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Shaw Kitchen Gardening. G. M, F. Glennt. Cottage Gardening. E. Hobday Garden Receipts. 0. W. Quin Potatoes : How to Grow. J. Pink . Culture of Fruit Trees. M. Du Breuil Tree Planter & Plant Propagator. S. Wood Tree Pruner. S. Wood Tree Planter, Propagator, & Pruner. S. Wood Grafting and Budding. C. Baltet . Bees for Pleasure & Profit. G. G. Samson I/- 1/6 1/6 1/6 2/- 2I- i/e 12/- 2/6 2/6 2/- 3/- 2/6 2/- 2/6 12/- 2/6 2/- 2/- 2/- 2/6 3/6 I/- 3/6 3/- 1/6 1/6 1/6 2/- 3/6 2/- 1/6 3/6 2/6 il- CROSBY LOCKWOOD & SON, 7. Stationers' Hall Court, E.G. MATERIALS AND CONSTRUCTION MATERIALS AND CONSTRUCTION THEORETICAL AND PRACTICAL TREATISE STRAINS, DESIGNING, AND ERECTION OF WORKS OF CONSTRUCTION By FEANCIS CAMPIN, O.E. TAST PRESIDENT OF THE CIVIL AND MECHANICAL ENGINEERS' SOCIETY; AUTHOR OF "iron bridges, girders, roofs, ETC.;" "mechanical ENGINEERING," ETC., ETC., ETC. LONDON CROSBY LOCKWOOD AND SON 7, 8TATI0NEES' HALL COURT, LUDGATE HILL 1891 [All rights reserved'] PREFACE. In writing the present treatise, my object lias been to produce a work dealing comprehensively with the subject of materials and their use in certain branches of construc- tive art, viz. the massive works usually intrusted to civil engineers and architects, and throughout I have carefully avoided the introduction of the higher branches of mathe- matical investigation ; and in so doing I have not omitted problems of the classes usuaUy treated by high mathema- tical processes, but have substituted simpler, but equally convincing, lines of argument for the more abstruse processes of analysis. It wiU be found that algebraical arithmetic, or simple forms of equations, supply the basis of calculation, and this basis is indeed amply sufficient for aU the theoretical reasoning that is called for in the consideration of the practical problems engaging our attention. From the above remarks it will be seen that the work is designed especially for all those readers who desire to become thoroughly acquainted with the theories of struc- tures and the practical application of resxilts in the simplest way, and not as a mathematical exercise. It may be advisable to say a few words in explanation of the stress I lay upon the importance of this simplicity of calculation. I857I VI PREFACE. There are comiDaratively few of those entering upon g mechanical profession who are thoroughly accomplished mathematicians, and once launched upon the business oi life— or what is equivalent to it, the probationary term which precedes actual remunerative employment— the tyro wiU not desire to give time to the study of abstruse science, beyond the point where it ceases to be absolutely necessary for his purposes ; and there are many who have only learned these exact sciences bit by bit as they have found them necessary. Another matter of common consideration is, that even i^ those who have become proficient at school and college in pure mathematics, this knowledge, unless sedulously main- tained and reinforced by after-study, rapidly decays, and is often only with great difficulty revived ; and the time absorbed by this reinforcement or revival is generaUy required for the purposes of more directly practical study. Although all structures should combine in themselvesj both strength and stability, I have, for the sake of clear- ness, separated the two classes as far as can conveniently be done for theoretical investigation; showing, however, their necessary connection in suitable places. In the examples taken to illustrate the methods of calculation, I have carefully selected cases such as occur in every-day practice, and carried them through, in order to leave no doubt or difficulty as to the practical applica- tion of the formulge. In conclusion, I would add that this work is not intended in any way as an elementary introduction only to the science of construction, but deals fully and finally with all the subjects included in its syllabus. FEANCIS CAMPIN. CONTENTS. HAPTER I. — InTRODTJCTORY — CONSTITUTION OF MATTER — ELAS- TICITY — Internal Forces — External Forces HAPTER II. — General Problems — Moments of Force — Balanced Forces .... HAPTER III. — Bending Stress HAPTER IV. — Framed Structures . HAPTER V. — Adventitious Bracing HAPTER VI. — Deflection and Distortion CHAPTER VII. — Iron Arches . Chapter VIII. — Suspension Bridges /HAPTER IX. — Columns and Struts /HAPTER X.— Joints and Connections . Chapter XI. — Combixations of Girders /HAPTER XII. — Practical Application of Formula hiAPTER XIII.— Economical Proportioning of Structures /HAPTER XIV. — Stability )hapter XV. — Retaining Walls )uAi'TER XVI. — Arches — Abutments — Buttresses Chapter XVII. — Piers and Foundations ... Jhapter XVIII. — Building Materials /HAPTER XIX. — Execution of Work Vlll CONTENTS. Chapter XX. — Strength of Materials 236 Table 1. — Ultimate Tensile Resistance op Timber . 243 2. — Ultimate Resistance of Timber to Crushing 243 3. — Transverse Resistance of Timber . . 244 4. — Ultimate Tensile Resistance op Metals . 244 5. — Ultimate Resistance op Cast Iron . . 24o 6. — Ultimate Resistances of Building Materials TO Crushing 245 7. — Modulus and Limit of Elasticity op Mate- rials • iii6 8. — Ultimate and Working Resistances of Vari- ous Matekials . , r . . .247 MATERIALS AND CONSTHTJOTION. CHAPTEE I. INTRODUCTO-RY - CONSTITUTION OF MATTER -ELAS TICITY— INTERNAL FORCES— EXTERNAL FORCES The adaptation of the various materials furnished by nature, or elaborated from natural products, to the pur- poses of constructive art, necessarily requires a certain amount of practical and technical knowledge on the part of the constructor ; but it should not be imagined that this knowledge is of so special a character, or so intricate in its details, as to limit its attainment to a select few, and it will be shown to be based merely upon careful and persistent observation, whence are derived data upon which, by an ordinary course of reasoning, the technical principles are founded. In the present treatise I shall carefully avoid clothing the demonstrations and investigations which will occupy our attention in the language of high mathematics, and shall use such expressions as may be familiar to those who have not been specially educated to consider the subjects here dealt with. Ifc is obvious that the commencement must be made by an inquiry into the nature of the materials presenting themselves to our notice, and therefore we must consider the constitution of solid matter generally, in order to s 2 MATERIALS AND CONSTRUCTION. ascertain by what properties it is rendered available for constructive purposes, and bow these properties act in enabling it to resist external agencies tending to its destruction or deterioration. In using the term destruction, I limit its application to the destruction of a certain body, only in so far as it is rendered useless for some specific purpose to which it is applied. All so-called solid matter really consists of numerous aggregations of very small particles, each such aggrega- tion forming a molecule, and these molecules are of the same materials as the whole mass. If by mechanical means a solid mass be broken down into small particles, each particle is still of the same nature as the mass of which it formed a part— that is, its chemical composition is not affected. In the solid mass itself the molecules are not in actual contact with one another ; the mass is not really solid, but is full of pores, or interstices; so the particles are sustained at some distance from each other, this distance forming a characteristic of the material— thus lead is a close and cork an open material. That the molecules of matter are not in contact is evident from the contraction of bodies under reductions of temperature, or from the effects of externally acting mechanical forces. If a mass of matter at rest be acted upon in such a way as to distort its shape, and when the acting force is removed it resumes that shape, such a body is said to be "elastic," and it is by virtue of its elasticity that it recovers its normal form. If the original shape is exactly resumed, then the elasticity of the material is said to be perfect, and no disarrangement of its constituent molecules has occurred ; but if the elasticity is impaired, then a per- manent set or distortion has taken place, which may or may not alter the actual strength of the material according INTERNAL FORCES. 3 to the circumstances under which it has been brought about. Let us picture to ourselves the condition of the small particles, or molecules, as they exist when aggregated together in a mass of matter at rest. All the particles are standing apart in space, balanced at certain distances from each other by forces which must be of antagonistic natures, such as attraction and repulsion ; for, did attractive forces alone act, the molecules would be in contact, while under the sole influence of repellent agencies they would fly asunder and the mass assume the form of highly attenu- ated gas, expanding and spreading without limit. It is not my purpose to enter upon any inquiry as to the nature or quality of these forces or their origin ; it is suffi- cient for the present object to know from observation that they exist in various degrees of intensity in all the mate- rials used in construction, and that we can ascertain their relations to external force by experiment, and so arrive at data as to the inherent strengths of different kinds of material. When a body is at rest, the two forces must just balance each other, and so keep the molecules in equilibrium. These forces are called the Internal Forces. By the action of any external force upon a body the equilibrium of its molecules is disturbed ; thus, if pressure be brought to bear upon it simply, the internal attractive force is assisted in the direction of the pressure, and the particles approach each other in that direction, partially overcoming the repelling molecular forces, although these again may act laterally, causing the body as it shortens to become wider : on the other hand, a pulling force will aid the repellent forces and lengthen the body, but those repellent forces become weakened in their lateral action, and as the body stretches it becomes narrower. These are direct forces, producing stress upon material, and into n2 4 MATERIALS AND CONSTRUCTION. them all other forces must be reduced in order to compare them with the direct resistances of solids to distortion or fracture. It was discovered a long time ago that the amount of extension or compression a body undergoes — that is, its actual lengthening or shortening — is, if its elasticity be perfect, in direct ratio to the intensity of the force pro- ducing it ; thus, if 1 0 tons will lengthen a certain piece of iron by one ten-thousandth part of its original length, then 20 tons wiU leugthen it by one five- thousandth part, > and so on. For purposes of comparison and calculation it is neces- sary to have tabular numbers to give the elasticity of the various materials ; for this end certain co-efficients, as they are called, have been thus determined: — Let the weight required to produce a certain measurable elonga^ tion of any given material be determined, the body ex- perimented upon being of equal dimensions throughout its length, one inch square and perfectly straight, with the weight so adjusted as to act accurately in the direction of its length. Then multiply the weight by the original length of the bar, and divide the product by the extension of the bar under the influence of the weight. The quotient is called the " modulus of elasticity " of the material, and is the weight that would, were such a thing possible, stretch the bar to twice its original length. The "modulus of elasticity" having been once deter- mined, it is easy to calculate the extension or compression of a body of given length and sectional area under any given stress, as we have only to multiply the length by the strain per sectional square inch, and divide the product by the modulus of elasticity ; as, acting through short dis- tances, the elastic resistance to compression is measured by the same modulus as the resistance to extension. I wiU now consider generally the action of external EXTERNAL FORCES. 5 forces that do not lie directly in tlie line of the internal resisting forces, for it will presently be found that it is with this class of strains we shall principally have to deal in regard to structures of all descriptions. In Fig. 1 let A B C D be a side view of the layers of molecules forming a beam supported at the points C D ; the material being supposed to be imstrained, the mole- A OOOOOOOOOOOOOOOOOOOOO B ooooooooooooooooooooo OOOOOOOOOGOO oooooooo o ooooooooooooooooooooo ooooooooooooooooooooo ooooooooooooooooooooo Q ooooooooooooooooooo cules will be uniformly arranged as indicated by the dots. Now let a force, W, be brought upon it so that it becomes bent, then it will assume the form shown by the diagram E F G H, where G and H are the points of support, which react upwards with a total force equal to W acting down- wards. It is evident that the molecules in the upper layer, E F, are crowded together by the change of form, whilst those in the layer G H are stretched apart ; the layers next to these external ones undergoing similar changes in a less degree, until at the layer I K there is neither crowding nor stretching. There will be compres- sive strain on the concave side then, of the beam and 6 MATERIALS AND CONSTRUCTION. tensile strain on the convex side, and the beam will endeavour to regain its normal form by the repulsion of its molecules, m, on each other, and the attractions of those, m', tending to restore each vertical layer, m m', to its original vertical position, by revolving it about a point in the layer IK. I K is termed the neutral layer, or neutral axis. This illustrates the internal resistances of a beam to bending as a number of pushing and puUing efforts acting along the two arms of a lever, those of opposite kinds being on opposite sides of the fulcrum. The intensities of these elastic resistances and their effects will be exactly ascertained when treating of the behaviour of materials subjected to bending or transverse stress. When material is placed between two edges so that on their being pressed towards each other a tendency to sever it arises, the strain is known as shearing strain ; this occurs on the rivets joining plates on which longitudinal forces act : a diagram will clearly illustrate the manner in which this stress acts. In Fig. 2 let A and B be two edges acting upon the opposite surfaces of the body E F in such a manner as to shear it along the line c d. The A/^ic action tends to force each mole- o o 000° 0000 cule downwards, and away from ^ oocoo°°°°° ^ ^"^^^ opposite it, and the result 00000°°°°° will be different according to the 0000 0-^° 000 o d !^^^ nature of the material. It may ¥ B happen that as a layer of mole- Fig. 2. cules is forced down from the op- posite layer, in coming opposite the layer next below, it will be attracted by that with sufl&cient force to maintain the continuity of the mass, if the shearing force be now stopped. Such a case is ex- COMPRESSIVE STRAIN. 7 liibited by lead ; but if this does not occur, the mass will Tbe divided at c d, and the molecules having been forced asunder, it is evidently tensile stress that has been called into action ; therefore, we should expect the shearing resistance of a body to be for equal areae equal to its tensile resistance, and this is found to be the general rule in non-crystaUine matter. The failure of bodies under compressive strain occurs in several different ways. If the member acted upon is not absolutely straight and of equal resistance per square inch in every part of any given section, it will give way by bending or crippling, without being actually crushed ; and when it so happens the con- vex side wiU be in tension and the concave in compression, the same as in a beam under transverse load. As it is commercially impossible to secure homogeneity or uni- formity of substance throughout the materials we use, it follows that failures under compression must, in elements of any length compared with their breadth or thickness, occur in the manner just described. In dealing with this question we are at the outset met by the difficulty that we do not quite know how the work will break, for it may be by transverse bending, or it may be by a process of crushing or splitting, and this will depend not only on the nature of the material, but also on the cir- cumstances in which it is placed. It is very seldom that an actual flattening out will occur practically. In Fig. 3 the methods of crushing are shown at A ; the upper part has wedged asunder the lower, and here there evidently are in action both shearing force along the faces of division, and tensile stress on the parts forced open. In fracture, as shown at B, shearing stress alone seems to come into play, but the angle wiU depend upon the qualities of the ^iiaterial experimented on. The calcula- Fig. 3 / 8 MATERIALS AND CONSTRUCTION. tions used in determining the proportions of columns and elements subject to compressive stress are of an empirical nature, being derived from extensive series of experiments. It is impossible to examine the internal action of the external forces without being struck by the manner in which every kind of force seems to incline towards conver- sion into tensile stress on the molecules, and it must always happen that rupture ultimately occurs by these molecules being pulled or driven beyond the limits of their spheres of mutual attraction, for so long as they remain within those spheres they cannot be separated and fall asunder. When bodies are distorted, and so kept for a length of lime, there is observed a tendency of the molecules to rearrangement by equalising the internal strains, and the less perfect the elasticity of the material the more exten- sive will be the adjustment thus occurring. Passing: on beyond the limit of elasticity of a material, we may yet stop short of actual rupture, but the integrity of the substance will have been invaded, some permanent distortion will have been caused, and consequently we may assume that a proportionate amount of damage has been done. I would here warn my readers against the abuse of the term " permanent set," as it is applied commonly to effects which have no more similarity to that which it really means than has the lightest stress to absolute fracture of material. Permanent set, in reference to structural details, means, actual molecular alteration in the internal arrangement of the substances acted upon, and it is incorrect to apply it to any other effect. The most common misapplication is as applied to the permanent subsidence of works due to the joints falling into their bearings, and defects in the mode of erection ; but some folks have even gone to the extreme of applying the term to the deflection due to a permanent load, wliich really should be called the permanent deflec- ELASTIC RESISTANCE. 