"against it." From what the Doctor has faid upon this Head, it follows, as he tells us, "That the "Force whereby Gravity is leffened in the Equa "tor is to the Force whereby it is leffened in any "other Part of the Earth's Surface as the Square of "Radius to the Square of the Sine of the Comple"ment of Latitude."

In the third Lecture our Author treats of Repulfion and Central Forces. With regard to the firft, he fays, "As Experience has convinced us, that there

are Powers in Nature, whereby not only the lar"ger Systems and Collections, but likewife the "Imaller Parcels and Particles of Matter are, in "fome Cafes, made to tend to one another; the "fame Experience will inform us of other Powers "in Nature, whereby the Parts of Matter do in "fome Circumstances recede and fly from each "other." Inftances of this he produces, both magnetical and electrical. From this Power it is, as he thinks, that the Leaves of the fenfitive Plant shrink and retire from the Touch of an approaching Hand. And to the fame Power, as he adds, we are to attribute the Elafticity of the Air; as alfo the Shaking off of the Particles of Light from the Sun and other luminous Bodies.

Befides the afore-mentioned Principles of Attraction and Repulfion, whereby, as the Doctor fays, Nature feems to perform moft of her Operations, and which, for that Reason, are very properly stiled active Principles; there is another, of a paffive Nature, commonly called the Vis infita and Vis inertie of Matter, a Force arifing from the Inertnefs or Inactivity of it; which Force, in any Body, is proportional to its Quantity of Matter: From this Force refult three paffive Laws of Motion, ufually called, by modern Naturalifts, The three Laws of NATURE: These our Author explains and estab lishes. I will here only name them:

The

The 1st of thefe Laws is, That every Body, in Proportion to its Quantity of Matter, perfeveres in its prefent State, whether it be of Reft or of uniform Motion in a right Line. As a Confequence of this, it follows,

Secondly, That all Motion is of itself equable and recti-lineal. And

Thirdly, That all Bodies which revolve about a Center must endeavour to recede from the Center.

Under the last of these Dr. Helbam handles the whole Doctrine of Central Forces, and in the Inveftigation thereof proceeds after the following Manner. First, He confiders two equal Bodies moving uniformly in two different Circles; and thence deduces one general Expreffion for the central Forces in the Terms of the Circle. Secondly, By fubftituting other proportional Quantities in the Place of those which conftitute the general Expreffion, he forms other general Expreffions for the fame Forces. Thirdly, By a proper Application of those Expreffions he determines the Laws of central Forces in particular Cafes, and at the fame time confirms each Law by an Experiment. The Performance of this Task takes up the Sequel of this Lecture; and it prepares the Reader for an Acquaintance with the Newtonian Syftem of the Univerfe.

In the former Part of the fourth Lecture our Author confiders the COMPOSITION and RESOLUTION of MOTION. What he has offered in relation thereto is founded upon the fecond of the preceding Laws of Nature, refulting from the Vis inertie of Matter; and is of fingular Ufe, as he fays, in Mechanicks; for by the Help of it, the Effects of Powers acting in oblique Directions are readily determined. In the latter Part of this Lecture the firft of the foregoing Laws of Nature is illuftrated. The Doctor therein proves, as a Contequence of it, "That Re-action is always equal to Action,

E 3

Action, and contrary thereto; or, in other Words, "that the Actions of two Bodies, one upon another,

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are constantly equal, and in Directions contrary "to each other; fo that whatever Change is made "in the State of one Body, whether at reft or in "Motion, by the Action of another, the fame "Change is produced in the State of the other by "the Re-action of the former; but the Tendencies "or Directions of thofe Changes are contrary "Ways."

