Let CD, fig. 28., be the pendulum in question, suspended from C, the upper extremity of the vertical axis CD, and let the ball or body B, by revolving about the said axis, describe the circle BE A H, the plane of which is parallel to the horizon; it is proposed to assign the time of description, or the time in which the body B performs a revolution about the axis CD, at the distance B D.

A

H

E

B

Conceive the axis CD to denote the weight of the revolving body, or its force in the direction of gravity; then, by the Composition and Resolution of Forces, already treated of, CB will denote the force or tension of the string or wire that retains the revolving body in the direction C B, and B D the force tending to the centre of the plane of revolution at D. But, by the general laws of motion and forces previously laid down, if the time be given, the space described will be directly proportional to the force; but, by the laws of gravity, the space fallen perpendicularly from rest, in one second of time, is g= 16 feet; 16.B D consequently we have CD: BD:: 16: the space described " CD towards D by the force in BD in one second. Consequently, by the laws of centripetal forces, the periodic time, or the time of the body revolving

in the circle BE A H, is expressed by the term T /2-CD, where = 161 3.1416, the circumference of a circle whose diameter is unity; or putting t to denote the time, and expressing the height CD in feet, we get t=6.2832

CD or, by reducing the expression to its simplest form, it

12 × 321

becomes t=0.31986 CD, where CD must be estimated in inches, and t in seconds. Here we have obtained an expression of great simplicity, and the practical rule for reducing it may be expressed in words, as follows:RULE. Multiply the square root of the height, or the distance between the point of suspension and the centre of the plane of revolution, in inches, by the constant fraction 0.31986, and the product will be the time of revolution in seconds.

EXAMPLE. In what time will a conical pendulum revolve about its vertical axis, supposing the distance between the point of suspension and the centre of the plane of revolution to be 39.1393 inches, which is the length of a simple pendulum that vibrates seconds in the latitude of London?

The square root of 39 1393 is 6-2561; consequently, by the rule, we have, 6.2561 x 0.31986=2-0011 seconds for the time of revolution sought. It consequently revolves 30 times in a minute, as it ought to do by the theory of the simple pendulum.

By reversing the process, the height of the cone, or the distance between the point of suspension and the centre of the plane of revolution, corresponding to any given time, can easily be ascertained; for we have only to divide the number of seconds in the given time by the constant decimal 0-31986, and the square of the quotient will be the required height in inches. Thus, suppose it were required to find the height of a conical pendulum that would revolve 30 times in a minute. Here the time of revolution is 2 seconds for 60+30=2; therefore, by division, it is 2+0.31986=6.2527, which, being squared, gives 6.2527=39 0961 inches, or the length of a simple pendulum that vibrates seconds very nearly. In all conical pendulums the times of revolution, or the periodic times, are proportional to the square roots of the heights of the cones. This is manifest, for in the foregoing equation of the periodic time the numbers 6.2832 and 386, or 12 x 32, are constant quantities, consequently t varies as CD.

If the heights of the cones, or the distances between the points of suspension and the centres of the planes of revolution, be the same, the periodic times, or the times of revolution, will be the same, whatever may be the radii of the circles described by the revolving bodies. This will be clearly understood by contemplating the subjoined diagram, fig. 29., where all the pendulums Ca, Cb, Cc, C d, and C e, having the common axis CD, will revolve in the same time; and if they are all in the same vertical plane when first put in motion, they will continue to revolve in that plane, whatever be the velocity, so long as the common axis or height of the cone remains the same. This will become manifest, if we conceive an inflexible bar or rod of iron to pass though the centres of all the balls as well as the common axis, for then the bar and the sev ral balls must all revolve in

Half the periodic time of a conical pendulum is equal to the time of vibration of a simple pendulum, the length of which is equal to the axis or height of the cone; that is, the simple pendulum makes two oscillations or vibrations from side to side, or it arrives at the same point from which it departed, in the same time that the conical pendulum revolves about its axis. The space descended by a falling body in the time of one revolution of the conical pendulum is equal to 3-14162 multiplied by twice the height or axis of the cone. The periodic time, or the time of one revolution, is equal to the product of 3.1416/2 multiplied by the time of falling through the height of the cone. The weight of a conical pendulum, when revolving in the circumference of a circle, bears the same proportion to the centrifugal force, or its tendency to fly off in a straight line, as the axis or height of the cone bears to the radius of the plane of revolution; consequently, when the height of the cone is equal to the radius of its base, the centripetal or centrifugal force is equal to the power of gravity.

These are the principles on which the action of the conical pendulum depends; but as we shall hereafter have occasion to consider it more at large, we need not say more respecting it in this place: before dismissing the subject, however, it may be proper to put the reader in possession of the rules for calculating the position of the centre of oscillation in vibrating bodies, in a few cases where it has been determined, these being the cases that are of the most frequent occurrence in practice.

