MECHANICS.

HE following Example of the Nature and Ufes of the
Mechanic Powers, will not, perhaps, be thought un-

neceffary, or at least, not improper in this Place..

Mechanics is a mix'd mathematical Science, which conAiders Motion and moving Powers, their Nature and Laws, with the Effects thereof, in Machines, &c.

That Part of Mechanics which confiders the Motion of Bodies arifing from Gravity, is by fome called Statics.

Mechanical Powers, denote the fix fimple Machines; to which all others, how complex foever, are reducible, and of the Affemblage whereof they are all compounded.

The Mechanical Powers, are the Balance, Lever, Wheel, Pully, Wedge, and Skrew.

They may, however, be all reduced to one, viz. the Lever.

The Principle whercon they depend, is the fame in all, and may be conceived from what follows.

The Momentum, Impetus, or Quantity of Motion of any Body, is the Factum of its Velocity, (or the Space it moves in a given Time,) multiplied into its Mafs. Hence it follows, that two unequal Bodies will have equal Moments, if the Lines they defcribe be in a reciprocal Ratio of their Maffes. Thus, if two Bodies, faftened to the Extremities of a Balance or Lever, be in a reciprocal Ratio of their Diflances from the Point; when they move, the Lines they defcribe will be in a reciprocal Ratio of their Maffes. For Example.

As

C

E

If the Body A be triple the Body B; and each of them be fixed to the Extremities of a Lever A B, whose Fulcrum, or fixed Point is C, as that the NB Diftance of B C be triple the Distance

CA; the Lever cannot be inclined on either fide, but the Space B E, paffed over by the lefs Body, will be triple the Space A D, paffed over by the great one.

So

So that their Motions or Moments will be equal, and the two Bodies in æquilibrio.

Hence that noble Challenge of Archimedes, datis viribus, datum pondus movere; for as the Distance CB may be increafed infinitely, the Power or Moment of A may be increased infinitely. So that the Whole of Mechanics is reduced to the following Problem.

Any Body, as A, with its Velocity C, and alfo any other Body, as B, being given; to find the Velocity neceffary to make the Moment, or Quantity of Motion in B, equal to the Moment of A, the given Body.-Here, fince the Moment of any Body is equal to the Rectangle under the Velocity, and the Quantity of Matter; as BAC are proportional to a fourth Term, which will be c, the Celerity proper to B, to make its Moment equal to that of A. Wherefore in any Machine or Engine, if the Velocity of the Power be made to the Velocity of the Weight, reciprocally as the Weight is to the Power; fuch Power will always sustain, or if the Power be a little increased, move the Weight.

Let, for Inftance, A B be a Lever, whofe Fulcrum is at C, and let it be moved into the Pofition a C b.-Here, the Velocity of any Point in the Lever, is as the Diftance from the Center. For let the Point A describe the Arch A a, and the Point B the Arch B. b; then thefe Arches will be the Spaces described by the two Motions: but fince the Motions are both made in the fame Time, the Spaces will be as the Velocities. But it is plain, the Arches A a and B b will be to one another, as their Radii A C and A B, because the Sectors A Ca, and B C b, are fimilar: wherefore the Velocities of the Points A and B, are as their Distances from the Center C.

Now, if any Powers be applied to the Ends of the Lever A and B, in order to raise its Arms up and down; their Force will be expounded by the Perpendiculars S a, and b N; which being as the right Sines of the former Arches, b B and a A, will be to one another alfo as the Radii A C and C B; wherefore the Velocities of the Powers, are also as their Distances from the Center. And fince the Moment of any Body is as its Weight, or gravitating Force, and its Velocity conjunctly; if different Powers or Weights be applied to the Lever, their Moments will always be as the Weights and the Distances from the Center conjunctly.-Wherefore, if to the Lever, there be two Powers or Weights applied reciprocally proportional to their Distances from the Center, their Moments will be equal; and if they act contrarily, as in the Cafe of a Stilliard, the Lever will remain in an horizontal

Pofition,

Pofition, or the Balance will be in æquilibrio.--And thus it it is easy to conceive how the Weight of one Pound may be made to equi-balance a thoufand, &c.

if

Hence alfo it is plain, that the Force of the Power is not at all increased by Engines; only the Velocity of the Weight in either lifting or drawing, is fo diminished by the Application of the Inftrument, as that the Moment of the Weight is not greater than the Force of the Power. Thus, for Inftance; any Force can raife a Pound Weight with a given Velocity, it is impofible by any Engine to effect, that the fame Power fhall raise two Pound Weight, with the fame Velocity: But by an Engine it may be made to raise two Pound Weight, with half the Velocity; or 10000 times the Weight with Tove of the former Velocity.

ARCHI

ARCHITECTURE.

A

RCHITECTURE may be defined the Art of Building, or of erecting Edifices, proper either for Habitation, or Defence.

Architecture is ufually divided, with refpect to its Objects, into three Branches, Civil, Military, and Naval.

Civil Architecture, (which is the only Part we fhall treat of in this Place) called alfo abfolutely and by way of eminence Architecture, is the Art of contriving and executing commodious Buildings for the Ufes of civil Life, as Houfes, Temples, Theatres, Halls, Bridges, Colleges, Portico's, &c.

Architecture is fcarce inferior to any of the Arts in point of Antiquity. Nature and Neceffity taught the first Inhabitants of the Earth to build themfelves Huts, Tents, and Cottages; from which, in courfe of Time, they gradually advanced to more regular and ftately Habitations, with Variety of Ornaments, Proportions, &c.

In the common Account, Architecture fhould be almost wholly of Grecian Original: three of the regular Orders or Manners of Building, are denominated from them, viz. Corinthian, lonic, and Doric: and fcarce a Part, a fingle Member, or Moulding, but comes to us with a Greek Name.

Civil Architecture may be diftinguifhed, with regard to the feveral Periods or States thercof, into Antique, Ancient, Gothic, Modern, &c.

Another Divifion of civil Archeteure, arifes from the different Proportions which the different Kinds of Buildings rendered neceffary, that we might have fome proper for every Purpose, according to the Bulk, Strength, Delicacy, Richness, or Simplicity required.

Hence arofe five Orders or Manners of Building, all invented by the Ancients at different Times, and on different Occafions, viz. Tufcan, Doric, Ionic, Corinthian, and Compofite.

What forms an Order, is the Column with its Bafe and Capital; furmounted by an Entablature, confifting of Archi

trave

trave, Frieze, and Cornice; and fuftained by a Pedestal. All which are delineated upon the annexed Plate.

The definitious Vitruvius, Barbaro, Scamozzi, &c. give of the Orders, are so obfcure, that it were in vain to repeat them without dwelling, therefore, on the Definition of a Word, which Custom has established, it is fufficient to obferve, that there are five Orders of Columns; three whereof are Greek, viz, the Doric, Ionic, and Corinthian; and two Italic, viz. the Tufcan, and Campofite.

The three Greek Orders reprefent the three different Manners of Buildings, viz. the folid, delicate, and middling; the two Italic ones are imperfect Productions thereof. The little regard the Romans had for these laft, appears hence, that we do not meet with one Inftance in the Antique, where they are intermixed. That Abuse the Moderns have introduced by the mixture of Greek and Latin Orders, Daviler obferves, arifes from their want of Reflection on the Use made thereof by the Ancients.

The Origin of Orders is almost as ancient as human Society. The Rigor of the Seafons firft led Men to make little Cabins, to retire into; at firft, half under Ground, and the half above covered with Stubble: at length, growing more expert, they planted Trunks of Trees an-end, laying others across, to fuftain the Covering.

Hence they took the Hint of a more regular Architecture; for the Trunks of Trees, upright, reprefent Columns: the Girts, or Bands, which ferved to keep the Trunks from burfting, expreffed Bafes and Capitals; and the Summers laid acrofs, gave the Hint of Entablatures; as the Coverings, ending in Points, did of Pedements. This is Vitruvius's Hypothefis; which we find very well illustrated by M. Blondel.

Others take it, that Columns took their rife from Pyramids, which the Ancients erected over their Tombs; and that the Urns, wherein they inclofed the Ashes of the Dead, reprefented the Capitals, whofe Abacus was a Brick, laid thereon. to cover the Urns: but Vitruvius's Account appears the more natural.

;

At length, the Greeks regulated the Height of their Columns on the Foot of the Proportions of the human Body: the Doric reprefented a Man of a strong, robust Make the lonic that of a Woman; and the Corinthian that of a Girl: Their Bafes and Capitals were their Head-drefs, their Shoes, &c.

Thefe Orders took their Names from the People, among whom they were invented: Scamozzi ufes fignificative Terms

to