——— V Univ.-Bibl. Siessen] ————.— ——— ——— ON rH© MECHANICAL PRINCIPLES EDIN BURGH: Printed for J. BALFOUR. M, DCC, LXXI1Y. ADVERTISEMENT. Wt PLE defign of this performance is to HM affift any perfon acquainted with the: fimpleft principles of mechanics to under- Gand the conftruction, manner of operation, and bef form of the ploug©; fo that, by attending tothe nature and ftate of the foil he has: to manages he may know what onftricion of this inftrument iscbeft fuited for accomplifhing the purpofes he has in and be enabled to give directions for If the Author is View 3 making it accordingly. fuccefsful in this attempt, (ion that he will render a there can be no que n important pi fervice to his country. a— ERRATA Note, line 4 for team read beam. 1. 25 for-adherent read diferent. ]. 7. for their fize read his ize, 1, 9. for raifed read varied. Pigg 4-Oe(Ue Ge HH. HE plough affords, in every civilized country, employment for almoft one ’ halfits inhabitants; and is the chief means of procuring fubfiftence for the whole. But, notwithftanding this great and ge- neral utility, and that agriculture has com- monly accompanied fcience and philofophy, the plough is an inftrument whereon theory has never condefcended to beftow the flight- eft attention.. Whether this neglect has a- rifen from the apprehended meannefs or dif- ficulty of the fubje&, or perhaps from both, I fhall not undertake to decide; but rather proceed to the more agreeable and ufeful tafk, the attempting to fupply the defeat, by an 6.‘ANE(SO Sees an inveftigation of the méchanical principles on which it is conftructed, with a view to determine its beft and moft advantageous form.| The moft corre&t general idea we can conceive of the plough, or the inftrument in mechanics whofe form and manner of ope- ration it moft nearly refembles, is that of a half-wedge™, abftrating from the beam and handles, which are fubfervient intirely to the purpofes of moving and managing it. This view, indeed, is fo varied and difguifed by a number of circumftances, that the refem- blance may not perhaps immediately appear. It will be proper, however, to keep it in our eye, as the beft ground-work to'which every part of the defcription may be referred: And, when jall deviations are explained and accounted for, the fimilarity will probably be found greater than is expected. The # ABC, fig. I. is a whole wedge. Divide the angle at B into two equal parts, by the line BD, which line will bife& the wedge, and point out its direCtion; and confequently DBC. or ABC, fig. IL willbe a half wedge. AB, fig. II. is the flat or left fide; BC is the right or projected fide; AC is the back; and the narrow fide ABC is the edge. 2S OW THE, PLOWGH Ff ~~ The plough, then, confidered as a half- wedge, moves on one of its* edges, with its flat fide towards the firm ground, and its inclined fide towards the ploughed ground. The face of the coulter, which re prefents the tharp angle of the wedge, cuts off the furrow from the unploughed land. The left fide of the plough being flat, and ap- plied to the firm ground, which cannot give way, makes the plough proceed in a ftraight line, and take off a furrow of equal breadth; and the right fide‘being inclined outwards, gradually removes the earth to a convenient diftance, turns, and breaks it. The left fide of the plough refembles very nearly the flat fide of the half-wedge, becaufe it is almoft wholly in the f fame plane, and has no inclination to the line of direction in which the plough moves, or the force * The line AD, fig. IL. reprefents the left fide of the furrow; AB the flat or left fide of the plough applied to the firm ground; BC its inclined, or right fide, applied to the ploughed land. + Differentthings are faid to be in the fame plane, when they are fituated in the fame plane furface, whether that furface be real or imaginary. bee i te ae force that pulls it adts. The neceffity of its having no inclination is obvious; for, had the direction of the jplough not coin- cided with the dire€tion of the force, but pointed either to the right or left, the con- ftant tendency of the inclination muft have been, to turn the plough from the right di- rection, either toward the furrow or the firm ground. And this is the reafon why° the plough is a half-wedge*. By its being a half-wedge, the direCtion of it coincides exactly with the direGtion of the force; whereas, had it been greater than a half- wedge, its direction muft have pointed to the * AD, fig. IL is the direction of the plough, or of the force that moves it. AB is the dire€tion of the plough, or half-wedge, according to note firft; and thefe two in this cafe coincide. Were the plough greater than a half-wedge, as ABC, fig. III. then, fuppofing ABE the direétion of the force, or the line of the furrow, DBF will be the natural di- rection of the plough tending to the left of the line of the force. Were the plough lefs than a half-wedge, as DBC, fig. IV. DBF being the line of force, ABE will be the natural dire€tion of the plough to the right of the line of force. OM cs ey ON THE PLOUGH. 4 the left of that of the force; and, confe- quently, its tendency been towards the firm ground. Had it been lefs, its direction muft have pointed to the oppofite fide, and its tendency onthat account been towards the ploughed land. The right fide of the plough deviates confiderably from the form of the inclined fide of the half-wedge. It is not, like the latter, perpendicular, but inclined a little to the horizon; by which means the plough now takes the figure of a half-wedge, whofe . upper edge is narrower than its lower. The defign of this part of its conftruction is to raife and turn the earth; for, as the plough is wider below than above, it firft infinuates its loweft and moft inclined part below the neareft fide of the earth of the furrow, rai- fes that fide gently up, and, penetrating full farther as it proceeds, gradually turns the earth over. Had the right fide of the plough been perpendicular to the horizon, or exaétly in this refpect refembled the wedge, it could not have raifed or turned the earth of the furrow, but muft have cut the earth out, and pushed it afide, with the B.?