Hence an infinite number of components may be drawn inclined at varying angles. If, as is generally the case, the components are to be at right angles, set off lines OA, OB, inclined at 90°, Fig. 39, 4; P represents the force for which components are to be substituted. From the extremity of P draw CA and Cв parallel to вO and AO respectively. Then oA and Oв are the required components.

The principle of the parallelogram of forces may be applied to the case of any number of forces acting at a point. In Fig. 39, 5, X, Y, and z are three forces acting at A. By constructing parallelograms, AB is the resultant of Y and z, and AC is the resultant of x and the previous resultant, AB; .. AC is the resultant of x, y, and z.

Two other laws of very great importance in engineering are those of (a) the triangle of forces, and (b) the polygon of forces. Strictly speaking, the first is a particular case of the second. The triangle of forces states that if three forces acting on a particle are in equilibrium they may be represented in magnitude and direction by the three sides of a triangle taken in order, and conversely, if three forces acting on a particle can be represented in magnitude and direction by the three sides of a triangle taken in order, these forces will be in equilibrium. Thus the three forces X, Y, Z, Fig. 39, 6, are represented by the triangle ABC :

ABY, in magnitude and direction.
BC= X, in magnitude and direction.
CA = Z, in magnitude and direction.

In this manner it is possible to test the equilibrium of any three forces; if lines proportional to them produce a closed triangle, as in the above example, the forces are in equilibrium. The vast importance of this theorem is seen in particular in the construction of crane diagrams. The load on the crane, the thrust on the jib, and the tension in the tie-rod constitute three forces; the load being given, a triangle drawn to scale gives the other two factors. In Fig. 39, 7, the vertical line AB is drawn to scale to represent the load, say 6 tons, and from the extremities of this line AC and BC are drawn parallel to the jib and the tie-rod. The lengths of these lines measured from the scale, give the compressive

load on the jib, and the tensile load on the tierod. Fig. 39, 8, shows the same calculation by the parallelogram of forces.

any

The polygon of forces is an extension of the triangle of forces, and states that if any number of forces acting on a particle can be represented in magnitude and direction by the sides of a closed polygon, those forces shall be in equilibrium. Given number of forces such as P, Q, R, S, T, Fig. 39, 9, they are tested for equilib rium by arranging them in the form of a polygon as shown, care being taken that its sides are parallel to the direction of the forces and, of course, proportional to them in magnitude. If the polygon closes, the forces are in. equilibrium. (If it does not, then a line drawn to close the polygon represents the resultant of the forces.)

The forces dealt with above are those which act at one point in a body. Those acting at different points and parallel to each other are called parallel forces. They may be like or unlike according as they act in the same or in opposite directions. It is self-evident that with two like parallel forces, as in Fig. 39, 10, (1) the resultant R will be equal to the sum of P and Q, and (2) R will act in the same direction as P and Q. The point a divides the line be into two parts. ab, ac, inversely proportional to the forces adjacent to them, that is, ab: ac :: Q: P, and .. ab x P = ac × Q.

But if the forces are unlike, Fig. 39, 11, then (1) the resultant equals the difference of the two forces, and (2) it acts in the direction of the greater of the two forces. The resultant will also act outside, instead of between the two, as in the case of like forces, but the point a is. determined as before.

If two unlike parallel forces are equal, they can obviously have no resultant. Their effect. is to produce rotation, and such a pair of forces is called a couple.

Force is also a term applied by sheet-metal workers to the upper die used in stamping.

Forced Draught.-The supply of the air necessary for combustion to boiler furnaces, under pressure above that of the atmosphere, by which combustion is intensified, and a correspondingly higher evaporative power obtained from a given grate area, and heating surface.

The idea on which the system of forced draught is based is this:-The air supply obtained from natural draught does not penetrate among the burning fuel and gases with sufficient velocity to produce perfect combustion; the presence of an excess of air is thereby rendered necessary in order to maintain the proper furnace temperature. But a large proportion of this excess is wasted. In forced draught, the air being driven with increased velocity, and in larger volume among the fuel and gases, becomes more intimately mixed therewith, and combustion is quickened and intensified. Although a much larger total volume of air is used than in natural draught, yet operat

New York City, a West Indian trader with compound engines, and 80 lb. steam pressure; developed from 17 to 18 I.H.P. from each square foot of grate area, with a coal consumption averaging 14 lb. per I.H.P. This was maintained for several years, the boilers being fed with salt water, except once in every three or four months when sailing from London; and remaining after over fifteen years of service practically as good as new. These results have been greatly exceeded since in other large ocean carrying steamers fitted with Howden's system.

There are cardinal differences in the systems of forced draught adopted. Omitting minor de

foot

ing more effectually, a higher rate of combustion and higher economy are obtained per square of grate area, and consequently per square foot of heating surface, than with natural draught. In some systems the air is cold, in others it is heated first.

