9« 





C( 



ilours and then 



Relations. 



[January, 





Observed. 



Calculated. 



Differences + . 



Differences — . 



A. 

 B. 



14-432490 

 13-033840 



I4*4325I7 

 I3*033839 



0*000027 



0*000001 



C. 

 D. 

 E. 



!2-45495o 

 11*189030 

 10 



12*454930 

 11*189003 





0*000020 

 0*000027 



F. 



' 9*225744 



9*225760 



0*000016 





G. 

 H. 



8*175214 

 7*464880 



8*175183 



7*464871 





0*00003I 

 0*000009 





0*000043 



0*000088 



These trifling differences are much within the limits of pro- 

 bable errors of observation. 



The foregoing seven equations give rise to the following 

 more general one, embracing all the wave-lengths : — 



^ + /; + c ^+/+o-+/*=:6E 2 f3E = 630. 

 They also produce the following series :— 



d = 100 c +/+g 



a-\-h-f = 200 a+f 



= 500 



= 600 



b + c 



a + b 



a+c+g+h = 



2a-\-h 



= 700 

 800 



= 3°o 

 = 400 



These relations, taken in connection with the agreement 

 between the wave-lengths calculated from the equations 

 and those obtained from observation, render it in the 

 highest degree probable that they have a true mathematical 

 basis. They show that these wave-lengths are interdepen- 

 dent ; so that no alteration can be made on any one of them 

 without involving a corresponding change in all the rest. 



Here the question arises — Do the intervals between any 

 of those fixed lines among themselves, or between them and 

 any other well known lines in the spectrum, correspond to 

 any of the musical intervals, so as to render it probable that 

 they are harmonically related ? The first case that pre- 

 sents itself for consideration is that of hydrogen, in the spec- 

 trum of which occur two of the principal fixed lines, C and F, 

 besides two other lines, designated as Hy 3 and Hy 4 . As 

 already mentioned, the wave-lengths of the three lines C, 

 F, and Hy 4 stand to each other approximately in the ratio 

 20, 27, 32. Now as respects F and C, the foregoing formulae 

 may be applied to ascertain the accuracy of this relation 

 between those two lines. Do they stand in the precise ratio 

 20 : 27 or 1 : 1*35 ? Taking the observed wave-lengths as 

 given by Angstrom, the ratio is 1 : 1*350206. Taking the 

 wave-lengths calculated from the formulas, the ratio is 



