l_3 s S 1 1 3 1 ^/OJnVD-JO^ %OJITVO-JO^ ^OF-CALIFOP^ ^OFCAllFOff^ pa S a i * ^lOSANCElfj^. N BRARYtf/- a I i ^lIFOftto X*~ > v ^, fe INIVER%. I PS-'Jp 3,^ ^ INV-SOl^ "v/ftHAINfHttV !NIVER%. ^vlOS-ANCElftu g f ^ -^ J/ ' I - '.Qm^" " v/Sa3AIN(l-3\\V 1ARY0/- ^-IIBRARY^ r ^i i ir" ^13DNV-SO^ I1VD-JO^ %OJ1TV3-JO^ AIIFO% ^OF-CAIIFO%, $\ r 'LI ^ i s <3 i s I I % & s I e I ^lOS-ANCElfju. ^ ^**v , % Us PRINCIPLES AND CONSTRUCTION OP MACHINERY : A PRACTICAL TEEATI8E OK THE LAWS OF THE TRANSMISSION OF POWER, AND OF THE STRENGTH AND PROPORTIONS OF THE VARIOUS ELEMENTS OF PRIME MOVERS, MILL- WORK, AND MACHINERY GENERALLY; RRANGED FOR THE USE OF (Ettginrm', BY FRANCIS CAMPIN, C.E., PHESIT)ENT CIVIL AN'i) MEi'hA.flfA f. hXCINEFK^' S')'r:TV LONDON: ATCHLEY & CO., 106, GEEAT RUSSELL STREET, publishers of (Engtnttnng & ^rtbitcttur;U wlorhs. [The right of Translation is Reserved.] LONDON : PRINTED BY P. GRANT, 3 & 4, Ivr LANE, PATERNOSTER Row, E. C. C 15 f REV. JOHN FREDERICK HARDY, M.A., fefe i IS RESPECTFULLY DEDICATED, As A MARK OF ESTEEM, AND IN GRATEFUL REMEMBRANCE, BY HIS FORMER PUPIL, (Tbe ^ulbor. a 379384 PEEFACE. IN issuing the present Treatise, a few words ex- plaining the motives of its production, addressed to those classes for whose use it is designed, seem not only appropriate but necessary, in order to account for the arrangement which has been adopted. The contents of the work are in substance a care- fully-revised digest of the author's oral instructions, which for some years past he has found successful in training pupils to a knowledge of that portion of Civil Engineering which takes cognizance of Machinery and Mill- work. The great bulk of treatises on Mechanics are cumbrous to the last degree, loaded with varieties of rules and overwhelming numbers of examples of their application, to determine the modification of forces and ratio velocities of gearing ; but in none of them has the Author found the laws of construction in reference to strength of parts set forth at all fully ; hence the Lectures given by him were specially arranged to show, not only the prin- ciples by which forces and velocities are modified, but also the mode of determining the least dimen- sions of all descriptions of mill- work and machinery, so that the reader may understand not only why a given machine produces a certain effect, but also //on- to make it practically. Sufficient examples are given in the first portions of the book to show the method of using symbolical formulae, wherefore in the latter parts the formulae are not all illustrated by arith- metical examples, as to have followed such a course would have inconveniently extended the bulk of the volume. The Author's aim throughout has been, in the first place, to explain the Fundamental Theoiies of Me- chanism in the clearest and briefest manner, so as to impress upon the mind general principle*, not special cases, and then to show the practical development of such theories, care being taken so to arrange the matter as to try the facidties of the mind as little as possible. FKANCIS CAMPIN. CONTENTS. PAGE INTRODUCTION 1 CHAPTER 1. FORCE OR PRESSURE 5 2. WORK, POWER, AND MOTION 11 3. GENERAL LAW FOR ALL MACHINES MODIFYING FORCE 17 4. CENTRE OF GRAVITY. MECHANICAL POWERS . . 22 o. ELEMENTS FOR CHANGING THE NATURE OF MOVE- MENTS 31 6. FRICTION 34 7. ON THE CONSTRUCTION OF MACHINERY AND MILL-WORK 36 8. STEAM AND HoT-Am ENGINES 56 9. BOILERS AND FURNACES 81 10. WATER-WHEELS AND TURBINES 112 11. PUMPS AND HYDRAULIC MACHINES 128 12. MARINE ENGINEERING 141 13. MATERIALS USED IN CONSTRUCTION 143 14. MANIPULATION OF TIMBER AND THE METALS . . 174 15. ON THE WORKING OF METALS COLD 187 16. JOINTS, BEARINGS, AND PACKINGS. 197 17. FOUNDATIONS AND FRAMING 210 18. ADAPTATION OF MACHINERY TO SPECIAL PURPOSES 220 19. PHYSICAL SCIENCE CONSIDERED IN RELATION TO MECHANICS 232 20. ELECTRICAL AND CHEMICAL MACHINERY . . . 261 21. MISCELLANEOUS 271 22. ESTIMATION OF QUANTITIES 277 CONCLUSION 280 PEINCIPLES AND CONSTRUCTION OF MACHINERY. INTEODUCTION. IN the majority of treatises on Mechanics, and perhaps more especially in those which are professedly of an elementary character, a great number of unnecessary divisions and classifications have been introduced, tend- ing to complicate rather than elucidate the questions discussed, and taxing the memory of the student by imposing upon it the duty of retaining a number of purely arbitrary systems of formulae or rules, instead of impressing upon the mind of the learner the main principles upon which all such formulae are based. Every kind of machine or structure met with in engi- neering practice is of necessity based upon some fundamental principle or principles which should be thoroughly comprehended by those who undertake to construct, modify, or improve upon, these machines or structures. It is very insufficient merely, as it were, to learn the action of one particular machine, without ascertaining the principle of such action and the extent of its application, for without this latter knowledge a thorough comprehension of the machine cannot be attained. Similarly in regard to structures, say lattice bridges, the student who merely learns by rote the rules for calculating the trussing of all (at present) known descriptions of lattice girders will find himself at a loss 2 PRINCIPLES AND CONSTRUCTION and incompetent to fulfil the duties he assumes should a new method of trussing be invented, according to which he may be called upon to design a bridge ; whereas had he mastered the principles which rule the arrangement of trussed girders, the matter would be one of no difficulty whatever. The intention of this work is to instil into the minds of engineering students and mechanics, in the simplest way, what may be termed the alphabet of engineering practice, and in order to render it available to as large a class of readers as possible, everything approaching to high mathematics will be carefully avoided, and all calculations restricted to the simplest language. It is, however, impossible to deal with the subject before us in a sufficiently lucid manner without employ- ing simple equations, upon which, therefore, a few words in this place may be appropriate. Suppose x to represent the quantity proposed to be found from an ordinary "proportion" or "rule of three" statement, such as the subjoined : 12: 45 :: 13 : x, then, according to the rule, _ 45 x 13 12 This is simply the same thing, but stated as an equa- tion. It is, however, convenient to have a general formula, for there may be many similar cases where the values of the first three terms are not as above ; hence replace 12, 45, and 13 respectively by the letters a, b, and c, then the general equation becomes ' -~ "> The value of an equation, or rather its equality, is not altered by either multiplying or dividing both its sides OF MACHINEBY. by the same multiplier or dividend, for " things which are double of the same are equal to one another," and " things which are halves of the same are equal to one another." (Euc., Axioms vi. and vii.) Hence Let the general equation (1) be multiplied by a, I X c = x x a but usually the multiplication symbol x is substituted by a period, thus a . x =. b . c The object of such an equation as this is evidently that three terms out of four being known, we may be able to find the unknown quantity : according to the terms represented by the letters, any one of the latter may present the unknown quantity ; therefore let an equa- tion be found for each : T Divide by x, then a = - Divide by c, then b = - Divide by , then c = - Divide by a, then x = In this case there are only multiplications and divisions to be performed ; but very commonly, as well as these, additions and subtractions will be found to occur, as in the equation following : + y=8*+$_*. . . (2) D We can, without vitiating the truth of the equation, subtract from or add a like quantity to both sides, for 4 PEIXCIPLES AND CONSTRtrCTIOX " if equals be added to equals the wholes are equal," and ' ' if equals be taken from equals the remainders are equal." (Euc., Axioms ii. and iii.) In equation (2) add m to both sides of the equation, z + y + m=3al + m + m = 3al + (3) 6 6 Or subtract y, x + y y = x = 3al + - m y . (4) D Both are true equations. From observation of the above process the following rule is drawn : If it is required to change a quantity from one side of an equation to the other, in so doing alter the sign of the quantity moved. Thus m in eq. (2) on the right becomes + m in eq. (3) on the left, and + y in eq. (2) on the left becomes y in eq. (4) on the right. These few brief remarks will probably be sufficient to explain the nature of a simple equation, so far as may be requisite to the comprehension of the formulae and analyses with which we shall subsequently have to deal. In concluding this Introduction it seems desirable to point out the general object of every machine or structure. This object, then, is to render some natural law or set of natural laws subservient to human pur- poses, to subjugate and guide the energies of the physical forces, either in motion or at rest, so that they may be expended at the places convenient and in manner suitable to our requirements. Thus, from coal dug out of the earth energy is developed to propel vessels on the ocean ; and by a skilful arrangement of materials vast loads are supported over chasms, and their weight transmitted to the piers or abutments on either side. OF MACHINERY. 5 Tlie main distinction in principle between a machine and a structure may be thus stated : A machine is used to apply physical force in motion ; a structure depends upon the laws of physical force at rest. The former is termed dynamic, the latter static force (from the Greek cvvapi, I move, and rnj/, I stand). CHAPTEE I. FORCE OR PRESSURE. FORCE or pressure acting upon any body indicates that such body is under some control which for the time being regulates the circumstances of its existence and condition ; but of forces there are several which, although capable of reproducing each other mutually, neverthe- less may be regarded as of different characters from the different phenomena to which they give rise. The natures of these forces will now receive our attention. According to the most generally received theory all matter is composed of minute bodies called atoms (from the Greek a privative, and TC/II/.S, I cut), which are indivisible, and by the building up of which molecules of matter are formed, by the aggregation of which again masses of matter are formed. The character of a molecule is that it consists of a number of atoms either similar or dissimilar chemically attracted towards each other ; but a mass of matter consists of molecules mechanically attracting each other : thus the mass of matter may be broken or crushed by mechanical means, but the molecules can only be disintegrated by chemical action. The atoms of matter, which Newton describes as being hard, impenetrable, and incapable of wear, form- 6 PBINCIPLES AND CONSTRUCTION ing a mass, are not in actual contact, as is evident from the compressibility of matter ; hence they must be balanced in certain positions, allowing greater or less intervals between them according to the nature of the body of which they are the component parts ; and to occupy such a position, two forces must be acting upon them, the one tending to bring them together, the other exerting a repelling force which unopposed would drive them asunder. The force tending to bring the molecules together is called the attraction of cohesion, and that which repels them is heat, and the molecules occupy positions dependent on the relative intensities of these two opposing forces. The intensity of the attractive force remains constant amongst the molecules of any given body, but that of the heat may be varied by external agencies; thus we can add heat to a mass of matter or deprive it of a portion of that which it already pos- sesses. In the former case the additional heat further opposing the cohesive force drives the molecules further apart, and the body expands ; but in the latter case the repulsive force being diminished, the molecules are drawn by the predominant cohesive attraction into closer contiguity, and the body contracts. It would be foreign to the purpose of the present treatise to dilate more fully upon these forces, as by so doing we should be trenching too much upon the sphere of physics. The next force to which we must allude is the attrac- tion of gravitation, by virtue of which all heavy bodies tend to approach one another. It is this force which holds the planets in their orbits, and to it is due the weight of matter. By gravitation ponderable substances fall to the earth, and by gravitation ships and balloons are supported in the aqueous and aerial oceans ; but in OF MACHINERY. 7 the last two instances the vessels are floated upwards because they are displaced by the superior gravitative force of the media by which they are sustained : they are forced up as a light weight is drawn up by a heavier one. Gravitation furnishes the measure for force, work, and power, as all forces, in whatever direction they may act, are always stated according to the weight of a mass which by reason of its tendency to fall to the earth would produce the same effect in a vertical direction. Thus, if a man push a carriage, exerting on it with his hand the same energy he would have to exhibit to sup- port a weight of thirty pounds, he is said to be pressing the carriage with a force of thirty pounds. The actual weight of a body does not affect the intensity of the earth's attraction for its parts, as a mass weighing ten pounds will fall no quicker to the earth than one weighing five pounds, nor any slower than twenty pounds' weight, as the effect of gravitation is manifest on each molecule of the mass independently of the neighbouring molecules, and were they all separate they would fall with the same velocity as they have when aggregated together in a solid mass. Not only do bodies gravitate towards the centre of the earth, however, but also towards irregularities on its surface and towards each other. The pendulum which in level country points when hanging freely to the centre of the earth, will when placed in the neighbourhood of moun- tains deviate from that position, being attracted in some degree by the masses of earth in its vicinity. Matter in general possesses a property termed inertia, by reason of which it will, if unacted Tipon by external agencies, continue in any state in which it may happen to be left by the last force that acted upon it ; that is to 8 PRINCIPLES AND CONSTRUCTION say, if a body is at rest it will remain so until some exterior force moves it, and if it be in motion it will con- tinue to move until some external resistance stops it. A body acted on by one force alone cannot be in a state of rest ; there must be at least two in operation, and these two must be equal in intensity and opposite in direction : in the language of statics these forces are termed action and re-action, hence the law of equilibrium of forces. To satisfy the conditions of equilibrium, Hie action and re-action must be EQUAL and OPPOSITE. If two forces only are acting, as a matter of course they must act in one and the same straight line, but in opposite directions. It not unfrequently happens that two forces act at a point so as to produce a combined effect ; it is necessary in that case to find what single force would produce the same effect as these two forces, which latter are sup- posed to be inclined at an angle to each other. Let two forces act at the point a, Fig. 1. Fig. 1, respectively in the directions of the lines a b, a c, and let their inten- sities be represented by the lengths of the lines a b and a c ; complete the parallelogram, abed, and join a d, then will the diagonal a d represent in direction and intensity the force equivalent to the two forces a b and a c. This is obvious at sight, for if we suppose the two forces acting to move a body from a, and each acts singly, first the body will be drawn to c ; and then c d, being equal and parallel to a c, will represent it and draw the body to d; but if both forces, maintaining parallelism to their initial directions, act continuously and at the same time, the body would really be moved along the diagonal a d. OF MACHINERY. If there be more than two forces acting at a given point, they may be solved by pairs by the ' ' Theory of the Parallelogram of Forces," until at last one force is found equivalent in intensity and direction to all of them together. All solid bodies are to some greater or less degree elastic, although in some, such as lead for instance, the elasticity is not easily perceptible ; elasticity being that property by which bodies when compressed, extended, or otherwise altered in form by external force, endea- vour to recover their former shape and size. If a weight be placed upon a spring balance, the spring is shortened in proportion to the weight placed upon it, and similarly if a weight is placed upon a solid mass there is induced a compression of the solid, and its ten- dency to expand to its original bulk produces the force sustaining the weight ; in short, the weight is the action, and the elasticity of the material supplies the re-action. Hence, when force is brought into action upon a fixed body, compression (or extension, as the case may be) takes place until the elastic resistance of the material supplies a re-action equal to the external force which has called it into operation ; provided always that the external force has not sufficient intensity to overcome the molecular attraction, and so rupture the body upon which it is acting. The reaction to every action which occurs on the earth might be reasoned out ; but to do so would be merely occupying a large quantity of space for no useful pur- pose, and the argument would be merely a series of repetitions of the example just given. Force may be transmitted from the first point of its application through either a solid, liquid, or gas, to operate at some distant point ; but if through a solid 10 PRINCIPLES AJTD COXSTEUCTION no mechanical appliance intervening the force can only ultimately act in the same direction as that in which it is first applied, or in one parallel to it. If, however, the force be transmitted through a liquid or gaseous medium confined in a vessel, the force may be received from such medium in any direction, regard- less of that in which the force was applied in the first instance. This difference is due to the distinctive cha- racteristics of solids and fluids, which are as follows : The weight of a solid body presses vertically towards the centre of the earth, but The weight of a fluid body presses equally in all directions. We must now pass on to describe "potential," or stored force. Perhaps as good an illustration as can be cited on this point is that supplied by a clock-spring when wound up ; a certain amount of force is communicated to the spring, and there remains stored up ready for use at pleasure ; while the spring is at rest this force is regarded as potential force, because although its pre- sence is not evidenced by any phenomena, yet it exists and is capable of being brought into action at any time. The same may be said of any weight raised and sus- pended over a body on which it may subsequently be required to exert pressure, or of steam or gas compressed in a close vessel, whether it be by actual forcing into the vessel more than it normally holds, or by increasing the tension of its normal contents by the effects of exter- nally applied heat. In conclusion, the forces which act upon all terrestrial matter may be arranged in two classes : Internal forces and forces acting externally. The internal forces are those upon which the form, properties, and constitution of various bodies depend in a normal state. OF MACHINERY. 11 The external forces are those which, proceeding from without the body, tend to move it from its position, alter its shape or bulk, or to destroy the cohesion of its parts. CHAPTEE H. WORK, POWER, AND MOTION. IN the previous chapter forces at rest have been treated of principally, but now we have to consider the results which accrue from forces accompanied by motion, that is from dynamic forces. When a force is exerted through a space, then WORK is said to be done ; if a resistance is overcome through- out the space passed through by the force, then uniform work is being done ; but if the resistance is all at the end of the space, then the work accumulated in passing through the space overcomes it. Work is usually ex- pressed in pounds lifted through feet as foot-pounds ; thus, if a resistance of 45 Ibs. is overcome through a distance of 50 feet, then the amount of work done is = 45 Ibs. X 50 ft. = 2250 ft. : Ibs. It matters not what direction the force is exerted in, whether to push a truck or lift a weight. By introducing a third element, time, comparative measurements of POWER are obtained. A horse, accord- ing to Watt, can lift 33,000 Ibs. one foot per minute ; hence, if a steam-engine be lifting 1,848,000 Ibs. one foot per minute, its power is 1,848,000 = =56 horse-power. 33,000 12 PEIXCIPLES AOT) CONSTRUCTION Hence, to find the horse-power exerted by any machine the following rule may be used : Multiply the weight or resistance by tlie speed per minute at which it is overcome, and divide the product by 33,000. Example : Let the resistance be equal to 503,089 Ibs. Speed per minute . . . 100 ft. 503,089 x 100 Horse-power = -- --- If a body fall freely, then the work, not being expended as it falls, is accumulated in it ; thus, if a weight of 15 Ibs. drops 10 feet, the work^accumulated in it will be 15 X 10 = 150ft.: Ibs. But supposing such a mass as a railway train in motion, then the accumulated work must be ascertained from the velocity ; it is equal to the weight of the train multiplied by the height through which it would have to fall to acquire a velocity equal to that at which it is moving ; but in order to find a rule to determine what this would be, we must ascertain the laws which govern the motion of bodies falling freely. From experiment it is found that a heavy body during the first second of its fall passes through 16'1 feet; hence its velocity at the end of the first second must be 32-2 feet per second, as at the commencement the velocity is and = 16-1 ft. the average velocity as found from the initial and final velocities. During the next second the body will pass through 32-2 feet, due to the velocity already acquired, and 16-1 feet, due to the continued attraction of gravita- tion, in all 48-3 feet ; and in the two seconds 64-4 feet ; OF MACHINERY. 13 it will also acquire another 32-2 feet per second, making a final velocity of 64-4 per second. Following this up, the distances and velocities corresponding to different durations of time will be found as follows : Let h = total distance fallen through, and v corre- sponding final velocity per second : Duration of fall in seconds. h V 1 16-1 32-2 2 64-4 64-4 3 144-9 96-6 4 257-6 128-8 5 402-5 161-0 From this table it is evident that the distance fallen through varies as the square of the time occupied by the fall, and the velocity varies simply as the time. Let t = time of fall in seconds, and g = 32-2 feet per second, then the following formula will serve to solve all cases relating to falling bodies : Let the time be 5 seconds, h = I X 32-2 x 25 = 402-5 feet fall in 5 seconds. Let the velocity per second be 100 feet, the fall to acquire such a velocity will be 10,000 = 155-3 feet nearly. 2 X 32-2 Again, to find the velocity, we have, by transposing the above equations, 14 PKINCIPLES AND CONSTRUCTION Let the time of fall be 5 seconds, v = 32-2 x 5 = 161 feet per second. Let the height of fall be 100 feet, v = -v/2 X 32-2 x 100 = 80-25 feet per sec. nearly. The weight of a body being = 7F", the work accumu- lated in it in falling through a distance = h, will be = W7i, and, also, replacing h by its value in the foregoing formulee equation (5). Accumulated work = - 2<7 Let a weight of 5 Ibs. be moving at a velocity of 20 feet per second, the accumulated work is _ 5 X 400 _ foot ndg 2 X 32-2 Taking the example of a train weighing 80 tons (I79,200lbs.), and moving at a speed of 20 miles per hour (29-3 per second), we find the accumulated work 40 = 2,388,840 foot-pound*. Again, let a cannon ball weighing 60 Ibs. leave the mouth of a gun at a velocity of 2,000 feet per second, the work accumulated in it will be = 6 X 4 ' 000 ' 000 = 3,726,708 foot-pounds. 