fecond, which is one, is to the fquare of 0,79 hundredth parts of a second, viz. 0,6241; so is the length of the pendulum which vibrates feconds, viz. 39,1196 to the length fought; that is, 1: 0,6241:: 39,1196; where fince the first number is unity, you need, according to the preceding rule, only multiply 39,1196 by 0,6241; and the product 24,4 is the diftance fought; fo that the centre of ofcillation C in the ftick AB is 24 inches and 4 tenths diftant from its extremity A; viz. about two thirds of its length.

Example 2. An irregular body fufpended by one end has been found to perform 20 vibrations in a minute. Required the diftance of its centre of ofcillation from the point of fufpenfion?

Here the time of one vibration is (0) 3 feconds; the fquare of which is 9; and 39,1196, multiplied by 9, gives 352,0764 inches, or nearly 29 feet, for the distance fought.

THE

of motion in a manner rather extenfive for an elementary work. The abftract mode in which this fubject has been delivered, may poffibly have deterred the novice from the ftudy of natural philofophy. Perhaps he expected that after every theoretical chapter his attention fhould be relieved by fome experimental application of the doctrine. But if fuch had been the plan, either the work would have been protracted to an immoderate length, or many useful branches of the theory would have been fuppreffed.

The importance of the doctrine of motion, and its being the foundation of almost all the phenomena of nature, were the motives which placed it before every other branch of natural philosophy, and the reader may perhaps be pleased to hear, that whoever understands the leading principles of the foregoing theory, will meet with very little diffieulty in the perufal of the following parts of philofophy,

J

lofophy. He will alfo find that the doctrine of motion, which he may formerly have looked upon as a difficult and almoft a ufelefs fubject of fpeculation, is of general and extenfive application. Every tool, every engine of art, every œconomical machine, all the inftruments of hufbandry, and of navigation, the celeftial bodies, &c. are constructed, and act conformably to the laws of motion.

The knowledge of this doctrine anfwers two extenfive objects. It ferves to explain natural appearances, and it furnishes the human being with ufeful machines, which enable him to accomplish fuch effects, as without that affiftance would be utterly out of his power.-The application to natural phenomena will be inftanced in almost every chapter of this work.The fecond object will be confidered immediately.

Mechanics, in its full and extenfive meaning, is the science which treats of quantity, of extenfion, and of motion. Therefore it confiders the state of bodies either at reft or in motion. That branch of it which confiders the ftate of bodies at reft, as their equilibrium when connected with one another, their preffure, weight, &c. is called Statics. That which treats of motion, is called Dynamics. Both thofe expreffions are, however, used in treating of folid bodies; for the mechanics of fluids has two denominations analogous to the above. It is called Hydroftatics,

Hydroftatics, when it treats of the equilibrium or quiefcent ftate, and Hydrodynamics or Hydraulics, when it treats of the motion, of fluids.

What belongs exclufively to fluids will be noticed in the second part of thefe elements. The equilibrium of folids has been fufficiently examined in the preceding pages, and will be taken farther notice of in the following; fince in treating, of motion, of actions, of forces, &c. it will naturally appear that when thofe forces are equal and oppofite to each other, an equilibrium takes place.

The active application of the doctrine of motion confifts in the conftruction of machines for the purposes of overcoming refistances, or of moving bodies. Thus if a man wish to remove a ftone of a ton weight from a certain place, for which purpofe he finds his ftrength inadequate, he makes ufe of a long pole, which being applied in a certain manner, actually enables him to move the ftone. Thus also another perfon may wish to convey fome heavy article to the top of his house, he makes use of a fet of pullies with a rope, &c. and by that means easily accomplishes his object.

Infinite is the number, and the variety of machines; but they all confift of certain parts or fimple mechanisms, variously combined and connected with each other. Of thofe fimple machines we can reckon no more than fix or at most seven; viz. the Lever, the Wheel and Axle, the moveable Pul

ley

Tey or System of Pulleys, the Inclined Plane, the Wedge, and the Screw*.

The action or the effect of every one of thofe mechanical powers, depends upon one and the fame. principle; which has been fully explained in chapter IV,V, and VI; but we shall for the fake of perfpicuity briefly repeat it in the following three or four paragraphs, wherein the attentive reader will find the principles or analysis of all forts of machines.

The force or momentum of a body in motion, is to be derived not merely from its quantity of matter, or only from its velocity, but from both conjointly; for the heavier any body is, the greater power is required to ftop it or to move it; and on the other hand the fwifter it moves, the greater is its force, or the ftronger oppofition must be made to ftop it. Therefore, the force or momentum, is the product of the weight or quantity of matter by the velocity. Thus if a body weighing 10 pounds

move

* The writers on mechanics do not agree with respect to the number of the mechanical powers. Some exclude the inclined plane from the number; whilft others reckon it one of the principal, and confider the wedge and the fcrew as only fpecies of it. The balance has been likewife reckoned a peculiar mechanical power. But it has been rejected by others, either on account of its being nothing more than a lever, or because by the use of a balance no additional power is obtained, which advantage ought in truth be the characteristic property of a mechanical power.