The centre of oscillation in a vibrating body is that point in the line of suspension, in which, if all the matter of the system were collected, any force applied there would generate the same angular motion in a given time as the same force applied at the centre of gravity. The centres of oscillation for several figures of very frequent use, suspended from their vertices and vibrating flatwise, are as follow:

In a right line, or parallelogram, or a cylinder of very small diameter, the centre of oscillation is at two-thirds of the length from the point of suspension. In an isosceles triangle the centre of oscillation is at three-fourths of the altitude. In a circle it is five-fourths of the radius. In the common parabola it is five-sevenths of its altitude. In a parabola of any order it

is (2n+ × altitude where n denotes the order of the figure.

3n+1

In bodies vibrating laterally, or in their own plane, the centres of oscillation are situated as follows; namely, in a circle the centre of oscillation 'is at three-fourths of the diameter; in a rectangle, suspended at one of its angles, it is at two-thirds of the diagonal; in a parabola, suspended by the vertex, it is five-sevenths of the axis, increased by one-third of the parameter; in a parabola, suspended by the middle of its base, it is four-sevenths of the axis, increased by half the parameter; in the sector of a circle it is three times the arc of the sector multiplied by the radius, and divided by four times the chord; in a right cone it is four-fifths of the axis or height, increased by the quotient that arises when the square of the radius of the base is divided by five times the height; in a globe or sphere it is the radius of the sphere, plus the length of the thread by which it is suspended, plus the quotient that arises when twice the square of the radius is divided by five times the sum of the radius and the length of the suspending thread.

In all these cases the distance is estimated from the point of suspension, and since the centres of oscillation and percussion are in one and the same point, whatever has been said of the one is equally true of the other.

HEAT AND COMBUSTION.

Having now explained at some length the mechanical principles with which the student of the steam engine ought to be acquainted if he wishes to get to the bottom of the subject, we shall next say something of the nature of heat and combustion, an acquaintance with which is equally necessary to his proficiency. Upon some, we are aware, these elementary elucidations will be thrown away, for the greater number of competent engineers are already familiar with such inquiries; and it is not to be supposed that we can add materially to their information upon these preliminary topics. But to a far larger number a treatise upon the steam engine would be a sealed book without such steps of easy progression; and our profession is, while aspiring to add to the information of the initiated, to open the subject of the steam engine up to those unacquainted with steam, or any other science.

There are three modifications of heat of which philosophers speak; sensible heat, latent heat, and specific heat. Sensible heat is the heat which is observable by the thermometer, or discoverable by the senses; and this kind of heat exists in every thing with which we are acquainted; for, as we know of nothing so cold but what it might be colder, there is nothing without a certain degree of heat in the whole range of our experience. The frosty atmosphere of our own climate, for example, is not so cold as that of Russia, while the Russian atmosphere, again, is more genial than that of the north pole; and even at the north pole some times are colder than others, and as cold arises merely from a penury of heat, there are variations in the degrees of heat even in the coldest situations, and consequently some existing and discoverable by the thermometer in all things.

Latent heat is defined to be that heat which is not discoverable by the thermometer, but is expended in producing a change of state, as in the liquefaction of ice or the vaporization of water. If an open vessel of water be placed upon a fire, the temperature of the water will not rise above the boiling point, or 212 degrees, however long the boiling be continued, although the water must have been all the while receiving accessions of heat from the fire. All the heat received over and above that requisite to produce the temperature of 212° is expended in the formation of steam, but the steam itself does not rise above 212°; and on account of the heat thus hiding itself, as it were, in the steam, it is called latent heat. The term, however, is a bad one, as the obvious explanation is, that heat is capable of producing two distinct effects; the one an elevation of temperature with the same volume, and the other an augmentation of volume with the same temperature; and these effects are equivalent and convertible. There is, therefore, no more propriety in saying that heat is latent when it does not elevate the temperature of a body than when it does not enlarge its volume, for in each case the effect proper to the application is produced, and to look for an augmentation of temperature, as well as an augmentation of volume, would be to reckon upon receiving the same thing twice over.

The latent heat of steam is said to be 1000°, which means that it would take 1000 times more heat to raise a pound of water into steam than to raise it one degree in temperature, or what is the same thing, the heat required to raise a pound of water into steam would raise 1000 pounds of water one degree. From this it appears that it requires about 5 times as much heat to raise any given weight of water into steam as would raise the same weight of water from the freezing to the boiling point. The freezing point is 32°, and the boiling point 2120, so that the amount of difference, or the number of degrees through which the temperature has to be raised between the freezing and boiling points, is 180°, and 180° multiplied by 51 is 990, or 1000 nearly.

Specific heat means the quantity of heat contained by one body at a given temperature compared with the quantity contained in another body at the same temperature. It by no means follows that the same weights of different bodies at the same temperature contain the same quantities of heat, any more than that the same bulks of different bodies contain the same quantities of matter, and the specific heat of a body indicates the quantity of heat it contains just as its specific gravity indicates its quantity of matter. The specific heats of a great number of bodies have been ascertained and arranged in tables just as their specific gravities, and the specific heat of water is taken as unity.