9 tion. I have thought it desirable to allude to this matter, as nothing tends more to confusion than the slovenly mis- application of technical terms. It is evident that the limit of elasticity cannot be exceeded with impunity, and practically a sufficiently wide margin of strength must be left. It seems only reasonable that the working strength of material should be taken in some pro- portion to the elastic limit of resistance and not to the ultimate resistance of the material, but up to the present time this latter ratio has been the guide almost universally. In some substances, however, it must be remarked the range of elasticity is so extremely small as not to be ob- servable, as in some kinds of stone, brick, &c., and the material appears to give way without previous alteration of shape, although we know that some such alteration must take place before the normal arrangement of the internal forces can be altered. As to the factors of working strength to be used in practice, I shall give those under the special headings of the various descriptions of constructive details upon which they bear. The resistances offered by structures to disturbing forces may be put in two classes : — 1st, the resistance due to the strength of the material — that is, to the cohesion of its con- stituent molecules ; this is properly called the strength of the work. 2nd. The resistance offered by the dead weight of material, which may operate in opposition to an overturn- ing effort, or to a force tending to slide its mass bodily on the surface on which it stands, or to both combined ; this resistance is the "stability" of the work. In the first form the force is directed to overcome gravity hy causing a body to lift and revolve about one of its edges until the centre of gravity falls without such edge, when the mass wiU altogether upset ; in the second, the b3 10 MATERIALS AND CONSTRUCTION. resistance to be overcome is that of the friction of the mass on the surface upon which it rests. I will here point out the nature of the resisting force of friction between surfaces. The surfaces are taken to be physically smooth and free from viscosity or any special property of attraction for, or repulsion of, each other. On account of the elasticity of matter, it follows that if a body rest upon another of larger surface than its surface of contact, it wiU to some extent sink into it, compress- ing the parts immediately beneath; hence, if the upper body be pushed along, it must as it were be pushed into a higher pa/rt, which, in its turn, sinks under the weight imposed upon it, so that virtuaUy, in moving the upper body, we are constantly pushing it uphill. As time is required for a substance to be compressed, it is evident that if the upper body be moved rapidly upon the lower it will not at any time sink as much as if it were allowed to rest on one spot ; hence the friction at starting, which is the friction of rest, is greater than the friction of motion ; and the friction of slow motion will be greater than that of rapid motion, so far as the surfaces themselves are concerned. The friction of surfaces, when the pressures upon them are slight, compared to what would be required to injure them, are taken as certain fractions of the insistent pres- sures, regardless of the areas in contact ; but it is evident that regarding the matter strictly, there should be some variation with area of surface exposed to a varying pres- sure: this, however, does not seem to be of suflQ.cient magnitude to demand practical consideration. Having determined the properties and capabilities of the materials at our disposal, it follows to consider the best modes of applying them for economic purposes : to arrive at these, the nature of the forces presenting themselves as acting upon structures and machinery must be carefully FRICTION OF SURFACES. 11 ascertained, in order that means may be taken for so con- trolling their directions and modifying their intensities, that our materials may be brought in the most advantageous way to oppose them. We have, then, this general problem to be divided and specially applied in each of the numerous cases that arise in every- day life. There are two numerical values or sets of quantities, which must be made equal to each other; they are the action and reaction of mechanical equilibrium, which can only be obtained by the opposing of opposite and equal forces, or of a number of forces that may be divided and resolved into two opposite equal forces. In the question before us, one set of forces is that due to loads, pressure of wind, and other external forces ; and the other consists of the resisting internal forces of the structure, or of its gravitative elfort, or its resistance to sliding, or the sum of any of these separate modes of resistances CHAPTEE n. GENERAL PROBLEMS —DIRECTION OF A FORCE — MOMENT OF FORCE-EQUILIBRIUM OF FORCES- SUBSTITUTION OF FORCES. The direction of a force is a straight line : we cannot speak of a force as moving in a curve, and the direction of a force at any moment is the direction in which it is then acting. If a force in action does not exert itself directly upon some body, but acts about some point as a fulcrum, then the intensity of the force multiplied by the distance at which it acts from the point about which it acts is called the "moment" of such force. Any form of simple lever exhibits two of these moments acting in opposition to each other, and by employing the method of calculating by moments all cases of forces acting about a centre may be dealt with. The distance at which the force acts from the point is the least distance from that point to the direction of the force under consideration. In Fig. 4, let the straight line a b represent the direction of a force P, and let it be acting about a point at c. If necessary, produce ^ Jed direction a I * r " to d, and from c draw the i straight line c e ai right ! angles io ah d: then c e will be the distance at ^- which the force P acts about the centre c, and the moment of such force will be Pxc (?. If P=4 tons and like that shown in Fig. 12, the Pig_ 12. moment of resistance will be found by first taking that of the whole area enclosing the section, and then deducting the moments of resistance of those parts that are away, thus: — _ s'. h'. d'^ _ s. h. d'^—sb'd' ^ MOMENT OF RESISTANCE. 25 -J5 n -which s' = the strain per sectional square inch at the J' distance - from the neutral axis, which is to s as d' is to 2 If the difference d d' is very small compared to d, it may be near enough for practical purposes to consider the moment of resistance of one of the parts shaded in the figure as equal to its direct resistance multiplied by the f distance of its centre of gravity from the neutral axis, and if the centre vertical member is of small proportionate area, it is neglected in determining the resisting moment of the section. I wiU take a fair practical sec- tion of such a beam, to see how near the truth the a]3proxima- tion will be. The external por- tions are 15 inches wide by 1 inch thick, the angle pieces being 3 inches along the back of each limb by ^ inch wide, and the vertical element \ inch wide. This latter by the first method is neglected in the calcu- lation. Determining the centre of gravity of the section as before, we have, taking the upper boundary as the axis of moments — 15 XlX 7-500 6 xiXli = 3-750 2|-XlX2|- = 5-875 17-125 = moment of area 20'5. 17-125 = 0-835 inches, 20-5 .vhich, deducted from 20 inches, half the depth, leaves 19-165 inches for the distance of the centre of gravity of the area a h from the neutral axis. This area is called the 0 36 MATERIALS AND CONSTRUCTION. area of the flange, the top and bottom elements of the beam or girder being known as the flanges. Taking the working strain at 4 tons per square inch, the sum of the moments of resistance of both, the flanges will be — 2x 19-165 X 4x20-5— 3143-06 inch tons. This has to be compared with the moment of resistance found by exact calculation from the formula— _ s h d'—s b' d'-'—s" b" b'" d'"' 6 The values of the second, third, and fourth strains must first be found ; they wiU vary with the values of dr— d' ,t dl' ,„ d" d d d Eeplacing the s, s", &c., by their values, we have 0 \d d d d I whence — ^=6^ • (l5x(40)'-8-75 X (38)»-5x (37)2-1 X (32)') = 3213-95 inch tons — being somewhat in excess of the approximate figures. It should be noticed that if the working strain is taken at the centre of gravity of the flange, that of the fibres beyond that point is somewhat higher; not that this usuallv is of any practical importance, but still no matter should be overlooked in dealing with questions of principle. If in the two flanges we are using different materials, so that there is not the same strain per sectional square inch on both, then this discrepancy must be made up by varying the areas of the flanges in order that the total ,i*sistanco shall be the same. If, hQwever, homogeneous material is used throughout NEUTRAL AXIS. 27 the girder, and the flanges are not of equal area, they will adjust the internal strains so as to produce equal moments of strain about the neutral axis, which will be at some intermediate point depending on the ratios of the areae. For example, let a girder have one flange 3 inches by 2 inches, and the other 12 inches by inches, and let us assume the elastic resistances to tension and compression equal per sectional square inch ; that is, that the modulus of elasticity is constant for both extension and shortening. The depth of the girder shall be taken as 20 inches, and the web omitted in the calculation. Let the distance from the centre of gravity of the top, which is the smaller flange, be X from the neutral axis, and that of the bottom or larger flange y. If s = strain per sectional square inch on the top flange, that on the bottom flange will be equal to s multiplied by the area of the top and divided by that of the bottom flange. The neutral axis is seen to be the fulcrum about which the moment of strain in one direction and the two moments of resistance in the other act, and it must so adjust itself as to suit the equilibrium of the three forces. This may be illustrated by considering the forces to act on the angles of a frame, as shown in Fig. 14. ale represents the frame, h e being in the position of a sec- tion of the beam, having the neutral axis lying somewhere between I and e, and it must occupy such a position that under the three forces given the frame shall be at rest. We know the mm of the moments of resistance, because that must be equal to the moment of strain, and the moment of strain is given, being W miiltiplied by the distance of its direction from the verticalline h e, and as its o2 28 MATERIALS AND CONSTRUCTION. direction is vertical, the position of the neutral axis higher or lower on i e will not alter the moment of force. When the force W begins to act, it pulls the point b and thrusts e, the amount of relative travel of these points depending upon the resistances offered by them ; but when equihbrium is established, the gross stress T must equal the gross stress C ; for if we regard the moment of W acting about C as a fulcrum to produce direct strain at T, or about T to produce direct strain at C, the result is the same as regards magnitude of the resulting direct strain, for in both cases the moment of strain is divided by b e, the depth of the girder. In the case taken the arese are as 3 to 1; hence the strains per sectional square inch will be in this ratio, and this will also be the ratio of the distances of the centres of gravity of the two flanges from the neutral axis ; hence x=15 inches and y=5 inches, and this places the neutral axis in the centre of gravity of the entire section. We can always then readily find the position of the neutral axis by determining the centre of gravity of any section with which it is necessary to deal. The moments of resistance for the above section will be for the top and bottom flanges respectively, a Sx2xsxx and 12xr5x g Xy, and the total moment of resistance is 4 =:6x4x 15 + 18X3X5=360+120=480 inch tons. If this be accurate, it should be equal to the moment of resistance of the top flange about e, or of the bottom flange about h ; the former is found to be 6x4x20 = 480 inch 4 tons ; the latter 18 x g X 20=480 inch tons. I will now collect together the three formulse for deter- mining the moments of resistance as ascertained above. For a form of section symmetrical in respect to the CANTILEVERS. 29 neutral axis, such as that shown in Fig. 13, the general expression assumes the form — M I ^ f r 11^ M=- — 3« h"^^ where there are n spaces to de- duct from the total moment of iresistance of the circumscribing section. In an unsymmetrical section, like that of Fig. 15, o o, the neutral axis, is at the centre of gravity, and h is the greatest distance of any fibre from it; B bhen— Fig. 15. 3 If we are taking the flanges only of the girder, d being oaeasured between the centres of gravity of those flanges, md A = area in square inches of smaller flange, M=s . A . d . Having investigated the nature and action of the internal resistances of the material, that of the external forces next pre- sents itself, and this I shaU treat in detail for the various forms in which it occurs, premising that in this chapter beams either of solid section throughout, or at least having a continuous web, Fig. 16. will alone be dealt with. In Fig. 16, A B represents a beam or cantilever, one ■l- 30 MATERIALS AND CONSTRUmON. end of which is fixed into a wall, the other end supporting weight, W. I is the length of the heam, measured from the wall to the point of attachment of the weight W. The moment of strain about any point will evidently be equal to the weight multiplied by its horizontal distance from that point ; so if the point be distant x ft., the weight being in tons, the moment is — M=W« foot tons ; if x=l, M=W^ foot tons, which is the maximum strain that can come upon the beam, as I is the greatest value to which x can attain. At A, the point at which W is attached, the moment of strain is nil , but there it commences, and gradually increases to the point of support. As the strain thus varies, so the section of the beam may be varied to meet it. Equating this moment of strain with the moment of resistance of the flanged girder — M=Wa;=« . K . d A=^^-^> s . a whence the other quantities being given, the necessary sec- tional area of flanges is found. The beam may be adapted to the varying strain by varying either its area or its depth ; but this question will be dealt with subsequently, after the theory of the external forces has been fully discussed. Throughout the ensuing cases the moments of strain will be equated with the moment of resistance of the flanged girder, that being the description almost invariably used for beams of any magnitude. At C D, Fig. 16, is shown a similar beam fixed at one end, and carrying a load uniformly distributed along its length (such a load might be its own weight, or a wall, &c.). Let the load be w per foot of length. The moment of strain is required at any point distant x from the free end, C, of the girder. The load affecting this point will evidently be that part of the whole load which is between the given point and CANTILEVERS. -31 the eiid of the beam; this length being x ft., the load upon it \s,wy.x, and this load being symmetrical in form, may be regarded as concentrated at the centre of its length, which is its centre of gravity, and is horizontally distant | from the given point at which the moment of strain is sought. There is then a load equal io w ,x acting at a distance ~ ; hence the moment of strain is — M=^.:rxJ-.^/,ifa;=U^=^-^, 2 2 2 and — M=^-r^-=«.A.e?.