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divided into three parts, we shall be entitled to one of those parts, in recompense for our patent licence, our drawings, &c. &c. Our own share of savings shall be estimated in money, according to the value of your coals delivered under the boiler, and you shall annually pay us that sum, during twenty-five years from the day you begin to work; provided you continue the use of the engine so long. And in case you sell the engine, or remove it to any other place, you must previously give us notice, for we shall then be entitled to our third of the savings of fuel, according to the value of coals at such new place. This is a necessary condition, otherwise the engine which we make for you at an expense of two thousand pounds may be sold in Cornwall for ten thousand pounds.

"Such parts of the engine as we execute at Soho we will be paid for at a fair price; I conclude, from all the observations I have had an opportunity of making, that our engines are four times better than the common engines. In boilers, which are a very expensive article, the savings will be in proportion to the savings of coal. If you compare our engine with the common engine (not in size, but in power), you will find the original expense of erecting one to be nearly the

same.

"Mr. Wilkinson has bored us several cylinders, almost without error; that of fifty inches diameter, which we put up at Tipton, does not err the thickness of an old shilling in any part; so that you must either improve your method of boring, or we must furnish the cylinder to you."

The reluctance of mining companies to relinquish the old engines, even on these terms, led them to propose to Mr. Watt to grant them a licence for the use of his condenser, to be applied to the atmospheric engine, without the introduction of other improvements. Such a proposition was made to him by Mr. Smeaton, in the year 1778, to which he returned the following answer:

"I have several times considered the propriety of the application of my condensers to common engines, and have made experiments with that view upon our engine at Soho, but have never found such results as would induce me to try

it any where else; and, in consequence, we refused to make that application to Wheal Virgin engines in Cornwall, and to some others; our reasons were, that though it might have enabled them to have gone deeper with their present engines, yet, the savings of fuel would not have been great, in comparison to the complete machine. By adding condensers to engines that were not in good order, our engine would have been introduced into that country (which we look upon as our richest mine) in an unfavourable point of view, and without such profits as would have been satisfactory either to us or to the adventurers; and if we had granted the use of condensers to one, we must have done so to all, and thereby have curtailed our profits, and perhaps injured our reputation. Besides, where a new engine is to be erected, and to be equally well executed in point of workmanship and materials, an engine of the same power cannot be constructed materially cheaper on the old plan than on ours; for our boiler and cylinder are much smaller, and the building, the lever, the chains, together with all the pump and pit work, are only the same.

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"We charge our profits in proportion to the saving made in fuel by our engine, when compared with a comone which burns the same kind of coals; we ask one-third of these savings to be paid us annually, or half yearly; the payment being redeemable in the option of our employer, at ten years' purchase; and when the coals are low priced, we should also make some charge as engineers. In all these comparisons our own interest has made us except your (Mr. Smeaton) improved engines, unless we were allowed a greater proportion of the savings."

Their exertions to improve the manufacture of engines at Soho is shown by the following letter from Mr. Boulton, in the same correspondence to Mr. Smeaton :

"We are systematising the business of engine making, as we have done before in the button manufactory; we are training up workmen, and making tools and machines to form the different parts of Mr. Watt's engines with more accuracy, and at a cheaper rate than can possibly be done by the ordinary methods of working. Our workshop and apparatus will be of

sufficient extent to execute all the engines which are likely to be soon wanted in this country; and it will not be worth the expense for any other engineers to erect similar works, for that would be like building a mill to grind a bushel of corn.

“I can assure you from experience, that our small engine at Soho is capable of raising 500,000 cubic feet of water 1 foot high with every 112 lbs. of coals, and we are in hopes of doing much more. Mr. Watt's engine has a very great advantage in mines, which are continually working deeper: suppose, for instance, that a mine is 50 fathoms deep, you may have an engine which will be equal to draining the water when the mine is worked, to 100 fathoms deep, and yet you can constantly adapt the engine to its load, whether it be 50 or 100 fathoms, or any intermediate depth; and the consumption of coals will be less in proportion when working at the lesser than at the greater depths; supposing it works, as our engines generally do, at 11 lbs. per square inch, when the mine becomes 100 fathoms deep."