The successful application of forced draught dates from about the years 1882-3, at which period several engineers were working at the problem simultaneously. At about that period it was applied to H.M. ships Satellite and Conqueror in the navy; and to vessels in the mercantile marine by Mr Howden and Mr Fothergill The first steamer fitted with Howden's system of forced draught in 1884, the

tails in respect of fittings and pressures there are two main distinctions, the Closed Stokehold, and the Closed Ashpit system. In the first the air is forced into an air-tight stokehold. In the second it is forced into an air chamber attached to the front of the boiler. The warships of the Royal Navy, including torpedo boats, are fitted on the first system. The second system is that almost universally adopted in the mercantile marine. The closed stokehold system has many disadvantages by comparison with the closed ashpit system. There is no adequate ventilation for the stokers, and the results of hard steaming are invariably leaky tubes, and disabled boilers.

The principal details of Howden's system of forced draught are the following:

The air for combustion is supplied by a fan (see Fig. 40) which discharges the air through a conduit into an air heating chamber above the smoke box, in which the air circulates round a series of tubes. The waste gases after leaving the boiler, and before entering the uptake, pass upwards through these tubes in the air-heating chamber, thus giving up part of their heat to the air, which then goes down passages at the sides of, or between the smoke boxes into an air-tight reservoir or chamber surrounding the furnaces. From this chamber the air is passed through the furnace fronts by valves into the ashpit, and over the fires through air-distributing boxes, in proportions exactly suited to the kind of fuel used, and the rate of combustion required, thus ensuring the most perfect combustion of fuel practicable.

The ashpits are separated from the furnace openings by means of dead plates extending between the boiler front and the outer plate of the casing. Separate valves are used for the admission of air above the dead plate into the furnaces, and below the dead plate into the ashpits, each being under perfect control. The furnace doors are double, the outer and inner ones being hinged in unison and moving together.

The air passes through holes perforated in the inner doors and also above them, and at their sides, and thence enters into cast-iron boxes within, whence it is diffused into the furnaces. The boxes also serve the purpose of protecting the inner plate and door from the intense heat of the furnace.

On the opening of a furnace or ashpit door for stoking, the air admission valves for that furnace are closed. No inrush of cold air can then occur. The air supply can be regulated by the admission valves for increasing or reducing the rates of combustion.

A good deal of experimenting has been done by Mr Howden in order to find out the most favourable methods and proportions of air admitted under forced draught, with their effects upon combustion and efficiency. Some of these Some of these experiments bore on the question of admitting the air both above and below the grate-bars.

It was proved that there might be excess of air supply in both localities. It is necessary, or at least very desirable, that air should be introduced above the grate. In boilers worked under forced draught the plan of forcing air into the ashpit alone is not sufficiently effective. In the case of a thin fire being kept, the air blast will blow the fire full of holes, and the diffusion of combustion will be incomplete. In the case of a thick fire being kept, there will be an insufficiency of air above to combine with the gases, the supply will not be distributed regularly, and much smoke and carbonic acid will be formed. Besides this, though a minor matter, the fire-bars become burnt away rapidly.

The admission of air above the grate favours the formation of the higher oxide of carbon, with corresponding high liberation of heat units. It also burns up the coal-gas liberated during the coking of the coal. Further, it checks the too rapid inrush of the air through the fire-bars, and lessens their liability to become burnt out rapidly. But as the fires burn down, from the first throwing in of the fuel to clearness, the amount of air supply above the grates ought, as Mr Spence once pointed out, to be variable. And Mr Howden found that at certain times if the admission openings above the grates were decreased, and those below increased by the same amount, a much higher rate of combustion took place than when the process was reversed. The increase in rate of combustion does not, however, necessarily involve an increase in economy. Moreover, the intensity of the heat is so great when the pressure is entirely through the ashpit, that the fire-bars can be melted thereby.

In Mr Howden's system of forced draught, as much as 9 to 10 lb. of water at 212° Fahr. can be evaporated from 1 lb. of Scotch coal, with a rate of combustion of 30 lb. per square foot of grate area per hour. The Navy Boiler Committee, when testing the machinery of the Cunard steamer Saxonia, found that the evaporation with ordinary Lancashire coal was 11.3 lb. of steam per hour, while the coal consumption per unit of power was 1-29 lb. per hour. Ib. per hour. As high as 50 lb. per square foot of grate surface has been burned per hour on boilers fitted with Howden's forced draught.

Some of the advantages of forced over natural draught are these:-More complete combustion, due to the more perfect diffusion and intermingling of the air, with the furnace gases. Higher evaporative duty from a given grate area, due to the larger quantity of fuel that can be burnt in a given time. Independence of weather and climate, a matter of value in calm weather. The greater rapidity with which the grate-bars can be cleaned, and the fires urged again into good condition. Inferior fuel can be utilised with forced draught. By means of the adjust able valves in the casings, the amount of draught and the rate of combustion can be regulated in any degrees within the range permitted by the fittings. By shutting off the

from the furnace front into the stokehold, and the latter is thus kept comparatively cool. There is no trouble with leaky tubes in the closed ashpit system, while the records of the closed stokehold system teem with the troubles due to leaking tubes. It is significant that no such trouble occurs with locomotives. The rate of combustion on the fire-grates of a locomotive is twice that on the fire-grate of a marine boiler, yet the locomotive tubes do not leak to any disastrous extent. Yet induced draught in the locomotive is used to a much higher pressure than the forced draught in any marine boiler. The difference between the use of forced draught in a marine, and induced draught in a locomotive boiler is this:-A very serious

draught, the furnaces can be kept still when the engines are not working. Or any single furnace can be shut off from the rest for a time. Another advantage is the reduction in size and number of boilers necessary to develop a given power. Or, with existing boilers, the advantage of immensely increasing their power, with a reduced consumption of fuel.