-. A- 2 2 . s . <^ The action of the load in producing strain upon the flange may be pictured to the imagination by supposing 0 w w to be a bent lever acting about the fulcrum m, having at one end, o, the pull of the load, and at the other the elastic resistance of the material of the flange. In the first case the horizontal arm of the lever is x, and the vertical d ; and in the second, the horizontal arm is and the vertical 2 arm d. As the strain increases as a?, and I is the greatest value of X, the maximum moment is when x—l. The rate of increase of strain differs in the two eases, being in the first as x, and in the second as xK If the two loads occur at once, the resulting moments of .strain must be added together to get the total moment : tlien — and as a general rule, where a number of different loads come upon the same elements, their effects may be calcu- '32 MATERIALS AND CONSTRIJCTION. lated separately for any given point, and th.e moments thus iound added together far a resultant total. In Fig. 17 are shown some beams variously loaded, each beam being freely supported — that is, the ends are not fixed down to the beds — at each end. In the case of A B the load W is at the centre of the span I. Now the load on a beam is carried by the sup- ports, and from the elastic nature of ma- terials, it imperative- ly follows that these points of support must be compressed by the superincumbent load, such compression continuing until the elastic resist- ance or reaction is equal to the load pressing downwards ; and as the load does press vertically downwards, so the re- action of the supports must press vertically upwards against the ends of the girder. Where the load is in the centre of the span, it is evident that it will be carried only half on each support ; hence the W downward pressure on one support is and as the reaction must be the same, the upward pressure of the support is W 2 ■ The moment of strain, then, at any point distant x from the nearest support, is this reaction multiplied by the distance at which it acts, that is, by x, giving — B D c X-t- E F t-V-t-o/ — f «--ac--. I :: ^ -* 7 H -1 Fig. 17. GIRDERS. 33 But if tlie calculations be continued, with x carried on beyond the load, so that it is not measured from the nearest support, then there will be two moments to deter- mine, for beside the upward force of the reaction at the support, there is the downward force of the weight W to consider. Let the point m be in such a position, and distant X ft. from the support A. The distance of m from B will be l — x, and the distance of m from W will be half the length less this distance, or ^—i^—xjz=.—^-\-x, or «— ^' which is the distance at which the weight W acts about the point m. Calling the forces acting downwards plus or positive forces, and those acting upwards minus or negative, the expression for the moment about m becomes — but the difference between x and I is the distance from m to B, the nearest support ; hence this formula corroborates the former, for measuring from B, we replace the x — / by — 05, and obtain — 2 ' the minus sign coming in as the upward forces are called negative ; but of course this does not affect the numerical value involved. By adopting some such system as this and adhering to it, the nature of the strains on the flanges will be indicated by the sign in front of the formula ; thus in this notation a minus sign indicates that the bottom flange is in tension and the top in compression, the beam being so bent down- wards that the under side is convex, and the upper concave. This notation will bo retained throughout the work. 34 MATERIALS AND CONSTRUCTION. C D shows anotlier mode of loading, there being a con- centrated weight at some point not at the centre of the span. The first step is to determine the reaction on the support from which x is to be measured. Let C be the support chosen, and the weight W be distant y ft. In order that equilibrium may be maintained, the moment of the weight W about the point D must be equal to the moment of the reaction on C about the same point, the former being plus and the latter minus in sign ; the distance at which W acts about D is I — y, and the distance at which E, the reaction, acts about D is / ; hence the moments are respectively — -Ex /and W^Z-y^ or-E; = W^;-y^ -R = W(/-y) . and the moment of this reaction about any point distant x {x being less than y) from C = — Ea; = — M = Q~y \^^ I s . a . I By taking a case where a? is greater than y, the formula will be proved as was the last, but the process being pre- cisely analogous, I shall not here occupy space with it. At E F another special kind of loading is shown, and one which is of importance, as it occurs very commonly in practice. Here there are two equal weights symmetrically disposed in respect to the centre of the girder. This being the case, the loads on, and the upward reactions of the two supports will be equal, each being equal to one of the loads, W. Let the distances of the loads from the ends of the girder be y in each case ; then, if x = the distance fi'om the nearest support to a given point between that support and the weight nearest it, the moment of strain will be GIKDERS. 35 M = — W . a;=5 . A . A = — ^^-^^ ; 8 . a and this moment -will go on increasing as x increases, until x=y, and if it be taken at a higher value still, then there ■will be two moments to deal with. Let a;' =y+ a, then because a is the distance at which the weight W acts downwards about the given point, but W«-Wa;'=:Wa-W (y+a)=W . {a-y—a)-—^y. Hence the moment of strain cannot exceed W y, and will remain at that value for all the length of girder between the two weights W. The reason is found by inspection to be that whatever quantity above y is added to the distance at which the reaction acts about the given point, such addition will be the distance at which the weight itself acts in the opposite direction about the same point. Here then is a case where the strain on the girder is not affected ly the value of the span of the girder— which, will be found unique. In the fourth case, G- H shows a girder having a number of concentrated weights upon it, scattered irregularly along its length, and being of various values. Let the weights be represented by W, W", &e., W placed at distances y', y", &c., to y" along the girder. First the total reaction on one support must be determined, and then any given point being known, the weights between such point and the support chosen will have plus moments, the re- action of the support of course giving a minus moment. The moment of the reaction of the support must equal the sum of the moments of all the weights about the other support, of course with the difference of signs, thus — ~nl=W'{l-y')+^Y"{l-y")^ .... +W(/"-/) W(l-y)+Wil-y")-\- . . .. +W'X^-y'') 66 MATERIALS AND CONSTRUCTION. and the moment of strain at a point distant from the chosen support will be M=W\f-i/')+W"(f-f)+ .... +W"-'(y"-/-0 The intermediate moments may be found from this expres- sion by replacing 3/" by x, where x exceeds y"-', but does not exceed y*. As the Ws and the y's do not follow any law in their changes, this formula must be worked out in detail from the quantities occurring in each particular case. The maximum strain has not yet been determined for the case of A B, where the load is central ; hence it will be necessary to return to it. It is observed from the formula M=— that up to the centre of the span the load increases as a;; it remains to be seen what will occur when X — more than i , and when two moments must be dealt with. Let tc'='--\-a, then a will be the distance at which "W M acts downwards about the given point, and the resultant moment of strain will be M=W.«-^^=W.-Y(| + .)=W(.-P_) whence it is evident that the arithmetical value decreases as a increases, or, as soon as the value x — ^ is passed, the moment of strain diminishes ; hence the maximum strain is when x—^-, and 2 M=-^f =~F_u. A. d. .-. A=:- 2 A A.H.d. GIRDERS. 37 [t will be observed that in tlie expression - — -, a can 4 2 lever exceed |, and consequently the highest value of a jives I a_l I _ 4 2~4 4"""' The strain is —o at the support B. The second case, 0 D, now requires examining as to the point of maximum strain. It is evident that the moment of strain continues to increase as x increases up to the ralue Now let x'—y-^a, then the moment of strain M=W a- ^^^-y^^ = W a-'^l-y\y+a)=Wa _ yf{l-y)y _ W{l-y)a I I ' From this we may observe what will be the effect of acreasing the value a. In the first term, W a, the term acreases as a increases, and in like manner the third term acreases as a increases, but is less than unity, there- are '^i^—V )^ ^^^^^ always be less than W a. The ratios f the two quantities being constant, the absolute differ- nee between them will increase, so that after passing the oaded point the minus strain will continually diminish owards the support D ; this diminution will continue until ) is reached, when a-=-l—y, replacing a by this value. I I lere being no strain over the points of support. From this it is evident that when a beam is loaded with 38 MATERIALS AND CONSTRUCTION. one concentrated weight, the maximum strain will be at a point directly under that weight. Let AB, Fig. 18, represent a girder supported freely at A and B, and loaded with a weight of ic tons per lineal 'mmmmM B A <---X\ >■ r 2 — > Fig. 18. foot, uniformly spread over its length. The strain is required at a point distant x from the support A. There is the portion of the load between the given point and A acting downwards, or positively, and the reaction of the support A acting upwards, or negatively. As the load is uniformly distributed along the length of the girder, it will be equally carried by the two points of support. The reaction of either support will therefore be ^ w.l and this reaction will act at a distance x about the given point. The downward force will be the portion of the load on the length x of the girder, or lo x, and this beinj considered as concentrated at its centre of gravity, will ad at a distance - about the given point. Taking, then, the difference of the moments, the resultant is X 10 L, tvx"' 10 I x -s. A. d •. A=- iO 2. s. d {x^-lx), considering the variable part of the expression x-—U will lead to the determination of the point of maximiin strain. TRIANGULAR LOADS. 39 When x-o the strain =o at A, and when x=l the equation becomes P—P=zo and the strain =o at B ; hence there is an intermediate point, at which the strain is a maximum. The loading being uniform (and symmetrical), the in- 3rease of the strain will be in the same ratio from the end B as from the end A, and the maximum strain must occur, therefore, at a point equidistant from both supports, which is at the centre, when x=l and 2 2 2 8 ~8 ^' ■ ~~8.V^' rhe total load is ^=w I, so that M:= — — as against — 8 N I when the weight was all at the centre, whence it tppears that the maximum moment of strain due to a niformly distributed load is one-half of that due to the ame load concentrated at the centre of the span. 40 MATERIALS AND CONSTRUCTION. AB, Fig. 19, represents a girder carrying a load dis- tributed in the form of a triangle : this case is a very important one, as in practice it constantly occurs when the girders of a bridge do not lie square to the abutments, as shown in the plan ah, c d. The road under the bridge runs obliquely to that over it. The bridge is carried by cross girders, e, resting on the main girders ah, cd, and it may be observed that the main girder carries a triangular loaded area, which is shaded in the figure. The load per lineal foot will not be the same throughout the length of the girder, but will vary with x, and in direct ratio to it. Let w)'=the load on the first lineal foot, then at the dis- tance X the load per lineal foot will hew'x; hence the load on a part of the girder extending from the support A to the distance x wiH be w x\ and this load being triangular 2 x in disposition, wOl have its centre of gravity -g- from A, so that the distance at which it acts about a given point at x from the support A is |, thixs making the positive moment , ^ X of strain w x-y.-^- The total load on the ^rder is w' P, for as the load up to any point distant x from A =w' x", the total load is found by making then it is w' x'^w P ; and as the centre of gravity of this load is | from the support B, the moment of the total load about B is w' The moment of the reaction of A about B is — E X ^ ; hence the reaction is — au(l its moment aboTit the giveu point is tliis quantity TRIANGULAR LOADS, 41 multiplied by x ; the resultant mgiUjgnt of strain on the beam is — AT _ ^2 V ^ T? ^ '^'^^ ^' ^ f ■>. n \ A 7 M- — WX X K. ;r=-— — = (a^_?2ar) = g. A. In this case the arese for different values of x must be calculated out for the whole length of the girder, which will not be sy mm etrical in the distribution of strains from each point of support. In the girders symmetrically strained it is sufla.cient to calculate the strains for one half, as the two halves have similar strains upon them. It wiU be interesting to ascertain the point of maximum strain. The strain continues to increase up to the point of maxi- mum strain, and then to decrease according to the formula w' — [a^—p x) ; that is, in the same ratio as ai^—P x. Now, as there is a point at which the strain ceases to increase and commences diminishing, it may be imagined to remain stationary for indefinitely slight variation of x at that point. Let x'=. distance from A corresponding to point of maxi- mum strain ; let a be an indefinitely smaU increase added to X ; now, if the strain remains the same, the numerical value of the increase of the first term must equal that of the second P x, in order that their difference may not be altered. As x becomes x'-\-a, the first term wiU be {x'-\-af = x^-\- 3x'^ a -f 3x' + a^; but as a is taken very small, Sx' a- will be very insignificant compared with 3x'^ a, and less stiU; hence these last terms may be neglected, leaving 3x'^ a as the amount to be added to the first term in — P X. The second term then becomes — I- (x' + a) = —{Px' + Pa); here the addition is P a, and this must be equal to the addition 3x'^ a if the strain is unaltered, thus — 42 MATERIALS AND CONSTRUCaiON. 3^'= a = I' a .-. Sx- z= P, —~, X— ^. = 0 o77 I, 3 \/ 3 and the maximum strain is — M = I' -Px) = |"'^(0-5v7 = 0-1283 w' P s. d It is unnecessary to consider the cases of partial loads, as in practice the total loads are required, for the structure must be proportioned to sustain the maximum strain, and this covers all beneath it. These beams have all been treated as freely supported at the ends, in which circumstance the intensities of the strains are quite independent of the material or form of the girder, but if the- ends be not free a striking difference is observed. Let the values of M be calculated for a series of values of X, and laid do^vn as shown in Fig. 20. A B is a line !«- OC » M — —■ TV Fig. 20. representing the length of the beam, and on this line the various values of x are marked off from A, and the values of M, corresponding to those values of x, are at each point marked otf at right angles to A B, giving points of which one is indicated at 7i; by joining these points a curve is formed, which is caUed the curve of strain, and the lines showing the values of M are called ordinates to that curve. A geometrical investigation would show that for a uniformly distributed load the curve of strain is a parabola ; FIXED GIRDERS, -13 for a concentrated load the lines of strain bound a triangle, and so forth, the lines varying according to the description of load. If the whole area of the curve be taken and divided by its length, it is evident the average or mean moment of strain will be the result. As the area of a parabola is its base midtiplied by two- thirds of its height, the mean strain on the uniformly loaded girder will be two-thirds of the maximum strain. The use of these ciu'ves when plotted wiU presently become evident. In Fig. 21 let A B represent a beam securely F Kg. 21. fixed at both ends, so that the section at A is retained in a vertical plane, and the same at B. If, now, the beam be deflected, it wiU take a form A (^— 2z )'_ _wP ~ 8 24* The strains over the points A and B are each z'j^w {l-2z) ^ ^_wP_ 2 2 12 Suppose a case occurs in which the beam is ^xed at one end only, being freely supported at the other, then there will be one point of contrary flexure, and it will be the same as if we take the part Q cc of the beam G H. What then will be the relation of Gr c to the span G c c ? G o e = I — z 0-2113 J = 0-7887 and ^1^11^ = o-26. Or in this 0-7887^ case z = 0-26 /, where I is the length of the beam fixed sl\ one end and freely supported at the other. Lot us look at the first case from another point of vie^ to render the result susceptible to proof. Suppose thq beam first to be freely supported at A and B. Then the FIXED GIRDERS, 47 top flange will be shortened and the bottom one lengthened when the load is upon it, and will appear as shown in the sketch. To bring the ends back to a vertical plane, the Fig. 23. top flange must be as much extended as it has been shortened, and the bottom flange similarly compressed; but the strain to do this must evidently be equal to that causing the existing compression and extension, which is two-thirds of the maximum strain ; hence the moment to be applied over each support (they will act in opposite directions as action and reaction) will be — 2 'IV /- iv P 3 ~8 ~l2' Applying this to the general formula for strain at any point on a uniformly loaded girder, this new moment being positive, 12 '~2 ~2r which at the points of contra-flexure will be— ■»«- _ ,wx^ _wlx wx^ wlx _ w? U'^ 2 ~r''-'2r~~2 12"' whence x'^ — I x z=. being the same equation as resulted from the former entirely diflPerent mode of reasoning. It is observable that accuracy here depends upon whether the material is homogeneous throughout, for if its 48 MATERIALS AND COXSTRUCTIOX. modulus of elasticity be not constant these results will not be strictly attained. So much for the uniform section, but the commoner case is where the section of the girder is not uniform through- out, but on the contrary is varied in proportion to the strain, so that the strain per sectional square inch is con- stant throughout the length of the beam. When the strain per sectional square inch is the same throughout, the beam will deflect in circular arcs of the same radius, and the points of contra-flexure will therefore occupy positions different from those assigned to them in the last case. In Fig. 24, let ab c dhe the line of beam under uniform strain. The radii e a,l g,c f being all equal, it follows that the arc ah ■= arc hi — arc ^■ c = arc c d, g h being drawn vertical and parallel to ae and df. Here, then, the distance from one end of the beam to the nearest point oi contra-flexure will be ~. 