could estimate. For I did not make an accurate Computation. So then the
Proposition holds true in every Ray apart, so far as appears by
Experiment. And that it is accurately true, may be demonstrated upon
this Supposition. _That Bodies refract Light by acting upon its Rays in
Lines perpendicular to their Surfaces._ But in order to this
Demonstration, I must distinguish the Motion of every Ray into two
Motions, the one perpendicular to the refracting Surface, the other
parallel to it, and concerning the perpendicular Motion lay down the
following Proposition.
If any Motion or moving thing whatsoever be incident with any Velocity
on any broad and thin space terminated on both sides by two parallel
Planes, and in its Passage through that space be urged perpendicularly
towards the farther Plane by any force which at given distances from the
Plane is of given Quantities; the perpendicular velocity of that Motion
or Thing, at its emerging out of that space, shall be always equal to
the square Root of the sum of the square of the perpendicular velocity
of that Motion or Thing at its Incidence on that space; and of the
square of the perpendicular velocity which that Motion or Thing would
have at its Emergence, if at its Incidence its perpendicular velocity
was infinitely little.
And the same Proposition holds true of any Motion or Thing
perpendicularly retarded in its passage through that space, if instead
of the sum of the two Squares you take their difference. The
Demonstration Mathematicians will easily find out, and therefore I shall
not trouble the Reader with it.
Suppose now that a Ray coming most obliquely in the Line MC [in _Fig._
1.] be refracted at C by the Plane RS into the Line CN, and if it be
required to find the Line CE, into which any other Ray AC shall be
refracted; let MC, AD, be the Sines of Incidence of the two Rays, and
NG, EF, their Sines of Refraction, and let the equal Motions of the
incident Rays be represented by the equal Lines MC and AC, and the
Motion MC being considered as parallel to the refracting Plane, let the
other Motion AC be distinguished into two Motions AD and DC, one of
which AD is parallel, and the other DC perpendicular to the refracting
Surface. In like manner, let the Motions of the emerging Rays be
distinguish'd into two, whereof the perpendicular ones are MC/NG CG
and AD/EF CF. And if the force of the refracting Plane begins to act
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