2 x 32-2 This well illustrates the immense destructive power which may be concentrated in comparatively small weights by causing them to move at high velocities ; for whereas the accumulated work varies simply as the weight, it varies as the square of the velocity. If the velocity of a moving body, such as a train, after attaining a certain point becomes constant, then the body is said to have a uniform motion, and the pro- pelling power is just sufficient to overcome the frictional OF MACHINERY. 15 resistances opposed to the motion of the body at the velocity acquired. Let the propelling force cease to act, and the body will gradually come to rest, the work accumulated in it being expended in overcoming the frictional resistances to the gradually 'deer easing motion of the mass. Any mass set in motion will, if unoperated upon by any fresh force, move continually in a right line having the direction in which the force imparting motion to the body originally acted, but through the intervention of another force the body may be caused to move in a curve instead of in a right line. Let a body in motion be compelled, by a cord of constant length attached to it at one end and to a fixed point at the other, to revolve about a centre describing a circle at each revo- lution. A rule is required to determine the tension on the cord, or the centrifugal force. In order to state the amount of force necessary to draw a body through any given space, we must consider the case in comparison with the earth's attraction, which produces an effect of g, or 32-2 feet velocity, in one second of time. The attractive for ce varies as the bulk of the body, hence the mass of a body is expressed by W 9 The normal direction of the moving body will be a tangent to a circle, and according to the laws of the circle (Cape's Mathematics, vol. ii., p. 233,) the distance which it will be drawn out of this direction by the ten- sion of the cord will be expressed for one second by _^_ 2 ; hence the centrifugal force will be, r if r = radius of gyration, Wv* = iorce in pounds. 16 AND CONSTRUCTION In order to make more clear the mode of comparing centrifugal force with gravitative attraction, a special case may be taken. Let a force be capable of imparting a velocity of 64-4 feet to a mass of matter in one second, then will this force have twice the intensity of the attraction of gravitation, and a body requiring 5 Ibs. pressure to sustain it against the latter will require 10 Ibs. to sustain it against the former. Let it be required to determine the centrifugal force of a mass weighing 15 Ibs., revolving in a circle 4 feet in diameter at a velocity of 20 feet per second, the centrifugal force will be = 15 X 4 = 46-58 Ibs. 4 X 32-2 Bodies may be caused to move in a great variety of curves, dependent upon the composition of the forces acting upon them; thus the planets in their courses describe elliptical orbits, the path being determined by the initial velocity and direction of movement combined with the attraction of the sun. Let the ellipse Fig. 2. shown in Fig. 2 represent the path of a planet moving round the sun S placed in one of the foci of the ellipse. The rationale of its movement is as fol- lows : If the body first have a motion impressed upon it acting in the direction a b, by the time the body would have reached e the attraction of the sun has drawn it out of the right line as far as e d, when it may UF MACHINERY. 17 be considered as again moving in a tangent to the curve; and again, when it would have reached e, the sun's attraction has drawn it to /, and so forth. It will be observed that during the passage through this part of the orbit, the sun's attraction is retarding the moving body, until at k its course is turned round and it approaches the sun, the attraction of which is now accelerating its speed, as is evident from the direction in which it is acting, as shown at i j ; thus the loss of velocity due to the sun's attraction in one half of the orbit is restored in the other half, so that when the body again arrives at the point a it is moving with its initial velocity. It would very rarely occur that a planet, moving under the influence of its initial velocity and the sun's attraction, would adopt a circular orbit, as, for such to be the case, the latter must first come into action when the planet is in such a position that a line drawn from the sun to it would be perpendicular to its motion, and in addition to this there would be required a certain definite relation between the velocity of the body and the attractive force of the sun. CHAPTEE III. GENERAL LAW FOB ALL MACHINES MODIFYING FORCE. WHEN a force acts about a fixed Fig. 3. point as a centre, the effort of this force reduced to the centre is termed the moment of the force. In Fig. 3 let a b show the direction in which a force p is acting ; its mo- ment about the point c is required 18 PRINCIPLES AND CONSTRUCTION to be determined. From the point c let fall a perpen- dicular c d upon a b, and let the length of this perpendicu- lar be represented by I, then the moment of the force p about the point c will be = P X I Thus, if the force have an intensity of 20 Ibs., and its distance be 3-5 feet, the moment of the force about the point c will be = 20 x 3-5 = 70 foot-pounds. In all appliances for increasing or diminishing the intensity of force there are two main points requiring primary attention the point of application of the force and the point at whiclwt is given off. In every case there is a tendency to produce motion, and whether it actually is produced or not, the proportions of the machine to secure equilibrium between force and resis- tance, whether at rest or in uniform motion, will be the It is one of the fundamental laws of natural science that force can neither be created nor destroyed ; hence, if a force is increased, as by means of a lever, something else is diminished, as the space through which the force acts. Let work be done on one end of a machine equal to 10 Ibs. acting through 20 feet, that will equal 200 feet-pounds ; and this may be given off at the other end of the machine in a variety of different ways, but only the same amount of work can be given off. (At pre- sent friction is disregarded.) If the part of the machine at which the work is given off moves 2 feet while the point of application moves 10 feet, then dividing the work done by the space through which the force passes, it is found that the intensity of the force will be *200 * - 100 Ibs. pressure OF MACHINERY. 19 thus the intensity of the force is increased by means of the machine five times, but the space through which it acts is diminished in like ratio. Again, if two forces act about a centre so as to pre- serve equilibrium, acting, of course, in opposite direc- tions, their moments must be equal. Let a force of 30 Ibs. act about a centre at a distance of 3 feet from it, the moment of force will be = 30 X 3 = 90 ft. : Ibs. at what distance from the same centre must a force of 12 Ibs. act in the opposite direction to balance this moment ? Let x equal the required distance, the moment of this last force will be 12 x x = 12 x but to satisfy the conditions of equilibrium the moments must be equal ; hence 12 x = 90 ft. : Ibs. wherefore, x = ^ = 7'5 feet. In this case, if the forces were rotating, the spaces passed through would be inversely as the forces acting, because the circumferences of circles vary as their radii, and the distances of the forces from the point about which they act are the radii of the circles of gyration of such forces, and from the above it is observed that these distances are inversely as the forces to which they refer; the force of which the intensity is 30 Ibs., having a distance of 3 feet, and that of 12 Ibs. a distance of 7-5 feet. The generallaw formachines formodifying or increasin g pressure (irrespective of friction) may now be stated : The pressure is to the resistance as the space through which the resistance is overcome in a given time is to the tpace through which the force acts in the same time. c 2 20 PBDTCIPLES ASD CONSTRUCTION By this law may be solved questions referring to every description of lever, pulley, toggle, train of wheels, hydrostatic press, or other similar contrivance. Let p = pressure or force in pounds, R =. resistance in pounds. s = distance traversed by force in a given time. S = ,, ,, by resistance in the same time. From the following four equations any one of these qiiantities may be found, the other three being given: S- - P ' 8 A few examples will serve to show the application of these formulae : A b is a lever supported Fig. 4. on a fulcrum at c, the points of resistance and force being , respectively at a and b, the ^ distance a c = 10 inches, and p R. b c 56 inches, a c, b c being radii of gyration of the points a and b, the spaces passed through in a given time would be a, 10 inches, and b, 56 inches ; hence, if it is required to equal a resistance of 114 Ibs., the force applied must be p = 1I4 X 10 = 20-36 Ibs. nearly. 56 Let a weight of half a ton be required to be lifted by a force of 80 Ibs., the distance a e being equal to 2 inches, then the distance b c will be 1120 x 2 s = - = 28 inches. 80 In these cases it must be understood that the distances a c, be, are employed instead of the spaces actually OF MACHINERY. passed through by a and b, because the ratios are the same, that is Fig. 5. 8 ac The principle of the hydro- static press is illustrated in the section shown in Fig. 5. a and b are small and large cylinders fitted with water- tight pistons or plungers, one Qp) being the point of appli- cation of force, the other (jK) that of resistance ; the cy- linders communicate with each other by means of the pipe c. The water flowing out of a into b evi- dently has to cover a much larger surface in the latter than in the former, and consequently the depth of a given quantity of water would be much greater in a than in b ; or, in other words, if the piston in a be forced down, that in b will be raised to a height less than that through which p descended, in proportion as the area of b is greater than that of a ; but the areas of circles vary as the squares of their diameters (Eire., Bk. xii., Prop. ii.) ; hence the distances ( and $) passed through in a given time by the points of force and resistance, in the present case, are inversely as the squares of the diameters of the respective cylinders to which they are applied. Let the diameter of the cylinder a be 1-5 inches, and that of the cylinder b 10 inches, then the spaces passed through by p and R respectively in a given time will be 2 s = 10 = 100 2 8 = 1-5 = 2-25 22 PRINCIPLES AND CONSTRUCTION hence a force being applied at p = 25 Ibs., the resist- ance it will be capable of balancing is, = 25xl00 =llll.ilb. 2*25 or nearly half a ton. CHAPTEE IY. CENTRE OF GRAVITY. MECHANICAL POWERS. IT has hitherto been customary, when treating on the attraction of gravitation, to explain the use of the term " centre of gravity ; " but in this treatise its considera- tion has been advisedly postponed to this chapter, in order that the reader might first be made acquainted with the principle of moments of force, as by pursuing this course we are enabled the more clearly to deal with our subject now. That point in any body at which the whole weight may be supposed to be aggregated together is called the "centre of gravity" of such body, and if suspended from this point it will remain at rest in any position in which it may be placed. A mass of matter may be re- garded as an assemblage of small particles or molecules, each and all exerting moments of force about a certain point, about which all such moments are in equilibrio ; this point will be the centre of gravity of the mass. It is required to find the Fig. 6. centre of gravity of two forces, p, / Fig. 6, distant from each other a b. Let c be the centre of gravity of OF MACH1NEBY, 23 the forces, then the moments of the forces about c must be equal, or hence, p _ cb p ae let p 24 and p' = 7, then the ratio will be P _ cb _ 24 y ~~ aTc ~ T or c will be of b c ; or as there are 24 parts in b , and 7 parts in a c (24 -f 7 = 31) of a b 31 Let a b = 27 inches, then and = - x 27 = 6-09 inches, 31 I c = x 27 = 20-91 inches. 31 The centre of gravity of any number of forces may be thus finally found by solving it first for one pair, then considering the two forces as acting at their centre of gravity, and determining the point for this and another of the forces, and so forth, In all symmetrical bodies the centre of gravity is evidently coincident with the centre of figure or mass. The simplest machine for modifying pressure or resist- ance is the lever, and after what has already been said the solution of all questions connected with it will be sufficiently easy. Let p = the force, d = its distance perpendicularly from the fulcrum ; R == resistance, D = its distance from the fulcrum, then PRINCIPLES AXD CONSTRUCTION These four equations will serve Fig. 7. for any kind of lever ; the wheel and axle shown in Fig. 7 is identical in principle with the lever. The radius of the wheel equals d, one arm of the lever, and the radius of the axle equals D, the other arm of the lever. The circular movement of any point in the periphery of the wheel is called its angular velo- city, of which the proper definition is as follows : The angular velocity of a, wheel is equal to the velocity of any point in the periphery divided ly the radius of the wheel. The inclined plane, wedge, and screw are all but differ- ent forms of one and the same mechanical element. Fig. 8 is an inclined plane ; it is required to determine what force will be necessary to support the weight TFupon it. Let p = this force, I = length of the inclined plane, and h = its height. It is evident that in order to raise the weight W vertically through the height 7, it must be moved through the distance I, hence the force moves through the distance I, while the resistance of gravitation only acts through the distance h ; hence p= TFx A, W = Fig. 9. A wedge consists of two inclined planes placed base to base ; the formulae are the same as above, but replacing OF MACHINERY. 25 I by L and h by 2h, which would be the thickness of the back of the wedge, supposing it to consist of two equal and similar inclined planes. If an inclined plane, a b (Fig. 9), be wrapped round a cylinder, c d, it will describe a screw about it, as shown by the dotted lines. At each revolution of the screw any body on which it acts will be moved through a space equal to the distance from centre to centre between two successive convolutions of the thread ; this distance is called the pitch of the screw. The screw is usually turned by a bar or lever, e f. Let the distance from the axis of the screw at which the force acts = Z, the pitch 6f the screw = p, the force == P, and resistance = R in one revolution the force will describe a circle of wliich the radius = Z, or will pass through a space equal to 6-2832 L; hence the formulae for solving questions connected with the screw will be as follows : p - R x P R = p x 6 ' 2832 L 6-2832 L ' J The toggle, Fig. 10, forms a Fig. 10. very powerful mechanical element. A B are two blocks, one fixed, the other capable of sliding in the direction a b, but offering a resistance, R, to motion ; a c, c I are two links jointed together at c, the force being applied in the direction of the 26 PEIXCIPLES AXD CONSTRUCTION arrow p, or at riglit angles to the direction of the resistance. While the force is moving through the space c d, the resistance will evidently be overcome through a distance equal to twice the difference between a e and a d. But (Era., Bk. i., Prop. 47), , / 2 1 = V <** ~ ^ hence the space through which the resistance is over- come is Let I = length of one link (a c), d = distance traversed by force (c d), R =. resistance, p =. force, then This gives the relation of force to resistance when the former is acting in the position shown, but as the re- sisting block moves so the force becomes more and more intensified, until, just as the links a c, b c, fall into the same right line, the ratio becomes infinite. We next have to consider the effects Fig. \ 1 . produced by arrangements of pulleys intervening between the weight or resistance and the force opposed to it. If but one pulley is used, and that one is fixed as at a, Fig. 11, it merely serves to change the direction of the force, and does not alter its intensity ; hence, in this case, OF MACHINERY. 27 When, however, move- Fig. 12. Fig. 13. able pulleys are used, the case is altered, and the force becomes inten- sified. In Fig. 12 it is evident that half the weight, W, is carried on each of the portions, a and b, of the cord; hence the tension on the cord is W 2 In Fig. 13 the weight is carried on the four parts, 0, b, e, d, of the cord, hence the tension on it in this case is W 4 So, in these two instances, the ratio of force to weight is, Fig. 12 : f = Fig. 13 : p = The following formula will apply to all combinations of this class where only one cord runs through the whole system of pulleys : Let p = force, W = resistance, n number of tnoveable pulleys, PRINCIPLES AND CONSTRUCTION In Fig. 14 are shown four moveable pulleys and four separate cords. It is a combination of systems of which each reduces the resistance by one half, hence the tensions are on W . W W , W 'T'*'T'' T>* 16. Hence the following for- mulae will serve to solve cases of this sort. Let n = the number of times one system alone will re- duce the weight or resist- ance, and x =. the number of systems combined, then Fig. 14. W In the case illustrated, the number of times one system will reduce the resistance is 2, the number of systems combined 4, hence W _ W p ~ 2 4th ~~ TG Of course in all cases of pulleys what is gained in intensity of force is lost in space passed through ; thus, in Fig. 12, the parts a and b of the cord have both to be shortened as much as the weight is raised ; hence the cord at p has to be drawn through a distance twice as great as that through which the weight is lifted or the resistance overcome. In machines which act by percussion, such as ham- mers, pile engines, &c., the effect is produced by OF MACHINERY. expending work, accumulated through a certain dis- tance, in a comparatively very short space. For instance, let the "monkey" of a pile-driving engine weigh 300 Ibs., and have a fall of 10 feet, then in each fall the work accumulated in the monkey will be 300 Ibs. X 10 ft. = 3000 ft.-lbs. If this work be expended in driving the pile % inch into the ground, then ( inch = -^ foot) the mean force exerted will be 2^2 = 72,000 Ibs. In order to vary the speed Fig. 15. obtained from a prime mover, wheels having teeth on their peripheries, called cog, toothed or spur wheels, are very com- monly used ; the general forms of some of these are shown in Fig. 15. A and H are two pa- rallel shafts carrying the spur wheels c and d. which, by gearing together, ensure a cer- tain ratio of velocity between the shafts ; and also the hold afforded by the teeth allows of power being transmitted from one shaft to the other. The dotted circles show the effective size of the wheels, that is, the size they would be if the motion were trans- mitted by mere rubbing contact without teeth ; they are called pitch circles, because the pitch, or distance from centre to centre of the teeth, is measured on them. When the shafts are inclined at an angle to each other, SO PRINCIPLES AND CONSTRUCTION " bevil wheels," as shown at e and/, are used. In this case the periphery of each wheel is conical, the apices of the cones being where the inclined shafts would meet if produced, as shown by the dotted lines. In both these cases the wheels revolve in opposite directions. If, however, the large wheel has the teeth inside the rim, as shown at A, and the small spur-wheel or pinion g works within the large wheel, then both wheel and pinion revolve in the same direction. The ratio of the angular velocities, or number of re- volutions made by the shafts, will be dependent upon the radii of the wheels, as the peripheral velocity will of necessity be the same for both wheels. Let the radii of of A and BberandE, and the number of revolutions made by them be respectively n and N, in a given time, then n = N X ,N=n X y ~H = nX ~r = N x v ./. 7V n Let the radius of A =. r 4 inches, its number of revolutions per minute = n = 30. The wheel is required to make 7 revolutions per minute ; its radius will be ^ = 30 x y = 17-1 inches at the pitch circle. As the teeth on both wheels are pitched at the same distance apart, it follows that the number of teeth on the wheels will vary also as the radii of the wheels. If both wheels are required to move in the same direction, an intermediate wheel is sometimes interposed between the driving wheel and that driven; this, which is called an idle wheel, has no other effect beyond reversing the direction of the motion. The shape of the teeth of wheels will be treated of in a subsequent chapter. Very commonly, instead of using toothed gearing (especially where the shafts are far apart and noise is OF MACHINERY. o! objectionable), pulleys or riggers, connected by belts or straps running round them, are employed ; in this case the ratio of the angular velocities of the shafts is deter- mined in the same manner as in the last, presuming, of course, that the belt does not slip. For some especial purposes toothed gearing of unusual forms is applied, the wheels assuming the appearance of ellipses, squares and lobed figures ; but it is unneces- sary here to describe them, though it may be advisable to observe that in setting out such work care must be taken that in every position the sum of the radii of the pitch lines, at the point between the centres of the wheels, is, equal to the distance between such centres. CHAPTER Y. ELEMENTS FOB CHANGING THE NATURE OF MOVEMENTS. The simplest modes of changing continuous rotary motion into reci- procal, or vice versa, are shown in Fig. 16. a is a shaft carrying a crank ab, to which is jointed a I, a connecting rod, b c; c, the end of the connecting- rod, is jointed to a block sliding between guides, e /, so the revolution of the crank will impart the required motion to the rod d. If we imagine the crank pin b enlarged PBINCIPIiES AXD COXSTllUCTIOX until its periphery extends beyond the main shaft a, the principle of the crank is maintained; but in the altered form the element is termed an eccentric wheel, or, for brevity, an eccentric. One is shown at C. C is the eccentric, j the main-shaft, i the geometrical centre of the eccentric, g a band surrounding it, sufficiently free to allow the eccentric to revolve within it, h a connecting rod by which motion is trans- mitted from the eccentric. Instead of the connecting-rod and guides a slotted link k may be used. This link is carried by two rods working in guides 1 1; to keep its motion rectilineal the lateral motion of the crank pin m is allowed for by the slot in the link. By making the slot sufficiently broad, an eccentric may also be used with this arrangement. Fig. 17 exhibits types of three descriptions of cams in most general use. A is a heart- shaped cam carried on a revol- ving axis b, the end of a rod c rests upon the edge of the cam, the rod passing between guides d. As the cam revolves it lifts the rod through a distance equal to the difference of the radii b c and b e, the mode in which it is lifted depending on the forma- tion of the periphery of the cam between c and e; the rod falls again by its own weight or by a spring or another cam. J? is a face-cam on an axis //,. the rod k working in guides I is pressed against its face by a spring or otherwise. The part g pushes the rod OF MACHINERY. 