ON OUR KNOWLEDGE OF SrECTBDM ANALYSIS. 121 



skilful mathematician to solve the inverse problem and to find out the 

 shape of a bell by means of the sounds which it is capable of sending 

 out. And this is the problem -which ultimately spectroscopy hopes to 

 solve in the case of light. In the meantime we must welcome with delight 

 even the smallest step in the desired direction. 



It is the object of the present report to bring together the various 

 attempts which have been made to trace a connection either between the 

 vibrations of the same body, between those of different compounds of the 

 same body, or finally between the vibrations of similarly constituted bodies. 



I. Comiection hetiveen the different periods of Vibration of one Molecide. 



In some acoustical systems the difiTerent periods of vibration are con- 

 nected together by means of a very simple law, and it was a natural idea 

 to trace the same law if possible in the luminous vibrations of molecules. 

 If the law holds good the periods of vibrations or the lengths of the 

 waves of light sent out by molecules ought to be in the ratio of small 

 integer numbers. The first published attempt to trace such a connec- 

 tion is due to Lecoq de Boisbaudran, who investigated the spectrum of 

 nitrogen' with special reference to this point. The spectrum in question, 

 which is the one appearing at low temperatures, is made up of two sets of 

 bands, one reaching fi'om the red into the green, and one reaching from 

 the green into the violet. Lecoq de Boisbaudran tried to show that 

 each band of the second set had a wave-length which was in the ratio of 

 three to four, with a corresponding band of the first set. The author 

 had, however, only a one prism spectroscope at his disposal, and the wave- 

 lengths as determined by him could not possibly possess that accuracy 

 which is necessary for an investigation of this nature. The more accurate 

 measurements of Thalen do not bear oat Lecoq's result. Thus, for 

 instance, two bands, 5064 and 6752, according to Lecoq, are nearly in the 

 required ratio ; if the agreement was perfect the latter number ought to 

 be 6748 ; but Thalen, though giving to the green band a number agreeing 

 fairly well with Lecoq's, puts the red band at 6786, differing very con- 

 siderably from 6754, the required value, if Thalen's measurement for 

 the green band is used. The other coincidences pointed out by Lecoq 

 are similarly disproved by more exact measurements. Inquiries such as 

 those attempted by Lecoq can only be conducted with advantage when 

 we have measured to the highest degree of accuracy which we can 

 obtain in our best instruments, and many of the apparent harmonic ratios 

 which at one time were thought to hold good had to give way when sub- 

 jected to a severer test. Mr. Johnstone Stoney,^ realising this fact, 

 has, however, pointed out one set of harmonic ratios which seems to hold 

 good to a high degree of accuracy. We know of folir hydrogen lines in 

 the visible part of the spectrum, and three of these are found to be in the 

 ratios of 20 ; 27 : 32. The wave-lengths of these lines are amongst 

 those best determined by Angstrom, and they were corrected by Mr. 

 Stoney for atmospheric refraction. The following table exhibits the very 

 remarkable coincidence. 



Table I. 



Observed Wave-length Calculated Values Differences 



h = 4102-37 . i X 131277-14 = 4102-41 . + 004 



F = 486211 . 'J^ X 131277-14 = 4862-12 . + 0-01 



C = 6563 9.^5 . -'- X 131277-14 = 6563-86 - -0 



' C. R. Ixix. p. 694 (1869). « Phil. Mag. xli. p. 291 (1871). 



