592 DR J. HALM ON 
the RypperG-THIELE formula could thus be experimentally demonstrated. Turning to — ' 
the upper part of the diagram, we find the transversals exhibiting the arrangements 
of lines in all the principal series. A smaller scale has been adopted in this case 
in order to keep the drawing within convenient dimensions, but otherwise the lines 
have been constructed on exactly the same principle as before. With regard to 
the intensity of the lines it must be noted as a general rule that the lines are strongest 
near the head and gradually decrease in brightness towards the tail, and that this rule 
applies to line-series as well as to band-series. Lastly, four specimens of band-spectra 
are exhibited by the four transversals nearly parallel to the ray Ow. In these cases, 
however, the scale had to be considerably enlarged, since otherwise the transversals 
would have been too close to Ow. The four series belong to the group »=0, and the 
drawing is so arranged that the points of intersection with the rays O,,0,,0,.... 
represent the 10th, 20th, 30th . . . . line of the band. 
In his researches on the band-series M. DesLanpres points out that the wave- 
frequencies of the lines of such a series are arranged in a manner similar to those of the 
sound-vibrations produced by an elastic transversely vibrating rod. Indeed we recognise 
without difficulty that the series of sound-vibrations are represented in our diagram by 
transversals parallel to O.. or it is well known from the mathematical investigations 
of Poisson, SEEBECK and others, that the wave-frequencies of the stationary transverse 
oscillations in a vibrating rod, with the exception of the two lowest vibrations, can be 
expressed by the relation 
vy _ (m+p)? 
ve (@+ ph)” 
where w depends on certain conditions under which the vibrations take place. But 
this equation is obviously of the form 
Ie a 
a Ceo CES “— 
and therefore agrees with the first of (5), if we assume v. =o, 1.e. if the transversal is 
parallel to Ow». The remarkable analogy between the sound-vibrations of an elastic 
body and the light-vibrations of a radiating atom or molecule is at least suggestive, 
Is it not, for instance, conceivable that the latter are caused by ‘standing waves” in 
the elastic system of electrons which constitutes the atom? If it were possible to find 
an elastic body of such shape and internal conditions that its transverse vibrations 
would satisfy the equation 
1 a 
= b, 18 
y—v, (m+pp—(@+ pp” io 
where b is a constant, instead of the simpler relation (17), which refers to the special 
conditions in a uniform rod, the series of transverse sound-vibrations emitted by such a 
body would be exactly analogous to the series of light-vibrations emitted by the radiating 
atoms of a gas or vapour. We could then, by varying the conditions on which 
depends, represent the acoustic analogies to the whole range of spectral phenomena 