33 back as the cam revolves through a distance equal to the difference between h g and i j. The third cam C has a groove in its face w, t, in which works a pin n, carried at the end of a bar 0, capable of oscillating on a centre p. As the cam revolves the bar o will vibrate by reason of the irregu- larity of the groove m m. Cams are very much used in machines where varying movements and those of an intermittent character are required. An intermittent movement is any movement of which whilst one part is always in motion the next has alternate intervals of motion and rest ; such as would be the case if the cam A were circular all round except at one place, as then the rod c would be at rest except when the one irregular part of the cam was passing under it, when for a short space it would move. The cam C is an intermittent movement, as part of the groove in its face is circular, and therefore does not move the pin n. In Fig. 1 8 is shown a spur Fig. 18. pinion working into a rack ; by the revolution of the' pinion the rack is caused to travel in a rectilineal direction. A similar change of motion is effected by a screw which works in a block or nut. This nut is prevented from turning by a guide or other restraint ; hence when the screw is turned the nut progresses in a straight line parallel to its axis. In like manner a screw may be caused to act on the teeth of a segmental rack or on those of a wheel, thus converting rotatory motion in one direction into the same but at right angles to its original direction ; this 34 PRINCIPIES AND CONSTRUCTION last combination is called a worm-wheel and tangent- screw. To enumerate one tithe of all the various cams and elements for changing motion would probably be impos- sible ; nor does it seem desirable in a work such as the present to occupy space by enlarging further on the subject, as sufficient examples have already been shown to make clear the principles upon which such mechanical contrivances are based, and these once thoroughly understood the mechanician will have but little trouble in setting out details suitable for the attainment of any special object which he may have in view. CHAPTER VI. FRICTION is that kind of resistance which is opposed to one body sliding upon another, or to a part of a machine moving when rubbing against another part, as the journal of a shaft against its bearings, a sliding block between its guides, &c. The law of the friction of solids is that the amount of friction varies simply as the weight or pressure acting upon the surfaces in contact ; nor is it in any way whatever affected by the extent of the rubbing surfaces, so long as they are sufficiently large to withstand the crushing effect of the pressure acting upon them. Let A B represent a slab having Fig. 1 9. a horizontal top surface, upon which is a weight W, or body, which is pressed against A by a force equal to W; from W let a cord be passed (parallel to A } OF MACHINERY. 35 over a guide pulley, ,'{S4 38 PRINCIPLES AND CONSTRUCTION massive and rigid, and so designed as to resist without sensible yielding all the thrusts and pulls brought upon it by the various parts of the machinery, for if the framework be not strong enough the machine will soon be useless. The following table gives the ultimate strength of materials per square inch of sectional TENSION. Swedish bar-iron Russian ,, English ,, Cast-iron ,, brass . copper . Wrought-copper Wire-rope . Ibs. 65,000 59,470 56,000 17,628 17,968 19,072 33,892 90,000 COMPRESSION. Cast-iron . Wrought-iron Brick . Portland stone Craigleith stone . Bromley Fall stone Purbeck stone York paving Granite. Ibs. 120,000 36,000 800 4,550 5,460 5,915 8,000 5,460 9,000 Having made these general remarks, we can now pro- ceed to consider the laws which rule the proportions of the different elements of machines. In the first place, it will be necessary to analyse the resistance of mate- rials to transverse strain. OF MACHINERY. 39 If two imaginary sections be taken infinitely close together in a rectangular beam when unloaded, and then a stress be put upon it, so as to bend it, as shown at A B, Fig. 20, then the sections may be considered to have crossed each other, as exhibited at a b, e d ; all the fibres above the neutral axis, which is supposed to be in the centre of the depth of the beam, as shown by the dotted line, will be compressed, and those below extended. It is evident that each fibre will be strained exactly in proportion to its distance from the neutral axis or point of intersection of the lines a b, and its reaction tending to resist the load will be equal to this strain. If S =. strain per square inch on the outer fibre a e, then that on any other fibre, e f, distant x from the neutral axis will be, if D depth of beam, and if the width be unity, the sum of all the strains wil be represented by the area of the triangle age, But all these forces or reactions may be regarded as collected at the centre of gravity of the triangle a g c, and acting about the point g at a distance equal to that of the said centre of gravity, which is _ 2 D 6 hence the total moment of force for the two sets of fibres, age and d g b, will be 40 PRINCIPLES AND CONSTRUCTION but the resistance also varies as the breadth, let the breadth equal b, then the general expression of moment of resistance for a rectangular beam the maxi- mum stress per square inch of section on which = S is if the stress be in pounds and the dimensions in inches, the moment will be given in inch-pounds (instead of foot-pounds). Action and reaction being equal and opposite when equilibrium is maintained, the moment of resistance will equal the moment of force. If a bar is fixed at one end and loaded at the other with a weight, W, the length being I inches, the moment of strain will be M = Wl hence, Wl = S b The safe working depth would therefore be, For cast-iron D = \/ - For wrought-iron D = 'V 900 b the first being a tenth, and the second an eighth of the breaking strain. If the bar be uniformly loaded, the moment of strain will be one half of that due to the concentrated load ; hence the formulae for a bar fixed at one end and uniformly loaded with a weight, W, will be For cast-iron D = / Wl V 1600 I OF MACHINERY. 41 For wrought-iron D = \/- W I 1800 b If the bar be supported at both ends and loaded in the centre, the moment of stress will be hence the formulae in this case are For cast-iron D = A / W l V 3200 I For wrought-iron D = / W I 3600 b Or if the load be distributed uniformly For cast-iron D A / W l V 6400 I For wrought-iron D = A / V 7200 b If a weight be placed upon the bar not centrally, then the length, I, must be substituted as follows : Let x and y respectively equal the distances of the points of support from the weight, then By a process similar to that pursued in reference to rectangular beams, the moment of resistance of a cylindrical bar may be found. The following formulae give safe working results for a cylinder supported at each end and loaded in the centre (if not so loaded replace / as above) : let I = length in feet, d = diameter in inches, W equal weight in pounds For cast-iron d = 3 A / 1_ V 120 For wrought-iron d = 3 J " * 42 PRINCIPLES AND CONSTRUCTION Large girders and bearers may be calcu- Fig. 21. lated in a simpler way. Let Fig. 21 represent a wrought-iron flanged bearer supported at both. ends. D =. depth in feet, I = length in feet, a = area of one flange, plate and angle irons in square inches, s = safe strain per square inch, W = load in tons at centre, then for the resistance of both flanges M~ s x a x d for the moment of strain, *= 4 hence 3 tons per square inch being taken as a safe strain, __ Wl ~vn> or if the load be equally distributed, _ Wl ~24Z> These general rules for estimating transverse strength apply to all kinds of machines ; hence require no special illustration here, as their application will appear here- after, as progress is made in the analysis of the laws which govern the proportions of prime-movers, machines and gearing. CYLINDERS HAVING PISTONS WORKING IN THEM. Two points have here to be considered : first, the bursting pressure ; second, the wear and vibration. The first is very simple. The pressures in the two halves Fig. 22. of the cylinder may be considered as acting and reacting against each other at any diameter, as shown in Fig. 22 by the arrows, tending to tear the two sections a and b ; hence if p = pressure per square inch, and OF MACHINERY. 43 r = radius of cylinder in inches, the strain on one part of the shell is pr but the question of vibration is not so easily solved, and, in fact, must be determined by experience. Taking the two strains together the following formula is found to give good practical results : d = diameter of cylinder in inches, p = internal pressure per square inch, t =. thickness of cylinder in inches -ii-+ CYLINDRICAL PIPES. These are cylinders (cast-iron) having only to withstand pressure with a certain allow- ance for wear, hence the same notation as above being used, t = ^L + 0-66 6000 BOLTS AND NUTS. Let the number of bolts holding a cover on a cylinder or other vessel having internal pressure = n, the pressure = p, D diameter of cover in inches, and d diameter of bolts, then from the tensile resistance of iron it is found d =r, In order that the nut may have a sufficient hold on the bolt, its thickness should not be less than half the diameter of the bolt, but it is usual to make the thick- ness equal to the diameter of the bolt. In some cases, such as in bearings, check nuts are used, which are thin nuts screwed down upon the main nuts to prevent their turning, and so becoming loose. COVERS AND LIDS. Covers and lids, under pressure, are subject to transverse strain, and from its laws, aided 44 PRINCIPLES AND CONSTRUCTION by practical observation, the following formulae are drawn: t thickness of cover in inches, p pressure on it per square inch, D = diameter of cover, C = height of curve of cover, both in inches f== 14400 x C For fiat covers let I = diameter, or if oblong, length of shortest side : " RODS UNDER TENSION ONLY. Allowing one tenth of the breaking strength as safe for working, the following formulae are found : Let W = the weight in pounds, d = diameter in inches . / -irr For cast-iron d = GO t/ W For wrought-iron d 36 HODS UNDER COMPRESSION. Let the rods be mode- rately short, so as not to yield by bending, then, For wrought-iron d = 48 \/~w~ For cast-iron d = 88 If these rods, either in tension or compression, are placed horizontally or at an angle, so that they are sub- jected to transverse strain, care must be taken to ascer- tain that they are sufficiently strong to bear such stress as may be due to their weights. HOLLOW CAST-IRON PILLARS. The following formula) are derived from experiments, and refer to columns of OF MACHINERY. 45 which the length does not exceed thirty times the diameter : Let d and d' = the external and internal diameters in inches, I = length in feet, and W = safe working load, It will be observed that the powers to which the quantities are to be raised are fractional, hence this formula can only be solved by the aid of logarithms ; but the following approximate rule is accurate enough for practical purposes : w = 4-4 H 3 x J**\_- i^x y^> V i x V i 3 CAST-IRON BOOKING BEAMS. Let W = weight in pounds at the end of beam, I = length in feet from weight to axis of beam, t = thickness in inches, and d depth in inches ; then from the laws of transverse strain, t = Wl 60 d 2 This rule is very suitable to determine the dimensions of main beams and side levers of engines, and other like elements. CRANKS. Let W = the weight in pounds acting on the crank, D = the outer diameter of its boss, and d = the diameter of the aperture made to receive the shaft ; / = length of the crank in inches from the centre of the crank pin to the centre of the shaft ; b = the depth of the crank boss : W I For cast-iron b = ---- 720 |2> 2 - d*\ W I For wrought-iron I = ----- 800 D* -d* 46 PBINCIPLES AND CONSTRUCTION REVOLVING SHAFTS. For transverse strain, load in the centre, let d = diameter in inches, W = load in pounds, I = length in inches For cast-iron d = For wrought-iron d = Tredgold's rule for water-wheel journals : d = diameter in inches, I length in inches, W = load in pounds : d =1 v~nv Revolving shafts, through which power is transmitted, are subject to a twisting force or torsional strain, hence the shafts must have sufficient strength in this respect. Long shafts are mostly determined for transverse, but short ones for torsional strain. Many years back cast- iron shafts were in vogue, but now they are almost entirely displaced by wrought-iron. The following for- mula is convenient for determining the diameters of main-shafts for prime-movers : Let HP = horse-power of prime-mover, It = number of revolutions of main- shaft per minute, d = diameter in inches =v 320 IIP R A very general formula for finding the diameter of secondary running shafting is *~\/LSL v R The proportions most suitable for the journals of revolving shafts as determined by experience are, if OF MACHINERY. 47 d = diameter and I length of journal inches (the journal being the part in contact with the bearings), For cast-iron I = 1-5 d For wrought-iron I = l'7o d If the weight, such for instance as a fly-wheel carried upon a shaft, be placed close to the bearing, then the transverse strain becomes insensible, and the shearing force has to be considered ; that is, the tendency of the weight to shear or cut the shaft close to the bearing. The ultimate resistance of wrought-iron to shearing force is about 54,000 Ibs. per square inch of sectional area ; hence the proper diameter being = d inches W = weight, will be d= V~W~ 65 FLY-WHEELS AND PLAE* PTJLLEYS. In proportioning wheels of all descriptions sufficient strength must be provided to resist the tendency to rupture through the tension caused by the centrifugal force of the mass in motion. First, in regard to the rim, let v = velocity in feet per second at the periphery, n = number of revolu- tions per minute, d = diameter in feet, w = weight per foot of the rim of the wheel, a = sectional area of rim in square inches, c centrifugal force. Then c for one foot of the rim of the wheel will be w x # 2 Treating this simply as a radial force tending to burst the ring, we find for the strain ( = $) on any section of the rim, 48 PRINCIPLES AND CONSTRUCTION Then, allowing 1,800 Ibs. per square inch as the tensile working strength of cast-iron, the sectional area should be 57,960 but, from the specific weight of cast-iron, it is found that Also, 19 v wherefore the limit to the velocity of wheels will be 2546 For cast-iron n = = 4427 For wrought-iron n = ^ The arms of the wheels should be strong enough to resist the centrifugal force of the whole rim, so that if it should be broken or flawed between every pair of arms, yet it will not come to pieces. Cast-iron wheels very frequently have arms of the form Fig. 23. shown in Fig 23, though sometimes they are made round or oval in section, v The section a I c d must be sufficiently <- - strong to resist the centrifugal effort of its portion of the periphery. Let a = the sectional area of the rim in square inches, d = diameter of wheel in feet, v = velocity in feet per second, and A = area of one arm, and JV = number of arms in the wheel, then the weight of rim W = a x 3-2 x 3-1416 d = . a . 10 d OF MACHINERY. 49 hence the centrifugal force on all the arms may be Wv* av* ~ 16-1 X d ** 1-6 but, n x d V 19 hence, _ a (n d _ ~ 577-6 The safe resistance of all the arms will be = A x N X 1800 1800 .4 JV. = A 577-6 a (n d) 2 1,039,680 N The strength of arms necessary to transmit power must next be ascertained. In this case the part a b alone will be taken as carrying the whole strain, the feathers c and T) CONSTRUCTION An ordinary factory boiler will burn about 1 5 Ibs. of coal per square foot per hour ; hence, if the engine is work- ing with a consumption of about 5 Ibs. of coal per horse- power per hour, the grate surface will be in the same proportion as above, and also the heating surface ; but, if an engine (condensing, for instance) be working at a consumption of 3 Ibs. of coal and S = 8-5 x HP Cr = 8-5x5 = 42-5 (say 43) Gr hence the value of C for such boilers will be '=*-' = --' In locomotive furnaces the greatest quantity of fuel is consumed per square foot of grate surface per hour, varying, in fact, from 40 Ibs. to upwards of 100 Ibs.; but this is, of course, due to the strong draught created by the blast. The range being so wide, it would be useless to give a special formula for grate surface, but the following general rule may be found useful : Let F = equal consumption per square foot per hour, / = con- sumption per horse-power per hour With some high-pressure engines the consumption of fuel per horse- power per hour is very heavy, amount- ing to 9, 10, or 12 Ibs. of coal, and this would give a ratio of grate surface to heating surface as 1 to 1 1 ; but OF MACHINERY. 89 past experience indicates that a mean between this and the ratio for a Cornish boiler will give most satisfactory results as regards evaporative efficiency ; the mean ratio will be As to the proper capacity for steam-boilers per horse- power, there has been much conflict of opinion. Mr. Fairbairn, after many years' experience, fixed upon 15 to 20 cubic feet as the proper allowance, after de- ducting the space taken up by the flues ; but the late Mr. Armstrong always maintained that 27 cubic feet per horse-power should be allowed, one-half of this space being for water, and the other half for steam. No rule, however, can be laid down in regard to the capacity of boilers which shall apply generally to all types, for much depends upon the construction of the boiler, the arrangement of the steam dome or chest, and other incidental matters too numerous to mention. The object in having plenty of steam space is to prevent great fluctuation from occurring in the boiler pressure every time steam is taken into the cylinder ; and also the steam, if drawn off close to the surface of the water, would be loaded with aqueous particles, which, being deposited as water at the bottom of the cylinder, cause much inconvenience, and even, in some cases, accident. This passing of water over into the cylinder along with the steam is called priming. When super- heating arrangements are applied, this suspended water is converted into steam, and the steam is then called dry ; in this state it is much less liable to condense in the cylinder, but it has the disadvantage, if highly super-heated, of drying and rendering inefficient the packings of the engine. 90 PEINCIPLES AND CONSTRUCTION The super-heating of steam does not largely increase its pressure, as so soon as all the suspended aqueous particles are converted into steam, and it becomes dry, it follows the law of permanent gases, and its expansion is slow. A very quick draught is not economical, as the quicker the draught the greater the quantity of heated air passing off, and the less time is allowed for the fuel to abstract the oxygen from the atmospheric air ; hence, any means which will so far cool the gases in the chim- ney, after they have passed over all the heating surface of the boiler, as to check the excessive velocity of the current, and at the same time apply the heat abstracted to some useful purpose, will effect some considerable economy in fuel. The waste gases from boiler furnaces commonly escape at a temperature of from 400 to 600 degrees ; but a considerable portion of this heat may be utilized, for, by causing the products of combustion to pass through tubes surrounded with the water intended to be supplied to the boiler, they will yield up as much as 225 degrees of heat to such feed- water. A fair allowance of feed- water-heating surface is 10 square feet per horse-power. A little reflection will show that it is easy to abstract heat from the escaping gases by the feed-water when none will any longer be yielded up to the water in the boiler. The transmission of heat from one body to another varies in rapidity as the difference of the temperature of the two bodies ; hence the water in the boiler takes up the heat quickest at the furnace end of the flue, after which, the rate of transmission gradually decreases as the temperature of the heat, air, and gases more nearly approaches that of the water and steam in the boiler, until, if the process is con- OF MACHINERY. 91 tinued long enough, the difference will not be sufficient to cause the heat to pass through the metal by which the water is separated from the heated gases in the flues. If steam is being generated in a boiler at a pressure of 60 Ibs. per square inch, the corresponding temperature of the water and steam will be 293 degrees ; hence, if the temperature in the furnace is 1,000 degrees, and that at the end of the flues 400 degrees, the differences of temperature will be for each place respectively, 1000 293 = 707 degrees 400 - 293 = 107 the ratio of the two differences being ft hence the rate of transmission of heat at the commence- ment of the flues is nearly seven times that at the end of the same ; or, in other words, one foot of heating sur- face at the furnace end is equivalent in evaporative power to seven feet at the chimney end of the flues. The thickness of the metal of which the boiler is made also affects the passage of caloric, hence the parts which are heating surfaces should not be made unne- cessarily thick. To return to the question of abstracting heat by the feed- water from the gases leaving the boiler flues, we find the difference of temperatures, if the feed- water be at 60 degrees, to be 400 60 = 340 degrees hence the feed- water surface will commence absorbing heat half as fast as the most efficient portion of the heating surface of the boiler, and this abstraction may be continued until the water is heated up to 200 degrees, or in some cases more. 92 PRINCIPLES AND CONSTRUCTION The rapidity of the conduction of heat also varies according to the metal through which it has to pass ; thus the relative conducting powers of copper, brass, and iron are as under : Wrought-copper . . . . 100-0 Wrought-brass . . . . 96-6 Sheet-iron 41-5 While treating of furnaces, the subject of smoke con- sumption may properly be dealt with. To consume coal-smoke has been, and often is, said to be a matter of ease, only requiring care to effect the object sought ; yet it is remarkable that generally the smoke is not consumed, although it is manifestly to the advantage of the users of steam-power to utilise it as much as possible, for smoke, properly so called, consists of a great number of very minute and finely-divided particles of carbon, which are carried up by the ascending draught, only ultimately to fall again as soot or " blacks " as soon as they come into cold or damp air. This carbon of course has a certain calorific value, and would serve to assist in evaporating the water in the boiler. In order to ensure the combustion of the smoke and gases not previously oxidised, a sufficient supply of air must be furnished for their thorough oxidation, the fire-bridge being a very good place to supply it ; but its temperature must not be so low as to cool down the unconsumed products of combustion to a temperature below that at which they will burn, other- wise the introduction of the extra quantity of air will be worse than useless, as its sole effect will consist in cooling the heated air and gases before they pass over the heating surface of the boiler, thus lessening the OF MACHINERY. 