CHAPTER VIII. OBSERVATIONS AND EXPERIMENTS ON THE VARIOUS KINDS OF MOTIVE POWER EMPLOYED ON RAIL-ROADS. THIS chapter will comprehend practical illustrations of the different species of motive power previously enumerated, deduced from the foregoing disquisitions, and from experiments made on their performances in actual use upon Rail-roads. For the sake of making a better comparison of their various effects, by classing those following the same laws together, I shall divide them into the following order :-. 1. SELF-ACTING PLANES. 2. ENGINE-PLANES. 3. HORSES. 4. LOCOMOTIVE-ENGINES. I. SELF-ACTING PLANES. The impelling force of this kind of motive power is gravity; it is confined, as previously stated, to descending planes alone, and, when employed in practice, their object is to effect the ascent of a train of carriages by the descent of a similar train more heavily loaded in a given time. The respective weights W and w of the descending and ascending train of carriages being given, we shall then have the following known quantities derived from the preceding experiments, viz. F. and f, by Table I. page 194, by Table II. page 214. Then, taking the friction and resistance of the several moving parts, as deduced by the foregoing experiments, and knowing the time of descent, we shall have for the preponderance of gravity, necessary to effect the passage of the carriages upon the plane in that time, and, in the case of a single train of carriages dragging a rope after them, In practice, therefore, we must either elevate the plane, or increase the number of carriages, until we obtain the requisite preponderance; but, in every case, it will be necessary, in order to secure the constant action in winter and summer, that the excess amount to that given by the above formula. Before dismissing the subject of self-acting planes, it may be necessary to state, that consi derable regard should be observed in forming the line into a proper descent, or into that in which the velocity of the carriages, on all parts of it, shall be as nearly equable as possible. The action of gravity causing bodies to descend with velocities uniformly accelerated, the motion of the carriages upon a plane with a uniform descent will be very variable; moving slow at first, then with an accelerated motion, as the square of the times employed in traversing the plane; and becoming very rapid at the end of the plane. The plane should not, therefore, be made with a regular and uniform descent; but such as, by making the descent more rapid at the top, will give an additional preponderance of gravity at the commencement, and cause the carriages to acquire the requisite velocity; and then, to diminish that descent on the remaining parts of the plane, in such a ratio that the diminution of preponderance will abstract as much gravitating force as, by diminishing the accelerative tendency, will compensate for the increasing velocity of the carriages, by the accelerating force of gravity, so that the two will counteract each other, and thus produce a uniform velocity in the carriages on the plane. The line of descent to perform these conditions is rather difficult to determine, but perhaps will approach somewhat near to that curve called a cycloid. 4 11. FIXED STEAM-ENGINES. To elicit the performance of steam-engines, fixed, and dragging carriages up planes inclined or parallel to the horizon by means of ropes, I have selected the four following experiments on engines that have been in use for some time, and which, I trust, will be sufficient to furnish data by which we may calculate the performance of engines upon other planes. Not to confine the data to one particular kind of engine, I have taken two low-pressure, or condensing engines, and two high-pressure engines. EXPERIMENT XXIII. Boulton and Watt's low-pressure condensing engine, with two 30-inch cylinders, steam 4 lbs. per square inch above the ordinary pressure of the atmosphere, rope-roller similar to A, Fig. I. Plate III., rope 74 inches circumference, same as employed in Experiment XIX.; length of plane 2646 feet, height or ascent 154 feet 6 inches, being the same as Experiment XIX. Time of drawing up 7 loaded carriages, each weighing 9408 lbs., similar to those employed in Experiments V. and VI., 620 seconds, the engine making 374 single strokes, 5 feet each. Then (302 × 2) x .7854 1413.72 area of cylinders and 1413.72 x 19.5 the pressure of steam in the boiler =27567 lbs. pressure upon the piston, which, in the experiment, was moved through 374 × 51870 feet; hence 27567 × 1870=51550290 lbs. moved one foot, the power of the engine. Also, by Experiments V. and VI. F 43 x 7=301 lbs. Also WS 28 lbs. the force required to overcome the vis inertia of the load upon the plane, or to cause it to describe that space in 620 seconds. Then 3845+ 301 +504 +284678 lbs. the resistance which, in the experiment, was moved through 2646 feet, whence 4678 × 2646 12377988 lbs., the resistance moved one foot. Therefore 51550290 power of engine, whence we have the effective power of the engine upon the load, compared with the pressure of the steam upon the piston, equal to 24 per cent. Velocity of piston, 181 feet per minute, load, 256 feet per minute. EXPERIMENT XXIV. Fixed engine, Boulton and Watt's double power, similar construction to the preceding, and same power, viz. with two 30-inch cylin |