When the air is partially heated before entering the furnace, as in Howden's system, there is economy in the utilisation of a portion of the waste gases, and there is no risk of the furnace being cooled down by a rush of cold air. When the front of the boiler only is encased with the air chamber, as in the Howden closed ashpit system, as distinguished from the closed stokehold system, there is no radiation of heat

indraught of cold air occurs when cleaning the grate-bars in a marine boiler worked under the closed stokehold system. This is necessarily done while the engines are running, and the draught in full force. But in a locomotive this is done while the engine is at rest, and there is practically no influx of draught.

From the first application of the Howden system to steamships, it has been a remarkable and continuous success. At the present moment there are about 2,100 large sea-going steamers fitted with the Howden system, and the number is rapidly increasing every year. The aggregate I.H.P. of these installations is fully 6,750,000. They comprise steamers for almost all the principal steamship companies of the world. The two large new express Cunard turbine steamers,

Lusitania and Mauretania, have their boilers fitted with this apparatus, while amongst the famous steamers running with it are the Carmania, Caronia, Empress of Britain, Empress of Ireland, Virginian, Victorian, La Provence, La Savoie, La Lorraine, Deutschland, Amerika, Kaiserin Auguste Victoria, &c., &c. Some of these steamers have also been fitted with Messrs Howden & Co.'s patent oil-burning system, which is worked in conjunction with their coal-burning 'forced draught system. The results of this combination have been exceedingly favourable. Modifications of the Howden system for application to water-tube boilers have also been applied with great success to warships. It has also been applied on land, to boilers of all types, Lancashire, water tube, &c.

The Meldrum system of forced draught is applied as shown in the illustrations, Fig. 41.

The essential features of the system are the steam jet blowers introduced into the ashpit, and through which superheated steam is blown among the fuel. The furnace casing is made to fit close to the boiler front, and the ashpit is closed, forming an air supply chamber. The plate by which it is closed carries the blowers. It also has an air-tight door through which the fine ash is cleared that falls through the gratebars. These, it should be mentioned, have only -in. spaces to permit of the burning of inferior fuel.

The superheater is fixed just inside the furnace front over the dead plate. The steam pipe is brought to one side of the furnace front, and connected to the superheater, while the outlet of the superheater leaves on the opposite side, and is coupled to the feed bar that supplies the nozzle at the head of the blower. The steam supply is capable of regulation by a valve. The air is taken in at the blower head, and forced into the ashpit chamber under a pressure which is adjusted to suit the fuel and the duty required. This being equally diffused under the grate forces the air up through the fire-bars among the fuel. These blowers are made practically noiseless when desired.

Forced Lubrication. The practice of supplying oil automatically to bearings under pressure by means of pumps and pipe arrange

ments. It is largely applied to high-speed engines, to turret lathes, and automatics. The necessity of supplying the lubricant under pressure instead of by gravity in engines, is, that gravity would not suffice to force the oil between bearings and shafts, between which. there is considerable pressure. And in machine tools doing heavy cutting the pressure is necessary, in order to provide a full flow to convey the heat generated away, which could not be done by the action of a mere drip supplied by gravity.

It is hardly possible to overrate the importance of forced lubrication in modern practice. In engines it means noiseless working; economy and wonderful freedom from wear characterise the system. Enclosed engines used in electric lighting run continuously for many months. without diminution in the supply of oil put into the crank chamber, and without sensible wear of journals and bearings. In the Belliss engines the pressure used is about 15 lb. per sq. in., and although the pressure on the bearings is greatly in excess of this, it has been pointed out that the relaxation of pressure on the return stroke in a double-acting engine permits the oil at these times to be driven between the bearing surfaces. Then during the fraction of a second occupied by the acting stroke, the film of oil cannot be squeezed out. In such a system, complete enclosure of the working parts is necessary, hence these are enclosed engines, otherwise the oil would splash out, and dirt get in.

In forced lubrication adopted in machine tools, the oil is bound to become dirty by contact with the metal being cut, and is therefore strained and filtered (see Oil Filter). The supply can be regulated by taps, and generally a spreader containing a row of openings distributes the oil along the work.

Force Fits.-See Limits.

Force Pump.-The essential feature of a force pump is the solid ram, substituted for the bucket valve of the suction pump. The force pump therefore does not depend for its efficiency on atmospheric pressure. The movements of the ram alternately create a vacuum into which the liquid enters through the suction valve, and force it out through a delivery valve. Liquids