4 In this case the same test cannot be applied as in th( last ; for the area varying to suit the strain, we cannot re gard the beam in the first instance as merely supported and then brought into the position of the fixed beam, a e Fig. 24. FIXED GIRDERS, 49 the theoretical section being nil at h and c, the beam would not stand under the first conditions. As the effective span of the central part is half the total span, or ^, the strain at the centre wiU be 8 V2/ 32 32. and that at the point of fixture — ■Kir V. ^ V. ^ I V. ^ ^ ^wP . , . ?>.tol M = M'X-X-+w y.-Y.~—~-=s.K.d.-.K = ^ — - 4 8 4 4 32 ol.s.d.. The duty of the -web or central part of flanged girders will now require examination, for it does not act merely as so much of the beam under longitudinal strain only, neither can it be considered as bearing shearing stress alone, but there is a vertical crushing, or rather crippling, strain brought upon it by the tendency of the flanges to approach each other when the beam is deflected. Before the intensity of the strain thus called into action can be determined, a formula must be found for reducing a tangential force to its radial component. In Fig. 25, let A represent a ring one foot deep, its diameter being equal to D. Assume this ring to be subject to internal pressure (as from steam, for in- stance), acting equally in all direc- tions, and therefore pressing radi- ally upon the interior of the ring. Considering the tendency to break the ring at the points h e, we find the forces acting will be those con- tained on the plane h c, which. Fig. 25. acting from opposite sides of such imaginary plane against each other, tend to force asunder the hemi-rings h d c, h e c: h c ■=. the diameter ; hence, if P = the pressure per square foot, the stress on the 50 MATERIALS AND CONSTRUCTION. two parts h and c is P x D, and the proportion borne by one section i or c of the ring is P x ^, or the force per square foot multiplied by the radius in feet of the ring. From this it is evident that the tangential strain is equal to the radial strain multiplied by the radius, and this will apply to any part of the ring, for the points of strain might be taken at any other points than h and c, and moreover the strain on one part of the ring would not be affected were the rest cut away, provided the extremities of the part left are properly secured ; hence the general formula — if on a curved element the force acts radially to such curve, the strain along the element will be the force per lineal foot multiplied by the radius in feet of the element at the place where such force is acting. The web of the girder, acting to maintain the normal distance between the top and bottom flanges, will be sub- ject to a radial pressure corresponding to the stress on and curvature of those flanges. The total strain is the same for either flange, as has been shown pre- viously (page 28), and this strain, divided by the radius of curvature of the deflected beam, will give the force upon the web tending to cripple it vertically. In order to determine the relation of this force to the longitudinal stress on the flanges, the radius of the deflected beam must be ascertained. Assuming the beam to be so proportioned that its flanges VERTICAL STRESS ON WEB. 51 are equally strained throughout, let (in Fig. 26)l = aic = length of girder, d = bf= depth of girder, E =ea = radius of curvature, D = central deflection = d h, L = difference in length of flanges after deflection = sum of the extension of the bottom flange and the compression of the top flange. The deflection of a girder being so small in comparison with the radius of curvature, we may assume de = ae — E, and aoz=ialc = l. Then (Euclid, prop. 35, Bk. III.) because, if any two right lines contained in a circle intersect one another, the rectangles formed by the segments of such right Knes are equal, and the diameter 2 E is intersected TO at d by the chord a c, therefore 2'R J) ■=. a d x d c =~. 4 Because ad = do = i-and (jV=:~, whence D= — = 2 V2/ 4' 2 E X 4 Then by similar triangles E : : : Z : L, which we also know to be true because the circumferences of circles are in direct ratio to their radii, whence E + : fffh ::^:ahc, but hf= ah c -\- Ij, and U d : a b c + L : :B. : a b c whence, as a ^ <; = we find in either case E L = E = 'L\ But D = Jl ... E = i- , E = I- =11 D = ^1 L 8E 8D' 8D L 8 — 10 >) )» d + -1^0- 3 — 10 + 1^0 3 1 0 + 1% .3 — 10 + ^ + -fo 7 — 10" -t »> » + 1^0- + iV -A + ^6 4 Besultant load + 2-5 -1-6 + 1-5 -•6 + •6 + •5 -•5 + 1-5 -1-5 + TRIANGULAR GIRDERS. 69 Each of these resultants multiplied by to B will be the oad for the corresponding diagonal. We must now con- lider the strains on the flanges. The increments on the )ottom flange will be for the end bars 1 and 10, the strains >n those bars resolved vertically and horizontally, or to the B B itrains on the bars, as — at the other intersections as The strains on the diagonals will be to the loads as ^ ; lence from the table are found the latter as follows : — On 5 and 6, s = -5 w B X'^ = ^?}^ i 4 and 7 the lame but tension, as will be the case in each second pair of )ars; on 3, 8, 2, 9, « = 1-5 w B X ^ — ^ ^ ^ J^ . on 1 d 2d jind 10, « = 2-5 1^ B X ^ = AifL^. ^ ' d 2d On the bottom flange, on 11 and 15, « = 5 «gB L ^ B_ 2d 2L 6w>B' i„ 5«;B2,3m>BL B ; on 12 and 14, s = — Y r— X — = 4i' ' 4:d ' 2 d Jj .1«'B\ ^„ 11 t^; B« , «; B L ^ B 13 w; B* on i<5, 8 — — — . X 4^;' 4(?'2«? L 4:d ' Nq wiU check this by taking the moments : about the apex there is the reaction of A = ^ ^ by its leverage 2 2 Bss the downward moments of the loads at a and h, giving, rhen divided by d, for the strain on 13, s = x — - 2d 2 ' 2wB^ + tv B ^\_ 25 B' _ 12 w B^ _ 13 w B^ d ) 4 d Td Td~' The top flange must now be dealt with, where the in- trements are in two parts, one for that brought on by the liagonal, and the other for the additional load ; the process B very similar to that for the cantilever. 70 MATERIALS AND CONSTRUCTION. The portion of tlie increment due to the additional load will at each apex he = wB X -^^-5-= , > the other part 2 a 2 a B being equal to the strain on the tie multiplied by ^. The Li strains will be on the top flange, on 16, « — ^^^^ X 5--}- 2d Xj wB^_4:wB^ ^^.^ 4wB^ , M^BL^B , wB^ 2d — 27- ' * = ^2d~ +-2^ ^ L + irr= 2 d This strain is checked by taking out the moments about the apex g\ thus, « = ^ ^ x 2 B — 2 d \ d ) d~ ~d d It is found from the foregoing that the strains on the diagonals increase from the centre of the girder towards the points of support in an arithmetical progression, 1, 3, 5, &c., with a difference of two ; so that one strain on the^j central triangle being calculated, the rest can be set down, and from the numbers so obtained the strains on the flanges may be found. It is worthy of observation that in the top flange the numerical coefficient of the total increment at any inter- section is the mean of the numerical coefficients of the strains on the intersecting diagonals ; thus on 1 6 we find at a, co- efficients of 1 and 2 in the table 2-5 and 1-5, of which the mean is 2, and the increment lifL^^ showing a coefficient 2 d — 2, and similarly &t h e lA"^ ^ = l. 2 I will now take a case in which the same girder is used, but to be loaded at the bottom instead of at the top. Under these circumstances it will be found that the bars 5 and 6 will have no strain at all upon them, for the com- TRIANGULAR GIRDERS. 71 >ression on each due to the load at the foot of the other 8 nullified by the tension produced by the load at its own oot, therefore theoretically these bars might be abolished, >ut in a practical sense they are requisite to support the op flange, otherwise there would be an excessively long dement in compression unsupported: the strains on the liagonals will be, on 5 and 6, « = 0 ; on 4, 7, 3, 8, s = . B X ^- = i^^; on 2, 9, 1, 10, . = + !i^ = ^ ^ Where there is not a central loaded apex it ,ppear8 from this that the strains increase as 1, 2, 3, &c., rith a difference of 1. The increments of strain due to the strains on the diagonals rill be determined as before, there being in this case only hese on the top flange. On the bottom flange the incre- aents due to increments of load will come, this being the nly increment at g. The strains on the top flange will ben be — Onab, s z= _ x = — = — ; on i c, « = — + a Li a d ' ' ?^ X ^ = ^ ^ ^ . Checking this by the moments, s ~ a Li a t;Bx2B— wBxB __ 3 B bottom flange the da ° trams will be, on 11, s = — x — = ; on 12, d 21, d d 'd ~ ^ L + 2-d = -2 d- ' ' = -2T toB^ 6^^;B2 SwB'' nx. t • ^-u- v .-u - — — i- = — = — 5 — Checking this by the mo- 2d 2d d & ^ , 2m;B X 2-5B — m;B (1-5 + 0-5) B lents, we have « = — ■ ^ — d 3wB^ d ' 72 MATERIALS AND CONSTHUCTION. When the girder is uniformly loaded it will be seen that all the bars pointing from the centre downwards towards the points of support are struts, and those in the reverse direction ties ; but structures designed to carry such a load as this are often subjected to partial loads, which alter the nature of the strains on some of the central diagonals, and this must be attended to, in order that the bars there used may be made of sections suitable to resist compression, even though they are ties under the maximum load. Assume that on a girder (Fig. 34) consisting of nine triangles a train has run, as shown by the larger circles, to the triangle next to that at the centre, and let the full load of girder and train be 3 w per lineal foot, w per lineal foot being the dead load on the girder ; then there will be on n o n Q A \A/VW\ B 1 < — 2.5 h — >| c i Pig. 34. the five triangles nearest A, w B on each apex = 5 B, of which the proportion passing towards B, and therefore ■* . . 2'5 B in compression through the bar g, will be 5 B x - — j — ~ ifLlL On the four triangles nearest B, the load on each apex is 3«i;B = 12?fB in all, of which the part passing towards A, and therefore putting the bar g in tension, is 12 w B X ^ ^ t]^at the tensile strain is the greater, and under this position of the loac the bar g will be a tie, and the bar / will be a strut ; ju8 the reverse of their conditions under the maximum load. I have so fully worked the details of the examples givei LATTICE GIRDERS. 78 in order to avoid the chance of a doubt in the student's oaind as to the mode of procedure, and I do not think it aecessary to take further examples in illustration. If there is more than one series of triangles crossing each other, then, of course, the strains on the bars are pro- portionately divided. The most ordinary angles used in practice for the diagonals are 60 degrees to the horizon, T g when = 1*154, and - = ri54, and 45 degrees to the a a L L B porizon, when =1-414, and = 2. ] Co (t The forms in which braced structures may appear are endless in their variety, and each new arrangement will probably call for some corresponding alteration of detail in determining the strains ; but as the centre lines of the elements form bases for the parallelograms of forces, there cannot be much difficulty in working any form out when the rationale of the method has been once fairly grasped, although it must be said that diligent care must be used to insure against missing anything. There are, however, certain typical forms which it will be desirable here to examine, of which I shall now take that shown at Fig. 35, which is known as a bowstring girder. A is one of the supports, and the load is carried on the bottom member, or the string of the bow ; the loads on the different joints being indicated by w', w", w'" . The bow is formed of straight elements, or if, for appearance' sake, it is curved, a line ^rawn in any bay from the centre of one joint with a diagonal, to that of the other end joint, must keep well within the depth of the element, otherwise it will be subject to an undue bending stress. This structure, which is purely a braced girder, must not (because to the uneducated eye it bears some resemblance to it) be confounded with the tied arch, where the upper liurved member is a true arch, having its abutments held K 74 MATERIALS AND CONSTRUCTION. together by a tie, and in whicli the diagonal counterbracing (as will be shown subsequently) carries no part of the load, but serves to support the tie and distribute the load when unequal, so as to prevent excessive distortion of the arch. The diagram of the half-girder is drawn to a scale of four feet to one inch, and for the paraUelograms of forces BOWSTRING GIRDEK, 75 the scale taken is forty tons to one inch. In actual prac- tice a much larger scale would be taken, but we are here limited to space, and even at this scale very close approxi- mations to accuracy may be obtained by using a weU- divided diagonal scale. The top member of the girder comprises the bars ah, he, cd, and de; the bottom member, ef, fg, gh, hi; the diagonals are, ah, hi, h g, g c, of, and/y&. A load of two tons per lineal foot is supposed to be on the bottom member of the girder, so it may be considered as aggi-egated at the points h, g, and /, where it amounts to w' = 13-05 tons ; w" = 9-1 tons ; w'" = 4-85 tons. These three added together wiU = 27 tons, which is the load on and the amount of upward reaction of the support A, which, acting verticaUy at the point e, is to be in the first place resolved into strains upon bars ed and e f. Make e P = 27 tons, complete the paraUelogram eP QE, join e Q, then e E wiU equal the tension on e f, and e Q the compression on e d. Produce e d to o, making do = eQ; this strain must be carried by the bars df; produce fd, and com- plete the paraUelogram dp o n : dp wHl he th.e strain on do, and dn that upon the former compression, the latter tension. On fd mark off /T = dn, and from / draw the vertical Hne fl = w'" — 4-85 tons ; complete parallelo- gram fTkl, then fk is the resultant of the strain on fd, and the weight w'". Prom/markoff /m=«E, and complete the parallelo- gram /^/m; /y wiU be the new resultant, which must be carried by the bars fg, /t;— tension on the former, and compression on the latter; produce // to s, making = fj, and complete the paraUelogram rsfq;fr is the strain on fg, andfq that on fc. Again, produce detov, making ov = dp, and fc to f, making ct=fq; complete the paraUelogram c f v tv, then e u is the resultant of the strains on dc and fc, and is sustained by the bars cb E 2 76 MATERIALS AND CONSTRUCTION. and eg. Produce g c, and complete the parallelogram r.xuw\ then cx \% the compression on c I, and o lo the tension on eg. Make gy-cw, and from ^ draw vertically y 2 = w" — 9-1 tons ; complete the paraUelogram ^yBz; will be the new resultant, which happen- ing to faU on the hne of gh, will be borne entirely by that bar, putting no strain on ^ 5 ; the total strain ough z=^fr + g B. Again, produce c J to D, making 5 D = c a? ; produce h h, and complete the paraUelogram J E D C, then h E will be the strain ham compression, and I c the tension on h h ; make A I = 5 C, and draw h L vertically equal to tv' = 13-05 tons; complete the parallelogram A L K I, then hK wiU be the resultant of the strain on h b, and the weight m^'. Make A V =/r +^B, and complete the parallelogram A K J V; J A will be the new resultant, to be carried by the bars h i and h a. Produce J A to N, making A N = J A, and complete the paraUelogram 0 N M A ; A 0 is the tension on hi, and AM the tension on Jia. From a mark off aP = I E, and complete the paraUelogram H P G making H P horizontal ; then, if the diagram has been accurately worked out, H P = A 0, and a H = M A. That being so, let us check our results by the system of moments. The reaction at e = 27 tons; the intermediate loads are distant from i as foUows '.—w' at 3-6 ft., w" at 9-45 ft., and w'" at 12-7 ft. The length eixB 13-85 ft., and the depth ia is 6-24 ft. The strain on A i wiU therefore be — 27 X 13-85 - (13-05 X 3-6 + 9-1 X 9-45 + 4-85 X 12-7) 6^24 ~ = 28-74 tons. The line AO scales 29-1 tons, showing a difference of 0-36 for errors in drawing the parallelograms of forces, not much over 1 per cent, of the total. The diagram being completed, the strains on the various bars can be sealed off, and the quantity of material required for each determined. In some cases, as for roofs, the load wiU be upon tho CRESCENT GIRDER. 77 top member, but the method of determining the strains will be analogous to that illustrated in this example. The crescent girder is a structure similar in principle to the above, and calculated in the same way, but it has the bottom or tension member considerably curved, so as to give the whole rib the appearance of an arch pointed at each end. This form is much used for roofs, having a very elegant appearance, and being, moreover, an economical form of rib. The ends of all these girders must be left free for expan- sion and contraction to take place, otherwise, under changes of temperature, they will be subject to undue strains, and in expanding may even bend and become permanently crippled, and, moreover, if firmly fixed at the ends, the tie must buckle, as it cannot extend imder the tension thrown on it ; in fact, by fixing the ends, the whole equi- librium of the structure is destroyed. I refer to this, as cases have occurred of the ends of a crescent girder being firmly screwed down, with the result of distorting the girder laterally, until, upon having its feet released, it assumed its normal shape. I have now shown the method of determining the strains on braced structures by sections, as in the lattice girder, and by reactions, as in the example last considered ; but there is another system of calculation by dividing the structure into primary, secondary, tertiary, &c., trusses, which is generally employed in determining the strains upon ordinary roof trusses, and these I shaU now proceed to investigate. In Fig. 36 A B C represents the commonest shape of truss for roofs of small span. CA, CB are called the rafters, 0 / the king rod, and A B the tie. Although in practice the rafters are in one piece, also the tie, I have drawn them as separate bars laid together, in order to show how the trusses are calculated. A B C is the primary, and Ad/jBef are secondary trusses ; others coming within these would be tertiary trusses, and so forth. 