made in a different Air (if made at all), I will also

add them.

Refraction of the Refraction of the Refraction of the Sun Degrees of Sun, according Moon, according and Moon, according Altitude. to Tycho. to Tycho.

to Lansberg

LANSBERG fets down the fame Refractions for the Sun and Moon; and Tycho makes a small Difference near the Horizon, thofe of the Sun greater, and at the fifth Degree equal; and afterward the Moon's Refractions fomewhat greater than those of the Sun: I confefs I do not fee why, except it be attributed to the weakness of the Moon's Light. And moreover, Tycho omitted Seconds, which are not to be neglected, if they approach near fixty, for they are of ufe in calculating the Height of the Air. But as for the Refractions of all the Stars they are equal, or very little different, if in one Air; but if the Air be groffer, the Refractions are greater. For Example, the Dutch, at Nova Zembla, found in Winter that the Sun began to appear after a Night of fome Months, when it was 4 Degr. under the Horizon, at least it's Limb; therefore the Refraction mfL is 4 degr. 30 min. the Cause whereof none have fufficiently explained.

AND then, when it was 3 degr. 45 min. under the Horizon, they faw it elevated above the Horizon 30 min. viz. it's upper Limb; therefore the Refraction mr L (for we must conceive mrs to fall under the Horizon, or rLg to be 30 min.) will be 4 degr. 15 min. and rLT 90 degr. 30 min. From this may be found the Altitude of the Air Lf, and the Density of the Air at Nova Zembla, which was clear at the time of Obfervation. And the Altitude of the Air is thereby found much greater, almost two Miles; nor will the fuppofition of a greater thickness in the Air help the Matter, as we shall shew in the following Propofition; because the Angle TfL cannot be greater than 85 degr. 30 min. (if nfL be 4 degr. 30 min.) tho' it will be greater if df be fuppofed lefs than two Miles; therefore the Truth of the Obfervation may be justly doubted of, seeing there is no fuch Obfervation any where; yea the contrary hath been obferved in the fame Place,

fee

SECT. VI. fee Chap. xxvi. Prop. xiii. at the end. Befides this, there can be no Reason given why the Air, after fo long abfence of the Sun, fhould be higher than when the Sun left them after it had been prefent a long time; rather the contrary should happen, the Air being made groffer and lower by Condenfation, as fome may urge that count the Height of the Air inconftant. Yet, when I confider these things more accurately, three Particulars occur to me that might confirm that Appearance and the great Refraction for the Obfervation cannot be denied, confidering that the Obferver understood Aftronomy, and faw the Sun above the Horizon for fome Days after, when it was ftill under the Horizon; nor must we doubt of the Number of the Days in the long Night they had, for when they came back they counted the fame Day of the Month, as their own People did, which could not be if they had mistaken before. For if we admit fuch an Altitude of the Air as is inconfiftent with the Refractions in the Temperate and Torrid Zone, we must say the Air is of the fame Height every where as truly in the Torrid and Temperate, as in the Frigid Zone. But, in the Torrid and Temperate, the upper Region of the Air is fo fubtile, that it doth not cause Refraction, but only the middle Region of it; and therefore no wonder if the Refractions in the Torrid and Temperate Zones are less; for the Air that causes them is lower, which should cause the Refraction to be greater; yet it must be much more rarified than the other Air. But to this it may be objected, that the Obfervations of the Sailors were made in a clear Air, as themselves fay; to which I answer, that yet 'tis not probable that the Air was then fo fubtile as the cleareft Air in the Torrid and Temperate Zone. Secondly, it may be faid that the Air of the Frigid Zone, when the Sun réturns to it after a long absence, is first refined in

the

the upper Region, and that the middle is fomewhat more gross, and therefore the Sun is feen by two Refractions, as the Stars are thro' Air and Glass, and a double Refraction depreffeth the Star under the Horizon more than a fingle one, and fo the Altitude of the Air of one Mile, or three Quarters, will be enough. Nor can it be objected, why doth not the fame thing happen when the Sun departs from that Air, and the long Night begins; for then 'tis probable the Difference of the thicknefs of the Air is lefs, because of the Sun's long Continuance; or we may fay the Exhalations are more grofs, in the Mornings of that Zone, after that long absence. Thirdly, if a double Refraction doth not fatisfy, and it will not be granted that the upper Region caufes no Refraction, as was faid, then it must be granted that the Air in that Place of the Frigid Zone was then much higher than in our Temperate Zone, and alfo much groffer (for 'tis only the Altitude that leffens the Refraction): but if there be a great thickness, the Refraction is much more encreased thereby, than 'tis diminished by leffening the Altitude. But the first of these three Caufes is beft, that supposes the Altitude of the Air to be two Miles (for it cannot be lefs in Nova Zembla where the horizontal Refraction is faid to be 4 degr. 30 min.): the other two lie under feveral Difficulties. We have faid it was the thickness of the Air that was the Cause why, the Altitude being the fame, the Sun was not feen for fo many Days after it ceafed to rife on the third of November; and fo we must anfwer, that the Cause may be the fame why the fame Dutchmen did not, on the thirtieth of May 1596, fee the Sun in the middle of the Night, in the Latitude 69 degr, 42 min. when it was not one Degree under the Horizon. But we have faid too much of this, occafioned by the difficulty of the thing; there

must

SECT. VI. must be, for an accurate knowledge of it, most accurate Obfervations. Yet we must not think, that if Obfervations of a Star, in different Elevations, do not give the fame Altitude, that therefore it hath different Altitudes, on account of the Difference of the Density of the Air, which is greater the nearer the Horizon; and therefore Obfervation will give a different Altitude, tho' it be the fame, for, in the Calculation, the Denfity, and confequently the Refraction, is accounted the fame.

PROPOSITION XXXI.

Having the Depression of a Star under the Horizon when it first begins to appear (that is, having the horizontal Refraction of a Star), to find the leaft poffible Altitude of that Air, in which the Refraction is made; and the Grossness of that Air and the greateft Quantity poffible by which it exceeds the Denfity of the Ether; that is, the greatest Refraction poffible. Or more generally thus: Having the Refraction of a Star, at it's apparent Altitude, to find the leaft poffible Height.

LET the horizontal Refraction be nf L, (Fig. 28.) or the Depreffion of the Star under the Horizon gfs or g Ls, when it first begins to appear, as it was in Nova Zembla 4 degr. 30 min. 'Tis known from the Doctrine of Optics, if a Ray, as sf, touch the Air in f; that is, if the Angle Sf or nfT be a right Angle, then the Ray is not refracted; but if the Star be under the Tangent, then no Ray can come to ƒ directly. Therefore it is requifite the Star be above that Tangent, and that s for nfT be less than 90 degr. Let it then be 89 degr. 59 min. or 90 itself, provided it be no greater than from nfT. Let there be taken the Angle of horizontal Refraction 4 degr. 30 min. and there remains the Angle TfL