proportions, a heavinefs and unwieldiness would arife, which would make them ufelefs to themselves, and difagreeable to the eye. In this as in all other cafes, whatever generally pleases taste, not vitiated by education, or by fabulous and marvellous relations, may be traced till it appears to have a just foundation in nature; though the force of habits is fo ftrong, and their effects upon our fentiments fo quick and fudden, that it is often no eafy matter to trace by reflection the grounds of what we find pleafing.

If feveral pieces of timber be applied to any mechanical ufe where jtrength is required; not only the parts of the fame piece, but the feveral pieces in regard to one another, ought to be fo adjusted for fize, that the strength may be always proportional to the frefs they are to endure.

This propofition is the foundation of all good mechanifm, and ought to be regarded in all forts of tools and inftruments we work with, as well as in the feveral parts of any engine. For who that is wife, will overload himfelf with his work tools, or make them bigger and heavier than the work requires? Neither ought they to be fo flender as not to be able to perform their office. In all engines, it must be confidered what weight every beam is to carry, and proportion the ftrength accordingly. All levers must be made strongest at the place where they are ftrained the moft; in levers of the first kind, they must be strongest at the fupport; in thofe of the fecond kind, at the weight; in thofe of the third kind, at the power, and di-minish proportionally from that point. The axles of wheels and pullies, the teeth of wheels, which bear greater weights, or act with greater force, must be made ftronger; and thofe lighter that have light work to do. Ropes must be so much fronger or weaker, as they have more or lefs ten

fion; and in general, all the parts of a machine must have such a degree of ftrength as to be able to perform their oflice, and no more. For an excess of ftrength in any part does no good, but adds unneceffary weight to the machine, which clogs and retards it's motion, and makes it languid and dead; and on the other hand, a defect of ftrength where it is wanted, will be a means to make the engine fail in that part, and go to ruin. So neceffary it is to adjust the firength to the ftrefs, that a good mechanic will never neglect it; but will contrive all the parts in due proportion, by which means they will last all alike, and the whole machine will be difpofed to fail all at once. And this will ever diftinguith a good mechanic from a bad one, who either makes fome parts fo defective, imperfect, and feeble, as to fail very foon; or makes others fo ftrong or clumfey, as to outlaft all the rest.

From this general rule it follows, that in feveral pieces of timber of the fame fort, or in different parts of the fame piece, the breadth multiplied by the Square of the depth, must be as the length multiplied by the weight to be borne; for then the ftrength will be as the ftrefs.

The breadib multiplied by the Square of the depth, and divided by the product of the length and weight, must be the fame in all.

One obfervation more, before I quit the doctrine of equilibrium or science of statics, which is, to inform you that the writings of the Platonists and Pythagoreans cannot be properly understood without a knowledge thereof. Their allufions to arithmetic, geometry, and ftatics, are very numerous; arithmetic they confidered as the fcience of mind; geometry as the fcience of ethics or moral virtue; and under fatics they couched judiciary and political knowledge.

They expreffed their notions of the principles

of

of all things in numbers; and measure, a geometrical term, was applied to moral action and virtue, as fetting due bounds to the paffions of the foul, marking out the lines of every duty, and afcertaining the exact medium between the too little and the too much, in every affection, energy, and action. Mankind in general have agreed with thefe philofophers, to use metaphors taken from ftatics, to exprefs their opinions of the different degrees of merit and demerit, the fubject of political juftice, Thus the terms heavy and light are every where applied to crimes and punishments. Thus likewife an important service to the ftate is termed weighty and momentous, whilst all little ones are termed light and of fmall moment. Hence in all Hence in all ages the ballance has been acknowledged as a fit emblem of diftributive or civil juftice; and the rectangular rule or plumb-line has been understood to be a fymbol or mark aptly reprefentative of commutative juftice. And the worth or weight of each part of the political fyftem is to be eftimated by greater or lefs importance or moment of it, to the prefervation of the fyftem; and by it's greater or lefs propensity to adhere to the center of all civil union, the laws of the civil conftitution.

the

OF COMPOUND ENGINES.

You have no doubt been often aftonished at the vast variety of compofition, of which feven fimple notes are fufceptible, and have contemplated with immenfe pleasure the great quantity of words formed from the twenty-four letters of the alphabet, and the infinity of numbers produced from unity. In the fame manner, from the fimple machines I have defcribed to you, compounded ones are formed by various combinations, fo as to ferve for different purposes, and yet the fame general

law

law takes place that I have already defcribed to you, namely, that the power and weight fuftain cach other when they are in the inverfe proportion of the velocities they would have in the direction wherein they act, if they were put in motion.

The mechanical powers, according to their different ftructure, ferve for different purposes; and it is the bufinefs of the fkilful mechanic to chufe or combine them in the manner that may be best adapted to produce the effect required. Befides raifing of weights and overcoming refiftances, one of the most useful problems in this fcience, is that of making a regular movement that may ferve to measure time with accuracy. It may, however, be proper to obferve to you here, that machines feldom owe their origin or improvement to confiderations deduced from the laws of motion; they are derived from other fources. It is from long experience of repeated trials, errors, deliberations, corrections, &c. continued throughout the lives of individuals, and by fucceffive generations of them, that the practical fciences derive their gradual advancement from aukward beginnings to their most perfect fta e of excellence.

To be a good mechanift requires the labour of a whole life; it is an art rather perfected by practice than theory; the principles of mechanism may be learned in books, but the art must be acquired by experience.

The knowledge of machines, in a theoretical view, confifts in knowing how to employ a given power, fo as to produce a required effect. To this end, it is neceflary in the first inftance to know accurately the nature and value of the power to be employed, and then to confider of the means and manner of applying this power to the bodies to be put in motion, fo as to obtain moft advantageously the defired effect.

If this effect can be obtained by fimple machines, it is useless to employ thofe that are compound; if a fimple one is not fufficient to answer the purpose, you must then have recourse to those that are compound.

TO COMPUTE THE POWERS OF COMPOUND ENGINES.

As notwithstanding the combination of fimple machines they ftill preferve their properties, the principles I have already laid down will be found fufficient for computing the effects. I. To difcover the mechanical power of any engine, it will be fufficient to measure the space defcribed in the fame time by the power and the refiftance; for the power always ballances the weight, when it is in the fame proportion as the velocity of the weight to the velocity of the power. Or, 2. By setting down the ratios of the power to the weight on cach mechanical power, the fum of thefe will be the ratio of the power to the weight; for when the ratio of the power to the weight is equal to the fum of the ratios expreffing the power and weight, there will be an equilibrium on each mechanic power.

Or,

1. Divide the machine into all the fimple ones of which it is formed; then begin at the power and call it one, and by the properties of the mechanical powers, find the forces in numbers which the first fimple machine exercises upon the fecond. Call this force one, and find the force in numbers with which it acts upon the third; and putting this force as one, difcover it's action on the fourth in numbers, and so on to the laft. Then multiply all these numbers together, and the product will be the force of the machine, fuppofing the firft power

one.