93 rapidity of the transmission of the heat, and in addition to this, increasing the bulk of waste air, which, leaving the chimney at a temperature higher or lower, accord- ing to circumstances, . carries away a quantity of heat proportional to the volume of air escaping into the atmosphere. It is very evident that, if the air could be kept in contact with the fuel until all its oxygen was taken up by the carbon and hydrogen of the same, a great in- crease of economy would ensue, as was shown by expe- riments with a plan patented by Moor and Shillitoe. According to Moor and Shillitoe' s method of working, instead of there being a free outlet from the flues into the atmosphere, the combustion was carried on under pressure, and the results obtained from some experi- ments conducted at Manchester were in the highest degree satisfactory. The up-take from a portable engine-boiler was closed by a valve lightly weighted, and the air required for combustion was forced into the fire-box ; a very vivid combustion was thus produced, accompanied by a great saving of fuel. By using this mode of working, the air is held in contact with the fuel until the latter has absorbed nearly all its oxygen, hence a much smaller quantity of air is required than that consumed in an ordinary furnace, and the quantity of waste gases is correspondingly reduced ; hence, also, the quantity of heat escaping through the chimney. If, instead of 150 cubic feet of air, 50 per Ib. of fuel will suffice, the quantity of heat carried off by the waste gases will be greatly reduced. In combining with the gaseous and solid parts of the coal the products of combustion formed will be in amount about 64 cubic feet, whereas in the ordinary way of managing the furnace it would 94 PRINCIPLES AND CONSTRUCTION never be less than 164 cubic feet per Ib. of coal, and very often amount to considerably more. Thus, by the use of the patent furnace, the loss of heat by waste gases is always reduced by about 60 per cent., and generally by a much larger per-centage. Also, the air being kept in contact with the fuel under pressure, the oxygen in contact with the fuel is a much larger quantity per cubic foot of air than when the draught is free, hence the combustion is far more rapid, and of necessity more vivid, than under ordinary circum- stances, and being more vivid the furnace is heated to a higher temperature, which favours the absorption of heat by the water in the boiler. The combustion being more rapid, the grate surface may be reduced to about one quarter of that used with a free draught ; and as the difference of temperature between the gases in the furnace and the water in the boiler is increased, the amount of heating surface may be proportionately reduced ; in short, for a given amount of steam evapo- rated per hour, the whole proportions of the boiler may be very materially reduced, and a saving of upwards of 40 per cent, of coal will be effected and all the smoke consumed. It may be interesting here to give some idea of the saving effected by letting into the furnace only sufficient air to maintain the combustion. In the ordinary case, 150 cubic feet of air are required per Ib. of coal, of which 50 feet are sufficient to supply the oxygen actually required for combustion. Of this air there will be 100 cubic feet over and above that actually required, and the specific heat of air, according to the experiments of Delaroche and Bernard, is 0-267, that of water being TOGO. Supposing the gases and products of combustion to leave the chimney at a temperature of OF MACHINERY. 95 400 degrees, the normal temperature of the air being 60 degrees, then the 100 cubic feet of air will have been heated 400 60 = 340 degrees. The weight of the air will be equal to about 8 Ibs., hence the number of degrees of heat lost, which might otherwise have been transmitted to the water to be evaporated, would be sufficient to raise the temperature of one pound of water 213-6 degrees. There is good reason, however, to believe that practically a much larger quantity of air than that above mentioned passes through ordinary furnaces. It may at first seem unaccountable that a system affording such beneficial results should not be generally adopted, but this is attributable to the fact that circum- stances prevented the inventors from introducing their plan at the time when it was first brought before the public, and since that the patent has been allowed to Although the principle of combustion under pressure has not been adopted in connection with the steam- engine, yet it is practically in use in some classes of hot- air engines Messer's, for instance, in which the piston in the working cylinder is driven by the pressure of the products of combustion issuing from a closed furnace. The air requisite for combustion and to propel the ma- chinery is forced into the furnace by an air-pump worked by the engine ; after yielding sufficient oxygen to the fuel the spare air and the heated gases are passed through suitable valves into the working cylinder. Some years back, when we examined one of these engines, it was reported to be working very economically, a result which is immediately referable to the mode of working the furnace. In this case the coal 96 PEDfCIPLES AND CONSTRUCTION was manifestly burned under a pressure somewhat in excess of that driving the engine. The conclusions then arrived at are that for the greatest economy of fuel there should be 1 . A slow draught current, 2. A rapid and vivid combustion, 3. A minimum quantity of waste gases at a minimum temperature ; and, by means of the above method of working, these conditions, impossible in the ordinary apparatus, may be easily satisfied. If this process be carried to per- fection, the escaping gases would consist simply of nitrogen, carbonic acid, and probably a little sulphurous acid ; and in the case of steam-ships, it might be dis- charged into tjie water. Thus, also, is a means afforded of raising steam of a very high pressure, as the in- creased temperature of the furnace will allow of the equally rapid transmission of heat to the water when steam is being generated under a higher pressure, and of course higher temperature. During the last few years very strenuous efforts have been adopted to introduce liquid fuels into use in steam- boilers, and there has been much controversy upon the merits and demerits of such a system. Undoubtedly the evaporative value of such fuel, when properly applied, is high, and it is compact for stowage (as in sea-going vessels) ; but, on the other hand, in hot climates there is a danger to be apprehended from the accumulation in the tanks of quantities of inflammable gases which may by some accident become ignited, when, of course, all efforts at extinction would be futile, and that such inflammable vapours would be formed is certain ; for instance, if a vessel were to start on a voyage with tanks full of hydro-carbon oils, OF MACHINERY. 97 although there would be no danger so long as the tanks remained full, but as soon as space was formed above the surface of the oil inflammable vapours would begin to accumulate, and more especially in tropical climates. We are informed, however, that under the directions of the Admiralty this subject is now being investigated, in order to determine some means by which this appre- hended danger may be obviated. Where tried liquid fuel has given very good results, both with stationary and marine boilers, the system which appears to give the best practical results being that invented' by Mr. E. H. Aydon. By this pro- cess the liquid fuel is carried into the furnace by a jet of steam acting through an appliance similar to the Giflard Injector, now commonly used for supplying steam-boilers with water. In considering the circumstances under which the combustion occurs, it is very desirable not to be misled as to the chemical re-actions which take place, as some people have thought that some decomposition of the super-heated steam associated with the dead oil takes place, which, if even it did occur, could not ultimately affect the results, as the decomposed steam would yet, by combustion, resume the condition of steam. In apply- ing the "Aydon" system, steam is first got up in the boiler by a coal fire, after which a thin layer is kept merely to ensure the ignition of the oil spray scattered into the fire-box by the steam jet. In the early part of 1867 an experiment was tried at Lambeth on this system, applied to a Cornish boiler of the ordinary con- struction, of which the following is an account : The oil was allowed to fall through a narrow orifice in a con- tinuous stream (the worst kind of creosote refuse being used) about one-eighth of an inch in diameter, at a 98 PRINCIPLES AST) CONSTRUCTION rate of about three gallons per hour. With this con- sumption the steam was maintained at a pressure of from 32 Ibs. to 35 Ibs. pressure per square inch. The amount of water evaporated was 10 cubic feet per 100 square feet of heating surface in the boiler. The cost of creosote refuse was from 1 10s. to 2 per ton; hence, taking the creosote used at Id. per gallon, the cost of fuel burned per hour would be 3d., and the work done was equivalent to that which would be given by 56 Ibs. of the best Aberdare coals at 1 2s. per ton, the value of which would be rather more than 6d. The evaporation of water, so far as it could be determined from the experiments, amounted to 19-5 Ibs. of water per Ib. of fuel consumed. The composition of creosote is as follows : in lib. of creosote there is Carbon .... 0-775 Ibs. Hydrogen . . . 0-080 ,, Oxygen .... 0-145 ,, hence the theoretical evaporative value of this creosote will be = 15 JO-775 + 4-28 (-08 - '^ 45 )| = 15-6 Ibs. water per Ib. of fuel. This, however, is the general analysis of creosote; hence it must be concluded that the quality used in trying the " Aydon " method must have been superior to that of which the analysis is given, for, even if it were admitted that the super-heated steam which enters with the oil is decomposed, yet, for reasons given above, this action could not ultimately affect the amount of water evaporated. OF MACHINERY. 99 The theoretical calorific value of petroleum may be found from the following analysis : Hydrogen . 12-5 = -125 Ibs. per Ibs. of oil. Carbon . . 87-5 = -875 hence the evaporative value = 15 j-875 + 4-28 x -125 j = 21-15 Ibs. water per Ib. of oil. The great economy of liquid fuel over coal is quite evident from the above statements ; but it has been further shown that a steamer making a round from London to Rio Janeiro, Monte Video, and Buenos Ayres, out and home, would actually effect a saving of 1,230 out of 2,235 by burning oil instead of coal. We will now pass from the furnace and fuel to the proportions of the various descriptions of boilers. General rule for horse-power of toilers. Let HP= horse-power, a = horizontal heating surface in square feet, A = vertical heating surface in square feet, then or let A = , then 8-5 . n if, for instance, a = 100 feet and n = 4, then Hp= 4X100 +100 = 14 . 7 horse . power . 8-5 X 4 TUBULAR BOILERS. For tubes having half their sur- faces exposed to the heat (as in the Cornish and H 2 100 PEDfCIPLES AIO) COKSTEUCTION Manchester boilers), let I = length in feet, d = diameter in inches, then for tubes having their entire surface exposed to the heat, it will be 30 To find the proper thickness for the outer shell of the boiler to resist safely the internal pressure, the following formula will serve : Let t = the thickness in inches, p = internal pressure in pounds per square inch above the atmosphere, r = radius of tube in inches, 8,000 Ibs. = the safe working tension per square inch, allowing for wear for solid work, and 6,000 Ibs. for rivetted work, then Solid work . 8000 Eivetted work . t = 2-^- 6000 The resistance of wrought-iron tubes to external or crushing pressure has been experimentally determined by Mr. Fairbairn, and the following formula, deduced from the experiments, will give the proper thickness of metal. Let t = thickness of metal in inches, I length of the tube in feet; d = diameter of tube in inches, or, if it be elliptical, the diameter corresponding to the flattest part of the tube, p = the pressure in pounds per square inch on the exterior of the tube, above the atmosphere, then 161,200 If the tubes be very long they may be virtually OF MACHINERY. 101 divided into shorter tubes by fixing in or round them stout angle-iron or tee-iron rings. Let there be a tube 30 feet long divided into three parts by two rings, then the virtual length of the tube will be 10 feet; let the diameter be 24 inches, and the pressure of steam 30 Ibs., then the thickness of the tube should be In boilers having flat sides, such as the common square marine-boiler, and the water space outside the fire-box of a locomotive engine, it is necessary to use stays, in order to prevent the sides from being bulged out. In this case it is evident that the plates are under the influence of transferable pressure ; hence the rule to determine the thickness of such plates is found from the general laws of the resistance of materials to that description of strain. Let ^7 = the pressure in pounds per square inch, d =. the greatest distance between stays in inches, t thickness of stayed plate in inches, then t = 0-008 d \f~p Let d = 10 inches, p = 25 Ibs., t = 0-008 x 10 /25 = 0-4 inch. The stays supporting the plate are, of course, subject to tensile strain. Let a = vertical distance between stays in inches, b = horizontal distance between stays in inches, p = pressure in pounds per square inch on the stayed surface, p = diameter of stays in inches, then \/a b p '*= -70- 102 PRINCIPLES AND CONSTRUCTION Let a = 10, b 8, p = 25, as in the last case, then If the vertical and horizontal distances are equal, the formula will then become The designs or types of boilers that have from time to time been brought forward are almost innumerable ; hence but a few of the leading forms will be noticed here. The old waggon-shaped boiler, fired underneath, has long been out of date, although a few of them may now be seen in some parts of the country utilized as tanks. These boilers were not intended to raise steam at higher pressure than 4 Ibs. to 6 Ibs. per square inch, the steam being then used only as a means of getting a vacuum, so that the effect of the atmospheric pressure upon the piston should propel the engine. The Cornish boilers are now very generally used for large engines where very high pressures are not required to be employed. These boilers consist simply of a cylindrical shell with flat ends, and a tube running from end to end through the boiler. The ends require to be stiffened by means of stays connecting them either with the shell of the boiler or with the tube. These boilers may have the furnace either placed inside the tube, or under the bottom of the boiler, in which case the tube is used as one of the return flues. Egg-ended boilers have a cylin- drical shell, terminated at each end by a hemispherical dome : they have nothing particular to recommend them, and appear somewhat more liable to explosion than other classes of boilers. Multitubular boilers are those which have in them a OF MACHINERY. 103 considerable number of small tubes through which the flame and heated air pass from the furnace. The object gained by this arrangement is that a large amount of heating surface is obtained with a comparatively small area "of flue, for whilst the sectional area of the tubes decreases as the square of their diameter, the heating surface diminishes as the diameter only ; hence, if the total area of the tubes be constant, the amount of heat- ing surface will vary as the number of tubes used to make up such total. In determining the number of tubes to be put into a boiler, it requires care to be taken to follow a middle course, for by putting in too many tubes they crowd each other so that the steam cannot get away quick enough from between them to allow the water to circu- late round them as rapidly as is desirable, in which case the evaporative value of the boiler is deteriorated, and the tubes are liable to be very soon burnt out, because the waterfails to take away from them the heat absorbed from the products of combustion with sufficient promptitude. About the worst case of crowding the tubes which has come under our notice occurred in a French locomotive, in which the space between the tubes was little more than three-eighths of an inch ; but we have known of cases in England where the evaporative efficiency of loco- motive boilers which had been over filled with tubes was actually increased by plugging up some of the tubes. Vertical tubes in multitubular boilers may, however, be put closer together than those which are fixed in a horizontal or inclined position, as they do not so much tend to retard the ascending and descending currents of water as the latter, as these currents rise and fall between the tubes instead of having to go round them. Although almost all multitubular boilers use the tubes 104 PRINCIPLES AND CONSTRUCTION as flues or passages for the heated air and products of combustion, yet this is not the most advantageous mode of construction ; it is better to have the water in the tubes and the fire outside them ; but for a long time makers were deterred from adopting this arrangement on account of certain practical difficulties connected with the circulation of the water. The superior strength of boilers having water tubes highly recommends their use in cases where very great pressures are required, for as the strength of a boiler varies inversely as its diameter, the relative strength of two boilers of the diameters D and d, for the same thickness of metal, will be .D d but as the larger boilers must be made of separate plates rivetted together, this will practically become 1-5 .D For actual strength let Craddock's boiler be considered ; n this the water tubes are three inches in diameter, and the metal is about one-eighth of an inch thick. From one of the formulae for thickness we have for solid work 8000 8000 t p = - hence, in this case, the safe pressure per square inch on the tubes will be 8000 x 0-125 p = = 666-66 Ibs. per square inch, 1*5 and the metal being thin will also favour evaporation by offering a comparatively small resistance to the OF MACHINERY. 105 transmission of heat from the products of combustion to the water in the tubes. Compare this with a cylindrical boiler, the shell of which is 4 feet 6 inches in diameter and f ths of an inch in thickness, being of rivetted work ; the safe pressure in this case will be p = 6000 2 X 7 - 375 = 83-3 Ibs. per square inch. In the construction of tubular boilers care must be taken to make the joints of the tubes perfectly sound, for if a leakage occurs the metal will rapidly corrode and the leak become worse ; a good and rapid circula- tion of the water must also be ensured to prevent the tubes from being burnt out. Of tubular boilers, having water inside the tubes, pro- bably the best is that invented by Mr. Edward Field, and generally known as the " Field " boiler. The tubes used hang down into the furnace, and may be applied to va- rious kinds of boilers. A very usual form of this boiler is shown in Fig. 34 : a is the fur- nace, b the chim- ney, c, c, water and steam space, d, d, the tubes j ?ig. 34 I a, C c c c 11 il a a Jl jl tube-plate i, i, and hanging down into the furnace. The detail shows a section of the upper part of one of 106 PRINCIPLES AND CONSTRUCTION these tubes. Into the outer tube y, and reaching nearly to the bottom of it, is dropped a smaller tube /, suppoited at the top by a metal feather and funnel- shaped deflector h. When the boiler is in action a very rapid current circulates down the interior tube and up outside of it, that is, in the annular space between the interior and exterior tubes. Without the deflector h, Mr. Field found he could get no circula- tion at all, and the result was that the water was blown out of the tubes and the tubes 9 burnt accordingly, but with it the circulation is perfect. The tubes are usually about 3 feet 6 inches long and 2J inches or 3J inches diameter and th of an inch thick, though, in special cases, they vary from these dimensions. One of these boilers was tried in comparison with a Cornish boiler, the particulars being as under, both doing exactly the same work, working at the same pressure, and with the same evaporation of water per hour. Cornish boiler, well set, with a good draught, and gene- rally economical ; 4 feet diameter, 14 feet long, flue 2 feet 8 inches diameter, fire-bars 2 feet long, dura- tion of trial 1 16 hours, consumption of coal 4 tons at 20s. per ton=8'24d. per hour. "Field" boiler. Vertical, with descending flue 3 feet 7 inches diameter, 9 feet high, duration of trial 69 hours, consumption of coke 2 chaldrons at 16s.= 5'56d. per hour. This gives for the evaporation per Ib. of coal in Cornish boiler 5-79 Ibs. water, and for the same per Ib. coke (the coke weighed 3,584 Ibs.) in "Field's" boiler 8-57, OF MACHINERY. 107 which is greatly in favour of the latter, as the evapora- tive value of coke is less than that of coal generally. The saving in cost of fuel by the " Field" boiler was 39 per cent. The heating surface of the Cornish boiler was 124 square feet, whereas that of the " Field" boiler was only 100 feet. The usual proportions for the "Field" boiler are 10 square feet of heating surface, and 0'5 square foot grate surface per horse-power. A 15 horse-power "Field" boiler was tested to ascertain its evaporative efficiency; it had then been two years at work. It was an upright boiler, 4 feet diameter and 10 feet high ; duration of trial 5 hours. 1,344 Ibs. of coke evaporated 11,022 Ibs. of water, or 8-2 Ibs. per Ib. coke. This, reduced to Ibs. water per Ib. of coke evaporated from 212 degrees, would be 9-8 Ibs. The tubes were 2J inches in diameter. In 1867 a Manchester boiler, 20 feet long, 6 feet 6 inches diameter, having two flues, each 2 feet in diameter, was fitted with 270 tubes 1 foot long, 2 inches diameter, radially fixed in the flues. The results of its trial were as follow : Duration of experiment 46 hours, consumption of Aberdare coals, at 20s. 6d. per ton, 3 tons, content of feed- water cistern 99 gallons, quantity of feed-water used 80 cistern-Ms, total quantity of water used 7,920 gallons, or 79,200 Ibs., =10-1 Ibs. of water evapo- rated per Ib. coal from atmospheric temperature, which, reduced to the boiling point, gives an evaporation of 12-3 Ibs. of Abater evaporated per Ib. of coal. The results obtained from a "Field" boiler fitted to a steam fire-engine show very strikingly the capacity given by this mode of construction. The water and 108 PRINCIPLES AJtD CONSTRUCTION steam space is entirely above the furnace, there being no water space round it. The diameter is 3 feet 6 inches, and the depth 2 feet 4 inches. The total height of furnace and boiler 5 feet 2 inches. The length of the tubes varies from 2 feet 3J inches to 1 foot 7 inches ; they are 1 inch in internal diameter, 1-16 inch thick; total length of tubes 797 feet ; heating surface 235 square feet (corresponding to a nominal horse- power of 23 h.-p.) ; steam pressure 160 Ibs. per square inch. The engines which work without expansion have two cylinders each 8f inches diameter, with 2-foot stroke, making 100 revolutions per minute. Total weight of machine 2 tons 18 cwt. The engine on trial sent a jet 210 feet high, discharging 1,200 gallons per minute; allowing nothing as lost by friction and disturbances of the atmosphere, this gives 76 horse-power as the useful effect, yielding 1 horse-power for every 3 feet of heating surface, which, be it remembered is vertical, and in the old-fashioned boilers 17 square feet of vertical heating surface would be allowed per horse-power. The thinness of the tubes seems remarkable at first sight, but they are amply strong, as shown by the annexed calculation. Let 8 = strain in pounds per sectional square inch of metal, then = '" Showing ample strength. We have seen a portion of one of these tubes which has for a considerable time been in use, but it is not in the slightest degree worn or deteriorated. The metal being thin, of course en- hances the rapid transmission of heat. Before concluding the present chapter it is desirable OF MACHDfEEY. 