts in 10,000. If, then, we 

 calculate the wave-numbers for this peculiar series of Mg by 



