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A common moveable steam-engine, working with a rope, will be cheaper than locomotive power, but not so convenient; if used, advantage should be taken in all cases of gravity. Loosening the ground with a plough, will be very advantageous where the soil will permit it, such as clay, marl, and sometimes shale; and as the quantity of work which can be done is limited by the tip, this must be paid every attention to. The usual mode, by running sidings out from the main line in the form of a fan, so to have as many tipping places as possible, requires modifying. At present the common practice is to take up and relay the rails as the embankment proceeds, which consumes a great deal of time, and gives a corresponding portion of trouble, instead of which, if longitudinal bearers are framed for each tipping place, these can be at once lifted up all in a piece, and carriad forward, and a rail put in behind them, in a very short space of time, and with one-fourth of the trouble which is found in the old way. When the embankment is not high, these frames may be supported from below on a railway, and be moved forward any length that may be required. A horse should be kept for tipping above, and he may take in three wagons at a time. By making the above frames to propel forward, and having a door in the bottom of the wagons, the quantity tipped may be very considerably increased.
Whenever the lead gets above 11⁄2 miles, and there is much to do, a locotive engine should be employed, the expense of which, including fuel, wages repairs, interest on capital, and provision for a renewal every five years, will not exceed 47. per day; the engine will take 24 wagons per trip, at 10 miles per hour, while a horse taking 3 wagons will only go 15 or 16 miles per day. That a great saving will ensue is clear, and may be thus shown. Let the lead be two miles, and the contractor required to tip 1200 cubic yards per day; this would require 150 two-yard wagons, besides spare ones and as a horse with three wagons would make four trips per day, or 24 yards per day, 100=50 horses, besides spare ones and tipping horses.Now these wagons are to be constantly travelling, and to keep these going there must be 24 always filling, and 24 tipping. This, with the requisite number of spare ones, will in the whole require about 220 wagons; whereas, with the engine, 24 travelling, 24 filling, 24 tipping, and 24 spare, total 96, is all that is required, say 100. Here then is a saving of 120 wagons at 201. each, or 2400l., which is considerably more than the cost of the engine, besides the 50 horses, which, with their harness, cannot be taken at less than 251. each, or 12501.
Again, take 50 horses' keep at 3s. per day, is 77. 10s. ; 50 boys at 1s. 6d., or 25 men going one to two trains, at 3s. is 37. 15s., total 11. 5s. per day, whereas the engine will not cost more than 47. Under very unfavorable circumstances, a mean of 15,000 trips gave for a distance of 1969 yards, 15 wagons per train, carrying 25 cubic yards, with a consumption of coal of 245 lbs., costing 2s. 4d., wages, 111d., repairs and sundries, 64d., total 3s. 93d. per trip.
The old way of working at the face of an excavation, and bringing it out by lifts, is now known to be more tedious, and consequently unprofitable, than running a gullet through at once, in which as many wagons as the contractor likes can be put in and filled, both by throwing in the earth from above, or having a stage over the wagons to run barrows on. To get the greatest quantity of earth, besides ploughing it, which plough may be often worked by a steam engine, the method called "falling" may be resorted to, that is, digging underneath and then splitting it on the top with wedges, and with the help of long iron levers, bringing down a lump containing several cubic yards at once.
The contractor will find it best to provide wagons, engines and rails, and to sub-let his labor to small gangs of about a dozen men each and a ganger. The best sort of rails for a contractor's use is the Trail, inverted so that the lower flang nails down on the sleeper, and requires no chair. 30 lbs. per yard will be enough, but from 40 to 50 lbs. is better, as these will do for anything, and 30 lbs. would be too light for clayey soils.
In any place where time is an object, the tip end of the embankment ought to be made much wider and steeper than it is intended, so as to get in more roads at the tip; and as the work proceeds, this extra width is pared off and thrown down below to increase the slope, which should be left a little too narrow at the bottom on purpose.
There is another mode of increasing the tip, by which the time of forming a large embankment may be reduced one-half. This method is to form the embankment at twice in the following manner:-Carry out the earth to the required width, say 20 feet high, and then come on and complete this with a second set of tipping places, say for 30 feet more in height; the wagons must run from the 50 feet level down to the 20 feet by means of inclined planes on both sides of the upper embankment, and from the width of the lower one, a great many roads may be put in at the tip; the upper part of the embankment is brought on in the usual way, and by this means the quantity tipped may be doubled.