109 to offer a few brief observations on the subject of boiler explosions. The theories which have been put forward to account for the explosion of steam boilers are numerous, and many of them extremely far-fetched, such as the elec- trical theory and the theory which presumes that the steam is first decomposed into its constituent gases, oxygen and hydrogen, which subsequently recombined with sudden and destructive violence. Instead of wan- dering so far into the field of speculation, a brief con- sideration of the plain facts under immediate observation will occupy our attention. In the first place, a great proportion of the boiler explosions which occur are due to weakness in the boiler, and such weakness may gradually be increasing and insidiously rendering it unfit for the duty it has to perform, unless a rigorous system of periodical examina- tion be adopted. As was the case with the boiler of a steam-tug which exploded on the Thames a short time since, stays in the interior of the boiler may yield or break and pass unnoticed until some catastrophe occurs, and perhaps even then the original cause of the accident may not be discovered, as all damage found in the boiler may be attributed to the final explosion. Other kinds of injuries may proceed unnoticed, such as corrosion from the exterior through dampness of the boiler setting, or the lodgment of water on the rivetted joints. Also the joints of the boiler, where angle-irons are used, may suffer burning from the heat not being taken up quick enough by the water to keep the joint rings or angle- irons at a sufficiently low temperature. If any part of the furnace crown be left uncovered by water it will become heated, and then being softened, will be forced out of its normal shape by the steam pressure. Danger 110 PBINCIPLES AND CONSTRUCTION is not to be anticipated by the sudden formation of steam through contact with red-hot metal which has been left uncovered, for, from the low specific heat of iron, that quantity of caloric which will raise one pound of water a given number of degrees will increase the temperature of eight pounds of iron by the same amount ; hence every pound of red-hot iron possesses but heat enough in cooling down to 300 degrees to evaporate one-tenth of a pound of water into steam ; hence, assuming in a ten-horse boiler 150 cubic feet of steam space, then, if the plate became red-hot to such an extent that 50 Ibs. of the iron is so heated, only 5 Ibs. of water would be evaporated ; and supposing the normal pressure to be from 60 to 70 Ibs. per square inch, even this comparatively large surface of iron becoming red- hot would only increase the pressure by about one-fifth, causing it to rise so as to range from 70 to 84 Ibs., cer- tainly not enough to explode a boiler having a safe working pressure of 60 to 70 Ibs. per square inch. One of the causes of boiler explosions (which we believe was first pointed out by Mr. Z. Colburn) rests in the body of steam interspersed throughout the mass of water, which, upon the pressure being removed from the surface of the water, will in escaping tend to carry up the whole body of water, and cause it to strike a violent blow on the crown of the boiler. The pressure of steam may easily be accidentally suddenly reduced, as by the introduction of cold water, the sudden escape of steam from the safety valve, or by starting the engine, &c. Over-pressure being put upon boilers, through the carelessness or ignorance of those in charge, may also be added to the causes of boiler explosions, but the means of preventing this are obvious. OF MACHINERY. Ill The accumulation of scale in boilers is a source of danger, inasmuch as, by obstructing the passage of heat from the plates to the water (the calcareous matter of which it consists being a very slow conductor), it allows of the plates getting heated or burnt, in either case weakening them ; and although many things have been patented, and more proposed, to prevent scaling in boilers, yet none of them appear to be satisfactory enough to be generally adopted. The precautions to be taken against boiler explosions may be stated thus : 1. Always keep plenty of water in the boiler. 2. Never open the steam valve or safety valve sud- denly. 3. Have one of the safety valves properly weighted under lock and key, so that the attendant cannot over- press the boiler. 4. If tolerably pure water cannot be obtained, have the scale removed sufficiently often from the boiler. 5. Do not overstrain the boiler in the testing prior to use (twice the maximum working pressure is quite high enough for the test to be carried). 6. Have the boiler periodically examined by a com- petent boiler-engineer. If these precautions be borne in mind and taken, there will be no danger of boiler explosions. As regards the inspection of boilers, some years back an attempt was made to organise a boiler association in London, similar to that established some years since in Manchester, but it did not succeed, and the undertaking had to be abandoned almost before its existence was made generally known ; this was in 1862, and it does not appear that any attempts have been made since to revive the plan in the metropolis, a matter to be 112 PEIXCIPLES AND CONSTEUCTION regretted, because such an association, besides saving manufacturers heavy losses, is also instrumental in preventing accidents which but too often end fatally. CHAPTER X. WATEE-WHEELS. WATER- WHEELS, although occurring of great number of different designs, may be classified in four general divisions, as follows : Undershot wheels, overshot wheels, breast (or pitch- back) wheels, and turbines. The motion of the first class is obtained from the velocity of a running stream of water which impinges against the floats of the water- wheel. The second and third classes are actuated by the weight of the water falling upon them; and the fourth by reaction. In this first place it is necessary to explain the laws of liquid pressure and motion. Let h = the height in feet of a column of water, p = pressure in Ibs. per square inch at the base of the column, then, since one cubic foot of water weighs 62*5 Ibs., p = 0-434 h the pressure of a column of water 45 feet in height will therefore be p = 0-434 x 45 = 19-53 Ibs. per square inch. FLOW OF WATEE THEOUGH OELFICES. If in a vessel of water an opening be made at a distance, x, below the level of the water surface in the vessel, then the velocity of the water flowing therefrom will be the same as OF MACHINERY. 113 would be acquired by a solid body falling through, the distance x. This at first sight may appear somewhat incomprehensible, but the following remarks may serve to set the matter in a clearer light : If any perfectly elastic body be dropped and unacted upon by friction, it will, upon coming into contact with another solid body, be compressed (by the accumulated work within it) and rebound to the height from which it descended, the accumulated work contained in the body at the moment of contact being equal to the weight multiplied by the height of the fall. If the body be so controlled that it cannot rebound, but is retained in its most compressed state, then, if it be sub- sequently released, it will spring up to the height from which it originally fell, by virtue of the accumulated work within it. If the body be released by the removal of the lower or supporting surface, the accumulated work would be expended downwards ; and if the atoms of the body be separate, it may be all expended in pro- jecting one atom. If a quantity of water be poured into a vessel, it will be compressed by its own weight to some extent, although the amount may not be sensible, and this compression will represent a certain amount of accumulated work ; if this accumulated work can be expended on one atom, it may produce motion propor- tionate to the weight of the mass above such atom. Let us suppose that an aperture is made in the vessel so that the bottom layer of atoms of water may escape, then will the whole mass above descend through a dis- tance equal to the thickness of such a layer, and in so doing will do work the same as would have been done by the descent of one layer of atoms through a distance equal to the height of the entire mass of water ; hence the velocity of efflux of water under pressure will 114 PRINCIPLES AND CONSTRUCTION be equal to that attained by a body falling the height of the head-water producing such efflux. Theoretically, if S = area of orifice in square feet, h = head of water in feet, and Q = cubic feet of water discharged per minute Q = c. S V~h c being a constant determined by experiment, replacing it we have Q = 297-6 S \/~h and by transposition, S = Q _ 297-6 J h h- <2 2 ~~ 88565 7 76"7">S' FLOW OF WATER OVER WEIRS. Applying the same laws to the flow of water over weirs and notch -boards, we have, if I = length of weir in feet, the other nota- tions remaining the same as above Q = 192-6 I \/H? FLOW OF WATER IN CANALS, TROUGHS, &c. Let * = sectional area in square feet, I = length of channel in feet, c = wetted perimeter in feet, Y = velocity in feet per minute V = 774-6 A/- and for the quantity discharged FLOW OF WATER THROUGH PIPES. The gravitating force which causes the flow of water in pipes evidently varies as the head of water divided by the length of OF MACHINERY. 115 pipe through which the water has to flow ; hence, if h = head or height of water in feet, and I = length of pipes in feet, the accelerating force will vary as h ~J The resistances are of a frictional character, and are re- presented by the following formula : Let v =. velocity in feet per second, C = circumference of the pipe, 8 =. sectional area of the pipe, and c = a constant to be deter- mined by experiment, then the resistances = V* X ~ X C o and as action and reaction are equal and opposite, the accelerating force must be equal to the resistances ; hence, if d = diameter of pipe in feet, hence, - = 4x|x, Let Q = the discharge in cubic feet per minute, then Q = v X 0-7854 d 2 X 60 ff = $ x 60 0-7854 . d* . 60 From Smeaton's experiments the constant c was found to be = -^^ ; hence the above formula becomes Q = 2356 y1. x or if D = diameter of pipe in inches, I 2 116 PRINCIPLES AND CONSTRUCTION The following coefficients may be found useful in practice : To reduce cubic feet to gallons multiply by 6 '25 ,, ,, pounds ,, 62-50 ,, gallons to cubic feet ,, 0-16 pounds 0-016 There are two methods of action by which water impresses motion and imparts power to water-wheels, either by its weight pressing on the wheel, or by impact of flowing water against float-boards, the work done being due to the vis vivd of the moving water ; some- times water acts in both ways at once, the work done being partly due to the weight, and partly to the vis vivd of the water. In any case, if the water is acting by weight, and h = difference of level of water at its point of supply to the wheel and at its point of discharge, and Q = quantity in pounds of water falling per minute, the power theoretically is 33000 or if v velocity of water per second, 2,125,200 but of course the actual work done is much less than this, being diminished by friction and loss of water. UNDERSHOT WATER-WHEHL. The undershot water- wheel is usually made with floats placed radially, or curved slightly backward, so as to get free of the water in leaving the tail-race. These floats may be so curved OF MACHINE Y. 117 that the water does not act by direct impact, but by pressure, as shown in the arrangement of Fig. 36. Fig. 36 : a is the shaft carrying the wheel of which c d is the peri- phery carrying the curved floats e e; a b is the bottom of the wheel-race, and it will be observed that the water comes tangenti- ally and without shock upon the wheel; the sides of the race should fit tolerably close to the wheel to prevent loss of water. A clearance of about one inch is sufficient. If the wheel were moving at the same velocity as the water it would receive no pressure from the latter, and if it were held still it would receive the greatest amount of pressure; but being at rest would give off no work or power, hence there is some relation intermediate between these two conditions existing between the velocities of the wheel and water which will produce a maximum effect. The less velocity that the water leaving the wheel has the more work is being done, as if H and h represent the virtual heads to produce the velocities V and v before and after the water acts on the wheel, the work done will vary, as Q [If -h\ 64-4 64-4 varies as J v 2 118 PRINCIPLES AND CONSTRUCTION and it is evident the smaller v is the greater will be the amount of work done. It has been found that undershot water-wheels give as good a coefficient of useful effect as can be obtained when running at half to one third the speed of the water propelling them. Let V = velocity of water in feet per second before acting on the wheel, v = velocity of water in feet per second after acting on the wheel, Q = quantity of water passing wheel in pounds per minute, the other notations remaining as above, then the horse- power will be where c = the coefficient of efficiency, hence _ Q.e 33000 I 64-4 2. 2,125,200 F 2 - v- but for falls under 6 feet c = from 0-33 to 0'4, hence the rule becomes practically, HP ( F 2 v 2 } 6,440,000 I j but the wheel be so designed that v = o, as should be the case to obtain the greatest economy, we have Q. F 2 HP = 6,440,000 OF MACHINERY. 119 These are for radial floats, but if curved floats be used the value of c = 50 to 60, hence the above formulae become TTTt ** ( TTZ ..2 I and if v = o 4,000,000 I Q 4,000,000 Fig, 37. OVERSHOT WATER-WHEELS. Overshot wheels are principally worked by the weight of the water in the buckets of the wheel, which weight being always on one side of the wheel causes it to revolve ; if, how- ever, the water has any velocity, which by impact assists in moving the wheel, the virtual head corre- sponding to such velocity must be added to the distance through which the water passes in acting on the wheel. A, Fig. 37, is the axis of an overshot water- wheel b, b, the buckets to catch the water from the pen-trough c, which sub- sequently flows out as at e into the tail-race d. Let h = the height of the water in the pen-trough above that in the tail-race, and Q = the 120 PKINCIPLES AND CONSTKUCTION quantity of water discharged in pounds per minute, then the horse-power will be Q.h.e 33000 but for overshot wheels c = 0*6, hence Q.k SP- 55000 The duty done by overshot wheels will to some consi- derable extent depend upon the form and size of the buckets, which should be arranged so as to avoid as much as possible the too early discharge of water from the descending buckets at e. When the buckets have openings, as shown at /, they are termed ventilating buckets. This form has come much into use of late. The buckets should be designed of ample size, so that they may not be more than two-thirds filled with water. If Q, = quantity of water in Ibs. per minute, N = number of revolutions per minute, n = number of buckets on wheel, then practically the content of each bucket should be Q C = 62-5 . N .n the result being given in cubic feet. In the case of the undershot wheel, the force acting on the wheel might be considered as acting upon the shaft with a leverage equal to the mean radius, that is, the radius to the centre of the float-board, but such is not the case with the overshot wheel. Supposing all the buckets to be full, the whole weight of water may be regarded as acting at its centre of gravity, which is distant from the centre 0-636 r OF MACHINERY. 121 r being equal to the mean radius at which the buckets are placed. To find the force or pressure exerted at the periphery of a spur-wheel of which D = diameter, and fixed on the water-wheel shaft, we have W = weight of water in buckets in Ibs., p = pressure 1-272 . r - W 1) If Q = quantity in Ibs. discharged per minute, the other notations being as above for c being a constant to allow for loss by the spilling of water out of the buckets, hence the practical formula will be, neglecting the friction of the shaft, which is about 5 per cent. Q.^g Q ~N~ whence, 0-572 . Q . r * = N.D. As regards the speed of overshot wheels, it may be observed that from 4 to 6 feet per second is very good in the results yielded, this velocity being at the periphery of the wheel. Let D diameter of wheel in feet, S velocity of periphery in feet per second, JV = number of revolutions per minute 8 = JV. D . 188-5 *=? 188-5. .AT jr= s - 188-5 . D 122 PRINCIPLES AND CONSTRUCTION hence, if S _ 5 feet, D- 1 37-7 N N r= 37-7 . D BREAST OR PITCH-BACK WHEELS. These wheels are somewhat similar in their action to overshot wheels, only the supply, instead of coming over the top of the wheel, is poured at some point lower down, as at g, Fig. 37. These wheels give a very good result. They are divided into two classes, high and low breast wheels, according to whether the water comes upon the wheel above or below the centre. The power of the wheel may be determined by the formula HP- Q.h 44,000 Fig. 38. TURBINES. Fig. 38 shows a horizontal section of a turbine of modern construc- tion. This wheel is fixed horizontally ; that is to say, with the axis vertical. A is the centre of the wheel where the supply of water is brought to it, b, b. fixed guides which lead the inflowing water into the most suitable direction to impinge upon the vanes c, c, in the moving rim D. Not only is this wheel driven by the impact of the water against the floats or vanes, but also by the pressure or reaction of effluent water on such OF MACHINERY. 123 vanes. If the wheel be properly constructed the water as it leaves should have been deprived of all motion, having given up its vis vivd to the turbine, hence the peripheral velocity of the wheel should be equal to that due to the head of the water under which it is working. Let D = diameter of wheel in feet, h = head of water in feet, JW = number of revolutions per minute, v = peripheral velocity per second, then = / 64-4 h but 3-1416 . D . N 60 hence, 153-2 1 N =. D For example : Let h = 20 feet, D = 2-5 feet. N = = 684-8 revolutions per minute. 2i'O If Q, = Ibs. of water passing through turbine per minute then the power is 33,000 For turbines c varies from 0-6 to 0-8, so for the better class of wheels taking the last constant, 4,125 These wheels are exceedingly valuable for neighbour- hoods where there are high sources of supply; they will work well either in or out of water. 124 PRINCIPLES AND CONSTRUCTION Fig. 39 illustrates Whitelaw's turbine or reaction wheel viewed in plan. This wheel has two arms a, a, revolving about a centre -p- g Q A, the water being sup- plied through this centre. As in the last case, the best peripheral space is v \/ 64-4 h the water leaving the tur- bine without motion. The arms are formed in the shape of an Archimedean spiral. The proportions of the machine may be determined by the following formula using the same notation as above 33,000 but c = 0-74 to 0-78, hence, assuming its value as 0-76, we have Let w = width of each discharging orifice, and D = diameter of machine, N = number of revolutions per minute 135 . HP 1000 h > which would probably amount to about 3-5 per cent, of the whole frictional resistances. In the construction of such pumps as those referred to, the suction and outlet pipes should, where practicable, have a diameter equal to that of the pump plunger or piston, in order to reduce the friction to the lowest possible amount. HYDRATOIC KAM. An ingenious apparatus known as the hydraulic ram is shown in Fig. 43 ; its object is, where there is a great supply of water with a moderately high fall, to cause a certain part of the Fi 9- 43 - supply to be forced up into a cistern by the flowing away of the greater bulk of the supply: a is an gasg^^^ air-vessel, from which a delivery-pipe e pro- ceeds to the cistern. 4 is the supply-pipe leading into a K 2 132 PRINCIPLES AKD CONSTKUCTION chamber e, whence the water flows away through a valve d until it acquires momentum enough to shut the valve d; the sudden check thus put upon the flowing water causes it, by virtue of the work accumulated in it, to open the valve / and force a portion of water into the air-chamber a, whence it passes away through the delivery -pipe e, after which the valve d again opens by its weight. The velocity to be acquired by the water in order that it may close the valve d, must be somewhat in excess of that which it would receive from a head that would give a pressure equal per square inch to the weight of the valve d. Let w = weight of valve d per square inch multiplied by 1-05, I = length in feet of supply-pipe, a = area in square feet of supply -pipe, v = velocity of water in feet per second, h = corresponding head of water, Q = water raised in foot-pounds, then h- " v = 12-15 yV the quantity of water in the conduit-pipe in pounds, I X a x 62-5 = q and the accumulated work in this will be hence, Q = 144 . I. a . w . Let the weight of the valve d per square inch be 0-25 Ibs., then w = 0-25 X 1-05 = 0-262 Ibs. OF MACHINERY. 133 Let a = 0-3 square foot, and I = 50 feet, then Q = 144 X 50 X 0-3 X 0-262 = 565'9 ft.-lbs. but this has to be reduced by a coefficient, as there exists a loss due to the shock of the water and the cur- rents created thereby. A general coefficient cannot with confidence be given, as so much will depend upon the design of a ram, for if the passages are properly curved much better results are obtained than if they be left square. It is evident that by means of this machine a proportionately small quantity of water can be raised to a level above that whence it is supplied. Amongst other similar things for raising water may be mentioned the application of water-wheels working pumps. HYDROSTATIC PRESS. The general arrangement of the hydrostatic press has been described in Chapter iii., but the mode of calculating the power of the complete machine is not there given. Usually the hydrostatic press is fitted with two plunger pumps, one of larger diameter than the other. The largest one is first used to bring the ram of the press up to its work, when the smaller one is employed to get the highest pressure. Let P = the greatest pressure in tons, D = diameter of ram in inches, d == diameter of small pump in inches, I = length of pump-handle or lever from point of application of power to the fulcrum, L = distance between fulcrum and axis of small pump, / = force in pounds applied to pump lever, then P = 2240 . d* L 134 PRINCIPLES AND CONSTRUCTION Let D = 10 inches, / = 50 Ibs., I = 40 inches, d = 1 inch, L = 3 inches, then The thicknesses of the pumps and cylinders, &c., may be calculated from the general rules already given, but great care should be exercised in order to ensure the supply of good castings, as a cylinder cast with bad metal, eyen if strong enough to sustain the pressure, will allow the water to sweat out through its pores, thus causing the pressure to be lost, an important difference in some trades where goods are left in the presses all night. The tables of presses are calculated as beams to resist cross strain, and ample strength should be allowed them, as it not unfrequently happens that they get unfairly strained through twisting or unequal stress coming accidentally upon them. HYDRAULIC LIFTS are in principle similar to the hydrostatic press, but, being used for raising weights, they have a greater stroke, and are usually worked by a head of water supplied from an elevated tank or other convenient reservoir. Let W = greatest weight in pounds to be lifted, D = diameter of lift-ram in inches, h = height in feet of water supply above the highest point to which the lift is designed to work Let W = 2000, h = 30 / D = 1-71 A/ = 13-88 inches. OF MACHINERY. 135 WATER-PRESSURE ENGINES. In some places engines somewhat similar in general construction to steam- engines, but worked by the pressure of water, are used. The great difference in the two kinds of engines con- sists in the fact that, whilst the steam-engine is worked by a very compressible and elastic fluid, the one now under consideration receives its motion from a liquid practically incompressible, a quality which very mate- rially modifies the arrangement of the valve-gear. The water being incompressible, it follows that the exhaust or outlet valve should remain open until the completion of the stroke, as otherwise the piston would be stopped by the confined water, or the machine strained or broken, The most convenient valves for these engines will be either equilibrium puppet-valves or piston- valves, opened and closed by means of tappets or cams. The speed of these engines is necessarily slow, the usual velocity of the piston being from 3 to 6 feet per second. The available pressure will be that pro- duced by the head of water minus the head due to the speed of the piston. Let h = head of water in feet, H = ditto due to velocity of engine, V = velocity of piston ,in feet per second, p = pressure in pounds per square inch on piston p = 0-434 JA - H\ H = ^l H = ~^> but if V = 6 feet per second, p = 0-434 h 0-242 136 PRINCIPLES AND CONSTRUCTION hence, if the total head were 30 feet, the effective pres- sure would be p = 12-778 Ibs. per square inch. If the valves be balanced the friction of the machinery may be taken at 6 per cent, of the effective power; hence, if P = pressure per square inch available for useful work, P = 0-94 j 0-434 A 0-242 \ = 0-408 h 0-227 This, of course, only applies to the best-constructed engines having but little friction in the water passages leading into the working cylinder. The thicknesses of the cylinder and pipes may be found from the rules given in Chapter vii. The horse-power of a water-engine may be deter- mined as follows : Let d = diameter of piston in inches, v = velocity of piston in feet per minute nrp _ h v '785 d 2 . Q-434 . e 33,000 taking c the constant as 0'8, h . v . d* . HP = 122,222 ARRANGEMENT AND PROPORTIONS or YALVES AND WATER PASSAGES. Pig. 44 represents a piston-valve arrangement, the principle of which is that the pressure of the water acts between two pistons of equal area fixed on the same stem or piston-rod, hence it has no OF MACHINERY. 