WHEEL. 



eonfidered as inclined planes. In order to draw the wheel 

 AB {Plate XL. Mechanics, fg. 13.) over the obftacle 

 D, M. de Camus, agreeably to the principles above laid 

 down, would have the horfe draw in the line H C ; where- 

 as Mr. Beighton fays, fince the obftacle is D, and the tan- 

 gent of the earth, or line of the floor, is at B, and the line 

 to be moved in is B D, an inclined plane ; the eafieil pofi- 

 tion of drawing, to get the wheel over D, is to draw in the 

 pofition of that inclined plane B T, or its parallel C i. As 

 all the radii of a wheel are equal, the pulling at the centre is 

 the fame as a balance in equihbrio ; viz. there is the fame 

 force at A as at B. But in the cafe of drawing in the ho- 

 rizontal line H C, when the obftacle is at D, the whole 

 force which the horfe has for drawing is by the fhort end of 

 the brachium = f D, againft the force or weight of the 

 long end of the brachium/ D = c C, which rauft be very 

 difadvantageous ; therefore, he fays, the line of traftion 

 fhould be b C. Defag. Exp. Phil. vol. ii. App. p. 542, 

 &c. 



Whilft M. Camus maintained that the line of traftion 

 fhould be an horizontal line, or always parallel to the ground 

 on which the carriage is moving, becaufe the horfe can exert 

 his greateft ftrength in this direftion, and becaufe the line of 

 draught, being perpendicular to the vertical fpoke of the 

 wheel, afts with thelargeft poffible lever, M. Couplet, confi- 

 dering that the roads are never perfeftly level, and that 

 the wheels are conftantly furmounting fniall eminences, even 

 in the beft roads, recommends the line of traftion to be 

 oblique to the horizon. It is, however, to M. Depar- 

 cieux (Sur le Tirage des Chevaux, Mem. Acad. Roy., 

 1760. ), that we are principally indebted for juft ideas on this 

 fubjeft. He has Ihewn in the moft fatisfaftory manner that 

 animals draw by their weight, and not by the force of their 

 mufcles. In four-footed animals, the hinder feet are the 

 fulcrum of the lever by which their weight afts againil the 

 load ; and when the animal pulls hard, itdeprefles its cheft, 

 and thus increafes the lever of its weight, and diminiihes the 

 lever by which the load refifts its effcfts. Thus in Plate XL. 

 Mechanics, Jig. 12, let P be the load, D A the hne of trac- 

 tion, and let us fuppofe F C to be the hinder leg of the 

 horfe, A F part of its body, A its cheft or centre of gra- 

 vity, and C E the level road. Then AFC will reprefent 

 the crooked lever by which the horfe afts, which is equiva- 

 lent to the ftraight one A C. But when the horfe's weight 

 afts downwards at A, round C as a centre, fo as to drag 

 forward the rope A D, and raife the load P, C E will re- 

 prefent the power of the lever in this pofition, or the lever 

 of the horfe's weight, and C F the lever by which it is re- 

 fifted by the load, or the lever of refiftance. Now, if the 

 horfe lowers its centre of gravity A, which it always does 

 when it pulls hard, it is evident that C E, the lever of its 

 weight, will be increafed, while C F, the lever of its refift- 

 ance, will be diminifhed, for the line of traftion A D will 

 approach nearer to C E. Hence we may fee the great be- 

 nefit which may be derived from large horfes, for the lever 

 A C neceffarily increafes with their fize, and their power is 

 always proportioned to the length of this lever, their weight 

 remaining the fame. Large horfes, therefore, and other 

 animals, will draw more than fmall ones, even though they 

 have lefs mufcular force, and are unable to carry fuch a 

 heavy burden. The force of the mufcles tends only to 

 make the horfe carry continually forward his centre of gra- 

 vity ; or, in other words, the weight of the animal produces 

 the draught, and the play and force of its mufcles ferve to 

 continue it. 



