328 REPORT—1899. 
The mean rate of vibration of the rays absorbed by naphthalene is 
less than that absorbed by benzene, and those of anthracene less than 
those of naphthalene. It follows from this that the vibrations within the 
molecules are not independent of but are a consequence of the funda- 
mental molecular vibrations, like the harmonics of a stretched string, or 
a bell, When the rate of the vibration is reduced by the increase in mass 
of the molecule, the rate of vibrations of the carbon atoms is reduced in a 
similar ratio. 
Tn the case of a vibrating string or tuning-fork, greater amplitude of 
vibration means a louder note; in the case of a luminous vibration it 
means a brighter light ; consequently the converse of this should hold 
good, that a greater intensity of absorption is caused by a greater ampli- 
tude of vibration in the molecules of the absorbing medium, the number 
of molecules remaining constant. Hence it follows that as the absorbing 
power of anthracene and naphthalene is, molecule for molecule, greater 
than that of benzene, the amplitude of vibration of the molecules of these 
substances is greater. Now, the mean rate of vibration of the rays 
absorbed by naphthalene and anthracene is less than that of the rays 
absorbed by benzene, though the character of the absorption is the same 
in each case. Hence we may conclude that though the wave-form is 
similar, the amplitude of the vibrations is greater, and the rate of vibra- 
tions is slower. 
From the foregoing views it will be observed that where X is the 
wave-length, 1/A is the oscillation frequency in a small unit of time ; 
omitting the correction for the refraction of air, which is a very small 
amount, and in representing absorption bands by inverse wave-lengths, 
we refer them directly to the oscillation frequencies of the absorbed rays, 
1/\, a very convenient mode of representing them. 
It will be seen in dealing with coloured substances that Gerard Kriiss, 
seven years later, in 1888,! also? gives expression to similar views, which 
are thus stated in his papers. 
Although the kinetic energy of gases gives some account of the trans- 
lation of molecules through space, yet no satisfactory hypothesis has been 
brought forward to illustrate either the rotation of the molecules about 
their own axes, or the interatomic movements within the molecules. 
These two last the author terms ‘inner molecular movements.’ From 
the undulatory theory of light, deductions may be drawn regarding these 
inner molecular movements, inasmuch as the vibrations of the ether, 
which fills the intramolecular space, are a resultant within that space 
of the velocity and amplitude of the molecular vibrations. 
Thus, if \ be the wave-length of a ray emitted by a substance, v the 
velocity of light, the number of vibrations, », which a molecule sends 
forth by movements of it as a whole and of its parts, can be determined 
by the equation, » = x . The phenomena of emission and of absorption 
spectra thus throw some light on the least and most extensive form of 
this inner molecular movement. The latter point is discussed, together 
with relation to the interatomic attraction, which is subject to the chemical 
constitution of the molecule ; inasmuch as the vibrations of the particles 
of a body are capable of being excited only by vibrations of a like period 
1 Ber. vol. xviii. pp. 2586-2591. 
2 Zeitschrift fiir physikalische Chemie, vol. ii, pp. 312~337, 1888. 