137 Fig. 44. tendency to move them in either direction, the pres- sure on one piston being balanced by that on the other, so that the two to- gether form a per- fect equilibrium valve, which re- quires no force to move it except that necessary to over- come its friction. The pistons may have metallic pack- ing. a a is the supply or pressure pipe leading from the reservoir to the engine, and discharing the supply of water into the valve-case I; c, c, are the two pistons fixed on the rod b to constitute the valve ; d, d, are exhaust passages leading into the waste-pipe e e, into which the water flows after doing its duty in the work- ing cylinder, which is in this case supposed to be double-acting ; f and g are passages leading to opposite ends of the cylinder ; i is a fixed pin or stud, on which a lever moves connected with the valve-rod h ; II is a tappet-rod carrying two tappets, one of which is shown at k, and these, acting on the horns j, move the valve at each end of the stroke. In the position of valve shown by the full lines the water is flowing into the cylinder through g and out through /; but, if the pistons be moved to the position shown by the dotted 138 PRINCIPLES AND CONSTRUCTION lines, the reverse occurs. In some cases an auxiliary valve-case and pistons are used to move the main valves, but this, of course, incurs an extra consumption of water. It is now necessary to determine the area of the water passages, which will be done assuming that they are curved so as to offer the least possible resistance to the passage of the water. From the formulae for flow of water through pipes, in the preceding chapter, we have h o C T = ** X ^ x . Let Q = cubic feet discharged per minute, and D = diameter of working cylinder in feet, = speed of piston in feet per second Q = 60 . a . 0-7854 D z but Q = 60 . v . S s . 0-7854 D 2 but \/ f X X hence *. 0-7854 . 0-617. 4 . iTc V 16200 h = 25-3 V h OF MACHINERY. 139 But the speed of the piston should for economy be = 3 feet per second, and h will be the head corresponding to the difference of pressure in the pressure-pipe and cylinder : or, hence this quantity is constant, and may be replaced in the formula making it, with sufficient accuracy for practice, S = 0-16 V-D 4 ^- C if the passages be square, however, C = 4 \/~S hence, in this case, S = 0-19 \/~Wl Let the length of the water passage be 5 feet, and the diameter of the working cylinder 9 inches, or 0'75 feet, then = 0-225 square feet = 32 -4 square inches, hence the inside length of one side of the water passage should be = 5-7 inches nearly ; the areas of the valves will of course be not less than that of the water passages, and the area of the exhaust passages and waste-pipe should be larger. 140 PRINCIPLES AND CONSTRUCTION If the above speed of piston and square passages be adopted as a general practice, the following formula will give the breadth of the passage : Let b = breadth in inches, and D = diameter of working cylinder in inches, I = 0-714 which, with the above figures, will become \/ 9 x 5 = 5-7 inches, the same as in the last formula. WATER METERS. In some instances water is supplied to consumers by quantity instead of on the principle of rating, and in such cases it is evidently necessary to have some convenient means of measuring the quantity so supplied. This has been most commonly effected by small ma- chines on the principle of the turbine or reaction wheel, the number of revolutions of which registers the qantity of water transmitted. Some forms have been made like water-pressure engines, the number of strokes of the engine registering the amount of water passed through the meter. If well constructed the latter class are most certain as to accurate measurement, but the former possess the advantage of allowing an uninterrupted cur- rent of water to pass through, which of course the latter cannot do, as the inlet and outlet valves must alter- nately be opened and closed to allow each meterful to be discharged and the registering vessel to be refilled. We have, however, seen and tried meters on the turbine system through which water was obtained without so much as one quarter of it being registered. OF MACHINERY. 141 CHAPTEE XII. MARINE ENGINEERING. ALTHOUGH the subject of marine propulsion may pro- perly be regarded as one requiring separate treatment, yet, so far as proportioning the power to the resistances to be overcome, and correctly arranging the dimensions of the propelling machinery, it may be dealt with in this chapter it being understood that the question of the form of lines will not be discussed, it being assumed in formulae for ascertaining the power requisite to pro- pel a given vessel that its lines are trochoidal. The resistance to the motion of a vessel passing through the water is caused by the friction of the water against the sides of such vessel, the same as in a pipe the resistance to the flow of water is due to friction. In the case of a vessel the distance through which the resistance is overcome varies, as v for a given time, v being = to velocity of motion in feet per second. Also the number of atoms moved in a given time varies as v, and the velocity with which they are displaced varies as v also, hence the sum of the frictional resist- ance varies as ' c s Filling in the constants found by experiment, we have the following formula for indicated horse -power : Let L = length of ship in feet at water-line, Cr = mean girth under water, v = velocity in feet per second, 142 PRINCIPLES AND CONSTRUCTION Let L = sum of lengths of bow and stern in feet, B = greatest breadth in feet HP = L ' & ' 9 * l ' 9 ' 87 ' Z} 95500 ( L , 2 ) or if L ; = Z, *-&[*?*] For example: Let L = 160 feet, G 15 feet, B 16 feet, Z, = 160 feet, v = 25 feet per second horse-power. COMPARATIVE EFFICIENCY. To find the comparative efficiencies of two or more vessels, criterion numbers may be obtained from the following formula, based upon the laws of fluid resistance : Let C = the criterion number, P = indicated horse-power of engine, D = displacement, S = speed THICKNESS OF IRON SKINS. The nature of the strain to which the iron skins of ships are subjected by the pressure of the surrounding water is evidently of a transverse nature, and to determine the thickness to withstand this pressure, the following formula, based on the laws of resistance to transverse strain, and the inten- sity of liquid pressure under given heads, may be used. The wrenching strain due to the yielding of the ship is supposed to be carried by the framing. OF MACHINERY. 143 Let t = thickness of the plate in inches, I = distance between ribs in feet, d = depth of immersion in feet CHAPTEE MATERIALS USED IN CONSTRUCTION. ALTHOUGH, in some parts of this treatise, we have had occasion to allude to some of the properties of certain materials, yet, in order to render the treatment of our subject complete, it is necessary to dilate more generally upon those substances used for the purposes of con- struction, which we now proceed to do. The strength of metals having been given already, will not again be inserted here. TENSILE EESISTANCE OF WOOD PER SECTIONAL SQUARE INCH. Oak Ibs. 17,300 Mahogany . Ibs. . . 8,000 Do 13,950 Walnut . . . . 8 130 / 8 000 Teak . 15 000 Do., English dry Beech j 12,000 17 709 Poplar t 6,641 ' ' } 4 596 Do 11,500 i 13,448 Alder . 14 186 Fir- ( 11,000 Chestnut, Spanish . Ash, very dry Do 13,300 j 17,850 I 15,784 12000 Do. ... Scotch Pine . Norway Pine Larch . . . . . 8,506 . . 7,818 . . 7,287 . . 10,224 Elm 13 489 Cedar . . . . . 4,973 20,582 144 PRINCIPLES AND CONSTRUCTION CoMPRESsrvE EESISTANCE OF WOOD IN CUBES OF ONE INCH. Ibs. Elm 1,284 American Pine . . 1,606 Ibs. White Deal . . . 1,928 English Oak . . . 3,860 Before the art of working in metal was to any considerable degree developed, timber was an almost universal material for the construction of various kinds of machinery, and at the present time in such localities as abound in timber it is very largely employed for those purposes, to which in countries possessed of pre- dominating mineral resources the metals are applied. In the felling and subsequent preservation of woods considerable care must be exercised, as if timber be not properly seasoned it soon becomes a prey to decay, and in consequence worthless. The usual time for felling timber is during the cold months, when the vegetative powers of the tree are almost dormant, and when they are also most free from sap. None of the woods, how- ever, are fit for use in the state in which they are cut down, for although no distinct circulation is going on within the heart-wood, yet the capillary vessels which permeate the tissue keep the tree moist throughout its substance, and therefore in an unfit state for use. If green or wet woods are placed in confined situations they become stained, and speedily yield to decay, a result which is avoided by careful drying with free access of air. On this account the timbers for ships should be cut out to their shapes and dimensions about a year before they are framed together, after which they should be left a year longer in the skeleton state to complete the seasoning, as in that state they become better qualified OF MACHINERY. 145 to resist the effects of exposure than if they were imme- diately covered in with planking. Other mischiefs almost as serious as decay also occur to improperly-seasoned woods ; round blocks cut out of the stem of green wood, or the same pieces divided into quarterings, split radially, and sometimes, but more rarely, in annular directions. Eound blocks cut from the entire section contract pretty equally, and nearly retain their circular form, but those from the quarter- ings become oval from their unequal shrinking. SEASONING AND PREPARING OF WOODS. The woods immediately after being felled are in some cases im- mersed in running water for a few days, weeks, or months, according to circumstances ; otherwise they are boiled or steamed. The object of thus treating the timber appears to be the dilution of the sap, after which the process of drying is carried on quicker and better, and the colours of the white woods are improved. The ordinary course, however, is merely to subject the mate- rial to a process of air-drying simply, but then the timber is usually reduced to sizes more nearly approach- ing those required for use, such as square logs and beams, planks or boards of various thicknesses, short lengths or quarterings, &c. The stems and branches of such trees as alder, birch, and beech, used largely by turners, frequently require no reduction in size ; if they do, they are split into quarterings ; but in either case they are stacked in heaps to dry. The smaller hard woods are much more wasteful than the timber woods, as, independently of their thick bark, their sections are frequently very irregular, indented, and ill-defined. Others are almost constantly unsound 146 PRINCIPLES A*T> CONSTRUCTION in their growth, and either exhibit central hollows or cavities, or cracks and radial divisions, which part the section into three or four pieces. All the harder woods require extra care in their seasoning, the difficulty of satisfactorily effecting which is often increased by exposure to the sun and hot winds in their native climates. The closeness of their texture also renders them less easily penetrable by the air, thus increasing the liability to crack, while their scarcity and expense also render their preservation a matter of great importance. It is therefore advisable to prepare them for their passage from the yard or store to the turning shop by removing those portions which must be neces- sarily wasted, so as the more thoroughly to dry them by more complete exposure to the air, before they are taken into a house, and care should be taken not to place them near a fire, or at first in a hot room. Many of the timber woods are divided in the saw-pit into planks, in order to increase the number of surfaces upon which the air can act in the process of drying, and also to leave less distance for its penetration ; after sawing they should never be allowed to remain in con- tact, and the partial admission of air often causes stain- ing and other mischief to arise. They should therefore be placed either horizontally or vertically in racks, or stacked in a pile with slips of wood in between them. Thin pieces will be about sufficiently seasoned in one vear's time, but thick wood requires two or three years' preparation before it is fit to be removed into hot rooms to complete the drying. Mahogany, cedar, rosewood, and other large foreign woods, require to be very carefully dried when they are cut into planks, as, notwithstand- ing the great length of time which elapses between their OF MACHINERY. 147 being felled and brought into use, they retain a great proportion of moisture as long as they remain in logs. The drying of woods, technically speaking, cannot be said to be completed until the wood ceases to lose weight by evaporation on the continued application of heat ; but to arrive at this degree of dessication would require two or three times as long as is usually allowed for the seasoning of timber. A good and expeditious method of completing the seasoning of wood consists in placing it in hot rooms having a free circulation of air, which enters at the lower part heated and dry, and therefore in an excellent condition to absorb moisture, and it leaves the upper part of the room charged with aqueous vapour taken from the wood which is under- going the process of dessication. This mode of pro- cedure is so expeditious that by its adoption two- thirds of the time required for common air-drying is saved. As a general rule, the specific gravities of woods will give a very fair idea of their comparative degrees of hardness. In order to render timber more durable than it is when merely air-dried various special processes have been invented, such as injecting its pores with corrosive sublimate, sulphate of copper, or creosote, the latter being practised to a very great extent for railway sleepers and other timbers placed in very exposed situations, liable to the combined action of moisture and air. GENERAL CHARACTERISTICS OF WOOD. Timber, on account of its great flexibility, comparatively speaking, is but little adapted for the manufacture of parts of machinery which reciprocate at high velocities, but its cheapness, toughness, and facility of being wrought L 2 148 PRINCIPLES AXD COXSTKUCTIOX render it useful for framework and parts of machines at rest or always moving in one direction. Although the specific gravity of timber is very low, yet in its use there is seldom any saving in weight, as from its correspondingly slight resistance to strains a much larger sectional area is required to resist a given strain where it is used than if metal be the material applied. The liability of wood to twist and warp, especially when exposed to damp and to alternations of tempera- ture, as well as its liability to combustion, are also dis- advantages weighing heavily against its use if other materials are available at a moderate cost. Some of the toughest kinds of wood are, however, used to a considerable extent for the teeth of wheels, and for this purpose are found to wear as well as iron ; in fact, in some cases, wheels with wood teeth will outlast the iron-toothed wheels in gear with which they work. Wood is also very useful as a packing material to place under portions of machines subject to concussion, so as to deaden the shock which would otherwise be trans- mitted to the parts below with almost its normal force. IBOX. The various descriptions of cast and wrought irons and steels used in commerce for the multifarious purposes of the manufacturer are obtained by suitable processes from certain minerals containing more or less iron, and which are known as iron ores. In these ores the iron exists chiefly in the form of oxides and carbonates. The oxides of iron are two in number : the protoxide and peroxide, or sesquioxide of iron. The first contains one atom or chemical equivalent of oxygen to each atom of iron, its chemical symbol being Fe. 0. (Fe. representing Ferrum, Lat., Iron, and 0. Oxygen). But the chemical equivalents, or atomic weights, are, 149 Iron 28, Oxygen = 8* ; hence the composition of protoxide of iron is, Parts. Parts. Iron .... 28 .. 77-78 Oxygen 8 . 22-22 100-00 The sesquioxide of iron contains two equivalents of iron to three of oxygen ; hence its formula is Fe2 0$, and its composition Parts. Parts. Iron . 28 x 2 . = 56 . . 70-00 Oxygen 8 x 3 . = 24 . . 30-00 100-00 There exist also in the ores containing the iron other substances, such as silica, graphite, alumina, &c., from association with which the iron must be removed ; but with many of these the iron is not chemically combined, and may, therefore, be readily freed. Carbonate of iron is a salt consisting of protoxide of iron combined with carbonic acid, the latter being composed of one atom of carbon and two atoms of oxygen, and, therefore, being represented by the formula C. 2 . Carbonate of iron will have the formula Fe. 0. C. 2 , or Fe. C. 3 . It occurs in many countries in the form of a light grey or buff massive stone in large quantities. The celebrated Styrian steel is prepared from this ore, which is com- monly termed Spathic Iron Ore, or Spherosiderite, and from this most of the English iron is prepared. The composition of carbonate of iron is Parts. Parts. Iron ... 28 48-27 Carbon ... 6 10-34 Oxygen . 8 X 3 = 24 41-39 100-00 * In the use of chemical nomenclature throughout this treat i-r, the old or Daltonian system of equivalents and formulae will be used. 150 PRINCIPLES AND CONSTRUCTION I l! S 5 3 O O o s s -g ,0 ,Q g lifii o c -* ^ IIIH I! Wl:l ! S g fill I i I < -S-T3 " =1 1^ 111 rAiifii.!rt ^ 6 6w o OF MACHINERY. 151 The iron is separated from the oxygen with which it is combined by the action of substances which, aided by heat, have fi greater attraction or affinity for oxygen than the iron has, and, therefore, deprive it of that element. Thus, if finely divided oxide of iron be sub- jected at a red heat to the action of hydrogen gas, the latter combines with the oxygen of the former to form water (H. 0.), and pure iron is left. In commercial processes, however, carbon in the form of coal or char- coal is the principal deoxodizer employed to free iron from its oxygen. The conditions of the iron in combination with the most important ores from which it is manufactured are as under : In Magnetic iron ore . . Fe. 0. + Fe2 3 Spathic or clay ironstone Fe. 0. C. 2 Eed hematite . . Fe 2 3 Brown iron ore (yellow j HQ ironstone, ochre, &c.) ) METALLTJRGY OF IKON. The metallurgy of iron, or practical extraction of the metal from the masses of matter in which it naturally occurs, is, as has already been shown, a process of a chemical nature in the first instance, although the subsequent treatment is chiefly mechanical. The first process with those ores which contain car- bonic acid, water, and sulphur, consists in roasting them in a suitable furnace, in order to expel those ingredients, after which the calcined ores will be ready for smelting. The operation of SMELTING depends, first, upon the tendency of most earthy and metallic substances to melt by heat ; next, upon the affinities of the substances put into the furnace together as causing them to decom- 152 PKEs'CrPLES A10) CONSTRUCTION pose each, other in fusion, and form new compounds by recombination of the different elements, and then upon the excessive gravity of the metallic iron, which causes it to sink through the mass to the bottom of the furnace. As regards this last point, it may be observed the specific gravity of all the other solid materials likely to come together in smelting (even in a coal or coke furnace) is not much more than twice that of water, whereas iron is seven times as heavy as water, bulk for bulk, and its gravitating tendency is, therefore, more than three times as great as that of the materials by which it is sur- rounded. In charcoal furnaces the gravitating tendency is considerably greater. The following diagram shows the materials which are usually brought to act upon each other in smelting furnaces, and the products which result from their mutual decomposition and recombination. PRODUCTS. Gaseous Atmospheric air. Solid. OF MACHINERY. 153 From this it will be seen that the fuel in combustion takes oxygen from the substances surrounding it, and its hydrogen passes away as water, its carbon as carbonic acid and carbonic oxide ( 0. 0.), whilst the flux dissolves the siliceous matrix, and so frees the iron, which, melting by the heat, descends to the bottom of the furnace, leaving the slag and cinder floating above in a nearly fluid state. The success of the process, of course, depends upon the means employed to carry it out ; if there be plenty of air and plenty of fuel, heat can be generated sufficient to fuse the most refractory and voluminous materials. As, however, both air and fuel are costly in their supply, it behoves the smelter so to mix and proportion the quantities of his ores and fluxes that fusion 'of both shall take place at the lowest possible temperatures, that it shall be the most perfect, and that it shall afford the greatest facilities for the separation and descent of the metal. Also, that by the presence of suitable substances all, or as many as possible of accidental impurities, may be neutralised or taken up, so that after its first separa- tion the iron shall not in its passage through the furnace enter into new and injurious combinations. This was very tersely but accurately expressed a very long time since by Rogw, the Welsh founder, who said, "In order to make iron you must first make glass." To cause all the substances which do not pass away from the furnace in the gaseous condition, of course excepting the iron, to assume the condition of a glassy cinder is the aim of the smelter, and it is from the quality of the cinder coming from the furnace that its working is practically judged of. In early times, and even now with some, the determining of the proportions of the different materials involved a tentative process, and the 154 PRINCIPLES AXD CONSTRUCTION rules laid down were the results of experience; but, with the development of chemical science and the exten- sion of theoretical knowledge, methods of calculating those proportions and the dimensions of the furnaces have arisen. In Fig. 45 a general outline of a blast furnace for iron-smelting is shown in vertical section, a represents the mouth of the furnace at which the fuel, fluxes, and ores to be treated are thrown into the fur- nace ; the part b b re- presents the shaft or cuvette of the furnace ; c the boshes, d the crucible, and e the hearth where the metal after reduction accu- mulates, being re- tarded by the dam /; g is termed the stack, and h the lining. Above the hearth the air necessary for com- bustion of the fuel is forced in through pipes called tuyeres (pronounced tweers), or, more commonly amongst workmen, " tue- irons." It would be exceeding our intentions to describe the mode of constructing the furnace, as its form is only introduced as necessary to make clear the explanation of the method of extracting iron from the ores in which it naturally exists, but it is important to give some idea of its average proportions according to the fuel intended to be used in it. They are contained in the following table : OF MACHINERY. 155 High Furnaces Anthracite Dimensions. Charcoal. using Coke. Coal. Stack height from foun- dation . . 25 feet. 50 feet. 35 feet. width at bottom . . 28 50 40 width at top . . . . 16J 25 33 Cuvette diameter at top 4 8 6 height of conical in- walls 25 33 11 height of cylindrical in-walls .... ... ... 8 width of boshes. . . 9| 15 12 angle of boshes . . . 55 deg. 65 deg. 75 deg. height of boshes . . 4J feet. 10| feet. 11 feet Crucible height of hearth 5 >? fM 5 n mean of length and breadth at top . . 2i 5 6 mean of length and breadth at bottom . 2 4 4 height of tuyere above hearth 1 2 1| Approximate capacity . 1000 cubic ft 4200 cubic ft. Time of descent of 20 hours. 