Lect. I. determined. by the Angle BOD, or the Arch LM, which is much less than the former Arch HL; and the Body, when it arrives at D, will be seen at the Point M of the Periphery NLM: But it takes the fame Time to defcribe DE which is equal to A B, or B D; and when it arrives at E, it is ftill feen at the Point M; fo that all the Time it is moving thro' the Arch DE, it appears almost immoveable, and, as it were, to ftand ftill. While the Body is continually going forward in its proper Orbit, and defcribing the Arch EF, when it comes to F, the Eye in O will fee it in L, and it will appear to have gone backwards in the Arch ML. So alfo, while it moves from F to G, at its Arrival at G, it will be seen at H in the very fame Place it appeared in when it was in A. So likewise, while it paffes from G thro' I to Q, the Spectator's Eye at O will obferve it, as if it had defcrib'd the Arch HKN. And tho' it is ftill going on in its Orbit, while it runs thro' the Arch QP, the Spectator will obferve it all that Time near the Point N, in a Stationary State. After its paffing by P, and going to A, it will appear to change again its Course, and defcribe the Arch NKH with very unequal Motions.

Optical Inequality.

Plate I.

Fig. 7.

If the Eye

THIS Inequality of Motion is call'd by Aftronomers the Optical Inequality: Because it is not really in the Bodies moved, but only apparent to the Eye which perceives it, arifing from the Pofition of the Spectator: For the Body all the Time moves uniformly forward, and if the Eye were in the Center, it would fee the Motion always perfectly regularly performed.

be placed IF the Eye were placed in any Point, as O, within the within the Orbit of the Body, but not in the CenCircle, the Motion that ter, and there the Spectator remained immoveable, is equal, may he would ftill obferve the Motions to be unequal, appear un- altho' the Body moved never fo regularly; and equal, but the Body can when at the greatest Distance from him, as at never be feen A, it would appear to be floweft; when it comes go back- neareft, it would feem to move quickest. This is change its plain; for the Arches AB and CD being equal, Courfe.

to

ward, or to

they

they will be described in equal Times. But the Lect. I. Angle DOC being greater than A OB, the Motion in D will appear fwifter than that at A. But in this Cafe the Body will never appear to ftand, or to go backwards, but always forward: And therefore, when a Spectator placed within the Orbit of another Body, and viewing its Motion, perceives it sometimes to go forward, then to ftand ftill, and afterwards go backward, we may from thence conclude, that the Place of the Spectator is likewife moved.

弟弟弟弟弟弟弟弟弟弟弟弟弟弟弟弟弟患

LECTURE II.

Of the Apparent Motion which arifes from the Motion of the Spectator or Obferver.

H

ITHERTO We have fuppofed the Spectator to have remained immoveable all the Time of the Obfervation: But if the Place of the Observer be likewife moveable, then there will be very different Appearances, and the Eye will perceive thofe Bodies to be at Reft which may have really a very quick Motion, and other Bodies may seem to be in Motion; which remain really at Reft: And not only thefe Appearances may be feen, but the Motion of Bodies may appear to be directly contrary to what they truly are; and Bodies which are really going Eastward, may appear to move towards the Weft. All which will be most easily declared and made plain from the Appearances obferved by them who fail in a Ship:

SUPPOSE a Ship carried by the Winds a fwift, but uniform Motion; the Paffengers neither perceive the Motion in the Ship, nor

with fail in a can Ship, perofceive not the Motion of any the Ship.

They whe

Lect. II. any thing in it that keeps the fame relative Place in the Ship For fince the Veffel and all its Parts retain the fame Situation and Pofition in respect of the Eye, their Images painted on the Retina will always abide in the fame Place, and therefore they must appear unmoved. Hence it is, that tho' every Thing in the Ship goes as fast forward as the Ship itself does; yet fuch Motions cannot be perceived by a Spectator that fits in the fame relative Place, and who has the fame common Motion with the Ship. But when the Spectator turns his Eyes towards the Shore, or upon Objects which are without the Ship, they will seem to be moved; for while the Ship goes forward, it carries along with it the Eye of the Spectator, by which But exter Motion of the Eye the Pofition of external Obnal Objects jects in refpect of itself will be changed, and without the their Images will fucceffively occupy different Ship will Leem to Places on the Retina; and therefore Objects without the Ship, which are really at Reft, will seem to be moved, whereas those that are within the Ship, and really in Motion, will appear to be at Rest.