From thefe remarks, then, according to Dr. Brewtler's 

 llatement, we may deduce the proper pofition of the 



line of traftion. When the line of traftion is horizon- 

 tal, as A D, the lever of refiftance is C F ; but if this 

 line is oblique to the horizon, as A^, the lever of re- 

 fiftance is diminiftied to C/, while the lever of the horfe's 

 weight remains the fame. Hence it appears, that inclined 

 traces are much more advantageous than horizontal ones, as 

 they uniformly diminifti the refiftance to be overcome. De- 

 parcieux, however, has inveftigated experimentally the moft 

 favourable angle of inclination, and found, that when the 

 angle D A F, made by the trace A d, and a horizontal line, 

 is fourteen or fifteen degrees, the horfes pulled with the 

 greateft facility and force. This value of the angle of 

 draught will require the height of the fpring-tree bar, to 

 which the traces are attached in four-wheeled carriages, to 

 be one-half of the height of that part of the horfe's breait 

 to that with which the fore end of the traces is connefted. 



This height is about four feet fix inches, and therefore 

 the height of the fpring-tree bar fhould be only two feet 

 three inches, whereas it is generally three feet. 



8. The utihty of broad wheels, in amending ^nd pre- 

 ferving the roads, has been fo long and generally acknow- 

 ledged, as to have occafioned feveral afts of the legiflature 

 to enforce their ufe. See Turnpike. 



Several excellent and well-devifed experiments have not 

 long ago been inftituted by Boulard and Margueron, which 

 have fatisfaftorily evinced the diftinguiftiing advantage of 

 broad wheels. See a Memoir prefented to the Academy of 

 Lyons, in the Journal de Phyfique, tom. xix. p. 424. 



Neverthelefs, the proprietors and drivers of carriages 

 feem to be convinced by experience, that a narrow-wheeled 

 carriage is more eafily and fpeedily drawn by the fame num- 

 ber of horfes than a broad-wheeled one of the fame burthen. 

 And though government allowed them to draw with more 

 horfes, and carry greater loads than ufual, they were per- 

 fuaded with difficulty to comply with the requifition of le- 

 giflature ; and methods have been ufed to evade it. Their 

 principal objeftion has been, that as a broad wheel muft 

 touch tlie ground in many more points than a narrow wheel, 

 the friftion muft of courfe be fo much the greater ; not con- 

 fidering, that if the whole weight of the waggon, and load 

 in it, bears upon many points, each fuftains a propor- 

 tionable lefs degree of weight and friftion than when it 

 bears only upon a few points ; fo that what is wanting in 

 one is made up in the other, and, therefore, will be juft 

 equal under equal degrees of weight, as appears by the fol- 

 lowing plain and eafy experiment propofed by Mr. Fer- 

 gufon. 



Let one end of a piece of packthread be faftened to a 

 brick, and the other end to a common fcale for holding 

 weights ; then having laid the brick edgeways on a table, 

 and letting the fcale hang under the edge of the table, put 

 as much weight into the fcale as will juft draw the brick 

 along the table. Then taking the brick to its former place, lay 

 it flat on the table, and leave it to be afted upon by the fame 

 weight in the fcale as before, which will draw it along with 

 the fame eafe as when it lay upon its edge. In the former 

 cafe, the brick may be eonfidered as a narrow wheel on the 

 ground ; and in the latter as a broad wheel. And fince the 

 brick is drawn along with equal eafe, whether its broad fide 

 or narrow edge touches the table, it ftiews that a broad 

 wheel might be drawn along the ground with the fame eafe 

 as a narrow one, fuppofing them equally heavy, even though 

 they fhould drag, and not roll as they go along. Befides, 

 as narrow wheels are always finking into tlie ground, efpe- 

 cially when the heavieft part of the load lies upon them, 

 they muft be eonfidered as conftantly going up hill, even on 

 level ground ; and tliejr edges muft fultain much friftion by 



rubbing 