Under favorable circumstances, a contractor ought to move 1000 cubic yards of earth per day at each trip, and this by the above process may be doubled, in fact the limit is the tipping, for, by running a gullet into the hill getters and fillers may be placed as thick as will leave them room to work, the quantity of which depends greatly on the weather, the average number of working days being from 200 to 230, in which may be got, by having night shifts in summer, and 3, 6 and 9 hours' shifts in spring and autumn, about 3000 working hours. Under many peculiar circumstances, it will be very advantageous to lay in a line of rails, and place huts on it for the workmen on wheels; so that their place of abode always follows up, and is close to their work, in fact a moveable village. Much, of course, also depends on the nature of the soil, as to the work which will be done in this time; generally a filler will put into a wagon from 15 cubic yards per day in stiff clay, to 25 cubic yards per day in loose sand, and by falling the earth as before described, 1 getter will keep three fillers going, so that to keep up 1000 cubic yards per day, will take from 60 to 90 men according to the nature of the ground.
Where there is much rock the natural stratification of it should be closely examined and attended to in the blasting of it, as a horizontal blast would in many cases bring down ten times as much as a vertical one, and the force of the powder will be increased by mixing saw-dust with it. The strength and disposal of the blasts must entirely depend on the nature of the rock, and also in some measure, on whether it can be used in the bridges, or other erections along the line.
The contractor will find it his interest to look out sharp for clay, and either to make his own bricks, or let his clay to a respectable brickmaker to make them for him, unless he happens to be very favorably situated as to carriage; he should also do all his wagon repairs, erecting temporary carpenters' and smiths' shops in some position adjacent to his heaviest work, but being careful they are so situated that they can be let or sold at the termination of his contract; he should always work towards his greatest job, and of course so apportion his men as to bring in the whole at one time at the end.
It may sometimes happen, that from unavoidable causes, a contractor
will find it impossible to continue his work, and occasionally this will be done intentionally. To guard against the last has been already adverted to, but to guard against the first is morally impossible; for there are so many cases in which a man, with the very best intentions, is yet borne down by the uncontrollable force of circumstances, that no human foresight can by any possibility prevent an unfavorable result. As a general rule, it will be best for the directors, in every prudent way, to assist and encourage a contractor, and by every means in their power to enable him to complete his work, provided it be seen that he really is desirous to get on. If prices have risen against him, or if he has made a miscalculation, it will be most decidedly the best thing for the company to increase the amount, to remit his retained money, or by any means to get him to finish his contract. If this be not done, the consequences will be very uncomfortable. His inability will have first become manifest by his employing too few workmen. If the checks which we have explained be put in force this is seen at once. He is served with a legal notice, that under the contract, the company will employ men if he does not, and charge their expenses against him. This will probably induce him to come forward and state what his difficulties are; then if the company do not assist him, he will tell them he must give up his contract; he is perhaps, a man of no capital, and his sureties are the same, so that the company have no resource but to take the work into their own hands. In the mean time, the work having fallen in arrear, there comes the tedious admeasurement of what has yet to be done, and two or three weeks' squabbling between his lawyer and the company's, as to the terms on which he is to give up the works, and perhaps references to umpires, each taking a week; then the company have to order wagons, engines, and tools of all kinds, and to find foremen, overseers, sub-contractors, and workmen, all at a vast expense, it being the fate of almost every public company to be charged higher than individuals. While all this is going on, the work is so much delayed that the line cannot be opened at the time which was intended, the proprietors loosing the whole proceeds. Then come the enormous expenses which are requisite to redeem the time as much as possible. Land has to be bought to make side-cuttings in order to form the embankments, and, in another place, to deposit the earth from the excavation, which is now to a great extent thrown into spoil; horse-runs are established at as many places as possible, to bring up the earth in barrows, and all this in addition to the regular work at the gullet and the tip; and when these things are taken into consideration, it will at once be seen, that the company ought never to agree to finish the work themselves, but as a dernier resort. There are on one of the railways in England, six contracts which were let for 600,0002., and which the company have had to take into their own hands at an expense of 1,200,000. In one instance, the cost of the contract was more than trebled so that any means should be resorted to in order to assist the contractor through his job; and we again repeat, that it is decidedly bad policy to take the lowest tender in letting the contracts. A man of character alone should be selected, and ought to receive every encouragement in the execution of his work.
THEORY OF THE STEAM-ENGINE.
