563 ON DRAUGHT. 



' Taking wheels completely in the abstract, they must be considered as 

 answering two different purposes. 



'First, they transfer the friction Avhich would take place between a 

 sliding body and the rough uneven surface over which it slides, to the 

 smooth, oiled peripheries of the axis and box, assisted by a leverage in the 

 proportion of the diameter of the wheel to the axis. 



' Secondly, they procure mechanical advantage for overcoming obstacles, 

 by introducing time proportioned to the square roots of their diameters, 

 when the obstacles are small as compared with the wheels ; and they pass 

 over transverse ruts or hollows, small in the same comparison, with an 

 absolute advantage proportioned to their diameters, and a mechanical one 

 proportionate to the square roots of these diameters. 



' Consequently wheels, thus considered, cannot be too large ; in 

 practice, however, they are limited by weight, by expense, and by 

 experience. 



' With reference to the preservation of roads, wheels should be made 

 wide, and so constructed that the whole breadth may bear at once ; 

 and every portion in contact with the ground should roll on without 

 any sliding. 



' It is evident, from the well-known properties of the cycloid, that the 

 above conditions cannot all unite, unless the roads are perfectly hard, 

 smooth, and flat ; and the felloes of the wheels, with their tire, are accurate 

 portions of a cylinder. These forms, therefore, of roads and wheels, 

 would seem to be asymptotes, towards which they should always approxi- 

 mate, but which, in practice, they are never Hkely to reach. 



' Roads must have some degree of curvature to throw off water, and the 

 peripheries of wheels should, in their transverse section, be as nearly as 

 [)0ssible tangents to this curve ; but since no exact form can be assigned to 

 roads, and they are found to differ almost from mile to mile, it is presumed 

 that a small transverse convexity given to the peripheries of wheels, 

 otherwise cylindrical, will generally adapt them to all roads ; and that the 

 pressure of such wheels, greatest in the middle, and gradually diminishing 

 towards the sides, "wdll be less likely to disarrange ordinary materials, than 

 a pressure suddenly discontinued at the edges of wheels perfectly flat. 



' The spokes of a wheel should be so arranged as to present themselves 

 in a straight line against the greatest force they are in common cases 

 likely to sustain. These must evidently be exerted in a direction pointed 

 towards the carriage, from lateral percussions, and from the descent of 

 cither wheel beloAv the level of the other ; consequently, a certain degree 

 of what is termed dishing must be advantageous, by adding strength, 

 whilst this form is esteemed useful for protecting the nave, and for obviat- 

 ing the ill effects of expansions and contractions. 



' The line of traction is theoretically best disposed, when it lies exactly 

 parallel to the direction of motion ; and its power is diminished at any 

 inclination of that line, in the proportion of the radius of the wheel to the 

 cosine at the angle. When obstacles frequently occur, it had better, per- 

 haps, receive a small inclination upward, for the purpose of acting with 

 most advantage when these are to be overcome. But it is probable, that 

 different animals exert their strength most advantageously in different 

 directions ; and, therefore, practice alone can determine what precise 

 inclination of the Hne is best adapted to horses, and what to oxen. 

 These considerations are, however, only applicable to cattle drawing 

 immediately at the carriage ; and the convenience of their draft, as con- 

 nected with the insertion of the line of traction, which continued, ought 

 to pass through the axis, introduces another Imiit to the sizeof the wheels. 



' Springs were in all likelihood first applied to carriages, with no other 



