le to penetrate into the
other transparent substance. For if the angle DAQ or CBA is such that
in the triangle ACB, CB is equal to 2/3 of AB, or is greater, then AN
cannot form one side of the triangle ANB, since it becomes equal to or
greater than AB: so that the portion of wave BN cannot be found
anywhere, neither consequently can AN, which ought to be perpendicular
to it. And thus the incident ray DA does not then pierce the surface
AB.

When the ratio of the velocities of the waves is as two to three, as
in our example, which is that which obtains for glass and air, the
angle DAQ must be more than 48 degrees 11 minutes in order that the
ray DA may be able to pass by refraction. And when the ratio of the
velocities is as 3 to 4, as it is very nearly in water and air, this
angle DAQ must exceed 41 degrees 24 minutes. And this accords
perfectly with experiment.

But it might here be asked: since the meeting of the wave AC against
the surface AB ought to produce movement in the matter which is on the
other side, why does no light pass there? To which the reply is easy
if one remembers what has been said before. For although it generates
an infinitude of partial waves in the matter which is at the other
side of AB, these waves never have a common tangent line (either
straight or curved) at the same moment; and so there is no line
terminating the propagation of the wave AC beyond the plane AB, nor
any place where the movement is gathered together in sufficiently
great quantity to produce light. And one will easily see the truth of
this, namely that CB being larger than 2/3 of AB, the waves excited
beyond the plane AB will have no common tangent if about the centres K
one then draws circles having radii equal to 3/2 of the lengths LB to
which they correspond. For all these circles will be enclosed in one
another and will all pass beyond the point B.

Now it is to be remarked that from the moment when the angle DAQ is
smaller than is requisite to permit the refracted ray DA to pass into
the other transparent substance, one finds that the interior reflexion
which occurs at the surface AB is much augmented in brightness, as is
easy to realize by experiment with a triangular prism; and for this
our theory can afford this reason. When the angle DAQ is still large
enough to enable the ray DA to pass, it is evident that the light from
the portion AC of the wave is collected in a minimum space when it
reaches BN. It appears al