A great deal of confusion has been cast over the subject of specific heat by the accredited definition of latent heat, which is said to be the heat absorbed by bodies during a change of state from solid to liquid, and from liquid to aeriform, whereas it ought to be the heat absorbed without elevation of temperature, whether there be a change of state or not. From the want of this stipulation, the heat produced by the compression of air, or the cold produced by its dilatation, has been ascribed to a change in the specific heat of the air, while the change of temperature due to a corresponding operation in the case of steam is set down as being due to a change in the latent heat. From the experiments of Watt and others, it appears that the sum of the latent and sensible heats of steam is a constant quantity very nearly; so that when steam is expanded, its latent heat is increased in about the same ratio in which its temperature is diminished; yet as there has been no change of state in the case of air, the depression of its temperature during ex

pansion is charged upon its specific heat, although that element is in reality guiltless of the transformation. We have thus the anomaly of that being reckoned specific heat in one country which is counted latent heat in another, for the steams of one climate are the gases of a warmer one; and if the same laws respecting latent and specific heat be not suffered to hold in the case of air, as in that of steam, the conditions of latent and specific heats resolve themselves into mere questions of latitude and longitude. Ether, which exists in the liquid form at the ordinary atmospheric temperatures of this country, becomes a permanent gas at the equator; and many substances which exist in the liquid state at Geneva become aeriform at the summit of Mount Blanc; and the only way to escape from the inconsistencies involved by the present doctrines on this subject is either to depose the steams from the position they now hold and set them upon the same ground the airs occupy, or, what, in our judgment, is better still, because opening a road connecting theory with experiment, to accept the definition we have indicated. The way in which this connection is to be made we

shall now endeavour to show.

It may not be known to some of our readers that all bodies are supposed to be built up of indefinitely small molecules of matter called atoms; and indeed, if it be admitted that there is such a thing as matter at all, it may be now taken for granted that it is thus constituted. These atoms are never broken up into fragments, but when bodies combine, a certain number of the atoms of the one mingle with a certain number of the atoms of the other, rejecting any excess of either that may be offered beyond the proportions proper to the compound, and this is what is understood by combining in definite or atomic proportions. Messrs. Dulong and Petit, from a number of considerations, have been led to believe that the specific heats of bodies are inversely as their atomic weights, or in other words that each atom of a body has the same quantity of heat, so that its specific heat will be great in the proportion in which the weight of its atoms is small, and consequently the greater number of atoms in it. The experiments, however, of these ingenious inquirers did not bear out this view of the case; but the discrepancy arises, in our belief, from the admission of a certain proportion of latent heat as an element of the investigation, so that the heat indicated, instead of being the true specific heat, is a compound quantity made up of latent and specific heats conjointly. In ascertaining the specific heat of iron, for example, the plan adopted was to heat the iron to a certain temperature, and plunge it into a vessel of water of which the temperature was known, and the rise in the temperature of the water was supposed to indicate the specific heat of the metal. But it is obvious that a contraction of the iron would take place when plunged in the water, the heat due to which would by its extrication go to increase the temperature of the water, and thus vitiate the result. If the amount of this heat were to be ascertained, and subtracted from Dulong and Petit's results, we have every confidence that the numbers obtained would then bear out their very ingenious hypothesis; and which from other considerations has the strongest probability to support it. And if the specific heats of bodies vary inversely as their atomic weights, it is plain that they cannot vary with the temperature, provided heat be im ponderable; for the weight of a body is made up of the weight of the atoms of which it is composed, and an atom cannot be heavier if the body be not heavier itself. If, therefore, the weights of the atoms be unaffected by temperature, and a fixed relation exists between the weights of the atoms and the specific heats, the specific heats cannot be affected by temperature either, and the specific heat of a body must be the same whether it be in the solid, liquid, or aeriform state, so that the specific heat of the same body remains unchanged under all its transmutations. This conclusion does not correspond exactly with experiment, for the specific heat of steam, for example, is rated at 847, that of water being 1. But there are very few of the experiments on the specific heats of aeriform bodies, upon which much dependence can be placed; as the investigation is one of infinite difficulty, from the delicacy required in the manipulation, and the minuteness of the result that is to be caught.

NATURE OF HEAT.

There are two theories in the field respecting the nature of heat the one regards it as a material substance, and the other as a mere undulatory motion in the molecules of bodies, or in a highly elastic and subtle fluid which pervades all space, and which is capable of transmitting vibrations As philosophers still differ upon this subject, it is not to be supposed that we shall perplex ourselves with it, especially as engines will work equally well whatever theory be the correct one. The inquiry, however, is not without interest, as, if the doubt were resolved, we should perhaps have such light thrown upon the modes of exciting heat as might greatly conduce to economy in steam machinery, and at least we should then be able to construct furnaces more scientifically. If heat be a material substance and not a mere quality of matter, the heat produced by the combustion of a given quantity of fuel in the internal furnace of a steam boiler must either enter the water, or escape up the chimney, and in this case the indication would be to make the combustion very slow, in order that it may be the more perfect: but, if heat be merely a vibratory motion in the particles of bodies, slow combustion may be carried too far, and it may become then an indication to cause the heat to be absorbed as near as possible to the spot in which it is excited, for the vibratory motions may

otherwise become faint or altogether cease without producing any adequate effect upon the water in the boiler.

COMBUSTION.

