cob Lias hah ect 
‘ 375 
medium, and out of one medium into another ; but he had 
not attempted to account for his hypotheses, nor to connect 
them together by any known principles of mechanics ; and 
the only evidence in favour of their truth, was the truth 
of the results to which they led. He had observed, how- 
ever, that these hypotheses were not independent of each 
other ; he had ascertained that the laws of reflexion at the 
surface of a crystal were connected with the laws of propa- 
gation in its interior ; and he had thence been led to con- 
clude that all these laws and hypotheses “ had a common 
source in other and more intimate laws not yet discovered.” 
He became impressed, in short, with the idea “ that the 
next step in physical optics would lead to those higher and 
more elementary principles by which the laws of reflexion 
and the laws of prepesasion are linked together as parts of 
the same system.” 
This step the author has now made ; and the present 
paper realises the anticipations scattered through the for- 
mer. Setting out with the general dynamical theorem 
expressed by the ee 
aE 
S§s dadydz (‘4 de °° ae si are aN \= -5 dxdydzdv, (1) 
dt® dt? 
where &, n, Z, are the displacements at the time ¢ of a par- 
ticle whose co-ordinates are x,y, z, and where the density 
| of the ether is supposed to be unity, as being constant for 
all media, the author determines the form of the function v, 
for the particular case of luminiferous vibrations, by means 
of the property which may be regarded as distinguishing 
them from all others—namely, that they take place entirely 
in the surface of the wave. From this property he shows, 
in the first place, that v is a function of the three dif- 
ferences 
dn df d& dé dan. 
ds dy tae dear 
KS 
