to difcern. Nothing, however, can be clearer, than that the existence of an agent or caufe may be known, though it may itself arife from fome prior cause of which we are ignorant; and it is enough that attraction really exifts and acts according to established laws, to juftify philofophers in admitting it in their explication of natural appearances.

BOOK I.

SECT. II.

Of Bodies in Motion.

CHAP. I.

OF THE MECHANICAL POWERS.

WHEN two heavy bodies or weights are made L by any contrivance to act against each other, fo as mutually to prevent each other from being put into motion by gravity, they are faid to be in equilibrio. The fame expreffion is used with respect to other forces, which mutually prevent each other from producing motion.

Any force may be compared with gravity, con- M sidered as a standard. Weight is the action of gravity on a given mafs (35, D). Whatever therefore is proved concerning the weights of bodies will be true in like circumftances of other forces.

Weights are fuppofed to act in lines of direction N parallel to each other. In fact, these lines are directed to the center of the earth, but the angle formed between any two of them within the space occupied by a mechanical engine is so small, that the largest

and most accurate aftronomical inftruments are fcarcely capable of exhibiting it.

The fimpleft of those inftruments, by means of which weights of forces are made to act in oppofition to each other, are ufually termined Mechanical Powers. Their names are, the Lever, the Axis and Wheel, the Pulley or Tackle, the Inclined Plane, the Wedge, and the Screw.e

2

Р In the theoretical confideration of these fimple inftruments, the parts they are composed of are imagined or fuppofed to poffefs no other properties than those which conduce to the purpose of their conftruction. Thus, they are all supposed to be without weight or inertia, and to move without friction. Many of thefe parts are taken to be mathematical lines, fome perfectly inflexible, and others perfectly flexible, reprefenting ropes. And these fuppofitions are allowable, because they imply nothing more than that the reasonings relate only to abstract notions or perfect inftruments; and it is confequently no more to be urged that there are no perfect inftruments, than that there are no perfect mathematical figures, at least that fenfe is able to discover or diftinguifh. For the difference between theory and practice is in fome cafes inconfiderable, and may in general be allowed for, without much difficulty, from the general principles of mechanics, when once eftablifhed.

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СНАР,

THE lever is defined to be a moveable and in- q flexible line, acted upon by three forces, the middle one of which is contrary in direction to the other

two.

One of thefe forces is ufually produced by the R reaction of a fixed body, called the fulcrum.

Let AG (fig. 11) represent an horizontal lever at s reft. At the point в, equidiftant from a and G, is placed the fulcrum D, and at the extremities A and G are hung the equal weights E and F. Then the lever will continue at reft, the weights E and F being in equilibrio, For it is evident, that if the line A & be moved on the fulcrum в, its extremities A and G will each be carried with equal velocities in the periphery of the fame circle. And because A G is horizontal, the actions of the weights EF will be in direction at right angles to its length; that is to fay, they will act in the direction of tangents to the faid circle at the points A and G; or they will act in the direction of those particles of the periphery, which may be imagined to coincide with the tangents. Each preffure, therefore, tends to move the corre→ spondent extremity of the line AG in that very line of direction in which only it can move. Suppose the preffure at G to be removed, and the whole preffure at A will be employed in depreffing the point A, or, which is neceffarily in this cafe the