Combustion is nothing more than a vehement combination of the constituents of coal with the oxygen of the atmosphere, and which only takes place at a high temperature. In all cases of chemical combination there is a transfer of electricity, and it is essential to combination that the combining bodies shall be in opposite electrical states. The rusting, or, as it is more learnedly termed, the oxydation of iron, is caused by the combination of the oxygen of the atmosphere therewith, and is therefore a process analogous to the combustion of coke or cinders, which might be described as the rapid rusting of carbon.

To maintain this rapidity of oxydation, it is indispensable that the air be quickly renewed, and hence the necessity in a furnace for the existence of a draught. The atmosphere consists of a mixture of two gases, oxygen and nitrogen or azote, in the proportion of 1 volume of the former to 4 of the latter. The specific gravity of oxygen is 1111, that of air being unity; and the specific gravity of nitrogen is 9722. Coal consists of charcoal or carbon united with hydrogen and other gases in very variable quantity in the different kinds of coal, and intermingled with sulphur and other impurities. The most flaming kind of coal is that which contains most hydrogen, whereas anthracite and coke contain little or none, and the earthy matter present in coal takes during combustion the form of ashes. 1000 lbs. of splint coal contains, according to Dr. Thomson, 647.3 lbs. of coke and 352.7 lbs. of volatile matter, while cannel coal contains in the same weight only 400lbs of coke, and as much as 600lbs. of volatile matter. Cannel coal, however, is not used in furnaces, so that we need not consider its peculiarities, nor is the splint coal now much used for the generation of steam, except in a few situations, for, although very effectual, it burns quickly away, and is not the most economical, except near the places at which it is dug. The Welsh coal appears to be the best adapted for the generation of steam with economy, and it consists chiefly of carbon, and has very little hydrogen in it. The combination of oxygen with carbon forms carbonic acid, and during the conversion the gas does not undergo any change of volume but only increases in density. The specific gravity of carbonic acid is 1.5277, so that a pound and a half of carbonic acid has half a pound of carbon in it, or in other words, every pound of coke or Welsh coal requires about two pounds of oxygen for its saturation. But the oxygen is mingled with nitrogen, from which it cannot detach itself, and for every two pounds of oxygen that enters into combination, seven pounds of nitrogen must pass through the fire, making a total of nine pounds of atmospheric air to every pound of coal, supposing that all the oxygen enters into combination. But this is never the case, and in the great majority of fires eleven or twelve pounds of atmospheric air will be required for the combustion of a single pound of coal, at the lowest computation, and sometimes the quantity much exceeds this amount.

Smoke is the product of the imperfect combustion of bituminous coal, caused either by a want of oxygen or a want of temperature. If analysed, it will be found to consist of uncombined carbon, carbonic acid and carbonic oxide, aqueous vapour, bituminous vapour, and the other volatile products of coal, nitrogen and atmospheric air, in varying proportions. There is often an intermixture, too, of sulphur, ammonia, and probably of cyanogen. In common language, a furnace is said to burn without smoke when no uncombined carbon is visible at the chimney; but even in such cases there may be a great waste of combustible material, by the formation of carbonic oxide in the furnace, which may be defined to be invisible smoke, and which may carry a large amount of carbon, which would otherwise have been productive of benefit, into the atmosphere.

Flame may be defined to be aeriform or gaseous matter heated to such a degree as to be luminous, and may be produced independent of any chemical change, as is shown in the discharge of voltaic electricity through an undecomposable gas. When flame is produced in chemical combinations, gaseous matter is always the cause of it. In the fiame of solid substances which contain carbon, such as coal, wax, &c., three effects are observable on the application of heat, 1st,- Volatilization; 2nd, Decomposition; 3rd, Ignition. Thus, in the flame of a candle the wax is first volatilized, being converted by the heat into vapour; this vapour by reason of its specific levity ascends into the body of the flame, where it is decomposed, carbon is separated, and that carbon by its ignition is the chief cause of the light. Thus the brilliancy of coal gas increases with the quantity of carbon entering into its composition, and the flame of the oxyhydrogen blow-pipe, where the heat is the most intense that has hitherto been produced, is almost invisible.

If air be admitted to a candle in deficient quantity it will smoke, because the oxygen will be monopolised by the hydrogen of the flame, and the carbon must then be thrown off in the form of soot. If the temperature of the flame of a candle be artificially lowered it will smoke, because after vaporization and decomposition, not heat enough is left to effect the ignition of the carbon. Thus, if a candle be left with a long wick, so much heat is given off from it by radiation that the candle smokes. If the point of a pair of snuffers or any other cold body be introduced into the flame, smoke is produced by the diminution of temperature; or if a small tin pan containing water be held over the flame, the bottom of the pan will soon be covered with

soot, on account of the heat absorbed by the water. The same thing may be shown more strikingly by means of a piece of wire gauze; if this be held in the very base of the flame, no carbon will be deposited on it, for decomposition has not yet commenced there; if it be held in the middle of the flame it will soon be covered with soot, on account of its cooling action preventing the ignition of the carbon resulting from decomposition; but if it be held again at the apex of the flame, no carbon will be deposited, for before the particles ascend so high, they have been ignited and converted into carbonic acid by uniting with the oxygen of the atmosphere. These examples will illustrate the action of a common furnace, in which, if after the decomposition of the gas in the coal there ceases to be a sufficiency of oxygen to form carbonic acid with the carbon of the gas, there must be a production of smoke, when bituminous coal is burned, whatever the temperature of the furnace may be; for carbon has never yet been vaporized, or even fused.

