PROFESSOR STOKES ON THE CHANGE OF REFRANGIBILITY OF LIGHT. 551 
placements. For simplicity’s sake, let us suppose for the present the parts of the 
foi’ces of restitution depending upon first powers of the displacements to be abso- 
lutely null. Then, when a molecule is disturbed, its atoms will be acted on by 
forces depending upon the second and higher powers of the displacements. These 
forces must tend to restore the atoms to their mean positions ; otherwise the equi- 
librium would be unstable, and the atoms would enter into new combinations, either 
with one another, or with the atoms of the surrounding medium ; so that, in fact, 
such compounds could never be formed. The condition of stability would require the 
parts of the forces depending upon squares of the displacements to vanish, but this 
is a point which need not be attended to, all that is essential to bear in mind being, 
that we have forces of restitution varying in a higher ratio than the displacements. 
If the parts of the forces of restitution which depend upon first powers of the dis- 
placements, though not absolutely null, be very small, the remaining parts must still 
be such as to tend to restore the atoms to their positions of equilibrium ; otherwise 
the stability of the molecule, though not mathematically null, would be so very 
slight, that such compounds would probably never form themselves, but others of 
more stability would be formed instead. Or, even were such unstable compounds 
formed, they would probably be decomposed on attempting to excite them in the 
manner in which sensitive substances are excited in observing the phenomena of 
internal dispersion ; so that whether they exist or not, they may be set aside in con- 
sidering these phenomena. 
2.31. Now when vibrations are performed under the action of forces which vary 
in a higher ratio than the displacements, the periodic times are not constant, but 
depend upon the amplitudes of vibration, being greater or less according as the 
amplitudes are less or greater. Suppose the molecular and ethereal vibrations 
already going on, and imagine the amplitudes of the former kept constant by the 
application of external forces. According to the value of the epoch of the vibrations 
of a particular molecule, the ethereal vibrations will tend, in the mean of several 
successive undulations, to augment or to check the vibrations of the molecule. For 
some time there will be a tendency one way, then for some time a tendency the 
other way, and so on, the opposite tendencies balancing each other in the long run. 
The lengths of the times during which the tendency lies in one direction, will depend 
upon the periodic times of the molecular and ethereal vibrations, being on the whole 
greater or less according as the two periodic times are more or less nearly equal. 
But since no external forces actually act to keep the amplitudes constant, when the 
ethereal vibrations are favourable to disturbance the molecule is further disturbed, 
and therefore its periodic time is diminished; and when they are favourable to qui- 
escence the disturbance of the molecule is checked, and therefore its periodic time is 
increased. If, then, the ether be vibrating more rapidly than the molecule, when the 
action is favourable to disturbance the periodic time of the molecular vibrations is 
rendered more nearly equal to that of the ethereal vibrations, and therefore the time 
4 B 
MDCCCLII. 
