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Prop, XVL

in several sorts of Rays emerging in equal Angles out of any res racking Surface into the fame Mes. diunii the Intervals of the following Fits of easy Reflexion and easy Transmission are either accurately, or very nearly, as the Cube-Roots of-the

'squares of the lengths of a Chord, which found \the Notes in an Eight\ sol^ la, fa, sol, la^ mi, fa, sol, with all their imtermediate degrees answering to the" Colours of those,Rays, according to the Analogy described in the seventh .Experiment of the second Part of the first Booh

HI S is manifest by the 13 th and 14th Ob servations.

Prop. XVII.

Is Rays of any fort pass perpendicularly hit6 several Mediums, the Intervals of the Fits of easy' Refexion and 'Transmission in any one Mediunl; are to those Intervals in any other ^ as the Sine of Incidence to the Sine of Refraction, when the Rays pass out of the first of those two Mediums into the second-,

'T H I S is manifest by the . 10th Observa*

tion*

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Prop. XVIII.

If the Rays which paint the Colour in the Confine of yellow and orange pass perpendicularly out of any Medium into Air, the Intervals'.of their Fits

of easy Reflexion are the %j~thpart of an Inch,

And of the fame length are the Intervals of their Fits of easy 'Transmission.

Hp H IS is manifest by the 6th Observation.

'From these Propositions it is easy to collect the Intervals of the Fits of easy Reflexion and easy Transmission of any sort of Rays refracted in any Angle into any Medium; and thence to know, whether the Rays shall be reflected or transmitted at their subsequent Incidence upon any other pellucid Medium. Which thing, being useful for understanding the next'part of this Book, was here to be set down. And for the same reason I add the two following Propositions.

Prop. Prop. XIX. Prop. XX.

If any sort of Rays falling on the polite Surface of any pellucid Medium be res eel ed back, the Fits of easy Reflexion, which they have at the point of Reflexion, stall fill continue to return; and the Returns stall be at dijhmces from the point of Reflexion in the arithmetical progression of the Numbers 2, 4, 6, 8, 10, 12, Sec. and between these Fits the Rays stall be in Fits of easy "Trans mijjion.

ID O R since the Fits of easy Reflexion and easy Transmission are of a returning nature, there is no reason why these Fits, which continued till the Ray arrived at the reflecting Medium, and there inclined the Ray to Reflexion, should there cease. And if the Ray at the point of Reflexion was in a pit of easy Reflexion, the progression of the distances of these Fits from that point must begin from o, and so be of the Numbers o, 2, 4, 6, 8, &c. And therefore the progression of the distances of the intermediate Fits of easy Transmission, reckon'd from the same point, must be in the progression of the odd Numbers 1, 3, 5, 7, -9, CSV. contrary to what happens when the Fits are propagated from points of Refraction,

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she Intervals of the Fits of fa/y. Reflexion ani easy transmission, propagated from points of 'Rejiexion, into any Medium, are equal to the Intervals of the like Fits, which the fame Rays . would have, if refraBed into the fame Medium in Angles of Refraciion equal to their Angles of Refexion.

in* O R when Light is reflected by the second Surface of thin Plates, it goes out afterwards freely at the first Surface to make the Rings of Colours which appear by Reflexion and, by the freedom of its egress, makes the Colours of these Rings more vivid and strong than those which appear on the other fide of the Plates by the transmitted Light. The reflected Rays are therefore in Fits of easy Transmission at their egress; which would not always happen, if the Intervals of the Fits within the Plate after Reflexion were not equal, both in length and number, to their Intervals before it, And this confirms also the proportions set down in the former Proposition. For if the Rays both-ingoing in and out at the first Surface be in Fits of easy Transmission, and the intervals and Numbers of those Fits between the first and second Surface, before and after Reflexion, be equal, the distances of the Fits of easy Transmission from either surface, must be in the fame progression after Reflexion as before; that is, from the first Surface which transmitted them, in the progression of the even Num

'•?' bers fcers o, 2, 4, 6, 8, &c. and from the second which reflected them, in that of the odd Numbers 1, 3, 5, 7, &c. But these two Propositions will become much more evident by the Observations in the following part or this Book.

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