446 ON DRAUGHTr 



bolsters, this 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 axletrees much nearer the floors of the waggons, 

 and, therefore, admit of a much stronger and firmer mode of attachment, 

 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 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 prac- 

 tice, 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 likely to reach. 



