t
of divers denser Mediums immediately into one and the same rarer Medium,
suppose of Air, are to one another in a given Proportion.

2. The Proportion of the Sine of Incidence to the Sine of Refraction of
one and the same sort of Rays out of one Medium into another, is
composed of the Proportion of the Sine of Incidence to the Sine of
Refraction out of the first Medium into any third Medium, and of the
Proportion of the Sine of Incidence to the Sine of Refraction out of
that third Medium into the second Medium.

By the first Theorem the Refractions of the Rays of every sort made out
of any Medium into Air are known by having the Refraction of the Rays of
any one sort. As for instance, if the Refractions of the Rays of every
sort out of Rain-water into Air be desired, let the common Sine of
Incidence out of Glass into Air be subducted from the Sines of
Refraction, and the Excesses will be 27, 27-1/8, 27-1/5, 27-1/3, 27-1/2,
27-2/3, 27-7/9, 28. Suppose now that the Sine of Incidence of the least
refrangible Rays be to their Sine of Refraction out of Rain-water into
Air as 3 to 4, and say as 1 the difference of those Sines is to 3 the
Sine of Incidence, so is 27 the least of the Excesses above-mentioned to
a fourth Number 81; and 81 will be the common Sine of Incidence out of
Rain-water into Air, to which Sine if you add all the above-mentioned
Excesses, you will have the desired Sines of the Refractions 108,
108-1/8, 108-1/5, 108-1/3, 108-1/2, 108-2/3, 108-7/9, 109.

By the latter Theorem the Refraction out of one Medium into another is
gathered as often as you have the Refractions out of them both into any
third Medium. As if the Sine of Incidence of any Ray out of Glass into
Air be to its Sine of Refraction, as 20 to 31, and the Sine of Incidence
of the same Ray out of Air into Water, be to its Sine of Refraction as 4
to 3; the Sine of Incidence of that Ray out of Glass into Water will be
to its Sine of Refraction as 20 to 31 and 4 to 3 jointly, that is, as
the Factum of 20 and 4 to the Factum of 31 and 3, or as 80 to 93.

And these Theorems being admitted into Opticks, there would be scope
enough of handling that Science voluminously after a new manner,[K] not
only by teaching those things which tend to the perfection of Vision,
but also by determining mathematically all kinds of Phaenomena of Colours
which could be produced by Refractions. For to do this, there is nothing
else requisite than to find out the Separa