6-7 Page Isaac Newton Book

 [ 6 ] Refraction be created out of Air into Water, the sin of Incidence of the red light-weight is to the sin of its Refraction as four to three. If out of Air into Glafs, the Sines square measure as I7 to II. In light-weight of alternative colors the Sines produce other Proportions: however the distinction is FO very little that it want feldom be confidered.

Suppofe so, that R S [ in Fig. I. ] repre-fents the Surface of ftagnating Water, which C within the purpose of Incidenec within which any Ray coming back within the Air from A within the Line A C is mirrored or refracted, and that i would understand whither this Ray fhall follow Reflexion: I erectupon the Surface of the Water from the purpose of Incidence the Perpendicular C P and turn out it downwardly to letter, and conclude by the firft Axiom, that the Ray when Reflexion and Re-fraction, Fhall be Found fomewhere within the Plane of the Angle of Incidence A C P made.

I Let fall so upon the Perpendicular C P the sin of Incidence A D; and if the mirrored Ray be defired, I turn out A D to B of that decibel be adequate to AD, and draw C B.

For this Line C B Fhall be the mirrored Ray; the Angle of Reflexion B C P and its sin B D being e-qual to the Angle and sin of Incidence, as they got to be by the fecond Axiom.

however if the refracted Ray be defired, I turn out A D to H, FO that D H is also to A D because the sin of Re-fraction to the sin of Incdence, that's ( if the sunshine be red ) as three to 4; and concerning the middle C and within the Plane A C P with the Radius C A defcribing a Circle A BE, I draw Parallel to the Perpendicular C P letter the road H E cutting the

Circun-

[ 7 ]

Circumference in E, and joyning metallic element, this Line metallic element fhall be the road of the refracted Ray.

For if E F be let fall sheer on the

Line PQ, this Line E F fhall be the trigonometric function of Re-

fraction of the Ray metallic element, the Angle of Refraction being ECQ; and this trigonometric function E F is adequate to DH,

and conſequently in Proportion to the trigonometric function of

Incidence AD as three to four.

In like manner, if there be a Priſm of Glaſs

(that could be a could be a with 2 Equal and

Parallel Triangular ends, and 3 plain and

well poliſhed Sides, that meet in 3 Parallel Lines running from the 3 Angles of 1 finish to the 3 Angles of the opposite end) and if the Refraction of the sunshine in pafling croſs this Priſm be deſired: Let ACB [in F'ig. 2.] repreſent a Plane cutting this Priſm tranverfly to its 3 Parallel lines or edges there wherever the sunshine the sunshine it, and let D E be the Ray inci- dent upon the firſt ſide of the Priſm AC wherever the sunshine goes into the Glaſs ; and by swing

the Proportion of the trigonometric function of Incidence to the

Sine of Refraction as seventeen to i realize E F the firſt

refracted Ray. Then taking this Ray for the

Incident Ray upon the ſecond ſide of the Glaſs

BC wherever the sunshine goes out, realize consecutive

refracted Ray FG by swing the Proportion

of the trigonometric function of Incidence to the trigonometric function of Re-

fraction because it to seventeen.

For if the trigonometric function of Inci-

dence out of Air into Glaſs be to the trigonometric function of

Refraction as seventeen to eleven, the trigonometric function of Incidence out of Glaſs into Air muft on the contrary be to the

trigonometric function of Refraction as I to seventeen, by the third

Axiom.

Much

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