On the Wheels and Springs of Carriages. S95 



tween a sliding body and the comparatively rough uneven 

 surface over which it slides, to the smooth oiled peripheries 

 of the axis and box, where the absolute quantity of the fric- 

 tion as opposing resistance is also diminished by leverage, in 

 the proportion of the wheel to that of the axis. 



Secondly, They procure mechanical advantage for over- 

 coming obstacles in proportion to the square roots of their di- 

 ameters when the obstacles are relatively small, by increasing 

 the time in that ratio, during which the wheel ascends : and 

 they pass over small transverse ruts, hollows, or pits, with an 

 absolute advantage of not sinking, proportionate to their di- 

 ameters, and with a mechanical one as before, proportionate 

 to the square roots of their diameters. 



Consequently, wheels thus considered cannot be too large: 

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

 and by convenience. 



With reference to the preservation of roads, wheels should 

 be made wide, and so constructed as to allow of the whole 

 breadth bearing at once ; and every portion in contact with 

 the ground should roll on it without the least dragging or 

 slide: but it is evident, from the well-known properties of the 

 cycloid, that the above conditions cannot unite, unless the roads 

 are perfectly hard, smooth, and flat; and, unless the fellies of 

 the wheels, with their tires, are accurately portions of a cylin- 

 der. These forms, therefore, of roads and of wheels, are the 

 models towards which they should always approximate. 



Roads were heretofore made with a transverse curvature to 

 throw off water, and in that case it seems evident that the peri- 

 pheries of the wheels should in their transverse sections be- 

 come tangents to this curve, from whence arose the necessity 

 for dishing wheels, and for bending the axes; which contri- 

 vances gave some incidental advantage for turning, for pro- 

 tecting the nave, and by affording room for increased stowage 

 above. But recent experience having proved that the curved 

 form of roads is wholly inadequate for obtaining the end pro- 

 posed, since the smallest rut intercepts the lateral flow of the 

 water ; and, that the barrel-shape confines carriages to the 

 middle of the way, and thereby occasions these very ruts, — 

 roads are now laid flat, carriages drive indifferently over every 

 part, the wear is uniform, and not even the appearance of a 

 longitudinal furrow is to be seen. It may, therefore, confi- 

 dently be hoped, that wheels approaching to the cylindrical 

 form will soon find their way into general use. 



The line of traction is mechanically 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 proportions 



3 D2 of 



