fion; and in general, all the parts of a machine must have such a degree of ftrength as to be able to perform their office, and no more. For an excefs 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 ftrength 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 strong or clumfey, as to outlast all the reft.

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 breadih multiplied by the fquare of the depth, must be as the length multiplied by the weight to be borne; for then the strength

will be as the stress.

The breadth multiplied by the fquare 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 fcience of ftatics, 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 flatics, are very numerous; arithmetic they confidered as the fcience of mind; geometry as the fcience of ethics or moral virtue; and under ftatics they couched judiciary and political knowledge.

They expreffed their notions of the principles

of

of all things in numbers; and meafure, a geometrical term, was applied to moral action and virtue, as fetting due bounds to the passions 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 likewise an important fervice to the ftate is termed weighty and momentous, whilft all little ones are termed light and of small moment. 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 estimated by the 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,

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, so as to serve for different purposes, and yet the fame general

law

law takes place that I have already described to you, namely, that the power and weight fuftain each 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 beft adapted to produce the effect required. Befides raifing of weights and overcoming refiftances, one of the moft ufeful problems in this fcience, is that of making a regular movement that may ferve to meafure 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. end throughout the lives of individuals, and by ceffive generations of them, that the practical onces derive their gradual advancement from aukward beginnings to their moft 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 mechanifm 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 firft 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 most 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 recourfe to thofe 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. 1. 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 each mechanical power, the fum of these 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 second. 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.

2. For

2. For wheel work, take the product of the number of teeth in all the wheels that act upon or drive others for the power, and the product of the teeth in all the wheels moved by them for the weight or instead of the teeth take the diameter. Otherwife thus:

In wheel work, there are always two wheels fixed upon one axis, or elfe one wheel and a pinion, or a barrel which fupplies the place of a wheel.

Of these call that wheel the leader which is acted upon by the power, or fome other wheel; and call the other, which is upon the fame axis, the follower, driving another wheel forward. The leader receives the motion, the follower gives it.

Then having the number of teeth, or the diameter of each, take the product of all the leaders for the weights, and the product of all the followers for the power.

The product of all the leaders gives alfo the velocity of the power, the product of all the followers the velocity of the weight.

The principles being clear, it will be fuperfluous to enter into the examination of a great number of machines; a few will be fufficient to render you masters of the subject.

OF SMEATON'S PULLIES.

I have already noticed to you some combinations of pullies. The conftruction of this mechanical engine is fo fimple, that it is of little importance whether it be confidered under the head of fimple or compound engines. Some variations in the conftructions thereof have been already noticed I fhall now lay before you the conftruction of a tackle of pullies, contrived by that excellent mechanic Mr. Smeaton, and which is not fo much known as it deferves to be,

The