(85.) The great improvement which has been introduced within the last half century, in the details of Watt's steam engine, will be rendered manifest by comparing the effects of a given weight of fuel here supplied by Mr. Boulton with the effects which the same weight of fuel is now known to produce in the best pumping engines worked in Cornwall. One of these engines, in good working order, has been known to raise 125,000,000 lbs. 1 foot high, by the combustion of a bushel of coals. But the average performance of even the best engines is below this amount. If we take it at 90,000,000, this will be equivalent to the weight of about 1 million cubic feet of water, a bushel of coals being cwt. It will therefore follow that, with the present engines, one hundred weight of coals is capable of raising about two million cubic feet of water one foot high, being a duty four times that assigned to the early engines by Mr. Boulton.

(86.) At the time that Watt, in conjunction with Dr. Roebuck, obtained the patent for his improved engine, the idea occurred to him, that the steam which had impelled the piston in its descent rushed from the cylinder with a mechanical force much more than sufficient to overcome any resistance

which it had to encounter in its passage to the condenser; and that such force might be rendered available as a moving power, in addition to that already obtained from the steam during the stroke of the piston. This notion involved the whole principle of the expansive action of steam, which subsequently proved to be of such importance in the performance of steam engines. Watt was, however, so much engrossed at that time, and subsequently, by the difficulties he had to encounter in the construction of his engines, that he did not attempt to bring this principle into operation. It was not until after he had organised that part of the establishment at Soho which was appropriated to the manufacture of steam engines, that he proceeded to apply the expansive principle. Since the date of the patent which he took out for this (1782), was subsequent to the application of the same principle by another engineer, named Hornblower, it is right to state, that the claim of Mr. Watt to this important step in the improvement of the steam engine, is established by a letter addressed by him to Dr. Small, of Birmingham, dated Glasgow, May, 1769:

"I mentioned to you a method of still doubling the effect of the steam, and that tolerably easy, by using the power of steam rushing into a vacuum, at present lost. This would do little more than double the effect, but it would too much enlarge the vessels to use it all: it is peculiarly applicable to wheel engines, and may supply the want of a condenser, where the force of steam only is used; for open one of the steam valves, and admit steam until one-fourth of the distance between it and the next valve is filled with steam, then shut the valve, and the steam will continue to expand, and to press round the wheel, with a diminishing power, ending in one-fourth of its first exertion. The sum of the series you will find greater than one-half, though only one-fourth of steam was used. The power will indeed be unequal, but this can be remedied by a fly, or by several other means.'

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In 1776 the engine, which had been then recently erected at Soho, was adapted to act upon the principle of expansion. When the piston had been pressed down in the cylinder for a certain portion of the stroke, the further supply of steam

from the boiler was cut off, by closing the upper steam valve, and the remainder of the stroke was accomplished by the expansive power of the steam which had already been introduced into the cylinder.

(87.) To make this method of applying the force of steam intelligible, some previous explanation of mechanical principles will be necessary.

If a body which offers a certain resistance be urged by a certain moving force, the motion which it will receive will depend on the relation between the energy of the moving force and the amount of the resistance opposed to it. If the moving force be precisely equal to the resistance, the motion which the body will receive will be perfectly uniform.

If the energy of the moving force be greater than the resistance, then its surplus or excess above the amount of resistance will be expended in imparting momentum to the mass of the body moved, and the latter will, consequently, continually acquire augmented speed. The motion of the body will, therefore, be in this case accelerated.

If the energy of the moving force be less in amount than the resistance, then all that portion of the resistance which exceeds the amount of the moving force will be expended in depriving the mass of the body of momentum, and the body will therefore be moved with continually diminished speed until it be brought to rest.

(88.) Whenever, therefore, a uniform motion is produced in a body, it may be taken as an indication of the equality of the moving force to the resistance; and, on the other hand, according as the speed of the body is augmented or diminished, it may be inferred that the energy of the moving force has been greater or less than the resistance.

It is an error to suppose that rest is the only condition possible for a body to assume when under the operation of two or more mechanical forces which are in equilibrium. By the laws of motion the state of a body which is not under the operation of any external force must be either in a state of rest or of uniform motion. Whichever be its state, it will suffer no change if the body be brought under the operation of two or more forces which are in equilibrium; for to sup

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