When an inflammable gas is mixed with an uninflammable gas in certain proportions, the mixture will not take fire, and cannot be exploded by the electric spark. The effect is similar to what would be produced by mixing water with oil, and the cause of the phenomenon is the same-the cooling agency of the incombustible substance. Thus the various incombustible gases bave different degrees of power to prevent explosion or combustion according to their densities, or, in other words, according to their cooling powers. The efficacy of carbonic acid and nitrogen, and of the surfaces of small tubes, or of the wire gauze of the safety lamp, in preventing explosions in coal mines, arises from the refrigeration accomplished by those substances upon the exploding mixture, so that the temperature is no longer sufficient for its continuous inflammation. By mixing one part of carbonic acid with seven parts of an explosive mixture of carburetted hydrogen and atmospheric air, or one part of nitrogen with six parts at the common atmospheric temperatures, the explosive powers of the mixture are destroyed. At the high temperature of a furnace the gases not concerned in combustion will have less power in preventing that operation; and it is found that steam and vapours which require a considerable heat for their formation will have less effect in preventing combustion than gases at the common heat of the atmosphere. It requires a very large quantity of steam to prevent sulphur from burning. Oxygen and hydrogen explode by the electric spark when mixed with five times their bulk of steam; and even a mixture of air and carburetted hydrogen, the least explosive of all mixtures, requires a third of steam to prevent its inflammation.

By an experiment of Rumford's, it appears that all bodies, whatever the activity of their inflammation may be, may be extinguished by cooling agency. Even the explosion of gunpowder may be thus arrested, and its incipient inflammation be extinguished by directing on it a strong blast of air. When we blow out a candle, we are indebted to the cooling agency of a blast of air for the success of the operation. A very simple and elegant illustration of the effect of cold in extinguishing flame may here be stated, and is as follows:- Let the smallest possible flame be made by a single thread of cotton immersed in oil; it will be found to be about one thirtieth of an inch in diameter. Let a fine iron wire of one one hundred and eightieth be made into a circle of one tenth of an inch in diameter, and brought over the flame. Though at such a distance, it will instantly extinguish it if cold; but if it be held over the flame so as to be slightly beated, the flame may be passed through it. That the effect depends entirely upon the power of the metal to abstract the heat of the flame, is shown by bringing a glass capillary ring of the same diameter and size over the flame. This being a much worse conductor of heat, will not extinguish it even when cold. If its size, however, be made greater, and its circumference smaller, it will act like the metallic wire, and require to be heated to prevent it from extinguishing the flame. Another similar experiment may be made by bringing a small metallic ball near a very small flame. If the ball be cold, or even if it be red hot, it will extinguish the flame, but if brought to a state of ignition, it will then cease to produce the effect.

Different degrees of heat inflame the different combustible gases resulting from the distillation of coal. Carburetted hydrogen mixed with air is not ignited by well burned charcoal ignited to the strongest red heat. Indeed, a fire made of well burned charcoal, that is, charcoal that will burn without flame, may be blown up to whiteness by an explosive mixture consisting of air and carburetted hydrogen. An iron rod at the highest degree of red heat, and at the common degree of white heat, will not inflame such a mixture, but when in brilliant combustion it will produce the effect. The flame of carbonic oxide will inflame an explosive mixture of air and carburetted hydrogen. Olefiant gas and carbonic oxide may both be inflamed by iron heated to redness or by charcoal; and hydrogen, which explodes when mixed with three sevenths of its volume of air, takes fire at the lowest visible heat of iron and charcoal, and the case is the same with sulphuretted hydrogen. Atmospherical air, when very considerably rarefied, is rendered unfit for supporting combustion. This fact was known to the earlier experimenters upon the Boylean vacuum, but the subject remained involved in considerable obscurity until investigated by Sir H. Davy. He has shown that flame ceases in rarefied air, not from a want of nourishment, but from want of heat, and that if its temperature could be preserved by some supplementary aid it might be kept burning. It is not, however, by the same degree of rarefaction of air that the combustion of all bodies is suspended, for, as might naturally be supposed,

By preserving heat in rarefied air the inflammation of bodies may be continued, when under other circumstances it would have beeu extinguished. Thus when camphor is burned in a glass tube, so as to make the upper part of the tube red hot, the inflammation continues even when the rarefaction is nine times; whereas it will only continue in air rarefied six times when the camphor is burned in a thick metallic tube, which cannot be considerably heated by it. The mechanical condensation of air does not adapt it for supporting a more vivid combustion. If air be condensed five times, and then iron wire be ignited to whiteness within it by the voltaic apparatus, the combustion will go on with very little more brightness than in the common atmosphere, and will not continue, as in oxygen. Charcoal, again, will not burn much more brightly in this compressed air than in common air; and indeed the whole of our experience goes to show that compression of the air does not increase the vehemence of combustion, provided always the air be kept stationary and be not used as a blast.