78 MATERIALS AND CONSTRUCTION. The load upon the roof will be regarded as concentrated at the points C, d, A, B. The weight at d is firstly supposed to come upon the secondary truss Kdf. Draw the vertical line d g equal the load at d ; complete the parallelogram dJigi, then d h and d i will represent the strains on d n and d f. Prom n mark off % ^ equal io dh\ this strain must be resolved vertically on the point of support, and upon the s 1/ //'^H^^ E i Fig. 36. bar n f. Complete the parallelogram nkl 711, then nm \^ the vertical component, and n I the strain on the bar n f. From / mark otf fo — di; this strain must be resolved between the king rod c f and the tie / n. Complete the parallelogram q op f, then fp — strain on /C, and fq = the strain on the tie fn. Upon the king rod there will also be another strain brought upon it by the other secoaidaiy IRON ROOF TRUSS. 79 truss /e B ; let C « represent the sum of these strains ; they must be resolved on the rafters C A and C B. Complete the parallelogram Crst, then C r is the strain on 0 A, and C t that on 0 B. The strain C r must be marked off from A towards C, and resolved vertically and on the tie A B. As the rafter is made in one piece, the strain upon it will be Or between C and d, and between d and A it will be Gr -\- dh; and in like manner the strain on the tie will be the sum of the strains on the ties n q and A B. At D E P is shown another form of roof truss, where there are tertiary trusses hD i, m'Ek, in secondary trusses Dj, I 'Ej, the whole resting in the primary truss D E F ; ffi, Ik are queen rods. In this arrangement the load at h is first taken, and resolved on A D, hi; then the load on ff, with that coming up, ^ i, from the end of D A i, and finally the load at F, with the strain on Fy brought up from the ends of the two secondary trusses Dj, I E/ After all the strains have been determined, they are added together as before. G- H I is another form of roof of light design, but not so steady as those preceding it. It consists of two primary trusses, Grl, H s I, leaned against each other at I, and tied below by the bar r a. In the first place, the loads &t klm are marked off on vertical lines, and parallelograms are completed as shown to determine the strains resulting from these loads on m I and mv, Ik and I r, and k Q- and k q. The strains on m V and h q will again have to be resolved, the former on V I and V I, the latter on ql and q Q. The strains on vl and q I will produce a resultant strain on I r, which, to- gether with the strain brought upon it by the load at I, will have again to be resolved on the bars r I and r G ; the strain on r I being resolved at I, normally to and ot. I G, and the strain on r G being resolved on G I and at right angles to it. The total thrust must be resolved hori- zontally and vertically to find the tension on r s. 80 MATERIALS AND CONSTRUCTION. The roofs carried by arched ribs and girders are of course calculated in the same way as the same elements when used for other purposes. In roof trusses, where the loads are actually distributed continuously along the rafters, it is evident that these elements undergo transverse in addition to longitudinal strain ; hence care must be taken that they be made suffi- ciently rigid to withstand such bending strain. From this effect of the load it will be found that in small roofs an apparently great excess of material must be employed in order to secure rigidity. In all the braced structures and arrangements of frames discussed in this chapter, the bars in them are aU parts be- longiag properly to such structures— that is to say, being necessary to them to maintain their equilibrium ; but in complicated works there occur systems of bracing which do not belong to any particular girder or member, so far as in helping it to resist the strains proper for it to bear, but which serve to connect the various girders and to pro- tect them against the action of external forces, against which their own construction does not provide. As bracings such as these appear to be quite distinct in their functions from those combinations which I have described, and of which I have investigated the principles above, I shall discuss them and their modes of application in a separate chapter CHAPTEE V. ADVENTITIOUS BEAOING. ^His bracing is tliat wliicli is added for the purpose of Bcuring solidity and rigidity in a structure, and is gene- ally applied to resist external causes of vibration, or, if iich vibration must occur, to cause the structure to act as a ^bole, not to be shaken about in detail, so that the solid lass of the whole structure may be brought into action '^hen any pa/rt of it is attacked by a vibratory force. This bracing, sometimes called counterbracing, occurs in 11 kinds of positions — vertical, horizontal, and diagonal — nd is of two kinds, plate bracing and bar bracing, the Ormer being used in the form of gussets to preserve the jugular positions of parts of a structure in relation to each ther ; but we have here more particularly to deal with bar racing. In Fig. 37, a I and c d represent a pair of bracing bars itended to maintain the proper form in the rectangular :ame to which they are attached. These bars may be mply riveted on, or they may be attached under what 1 called initial tension, and this I propose to discuss before oing further. If the work is put together merely as a fit -that is, no strain is on any part of it by reason of process f manufacture — let us examine the action when a disturb- ig strain comes into play. Let a force P act at c, in the irection shown by the arrow ; this will tend to open the B 3 82 MATERIALS AND CONSTRUCTION. angles a c i, a d I, and diminish the angles d a c, d h c, to compress c d and elongate a h. The letters ah c d are to be taken as placed at the centres of the pins connecting the bracing bars with the rectangular frame. In ordei' that the bars may act properly they must not be riveted together at their intersection e, for if they are so riveted any disturbing force will bring transverse strain upon them. It is very important that bracing should act as soon as possible, that it should not allow much distortion to take place before its effect is felt in opposing it. To get this quick action initial tension has been applied ; that is, the already acting with this amount of force to resist it: but on the other. hand the other bar (that that would b€ shortened by the distortion) is by the same amouni assisting at the distortion, so that so far nothing is gained in resistance to distortion by the use of initia strain, and therefore it is an unnecessary addition to th( stresses to which the bars will in the ordinary course oi affairs be subject. If it is proj)osed to use initial straii to make sure that the bracing bars are not loose, then th( point of bad workmanship is touched upon, and if that b( admitted it is as likely to occur in one case as in another then if the initial tension is carelessly applied there maj Fig. 37. bars are put on, and so adjusted that when the structure is un- disturbed they aU. have a certain amount of tension on them. At first sight this seems like getting a good hold of the work, but let us see what actually happens. Suppose the initial tension to be one ton per sectional inch of bar, directly distortion commences one bar (the one being length- ened by such distortion) is ADVENTITIOUS BRACING. 83 be more of it on one bar titan on anotlier, so tliat under mch circumstances we start with a tendency (which will be always in action) to become distorted actually resident in the work itself, and this is certainly about as bad a state of affairs as can be imagined. In order to ascertain the action of the bracing bars, we must observe if the lengthening and shortening efforts are the same under distortion, for if not then we may find a good reason for using initial strain. If (in Fig. 38) the frame ah c dhe distorted to the posi- tion shown by a' b' c d, it will be found that the shortening 3f the line h c will exceed the lengthening of the line a d ; and that it should be the case is evident, for if we suppose the frame ah c d to collapse entirely, so that the point h lies upon c, and the lines a \h, h d shut up ojx a c, c d, it will be observed that the point h will have travelled through the length of a diagonal h c, while the point a has travelled through a distance equal only to the difference between the length of a diagonal and that of two sides. If, for example, the frame were square, calling each side equal to 1, then the diagonal will be equal to 1-414, so the dis- tance travelled by I will be 1 - 414, while that passed through by a will only amount to 2 — 1-414 = 0-586. If, then, initial strain be applied, the force assisting dis- tortion will diminish very rapidly : considering that in this case ties are also practically more effective than struts, it seems probable that the judicious use of initial strain in some classes of eounterbracing may be advantageous. Another point may also be noticed, which is, that with- Fig. 38. 84 MATERIALS AND CONSTRUCTION. out initial tension, the bar under compression rapidly becomes more strained than that under tension, whereas in the other case it first loses its initial tension, and then starts to overtake the amount of strain on the tie, so that the ultimate stresses may be more equal. In Fig. 39, let alhg represent a pier consisting of two columns braced together as shown. If there were merely superincumbent weight to be sustained, no adventitious bracing would be requisite ; but there are vibration and the wind to be withstood, and that force of the wind wiU be not only on the pier itself, but also on the superstructure, whatever it maybe. If the wind be assumed to be blowing in the direction indicated by the arrow, its efiect will be to take a part of the weight off the column I h, and put xi onag ; that is, assuming the pier to be solidly braced together. Let H = height of pier, and B = breadth of base from centre to centre of columns, W = load virtually removed from A to ^, P total pressure of the wind on the pier, including that on the superstructure. Let H' = the height to the centre of pressure of the wind, then the moment of its force about h will be P X H', and the extra pressure •p XT/ or load upon g will be W = ' and this must all pass through the bracing bars. I shall consider the bars as attached without initial strain. The load W is virtually suspended at the points b, d, f, and h, one-sixth of it being taken by each of the diagonal bracing bars. There will then be a compression onb c, d e, f g, and g h, and tension on « 3, « d, cf, and e h. If the height 1<— B— "»i Fig. 39. PIER BRACING. 86 of the pier is equally divided by the bays of bracing there will be no strain on c d and e /, because the tension of one diagonal is equilibrated by the compression of the follow- ing one, for if the pier is sufficiently rigid, we may assume the tensions and compressions on the diagonals as equal. Let L = length of diagonal. TTT X The amount of strain on each diagonal will be — X 6 i H TT^ - Calling B' the distance between the pins of the diagonals measured horizontally, the strains "W TV P TT' Tl' acting horizontally wiU be ^- > X E, but W = Z; "^--l = «; E E = -. . If the Sv 8 V arc were circular the radius would be = + , according to the properties of the circle ; the are we have is a para- bolic arc, of which the crown is the vertex. The roadway may be carried either above or below the arch, the former being the most usual for arches with free abutments, the latter for tied arches. In either case the road girder, or the elements transmitting the load to the arch, should be sufficiently rigid to distribute con- centrated loads, so that no undue distortion of the arch occurs. The amount of rigidity requisite will depend upon the ratio of the live or moving loads to the dead weight of the structure; the greater the latter is in proportion, the less will be the disturbing influence of the former. We must now consider more particularly the effects of unequal loading upon the arch. The principle of moments may be applied to the calculation of the thrusts in this case, the same as it has been to the strains in those fore- going. I will first apply it to test the formula for the thrust at the crown. Under a uniform load the centre of gravity of the half- arch will be ~, from the nearest abutment, and the vertical reaction of the abutment (the vertical component of the thrust on the abutment) will be acting at a horizontal distance ^ from the crown. The vertical distance of the crown from the abutment ^is v ; hence we have for the 102 MATERIALS AND CONSTKUCTlON. moment of strain — X — — — X - 2 2 2 4 moment of resistance T x v. to P m w ''1; for tlie T^; = — the same as above, with the negative sign showing the character of the strain ; that is, compressive on the top member. Let Fig. 47 represent the curve of thruat on an arch loaded only with its own weight and the dead weight of the roadway, and let this be 2 tons per lineal foot; the span 80 ft., and the rise 20 ft. ; then the horizontal thrust at the crown will be = 80 tons. Let a load W = 8 V 5 tons come upon the arch at a point midway between the Fig. 47. abutment A and the crown or centre. The virtual crown of the arch will not now be at the centre, and we must find its position, which will be at some point where the two parts of the structure exhibit equal positive moments about the abutments. The moments about A will be, if the point required be distant y feet from A, ^^^^ + and the moment about B will be w {I — y) X ^-^-^ = ^ 2 ^ {l?-2lyAr y~) ; equating these, + = ^{r'-2ly + f-); r + 100 = 6400 - 1(50 y f; y.,y = 6300 160 IRON ARCHES. 103 39-375 ft. : tliis is where the horizontal components are equal. Takrag now the moments ahout this point, the horizontal thrust will be found. Let v = the rise at this point ; as it is so near the crown, in this case it may he taken as 20 ft. The reaction on B wiU he ^ + ^ = 80 + 1-25 = 81-25. 2 4 The weight of structure hetweenB and the virtual crown is w X 40-625=81 -25, and this acts at a mean distance 20-3125 ft. TV .X. ^ • 81-25 X 20-3125 — 81-25 X 40-625 _ Hence the thrust is, — 1650-39 - 3300-78 ^ _ 3^.52 (nearly). 20 \JJ In the enlarged diagram, Fig. 48, is seen the amount of distortion at the point tinder W, and at a cor- responding point in the other side of the arch due to the load W. a is the centre of the arch, pig_ 43. and h the crown dis- placed ; then c c is the curve of strain due to the uniform load, and dd the distorted curve due to the presence of W. The curve is depressed under the load W, and elevated on the opposite side of the arch. It seems advisable to insert the general equation of which we have worked out this example. Let z = distance of W from abutment A, the other nota- tion remaining as we have it above ; then — After the curves of strain due to the extreme loads have been determined, and the rib so proportioned as to include 104 MATERIALS AND CONSTRUCTION. them all, it only remains to adopt sectional arese in accordance with the thrusts coming upon the different sections of the arch. Extending the above example, where it was found that under the uniform load the thrust at the crown was 80 tons, we find that the thrust at the abutment will be — t = V(80f+(807 = V12800 = 113-13 tons. Iron ribs are liable to expansion and contraction (the same as girders) under changes of temperature, and this occasions also change of form. In order to meet the re- quirements of the altering inclination of the ends of the arch, the faces of the abutments have been in many cases made curved; in some a convexly rounded end is sup- ported in a concave abutment ; in others, a slightly con- cave end rests on a slightly convex abutment, the radii being different; but this arrangement has the disadvantage of giving only a narrow band of bearing surface, and rendering the structure more liable to vibration than when a more ample bearing surface is provided. There is also some alteration of form, accompanied by a movement on the bearing surfaces, when, under the influence of a load, the arched rib shortens under the compressive strain, and the radial end surfaces approach more nearly the vertical position. CHAPTEE YIII. SUSPENSION-BEIDGES. In Eig. 49 is sliown the general form of a suspension- bridge at A E. A B C D E is tlie main chain, to which, the road girders are attached by the vertical suspending-rods ; the main chain is securely fastened at A and E, and passes B D h db f I j Fig. 49. over saddles or rockers on the towers or piers B G and DH. Let a h represent a part of the chain enlarged, a being the central or lowest point, and h m a portion of the road F 3 106 MATEiilALS AND CONSTRUCTION. girder, carried on the suspension-rods c d,e f, gh, &c. Tlie strain at a may be calculated by a formula similar to that used for the crown of the arch, the only difference being that the chain is in tension and the arch in compression. If then I = the span in feet, v the fall of the chain at the centre, w the load per lineal foot, and T the horizontal tension at a, T =^^. On the horizontal line c a mark ' 8 V oflP c w = T, and on the vertical line c d mark off c o equal to the load on the rod c d ; complete the parallelogram npoc, then p c will be the strain resulting from T and c o, and its direction will be that proper for the link following a c \ produce p oio e, the head of the next suspension-rod, and make e q — c p. Make er ■=. the load on the rod e f; com- plete the parallelogram qsre; then s e wiU be the tension on and direction of the link eg, and in like manner the tensions and directions for the remaining links may be found. The horizontal strain must in the first place be found from the general load, in a manner precisely analo- gous to that employed in the case of the arch. It is to be noticed that at the piers where the chain passes over a saddle or rocker the tension is equal on both sides of the'pier, being unaltered by the change of direction, the same as when a strained rope passes over a pulley. There being no rigidity in the chain, it will alter its form so as to suit its centre line to every variation of load ; hence the suspension-bridge is intrinsically unstable. To render such a structure practically satisfactory, some means must be adopted to distribute the load as far as possible in a uniform manner; a stiff roadway girder at h m wiU effect this, and it is also facilitated by using two chains, one above the other, and attaching the head of the suspension-rod to a saddle-plate resting on the two chains, as shown at Fig. 50. a is the head of the suspension-rod, joined by a pin to the lower part of the triangular saddle- StrSPENSION-BRIDGES. 