40 hours. The form of cuvette used with anthracite coal is shown by the dotted lines in Fig. 45. The action of the fur- nace upon the ingredients placed in it as they pass downwards, is as follows : In the upper portion of the shaft the ore is heated to redness that is to say, it is roasted; the water, carbonic acid, and sulphur being expelled, and also the carbonic acid of the limestone in the flux escapes here. Further down, under the influence of more intense heat, the carbon of the fuel reacts upon the oxide of iron, carry- ing off its oxygen in the form of carbonic oxide, which on coming in contact with the atmosphere at the mouth of the furnace is consumed and converted into carbonic acid, occasioning in its combustion the bright flame 156 PRINCIPLES AND CONSTRUCTION which is seen to issue from the mouths of blast furnaces. In the boshes, where the greatest temperature is maintained, the reduced iron melts and falls in drops upon the hearth, together with the silica, lime, and clay ; these latter form a slag which floats upon the top of the iron, whence it can be drawn off when necessary. After having heated to 200 degrees or more the air requisite for combustion, it is forced by suitable blowing machi- nery into the crucible part of the furnace, where a heat of from 2,200 degrees to 2,550 degrees Fahrenheit may be produced. In proportion as the melted iron and slag are drawn off from the hearth, fresh charges of ore flux and fuel are fed into the mouth of the furnace, and thus the smelting may be continuously carried on for five or six years, according to how the furnace holds out. Fuel is one of the most important materials in smelt- ing both as regards quality and cost. The object in the use of fuel is principally to obtain the requisite heat, but it also acts as a reducing agent in separating the metallic iron ; hence its value will be proportionate to the amount of carbon it contains. Wood, which may generally be taken as half carbon, and half oxygen and hydrogen, in the proportions to form water, is too poor in carbon to be serviceable, and compared with coke, bulk for bulk, its capacity to generate heat is but one-fifth of that of the latter. The presence of hydrogen in fuel, although it promotes in- flammability, does not in blast furnaces act as a reducing agent on the ore, hence it is a disadvantage in fuels for smelting purposes. Therefore, raw coal, turf, lignite, and brown coal are unsuitable ; but pressed and charred turf is extensively used on the Continent, and is said to produce a charcoal of peculiar value. OF MACHINERY. 157 The general fuels used are wood in the form of char- coal, coal, and coke. Charcoal is prepared by charring wood either in stacks or ovens, and coke may be obtained from coal charred in gas retorts or in ovens constructed on purpose, the latter producing a much harder and better material than the former. The yield of charcoal in proportion to the wood from which it is made, is found to be Charcoal prepared in kilns . . 18 to 22 per cent. ovens . . 20 25 The quantities of coke yielded by coal are very variable; but ovens give a yield about 10 per cent, greater than that obtained from gas retorts. Gas-coke is cheap, but unsuitable for furnace use. Coal in coking yields . . 45 to 90 per cent. Average of all qualities . 63 ,, In regard to VOLUME, most coals expand in coking ; some, however, do not alter in bulk materially, and those of which the earthy matters are principally of an aluminous character sometimes shrink. The average composition of good coke may be thus represented : Parts. Carbon 82 Earthy matters 15 Volatile 3 100 If coke contains more than 15 per cent, of earthy matters it is not suited for smelting, for, in all cases, these earthy matters can serve no useful purpose, and merely act as absorbents of heat. Good coke may be inferred from its not having undergone great change in volume or shape, its colour 158 PRINCIPLES AND CONSTRUCTION being iron grey, or nearly that of graphite, from its having a lustre more silky than metallic from much hardness, elasticity, and resistance to impact, from a texture more fibrous than compact, imparting sonorous- ness when struck, and its specific gravity should some- what exceed that of water. The following table shows the probable consumption of fuel per cent, of crude iron from ores of different degrees of richness : Per-centage of Metal Per-centage of Fuel Consumed . in Ore. Charcoal. Coke. Fusible Ores . 25 to 30 66 to 90 110 to 150 30 , , 35 90 110 150 180 35 , , 40 110 130 180 220 Ores of mean fusibility 30 40 110 140 180 240 40 50 140 180 240 300 50 60 180 210 300 360 Refractory Ores 30 40 160 200 275 350 40 50 200 , , 250 350 , , 400 50 , , 60 250 , , 300 400 , , 500 Anthracite coal may be regarded as very similar to hard-coked coals, whose constitution its own much resem- bles, as is shown by the subjoined analysis : Parts. Carbon 88-7 Earthy matters 7-4 Volatile matters . . . . . 3 '9 100-0 FLUXES. It is but very seldom that ores of iron can be smelted by the fuel without the use of fluxes, which are matters containing no metal, or but very little, the object of their use being to promote fusion. Although the earthy bases most easily accessible, silica, lime, OF MACHINERY. 159 alumina, and magnesia, are, when taken singly, almost infusible, yet when combined, two and two, three and three, &c., they become fusible at readily attainable temperatures, and their addition to the ferruginous ores in the furnace materially assists in bringing the latter into a state of fusion. It may here be observed, as a practical maxim, that, in addition to the silica, alumina, &c., constantly present in the ores and fuel, the positive flux most commonly used is lime, in the form of shells, limestone or chalk, and the proportions in which it is supplied, on the average, are : In charcoal furnaces l-14th the weight of the other solid ingredients ; In coke furnaces l-8th the weight of the other solid ingredients. In general, the whole of the solid material (except the metallic iron) may be taken as of the following compo- sition : Parts. Parts. Silica 45 to 60 Lime 20 30 Alumina . . . . 10 ,, 15 Magnesia . . . . . 10 ,, 25 Oxide of Manganese . . . 15 ,, 20 100 If all the four first mentioned are together present at one time, the most fusible proportions in which they can exist are Parts. Silica 35-2 Alumina . . . . .31*7 Lime .19-1 Magnesia 14-0 100-0 The atmospheric air now remains to be considered as 160 PRINCIPLES AND CONSTRUCTION the only material used in smelting not yet treated of, and which must be regularly blown into the furnace to keep up the combustion. It is, therefore, of very great importance that its supply should be properly managed, and when the enormous quantities of it that are required are taken into consideration, its influence and effect can be better appreciated. The following is an average statement derived from practice : Charcoal Solid. Furnaces Gaseous. Coke. Solid. Furnaces. Gaseous. Volume of materials in cub. ft. 0-295 900-0 1-06 3000-0 Volume of do. proportionate 1-000 3050-0 1-00 2830-0 Weight of do. inlbs. permin. do. proportionate 26-82 1-00 75-0 3-022 102-12 1-00 269-0 2-634 In round numbers the volume of the air injected into the furnace in a given time is 3,000 times that of the other materials supplied, and its weight three times as great. The elements used above would also show that about nineteen tons of air are required for the manu- facture of one ton of iron. Iron is manufactured both with cold and hot blasts, and there has been a great deal of discussion as to the relative strengths of the products, a strong prejudice having existed against hot-blast iron ; but this opinion is exaggerated beyond what is warranted by actual experiments. The following statement shows the rela- tive resistances of metals prepared with hot and cold blasts to resist strains of different descriptions : Stretching. Crushing. Transverse. Impact. Cold-blast iron 1000 1000 1000 1000 1000 Hot-blast . 913 1033 963 1005 935 The hot-blast method works easier, and produces a greater yield than the cold-blast, and by it more refrac- OF MACHINERY. 161 tory materials may be reduced than by the latter, and it is also accompanied by a notable economy of flux and fuel ; the saving in fuel on the average may be stated for Coke furnaces at 32 per cent, from temperature of 330 F. Charcoal do. at 20 " " 390 F. Moreover, the use of hot blast allows of the adoption of certain raw coals, which could not otherwise be employed. As regards the general quality of the metal produced, it is a grey foundry iron with a more uni- formly cubic crystalline form than is observed in the iron yielded by cold blast. We must now speak of other products of the blast- furnace. The following analysis shows the composition of cinder averages when the furnace is doing good work : Charcoal Cinder. Coke Cinder. Silica 53 43 Lime 22 35 Alumina .... 16 14 Magnesia .... 5 4 Protoxide of Iron 4 4 Too" 100 The gaseous products of the furnace may be taken to consist on an average of Parts. Nitrogen 56 Carbonic acid 19 Carbonic oxide . . . .16 Carburetted hydrogen ... 2 Steam 7 100 The physical properties of iron now require our care- ful attention. The colour varies according to the pro- portion and mode of combination of the crude iron with 162 PRINCIPLES AND CONSTRUCTION its chief foreign ingredient, carbon, from dark grey to silvery white. Dark grey crystalline iron, with its small facets, is considered suitable for foundry purposes for making castings ; as its colour brightens and becomes more silvery it is considered more suitable for conver- sion into wrought-iron. In order to produce malleable or wrought-iron from crude iron it is necessary to eliminate the carbon con- tained in the latter, which is done by subjecting it to the action of atmospheric air while in a state of fusion, thereby oxidizing the carbon and carrying it off as car- bonic acid or carbonic oxide. This process may be accomplished by stirring the molten metal about in a refinery, or in a puddling furnace, or by forcing air through the liquid mass, as in Bessemer' s process. Steel in composition is between cast and wrought iron, as it contains a certain proportion of carbon, that element existing in combination with the metal in the proportion of about 2 per cent. Steel may be made from malleable bars by keeping them for a length of time at a red heat in contact with powdered charcoal, then the iron, taking up a suitable portion of carbon, becomes converted into steel. This process is termed cementation, and the furnace in which it is carried out a cementing furnace. Steel may also be produced from crude iron by Bes- semer' s process, by forcing air through the melted cast- iron until all the carbon except that required to consti- tute steel is eliminated from the mass under treatment. The average specific gravities of different irons are (water being 1-00) Crude iron foundry or grey iron . . 7*0 Crude iron forge-pig or white iron . 7-5 Malleable iron 7'6 OF MACHINERY. 163 The effects produced by various foreign ingredients upon the quality of iron are worthy of careful study : Sulphur renders iron exceedingly fusible and brittle at all temperatures, especially when hot, thus giving rise to a quality which is known as red- short-ness. Phosphorus imparts cold-short-ness to iron, making it brittle at low temperatures, though not to the same extent that sulphur does. Occurring in quantities not exceeding per cent., it increases the hardness without injuring the tenacity of bar iron, but in larger proportions it exerts a deleterious effect on the metal. Antimony has a great affinity for iron, and, combined with it in the proportion of J per cent., renders it very brittle when hot. When the metals are in proportion of their chemical equivalents iron 28 parts to antimony 129 the elements are inse- parable by the highest degree of heat. Arsenic in the proportion of 1-6 per cent, has been noticed to entirely destroy the tenacity of iron. Chrome united with iron produces alloys hard, brittle, and crystalline. When the chrome is present to the amount of 60 per cent, the alloy is hard enough to scratch glass as deeply as a diamond. 1 to 2 per cent, hardens cast steel without diminishing its malleability. Copper in the proportion of 1 to 2 per cent, increases the tenacity of crude iron, but its presence in malleable iron injures its property of welding, and in large proportions makes it red-short. M 2 164 PRINCIPLES AND CONSTRUCTION Manganese is most commonly found associated with iron in small quantities ; up to If per cent, it hardens the metal without impairing its tenacity ; it also diminishes the fusibility of iron. The tendency of ores containing manganese is to yield a metal easily convertible into steel. Nickel renders iron whiter, less oxidizable, and less ductile than it is when unalloyed, otherwise the iron is of good quality. Palladium, Rhodium, Iridium, and Osmium cause iron to become hard and brittle ; the presence of any of these to the extent of 3 per cent, enables the iron to be tempered like steel. The following table is interesting as showing how the quality of iron is affected by different proportions of carbon associated or combined with it : Iron half-converted into steel contains one 150th of carbon. Soft cast-steel capable of welding contains one 120th of carbon. Cast-steel for common purposes contains one 100th of carbon. Cast-steel requiring more hardness contains one 90th of carbon. Steel bearing a few blows, but unfit for drawing, con- tains one 50th of carbon. First approach to steely-granulated fracture contains one 30th to one 40th of carbon. White cast-iron contains one 25th of carbon. Mottled cast-iron contains one 20th of carbon. Carbonated cast-iron contains one 15th of carbon. Super-carbonated crude iron contains one 12th of carbon. OF MACHINERY. 165 Cast-iron and steel admit of being prepared in hard or soft state. Thus, if a casting is required to have a portion of its surface hard, that side of the mould con- sists of some substance (as iron) which will rapidly cool the metal which is run in contact with it, thus producing a very hard surface. Castings thus made are called, from the method employed, chitted castings. Steel is hardened by raising it to a red heat and plunging it into salt water ; but this process renders it absolutely hard and brittle, hence, for most purposes, this must be lowered by tempering, which consists in heating the hard steel to a temperature depending upon the purpose for which it is intended to be used; the right temperature is commonly recognised by the work- man from the colour of the film of oxide which forms on the steel, as shown by the following table : Colour of Film. Ten ip. Use. Very pale straw yellow 430 deg.-v A shade of darker straw C Tools for metaL yellow 440 ) Darker straw yellow 470 > Tools tat wood and screw taps, Dark yellow .... 490 S &c. Brown yellow . . . 500 ^ Yellow tinged slightly (.Hatchets, chipping chisels, and with purple .... 520 1 othe T percussive tools, saws, &c. Light purple .... 530 Dark purple .... Dark blue 550 570 | Spring JS. Pale blue 590 M \ Paler blue Paler blue tinged with 610 ' ) Too soft for the above purposes. green 630 J Iron castings are rendered soft by abstracting a por- tion of their carbon, whereby they are partially (or, if thin, entirely) changed to the condition of malleable iron. In order to effect this decarbonization the castings are Ibb PRINCIPLES A]S T D CONSTRUCTION put into boxes or cases surrounded with pounded iron- stone and submitted to heat, or metallic oxides may be used. Thus the carbon is oxidized out of the metal to a certain depth from the surface. After being heated for a sufficient length of time the castings are allowed to cool very gradually. Wrought-iron may be case-hardened by a very sim- ple process, which converts the outside of the forg- ing or casting for a certain limited depth into steel, which is hardened in the usual way by sudden cooling. The articles to be case-hardened are placed in a case and surrounded on every side by powdered bones, hoofs, skins, or leather, with which the case is filled up, being then securely fastened air-tight, and put in a furnace raised to a red heat, and maintained at that temperature for a period of from one to five hours, according to the depth to which it is desired that the case-hardening may penetrate. On removal of the partially-converted articles, while still hot, they are hardened by sudden immersion in cold water. A very thin, or even perhaps discontinuous, coating of steel may be produced on iron by burying the latter at a red heat for two or three minutes in powdered ferrocyanide of potassium (the common yellow prussiate of potash of commerce), a salt which is prepared from various animal matters. The steely surface thus obtained is not nearly so good and durable as steel made in the usual way and ham- mered, and generally the cementation does not pene- trate to a depth of more than one- sixteenth of an inch; nor is it necessary that it should do so, as the object of case-hardening is to increase the durability of the surface without impairing the general strength and toughness of the article operated upon. OF MACHINERY. 167 The introduction of cheap steel has done much to decrease the practice of case-hardening certain small articles of manufacture. According to Dr. Thompson's analysis of some cast-steel from a manufactory near Glasgow, it contains a very slight proportion of silicon, but this does not appear to be essential. The composi- tion of the sample was Parts. Iron 99 Carbon with some silicon . . 1 100 This very nearly corresponds to the formula, Fe2o C., which would give Parts. Parts. Iron . . 28 X 20 = 560 . . 98-94 Carbon ... 6 . 1-Q6 100-00 COPPER is the next material demanding attention. The ore from which the copper of commerce is prin- cipally obtained contains the metal in combination with sulphur, as a sulphuret or sulphide of copper, generally accompanied by sulphide of iron, as in copper pyrites ; thus, in addition to the sulphur, there is the iron to be eliminated. The process of extracting copper from its ores is exceedingly lengthy and tedious, and requires great care on the part of those conducting it ; and it consists of a considerable number of separate operations, through all of which the material must pass before it is fit for the market. In the first place, the ores must be roasted or calcined, in order to convert the copper into oxide of copper and the iron into protoxide of iron, the sulphur being expelled in the form of sulphurous acid. Secondly, the roasted ore must be melted with charcoal 168 PEINCIPLES AND COIs'STKUCTION and some siliceous substance in a suitable furnace, by which means metallic copper and carbonic oxide are formed from the oxide of copper and charcoal, and sili- cate of protoxide of iron (or iron slag) from the pro- toxide of iron and quartz. This appears simple enough as thus stated, but the actual establishment of the reac- tions to bring about the desired end in practice is in reality so difficult that the roasting and melting have to be repeated from ten to twenty times alternately in some cases, in order to get rid entirely of the sulphur and iron with which the copper is associated. The melted mass, which is obtained when about half the sulphur and iron is removed, is called matt, or crude copper, and black copper when it contains only about 5 per cent, of these two substances. The ultimate refining of black copper is effected by remelting the metal, exposing it at the same time to the action of the air, whereby the remaining iron, sulphur, and foreign metals, such as lead and antimony, which may be present, are oxidized before the copper (which has a less affinity for oxygen), and thus are separated from it. During the various processes some of the slags which are rich in copper may be reworked with fresh ore. In some stages the removal of the sulphur may be facilitated by stirring the molten metal with a stick of green wood, which probably acts by the moisture sup- plied by it decomposing the sulphide of iron, and form- ing oxide of iron and sulphuretted hydrogen. The species of furnace chiefly used in the reduction of copper is that known as the reverberatory furnace, of which a vertical section is shown at Fig. 46 ; it admits of the regulation of the chemical reactions to a very great nicety, a is the fire-grate, and I b the bed or sole of the furnace, whereon the materials to be treated, OF MACHINERY. together with any re-agents which may be requisite, are placed ; c is an outlet which can be opened at pleasure for the withdrawal of slag, &c. ; e and / are doors to allow of the observation of the state of the furnace; d is the chimney-shaft. The charges of metal are drawn through a door in the side of the furnace. Fig. 46. Now, it is evident in this arrangement that, by regu- lating the quantity of fuel and air admitted to the fur- nace, there may be either excess of air passing over the sole, producing an oxidizing effect, or, on the other hand, by reducing the quantity of air below that requisite for the complete combustion of the fuel, there will be car- bonic oxide passing over the materials tending to de- oxidize them. When the ores are combined with oxygen instead of sulphur, the operation of working them is much easier, as they yield metallic copper by merely treating them with charcoal, which abstracts the oxygen ; but such ores are unfortunately too rare to afford anything approaching to a sufficient supply of copper to meet the demand. Copper possesses certain physical characteristics which render it especially suitable to particular purposes. It is slow to oxidize when compared with iron ; is tough 170 PRINCIPLES AND CONSTRUCTION and extremely ductile, the latter property allowing wrought copper to be drawn into exceedingly fine wire and beaten into almost any conceivable shape. Thus copper pans, kettles, and parabolic reflector-backs may be beaten up out of flat sheets of copper. It is useful for lining air-pumps, and as a material for other pumps when alloyed with some other metals, and more espe- cially in such machinery as is subject to sea water or foul water, which would rapidly corrode iron. Copper may be to some extent hardened by hammering, and the tenacity of cast copper may be greatly increased by the addition of about 3 per cent, of phosphorus, which is introduced into molten copper without great loss by first coating it with a layer of copper for pro- tection. LEAD, the next of the useful metals upon which we shall dilate, is largely used in the arts. The following ores of lead are the most important : Gralena, or sulphide of lead, has metallic lustre and a crystalline structure distinctly derived from the cube. It is a compound of lead and sulphur in atomic propor- tions, consisting of Parts. Lead 86-67 Sulphur 13-33 100-00 and has a specific gravity of 7*6. Its colour is blackish grey. Native minium, or red lead, is of a lively red colour, but sometimes inclining to orange ; it has an earthy aspect, and specific gravity from 4-6 to 8-9 : it is rare. Carbonate of lead (white lead), when pure, is colour- less, and transparent like glass ; its specific gravity is from 6 to 6 7. OF MACHINERY. 