- fame 1 Cla PE 6 est Ae? fame furface uppermoft, as a common wedge feparates the parts of any body be- tween which it is made to pafs. The earth now being caifed ups the next ftep is to place it on its edge, or lay it on its back, as fhall be judged moft proper. Forithis purpofe, the mould-board is gene- rally made fteeper, or lefs loping toward the hinder than the fore-part. But what chietly produces the effect now fpecified is, the rai- fing of the hinder part of it above the level of the fore-part.© By this conftruction the mould-board rifes and projects atthe fame time*. The preflure on the different parts of the earth of the furrow takes place inva correfpondent manner; the loweft parts are leat preffed, the higher ones{till more, ac- cording to their height. It is abundantly plain, that, by this form, the plough muft place the earth on its edge, or turn it more or lefs over, according as the proyeCtion and inclination of this part are greater or lefs; and alfo that the refemblance to the wedge, * AB, fig. 5- reprefents the furface of the ground or plane, on pihich the plough moves; BK, the rife and projection of the mould-board above that plane. et ON yr oe PL OVC.»* xm wedge, in this view, would. be exprefled by cutting away the right hand angle of the edge on which it moves. Any perfon in.the leaft acquainted‘with the inftrument under confideration, will eafily perceive, that the defcription. now given of the right fide of it, refers to the plough with the plain mould-board..‘The curved mould-board* is a little different in form, aéts in a different manner, and is in- tended for a different kind of foil. It does not, however, oblige us to relinquifh the comparifon with the wedge, which will be found here equally convenient and fer- viceable as before. The curved mould-board is in general more perpendicular to the horizon than the plain one. But the fore-part, inftead of being plain, is bent into a curved figure, re~ fembling a little the bow of a fhip, fo that here the upper and lower parts of the plough are nearly of the fame breadth. Towards the other end, this board projects a good deal more above than below; and here the plough is wider above than below. It is eafy * See figure 6. 12 Axa mses A eafy to perceive, how thefe changes in fi- gure produce their correfpondent effects. For, as this board is, or ought to be, ufed in land fo loofe that it does not rife whole, the curve at the fore-end turns over fud- denly the earth of the furrow, and, in fo doing, feparates and bruifes it; and the pro- jetion on the other end lays it floping backwards, to prevent its falling again into~ its former place. The hinder part of this board has no elevation; for, if it had, as the earth it moves through has not much cohe- fion, and does not rife whole, a great part of it would not be ftirred at all; which it is plain would happen to all the earth that thould lie below the elevation. It is alfo eafy to perceive, from the de- {cription, how a few not very confiderable changes in the inclined fide of the half- wedge, would reprefent the figure of this mould-board*.. Another * Suppofe BC, fig. 7. a thick plain block, out of which a curved mould-board is to be formed; it mutt rife by a fmall projection above the plane from CtoD, and by a ftill greater projection from D tg B, onthe upper fide, but not on the lowes. OM THESPEOUGH. 13 ~ Another circumftance, wherein the plough departs from the figure of the half- wedge is, the fituation and inclination of the coulter f. With regard to fituation, the coulter is not placed where the inclination of the mould-board begins. which would render the refemblance more compleat, but ata confiderable diftance before it; fo that the plough acts, for fome time, as a cutting inftrument, before it begins to a&t as a wedge. Or, the plough may be confidered as a wedge whofe inclination is different at different places, very{mall for a certain length, but very confiderable afterwards. This fituation of the coulter is a very fimple but ingenious contrivance; for it both di- minifhes the refiftance, and makes the plough move with more feadinefs. It di- ».minithes confiderably the refiftance; becaufe the earth of the furrow is feparated and broken in fome meafure, before the mould-board reaches it, and in this loofe ftate more readily gives way to the projec- tion of the board. Had + Figure 5. and 6, “4 MNCL Sa F Had the coulter been placed where the inclination of the mould-board begins, the earth muft have fallen upon the rifing fide of the board almoft entire, and refifted pro- portionally more according to its greater firmnefs. This fituation alfo greatly promotes the fteady motion of the plough, by lengthen- ing confiderably the part that moves below the furface; for the longer-or fhorter this part is, the more or lefs fteady muft the mo- tion be. Now, by the fituation of the coul- ter, the plough gains the fame advantages in point of length as if it were one continu- ed wedge; and confequently muft be much lefs apt to be pufhed out of its direction, than it would be, if made fhorter, by having the coulter placed nearer, or joining to the mould-board. This fituation promotes fteady motion from another caufe. The foil. towards the furrow is always a little lefs firm, than that at fome diftance frorn it, being loofened by the treading of the cattle and rubbing of the plough. On this account, there is a conftant tendency in the plough to leave the firmer ground, Ventre nr 7 ee ON#T HES PLOUGH. a§ ground, and deviate towards the ploughed land, where the refiftance is lefs, becaufe the foil is loofer. To counterbalance this tendency, the coulter is fet inclining a little to the left*; fo that at the point it rifes fomewhat above the plane of the left fide, and is one exception to what was formerly ob- ferved, that this fide is all in one plane; and thus the coulter, both by moving in firmer ground, and by being inclined to the plane of the left fide of the plough, communicates a more fteady and uniform motion to the whole. Now, the fame inclination would not have produced the fame effe€ts, if the fituation of the coulter had been at or near the mould-board; becaufe the obftruGions, in that cafe, ating on a fhorter lever, would produce correfpondently greater- quences, and for this reafon difturb more the motion of the whole machine. The other particular formerly mentioned, was * Suppofe theline AF, fig. 7. to reprefent the plane of the left fide of the plough, F the point of the fhare or fock; then the point E may exprefs the lower end of the coulter placéd to the left of the plane., 16 A N E: S38. A..Y was the forward inclination of the coulter, The advantages of this pofition above a per- pendicular one are very confiderable. It balances the upward direction of force, which, without this, in fome meafure con- trary direCtion of the coulter, would foon bring the plough out of the ground altoge- ther*. It diminifhes the refiftance in cut- ting the foil by converting it into oblique in- ftead of being dire€t, which it would be by the perpendicular pofition. It laftly facili- tates greatly the cutting or tearing up of roots, by making them flide upon its edge, by which means, they are not only more readily but moreeafily cut or torn afunder, as the plough aéts againft them with a fhorter lever the higher they rife. The laft circumftance to be taken notice of is the form and ufe of the fhare, com- monly called in Scotland the fock. In ge- neral, it is almoft an exa& reprefentation of ‘the * GB, fig. 8. is the inclination of the coulter, CED is the direétion of the force, if there is only one force applied, and the mean direction, if there be two forces applied that act in different direCki- ons, as fhall be afterwards explained. a @NLTHE BTOUGH ii, the lower edge of the wedge, continued for- ward to the point of the coulter*.‘Theufe of itis to cut out, and raife up the under furface; while the coulter performs a like operation on the fide. For this purpofe, it is generally made up of two different forms, fuited to the two different ftates of a hard or a loofe foil. If the foilis of the firft kind, the fhare is made tapering in fuch amanner,° that its point pafles nearly under the middle of the earth of the furrow; and confequent- ly deviates a little from the plane of the ieft fide of the plough. The point is made ta- pering, becaufe by this form it penetrates more eafily; and as the foil has great cohefi- on, by pafling under the middle of the earth of the furrow, it raifes up the whole. The other form of this part of the plough is calculated for the loofe kind of foil, which has fo little cohefion, that it cannot be moved by penetrating below any particu- lar part of it, but almoft the whole of it muft be cut or fcooped out, before it can be raifed."To produce this effet, the point . C of * See fig. 6, 18 fe ES 72°" of the fhare lies in the plane of the left fide of the plough, becaufe the greateft refiftance muft be on that fide; and from the point it has a fharp edge projecting towards the right, called the fin or feather of the fhare, which penetrates below the earth of the fur- row, and cuts it out. I have been fo minute in the defcription of this inftrument for two reafons. The firft is, that its manner of operation, and the effect of every part of its conftruction, may be perfectly underftood, fo that any perfon may comprehend what form is neceflary to lay the foil in the fituation he fhall judge moft proper, and be enabled to give directi- ons for making it accordingly. The other reafon is, to lay a foundation for the application of fome theory, by fhow- ing that the form and operation of the plough are reducible to mechanical princi- ples, and that from them conclufions may fairly be drawn towards determining its moft advantageous figure. The beft plough is certainly that which, all other circumftances being equal, is pulled by leaft force. But, if it fhall happen, which So Ee SS On THE PLOUGH WwW which may probably be found to be the cafe, that the plough which requires the leaft force cannot have all other circumfances equal, the next inquiry will be, how to form compenfations, fo that the effect of thefe de- trimental circumftances may be felt as little as poflible. With a view to determine the firft of thefe points, namely, the form of the plough moved by leaft force, all the pains already taken to reduce it to the figure of a half wedge have been beftowed. The deviati- ons, though very confiderable, were not fo great as to invalidate any confequences drawn from the one to the other; becaufe they changed a little the regular figure, without altering at all, or very little, the manner of operation; and it is evident that a change in the latter only can have any confiderable effe& upon the common con- clufions. But, although the differences in figure fhould have a greater effect than can reafonably be fuppofed, yet they cannot be fo confiderable as to produce any mate- rial error in practice. It is furely not necef- fary to obferve, that the common method of moving 20 A N Bo Stas Ary moving the wedge by ftrokes, at intervals, compared with the continued action that pro- duces the motion of the plough, is no ob- jection againft the analogy between them, as the total fum of the force requifite to pro- duce the fame effect muft in both cafes be equal. The determination, then, of the form of the plough moved by leaft force, feems re- ducible to this fingle queftion. Suppofing any number of wedges of equal backs, but of different lengths, what is that particular length which meets with leaft refiftance, in moving through fucha loofe fubftance as earth, the fize and cohefion of whofe parti- cles are nearly equal? I have fuppofed the backs of the wedges of equal thicknefs, becaufe the greateft breadth of the ploughs compared together muft be equal, as fuch only can be ima~ gined to do the fame quantity of work in the fame time. I have likewife fuppofed, that the fize and cohefion of the particles of earth are nearly-equal, both becaufe in drawing general conclufions all particular accidental circumftances muft be abftracted from, and becaufe ploughed earth in fome meafure TT OW ithe PL OUcG HH.. 21 meafure approaches this ftate, and does it the more, the higher it is cultivated, by being pulverifed and cleared of obftruétions. Now, it feems abundantly evident from theory, that, abftraGting from friction, the {um of the refiftance which different wedges, whofe backs are equally thick, meet with in {eparating the parts of any folid body to the fame diftance, muft be nearly the fame. Theory teaches what common. fenfe indeed dictates, that the longer wedge requires lefs force to move it through the fame fpace; but this is a conveniency, or an apparent advan- tage only, and no faving of force upon the whole. Becaufe the longer wedge, in mo- ving through the fame fpace, does not over- come an equal quantity of refiftence. In order to overcome the fame refiftence, the longer; wedge muft move through a fpace at leaft as much greater than the fhorter one, as the length of the former is greater than that of. the latter. So that the gain of force upon the whole will be nothing, as the longer wedge lofes as much one way as it faves another*, This * From the theory of the wedge, the power is to the refiftence as half the back to one of the fides; confequently, ee 22 A. WN EY. Sa a This is the cafe in cleaving wood, or any folid body, where all the refiftence is gene- rally accumulated on{mall portions of the oppofite fides of the wedge.‘The circum- {tances are a little different; but the quanti- ty of force will likewife be found to be e- qual, in moving wedges of different incli- nations through fuch a loofe body as earth. In this cafe, as before, the longer wedge meets the refiftence more obliquely than the fhotter; but, to counterbalance this advan- tage, the refiftence acts a proportionally long- er time*, For, fuppofing both wedges to move confequently, if the back remain the fame, while the fide is increafed, the refiftance will be diminifhed in proportion. The fide indeed does not increafe quite fo faft as the length of the wedge does; but, when the difference between the half back and the fide is confiderable, as in the prefent cafe, it will do fo very nearly. Hence the refiftence in the fame {pace is diminifhed very nearly as the length in- creafes. And as the whole fpace is greater in that. proportion, the fum of the force in both cafes will be equal. * Let ABC, FHG, fig. 9. and 10. be two wed- ges of equal backs, AC, FG, but different lengths AB, et| ON THE BLOUGH. 2. move with the fame velocity, and confe- quently to lay off from the broadeft part of them the fame quantity of foil in the fame time; yet the{pace of time that any particle acts againft the longer wedge will be as much longer than the time it acts againft the fhorter, as the obliquity of the former is greater than that of the latter. What has been proved of the whole wedge muft hold equally true of the half one; for, abftraGiing as before from friCtion, the latter, in the fame circumftances, muft meet with exadtly. half the refiftence of the former. It feems to follow from this reafoning, that all ploughs which are of equal breadths, whatever their lengths be, fhould be pulled by equal force. This would certainly be the cafe, were the circumftances above mention- ed the whole that fhould be taken into the account, or had the particles of earth, like thofe of fome fluids, little or no friGion a- mong AB,FH, the particles a€ting in the direion DE do it with a greater obliquity, or a fmaller angle DEB, than the particles a€ting in the direGion KL with the greater angle KLH; but the aétion of the for- mer takes place along the longer line BE than HG. sa MONON SUR Ae mong themfelves, and very little againft any folid body over which they move. But the particles of earth have a confiderable friction among themfelves, and againft any body o- ver which they move; and therefore muft confiderably retard the motion of a body moving through them. Here, then, feems to be the circumftance that muft be decifive of the form of the plough moved by leaft force; for, it is plain, it muft be the one that has the leaft fri€tion, or that removes the particles of earth to an equal diftance with the leaft rubbing upon itfelf. Now, the plough that does this, rauft be the one that expofes leaft furface to the foil; for, the greater the furface, the greater al- ways mutt be the quantity of particles that rub at the fame time, and confequently the greater the fum of the friction. To be perfedtly fatisfied of the truth of this propofition, 1 made experiments by mo- ving half wedges of different lengths, but - of the fame thicknefs at the back, through {fand,. I caufed make four half wedges, whofe lengths were to one another as the numbers 3, 45 5» 6. I computed pretty ac- curately ONeTEER PLOUGH. 2.5 curately the furface of each of them, and found, that the weights that moved them were very nearly proportional to their fur- faces*. Thefe experiments are a proof, not only that fri€tion is in proportion to the furface of the plough, but alfo eftablith the preceed- ing theory; namely, that, abftracting from this circumftance, the refiftence made to all wedges of the fame thicknefs, whatever their lengths be, is the fame, in producing equal effects. Now, of all wedges of equal backs, the fhorter have always lefs furface. Hence follows this general conclufion: Of all ploughs of the fame breadth, thofe that D have * I put a quantity of fand upon a large table, and then moved the wedges through it by a weight fut- pended on a thread that run over a pully fixed on the edge of the. table. I taok all the care I could to bring the fand into the fame{tate every time the wedges were pulled through it; and repeated the experiment many times, with very nearly the fame refult. 26 ARMO TE- Sate ay have the greater inclination, and confe- quently are fhorter and expofe lefs furface to the foil, are pulled by lefs force. In confirmation of this doctrine, it may be obferved from experience, that this is re- markably the cafe with the iron plough, which is univerfally allowed to be pulled by lefs force than any other. It has however difadvantages that have hitherto prevented its general ufe, and probably will continue to do fo; the only reafon for mentioning it here, is the authority it affords in favour of the preceeding conclufion, which is fo con- fiderable, as not to have efcaped the grofs obfervation with which things of this na- ture are generally attended to. It was formerly hinted, that the plough pulled by leaft force would probably be found to have difadvantages, which, in fome meafure, counterbalance the advantages a- rifing from this circumftance. The chief of thefe is, that it moves unfteadily, and, on this account, performs its work more imper- fectly. The OM Fi WE oaPk O UG GE. 23 The reafon is, that, by being fhorter, it moves upon a{maller bafe, and is much lighter in proportion; fo that itis much more eafily turned out of its direCtion, by any unequal exertion of the force,or extraordi- nary refiftance in the foil. Experience will remove almoft entirely any inconveniences proceeding fram une- qual exertions of the force. But it will be extremely difficult, if not impoffible, to re- move every extraordinary interruption in the foil. Cultivation, however, tends to re- move thefe; and the more the foil is cultivated, the fewer of them will remain. What particular length of the plough is adapted to the various degrees of cultivation, it feems impoflible to give any rules how to de- cide. This muftbe!determined by experience and obfervation taken from circumftances on the f{pot, with the help of the following - general rule,‘thatit ihould be made as ‘ fhort as poflible’. From this view of the fubject, one might ealily deduce the hiftory of the old Scots plough, though otherwife entirely ignorant ; of 28 A N BE Seo AT itt. The whole conftruction of this inftru- ment marks its being intended for a foil in the moft uncultivated ftate, abounding with obftru€tions of every kind. The great length of the part that moves below the furface, and the exceflive ftrength and weight of all its paris, plainly fhow the great occafion that the contrivers had: to prevent its being turned afide, or broken to pieces by the numerous and obftinate interruptions to which it was expoied. The elevation alfo of the hinder part ot the mould-board, and the tapering of the hare; evidently imply a foil fo hard, or fo clofely bound together by the roots of vegetables, as to rife entire and unbroken. The original contrivance of this machine might be extremely well adapted to the cir- cumftances in which it was firft'employed, and certainly is fo fill to the fituation in which it is generally ufed; but it feems im- proper to continue to employ it of the fame fize and weight, where the circumftances that gave occafion to that ftrong and heavy conftruction have no longer exiftence, and in foils that have attained a confiderable de- gree of cultivation. From + See fig. 7; ON{THE PLOUGH. 29 From the preceeding reafoning it appears what form of the plough is moft advanta-_ geous, fuppofing it a half-wedge, and that its properties are to be determined from the_ theory ofthatinftrument. But perhaps it may be afked, whether this is the beft figure, and whether fome other might not be attend- ed with greater advantages? A fufpicion that this might be the cafe, feems to have given rifeto the curved mould-board, which has already been defcribed. The figure of a thip has alfo been quo- ted, and an analogy apprehended or i“ magined between the motion of it and that of the plough. It has been fuppofed, that earth in a ftate of perfe&t cultivation ap- proaches the nature of a fluid, and that the figure moft proper for moving through wa- ter, istherefore beft adapted for moving through foil. It is evident, from what was formerly ob- ferved concerning the direftion of the force that pulls the plough, that the refemblance to the figure of a fhip can only take place on the right fide; and that the left fide mutft infallibly be plain, becaufe in this form on- ly Retains ‘ than the plain?’ se OA OE Sek ly can the direGion of the plough coincide with the direGtion of the force. The matter then is reduced to this queftion,‘ Whether ‘the right fide of the plough can admit of ‘ any curved figure, that meets with lefs re- ‘{tenceand performs work as well or better That no curved figure can meet with fo little refiftence as the plain, fuppofing al- ways the greateft breadth in both cafes the fame, even in moving through a fluid of very little tenacity or fri€tion, feems abun- dantly evident from this fingle confideration, that it muft conftantly drive the fluid more be- fore it. The plain allowsthe fluid to flide eafily along its furface, and confequently meets with lefs refiftence; but the leaft curve or bending ¢ above the plain muft more or lefs repel the particles towards the parts from which they came, or in the dire&tion in which the furface moves, and therefore be expofed to proportionally great- er refiftence. This + See fig. 7. ST TE _ ON THE: PLOUGH. 31 This is obvioufly the cafe in the motionof| a fhip of the fharpeft bow; and there can be| no queftion, if the fore-part of a fhip were made in the figure of a wedge, it would meet with lefs refiftence than in any curved figure of which it can be formed. But fuch a fhip would be altogether unfit for the pur- pofes of navigation; for fhe could bear very little fail, and the leaft hard gale would run her down.‘This is the reafon why hips with the broadeft bows are the fafeft, though the worft failers. The refiftence made to the plain figure will be ftill proportionally lefs in moving through fuch a body as earth, whofe parti- cles have a confiderable fri@ion and cohe- fion.. The curved figure, in this cafe, be- fides pufhing the particles before it, muft+ be expofed to more frition, as its furface is larger; for it is evident that the leaft curve Ny muft make the furface greater than if it were plain. Tolprove experimentally what has been ad- vanced, I procured ahalf-wedge of the fame greateft breadth with thofe formerly men- tioned, but rifing on the right fide with a gentle ga 3 ENG BOS a gentle curve. I found that it always turn- ed afide to the left of the direction of the force, pufhed the fand more before.it than the plain half-wedge, and was refiftedin a confiderably greater proportion than that of its furface. Hence it appears, that the wedge is the figure that meets with leaft refiftence, and confequently that the curved mould-board requires more force to pullit than the plain f. There feems alfo to be great reafon to doubt, whether the curved mould-board per- forms better work than the plain. That it bruifes and feparates the foil more, mutt be admitted; but in the naturally loofe earth, wherein it muft be ufed, this can be per- formed + It will perhaps be objeéted here, that this doétrine contradi€ts what Sir Ifaac Newton has ad- vanced concerning the folid of leaft refiftence 5 which is well known to be different from the wedge. But in anfwer, I beg leave to obferve, that that folid isa mere jeu d’ efprit, which prefented itfelf to its great author in the courfe of other inquiries, which neither he, nor any body fince his time, has at- tempted to apply to any ufe, and which probably never can be applied to any, at leaft it cannot to the prefent fubject. ON THE PLOUGH. 3 formed very eafily by another inftrument of agriculture, and when land is ploughed for fallow, the more it is broken the worfe. It may be faid indeed, that this board might be applied to the plough conftruéted for a foil that rifes entire, where it would be of fingular ufe in breaking and reducing it. But this is what has never been thought proper to be put in practife: Andindeed it feems very uncertain whether a foil that rifes en- tire, could be broken by any curve of the mould-board, that would not render this machine intolerably hard to draw, from its natural figure, already extremely heavy and difficult to move. Hitherto I have defcribed the figure of the plough, and explained its manner of operation; I have inveftigated the properties of it; and endeavoured to determine its moft advantageous form: It only remains, that I point out the principles on which the pofi- tion and proportions of its particular parts depend, efpecially thofe of the beam and handles. The beam is entirely fubfervient to the purpofe of moving the plough; its pofition, E therefore, a. OAONPO FA Se A therefore, and dimenfions mutt be deter- mined by the ftruture of the machine. it moves, and the direétion of the force that acts upon it, which are the only circum- ftances that can affect it. Ifa wedge were driven into any body. whofe preffure and friction are equally di- {perfed overthe fides of the wedge, common fenfe and experience dictate, that, to move it ftraight forward, the force muft be ap- plied, as near as poflible, to the middle of sts back. But, if the preflure and fri€tion are not equally difperfed, or take place more towards one fide of it than the other; then the force mutt be applied on the back, as much nearer that fide as the preflure and friGion on it are greater. All which in theory means no more than this, that, to move the wedge ftraight forward, the force mutt be applied fo as to move the cen- ter of refiftence* in that direction. In * The center of gravity, is the point at which allthe weight of a body may be fuppofed accu- mulated, on its being fufpended. The center of refiftence, ee oar Ee ON THE PLOUGH. 35 In the fame manner, if a wedge were moved through fand, or fuch a body as earth, on:one of its edges, and had more preffure or friction on its lower‘than its higher parts, to make it hold a horizontal direction, the force behoved to be applied on its back, as much lower than the middle, as the refiftence on that fide is greater. Now, if inftead of the force applied to its back, it were pulled forward by an equal force applied to its face, this force muft act in a horizontal line beginning from its cen- ter of refiftence. Hence it appears, that, were the plough a perfect half-wedge, the _ only direétion of the force that could move it ftraight forward, would be a_ horizontal one, pafling as much below the furface of the foil as this center is fituated below.it; and that a direétion fo much above this, as that refiftence, isa point at which is accumulated all oppofition to its motion forward. This oppofition arifes from the inertia of the body itfelf, and the refiftence and friction of other bodies. The center of refiftence will always approach that fide on which the obftru€tions are greater. 36 A N BS sa 2S that of animal force muft unavoidably be, would very foon bring it out of the ground altogether. To prevent this laft confequence, the plough is fo formed as to have a conftant tendency to penetrate deeper into the earth, which it acquires chiefly by the inclination of the coulter; and from this circumftance arifes the neceflity of an upward direCtion of the force, to balance the downward ten- dency of the machine, and the convenient application of animal force in order to pull ifs: The proper line, then, of force that moves. the plough, fhould begin from its center of refiftence, with fuch a direction upwards, as juft to balance the tendency of the machine downward; for in this cafe only can the motion be performed ftraight forward. Now, this line, it is evident, in coming upward from the center of‘refiftence, be- hoved to pafs through the firm ground be- fore the plough*, and cut a paflage for it- felf * Suppofe C, fig. 8. the center of refiftence, CD the line of draught; the real line, if there is only ON THE PLOUGH. 37 felf as it moved along, a thing at firft fight utterly impracticable. But the fame pur- pofeisanfwered by the beam, as if what has been obferved were really poffible; and this is the circumftance that determines all at once both its ufeand length. For the beam muft be fo placed, and be of»fuch a length, as to coincide with a point of this line of direc- tion, at a convenient height above the fur- face of the ground, and by taking it up here, fuperfede the neceffity of its being continu- ed farther down; fothat the effect is per- feétly the fame’ as if the force acted on a line coming direétly from the center of refift- ence. The beam muft be fituated at a conveni- ent enly one force applied, but the mean line, if two, found by bife€ting the angle which the direCtions of the two forces make with one another; without a team, this line CD mufthave been fixed at C, be- low the furface of the earth KH; fo that the fur- face of the ground would have interfered with the direétion of it. This is prevented by the point of the beam that takes up this line at E, as near the fur- face of the earth as poflible. So that the point of the beam lies in the line of force pafling to the center of refiftence. ~ Sas ace ein — acdsee ete aS—= -— pea @ AN E:SSEA wW ent height above the furface, to avoid the interruptions to which it might otherwife be expofed; and therefore, fuppofing the downward tendency of the plough deter- mined, and the upward direction of the force.neceflary to balance it, the beam muft be made longer or fhorter, till its point fall into a point of the height required in the inclined line of the force. Now, the greater the downward tendency, the more upward muft be the dire&tion of the force; and, confequently, the fooner muft the beam meet with it, that is, muft be the fhorter. On the other hand, the lefs downward the tendency, the lefs upward will be the direc- tion, and the farther muft the beam be ex- tended befere it meets with that line, and confequently will be the longer. This do&rine would be exaCtly confor- mable to fat, and the ploughs with the more inclined coulters would always have the fhorter beams, and thofe with the. lefs inclined ones the longer, were it not that the dire€tionof the force may eafily be changed, by yoking the cattle nearer or farther from the point of the beam. Hence it hap- pens, — ee OL ee ON THE PLOUGH, 39 pens, that a plough may have a great down- ward tendency, and alfo a long beam, and the effect of both counterbalanced, by placing the cattle very near, which will give a great upward direCtion to the force. On the other hand, a plough may have a fmall inclination and fhort beam, and notwith- ftanding have downward tendency enough, by placing the cattle at a confiderable diftance, which will give a lefs upward di- rection to the force. Since, then, thefe cir- cumftances may be, and always are made to counterbalance one another, it will be afked, perhaps, whether it is of any confequence in what mannerthey do it, and whether there are any principles that determine ex- actly the beft length of the beam, the moft proper inclination of the coulter, andthe moft advantageous pofition of the cattle? With regard tothe beam, it fhould be made as fhort as poffible; becaufe the fhort- er itis, it will be much lighter in proportion, without being more in hazard of breaking, the only danger to which it is expofed, A beam is plainly a lever, on which confe- quently the longer it is, the force tending to break, oo Te Se, GT NS Ep RRB ond ait — —_™ —————— Sshedkabed el : ao AGN CE’ Sdgta# break it muft a& with greater advantage; and as the weight of adherent bodies equal- ly ftrong increafes much fafter than their length*, the fhorter beam will be equally ftrong and much lighter at the fame time. The longer beam, however, has one ad- vantage over the fhorter, which is, that it contributes more to make the motion fteady, and this it does by being a longer lever. Any extraordinary interruption muft put all the parts of the plough in fome mea{ure * Similar folids, and fuch only can be equally ftrong, are to one another as the cubes of their lengths.[Euclid b. 12. prop. 2. M¢ Laurin’s account of Sir I. Newton, p.170.] Suppofe two bodies, whofe lengths are as 2 and 3. The cubes ofthefe numbers, are 8 and 27-_ Which laft num- bers, if the bodies are of the fame kind of matter, will exprefs their different weights. Hence it ap- pears, if the length of a body be increafed only in the proportion of 2 to 3, its quantity of matter muft be augmented fo much, to make it equally{trong as be- fore, that its weight becomes three times and near a half greater. This is the reafon that the larger a- nimals of a kind are not ftronger in proportion to their fize than the fmaller, becaufe their quantity of matter does not increafe fo faft as their bulk. Ifit did, they would be rendered perfeétly unwieldy and a burden to themfelves. ON THESPLOUCH. A meafure out of their proper direction, and thofe moft that are at the greateft diftance fromthecenter; confequently, an obftruction that moves the fhare only a very little up -or down, will make the point of the beam defcribe a large portion of a circle. But the longer beam, by defcribing a larger portion than the fhorter one, will be fooner refifted, by the dire€tion of the force, and, therefore, fooner brought back to its proper pofition; fo that the fame obftru€tion will lefs difturb the motion of the plough with the longer beam, than the one with the fhorter. But, unlefs the interruptions are nume- rous and obftinate, this circumftance can- not be of much moment; betaufe the great- eft difference in length cannot be very con- fiderable. Here alfo it appears, that, by means of the beam, the plough acquires a more fteady and equal motion than if it were pulled by a line running dire€tly to the center of- fiftence. For, in the latter cafe, the direc- tion of the force could not have contributed F any Bo WCE shen a any thing to corre&t the effect of obftructi- ons, which always muft be done more or lefs by the intervention of the beam. Now, the way to have the fhorteft beam, is to place the point of it as near the furface of the ground as poffible; for this plain reafon, that, whatever the direction of the force be, the lower the beam is fet, they muft the fooner coincide. What the height of the point of the beam“fhould. actually be, it is impoffible to decide in general, be- caufe it muft be different in different cir- cumftances; and every perfon muft deter- mine for himfelf, from the fituation of the furface he has to cultivate. Ihave fpecified the point of the beam, as it is the part of it that can meet with any interruption; for cuftom has very properly formed it farther back into a confiderable curve, to prevent the plough from being incommoded, or choaked up by ftubble, or any loofe thing collected by the inclination of the coulter. With refpeét to the inclination of the coulter, I have already illuftrated the fupe- riority of this pofition to a perpendicular one; and am now to inquire, whether there is ON THE PLOUGH. 43 _ js any one inclination preferable to another. This queftion feems eafily decided; for the moft advantageous inclination is certainly the one that is expofed to leaft refiftence; but the one expofed to the leaft re- fiftence is the greateft, becaufe it meets the refiftence at the greateft obliquity; and hence it feems evident, that ploughs with moft inclined coulters thould be moft eafily drawn. This confequence would certainly follow, Gf the inclination of the coulter had no effect upon the laft mentioned circumftance, the direction of the force; or if it were in- different to the cattle, whether they pull more or lefs horizontal. But it is by no means indifferent to the cattle, in what di- rection they pull; for the moftadvantageous oneisplainly very near tohorizontal f. The reafon * Cattle pull with moft effect ina horizontal line pafling through their center of gravity. If they are obliged to pull from a point above or below this center, they muft bend their bodies from their natu- ral and moft eafy pofition, till they bring their center into their line of draught. The horizontal direction allows 44 ADRES ST aa Ve reafon is, that, by pulling in this manner, their whole force is employed in promoting motion in the direCtion in which them- felves move; whereas, in pulling either up- ward or downward, they ac obliquely to the direction forward’; and confequently part only of their farce can be exerted in that direction; and this part will be pro- portionally fmaller, the more upward they pull. Hence then it follows, as the great- er the inclination of the plough, the more upward always muft the cattle pull, that all the advantage gained by the inclination is loft by the direction of the force, and that, on the whole, no one inclination is prefe- rable to another. The only exception to this general conclufion is the cafe of land in a low ftate of cultivation, infefted with ftrong roots of vegetables, which will flide more readily on the face of the coulter the more it allows them to a&t in the moft natural and eafy pofi- tion. Befides, it is the horizontal direction that pro- motes motion forward; for, if they pull upward or downward, a part only of their force can be employ- edin the horizontal direction, as is plain from the refolution of forces, GN THE PLOUGH" 4 it is inclined; for which thofe who havea foil in this ftate to cultivate, muft make an allowance. The ufe of the handles, is to regulate the motion of the plough. If the downward tendency of the coulter and the upward di- rection of the force were exactly balanced, and the refiftence of the foil uniform, there would be very little occafion for handles, becaufe there would be nothing to turn the plough from the right direction. But, as it is extremely difficult to have matters fo nicely adjufted as now fuppofed, even though the beam and coulter are made moveable by wedges from their original pofi- tion, till an equilibrium takes place; and as itis impoflible, that the refiftence of the moft cultivated foil can be uniform, the handles become neceflary to correé&t any little defect in the original conftru@tion, and to apply an immediate remedy to any devi- ation arifing from extraordinary interrup- tions. For this purpofe, they act as levers, which may be confidered as heginning from the center of refiftence; and it is evident, that the longer they are, they have the greater ~ a —EEE Ree ee er, Sent choeee Ra Hed 6* ASW Oo RT SiS TA PY greater power, and the fhorter the lefs. Their beft length and height will be thofe which allow them to be moft eafily and conveniently managed, or which oblige the perfon that holds them to bend his be- dy as little as poffible. In this view, their height muft be fuited to their fize and their length to his ftrength. If the foil bein a tolerable ftate of cultivation, and the ma- chine well conflruéted, they will not need to be very long; and the fhorter they are, provided the perfon that holds them have ftrength enough to manage them, the bet- ter; for he will be obliged to bend his bo- dy lefs to produce the fame effect. As I have faid, the handles may be con- {idered as levers beginning from the center of refiftence, it will perhaps be afked, Whe- ther this is,in all cafes, ftrictly true; and how we fhall be able to decide, whether it is fo or not? To do this accurately, we fhould be determined exa@tly with regard to the fitua- tion of the center of refiftence. But the truth is, this determination cannot be made by any principles or operation previous to actual trial; becaufe it depends upon the friGtion and refiftence of the foil, which muft vary ee eee ON THE PLOUGH. 47 vary confiderably according to circumftan- ces. Could this center be accurately found, a plough might be conftructed at once, that would perform its work perfe@ly, without further alteration; and there would be no neceflity to leave the principal parts in a ftate moveable by wedges to obtain their true pofition. In working, however, this center may be very nearly determined; be- caufe it will always be found in the line of direétion of the force produced downward from the point of the beam; and we may be affured this line pafles through the center, when it exactly balances the inclination of the coulter. But, before application to ufe, the fituation of the center can only be guef- fed at, which, indeed, by the aid of experi- ence in fimilar cafes, may be done with a good deal of accuracy; at leaft, fo accurately, that a{mall alteration in the pofition of the beam, which is left practicable on purpofe, will remove the bad effect of any error that may be committed in the conftruction. This center will commonly be found a few inches above the middle of the fhare, though, \ =