= Now this force may be found as follows:-The triangle ABC is similar to the triangle AK F; for the angle FAK the angle CAB= the angle EG F; and the angles ABC and AK F are each right angles; therefore AC: AB::FA: AK; but FA: AK as the length of the plane is to its height; that is, AC: AB::/: h; and as the line A C represents the weight of the carriage, or W, Wh we have W AB::l: h; or, A B=. = the force represented by the line A B. The power required to draw a carriage on a horizontal may be represented by the for We then have, for the power required to draw a wag gon or coach up an inclined plane, the formula, pebble pavement; and for the power required to draw the same waggon down hill, the same formula, only making In these formulæ, W=the weight of the waggon wheels and load: for although it might at first sight appear that we should make use of the weight on the axle, or that represented by the line C B, to calculate the resistance, yet it is not so; for the pressure on the axles will be equal to the joint action of the weight on the axles and the moving power, and this will be the force represented by the line A C or W, so that no correction of the weight is necessary. The resistances arising from part of the weight being *See Mémoire sur les Grandes Routes, &c. de M. F. de Gerstner. thrown from the front axles to the hind ones, in consequence of the inclination of the traces, and the line of draught not passing through the centre of gravity of the carriage, may be omitted in a general investigation; also the correction that should be applied to the resistances where the carriage is on an inclined plane; because it is evident that there is less weight on the surface than if the carriage stood on level ground, and also from the hind wheels bearing a greater pressure than the front ones, in consequence of the line of gravity falling nearer to the hind wheels; as the difference that will take place in the draught, in consequence of these, will be inconsiderable in general practice, and, should extreme accuracy be required in any particular case, it will be easy to make the necessary calculations. The following experiments were made with the waggon the axles and wheels of which had been previously made use of for the experiments on friction. 1. Half a ton of stone was put in the waggon, as nearly as possible in the centre between each axletree; the waggon was then drawn over a timber platform, perfectly horizontal, by weights suspended from a line: to effect this, it required 50 lbs. 2. A ton of stone was placed in the waggon, half a ton over each axletree, and the power required to draw the waggon over the same surface was 70 lbs. 3. A ton and a half of stone was placed in the waggon, and distributed equally over each axletree; the weight or power required to draw the waggon was then found to be 90 lbs. The resistances arising from the friction of the axletrees in the above experiments were then calculated for each wheel from the formula before given, and the total resistance arising from the axles, thus determined, was subtracted from the draught or power found by experiment as requisite to draw the waggon; the difference gave the resistance of the surface caused by the penetration of the wheels into the timber surface. The results of these experiments are given in the following Table: By a considerable number of experiments with the same waggon, on roads of different kinds, the draught was found to agree very nearly with the results calculated from the empyrical formula, = in which W the weight of the waggon; w, the load; c, a constant number, which will depend on the surface over which the waggon is drawn; and v, the velocity in feet per second. By putting v=3'7, which was the velocity used in the foregoing experiments, the constant number for a timber surface was determined, and found to be equal to 2. For other surfaces, the value of c may be taken as follows: On a paved road 2 On a well-made broken stone road in a dry clean state 10 13 32 On a well-made broken stone road covered with dust 8 |