our Eyes, but turn a little afide from the ftrait Courfe, as foon as they enter the Air; which is called, by Writers in Optics, their Refraction. THAT Part of Optics which treats of the Refraction of Light is very fine. Experience teftifies, that the Rays coming from any Object out of one Medium into another more grofs, or more fine, do refract or turn afide: the Thing is plain from a common Experiment. Take a Veffel, to the Bottom of which fix a Globe of Gold, or Brass, or Peice of Money, then go from the Veffel 'till you cannot fee the Money for the Sides of the Veffel, then fill the Veffel with Water and you will fee the Money; which fhews, that the Rays coming from the Money as they go from the Water into the Air turn from their Courfe, before they can come to the Eye; which is called Refraction, because the Line is broke, as it were, coming from Water to Air. THUS, Let the Center of the Earth be T, (Fig. 28) and L the Eye on it's Surface, and drf the Surface of the Atmosphere, or Air; and therefore no Ray can come to the Eye at L, which is under Lfg for the Rays below would fall on the rifing Part of the Earth Lo; and thus no Star can appear by a ftrait Ray 'till it come to the horizontal Line Lfg, but the Stars appear before that, while they are under Lg: for Example in S, from which no Ray can come ftrait to the Eye, but must be refracted; i. e. the Line or Ray Sf coming into a thicker Medium at S, on the Atmosphere, is refracted and runs on in the Line fL, tho' it was directed to n, and thus the Star appears before it comes to the horizontal Line Lfg. THUS the Star in is not seen by the direct Ray fr, but by the refracted Ray r L, tho' it was directed at the firft to m; and therefore the Star at appears higher by the Refraction than it really is, it's Height being the Angler Lg or the Arch xg, as if it were in the Point x when it is really in f. THIS being the Law of Refraction, that the Rays going into a groffer Medium, turn to the perpendicular at the Point of Incidence, as here fis the Point of Incidence, and Tf the Perpendicular drawn thro' f, thro' the Superficies drf; therefore the Ray Sfn will be refracted towards fT that from fn it may become ƒ L. AND thus the Line or Ray r m becomes r L : but the contrary happens when the Ray goes into a fine Medium, for then it goes from the Perpendicular. BESIDE it is the Nature of Refraction, that the Rays falling perpendicularly on the Superficies of another Medium, are not refracted, but only thofe that fall obliquely, and those are the more refracted the more obliquely they fall. Thus the Rays S T, ST, M dT being perpendicular to the Superficies are not refracted, but the Rays Sf, fr that fall obliquely are, and Sf more than fr. FROM whence it alfo follows, and is manifest by Experience, that the nearer the Stars are to the Horizon, their Rays are the more refracted, and the higher they are, the less; and Aftronomers have found, that when a Star is twenty Degrees high, the Refraction is infenfible, tho' there is still a fmall Refraction. AND Mathematicians, fkilled in Optics, have by Obfervations found the Laws of Refraction of all oblique Rays, and that in every Medium there is a conftant fixed Proportion between the Sine of the Angle of Incidence and of the refracted Angle (i. e.) between the Angle nfT and LfT, the Angle nfL being the Angle of Refraction; and fo in the Refraction of the Ray frm. Therefore the fame Proportion that is between the Sine of the Angle Angle Tfn and the Sine of the Angle TfL, the fame is between the Sine of the Angle Tr m and the Sine of Tr L. Therefore if the Quantity of Refraction be known by Obfervation at one Elevation of a Star, the Quantity of Refraction for all other Elevations may be known (†). (t) It is of great Moment in the making of exact Aftronomical Obfervations, to know the Refraction which the Rays of Light fuffer in paffing thro' our Atmosphere. This was determined by the learned Mr Lowthorp, by an Experiment made before the Royal Society, and fhewn to be as the Sine of the Angle of Incidence and Refraction. See Philos. Trans. No 257. But this Experiment being queftioned by the Royal Academy of Sciences at Paris, who had not the fame Succefs, [fee their Memoirs for the Year 1700] Mr Lowthorp repeated it at the Requeft of the Royal Society, and Mr Hauksbee also performed it with much greater Accuracy. See Hauksbee's Phyfico Mechanical Experiments p. 175 and found the Proportion betwixt the Angle of Incidence and Refraction was as 1000000 to 999736; fo that the refractive Power of the Air to bend a Ray of Light from it's ftrait Courfe in coming out of a Vacuum, or the Difference of the faid Sines, proportionable to the Sines themselves, is 2641000000 Parts. And the Experiment being feveral Times repeated, he found that this refractive Power exactly answered to the Proportion of the different Denfities of PRO the Air thro' which the Ray paffed, fo as to be twice or thrice as large when the Air had twice or thrice the Denfity. Whence we have an easy Rule for finding the Refraction in any Time or Place, as being always correfpondent to the Denfity of the Air. But the Denfity of the Air may be measured by a joint Obfervation of the Barometer and Thermometer. For as the Spaces, poffeffed by the Air, are reciprocally proportional to the Weights that comprefs it [fee the Note upon Propofition 7. above] and it's Density reciprocally as the Space it poffeffes, the Denfity of the Air must be proportional to the Weight that compreffes it, or the Weight of the incumbent Atmosphere; that is, the Height of the Quickfilver in the Barometer. And this will be the Cafe if the Heat of the Air remain the fame. But if the Height of the Barometer be known, the Denfity of the Air is reciprocally proportional to the Spaces marked against the Degrees of the Thermometer in the Tube above. [See the Note to Propofition 8.] Whence it follows, according to the known Theorem of compounding Ratios, that the Density of the PROPOSITION XXII. The Atmosphere or Air caufes the Sun and other Stars to appear before they come to the Horizon at rifing, or after they are paffed it, at fetting; and appear bigher than they really are, while they are under twenty Degrees of Elevation. THE Caufe is fufficiently explained in the preceding Propofition. We may add fome Experiments or natural Phænomena. When the Dutch wintered in Nova Zembla, the Sun appeared to them fixteen Days before it came to the Horizon, that is, when under the Horizon four Degrees, and that in a clear Sky; and famous Aftronomers have the Air is always as the direct Ratio of the Heights of the Barometer, compounded with the reciprocal Ratio of the Spaces marked against the Degrees of the Thermometer. • For Example, at the time the Experiment was made, the Height of the Barometer was 29 Inches, 71⁄2 decimal • Parts, and the Thermometer at 60, over against which the Space of 137 Parts is marked; Then, it must be enquired, what the Denfity of the Air is, when the Barometer is up at 30 Inches, and the Thermometer 50 degr. below the Line of Freezing, then the Column of Air in the former Experiments 'will not poffefs above the Space of 126 Parts; fo that the Density of the Air fought for, will be to the Density of the Air at the Time the 30 X 137, to 29, 71⁄2 x 126; or as 4110 to 3748. 5. And hence may be underftood the Reafon why the Dutch who wintered in Nova Zembla, found fo great a Refraction. See Set. vi. Chap. 19. Prop. 30. For hence we understand, according to the Obfervations of the French and others, (see Hift. de l'Acad. Scien. 1700, 1706, and La Mefure de la Terre) that the Refractions are greater towards the Poles than near the Equator, and greater in the fame Place in the Morn ing or Evening than at Noon; tho' there be no Difference perceived in the Height of the Barometer. For all this feems to proceed from the fame Cause viz. the greater Density of the Air by reafon of Cold. Jurin's Appendix. found found, with Tycho, that, with us, when the Air is clear in the Morning the Sun is seen elevated above the Horizon thirty four Minutes, while 'tis yet under the Horizon and it's Limb but just touching it, and as long in the Evening. THUS the Virgin's Spike appears when 'tis thirty two Minutes under the Horizon, for it feems to rife when the Lion's Tail is thirty four Degrees, thirty Minutes high, and on the fame Point. But thefe two Stars are diftant thirty five Degrees two Mi nutes. PROPOSITION XXIII. The groffer the Atmosphere is, the Refraction is the greater, (other things being alike) i. e. there being the fame Elevation of the Star, and the fame Height of the Air. THUS the Angle nfL, (Fig. 28.) which is the Angle of Refraction, is the greater, or the refracted Ray fL comes nearer to ƒ T the thicker the Atmosphere is, which thofe fkilled in Optics have found in all kinds of Mediums. PROPOSITION XXIV. The groffer the Air is, the more the Star is under the Horizon when it first appears. THE Ray Lf (Fig. 28.) is refracted and first fhows the Star, and LfT is the refracted Angle; and Sfn being the incident Ray, nfT will be the Angle of Incidence, and n f L the Refraction. LET us then fuppofe the Air fd LO to be groffer than when it made the Refraction nfL, it will thus make the Angle of Refraction greater, viz. of L, and the incident Ray will be Kfe. There-. VOL. I. Gg fore |