This Doctrine is fomewhat paradoxical at first Sight, to Perfons unused to thefe Speculations, or who have never feen thofe Experiments which evince the Truth of it. When fuch a one preffes a Stone with his Finger, he never imagines the Stone equally preffing it; or when he fees a Horfe drawing forward a Load, fuppofes the Load drawing back the Horfe in any Degree. But the Readers of this Lecture will be convinc d, that the Cafe is no otherwife, and exactly conformable to the foregoing Reprefentation. As this Law obtains in all Kinds of Attraction whatsoever, fo likewife does it in refpect of Strokes or Impulfes made by Bodies one upon another; the Force of two Bodies, ftriking each other, equally, affecting the Motions of both, and producing equal Changes therein towards contrary Parts. "On this Equality of A&tion and Re-action, as he adds, do the feveral Laws which have been col"lected concerning the Collifion of folid Bodies in "a great Measure depend:' Which Laws, as they relate to Bodies void of Elafticity, he explains in the laft Pages of this Lecture; in doing whereof he lays down one general Propofition concerning the Collifion of fuch Bodies, whence he deduces the Laws of particular Cafes, and at the fame time confirms each Law by an Experiment.

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In the fifth Lecture our Author fpecifies the Effects of the Collifion of elaftick Bodies: And the Method

he

he observes in treating of the Percaffion of elaftick Bodies is this: First, To lay down one general Pro-' pofition concerning fuch Percuffion; and then, Secondly, To deduce the Laws relating to four general Cafes mentioned in the laft Lecture, and to confirm each of those Laws by Experiments.

In the fixth and feventh Lectures our Author gives an Account of those we call the mechanick Powers, viz. The Ballance, the Lever, the Pulley, the Axle in the Wheel, the Wedge, and the Screw. As a Preliminary to his Differta ion on thefe Heads, he has, at the Beginning of the fixth Lecture, a Difcourfe on the Centre of Gravity; that Point in every Body, about which all the Parts of it are in. Equilibrio. He defcribes the Properties thereof in order to our conceiving a clear Idea of its Nature. He then gives us an eafy and perfpicuous Reprefentation of the Form and Ufes of the above named Powers, with an exact Computation of their refpective Forces. Let me add, that in the eighth Lecture, the Effects of thefe Powers when combined, and compofing various Kinds of Engines, applicable to many invaluable Purposes, are diftinctly specified and accounted for.

The ninth Lecture is on the Friction of moved Bodies. This is a moft curious Subject, which our Author has illuftrated in a Manner as familiar as can be. He has fhewn whence it proceeds. He has rectify'd fome mistaken Notions concerning the Caufe of it. He has pointed out the Methods whereby the Resistance to Motion, arifing therefrom, may be avoided as far as poffible. The unfpeakable Advantages of Wheel-Carriage are too obvious to need mentioning; but with Pleasure we here fee the Principles unfolded from whence they fpring, how they operate, and by what Means they are to be applied fo as to answer the moft beneficial Intentions.

In the tenth Lecture our Author explains the chief Properties of the Pendulum: And to prepare the Way, he lays down and demonftrates feveral Propofitions concerning the Motion of Bodies, down-inclined Planes, and curve Surfaces. He then confiders the Pendulum as applicable to horological Machines. The vaft Improvement these have received by the Means of it is univerfally known; they have thereby been brought as near to Perfection as they feem capable of; and yet, thro' the remedilefs Imperfection of this very Affiftant, they are prevented from attaining the higheft Pitch of it: As the Doctor has fhewn very evidently.

The eleventh Lecture delivers the Doctrine of PROJECTS. As this cannot be rightly apprehended without fome Knowledge of the Parabola; our Author, by way of Introduction, fhews the Manner wherein that Curve is generated, and specifies fuch of its Properties, as he has Occafion to make ufe of in the Explication of this Subject. After this he demonftratively affigns the Velocity of a Project in any Point of a Parabola. He fhews how to determine the Direction wherein a Project must be thrown, in order to hit a Mark; the Pofition of the Mark, and the Velocity wherewith a Project is thrown from any given Place, being given: Aş alfo in what Angle the Direction of the Projection must be elevated, fo as to throw a Project, with a given Velocity, to the greatest Distance poffible on the Plane of the Horizon. Indeed all that he offers on thefe Heads is abfolutely true, only on a Suppofition of the Motion of Projects meeting with no extrinfic Impediment or Disturbance; whereas there are two, which he confiders: The firft is the Re fitance of the Air; which affects all Projects whatfoever that move in it: The fecond, which inquences thofe only that are thrown by the Force of

Gunpowder,