107 plato, of which one of the upper corners is carrieu. on the pin h of the lower chain, and the other is held by a pin c resting on the upper chain. The next suspension-rod will have its saddle carried by one of the ordinary pins of the upper chain, and by a pin resting on the lower chain. One saddle-plate must not be pinned to hoth chains, as that would interfere with their adapting themselves to varying loads, and so lead to vibration and distortion of the suspending-rods. As an arch, instead of being sus- tained by solid abutments, -pj^ may have the thrust at the haunches opposed by a tie, so the pull of the chains, instead of passing away to anchorages at the ends, may be opposed by a strut or horizontal compression member passing from B to D (Fig. 49), and in that case the strain on such strut wiU be equal in intensity to the horizontal tension on the chain. Also the arch and chain may be combined, as in the Albert Bridge at Saltash, the parts of the structure being so proportioned that the thrust of the arch is met and balanced by the pull of the chain. The roadway may be above or below the chain, but is usually placed in the latter position. Many varieties of suspension-bridges have been designed with the view of obtaining a structure more inherently stable than the ordinary form, and one of the most strik- ing of these is what we may call the half-chain bridge, invented some years since, and possessing many features to recommend its adoption, although, probably from its being but little known, it does not appear to have come into use, at least in this country. 108 MATERIALS AND CONSTRUCTION. In Pig. 51, tills arrangement of chain is shown in eleva- tion at A, and in plan at B. The lower ends, I and d, of the semi-chains are secured to the lower parts of the towers over which the upper ends pass, being anchored in the ordinary way. In this system it is also to be noticed that the chains do not hang in vertical planes, the lower ends being brought closer to the centre of the roadway than the upper ; and this secures more stability, as it throws the suspension-rods out of the vertical, as shown in the cross section at C, where s and t are the upper and u and v the lower chains, s lo and t z being the suspension-rods. In SEMI- CHAIN BRIDGE. 109 the ordinary suspension-bridge witli vertical rods, if by any force the structure is caused to vibrate laterally, there is merely its own weight to resist such vibration, but in the section here shown any lateral movement causes the strain on one side rod to become greater than that on the other opposite it ; hence a strong tendency to resume its normal position. The angular disposition of the rods wiU bring upon them strains greater than the load in the ratio of their lengths to their vertical heights, and this will lead to a lateral stress on the chains, tending to overturn the piers inwards, therefore they must be held in position by struts connecting the tops of the opposite towers. e f represents our semi-chain, with its suspension-rods h i, j k, &c. The strains will be the same as on the half of a complete chain of the same form and fall, its span being double that of the semi-chain. In this bridge, as con- structed, the road girder was not continuous, but consisted of a series of short longitudinal girders equal in length to the distance between two suspension-rods ; and this to avoid the vibratory wave sent forwards in a continuous road girder by the rising of that girder in the bay next in front of that on which the load is_^ entering ; but the discontinuous arrangement has this disadvantage, that it does not distri- bute the load over several suspension-rods, as does the rigidly continuous road girder. It is obvious that the semi-chain wiU be much less liable to continued pendulous vibration than the complete chain, and from its position, lying as it does in an inclined plane, it will have on it an initial strain, which is of great service under lateral disturbance ; for if it be supposed that the platform is thrown aside until the suspension- rods occupy the positions shown by the dotted lines 5 w', t there is evidently a great effort on the part of the rod s w' to swing back with its load into the normal position, while at the commencement of such return there is no resistance offered 110 MATERIALS AND CONSTHtfCTIOlSf. to it from the side 2', althougli, as tlie platform approaches its proper place, the rising of the end z' of the rod t z checks the onward vibration of the platform. In the ordinary bridge the suspension-rods appear to act like two isochro- nous pendulums connected by a Hnk. Before leaving this subject I must mention the anchorage of the main chains. The chain e d, Tig. 52, maybe carried Fig. 52. over a saddle, and so brought into a vertical direction, and passing below the ground line a h, be anchored beneath a mass of masonry e /, the weight of which should be at least twice the maximum strain that can be put upon the chain. In another arrangement the chain is anchored behind a mass of masonry, as shown at i k, g h being the ground line. In this case the stabihty of the masonry is relied upon ; in both cases the work must be so executed that the masonry behaves as if it were one solid mass : the method of executing this part of the work will find its place in the chapter on Eoundations. CHAPTEE IX. COLUMNS AND STEUTS. The conditions under whicli materials yield and fail vvlien subjected to compressive force are very various, and they have not been sufficiently ascertained to enable a rational theory of resistance to compression to be formed : hence empirical formulae form the only resource. By empi- rical is meant a formula deduced directly from experiment, the laws of variation as well as the constants being obtained therefrom. As might be expected, the results so obtained are not so satisfying to the thoughtful mind as those derived from a combination of pure reasoning and experi- ment ; but still in the absence of the latter we must, until more light shall be thrown upon the subject, be content to put up with the former. Under certain known conditions the stress may be cal- culated, as for instance when a force acts rectilineally on a curved member, and passing outside its section, gives rise to a bending moment. It may be interesting to examine the effects of loads on straight elements, assuming that tlmj will lend under the superimposed load. Let there be a bar 3 feet 6 inches long and 1 inch square placed horizontally on supports 3 feet apart, and loaded at the centre with 0-2 ton ; then, according to the formulae in a former chapter, if the bar be of cast iron its deflection under this transverse strain will be, 112 MATERIALS AND CONSTRUCTIOJi. -^_'W P _-2 X S"" _ Q.ggg .^pj^ ^j^g moment of 14.m 14 X 1 strain of the load producing this deflection wiU be M = "W"-^ __ 2 X 3 _ .jg £qq^ ^Qj^g_ ;p2j^g central moment of 4 4 _ strain due to a force acting on the ends will be equal to the intensity of the force multiplied by the central deflec- tion, or W D if W = the force on the end. To find then the end load to produce a central moment equal to the above, the two expressions must be equated, giving M = •15 = W D = W X .•.W= 4-67 tons. Thisload, though acting compressively in direction, produces both tension and compression on the bar, and the tensile resist- ance wiU be the measure of strength of the bar, taking half the moment as being upon half the section ; that upon the half in tension is 0-075 ft. ton, or 0-9 inch ton. The maximum tensile strain will be found by inverting the expression M = ; thus s = - = 10'8 tons, which would exceed the strength of ordinary cast iron, unless the resistance of flexure is included (as explained in the chapter on Bending Stress), including which the tensile re- sistance, as found from the ultimate moment 8,000 inch lbs., becomes 48,000 lbs. per square inch, or 21-4 tons per square inch. The deflection, however, wiU not be of the same character under compression by direct and transverse stress in re- spect to the moment of strain at any part ; under the latter the strain commencing at each point of support increases simply as the distance from the point of support to its maximum at the centre; but under direct pressure the moment at any point is the load multiplied by the deflec- tion at that point. Now it is easy to imagine a sample of iron having one place much weaker than the rest, or it COLUMNS. 113 maybe, from some defect in the casting", that it is not actually straight ; then the strain may pass axially from each end to such a point, the deflection all occurring at that point. In saying the deflection all occurring at such a point, the additional deflection due to bend- ing is intended, the form of the bar being some- what of the form shown in Fig. 53 ; then wherever this point is situated will be the position of maxi- mum deflection, and of maximum strain in conse- quence. In the foregoing examination I have regarded the compressing strain as acting at the centre of the ^ig- 53. bar, but practically that will only occur while the bar does not deflect, for as soon as deflection commences the pressure will act only on the sides a and h of the end sections of the bar, thus reducing the moment. But in the first place the load must act centrally, for an initial pres- sure at a and I would deflect the bar in a direction the opposite of that shown. The calculated (from experiment) resistance of such a column as that taken above is 8'1 tons, so if we consider the bar as breaking by deflection, it is clear that the tensile strength is not in this class of strain augmented by the resistance of flexure. One very striking difference in the behaviour of the material under the transverse and the compressive deflect- ing forces must be noted. Under transverse strain the ultimate strength of the bar is not affected by variations in the modulus of elasticity, which only affects the amount of deflection ; but under the compressive force the less the modulus of elasticity the greater the deflection, and there- fore the greater the moment of strain under a given com- pressing force, and therefore practically the less the ulti- mate strength. It is evident from this that the iron selected for elements 114 MATERIALS AND CONSTRUCTION. in compression should be of a quality exhibiting a high modulus of elasticity. When a bar does not fail by de- flection and cross breaking, its rupture may occur by shearing at some plane more or less inclined to the axis, as at g h or f i in Fig. 54, representing part of a column of which al \b the axis. Taking ^ the action on the plane g h, make ce— the 9 load ; this must be resolved in the directions of the line of fracture, and a line at right angles to it, the parallelogram being that shown dii ck el', and in like manner for the plane / i, the parallelogram will he c n e m, Fig. 54. c h and c n being the shearing forces re- spectively acting parallel to the planes g h and / ^. The maximum strain wiH be found to occur when the angle of the plane of rupture is 45 degrees to the axis of the bar, then the strain parallel to the plane of tupture wiU be = and the area on which this strain acts 1-414 is the sectional area of the 'bar at right angles to its length, multiplied by 1-414. It is evident, however, that this mode of rupture can only occur in columns of small length in ratio to the diameter, or least thickness, for if the resultant c m fall outside the base of the column, there must be bend- ing strain. Taking the plane at the angle given above, and resolving it at the centre or axis, the base of the column must have a width equal to its height. From experiment it is found such a column would crush with 36 tons for a square inch. The proportion of this 36 acting parallel to the plane of fracture would be -j7|j^ — 25-4 tons. The area of sheared section wiU be, for the bar 1 inch square, i-414 square inches ; hence the shearing COLUMNS. 25'4 • • strain per square iucli = ^^4. ^^^^ (nearly). This is a very high standard, but the experiments upon which the formulse were based were made upon metal of superior quality. A considerable difference in strength will be found to exist between elements having flat properly bedded ends and such as have jointed ends, or ends upon which the column can turn, for the flat ends aid in resisting deflec- tion; and it may be observed, as in the deflection of columns the extended side is that on which the compres- sive load is most directly resting, there will be a great tendency for the deflection, when it does occur, to happen suddenly, perhaps instantaneously, with rupture, and so pass unnoticed. I will now insert the empirical formulse, which have been derived from the experiments of Hodgkinson and others. The formula for timber is Love's, those for metal are Gordon's. The diameter or thickness is always to be measured the thinnest way of the column ; thus, a column 6 inches by 4 inches would be said to have a thickness of 4 inches for the purposes of calculation. Let W = breaking load in tons per sectional square inch of column ; r = the length divided by the least diameter ; C = ultimate resistance to compression in tons per square inch. For Timher, W = For Cast-iron, cylinders, solid or hollow, flat ends, W = 3 ; jointed ends, W = ^2 ' J ' 1 + — i + — - ^400 100 116 MATERIALS AND CONSTRUCTION. For Cast-iron rectangular columns, flat ends, W = ■ 36 1 + -^ 500 jointed ends, W = 36 ^ 125 For Wrought-iron solid rectangular columns, W = 16 For Angle, Tee, and Channel Iron, W = 19 1 + For Mild Steel, solid round pillars, W = 900 30 3000 rect- 1 + 1400 angular pillars, W = 30 1 + 2480 For Strong Steel, solid round pillars, W 51 ^ + 900 iv'ictang'ular pillars, W = 51 1600 CHAPTEE X. JOINTS AND CONNECTIONS. The strength of any structure is limited by that of its weakest part, and in order to obtain the most satisfactory results all the parts should be equally strong. In practice it is not possible to secure absolute equality of strength throughout our work, but this should be studied as closely as is practicable, and at all events care must be taken that the strength nowhere falls helow a certain limit. The student, having made himself proficient in the fore- going formulae, can readily determine the arose of the various elements of any structure he may have intrusted to his care ; but when this is done there arises the question of arrangement of joints for the connection of the parts, and the transmission of strain from one to another. The sizes in which materials can be obtained have to be considered, and the joints arranged so as not to interfere with one another. The lengths in which bars and plates are rolled vary in different districts; thus plates 21 feet long are common in the Cleveland District, whereas about 1 6 feet rules in Staffordshire. A great deal depends upon the quality of the iron and its peculiar characteristics, and it is not advisable to insist on excessively long plates, for by extending the dimensions the fibre of the metal may be strained in manufacture, or in avoiding this the maker may be led to use a class of iron of a more yielding character, 118 MATERIALS AND CONSTRUCTION. ■--] T •--] and inferior in strength tliroughout. Other points also require regarding, such, as convenience of handling and erection ; for girder work generally 20 feet should be taken as the outside limit of length for plates ; but angle irons of moderate section may be run up to 30 or 35 feet in length, but this is rather awkward to manage, and it is more convenient to keep to shorter lengths. For the sizes of timber no general rules can be laid down of any practical utility. I will commence with the joints of timber structures. The liability of timber to split along the line of the grain calls for great precautions in setting out the joints in this material. Joints in compression will be most satisfactorily made by butting the ends accurately to- Fig. 55. gether, as shown at a h, Fig. 55, and keeping them in juxtaposition by sur- rounding the joint with a box, shown in section at e f, and secured from slipping by bolts passing into or through the timber. Another form of butt joint is shown at c 3, in which the ends of the timber are stepped together and secured by bolts. This form is correct if the two pieces of timber are of exactly the same quality as regards elasticity ; if not unequal straining may occur from the piece, say g h, being more compressible than the other tongue/ when the one side yielding more than the other, the post will be more liable to deflect laterally. There is also more difiiculty in insuring a fair bearing at i and h than there is in obtain- ing a uniform bearing in simple butt joints. Joints subject to tensile stress will be generally more complex than those in compression, and in every case some sectional area will be lost. The most common method is by scarfing, as shown in Fig. 56. At a 5 is a plain scarf, bolted together by bolts passing through thin wrought- TIMBER JOINTS. 