From the experiments of Despretz* it does not appear that the quantity of heat given out by charcoal during combustion is greater or less in condensed oxygen gas than in gas of the common density; and he is of opinion that the same uniformity would be found to obtain in the combustion of sulphur and other bodies which burn in oxygen without a change of volume.

If we knew the precise nature and quantity of the combustible matters in smoke, and the temperature of the smoke as it emerges from the furnace, we could, by a very simple calculation, tell what would be the amount of advantage or disadvantage resulting from the admission of a sufficiency of air to perfect the combustion, supposing the cooling agency of the boiler to be absent. But in all practical cases, this is a quantity which must be considered, the combustion of smoke being of diminished importance when the heat generated is not absorbed by the boiler; and when the heat is so absorbed, the effect is to extinguish the flame, in a way similar to that in which the ring of wire operated on the small flame of a lamp in one of the experiments we have recited. If the flame resulting from the combustion of the smoke does not act upon the boiler, no calorific effect can of course be obtained from it, and there will be an increased consumption of fuel. When it does impinge upon the boiler, there is a danger that the cooling agency of the boiler, when conjoined with that of the nitrogen, carbonic acid, and cold air, will so diminish the temperature that the flame will be extinguished.

It has been already mentioned that one part of nitrogen, when mixed with six parts of an explosive mixture of carburetted hydrogen, or one part of carbonic acid with seven parts, destroys at common temperatures, the combustibility of the mixture. These proportions will of course be very much altered at the temperature at which smoke emerges from a furnace; but even in that case, the temperature of the smoke is so much beneath that of visible flame, that the effect of the nitrogen and carbonic acid will necessarily exert a powerful influence; and the difficulty of consuming or obviating smoke is greatly increased, or rather, we should say, altogether caused, by the presence of these gases. The combustion of smoke, however, is by no means impossible, notwithstanding these impediments, and in large towns the smoke nuisance has risen to so intolerable a pitch that its suppression we look upon as being now inevitable. During the last year a parliamentary committee has carefully investigated the means by which smoke may be done away, and has recommended that a bill be brought into parliament for the suppression of the nuisance. In this recommendation we cordially concur; for there is nothing of which we are more confident than that manufacturers and others would very quickly find out means of obviating the smoke emitted by their factories if it were made penal to produce any. Of the prevention of smoke in the case of house fires we are by no means equally sanguine; and indeed the expense of new grates or other machinery in all the fire-places of a great city would be a serious barrier to the introduction of such an improvement, even if it were known to be feasible. But in the case of furnaces, and other close fires, we have no such doubts; and as the question of smoke-prevention forms not only a part of the general subject we have undertaken to discuss, but is of great interest at the present moment to almost every member of the

* 37 Anu. de Ch. et de Ph 182.

community, we shall here introduce such remarks upon the subject as, without leading us into any practical details, will indicate some of the modes in which the desired innovation may be accomplished.

The whole of the smoke-burning furnaces that have been hitherto projected may be classed roughly under two general heads. In the one the smoke is burned by passing through, over, and among the burning fuel; and in the other it is consumed by the admission of a stream of air at the bridge, or in some other part, to mix with and consume the smoke after it has left the fire. It is necessary, indeed, in all cases of the combustion or smoke, that air should be present; for carbon, by which the colour of smoke is imparted, cannot be fused or dissipated in any way within a furnace without oxygen; but in some cases the oxygen already mixed with the smoke is sufficient for its combustion; and all that is wanted in such a case is its subjection to an elevated temperature. Papin proposed to consume smoke by causing the draught to pass down through a fire, and this draught might be maintained by means of his cylindrical blower or fan. This scheme was in part revived by Franklin, who contrived a stove for burning its own smoke in which the air descended through the fuel. Watt employed in his early trials a hopper through which a current of air was solicited to descend; but he found this difficult to manage, in consequence of the caking of the coal; and he in consequence relinquished the plan in favour of a dead plate at the mouth of the furnace, which when conjoined with a slow combustion and careful firing, is found to be very effectual. The raw coal is first placed upon this dead plate, upon its introduction to the furnace; and the smoke and gases proceeding from the coal on the application of heat are consumed in passing over the incandescent fuel. In some cases, air is admitted at the furnace door, and in other cases not, the alternative being contingent upon the rapidity of the draught and the thickness of the stratum of fuel maintained on the fire bars; for when the draught is quick and the fire thin, enough uncombined oxygen will escape up through the fuel to accomplish the inflammation of the combustible parts of the smoke. The coal in this plan has to be pushed back from the dead plate into the active part of the furnace as soon as its gases have been expelled an operation attended with more trouble than the ordinary method of firing, and therefore very generally neglected.

