fhadow, (as it really is in the Moon) it is most evident that we could not determine the Figure of the fhadow near fo nicely, as in the former cafe. We fee then that by the Earth's fhadow upon the Moon, its Figure is not to be determined with any tolerable exactness.

The third obfervation the Theorist would have us make, is about the return of the Sun to the Polar parts of the Earth, whether that be according to the rules of a Spherical furface. But this method is as little to be rely'd upon as any of the reft. The various refractions of the cold and thick Atmosphere, make all obfervations that are made there, very doubtful and uncertain: Befides, the Latitudes of thofe places that are near the Poles, are not exactly determin'd, fo that there is no trusting to obfervations that have been already made, and I believe no body will go now to thefe places and Winter in them,on purpose to make new and more exact obfervations to determine this controversy.

The Defender, having thus pointed out the Theorift's own obfervations, comes now to confider the arguments that are brought by thofe, who say that the Earth is of a broad Spheroidical Figure. He tells us, that the learned Mr. Hugens thinks it may be prov'd by experiments made about the different Vibrations of a Pendulum in different Latitudes; and brings an instance of an experiment made at Cayenne in America, where it was observ'd, that a Pendulum Vibrating in a fecond is fhorter

fhorter than one at Paris that performs its Vibrations in that time; from which he fays, he concludes that Gravitation is lefs under and near the Equator than towards the Poles, and from thence, that the Figure of the Earth is protuberant and rifes in the middle, its shortest Diameter being betwixt Pole and Pole.

We fee here that our Author afcribes the observation about the Figure of the Earth, drawn from an experiment of Pendulums to Monf. Hugens, whereas it was Mr. Newton who first made the difcovery, from whom Mr. Hugens had it; and this Writer in justice ought to have afcribed it to its true and genuine Author. But this is not the first time that the honour of feveral noble Inventions, which the World owes to that excellent Geometer and Philofopher, has been given to others.

The Defender tells us, that there are several things to be confidered before we come to the conclufion; first the matter of fact, concerning the inequality of Vibrations of equal Pendulums in different Latitudes; and then the inferences made from that inequality. As to the matter of fact, he tells us, that it was Mr. Richer who made the experiment, whofe Perfon or Character he does not know, or whether his relation be extant in Print. "Tis strange, that the Defender thinks that no body is to be trufted in a Philofophical experiment; but thofe whofe Perfons and Characters he

[.

knows,

knows, Has he fuch an univerfal acquaintance, as to have an exact knowledge of all those who are fit to make Obfervations and Experiments in Natural Philofophy? Certainly he must think, that the Gentlemen of the Royal Academy are better Judges of that than he is. Monf. Richer was chofen by them, and fent at the command and charges of the French King, to make Obfervations in the South parts of the World; and doubtless, when thefe Obfervations were to be made by order, and at the expences of their King and Patron, they would never choose any but one whom they knew to be well qualify'd for fuch an undertaking. And Monf. Richer himfelf has juftify'd the judgement of those that chofe him, by his excellent Obfervations, both Aftronomical and Phyfical, that have been fo well received by the Learned. Among the reft, he gives us an account of this Obfervation about the Pendulum very exactly; He tells us, that during the ten months he tay'd at Cayenne,there fcarce paffed a week in which he did not make the Obfervation, and found it always the fame.

Monf. Vaun, Monf. Hayes, and Monf. Du Glofs, were alfo chofen by the fame Academy, and fent to the Ifland Goree in Africk. They had it particularly in their inftructions, to make Obfervations about the Pendulums; which they did, and confirm'd the Experiments made by Monf. Richer. We may fee a particular account of all their Observations

in

in the Receuill des Obfervations faites en divers Voyages per l'ordre de fa Majefté, in Fol. printed at the Royal Prefs in Paris.

To all this we may add, that the ingenious Mr. Halley when he went to St. Helena, (having first fitted the length of his Pendulums for Vibrating feconds at London) found afterwards that length at St. Helena to be too great; and therefore he was forced to fhorten it, that it might Vibrate feconds there; tho' he did not then obferve the exact difference between them. These repeated Experiments I hope will put the matter of fact paft all doubt.

But (fays our Author) even Monf. Hugens fpeaks dubiously of the Experiment. This I deny; for Monf. Hugens never in the leaft doubted of the Experiment, viz. That a Pendulum Vibrating feconds at the Equator, muft be fhorter than a Pendulum performing its Vibrations in the fame time at Paris; for he has given evident demonftration that it must be fo. Monf. Hugens only doubted whether Monf. Richer had obferved exactly the difference of their lengths; being fully affured in the mean time that there was a difference, as will be plain to any body that will be at the pains to read his Book. The reafon why he doubted if Monf. Richer had given us the exact difference was, because he found that the difference obferv'd by him, did not anfwer the numbers he brought from his own Calculation, which proceed upon a fuppofition that

Gra

Gravity at all diftances from the Center is the fame.

But it seems the Defender does not fee the confequence which is drawn from thence, viz. That Gravity must be lefs at the Equa tor than at the Poles, and therefore wishes that it were prov'd by other Experiments. It is ftrange and surprising, that this Author fhould know exactly how the Earth was made, by what Principles and Laws of Mechanifm the World was framed, how the Deluge overfpread the World, and what way the Mountains arofe, and yet fhould be ignorant of fo plain and eafy a piece of Mechanifm as this, which has not the hundredth part of the dif ficulty or intricacy of those which he pretends to know. Well, to convince him I will here repeat the demonftration somewhat plainer than I did in the Examination.

Let us fuppofe two bodies moving in two equal Cycloids; it is demonftrated by Mr. Hugens that the time of the defcent thro' these Cycloids, is to the time of the descent thro the Axis of the Cycloids always in a given proportion, viz. as the Semiperiphery of a Circle is to its Diameter; and therefore if the time of the descent or vibration in these two equal Cycloids, fhould be unequal, the time of the defcent thro' their Axes will be alfo unequal. Now the Axes of the Cycloids being equal, and the time in which the Bodies move thro' them, unequal, it is evident that the

two