119 A o . o o e Qf—-mj—x> if o o o iron plates c c and dd, of wMcli the object is to spread the pressure of the bolt heads and nuts over the surface of the — r r— i r— ■ i— i r-.^ timber, and so prevent them from cutting into it, as they ^ otherwise would, is an elevation of the side of the beam, having a plate on it. If these plates be not used, square wrought-iron washers should be placed under each Pig. ge. ""^ head and nut, these washers being of a good size, such as 2^ inches square for a f-inch bolt, and so forth. In this arrangement the whole of the strain is trans- mitted as shearing strain through the bolts. In the first place, therefore, the sectional area of the bolts must be proportioned to the tensile strength of the beam. The strengths used in the examples wiU be taken from the working resistances given in the table at the end of the book. Let the beam be of ehn, 6 inches deep and 3 inches thick, then at 1 ton per inch its working strength wiU be 6x3x1 = 18 tons. The shearing resistance of wrought- iron bars (from which the bolts are made) being 4^ tons per sectional square inch, the gross area of bolts required square inches. But we cannot get the full strength of the beam, for there wiH be a loss of sec- tion by the bolt holes ; if there be two f -bolts opposite each other, as shown &t ef, there will be H inches taken off the width of the beam, and its working strength wiU be reduced to 4-5 x 3 X 1 = 13-5 tons, and the area of bolts required will be ^^-r = ^ square inches. The sectional will be — =4 4-5 120 MATERIALS AND CONSTRUCTION. area of a f-inch bolt is 0-44 inch, so the number of bolts of that diameter required will be seven, and for uniformity we should use eight, as shown in Fig. 56, and more- over it is advisable to have an excess of bolt area where it can be obtained without further reducing the area of the beam, as we cannot be certain that all the bolts will bear equally on the timber. So far, then, the strength of the bolts is secured, but failure may occur by their cutting out of the timber by detruding a piece equal to their diameter. If the work is sound, each juece of timber detruded will have to be sheared in two j)lanes, through a distance h in the case of the outer row of bolts, and m in the central row. Should, however, the timber, by contracting on the unyielding iron of the bolts, crack, there will only be left one complete plane of shearing upon which to rely, and accordingly this one plane is all I shall take. The shearing resistance is ^th of a ton, hence the shearing area must be = —— = 108 square inches, and the area •125 will be the breadth of the beam multiplied by the total length of the surface to be sheared. Let I — this length, then area = 3x^=1 08; ^=1^ = 36 inches. If the o bolts in line are put 6 inches apart, centre to centre, and the timber overlaps 2 inches at the end, the shearing length will be for the two outer rows 28 inches, and for the centre 11 inches, making 39 inches in all— something in excess of that absolutely required. In the mode of scarfing shown at g h, the detrusive re- sistance of the pieces hooked together is relied upon, and thus the cutting action of the bolts is avoided, the duty of the latter being to keep the surfaces of the joint in con- tact. It is evident that the sum of the lengths of the parts sustaining detruding force must (if the bolts are not to be regarded as assisting) be to the effective depth of the beam TIMBER JOINTS. 121 as the resistance to tension is to the shearing resistance ; that is, in the present case the line of detrusion must be 8 times the depth of the beam, therefore the length of the joint must be 16 times the effective depth of the beam. If, then, the beam loses H inches of its depth by the necessary- cutting at the joint, the length of such a joint will be 16 X 4'5 = 72 inches, or 6 feet : of course, if the strain is partly taken by the bolts, this length will be proportionately reduced. In joints of beams under transverse strain, this will be partly compressive and partly tensile, and must be dealt with accordingly. Connections of parts must now be examined. In Fig. 57, a is an upright connected with a horizontal tie S ; it is tenoned in, and secured by a thin iron strap, ^ * which embraces the beam h, and is fast- ened to the upright a by bolts passing through it. Sometimes wrought-iron tie bolts are used, run- ning the whole length of the upright, to tie the members together, but this does not seem to me as compact as the joint here described, g shows the end of a strut notched into the end of a tie ef, and held in position by a strap A, secured to the tie ef by a bolt i. Here the detrusive resistance of the timber at e is relied upon, and its area of detrusion must be proportioned to the strength of the tie ef, for it is evident that the horizontal strain put upon e/ by the strut g will be that acting detrusively at e. In the lower sketch the end of the strut h abuts against a chock of wood or snug n o, bolted Fig. 57. 122 MATERIALS AND CONSTRUCTION. on to the tie beam I m ; here the shearing resistance of the bolts is relied upon to carry the strain. At d the ends of three timbers are shown as connected by being passed into a special casting made to receive them, where they are secured by bolts passing through the casting. The wrought-iron plates and straps to which I have referred are very thin, varying in thickness from 1^6- inch upwards, according to the size of the timbers they connect. In such a place as e all the strap has to do is to support a portion of the weight of the tie beam b. The strap h may be called upon to sustain the thrust of the strut g, in case the timber at e shotdd give way and become detruded; hence in this position stronger metal will be required, and sufficient must be used to provide against such an accident, as the slipping of that strut would probably issue in the collapse of the whole structure of which it forms a part. It is obvious that every care should be used to avoid as much as possible cutting into the timber, and so reducing its sectional area ; and, moreover, if the sectional area be kept uniform, there wiU be less chance of the element be- coming warped under the influence of damp or heat than if it be varied in dimensions. I shall now pass on to the consideration of the joints and connections used in iron structures. Let it be required to join two bars, a and b, under tensile a Fif?. 58. strain by a cover or joint plate c, Fig. 58. Let the bars be 4 inches wide by | inch thick ; the strain wiU tend to pull the bars apart by shearing through the rivets. Let the rivets be | inch in diameter, then the area of each one RIVETS. 123 in cross section will be 0-6 square inch; the area of bar, less loss by rivet hole, multiplied by the working stress of 5 tons, or (4 — 0-875) x 0-75 X 5 = 11-71 tons, which is the strain to be carried by one set of rivets from the bar a to the cover plate c, and again by another set of rivets from the plate c to the bar I. The working shearing re- sistance being 4-5 tons per square inch, the strength of each rivet will be 4-5 x 0-6 — 2-7 tons ; hence the number of rivets on each side of the ioint will be ^'^'^^ or 5 rivets 2-7 ' ' for something more than 4 rivets being requisite, wo can- not have less than 5, as shown in the figure. Had there been two joint plates, one on each side of the main bars, each rivet would have two sections acting; hence in this arrangement only half the number of rivets used with the single cover are neces- sary. It is necessary to con- sider the proportions of the various dimensions of the rivets, and to arrange them carefully, for upon the quality and disposition of this part of the work the safety of a struc- ture depends, as much as upon the correct proportioning of the main elements. The rivets, when cold, must necessarily be of less diameter than the holes they are intended to fill, for they wiU of course expand when heated; hence care must be taken that when in the holes they are properly ham- mered or pressed up to fill them. Under ordinary cir- cumstances, the rivets probably do not exactly fill the holes, and therefore hold the plates together against lougi- G 2 1 h Fig. 59. 124 MATERIALS AND CONSTRUCTION. tudinal strain by friction, until by the vibration of strains the rivets are pulled so as to bear against the holes in which they rest. This will account for the leakage through rivet holes, and in fact leakage will show that the riveting is imperfect. In order to secure the filling of the rivet hole it is evident that the hammering up of the rivet should be continued until the metal of the plate surrounding the rivet body is of the same temperature as the rivet itself, so that it may all shrink toe/ether in cooling. Hand riveting seems more favourable to this result than power riveting, but the latter possesses advantages more than counter- balancing this. I will first consider the necessary size of the rivet heads : the greatest strain to which the heads will be liable will be that due to the contraction of the bodies in cooling, and this will not exceed 10 tons per sectional square inch of rivet body, as that is the limit of elasticity, and at that strain the rivet will stretch. In the direction in which a rivet will pull out of its head, parallel to the fibres, the resistance does not probably exceed f of the shearing strength across the grain ; hence the working strain along the grain should be taken at 4-5x0-8 = 3-6 tons per square inch. lid = diameter in inches of body of rivet, then the maximum puU on the head will be 0-7854 d'^ X 10 = 7-854d~ tons. The shearing area in the head will be the circumference of the body multiplied by the height a, Yig. 59 ; and its resistance at 3-6 tons = 3-1416 dx a y. 8-6 =:U-31d.a., as the resistance must be equal to the strain 11-31 = 7-854 .-. a = 0-694 d, or the height at the place indicated by the dotted line should never be less than -/o the diameter of the rivet. This strain, moreover, must not put on the plates a greater compressing strain per square inch than the workmg stress of 3-5 tons, and to this the annular area of the under side of the rivet head, must be adapted. Calling D RIVETS. 125 the diameter of the rivet head in inches, the annular area multiplied by compressive working stress wiU be 0-7854 (D^ - d^) X 3-5 = 2-7489 (D^ - d'), say, 2-75 (D^ - d'). Hence 7-854 = 2-75 — 2-75 <^^ I> = 1-96 d, which means, practically, that the diameter of the head should be twice that of the body of the rivet. A sufficient length must be allowed over that required by the thickness of the plates passed through to make the second head, and the least that can be put for this is Vid, or, practically, li- diameters. If the quantity is slightly in excess, and forms a collar, this collar should not (as is sometimes done for appearance) be cut off, for in so doing the chisel will most likely cut into, and so weaken the plate upon which the rivet head bears, and the collar will not be noticed when the work is painted. If these proportions are adhered to, the rivet will be right for either shearing or tensile stress, which latter occurs when it hangs upon its head, and bears a longitudinal strain, which will not exceed 5 tons per inch, or one-half of that for which the head has been calculated. Having determined the proportions of the rivet, the re- lations of the rivet holes to the bars or plates to be joined, and their distances from the edges and from each other, remain to be considered. The distance of the rivets in line from centre to centre is called the pitch of the rivets. At e is shown a rivet in section in a hole near the end of the bar, the strain being in the direction of the arrows, tending to tear the end of the bar open. Eupture of the end of the bar may occur in different ways : the bar may tear open from the rivet to the end, or it may tear laterally through the dotted line ff, or the rivet may push a piece out, though this latter is very improbable in iron (not being liable, like timber, to detrusion). The metal may also be damaged by the compression put upon it by the rivet. The part under compression at f will exhibit a section equal to the diameter of the rivet multiplied by the thickness of the 126 MATERIALS AND CONSTRUCTION. plate. Taking the stresses as before, shearing at 4*5 tons, and compression at 3*5 tons, and dealing with one shearing section only of the rivet, its strength will be 0-7854 X 4-5 = 3-534 d'^. Let t — the thickness of the plate in inches, then its working strength to resist the compression from the rivet will be, 3-1416 X t y, Z-b — lldt; for these to be equal 3-534 d"^ — lldt, and the thickness of the plate must not be less than one-third of the diameter of the rivet. Next, as to breaking through the line g ; each side of the bar (if the rivet is central) will take one-half of the strain on the rivet, or 1-767 d^ tons. The resistance will be the length g multiplied by the thickness, and by 5 tons tensile strain = 5.y.^= 1-767 gt = 0-ZbSd\ Hence if were at its limit of |, g =0-353 - 5.0 --> 6.0 ---5.0 - i-- 5.9— > 1 Fig. 65. manent way, 400 lbs. per yard of double line. The aret carried by each cross girder is 27-5 X 4 = 110 square feet the loads will be — Plates . . . 110 X 12= 1320 Ballast ... 110 X 120 = 13200 Permanent Way H X 400 = bZ2> 15053 lbs. = 6-72 tons ; which, added to 22-5 tons running load, gives 29-22 tons, t which must be added the weight of the cross girder. Th girder will be of uniform section, its depth in the centre -iV of its span ; hence its weight will be, taking the co- efficient from the table, 29-22 X 0-00213 = 0-06224 ton CROSS GIRDERS. 149 per lineal foot ; the total -weigtt is 0-06224 X 27-5 = 1-712 tons, making the total weight to be supported by the cross girder 29-22 4- 1-712 =30-932 tons, say 31 tons. The maximum strain on either flange will be = 38-75 ^ 8 X 2-75 tons. The effective depth, being of the span, is 2*75 feet. The area of the top flange in compression will be = 11-07 square inches, gross area; the nett area of bottom flange to resist tension will be ° ^: =8-61 square inches. For work of this size the flanges will be joined to the web by angle irons 3 inches by 3 inches, by J inch thick, the rivets being |-inch diameter, pitched 4 inches apart from centre to centre. This angle iron rolled full will have an area equal to a bar 6 inches by i inch, and in order to get the angle iron of the area calculated upon, it is best to mark it on the drawing by its weight instead of thickness thus : 3"x 3''x 10 lbs. per foot, instead of 3"x 3"x i". After deducting the area of the angle irons, there will be 11-07 — 6 = 5-07 square inches required. For convenience in attaching the buckled floor plates a wide top flange is required ; hence the remaining area will be made up by a plate 12 inches wide by -iV inch thick. For the bottom flange nett area is to be taken, as in tension the rivet holes are loss on the section : in each angle iron there are two f-inch rivet holes, so the nett area of each equals 4-5 X •5=2-25 square inches, making 4-5 square inches for the two ; 8-61— 4-5=4-11 square inches to make up by flange plate ; 8^ inches wide by ^ inch thick wiU be the nett area required as nearly as it can be met, and to this must be added 1^ inches width for two rivet holes, making 10 inches by ^ inch. The web should be J inch thick ; hence the cross section will be as shown in Fig. 66. The effective depth has been taken as 2-75 feet; 150 MATERIALS AND CONSTRUCTION -12— >! 11. that is, between the centres of gravity of the flange arese. These centres of gravity must be found. If the moments of the areae of the different ~F~^-^/i6 parts of a flange be taken about a line '■■3"3">^'la parallel to the top of the section, and their sum divided by the total area of the , 7 > — X „ / ^ But as / is taken indefinitely d- + df s d^ + df small in relation to the value d f, as compared with, d^, may be neglected ; hence, dividing both sides of the equation by /, we find 12 t-^~^ — ^^. Multiplying S * (a/ S * (v both sides hy d, 12 td = '^— ^-ll^ or a' = a. Hence s d s d the sum of the arese of the flanges will equal the area of the web section when the weight of the whole is a minimum. From the foregoing equations the value of d at any point may be found, for 12 i5 = ^LL± • ^ = _ sd-" sd^ ' 12. s.d' and ^ = -J^^l = ; 12. s.d^' 12.