move,

IF, while the Ship is moving very fast forward, a Ball of Lead, or any other heavy Metal, were let fall from the Top-maft, the Paffengers in the Ship will obferve the Ball to fall perpendicularly downwards, and it will fall upon the Deck juft by the Foot of the Maft, after the fame manner as it would fall were the Ship at Reft. But notwithstanding this, the true Motion of the Ball is not in the The Motion Perpendicular, but in an Oblique Line, in which of a Ball it defcends; and a Spectator in another Ship falling down which is at Anchor, will eafily obferve this Obliquity and Curvity of its Way, while it falls thro' the Air. The Reafon of this Appearance is eafily fhew'd: For according to the first and principal Law of Natural Philofophy, a Body once put into Motion, endeavours to retain that Motion, and to continue moving in the fame Direction. Now the Ball, while it was held at the Top-maft, went forward with the Ship, and had its Motion communicated

in a Ship.

to

to it; and therefore, after it is left to fall, it will Lect. II. retain the fame Force to go forward as it did before; and at the fame Time, its Weight carrying it downwards, it will both go forward and defcend: For the two Forces, one communicated by the Ship, and the other from Gravity, will not hinder or diminish one another, they not being contrary. It will therefore be moved as faft forward, and as much downward, as it would be, did the two Forces act upon it feparately at different Times. By these two Forces acting together, the Rectitude of its Way is only hindered, which it would have, did the Perpendicular and the Horizontal Forces act feparately; and the real Way of the Ball thro' the Air is a curve Line, exactly like that which a Body takes when it is thrown according to an Horizontal Direction: And in fuch a Line it will be obferved to move, by a Spectator placed near it in another Ship which is at Reft. Befides, fince the Ball and Maft are both moved forward with the fame Velocity, they will always remain at the fame Distance from each other, and therefore the Ball will touch the Deck juft by the Foot of the Maft. Moreover the Motion of the Ball forward is common to the Ship, and all its Parts, as likewife to the Paffengers that are relatively at Reft in the Ship. But we have before fhewed, that the common Motion could not be obferved by the Paffengers in the Ship, and therefore it cannot be perceived neither while the Ball is falling. Wherefore the only Motion that can be feen, will be that which is impreft upon it by its Gravity, which is peculiar to the Ball, and by which it defcends. And therefore the Paffengers will fee the Ball defcending only in a perpendicular Line. Experiments have been often made, which demonftrate that all we have faid is exactly true.

IF any Perfon fitting at the Ship's Head, fhould The Mothrow a Ball towards the Stern with the fame Ve-tion of a Ball thrown locity that the Ship goes forward, that Ball would within the neither go forward nor backward; and if there Ship. were no Gravity, it would remain immoveable:

But

Lect. II. But because Gravity acts upon it, it will really defcend in a Perpendicular Line, and a Spectator in a Ship at Anchor would obferve it defcending in a Right Line. For the Force impreft upon it when it is thrown, will only destroy the firft Force communicated to it from the Ship, to which the Projectile Force is contrary and equal. But for all this, the Paffengers will not perceive this perpendicular and direct Motion; but they will fee the Ball go towards the Stern with the fame Force, as it really would have done, had the Ship been at Reft, and the Ball been thrown with the fame Force to the Stern.

en.

BUT if the Velocity with which the Ball is thrown toward the Stem fhould be less than that of the Ship, the real Motion of the Globe will be forward, in the fame Direction in which the Ship goes, but flower than it; for the whole Motion communicated by the Ship will not be deftroy'd, and there will ftill remain a Part of its former Motion, by which it will be carried forward, tho' not fo faft as before. But the Paffengers will perceive no fuch Motion, but they will obferve the Ball to be moved in a Line directly contrary to its real Motion, with that very Velocity that it would have, were it thrown when the Ship is at Reft: Hence it is plain, that Bodies may appear to have a Motion directly contrary to their real and abfolute Motion.

An Objecti- BUT fome may object, that the Ball thus thrown, will really hit the Stern of the Ship, and impress on it a confiderable Blow, which it could not do, had it not a Motion towards the Stern. But this Difficulty is easily removed; for tho' they that are within the Ship fee the Ball go and hit the Stern, a Spectator without, who is not in Motion, will obferve that the Ball does not come upon the Stern, and give it a Stroke, but that the Stern rushes upon the Ball, and acts upon it with all its Force: And the Force of the Stroke which each Body receives, is the fame as if the Ship had been at Reft, and the Ball had fallen upon it with

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the