LECTURE XXXII. OF THE DIFFERENCE BETWEEN PRACTICE AND I HAVE, in what I have already faid on these fubjects, paid very little attention to the phyfical 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 supposed 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. 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 circumftances 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 these 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 caufes 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 fimooth bodies appear to the eye, yet if you examine their furfaces with a microscope, you will discover numberlefs inequalities. When a body is moved upon a plane, the prominent parts of the body must 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 promin tarot lie entionally raised abi Parts time lifted up, and, as it were, raised on an inclined plane equal to those protuberant parts, which will impede and diminish the effects of the moving power. It is not poffible to adopt any theory that will take in all the circumstances that occur in practice, for the quantity of friction between the fame bodies will vary under different circumftances, as their inequalities may be varied ad infinitum; not only by the nature of the bodies, but alfo by the degree of perfection they may receive from art. An experimental investigation, therefore, on the machines themselves, will always be more fatisfactory than any deductions from theory. Among the later writers on this fubject, Mr. Vince and Mr. Coulomb† claim the moft attention, particularly the latter; whofe tables, fhewing the frictions of different fubftances, may be found of confiderable ufe; but as they are too long for our purpofe, I fhall lay before you the contents of Mr. Vince's paper. The experiments of Mr. Vince were made to determine, 1. Whether friction be an uniformly retarding force. 2. The quantity of friction. 3. Whether the friction varies in proportion to the preffure or weight. 4. Whether the friction be the fame, on which foever of it's furfaces a body moves. To refolve these questions, a plane was adjufted parallel to the horizon; at the extremity was placed a pulley, which could be elevated or depreffed, fo as to render the ftring which connected the body and the moving force parallel to the plane. A divided fcale was placed by the pulley perpendicular to the horizon; the moving force defcended * Vince, Phil. Transactions. + Coulomb, Memoirs de l'Academie des Sciences defcended by the fide of this fcale. A moveable ftage was placed upon the fcale, which could be adjusted to the fpace through which the moving force defcended in any given time; which time was measured by a well-regulated pendulum, vibrating feconds. Now if friction be a uniform force, the difference between it and the given force of the moving power muft be alfo uniform, and therefore the moving body muft defcend with an uniformly accelerated velocity, and confequently the fpaces defcribed must be as the fquares of the times, juft as when there was no friction, only they will be dimirifhed on account of the friction. A body was placed upon the horizontal plane, and a moving force applied, which, from repeated trials, was found to defcend 524 inches in 4". The stage was then removed to that point to which the moving force would defcend in 3", upon the fuppofition that the fpace defcribed by the moving power were as the fquares of the times, and it was found to agree very accurately with the time. The ftage was then removed to that point to which the moving force ought to defcend in 2", and was found to agree exactly with the time. The fame was tried for 1", and the coincidences were ftill exact. To find whether a difference in the time of defcent could be obferved by removing the ftage a little above, or a little below the pofitions which correfponded to the above times, the experiment was tried, and the defcent was always found too foon in the former, and too late in the latter cafe, which proves that the forementioned fpaces corresponded exactly with the times. Each defcent, for greater certainty, was repeated eight or ten times. The experiment was alfo tried with different moving forces; in all which the fpaces coincided with the times. A great 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 increafed with the velocity; but upon covering bodies with paper, the confequences agreed with thofe already related. as 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 moquantity of matter tion upon the horizontal plane by any moving force, if both the weight of the body and the moving force be increased 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 increafed 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 defcribe the fame fpace in the fame time. Hence |