The method of admitting air, either at the bridge or in some situation beyond it, in order to accomplish the combustion of the smoke, is, in the case of furnaces unprovided with any feeding mechanism, attended with the very obvious objection that it is a thing impossible duly to apportion the admission of the air to the varying wants of the fire; so that there will generallly be either too little air gaining admittance, or too much in the latter case not merely interfering with the combustion of the smoke, but seriously cooling the boiler. With very careful and scientific firing, indeed, such as an experiment may obtain, the smoke is found to be very effectually obviated by the admission of air, and a saving in fuel to the extent of 12 or 14 per cent. may be realised; but under the average circumstances of firing there is no gain by the admission of air, but rather a loss; and the plan, therefore, though often revived, and sometimes under very imposing names, by successive projectors, has never been brought into extended practice. It is only in cases where self-acting fire-feeders are employed, that the plan of burning smoke by an admission of air into the flue is at all applicable; for there the production of smoke being nearly uniform, the air orifice may be adjusted with much nicety to its requirements, and needs no subsequent alteration. Even under this modification, however, we do not look upon the plan for consuming smoke by admitting air at the bridge or in the flues as the best that is available; and the addition of fire-feeding mechanisms would be a heavy expense as a preliminary condition, and could not be applied to existing boilers in all cases.

We reserve for the practical part of this treatise any thing that we may have to say respecting the merits of the rival smoke-burning schemes that have latterly contended with one another for the countenance of the public; but we would here desire to explain, that the method by which the nuisance of smoke might in the most difficult cases, as in steam-vessels, be most easily and effectually obviated, lies, in our apprehension, in leading the smoke without any new intermixture through a perforated fire-brick bridge, which would answer very nearly the same purpose as a second fire. This bridge, however, to be effectual, would require to be of a considerable length, and should have several breaks in it, so as to agitate the smoke in its passage; but at the same time it should be so made as to be capable of being easily cleared, for a crust of ashes will be found to form upon the fire-brick surface, which will require to be swept away occasionally. The depth of fire upon the bars, and the intensity of the draught, must of course be so regulated, that air enough will ascend through the fire to accomplish the combustion of the smoke, and it is important that the fire be fed often and in small quantities at a time. But if the smoke be agitated when in a hot state and at the same time the ordinary excess of oxygen be present, the carbonaceous portion of the smoke will be burned very effectually. Furnaces will generally cease to smoke when a very bad back-draught comes upon them, as the agitation of the air in that case facilitates the combination of the combustible parts of the smoke, with its intermingled oxygen; and in an air furnace for melting iron, where the smoke is deflected down upon the hot metal, all appearance of carbon ceases when the furnace has reached an elevated temperature. Nor is this owing, in the cases to which we allude, to the formation of carbonic oxide, but arises merely from the combustion of the smoke in consequence of the agitation it undergoes on the flame H

bed, and the high temperature to which it is subjected. It would no doubt greatly facilitate the burning of smoke in furnaces generally if the heat were prevented from entering the water of the boiler by a fire-brick casing, or some other such means, until after the smoke had been consumed, for the temperature thus retained would much facilitate combustion. But it is not certain that a loss of effect would not result from this innovation, though if the heat producible by a unit of coal be a constant quantity, and cannot cease to exist without producing a corresponding effect upon other bodies, it is difficult to see in what way a loss of effect is possible. In that case any heat the coal produced would necessarily enter the water if it did not escape at the chimney, and if less heat were communicated by the furnace, a proportionably greater amount would be communicated by the flues; but the subject is involved in too much obscurity to give worth to any hypothesis, and we have as yet no experiments upon this point that are adequate to resolve our doubts.

A good deal of interest has been at various times excited by the peculiar formation of the Cornish boiler; one property of which is, that it generates steam with very little smoke, as well as with considerable economy of fuel. This result is usually attributed to slow combustion; and certainly a most important thing in the design of any measures for the combustion of smoke is to give as much time as can be afforded for accomplishing the combination, as well as to make the intermingled gases as homogeneous as possible. A large part of the smokeless virtue of the Cornish boilers, however, is to be attributed to the nature of the coal usually employed there, which contains very little hydrogen; and consequently only a small proportion of that bituminous material out of which smoke is formed. These circumstances, whatever be their several values, certainly, when taken together, go to produce a very satisfactory result; and in boilers operating on the Cornish plan, and with the Cornish, or rather the Welsh fuel, an almost inappreciable quantity of smoke is generated. Several of these boilers have of late years been set up in London, and furnish certainly a strange contrast to the vehement smoking of the ordinary metropolitan fires. Of these the boilers employed for driving the machinery of Mr. Thomas Cubitt's factory, at Vauxhall Bridge, has probably attracted the most attention; and no one, indeed, looking to the small quantity of smoke which escapes from that monumental chimney, could imagine that there was a boiler of any kind in that situation. The necessity of using Welsh coal, however, to produce this result, is certainly an objection in the case of London furnaces, for Welch is dearer than Newcastle coal in the metropolis; yet this extra expense is but a small consideration when put against the inconvenience and insalubrity caused by smoke in large cities, and it should, we think, be made imperative that those who do not feel disposed to dispatch their smoke by any other method should use the Welsh or some other smokeless coal, so that they may cease to be with impunity manufacturers of a nuisance. The greatest manufacturers of smoke, however, in London, are the brewers, distillers, and chemical manufacturers, to whose operations the expedients of the Cornish boiler will probably not apply. But there will very soon be discovered expedients that will apply in every case if the production of smoke be only made punishable. Those who cry out the most loudly against the hardship of being compelled to extinguish a nuisance which is not known to be susceptible of abatement, are in most cases conscious all the while that the prevention of smoke is possible, though it at first might be attended with some trouble, and they will be very quick in finding a remedy when their works are prohibited against going on upon any other condition.

