558 ON DRAUGHT. 



of the wheel from the stone, which will tend to impel the mass forward, with 

 exactly the same force as was required to draw it up to the top of this impedi- 

 ment. Without this elasticity it would be necessary to raise the whole load with 

 a sudden jerk, and thus instantaneously impart rapid movement to the whole 

 mass, which would absorb much power, and which would by no means be 

 returned by the load falling down from the stone. We see, therefore, that the 

 use of springs is to enable the wheels to rise and fall according to the inequalities 

 of the ground, while the load continues one constant equable motion. The 

 advantages of this action are very clearly pointed out, in a letter addressed to 

 the Committee on the Highways of the Kingdom, by Mr. D. Giddy, and given 

 in the Appendix to their first Report, printed in the year 1808 ; and this letter 

 explains so clearly, and in such few words, the whole theory of wheels, as well 

 as springs, that we think we cannot do better than quote it at length : — 



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

 answering two different purposes. 



" First, they transfer the friction which 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 approximate, but which, in practice, they are 

 never likely 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 possible 

 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 sufficiently adapt them to all roads ; and that the pressure of such wheels, 

 greatest in the middle, and gradually diminishing towards the sides, will 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 either wheel below 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 obviating the ill effects of expansions and con- 

 tractions. 



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



