rism
was less than that of the first, the produced Axes of the Spectrums _tp_
or _2t 2p_ made by that Refraction did cut the produced Axis of the
Spectrum TP in the points _m_ and _n_, a little beyond the Center of
that white round Image S. Whence the proportion of the Line 3_t_T to the
Line 3_p_P was a little greater than the Proportion of 2_t_T or 2_p_P,
and this Proportion a little greater than that of _t_T to _p_P. Now when
the Light of the Spectrum PT falls perpendicularly upon the Wall, those
Lines 3_t_T, 3_p_P, and 2_t_T, and 2_p_P, and _t_T, _p_P, are the
Tangents of the Refractions, and therefore by this Experiment the
Proportions of the Tangents of the Refractions are obtained, from whence
the Proportions of the Sines being derived, they come out equal, so far
as by viewing the Spectrums, and using some mathematical Reasoning I
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