THE TEMPERATURE AND ELASTIC FORCE OF STEAM.

Steam, as all our readers know, is an elastic fluid generated from water by the application of heat. It is, in fact, water in a high state of rarefaction, or so impregnated with caloric, or the matter of heat, as to assume the state of an aëriform or elastic fluid. When steam is confined in a close vessel in contact with the water that produces it, the effort by which it endeavours to expand itself and enlarge its volume, or to separate the parts of the vessel that confines it and set itself free, is called the elastic force of steam. In estimating the mechanical action of steam, the intensity of its elastic force must be referred to some known standard measure, such as the pressure which it exerts against a square inch of the surface that contains it, usually reckoned by so many pounds avoirdupois upon the square inch. The intensity of the elastic force is also estimated by the inches in height of a vertical column of mercury, whose weight is equal to the pressure exerted by the steam on a surface equal to the base of the mercurial column. It may also be estimated by the height of a vertical column of water measured in feet; or generally, the elastic force of any fluid may be compared with that of atmospheric air when in its usual state of temperature and density: this is equal to a column of mercury 30 inches or 2 feet in height.

When the temperature of steam is increased, respect being had to its density, the elastic force, or the effort to separate the parts of the containing vessel and occupy a larger space, is also increased; and when the temperature is diminished, a corresponding and proportionate diminution takes place in the intensity of the emancipating effort or elastic power. It consequently follows that there must be some law or principle connecting the teraperature of steam with its elastic force; and an intimate acquaint

ance with this law, in so far as it is known, must be of the greatest importance in all our researches respecting the theory and the mechanical operations of the steam engine. The precise form of the expression which expounds the true mathematical law or principle of elasticity, has never yet been rigorously ascertained, but recent investigations have put us in possession of numerous empirical forms, by which the results of several classes of very delicate and valuable experiments are represented with a sufficient degree of exactitude to answer all the demands of practice. These forms we mean to compare with one another, in order to deduce an expression that may best represent the average results obtained, and may at the same time be easily applicable to the uses of the practical engineer.

It is not our intention, however, nor would it be consistent with the plan of our performance, to trace the steps of investigation by which these multitudinous formulæ have been elicited; but we may state that the general mode of procedure is by reference to a curve of such a nature, that the co-ordinates are respectively indicated by the temperature of the steam, and the corresponding elastic force. This curve will be variously expounded according to the manner in which it is considered, but in every case, the exponent expressing the order or degree of the curve, is that which indicates the law of elasticity, and is that only whose value can be expressed by a legitimate formula. The other constants or coefficients by which the equations are affected, having their values depending on some gratuitous conditions, are beyond the powers of a direct analysis, and are, therefore, only deducible by some indirect process of approximation or trial and error, a mode of procedure often resorted to by analysts in reducing expressions of a complex and intricate character. But notwithstanding that it is foreign to our plan to enter into long and elaborate dissertations respecting the dilatation and compression of elastic fluids, we should yet consider our labours as being very imperfect, did we not, in one instance at least, lay before our readers the method of detecting the law of elasticity; and in order that the process may be the more easily understood, we shall previously resolve the following very elegant and useful problem :-To find a theorem, by means of which it may be ascertained when a general law exists, and to determine what that law is, in cases where it is known to obtain.

Suppose, for example, that it is required to assign the nature of the law that subsists between the temperature of steam and its elastic force, on the supposition that the elasticity is proportional to some power of the temperature, and unaffected by any other constant or coefficient, except the exponent by which the law is indicated. Let E and e be any two values of the elasticity, and T, t, the corresponding temperatures deduced from observation. It is proposed to ascertain the powers of T and t, to which E and e are respectively proportional. Let n denote the index or exponent of the required power; then by the conditions of the problem admitting that a law exists, we get, T: E: e; but by the principles of proportion, it is,

t

t e

e

TE; and if this be expressed logarithmically, it is nxlog. = log. and by reducing the equation in respect of n, it finally becomes

E'

The theorem that we have here obtained is in its form sufficiently simple for practical application; it is of frequent occurrence in physical science, but especially so in inquiries respecting the motion of bodies moving in air and other resisting media; and it is even applicable to the determination of the planetary motions themselves. The process indicated by it in the case that we have chosen, is simply, To divide the difference of the logarithms of the elasticities by the difference of the logarithms of the corre sponding temperatures, and the quotient will express that power of the temperature to which the elasticity is proportional.

Take as an example the following data:-In two experiments conducted by Mr. Southern, with his customary attention to accuracy, it was found that when the temperature of steam was 250-3 and 343 6 degrees of Fahrenheit's scale, the corresponding elastic forces were 596 and 238-4 inches of the mercurial column respectively. From these data it is required to determine the law which connects the temperature with the elastic force on the supposition that a law does actually exist under the specified conditions. The process by the rule is as follows: