Heavens, contained within the Circle whofe Radius is CP or Cr, can be seen directly from H; but only by the Refraction made in our Atmosphere: Therefore no fuch Points whatsoever, were it even a Part of the Surface of the Sun, can appear within the Apparent Limb of the Earth, but only upon or near this very Limb; and that with a very small Breadth or Thickness. 19. Thus from whatfoever Place called hereHthe Globe of the Earth be feen, as fuppofe from the fixed Stars, or from the Moon, or from the Sun, or from Venus, or Mars, or from a Comet, &c. it may be faid; A As the Distance CH; Is to the Semidiame- B ter CQ of the Globe of the Earth: So is the Radius of the Tables; To the Sine of the mathematical Apparent Semidiameter of the Earth as feen from the Point H. And as CH; Is to CP or CP perpendicular to HX or Hx: So is the Radius of the Tables; To the Sine of the visible Semidiameter of the Earth, as increased by the Effect C of the Refraction; or by the Distance of the Point P or P from Qor from the Surface of the Earth. 20. Let the right Line AECLA be perpendicular to the Diameter oCN. And let the Arc Al or EA in the heavenly Sphere fubtend an Angle of 198, in reference to an Eye placed at the Distance CH over against C perpendicularly to the Plan of this Figure; that is, an Angle equal to twice the Refraction of Light in our Atmosphere. And upon the Diameter El conceive the Circle EKKI whofe Center is C. And I fay that if a fixed Star fhould be fuppofed to defcribe behind the Earth confider'd as unmovable the right Line AECIA, it will appear almoft as unmovable near the Point A, feeming to flacken its E Courfe gradually there, till the Star itself, in about two Hours Time, has reached the Point I And then, and not before, it will difappear in A. 21. But as foon as Star comes to the Point E, its Image will appear fuddenly in the oppofite Point A, upon the Circumference of the apparent Dife of the Earth: From whence or the neighbouring Points it will not depart, F till the Star itself has actually reached the fame Point A. Whereabout having feemed to continue all the while that Line ECIAZZ is defcribing that is for about two Hours; the Star itself coming at laft to Z or z will then go on full speed and purfue its Courfe. 22. And fo, all the while that the Star, or any other the like Lucid Point, as feen from the G erected Point H, defcribes the Line EI; the Star will appear almoft unmovable near A and A. But the Arc zA and ZA, or Az and AZ, would be defcribed, in an open Skie, in about 70.01 6 Seconds. 23. Bat if a Star feen from the erected Point H, or from the Moon, &c. defcribes behind the Earth, on the Side where x lies, the H Curve D, which does not reach the Circle whofe Diameter is EI; Then conceive inually a right Line paffing thro' C and Center of the Star. And that Line will continually give, very near the Circum◄ ference of the Dife OANAP, the Point where the Star appears. Which, by confe quence, will not be eclipfed at all: But will all the while feem to flide along near the ap parent Limb of the Earth, and to defcribe Curve close by the Arc DND. And the like must be understood, if that Curve was situated on the Side of o. the 24. And thus, if the Star defcribes a Curve BKKB or DKKD, paffing at a Distance from C fmaller than 8' Minutes; Then, an indefinite Line, drawn from C thro' the Star, or thro fhew, near the Circle OANAP, any other the like Lucid Point, will always Place, or the two oppofite apparent Places of apparent the Star, f. in reference.to the erected Point H; by reafon of the Refraction in our Atmo Sphere. And all that while, the Star being in a right Line drawn from C to the Circumfe rence, will feem to flide along very near to even, for fome critical Moments, or Circumthe apparent Limb of the Earth; and a right Line drawn from C to D cuts the Curve ftances, in a retrograde Manner; as when or to the right Line YKCv, at about 8' Mi DK. And as foon as the Star comes to K, nutes from the Center of the Earth; then the Star will begin to appear alfo in the Opposite parent Dife of the Earth. And from thence Point, v, where it will feem to touch the apit will feem to move (and that very near the Limb of the Earth) from v to V, in a retrograde Manner; and to difappear in V placed foon as the Stan itself reaches the Point K. upon the Limb and the right Line KCV, as Points in the Heavenly Sphere, as fuppofe a And fo the Star, or any other chofen Lucid will appear at once near the Limb of the Earth Point chofen in a certain Segment of the Sun, in two different and diametrically oppofite KK; but feems to defcribe, near the Circum? Places, while it really defcribes the Curve ference of the apparent Difc, two Curvest YY and VV. Which must needs afford a very fingular and curious Sight. 25. Therefore this being premifed, we muft, fent the Eclipfes of the Sun and of fixed Stars. in order to make a regular Projection (to repre by the Moon) eftablish first the exact Propor of the Moon: And at the fame time find the tion between the Diameters of the Earth and Quantity of the horizontal Refraction of Light in her Atmosphere. These two Things I have actually done, or found out Methods to Knowledge of the Sun's Parallax, Whereby do them from Obfervations, and from the true. not only the Errors made in the Projection for chiefly in giving, in the Projection, a falfe Solar Eclipfes are manifefted which confift Proportion to the Diameters of the Earth, of the Moon and of the Sun, on one hand; and on the other hand in taking no Notice of the Moon: But whereby it appears alfo, That, if Refraction of Light in the Atmosphere of the the ordinary Projection accounts to nearly for the Phenomena of Solar Eclipfes, it is only becaufe the Errors in the Projection are counterballanced by an equivalent Dark G ill e 1 the Neglect of a due Allowance for the aforefaid Refraction of Light. And this Confideration has afforded me one Method for finding that Refraction: Befide which I have fome other Methods for the fame Purpofe. 26. But as to the Occultation of fixed Stars A by the Moon, the Error will remain intire : Neither can it be avoided by any Compenfation; but only by an indifferent Knowledge of the Parallax or Distance of the Sun; and a true Knowledge of the Proportion of the real Diameters of the Earth and of the Moon; and of the Refraction in the Horizon of the Moon; and of the Diftance of the Moon B from the Obfervator. Now these Particulars cannot be truly and nicely stated without my Theory: But with it they may. Which being done once for all, at least courfely for the Parallax of the Sun, and nicely for the Diameters of the Earth and of the Moon, and for the Refraction of the Moon's Atmosphere: The Refult of it in short will amount to the C following Rule, Mr FACIO's Taft REPLY to Mr to PP R SIMPSON calculated, p. 674, MR the Sun's Dentity E, to be to the Dd A3 Dd a 3 PP Earth's Denfity e; as And therefore, dividing by Dd, he con cludes, with much Appearance of Truth, but erroneously, as Sir Ifaac Newton feems the fame as that of ppas to PPA3. alfo to have done, that Proportion to be 27. From the apparent Semidiameter of the Moon; as increafed by about two or three Seconds, because of the Refraction in her Atmofphere; fubftract twice that whole Refraction: And the Remainder will give the Semidiameter, of the Circle or Space, in the Celestial Sphere, which is intercepted from eur Sight by the Interpofition of the Moon. D And from hence, and what I have already fad, depends the Correction of the Calcula tions of the Immerfion and Emerfion of fixed Stars eclipfed by the Moon. But these Stars, moving along the Dife of the Moon, will feem to ftick much clofer to it, than we find they would do in reference to the apparent Difc of the Earth, E 28. I concluded once upon fome Suppofitions, A 2. I fhew'd, p. 675, That this Way of arguing conceals a hidden and dangerous Paralogifm, becaufe here the Quantities and D depend upon each other, in as much as is equal to A: And there. fore the aforefaid Proportion of E tole is Dd a 3 Ddr3 $3 really as D PP to PP D3 3. But Mr Simpfon, p. 755, anfwers, That tho' my Reafoning about the Value of D [or A] be juft; yet it has noof a3 pp to 'A PP for exprefling the Denthing to do with his aforefaid Proportion fities of the Sun and Earth. And he finds fault with my putting in Dd into each of those Terms, and thereby making their Values to become uncertain. 29. But as to the rectifying the Theory of 4. I own that if I did fo, without the genuine Characters of an accurate DemonItration, his Cenfire would be juft. 5. But is it I that infert Dd without Caufe into his indeterminate Proportion No? Or is it himself, who having originally Dd in that very Proportion, frikes It out, without perceiving the Danger of his fo doing? and thus making that which was indeterminare, to become determinate? 6. Sir Ifaac Newton, notwithstanding his invincible Prepoffeffion, was however fenfible of the Danger of trufting to a Calculation like that of Mr Simpson. For otherwife he could never have thought of reducing the Sun's Parallax to 9 Seconds, as Mr Whifton fays he did before his Deccafe. Nor would Sir Ifaac have faid, (p. 405) Si Parallaxis Solis ftatua tur major vel minor quam 10" 30", debe bit quantitas materia in terra augeri v Whic diminui in triplicata ratione. Rule agrees exactly with my Equatio PP PP Mr URBAN, TH HERE is in the Magazine for October, a Scheme I propofed for the Latitude and Longitude at Sea, against which I have received but two Objections, which being easily A answered, I am the more encouraged to defire you would infert the following, with the Improvement I here give. First it's faid that I fuppofe the Latitude, the Hour by a Star, and the horizontal Refraction may be known more accurately than they can be found; but tor anfwer, they may be all found near enough, as will appear by the Demonftration following. *B T H E B R Let the primitive Circle be the Horizon, and the prick'd Circle an Almicanter in which the Star is when it fets or rifes, and N the Nadir, and P the S. Pole. If then I fee a Star fetting near the North Point at S, and in about half an Hour another at O, in which Time S is gone to B, but the Point S remains, then the Angle SPB is 7° 30 Min. for the half Hour, which being taken from OPB the Difference of their R. Afcenfions, gives OPS, which, with PS and PO, the 2 polar Distances, gives OS: In a little Time after, the 3cars, S, rifes at T, and having the Time of its being under the Horizon, I have SPT, and two including Sides which are equal, gives ST; and having before the two Angles OPS and SPT (i. e.) their Sum OPT, that Angle, with OP and PT, gives alfo OT: I fay, the three Chords of thefe three Arches, OS, ST, OT, being in the Plane of the Almicanter, determine its Radius, which is the R. Sine of its Distance from the Nadir, which being taken from 90 gives the Refraction. D E And for the Hour, the Angle NSO (found G by the three Sides) being taken from the before known Angle PSO, gives PSN, which, with the two including Sides, gives PN the Comp. of the Latitude, and likewife SPN the Hour from 12 by the Star. Thus they are all three found by one Figure. At the first Appearance of her Vertex, if the Sea be fmooth; or if rough, I am to be 30 or 40 Foot high, where I can fee 8 Miles off, at which Diftance the Height of a Wave is inconfiderable; I obferve the Hour, Minute, and Second, by a Star, and fo, by the Moon's Node, the Difference of their R. Afcenfion; and fuppofe it an Hour before 6: Then in the Figure, MN being the Moon's Path, and N the Node, the Angle EPN is 15°, and PE being 95, and PEB the known Latitude, I can find PB, which taken from NP I have BN; alfo I can find PBE, or EBN, which, with PNM, the Angle the Moon's Path makes with the Meridian the Node is in, will give Nn: Then I want only nC, to know how far the Moon's Center is from the Node, whofe Place may be known to 2 or 3 Seconds, tho' the Moon's Place not to half a Degree; if then I fubftract the Refraction from the Moon's Pa rallax, and the Minutes the Horizon is depreffed by my being 40 Foot high, from the Remainder (which may be known by Wright's Table in his Correction of Errors) I fhall know how much the Moon's Vertex, and fo her Center, is above the Horizon (i. .) CO, which, with the Angle n, gives Cn to be added to Nn, and I have her Distance from the Node, or her Place at that Hour by the Node; or becaufe the Node is too moveable, by the first Star of Aries; and fuppofe it is 4 Hours by the Star the roth of January, if I add the Moon's periodic Revolution, corrected by the Moon's Apogee, the Node, and the Sun's Place (on which, by Sir Ifaac Newton, it de Here, indeed, I fuppofe the Ship at reft; but fuppofing her to fail 10 Leagues Southpends) I fhall have the Moon there again fome Wet in 2 or 3 Hours, it's eafy to find the Difference of Latitude and Longitude for fo short a Time; and if the latter be turned to Time, is to be fubftracted from the Time it hath en under the Horizon, and if by the former afcenfional Difference be leffened, that time in February, and if to that Time I add another Period, I fhall have her there again another Time in March, and fo through the Year, which will give her Place 12 Times; and if 12 Obfervations are made, we shall have her Place for 144 Times; and if 30, for 360 Whether there be an external Heaven and Hell. Times. A Table being thus made, which if it happens to be marked in the Table, he A Note, If he hath the Moon's Place within Answer to the Question about Suicide, " D E End for which Men enter into Society, G Mr. S. U. 13 Mount Wallin, 1737. Defire the Favour of you to publish the following Questions, to your faghcious and learned Correfpondents. 1ft, Whether there be in reality any other Heaven and Hell, befides the Heaven and Hell which confift in the Happiness and Mifery that are effentially annex'd to Virtue and, Vice? By Virtue, I mean morally acting agreeably to the Truth and Fitnefs of Things: i. e. When one understands what is right and fit to be done, he does then, against any Difficulties and Temptati ons whatfoever, as far as lies in his Power, act agrecably thereunto. Vice, I mean the contrary, i. e. a morally acting, either by reafon of Temptation, or without Temptation, what the Understanding at the fame Time perceives to be unfit and wrong: A Confcioufnefs of the former, thus ftated, gives Eafe and Pleafute to the Mind; fo on the other hand a Conciousness of Pain. This being granted, I ask, By 2dly, Whether the Mind when let loofe and dilentangled from bodily Incumbrances, may not have a vailly greater Feeling of fuch infeparable Pleafure, or Pain, proportionably as it has been more or lefs virtuous or vicious here in its State of Probation? if the Affirmative will be granted, I ask how can it follow from the Nature of the Thing, that there fhould be any other extraneous Heaven and Hell? feeing that all the Creation, as far as we know it, there is fuch neceffary Harmony and Correfpondence between Things in their Causes and Effects, as one in my Opinion might juftly say in this Cafe with the Philofopher, Nun-fit per plura, fi quam- fieri 3ly, Whether the Scripture Doctrine in relation to Heaven and Hell, when confidered in its fpiritual Senfe (abftracted from Metaphors and Metonymys, or from Things material put to fignify Things fpiritual) does amount to any Thing else besides the Heaven and Hel of fuch Happiness and Milery, as ar the juft and immutable Confequences o Atque fi hoc etiam Natura præfcribit, ut Ho- Your Correfpondent from Maidstone, indeed, fays in your Mag. for July p. 421. E. C That a Society of Men united by folemn Compact for the Preservation of their Lives and Eftates, and Promotion of Virtue, have it in their Power to make fach Laws D as may be neceffary to fupport the Society, and preferve the Compact from Violation, and may lodge the executive Power of thefe Laws in the Hands of any Perfon they think proper. If then the publick Peace and Welfare of this Society cannot fubfift without the Infliction of Capital Punishments, which is the Cafe in every Government, the People may empow er the fupreme Magiftate to punith with Death; because the publick Good is of greater Value than the Life of any fingle Criminal who is an Enemy to all Laws, and acts in Defiance of them. E F Here he affert that Capital Punishments are neceffary in every Government for its Peace and Welfare, and therefore the Magiftrate has Power to inflict them. Both thefe Affertions appear equally falfe. Society has no doubt a Power to ufe neceffary Means for its Prefervation, but I am yet of Opinion that inflicting of Death is not neceffary, nor fuch a Power juft. For as Mankind firft enter'd into Society for Self-prefervation, fo all the Laws they came under were but as fo many Means for that End. This was the fole Defign of affociating, i. e. the Prefer-G vation and Happiness of every Individual. -No Man would have enter'd into Society on any other Terms, nor parted with his Goods for the Support of the Government, but with this View. Wou'd any Man have parted with Share of his alienable Right, but to fecure the Reft, and what is alfo unalienable, viz. his Life. No. But is not the Magistrate's Power of inflicting Death, affuming what is alienable? Is not this making Man in his worse than in a natural? In H of punishing with Death, or taking awa Life. But in Society Mens Lives are taken for Trifles, which Men in a natural State wou'd fcarcely regard, far lefs pursue to Death. ere it is to be obferved, that altho' the Your Correfpondent fays, ib. p.) 421. H.) Offender himself, as a Member of the Socie ty, had fubfcribed to the Laws by which he is punished, yet his own Authority was not fufficient to make thefe Laws, but the Affent of the whole Society was requifite, who all agree in one Voice to cut off any fingle Member that fhall be found corrupt and deftructive of the whole Body.' No fingle Member, if proper Methods were ta- |