in a fecond, will be equivalent to 30 pounds, moving through one foot in a fecond. This will be 30 divided by 22, or 1 pounds. Were a fly of this kind to be applied, and the machine fet a going, the fly would be able to lift the peftle once after the moving power was withdrawn; but by increafing the weight of the fly to ten, twelve, or twenty pounds, the machine, when left to itself, would make a confiderable number of ftrokes, and be worked with much lefs labour than if no fly had been used. It is certain, however, that the fly does not communicate any abfolute increase of motion to the machine; for if a man, or any animal, is not able to fet any mechanical engine in motion without a fly, he will not be able to do it though a fly be applied, nor will he be able to keep it in motion, though fet a going with a fly, by means of a greater power.

* Encyclopedia Britannica, vol. x. part ii.

LECTURE

LECTURE XXXII.

OF THE DIFFERENCE BETWEEN PRACTICE AND THEORY IN MECHANICS.

HAVE, in what I have already faid on thefe fubjects, paid very little attention to the physical properties of the materials of which machines are compofed, or of the alterations thefe properties occafion in their effects. The propofitions that are demonftrated with the utmoft mathematical rigour, are not found to anfwer in practice, and the difference can only be allowed for and eftimated by experimental inveftigation.

In eftablishing the theory, I have fuppofed that machines did not rub against each other, and fo interrupt their ufual workings; I fuppofed that all the planes on which they moved were even, all the levers inflexible, and that the air gave no resistance: but this is not the cafe in practice; all these are impediments.

Whenever motion is communicated to a body, a certain refiftance must have been overcome by the moving force. This refiftance is of various kinds: 1. The inertia of the mafs moved. 2. That of it's weight, or other abfolute force, oppofed to the action of the moving power. 3. Obftacles by which the moving body is retarded in it's progrefs. Many circumstances relative to the moving forces which are exerted on bodies, in order to produce motion, must be attended to in order to proportion the means to the end, and to produce the

defired

defired effect, with all the advantages of which it is capable. It is a due obfervation of thefe and other particulars, which contributes to render mechanic inftruments perfect, and the neglect of them defective in their conftruction.

It will therefore be neceffary for you, in applying theory to practice, to confider all the phyfical circumftances which are capable of producing any diversity in the effects, how far they diminish motion, and to determine by experiments the laws that govern thefe circumftances, and the abatements to be made to make practice coincide with theory.

Even here, however, it will be neceffary to confider the machines as well made, as no rules can ever apply to the ignorance or errors of bad

workmen.

Among the various phyfical causes which occafion a difference between the theory and practice of machines, you may confider two as the most important, and the moft general: 1. The weight of the parts of which the machines are framed. 2. The friction of one part of the machine against another.

OF FRICTION.

However plane and fmooth bodies appear to the eye, yet if you examine their furfaces with a microfcope, you will difcover numberlefs inequalities. When a When a body is moved upon a plane, the prominent parts of the body muit neceffarily fall into each other's cavities, and thereby create a refiftance to the motion of a body; for the body cannot be moved, unlefs the prominent parts thereof be continually raised above the prominent parts of the furface whereon it flides; and this cannot be done, unless the body be at the fame

A great number of experiments were made with hard bodies, or thofe whofe parts fo firmly cohered, as not to be moved inter fe by the friction, and in each experiment bodies of very different degrees of friction were chofen, but the refults all agreed; we may therefore conclude, that the friction of hard bodies in motion is a uniformly retarding force.

Experiments were made to determine whether the fame law obtained for bodies when covered with cloth, woollen, &c. and it was found, in all cafes, that the retarding force increased with the velocity; but upon covering bodies with paper, the confequences agreed with thofe already related.

The next queftion is to determine whether friction, cæteris paribus, varies in proportion to the weight or preffure. Now if the whole quantity of the friction of a body, measured by a weight without inertia equivalent to the friction, increases in proportion to the weight, it is manifeft that the retardation of the body, arifing from friction, will not be altered; for the retardation varies quantity of friction hence, if a body be put in mo

as

quantity of matter tion upon the horizontal plane by any moving force, if both the weight of the body and the moving force be increafed in the fame ratio, the acceleration arifing from that moving force will remain the fame, because the accelerative force varies as the moving force, divided by the whole quantity of matter, and both are increased in the fame ratio; and if the quantity of friction increases alfo as the weight, then the retardation. from the friction will, from what has been faid, remain the fame, and therefore the whole acceleration of the body will not be altered; confequently the body ought, upon this fuppofition, ftill to describe the fame space in the fame time.

Hence

the fame time, when both the body and moving force are increased in the fame ratio, you may determine whether the friction increafes in proportion to the weight.

A body weighing 10 oz. by a moving force of 4 oz. described in 2" a space of 51 inches; by loading the body with 10 oz. and the moving force with 4 oz. it described 56 inches in 2"; and by loading the body again with 10 oz. and the moving force with 4 oz. it described 63 inches in 2".

A body whofe weight was 16 oz, by a moving force of 5 oz. defcribed a space of 49 inches in 3"; loading it with 64 oz. and the moving force of 20 oz. the space defcribed was 64 inches.

From thefe experiments, and many others of the fame kind, it appears, that the space described is always increased by increafing the weight of the body and the accelerative force in the fame ratio; and as the acceleration arifing from the moving force continued the fame, it is manifeft that the retardation arifing from friction must have been diminished, for the whole accelerative force must have been increased, on account of the increase of the space defcribed in the fame time; and hence, as the retardation from friction varies as the quantity of friction

quantity of matter

the quantity of frion increases

in a lefs ratio than the quantity of matter, or weight of the body.

The third queftion Mr. Vince proposed to determine was, Whether the friction varies by varying the furface on which the body moves?

Let us call the greater surface of the body A; it's leffer furface a. Now the weight on every given part of a, is as much greater than the weight on an equal part of A, as A is greater than a. If, therefore, the friction was in proportion to it's weight, it is manifeft, that the friction on a would VOL. III.

be