350 Spontaneously Reversible Spectral Rays. TJune, 
What a palace in cloudland would G. H. von Schubert 
and Heinrich Steffens have built up from these analogies 
had they been known half a century ago ! . 
Unfortunately the simplicity of these numencal lelations 
always vanishes if we substitute for the contemplation of the 
spedtral images a precise numerical deteimination of the 
wave lengths. The path of speculation therefore seems in 
that direction as if brought to an abrupt close. 
This want of success, however, should not discourage 
observers, though the hope of finding a simple law like that 
of musical harmonics springs from a pieconceived idea which 
should at once be swept aside. This law of whole numbeis 
applies only to a very special form of sonoious bodies, the 
type of which is a cylindrical column ofveiygieat length as 
compared with its section. If the form of a vibrating, body 
deviates from this special type the relation between the 
numbers of the vibrations of the successive notes becomes 
very complex. . 
This simple remark is sufficient to show that it would be 
childish to seek for a general law in a relation as simple as 
that of the harmonics of musical instruments. This would 
be to invest the structure of incandescent molecules with a 
mechanical constitution, which neither chemical noi phy- 
sical phenomena seem to justify. Less simple laws do not 
succeed better, and this need not surprise us. The foie* 
going considerations show that we might expect tofind, inoidei 
to define the distribution of the spectral rays, very complex 
fundtions depending on the chemical natuie of the element, 
on the molecular strudture of the vapour, and the conditions 
of vibratory excitement. 
In fadt what appears to have smitten with barrenness all 
efforts made towards the solution of the problem, is that 
observers have thought it necessary to impose upon them- 
selves a priori the fundtion destined to lepiesent the succes- 
sion of spedtral rays. On the contrary, M. Cornu thinks it 
necessary to rejedt every preconceived idea as to the mathe- 
matical expression of the phenomenon, and to search expeii- 
mentally if there do not exist special fundtions, whether 
expressible or not by the ordinary analytical symbols, which 
are capable of uniting under some common law these series 
whose regularity and periodicity are evidently not fortuitous. 
Considered from this point of view the question assumes 
a novel phase. The immediate problem consists in search- 
ing, if there are not found in all spedtra certain groups of 
rays presenting characters in common, independently of the 
chemical nature of the incandescent vapour. 
