140 ON DRAUGHT. 



l)olsl(>rs; tl 13 admits of considerable play in the parts, and except in new, 

 built or very strong waggons, there is never that firm connexion between 

 the load and the wheels, which we have stated to be necessary. Large 

 wheels would bring the axletrecs much nearer the floors of the waggons, 

 and, therefore, admit of a much stronger and firmer mode of attachmei;t, 

 which would be found to produce a very considerable effect in diminishing 

 the draught. 



We have been very particular in confining our observations to longitudi- 

 nal elasticity, or yielding in the direction in which the power is applied, 

 and in which the progressive movement takes place; because elasticity in 

 any other direction, instead of increasing the draught, tends very much to 

 diminish it. Let us suppose the load placed upon perfectly easy springs, 

 which allow it to move freely in every direction, except longitudinally, 

 when any one of the wheels comes in contact with a stone, the elasticity of 

 the spring will allow it to run over the stone without sensibly raising the 

 load which is upon it, and the force which is required to pull the wheel 

 over the stone, will be restored again by the descent 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 impediment: 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 obsta- 

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

 when t!ie 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. 



" ^Vith 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 of the wheel, In contact with the ground, should roll on 

 H-ithout any slidinir. 



" 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 likel} to reach. 



