TRANSACTIONS OF THE SECTIONS. 3 
mencing with Fresnel, more than half a century ago, the history of physical optics 
is a history of efforts, constantly repeated, to frame what M. de St. Venant has 
called “a really rational theory of light.” 
Take, for example, the repeated attempts to reconcile the mechanical principle of 
continuity with the optical phenomenon of double refraction. When the movement 
which we call light passes from one medium to another, if the molecular movement 
be continuous, it is hard to see how the elastic force of the «ther can be different 
at different sides of the plane of separation. It would seem, then, that the principle 
requires that the elastic force of the ether should be the same in all media. But if 
it be the same in a crystalline as in an uncrystalline medium, it ought to be the 
same in every direction; and if it be the same in every direction, how are we to 
account for the phenomenon of double refraction? The effort to overcome this 
difficulty may be said to have engaged the attention of Cauchy during all the latter 
part of his life. The same question was taken up after his death by other writers, 
among whom I may mention M. Boussinesq as the most recent, and is to this day 
a question of great interest to mathematical physicists. Iam not now inquiring 
whether the reasoning which I have just stated be valid, or whether the difficulty, 
which some writers do not appear to haye felt, be real. I allude to it only as a 
proof of the anxiety felt by men who have borne the greatest names in optical 
science to have a complete mechanical theory of light. It would be easy to mul- 
tiply instances, affecting all the great phenomena of optics, which evince the same 
anxiety. 
Mescther and even stronger proof of the firm footing which the undulatory theory 
has obtained in the world of science is the familiarity with which we use the terms 
of that theory, as if they denoted actual physical realities. When, not long since, 
much labour was expended in calculating the wave-lengths for the several rays of 
the spectrum, there does not appear to have been among physicists any conscious- 
ness that they were discussing, and even professing to measure, things which had 
no existence but in the fancy of mathematicians. On the contrary, we have come 
to speak of wave-lengths quite as freely and as familiarly as we speak of indices of 
refraction. Nor is this true only of detached memoirs, which might be supposed to 
represent only individual opinion. The language and the principles of the undu- 
latory theory have found their way into our ordinary text-books—a sure proof that 
these principles have been generally accepted by the scientific world. Iam notnow 
discussing the question whether, regarded as an indication of scientific progress, this 
fact is favourable or unfavourable. I only say that it zs a fact. M. Comte has done 
all that the hard words of a man of great genius could do to banish theories of 
light from the domain of science, but his greatest admirer will hardly say that he 
has been successful. 
I pass to the consideration of another branch of science, closely connected with, 
and indeed including, physical optics, and exemplifying, even more strongly, the 
desire of scientific men to extend the sway of mathematics over physical science— 
I mean, Molecular Mechanics. This branch of mechanical science (if, indeed, it be 
not more correct to say, this science) is altogether modern. Fifty years ago it had 
hardly begun to exist, and even now it is in a very imperfect condition. Imperfect 
as it is, however, it has advanced far enough to mark the progress of science in the 
direction which I have indicated. And as itis ascience more general than physical 
optics, the indications which we can gather from it are more important. Physical 
optics does not take us outside our own Section; molecular mechanics shows a 
marked tendency to carry mathematical analysis into the domain of chemistry. If 
it shall ever be possible to establish an intimate connexion between this latter 
science and theoretical mechanics, it is probably here that we shall find the con- 
necting link. In truth it is impossible to contemplate the ever-growing tendency 
of science to see in so many natural phenomena varieties of motion, without anti- 
cipating a time when mathematical dynamics (the science which has already 
SB iliced so many of the phenomena of motion beneath the power of mathematical 
analysis) shall be admitted to be the universal interpreter of nature, as completely 
as it is now admitted to be the interpreter of the motions of the planets. I do not 
say that it will ever be. I do not even say that it is possible. It is no true philo- 
sophy which dogmatizes on the future of science. But it iscertain that the current 
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