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 Ph nomena of Colours
which could be produced by Refractions. For to do this, there is nothing
else requisite than to find out the Separations of heterogeneous Rays,
and their various Mixtures and Proportions in every Mixture. By this
way of arguing I invented almost all the Ph nomena described in these
Books, beside some others less necessary to the Argument; and by the
successes I met with in the Trials, I dare promise, that to him who
shall argue truly, and then try all things with good Glasses and
sufficient Circumspection, the expected Event will not be wanting. But
he is first to know what Colours will arise from any others mix'd in any
assigned Proportion.
_PROP._ IV. THEOR. III.
_Colours may be produced by Composition which shall be like to the
Colours of homogeneal Light as to the Appearance of Colour, but not as
to the Immutability of Colour and Constitution of Light. And those
Colours by how much they are more compounded by so much are they less
74