12 
oo 
ever, to be fundamentally different from that of M. Cauchy ; 
and in fact he was led to this form of the integral by other 
considerations before he was aware that he had been pre- 
ceded in the deduction. 
The remainder of the present communication is taken up 
with the discussion of the relation between the coefficients 
wu and k, which expresses the law of dispersion. Following 
M. Cauchy,* the author has transformed this relation by 
converting the triple sums into triple integrals; and he has 
found that, by applying this transformation at an earlier 
stage of the investigation, the resulting relation is deduced 
with great simplicity. 
The relation between uw and #, for the vibrations in the 
plane of the wave, has already yielded to M. Cauchy the 
probable result, that the molecules of the ether repel one 
another according to the inverse fourth power of the distance. 
When this law of force is substituted in the corresponding 
relation for the xormal vibration, the author finds that the 
: u ‘ Ae a 
resulting value of ze oF of the velocity of propagation, is in- 
finite ; so that the normal disturbance is propagated énstan- 
taneously, and gives rise to no wave. Thus the hypothesis 
of transversal vibrations seems to be established on theore- 
tical grounds. 
The author finally gives reasons for concluding that the 
theory, inits present form, is insufficient to explain the phe~ 
nomena of light in bodies ; and that it becomes necessary in 
this case to take into account the action of the material 
molecules. This extension of the theory will be given in 
a future communication. 
3. “On the Composition of Thebaine.” By Robert J. 
Kane, M. D., M.R.I.A., Professor of Natural Philosophy 
in the Royal Dublin Society. 
* Nouveaux Exercices de Mathematiques. Livraison 7™°. 
