1881.] On Harmonic Ratios in the Spectra of Gases. 3^3 



Taking all these considerations into account, the following seems to 

 me to be a fair summary of my results for the iron spectrum : — ■ 



1. There is a real cause acting in a direction opposed to the law of 

 harmonic ratios, so far as fractions formed by numbers smaller than 

 seventy are concerned. 



2. After elimination of the first cause a tendency appears for fractions 

 formed by two lines to cluster round harmonic ratios. 



3. Most probably some law hitherto undiscovered exists, which in special 

 cases resolves itself into the law of harmonic ratios. 



The subject is of sufficient importance to make further investigation 

 desirable. We might, for instance, confirm the laws which we have 

 found to hold in the iron spectrum by treating in the same way some 

 other spectrum having many lines, as those of manganese of calcium , 

 But it seems to me to be more promising to increase the accuracy of 

 measurement in the special cases where harmonic ratios have been 

 found. There are, for instance, two lines in the iron spectrum which 

 are in the ratio of 2 : 3. By using a diffraction grating we might test 

 this coincidence to a great degree of accuracy by seeing how far the 

 more refrangible line in the third spectrum coincides with the less re- 

 frangible line in the second spectrum. Account, of course, must be 

 taken of atmospheric refraction ; reflecting surfaces only ought to be 

 used. I hope to try this plan before long, but in order that others 

 might have the same opportunity, I append a list of all lines which 

 are nearly in the ratio of some fraction formed by integer numbers 

 smaller than ten. 



Angstrom's numbers corrected for atmospheric refraction are used. 

 The table explains itself, but it is perhaps wise to remark again that 

 the number of these coincidences is not larger than one would expect 

 by the theory of probability, and that therefore all of them may prove 

 to be accidental. 





Fraction. 



Calculated. 



Observed. 



Difference. 



6009-33 



2 



3 



4006-22 



4006-03 



- 19 



5603-40 



3 



4 



4202-55 



4202-74 



+ •19 



5598'88 



3 



4 



4199-16 



419916 



±-oo 



5576-59 



3 



4 



4182-44 



4182-53 



+ 13 



5340-82 



3 



4 



4005-62 



4006-03 



+ •41 



6302-47 



4 



5 



5041-98 



5041-67 



-•31 



5430-47 



4 



5 



4344-38 



434433 



-•05 



5340-82 



4 



5 



4272-66 



4272-54 



-12 



5264-07 



4 



5 



4211-26 



4211-09 



-•17 



5227-85 



4 



5 



4182-28 



4182-53 



+ •25 



5193-27 



4 



5 



4154-62 



4154-96 



+ •34 



6231-66 



5 



6 



5193-05 



5193-27 



+ •22 



6003-91 



5 



6 



5003-26 



5003-50 



+ •24 



5987-99 



5 



6 



4989-99 



4989-85 



-•14 



VOL. XXXI. 2 c 



