TfL 85 degr. 29 min. the greatest that can be ; then if it be made as the Sine TfL is to the Radius, fo is LT to Tf, which is the least Altitude of the Air poffible. For because the Sine TfL is the greatest that can be, the fourth Proportional Tf is the least that can be, if the middle Terms, viz. the whole Sine T Lf and TL, be still the fame: if the Refraction of the Ray, that appears at the Horizon, be not given, but the Refraction in the Altitude x Lg, we may work the fame way in the Triangle LrT.

LIKEWISE the Proportion of the Sine of the Angle nfT 89 degr. 59 min. to the Sine TfL 85 degr. 29 min. will be the greateft poffible Proportion between the Denfity of the Air and that of the Æther.

PROPOSITION XXXII.

Having the Altitude of the Air, and one Refraction in it of a Star in a certain Altitude, to find the Law of Refraction, or the Proportion of the Sine of the Angle of Incidence, to the Sine of the refracted Angle; or to find the thickness of the Air by that Refraction.

THE Altitude of the Air must be greater than that we found to be the leaft poffible, otherwise the Refraction is not right taken, and the Problem is impoffible. (Fig. 28.) Let it therefore be greater, fuppofe Tr; and alfo let the Refraction in the apparent Altitude x Lg be mr L. Then there may be found the refracted Angle TrL (having Tr, TL, and the Angle TLr) to which Tr L if you add mr L, you will have the Angle of Incidence mr T, and the Proportion of the Sine mr T to the Sine LrT; which will be the Rule of refracting VOL. I. Hh

in

in that Air, or the Proportion of the Air's Denfity to that of the Ether.

PROPOSITION XXXIII.

Having the Altitude of the Air, and the Refraction of a Star in one Altitude; to find the Refraction in another Atitude.

FOR Example, let the Altitude of the Air be Tfor Tr, and the Refraction nfL at the apparent Altitude 0, and the horizontal Ray is the refracted Angle. Then let there be given the apparent Altitude r Lg or xLg, and let the Refraction be found by the preceding Propofition, or the Proportion of the Sine n fT to TfL. Then in the Triangle Tr L, having Tr and TL, and the Angler LT, find the Angle TrL; and as the Sine TfL is to the Sine Tfn. So let Tr L be to another Sine, which will be the Sine of the Angle mr T, from which take Tr L, and there remains the Refraction mr L which was fought. THE Antients used a more intricate and alfo a falfe Method for finding it.

PROPOSITION XXXIV.

Having the Altitude of the Air, and the Law of Refraction; to find the Refraction at the apparent Altitude of the Star, and from thence the true Altitude.

THIS is the fame with the former, where the Law of Refraction was to be found from a given Refraction in a given Height. Examples for working may be taken, from the Table laid down before,

Of the Reflection of Light in the Air.

PROPOSITION XXXV.

The Rays of the Sun and Moon are not only refracted after they have entered the Atmosphere, but also reflected from the Particles of Air, or beat back as it were from a rough Mirror, because of the irregular Situation of the Particles.

FOR if otherwife, no part of the Atmosphere would be lucid, except that the Sun is above; and the Sun being in the Eaft, the Air in the South and Weft would be dark; therefore as fome Rays pafs thro' the Atmosphere, fo fome are reflected feveral Ways, from one Particle to another, and thus they make the Air lucid.

PROPOSITION XXXVI.

Reflection of the Rays of the Sun from the Particles of Air, is the chief Caufe of the Twilight, that is in the Morning and Evening.

THIS is evident from the preceding Propofition; for as the Sun being in the Eaft, it's Rays, darted to the Weft, are reflected to our Eyes, and fo render the Weft Part vifible; fo the Sun being under the Horizon, it's Rays fhot into our Air, are reflected to our Eyes from the Eaft in the Morning, and from the Weft in the Evening.

PROPOSITION XXXVII.

The first of the Morning Twilight, that is, the enlightned Air in the East, and also the end of the Evening Twilight, begins when the Sun is about 18 degr. under the Horizon.

THIS Propofition is built on Obfervation; for if in the Morning, fuppofe about one or two o'Clock, we obferve narrowly towards the East, when a little white Colour begins to appear in the Air to the Eaft Part of the Horizon, and note the Hour and Minute, we may thence know the Depreffion of the Sun.

WE here fuppofe that the Air is clear, of which there being a great Difference, fome have therefore thought the Twilight begun and ended at the twentieth Degree under the Horizon, others only at the fixteenth Degree; for the groffer the Air is, the Twilight is the lefs fenfible; the contrary of which we faid happened in the Refraction, which is then moft fenfible.

PROPOSITION XXXVIII.

The Altitude of the Air, or the Matter that causes the Twilight, cannot be known from the Quantity of Twilight, as fome have thought; nor does the beginning of the Twilight proceed from a fingle, but a double Reflection.

Let TLb (Fig. 29.) be the Earth, gfom the Bounds of the Air, and L the Place of the Earth in which the Twilight appears, or the Light in the horizontal Airf, and therefore f L, is the Ray reflected from the Air f, and the incident folar Rayƒg S. Mathematicians, who have written of the Twilight, will

have

have the incident Ray in f, which makes the reflected Ray fL, to come from the Sun s; and becaufe no Ray can come to ƒ from the Sun, while the Sun is under the Tangent fbs; therefore when the Sun comes to the Tangent fbs, for Example to s, then doth the Ray begin to come to f; and because they will have the Reflection to be from f, as from a concave Mirror, therefore Tfb must be equal to TfL; and because the Sun is found to be 18 degr. under the Horizon, nfs must be 18 degr. and Lfb 162 degr. and Tfb or TfL 81 degr, and LT 9 degr. from whence Tf is found 174 German Miles (as Clavius and Nonius make it) and the Air about eleven Miles: nay Albazen and Vitellio make it thireen Miles.

SO great an Altitude of the Air is not to be allowed as difagreeing with other Phænomena, and being founded on a falfe Hypothefis, that the Ray gbs, which makes the reflected Ray fL, comes from the Sun itself, which is falfe; for it comes, by Reflection, from another Ray, for Example from the Ray gl. And that it is not neceffary to make a fmall Light in 5, that the Ray fg fhould come from the Sun itself, but that another Ray may serve, is proved from hence, that we fee, in the western Air, fome Light before the Sun rifes, tho' 'tis certain no direct Ray can come from the Sun to the western Air, but from another Particle of Air, for Example from ƒ and o; and fo the reflected Ray Lm comes from the incident Ray fm which is reflected from the incident Ray gf, and again gf from another g L.; which perhaps comes again from another. Secondly, 'tis worth remarking, that they have made the Reflection from the Air as from a concave Mirror; the Center of which Cavity is T the Center of the Earth, which is falfe; for the Rays reflect from the Air without any regard to the Center of the Earth, but to their Superficies,

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