In the calculations relative to locomotive engines we shall introduce three terms more: the first to express the resistance of the air against the train in motion, a force which, increasing in the ratio of the square of the velocity could not be neglected without error; the second to represent the resistance offered by the engine itself in the transport of its own weight on the rails;
and the third to take account of the force expended by the engine in animating its fire, according to the method in use in those engines. But as these divers circumstances do not in general occur in stationary engines, we will omit them at present, it being easy to reproduce them in the particular cases as it may become necessary.
From what has just been said, the resistance R may be replaced by
We shall then substitute this value in that of v, and at the same time make
an expression, which in the case of l'=l, that is to say, for unexpansive en
is nothing else but the absolute volume of the steam correspondent to S, in contact with the liquid at the pressure R. Therefore, to have the velocity v, we must calculate the volume of the steam which corresponds to the volume of water S, supposed immediately transformed into steam at a pressure equal to the resistance R, afterwards divide that volume by the area a of the piston, and lastly, multiply the quotient by the quantity k, of which we have a little before given the developed expression.
The formula (1) contains the general relation between all the data of the problem, and will serve us to solve successively the different questions we have proposed elucidating. It will, however, be observed that the homogeneity of the formula requires that the dimensions of the engine a, l and be expressed in the same unit as the volume of water evaporated S, and that the pressures per unit of surface P, r, and p, be also referred to the same unit as S. We mention this circumstance because these various quantities are usually referred to different units, according to what may be, in practice, the most convenient manner of expressing each.
Besides, from the mode of our reasoning itself, it is to be understood that the quantity S, in the equation, is the effective evaporation of the engine; that is, it represents the volume of water which really enters the cylinder in the state of steam, and there acts upon the piston. If then, from any mode of construction of the engine, it should occur that a portion of the steam generated in the boiler, escape without acting on the piston, that portion is not to be considered as included in the quantity S, and ought, therefore, to be deducted before all calculation.
The formula just obtained will give the velocity of the piston for any load r, when the dimensions and different data of the engine contained in the equation are known. This formula is general, and applies to every kind of rotative steam-engine. If the engine be expansive, it will suffice to replace by the length of the stroke traversed when the steam begins to be intercepted; if the engine be unexpansive, it will suffice to make l 1. If there be condensation, p, must be replaced by the pressure of condensation; and if the engine be not a condensing one, p is to be replaced
by the atmospheric pressure. However, before making these deductions relative to the different systems of engines, we shall continue to seek the general formulæ for all the problems we have undertaken to solve.
Let it only be observed, that the velocity of the piston in a given engine, is totally independent of the pressure at which the steain is formed in the boiler, and that, on the contrary, it depends essentially on the evaporation S of the boiler per unit of time, and on the total resistance [(1+6)r+p+f] opposed to the motion of the piston.
Section III-Of the load of the engine, for a given velocity.
The analogy we have just obtained will show reciprocally the reistance a known engine can set in motion at a determined velocity. In effect, it suffices to draw from it the value of r; or rather, as r is only the resis tance per unit of surface of the piston, it will be preferable to have the whole resistance, by taking immediately the value of a xr, that is,
From the form of this expression, it would appear at a first glance, that on making v=0, that is, on supposing the velocity null, the result would be an infinite load; but on examining the formula more attentively, we soon perceive that the result would by no means be such.
In effect, if v=0, it follows also that S=0; for S is the quantity of steam which effectively traverses the cylinders in a unit of time; and no quantity of steam whatever can traverse the cylinders without moving the piston, and consequently creating some velocity in the engine. If, then, the velocity be supposed equal to zero, we must necessarily have at the same time S=0. But, making at once v=0 and S=0, we find
and not ar∞, as it first appeared.
Thus, in this case, the formula reduces itself to the indeterminate form; but it is to be observed, that the present formulæ give the effects of the engine, only after the uniform motion has taken place. Now we shall presently see that, for a given evaporation S, the uniform velocity can never be less than
since it is that which corresponds to the passage of the steam into the cylinders, at its state of greatest density, and that at any other density, that steam would form a larger volume, and consequently could not traverse the cylinders in the same time, without producing a greater velocity. All supposition of less velocity than this, is then inadmissable in this problem, as being incompatible with that state of uniformity of motion, for which alone the effects of machines are calculated.
Section IV-Of the evaporation of the boiler, to produce wanted effects. To find the evaporation of which an engine ought to be capable, in order to set in motion a certain resistance rat a known velocity v, the value of S must be drawn from the same equation,
This equation gives the quantity of water the engine ought to be capable of evaporating and transmitting to the cylinder per minute. It will then be easy, according to the mode of construction intended to be used for the boiler, and the practical data proper to estimate the quantity of water