171 Galena, or sulphide of lead, is, however, the only ore which is sufficiently abundant to become the object of mining and metallurgy, and in its treatment, after the due sorting, cleaning, and grinding, is usually reduced in reverberatory furnaces. The sulphur, in combina- tion with the metals as sulphides, is so firmly asso- ciated with them by chemical affinity that it cannot easily be expelled, hence it is necessary to have recourse to a circuitous method ; first, the sulphide must be con- verted into an oxide of the metal, and the oxygen must then be expelled to free the metal. The galena is heated or roasted with free access of atmospheric air, the result being that the lead becomes oxide of lead, the sulphur escaping as sulphurous acid, but there is also a small portion of sulphate of lead formed during the process. After roasting, then, the galena leaves a mixture of oxide of lead with some sulphate of lead, which may be reduced by heating in a blast or' reverberatory furnace with charcoal. Another method of freeing lead from sulphur consists in heating the galena with a metal which has a greater affinity for the sulphur, and therefore replaces the lead : such a metal is iron. Thus iron and sulphide of lead, heated together, will yield lead and sulphide of iron. In the reaction one atom of iron replaces one atom of lead : hence 28 Ibs. of iron will suffice to throw down 104 Ibs. of metallic lead. Physically the characteristics of lead are distinctive ; it has little or no elasticity, is very ductile and flexible, possesses but little strength in any direction, and is fusible at a low temperature (600 P.), and has a very high specific gravity 11-5. TIN is a white metal possessing considerable lustre, 172 PRINCIPLES AND CONSTRUCTION in bars ; it makes a peculiar cracking noise when bent ; its specific gravity is 7-2, and melting point 446 F. Tin is prepared in the smelting houses in a simple manner from tin stone, which consists of peroxide of tin with some arsenic and iron. The ore is first finely stamped, after which it is roasted, whereby the arsenic is volatilized and the iron oxidized. It is then washed with water, whereby the lighter particles of stone, and to a great extent the oxide of iron, are carried away. Finally, it is fused with charcoal in a blast furnace, and a reaction taking place, carbonic acid and metallic tin result, the latter flowing from the bottom of the furnace. In the mechanical arts tin is almost entirely used in connection with other metals. ZINC has a specific gravity of 6-8, is a white metal, and will show a certain amount of ductility at a mode- rate heat. It is prepared from carbonate of zinc, which by the miners is called calamine, in order to convert which into metallic zinc the carbonic acid and oxygen must be expelled. The first is effected by calcination in furnaces, the latter in the same way as is applied to iron ores, by heating to redness with charcoal; but this cannot be done in open furnaces, as the reduced zinc would evapo- rate and burn, again becoming converted into oxide of zinc. The vessels used in which to treat the zinc ores are called muffles, and are, in fact, a species of retorts made of clay ; into these retorts the calamine and char- coal are put and raised to a red heat, then the carbonic acid and evaporated zinc pass away through the neck, the former to escape, the latter condenses and falls in drops into a vessel of water. The zinc of commerce always contains a small quantity of iron and lead, but if the amount of the latter OF MACHINERY. 173 is more than 1| P er cent., the zinc becomes brittle and cannot be rolled into sheets even when heated. There are several alloys which are largely used in the construction of machines, and which must therefore not be overlooked. An alloy is a mixture or a mechanical combination of two or more metals, in contradistinction to a compound which is a chemical union ; but although the combination of the different components is mecha- nical, yet the physical properties of the alloy are not to be deduced from those of the metals entering into its composition. Brass, much used for bearings for the revolving shafts of machinery, and for bushes, and various minor details, consists of copper and zinc. Gun-metal or bell-metal is a very hard alloy, useful for small cams, valves, pumps, &c. ; it is composed of copper and tin. There are also other alloys of copper, such as Muntz's yellow metal, Ger- man silver, &c., which are applied to specific purposes. The following is a list of the most useful alloys, and the proportions in which their component metals are associated : Bismuth 1, tin 2 Cowper's alloy, for rose-engine and eccentric-turned patterns to be printed from. Bismuth 2, lead 4, tin 3) Bismuth 1 , lead 1 , tin 2 j Coilstitute pewterers' soft solders. Copper 5, zinc 1 red sheet brass, made at Hegermiihl. Copper 2, zinc 1 brass that bears soldering well. Copper 2, zinc 1 ordinary brass. Copper 16, zinc 9 ) Copper 16, zinc lOf j The two extremes of Muntz's metal. Copper 4, zinc 3 spelter solder for copper and iron. Copper 1, zinc 1 spelter for brass. Copper 1, zinc 8 metal used for lap and polishing discs. Copper 16, tin Isoft gun-metal. 174 PRINCIPLES AND CONSTRUCTION Copper 12, tin 1 gun-metal for mathematical instru- ments. Copper 10, tin 1 wheel metal for small-toothed wheels. Copper 8, tin 1 Brass ordnance or hard bearings for machinery. Copper 6, tin 1 very hard bearing metal, too brittle for general use. Copper 2, tin 1 speculum metal. Copper 2, lead 1 pot metal. Copper 32, tin 3, zinc 1 pump metal ; has great tenacity. Copper 32, tin 5, zinc 1 bearing metal for very heavy weights. Lead 3, tin 1 coarse plumbers' solder. Lead 1, tin 2 fine solder. There are a variety of other alloys made, but they are used for purposes which do not come within the compass of the present work, being applied to the manu- facture of articles of ornament rather than utility, or as substitutes for the precious metals. CHAPTEE XIV. THE MANIPULATION OF TIMBER AND THE METALS. IT is most essential that anyone designing machinery shall be thoroughly acquainted not only with the in- trinsic properties of materials, but also with the methods of manipulation by which they are converted to such purposes as they may suit. Otherwise it is not only possible but probable that details of machines may be drawn and specified to be made of materials which are highly insuitable, or which can be wrought into the required form only at great expense, or in some oases not at all. OF MACHINERY. TIMBER. Although, timber is but little used in the construction of machinery in" localities where iron is plentiful and cheap, yet in some places it is applied for framework or even for some of the moving parts ; hence it is necessary to explain the proper method of making the connections between different parts so as to secure the requisite strength and rigidity. In Fig. 47 A represents an inclined timber liable to a thrust ; it is jointed to the tie as shown, the end resting in a notch, ., Fiq. 47. and having a rib or fea- ther on it, shown by the dotted line c, to maintain its lateral position ; it is held in its place by a bolt and nut, or by an iron strap passing the end of A and bolted through B. A trussed frame is illustrated at c, Fig. 48 ; it consists of three top pieces in compression, one horizontal tie at the bottom, two upright struts e, e, and two iron tie- bars d d, by the tightening up of which the whole frame is brought firmly together and the different parts are prevented from slipping out of their proper positions. By an addition to this arrange- ment a rectangular Fig. 48. 176 PRINCIPLES AND CONSTRUCTION frame is produced as shown at D ; it is in construction similar to the last. The parts of frames are in many instances joined by means of tenons and mortises, and in making these particular care should be taken. E is a section of a bad or slovenly joint, F of a good one ; in the former the mortise is cut true on the surface, but somewhat undercut towards e e, hence the tenon /, being par- allel, will not fit firmly, and there will therefore be a tendency to wriggle or shake about, which, if the joint be subject to vibration, will soon render it defective. In F, on the contrary, the mortise is cut to a pattern or template, and is tapered slightly so as to be smaller at the bottom than at the surface where it commences ; the tenon is cut paralled and forced or driven into the mor- tise, where it is secured by an iron strap, as shown by the dotted lines passing round the joint and secured by bolts to the timber carrying the tenon ; this strap may rise above the surface of the timber, or a recess may be cut to allow of its lying flush where necessary, but of course to a certain extent the framework is weakened by cutting away any portion of its substance to form such recesses. For purposes requiring more rigidity than can con- veniently be obtained with timbers of a reasonable size, a piece of bar iron is frequently placed in the centre between two layers of wood, the three being secured to- gether by bolts, as shown by the elevation G and the transverse section H. In the latter * i is the piece of iron, which is commonly termed a flitch plate. It is always placed so that the bending strain upon the timber acts in the direction of i, as, if it acted in the direction indi- cated by the arrow, the flitch plate would not materially add either to the strength or rigidity of the element. OF MACHINERY. 177 When timbers require to be joined in the direction of their length, it is effected by a process termed scarfing, which may be either lateral or transverse. Three methods are 49 ; in the two ^ j >^ ^Pli lateral methods ~ <& ^ dli ui the ends of the pieces to be joined are ta- pered off and notched accord- ing to the di- rection in which the strain will act ; the extremities thus prepared are placed in contact, and retained so by bolts and nuts, as shown, a I represents a suitable scarf to resist a tensile strain, and e f the mode of notching when the timber is subject to a compressive strain ; c, d, are the ends of two timbers prepared for transverse scarfing ; the tenon-like projections^,^, on the piece d enter the recesses shown by the dotted lines at h, h, on the piece e, and are there secured by a bolt and nut. This style of scarfing is chiefly suitable for com- pressive strains, such as come upon uprights, &c. When timber is used for the manufacture of spring beams to receive accidental impact, as in the spring beams of Cornish pumping-engines, &c., they are made of a number of thin layers of timber put together some- what after the fashion of carriage springs, the ends being carried in iron boxes or straps which, while hold- ing them laterally in position, will yet allow them in bending to slide slightly one upon another ; similar beams may be used to quicken the strokes of tilt- hammers, &c. N I 178 PKIXCIPLES AXD CONSTRUCTION We will conclude our remarks upon timber by show- ing the different purposes to which the various species are specially adapted, together with their weights, the latter being given for them both in the green or wet state and in the dry or seasoned condition ; the first will be marked g, the second d, and the weights given in pounds per cubic foot : Acacia For sills, wall-plates, posts, fences, and tree- nails, harder, tougher, and more elastic than the best oak weight, g 63-2, d 48-5. Alder Valuable for piles and other subaqueous work weight, g 62-3, d 39-5. Ash Useful for beams, joists, and wheels weight, g 65-0, d 50-0. Beech Useful for piles and for teeth of wheels weight, g 66-0, d 50-0. Elm Used for planking, piles, and wheels weight, g 70-0, 3 x 2 x 3 4-71 As an example let us take the forked connecting-rod of a steam-engine ; in this case the bolt will evidently carry the strain upon two sections. Let the strain on the link be 14 tons, then the diameter of the bolt or pin will be D A/ = 1-73 inches (say), If inches. The minimum diameter of the body of the link will be about 2^ inches ; hence, if 2 inches be the sum of the thickness of the two arms of the forked end of the con- necting-rod, then inches. In the classes of rigid joints shown at e d and ef, a number of rivets or bolts are used. In the former case the joint is lapped, as the strain is transmitted direct from one part to the other. Let S = strain in tons, d = diameter of rivets in inches, n = number of rivets, and 4 tons safe strain per square inch, then S = 0-785 . d 2 x n X 4 hence, S S 0-785 d 2 x 4 3-14 d* In the second joint, which is butted, the strain is trans- 200 PRINCIPLES AND CONSTRUCTION mitted first from e to the cover g, and thence to /, there- fore the above number of rivets must be put in on each side of the line of juncture, the total number of rivets in this case being, 8_ _ 8 ~ 0-392 d z x 4 ~ 1-57 d* If there be two cover plates, one on each side of the plates to be joined, then will the rivets carry the strain on two sections, hence half the number of rivets will be required. It has been determined experimentally that the relative strengths for solid and rivetted work of boiler plate is, Solid plate . . . .100 Single-ri vetted joint . . . 56 Double ,,,,.. 70 The bolts and nuts must be also so proportioned that the head shall not strip off, nor the nut under a less strain than that which will tear the bolt asunder. The strain, in passing from the body of a bolt to its head, tends to shear off the annular portion of metal by which the overhanging part of the head is formed ; the surface to be sheared will be, if h = height of head, = d X 3-1416 x h and the area of the bolt is = d 2 x 0-785 taking the relative resistances of the metals to tensile and shearing strain as 5 to 4, we have, d x 3' 1416 x h x 4 = d* x 0-785 x 5 h- 5d "W but the heads are very seldom made less than one half OF MACHINERY. 201 the diameter, and most commonly equal to the dia- meter. In the case of nuts it is to he considered that there is not the same continuity of hold that there is in the solid metal, hence they are made with a minimum length equal to twice that given by the above formula, hence for nuts we have, -.- Sometimes joints are made by joint tubes having right and left handed threads cut in them, so that by turning the joint tubes, the bars are tightened up or slackened as circumstances may require. When joints are made by means of keys, wedges, or cotters, the area of the cotter must be determined similarly to that of the bolt, which is done by replacing 0-785 d 2 in the foregoing formula?, by E x W, where li is the breadth, and W the thickness of the cotter in inches. In joints where the pressure is entirely compressive, the bearing area must be made sufficiently large to prevent any spreading, or great and unnecessary wear on the surfaces in contact. These connections often occur in the toggle joints of Stanhope and certain other presses. In bars, such as long pump rods, which require to be occasionally disconnected, a species of scarf joint is much used, as shown in Fig. 55. The scarfed ends a, 4, being Fig. ^ placed together, the box c is slid over them to hold them in position. The strength of the necks of the rods must be duly proportioned. The proper diameters of rivets to join two plates of PRINCIPLES AOT) CONSTRUCTION given thicknesses together, as determined by long ex- perience, are stated in the following table : Thickness of Plate. Inches. Diameter of Rivets. Inches. Thickness of Plate. Inches. Diameter of Rivets. Inches. 1/4 1/2 5/8 3/4 5/16 5/8 11/16 7/8 3/8 5/8 3/4 7/8 7/16 5/8 13/16 7/8 1/2 3/4 7/8 1 9/16 3/4 15/16 1 1 1 The diameter of the nut may be made about 1-75 diameters of the bolt, or in extreme cases twice the diameter of the bolt. In making the joints of pipes under pressure and cylinder covers, &c., the first step is to arrange to have a sufficient number of bolts to carry the strain. A bolt of good sound malleable iron, one inch in diameter, should safely support a tensile strain equal to 10,000 Ibs. ; hence if p = total pressure on joint in pounds, d =. diameter of bolt in inches, w =. number of bolts, then - P 10000 X d* 10000 x n thus if there be a joint in a steam pipe, of which the diameter is four inches, and the pressure per inch is 80 Ibs., then the total pressure on the joint will be = 0-785 x 16 x 80 = 1004-8 Ibs. OF MACIimEKY. 203 hence the minimum diameter of bolts to secure this joint must be d = A / 1004 ' 8 = o-025 inch, or 3-16 bolts. V 10000 X 4 Bolts so small as this, however, would not be used in practice. To take another example, let the joints of an air vessel be under a pressure due to a head of water equal to 200 feet, and let the diameter of the air vessel be 7 feet, there being 44 bolts in the joint, giving a distance of about 6 inches between the bolts : The pressure per square inch will be = 200 x 0-434 = 86-8 Ibs. per square inch ; the area of the vessel at the joint in square inches = 49 x 0-785 x 144 = 5541 square inches ; hence the load on the bolts = 5541 x 86-8 = 480,958-8 Ibs. For simplicity, this maybe called 481,000 Ibs., then the diameter of the bolts required will be =v; 4810 = 1-09 inch (say), 1J inch 10000 X 44 diameter. In respect to bolts, as in all other matters of construc- tion, it is found that when we have to deal with small quantities and light strains, it is not practicable to keep 204 PRINCIPLES AND CONSTRUCTION the dimensions down nearly so low as is shown to be safe by calculation, and, moreover, all elements must be sufficiently massive to withstand accidental blows and concussions. In all descriptions of joints, the parts to be joined together should be made true so as to fit, otherwise an undue strain, will be thrown upon the bolts, or perhaps a side or twisting stress. Of course in steam and water joints it is necessary, generally, to interpose some material to render the joint tight, for this purpose canvas covered with a mixture of red and white lead together in about equal parts may be used, the lead being moistened, if necessary, with boiled oil to make it spread. In all cases where the main nuts of a joint cannot be jammed down hard upon the parts which they hold, as with the nuts on bearing caps, cross-heads of piston and connecting rods, a second thinner nut is used which is called a guide or check nut ; by screwing the latter tight upon the main nut both are effectually secured from moving. In some instances also, guards made of thin iron to fit the nuts are used, which, by closely encircling them, prevent their turning. BEARINGS. The bearings of machinery being those parts in which naturally the greatest amount of wear takes place, it is very important that much care should be given to proportioning their dimensions, and to the selection of materials from which to manufacture them. The requirements to be satisfied are to have the greatest steadiness of working, with a minimum wear and mini- mum friction, so as to require the least quantity of unguent for lubrication. OF MACHINERY. 205 Fig. 57 shows a side elevation of the ordinary kind of bearing for revolving shafts and elements having an oscillating motion, and a vertical section of the same taken on the dotted line x a is the lower / part, which is called the plummer-block, usually of cast-iron ; b indicates the bearings or brasses, made each in the form of a semi- cylinder, of gun-metal or bearing metal ; c is the cap of the plummer-block, by which the brasses are kept in position, the cap being secured by the bolts and nuts d, d. In light work sometimes the whole bearing is made of brass. For wrought-iron shafts the length of bearing should be T75 times the diameter of the journal of the shaft, which is that part which lies in the brasses. If a sufficient length of bearing be not given, especially in machines that are liable to much vibration, the journals will work about in the bearings, and the whole machine soon becomes shaky. This may frequently be noticed with some ill-contrived marine-engines, where, apparently in order to save room, the bearings have been made much too short. In the construction of bearings and journals, the former should be bored and the latter turned as truly as possible, after which the fitting of them accurately together may be completed by scraping. In this pro- cess ruddle or other colouring matter is rubbed on the shaft, which is then slightly worked on the bearings to show the most prominent parts; the operator then reduces these parts with a scraper, and the process is repeated until a satisfactory result is obtained. As the bearings wear away they are brought together 206 PRINCIPLES AST) COXSTBUCTIOir by tightening the nuts d, d, and where there is a de- cided tendency to wear oval, as in the bearings of a steam-engine, the plummer-blocks should be so arranged that the thrust and pull act relatively in the direction of the dotted line x , that is to say, at right angles to the diameter on which the brasses are separated. A great variety of metals and alloys have been tried for bearings in order to obtain the most durable com- bination available ; brass, gun-metal, hard white metal, steel and glass, have each had their trial, but almost universally brass and gun-metal are used for the bear- ings for wrought-iron shafts, and if kept well lubricated the results are tolerably satisfactory. If an unguent could be found sufficiently permanent not to be squeezed out of the bearings, then the nature of the material would not much affect the friction, as the rubbing surfaces would in fact be of the unguent, and not of the metals upon which it is spread, then the hardest material would be the best that could be used for the bearings, as that would wear the slowest. There is some trouble about the efficient lubrication of bearings, both in regard to the kind of unguent used and the mode of applying it so as always to keep the bearing sufficiently oiled or greased and yet not waste the substance used for that purpose. The unguent should be sufficiently cohesive not to be readily forced out from between the shaft and bearing, yet it should not be of a gummy or clogging nature, in which case it would cause the bearing to become hot. In every case vegetable oil is far preferable to mineral, no matter how pure the latter, for it is apt to decompose into certain compounds injurious to the surfaces of the metals with which it is in contact. OF MACHINERY. 207 A great variety of contrivances have been applied for the regulation of the supply of oil to machine bearings, some being on the same principle as a common lamp, sucking up the oil by a cotton wick, and allowing it to fall drop by drop through a hole in the plummer-block on to the journal of the shaft, while others have acted as pumps, making one stroke for every revolution of the shaft. This latter is an improvement, inasmuch as the oil is not supplied to the shaft when at rest, during which time it would be merely running away to waste. To at- tempt to describe the varieties of these apparatus would occupy more space than they are worth, notwithstanding the importance of the subject, but we may mention that an oil vessel has been introduced, and in use for some time, which seems to work satisfactorily. It is called the needle lubricator. PACKINGS. The object of packing is to allow moving parts to work in contact without permitting the passage between them of certain liquids and gases. In Tig. 58 different methods of packing are illustrated, a I repre- sents a cylindrical rod, such as a piston or slide rod, which is required to work steam and air tight through a plate. Upon this plate is formed a box or gland 208 PRINCIPLES AND CONSTRUCTION called a stuffing-box, e. This box, which is cylindrical, is somewhat larger in its internal diameter than the rod which works through it. d is a flanged cylinder bored out to fit the rod closely but yet not tightly, as the rod has to slide to and fro within it ; the outer surface of this cylindrical piece is accurately turned to fit into the box c, which is bored out to receive it. The mode of using the stuffing-box is thus : Into the cavity e around the rod is pretty tightly packed a plait of untwisted rope or gaskin, which has previously been been well saturated with Eussia tallow, or some other unguent of equal efficiency; then the part d is placed upon this packing and tightened down upon it by means of the screws and nuts shown ; by this pressure the packing is caused to lay close against the rod, so as to prevent the passage of air or steam by it, whilst, being freely lubri- cated, it allows the rod to move with but little friction. As the packing wears away, the nuts are screwed down so as to keep the Joint air-tight until there is not suffi- cient of the material left in the box, when it must be opened, emptied, and re-filled. In small glands the bolts are frequently dispensed with, the part d of the gland having a thread cut on it so as to screw down into the stuffing-box. Various materials besides hemp may be used for stuffing, metal rings of a conical form, shown at JT, have been applied, also india-rubber, but for steam joints we certainly give the preference to gaskin. The object of introducing other packing material is to obviate the inconvenience of frequent re- packing. In using india-rubber packing we have found a great liability to cut longitudinal grooves in the piston rod. The length of the glands is regulated by the circumstances of the particular case, according to the amount of pressure to be resisted and the nature of the OF MACHINERY. 209 material used for stuffing ; if it be made longer than is necessary undue friction is created. For hydraulic machinery, leather packing is commonly used. / is the ram of a hydrostatic press working in the cylinder/. In the upper part of the cylinder is turned a recess in which is placed a leather collar of an inverted U section, having between its sides a copper ring to prevent its collapse ; this collar, shown in place at (/, is illustrated in section more clearly at