(328.) If a carriage were capable of moving on a road without friction, the most advantageous direction in which a force could be applied to draw it would be parallel to the road. When the motion is impeded by friction, it is better, however, that the line of draught should be inclined to the road, so that the drawing force may be expended partly in lessening the pressure on the road, and partly in advancing the load. Let W, _fig. 181._, be a load which is to be moved upon the plane surface A B. If the drawing force be applied in the direction C D, parallel to the plane A B, it will have to overcome the friction produced by the pressure of the whole weight of the load upon the plane; but if it be inclined upwards in the direction C E, it will be equivalent to two forces expressed (74.) by C G and C F. The part C G has the effect of lightening the pressure of the carriage upon the road, and therefore of diminishing the friction in the same proportion. The part C F draws the load along the plane. Since C F is less than C E or C D the whole moving force, it is evident that a part of the force of draught is lost by this obliquity; but, on the other hand, a part of the opposing resistance is also removed. If the latter exceed the former, an advantage will be gained by the obliquity; but if the former exceed the latter, force will be lost. By mathematical reasoning, founded on these considerations, it is proved that the best angle of draught is exactly that obliquity which should be given to the road in order to enable the carriage to move of itself. This obliquity is sometimes called the _angle of repose_, and is that angle which determines the proportion of the friction to the pressure in the second method, explained in (323.). The more rough the road is, the greater will this angle be; and therefore it follows, that on bad roads the obliquity of the traces to the road should be greater than on good ones. On a smooth Macadamised way, a very slight declivity would cause a carriage to roll by its own weight: hence, in this case, the traces should be nearly parallel to the road. In rail roads, for like reasons, the line of draught should be parallel to the road, or nearly so. (329.) When ropes or cords form a part of machinery, the effects of their imperfect flexibility are in a certain degree counteracted by bending them over the grooves of wheels. But although this so far diminishes these effects as to render ropes practically useful, yet still, in calculating the powers of machinery, it is necessary to take into account some consequences of the rigidity of cordage which even by these means are not removed.