•"'Hit s,;, ntijir Inti. lligt nee. 



Wood on resonance spectra has been successfully attacked l>v 

 L Sii.r.Kusrioix. since the paper requires a fairly large amount 

 of elementary mathematics for the adequate exposition of the 



subject, the following non-analytic outline is, in the very nature 

 of the ease, only suggestive and highly fragmentary. 



A resonator obeying the equation x + kx + A J -.r — is called 

 a Hookean resonator by the author for the obvious reason that 

 the institutive force is assumed to conform to Hooke's law (force 

 = N^x/m). When such an oscillator is acted upon by an external 

 force of frequency n it will execute vibrations of the same fre- 

 quency a but will not perform oscillations of any other frequency. 

 Consequently this simple type of resonator cannot be responsible 

 for all the lines of one series in Wood's resonance spectrum. If, 

 on the other hand, the term N'x be replaced by a non-linear 

 function of x, an impressed force of frequency N will stimulate 

 oscillations of frequency N together with an infinite number of 

 other frequencies. It follows at once that the excitation and 

 emission of fluorescent line spectra may be described mathemat- 

 ically by writing either x + kx + j¥*x = c u e iNt + e^" 1 ' + c^e'"-' + 

 . . ., or x + kx + JV 2 x + f(x) = c o e' Nl . The first equation is tan- 

 tamount to postulating that the atoms of the radiating vapor 

 behave as if each contained a Hookean resonator under the simul- 

 taneous action of forces of all the frequencies n a = JV, w„ ».,, rc 3 , 

 etc. The second equation is an expression of the hypothesis that 

 each atom contains an appropriate non-Hookean resonator acted 

 upon by c a e' M /m oidy. f(x) is some non-linear function of the 

 displacement. The equivalence of the two methods of treatment 

 is manifest, for the non-Hookean resonator will be the "appro- 

 priate " one when, and only when, the supplementary term -f(x) 

 ultimately reduces to c^'" 1 ' + c 2 e'" 2 ' + . . . The first equation is 

 best adapted to the study of the properties of each line of the 

 spectrum separately, whereas the second form is required only 

 when we desire to make a guess concerning the law of succession 

 of the lines of the spectrum. So much for the underlying prin- 

 ciples of the mathematical investigation. 



By making use of the second equation and assuming the form 

 ax'' ior f(x) Silberstein deduces the solution Hj== M — j(l — p)N~, 

 j = 0, 1,2,3,. . ., whence 8h = ( I —p)N. This means that the 

 lines of the resonance spectrum succeed one another at constant 

 frequency-intervals. When Wood's wave-lengths for iodine fluo- 

 rescence are transformed into numbers proportional to their fre- 

 quencies, it is found that the intervals are constant within the 

 given limits of experimental error. Hence the theory accords 

 with the facts. The values of p for three different series are 

 0-9889, 0-9882, and 0-9881 corresponding respectively to- 

 8n = 202-53, 203-ei, -and 205-38. 



Throughout the rest of the paper the first equation is alone 

 employed. The author deduces the following results which are 

 especially important for the reasons that none is in contradiction 

 with known facts, new phenomena are predicted, and unexplored 



