De Pambour gives the value of and that of e=1'17 for a cubical body, =1'07 for a train of five carriages, =1.05 for a train of fifteen carriages, and =1'04 for a train of twenty-five carriages ; but the learned author seems to consider the truest value of e to be =113. It is generally considered that the valise of f"=0.16 ; the value of f" has not been ascertained by direct experiment, but it is known to be considerably greater than f".
The practical conclusions drawn from the examination of these for mulm are : 1. The resistance is diminished by diminishing the diameter of the axles, and increasing that of the wheels. 2. It is desirable to diminish the weight of the carriages as far as may be consistent with safety. 3. The resistance in traversing a curve is increased in propor tion as the radius is decreased. 4. The useful effect of locomotives is materially affected by their rate of motion, and economically there are serious objections to high rates of speed.
The experiments of Messrs. Gouin and Chatellier show also that a great portion of the resistance of a train arises from the frictions pro aluced by the frame of the engine, and the frictions of its machinery. found that, in fact, when the resistance of the whole train was equal to 0'0105 per ton, that of the carriages alone was 0.00625 ; that created by the frictions of the machinery alone, without reference to the load, was 0.0025; and the resistance created in the machinery by the pressure of the steam, was 0.00175. The 'speed in this case was about 28 miles per hour, and the experiments were tried on an incliiie of 1 in 125; the weight of the train was 60 tons, and the weather quite calm. Finally, it may be stated that it is usually considered that taking into account both the variable and the constant resistances to be encountered on railways the force required to ensure the traction at speeds of 20 miles an hour is equal to th of the load; and that if the speed should exceed 30 miles an hour it becomes thth of the quantity.
The method of finding the resistance which an engine opposes to the effort made by the steam to put it in motion, is as follows : Multiply the area of one of the two equal pistons in square inches by the pressure of the steam on a square inch of the piston in each cylinder, when that pressure is just sufficient to cause the engine to move ; the product is the pressure on each piston. Then, since the
piston makes two strokes while the wheel .of the engine turns once round, the velocity of the piston is to that of the engine as twice the length of the stroke is to the circumference of the wheel ; and, the resistances being inversely proportional to the velocities, we have — eircuinf. of wheel : twice the length of the stroke : : pressure on both pistons : the resistance, or inertia, of the engine.
But the resistance increases with the load which the engine has to draw ; and, in order to determine it when attached to a train, the above pro portion may be used ; but the pressure on the pistons, instead of being found as before, must be taken when the engine and train are observed to have a uniform motion. Then the fourth term of the proportion being diminished by the known resistance of the train, will give the resistance of the engine alone.
From the experiments of Mr. the following values of the resistances experienced by loaded carriages on level roads have been determined. On a good pavement the resistance is of of the weight of the carriage and load ; on a broken surface of old flint, 5A3 ; on gravel, and on a well-constructed railway, from to By experiments made on the force (of traction) required to give motion to vessels on canals, it is found that the resistance varies nearly as the cube of the velocity; and this great deviation from the general law of resistances is probably caused by the reaction of the eider of the canal against the water displaced by the vessel. It deserves, however, to be mentioned, that when the velocity of the vessel is considerable, the resistance has been found to experience some diminution, perhaps on account of the water momentarily displaced, from its inability to escape laterally, becoming condensed, and thus giving superior buoyancy to the vessel, the immersed part being lose, the pressure of the wate against the front will also be less.
Mr. Barlow observes that, with small velocities, the force of traction on canals Is leas than on railways; and when the velocity is equal to four miles per hour, the forces aro equal. Beyond tide velocity the advantage is in favour of the railway.