^.5 12. ^.s^ ^' ^ — J 2 — — 0- Changing the sign brings this to a rational quantity without altering the value of the differ- ence between x and I, and d = \/ ^ ^ — (I — x). V 12 .t . s A comparison of this equation with those given in any text-book on conic sections will show that the variations of d coincide with the ordinates to a semi- ellipse, of which the span of the girder is the major diameter. Determining then the depth at the centre, and drawing by any ordinary graphic method a semi-ellipse, the most economical form of the girder is obtained ; the depth at the centre is found by making x = -L when d - \/ (l — - )= ^ V 24 . 5 . s \ 2' \/ \i~. t.s Assuming now that the girder is to be made semi- elliptical in elevation, the formula for the strain at any ECONOMICAL PROPORTIONS. 175 point will be found by inserting the value of d ; thus, if S = strain on either flange, ^_'W wl X w{3? — Ix) g2 uo {x^ — Ix) ~ Td YJ ~/~wx , 4 2V 12". ^7^'^''"^'* 12.^.5 — ^iw.t.sia? — Ix), and S =\/3 w .t . s {a? — Ix). The next point to be considered will be, in the web of the lattice or triangular girder, to determine the most economical angle at which to place the bars. Taking all the bars to be at the same angle with the horizon, the length of a bar will be the square root of the sum of the squares of the depth, and half the base of a triangle ; thus, if 5 = distance between the apices of two triangles, and d — depth of girder, and L = length of a lattice bar, then L = ^ + d^. If W = the load on any lattice bar, and S = the strain, S = W. ^. The num- ber of lattice bars will be , where I is the length of the h girder. The sectional area of the lattice bars will vary as the strain ; hence the total weight of the web will vary as the strain multiplied by the length of one lattice bar, W L and by the number of lattice bars, or will vary as —~ X L X = ^ . Eeplacing \2 by its value, we have b do 2 AV Hs for any particular case constant, and it is required to find the relation between h and d that will give a minimum value to + f ^ . Let I = ad, a being the ^4id 0^ h , d a d , d a , 1 yr. , value sought, then -r^-r t-j + —j — t "t " "® ®' 4id h 4d ad 4 a' 176 MATERIALS AND CONSTRUCTION. either increased or diminished when at its minimum by an indefinitely small quantity, the results will be the same, as the value of the whole expression is rising on either side of that particular value of a. Let the value of a be increased by / for one side of the equation, and diminished by / for the other side, then the two values of ^ + i will be ^-^^ + — ]—?= ^ T'^ -\ — 4a 4 a+f 4 a—f thorefore«i + ^53' 36° 30' 36° 53' 33° 50' 31° to 35° 36° 30' 21° 60' 16° 40' to 35° 8° 30' to 14° 11° 20' to 26° 30' 11° 20' to 31° 27° 40° 38° 22° 28° 50° 39° 45° 45° 16° 46° 55° The angles of repose for the earths are those at which these materials wiU permanently stand, not the angles at FORCE OF WIND. 183 which they first break away, which, for reasons shortly to be shown, are much steeper. The structures which depend upon their stability for their safety are arches in masonry, abutments, buttresses, retaining walls of various descriptions, sea-walls and break- waters, chimneys, towers, lighthouses, and all structures liable from their localities to be washed away or blown over bodily. Large bridges in exposed and stormy places are at times called upon to resist overturning forces of great magnitude. The general force of the wind is given in the following table : — Description of Wind. A hardly perceptible wind A pleasant wind . . . Brisk gale Very brisk . . . . . Very liigli wind . . . Storm Hurricane Tornado Velocity in Miles per Hour. Velocity in Feet per Second. Force in lbs. per Sqviare Foot. 1 1-47 0-005 5 7-33 0-125 10 14-67 0-492 20 29-34 1-968 30 44-01 4-429 50 73-35 12-300 60 88-02 17-710 75 110-00 27-700 100 146-66 60-000 The actual measured force of waves has been found to amount to 4,335 lbs. per square foot at Skerry vore, 3,013 lbs. at Bell Eock, and the highest observed 6,000 lbs. CHAPTEE XV. RETAINING WALLS. EETAmma walls are of various descriptions, viz. retaining walls for water, also called dams ; retaining or revetment walls for earth, either carrying a bank level with the top Fig. 78. of the wall, or surcharged. I wUl take the retaining wall for water first. In Fig. 78 c ab d is the section of a wall for a reservoir side. The shaded part shows a wall of DAMS. 185 puddled clay which runs through it to prevent leakage ; this puddle is continuous with that running under the bottom of the reservoir. As this puddle wall divides the dam as it were into two walls which are not tied together, hence the pressure of the water must be sustained by one of these walls. If there is no leakage, the inner wall will bear the load ; if there is free leakage up to the puddle wall, the outer wall will sustain the pressure of the water. The puddle wall itself is not taken as bearing any part of the load. The working of the first case is shown at A. The pressure of the water will in all cases be at right angles to the surface upon which it presses. For weights a length of wall of 1 foot is taken ; also the same thickness of water. Let e e' be the water level, then draw w'' + ^ - = 188 MATERIALS AND CONSTRTTCTION, 187-5 D--_^^ /187-5 _ 3 3 tv W 4 ' V —W~ ~4~' ~ THs, by filling in the numerical values taken above, be- comes ^c=, / 187-5 X 900 _ 3 X6-25 _ 7-5 _ feet. The resistance of the outer part of the waU wiU be greater, as it wiU tend to overturn on the edge c, when the leverage becomes B — x. In this particular case the value of X — 3^^'+3e<>Xgc+7c^ _ 3 x 6-25 + 7-5 x 33-69 + 1135 6w + 3.ec 15 + 101 = 12-12 feet, and B — x — 21-57 feet; hence for the outer waU, Wa;(B + M;) = 62-5D'-; W x{2w-\-e c)=62-5 T>\ .-.ec 62-5 D'- o 62-5 x 900 ^ m to ^ ^ t ^-u — 2w=—— — — r-— 5 = 21-73 feet. In the W.:^; 120x21-57 first expression for e c, the value of is so smaU as to make no practical difference to the root of the whole ex- pression of which it forms a part ; omitting it woidd only alter ec to 33-74 feet, and as we do not work to an inch in structures of this description, the small value may be omitted, and the formula, thus simplified, wiU stand e = W, ^ = H. 0. W thus a plumb wall to support a bank of average compact eartb 20 feet in height woTild require its thickness ^ = 20 X "364 = 7-28 feet, or 7 feet 3^ inches. "When the wall has a battered face, the centre of gravity will not fall over the centre of the base, but nearer the back of the wall, giving a greater leverage to its overturning resistance. The sec- tion of the battered wall will be as shown in Fig. 80 by alcd. If this is considered in its elements, the moment oi ace about e wiU be its weight multiplied <^^>f9 being a vertical line drawn through the centre Ice of gravity of the triangle ace; ch— The moment of a e dh, if hi be a vertical line drawn through its centre of gravity, wiU be its weight multiplied by ei -\- ce, ei being half the thickness a h, and c e the amount of batter on the face of the wall. Let B = the batter on the face, so, if the batter is 1 to 8, B ^ ; the back I d oi the wall being plumb, then the moment of resistance to overturning about the point c will be M = g +Hx^x[~ + HxB])xW H X _j_ 2;2 X ^ X b). Equating Fig. 80. (Hx^Alx^HxB = W ( 2 B? X B^ + 3 ■ 2 this with the overturning moment, and taking 3 as th^ C\ w /HI B2 ■ \ 3 3 factor of safety, 2 ^ 194 MATERIALS AND CONSTRUCTION. W. t. Bj ; whence + 2 H. ^. B = ^ — - ~ Adding H'^. to Lotli sides of the equation, and then taking the square roots, + 2 H. ^. B + H.^ B^ — ^ W -~^+ff.B^ = _^_-__; and^ + H.B. If 2 be taken as the factor of safety, then ^ = H a/ "^'^^ ^ ~ T^^^g latter formula, let it be applied to a wall 10 feet high, the weight of the wall per cubic foot being equal to that of the earth, -which is to be taken as compact earth, the batter 1 in 8, ^ = 10 X ^ / 2 X •364^" , -125^ - 10 x -125 = 1-8 feet V 3 3 thick at the top ; adding on the batter ^th of the height, the thickness at the ground level becomes 1-8 + ^ = 3-05 8 feet. This formula is commonly used where the ground is not treacherous, but of course the ratios oi w to W are filled in when they are not the same. Thus a masonry wall wiU weigh 130 lbs. per foot, and rammed earth 100 lbs. per cubic foot, which would reduce the above thickness at the top to 1"45 feet. The foregoing investigations refer to retaining walls carrying banks having a horizontal top surface, and it is interesting to notice that the formula for moment of hori- zontal thrust will apply to water. The formula arrived at for water was M = 10-416 D^*, where D = H : that for the overturning moment of earth is M = — As water has no angle of repose, C vanishes ; to = 62-5 ; hence COUNTRT^FO'RTS. 195 M = X 62-5 = 10-416 H^, the same as the previous B expression. When the -wall ab dc is loaded, as shown in Fig. 81, it is said to be surcharged, and in this case not only is there a greater load upon the waU, but the centre of pressure acts higher up than one- third its height : in this case it is simplest to de- termine the horizontal thrust by the graphic method, and then equate its moment with the moment of resistance of the wall. Sometimes retaining walls are made with counterforts in front, as shown in the plan A B, where 0 C are the coun- terforts ; these have the effect of increasing the leverage of the wall, and therefore its moment of resistance, as it must to upset turn over on the edges h h, instead of k h, provided the masonry does not give way at the joint of the counterforts with the wall. In order to strengthen the wall between the counterforts, it is sometimes made arched in plan, as shown by the dotted lines ; this wiU materially assist in preventing it from bulging between the counter- forts, and in fact such walls should always be so built. Counterforts leliind the wall are not nearly of so much use, as they do not increase the moment of resistance of the other material composing it, though because their own centres of gravity are carried back further from the edge, they are in themselves of more value than the same quan- K 2 Fig. 81. 196 MATERIALS AND CONSTRUCTION. tity of material distributed equally on the back of the wall. Walls requiring a great resistance may sometimes be made hoUow, but care must be taken that the weight of material is sufficient to resist the horizontal thrust acting to slide the wall on its base, or these hollow places — pockets or voids, as they are termed — should not be carried com- pletely down through the wall, but left with a sufficient bottom for them to be filled up with earth or concrete, preferably the latter, which by its weight will add to the stability of the structure. If a retaining wall carry a superposed weight, its stability will be proportionately increased, and this is the case in retaining walls carrying bridges, and also in the abutments of arched bridges. It is a common practice to caU the supports of bridges abutments, but this is inaccurate except for arches and certain trusses that abut on and thrust against their supports ; in the case of girders the bridge merely puts a weight or vertical pressure on the supports. I therefore avoid applying the term abutments to these supports, piers being a more suitable expression. In arched and trussed bridges the piers are intermediate supports, on which there is, under the full load, only vertical weight, the thrusts from the arches on either side balancing each other. Retaining walls, when calculated, invariably look heavy both on paper and on the ground, and there is therefore an inclination to cut them down in size : no doubt they form a very heavy class of work compared with structures of strength, and it is necessary they should be so, for in making them we are opposing weight to weight, and the resisting mass must bear some proportion to that endea- vouring to overthrow it. I call attention to this point espe( ially to caution students against this inclination to diminish the section, for that which is calculated will be DRY RETAINING WALLS. 197 practically requisite, and in no case would I let the factor of safety be less than 2. There have heen many instances of retaining walls falling down, and more of others which, although they have not actually fallen, have bulged and shown signs of weakness, requiring to be cobbled and patched up either temporarily or permanently, so far as anything connected with such a structure can be said to be permanent. The way in which the temporary support saves the work is by holding it up until the earth behind it, which had been disturbed by building operations, be- comes settled down and hardened again, so as to be more in a position, to stand by itself than it was when the wall was first completed. For places where material is of no consequence, d/ry re- taining walls are frequently built, having only the coping in mortar. They must be much heavier than mortared walls, and although good enough for small heights, are not to be recommended for large or heavily loaded walls. CHAPTEE XVI. ARCHES— ABUTMENTS— BUTTRESSES. Conditions similar to those attending the stability of a retaining wall are imposed in the case of an arch : no part of the arch must turn upon one or other of its edges, and the joints must make a proper angle with the line of thrust, which throughout the length of the arch should lie in the middle third of the depth or thickness of the arch. As has been shown in a previous part of this work, the tangential force due to a radial force — w r, where w is the radial force per lineal foot, and r the radius in feet of the element on which it acts, at the point of its action ; and this formula will give the horizontal thrust at the crown of an arch, carrying at that point a load w per lineal foot, and having a radius r at the crown -.iQip — wr. In Fig. 82 let the arrow P represent the direction of the force p acting at the crown of the arch. Through the centre of gravity of each arch stone, or voussoir, and its accompanying load, draw a vertical line, as oX ef, g h. This for each voussoir will pass through the centre of gravity of a mass comprising the voussoir itself, spandrels and inter- nal bearing walls, arches or flags upon the voussoir, also superposed pavement, ballast, and other load. Produce the direction of the arrow P to intersect e f at a, and make ah=^p; mark o& a d equal to the load on the voussoir D, complete the parallelogram abed, ac will be MASONRY ARCHES. 199 the resultant thrust on the first joint ; produce this resultant to intersect the second vertical in i, and make i k— a c; make i m equal the load on the voussoir E, and complete the parallelogram ililm\ the residtant thrust on the second joint. By continuing this process the resultant thrust on each joint in succession is found, and finally that on the last joint B, giving the thrust on the abutment T. Through the centre of gravity of the abutment C, draw the vertical line n o, and produce the resultant T to intersect it at q ; make qt-=-T, and q s equal the weight of the abut- ment ; complete the parallelo- gram qtus, then qu the resultant thrust, which should pass through the middle third of the base of the abutment, to give a factor of safety 3 : if it only comes within the middle half, the factor of safety is 2. It is obvious that if any dis tribution of load be given, the curve of thrust may be determined as above, and from it the form proper for the arch ; and on the other hand, a form of arch being given, the distribution of load necessary to keep the line of thrust in the right course can be determined. In the latter case the parallelograms being drawn to fit the centre line of the given form, the ratios ad to ab, im to ilc, &c., give the proportions that the loads must bear to the thrusts. As a guide to determining the thickness of the arch at the crown the following formulae may be adopted : — Let d — depth of keystone in feet, r = radius of arch at crown 200 MATERIALS AND CONSTRUCTION. in feet ; then for a single arch d=. y 0-12. r, and for one of a series of arches d = ^ 017. r. These proportions have heen found satisfactory in practice. If the load is uniformly distributed horizontally over the arch, it will be found that the rise of the arch will be one- fourth of the span. To determine the amount of the thrust at any point, the horizontal thrust p at the crown must be resolved with the vertical load between the crown and the point at which the thrust is required ; the three quantities will then be repre- sented by the three sides of a right-angled triangle as at ah c, where ah = horizontal component, i c = vertical com- ponent, a c = resultant thrust; z=.~ah'^ ■\-~V^. Taking w as the uniform load per foot along the arch, horizontally measured, the thrusts will be, at the crown, wr; dX the springing, T = y)2 + if i _ gp^n in feet; or (as has been demonstrated in the chapter on Iron Arches), if Y = rise of the arch, P = and T = Eesolving the thrust on the abutment vertically and horizontally, the horizontal force wiU be equal to the thrust at the crown ; but acting at the springing, the vertical force is equal to half the weight of the arch : this latter aids the stability of the abutment. If H be the height of the springing from the ground, the overturning moment will be p x ^ — ^ X H. The moment of resistance to over- turning will be for the abutment itself, if its height be h, MASONRY AKCHES. 201 and its weight W per cubic foot, = W x t xAx — = 2 W. h f — '—^ — , and the moment of the superincumbent load = therefore 2 8. V 2 2 In determining the stability of massive stone bridges, the weight of the traffic may be ignored in comparison with that of the structure, as it cannot sufficiently vary the line of thrust to practically affect the structure. Suppose an arch of 200 feet radius at the crown is to be built of granite, the thickness of the keystone, that is, the depth of arch at the crown, = ^-12 x 200 = 4-89 feet, or practically 5 feet. The weight of the stone is 164 lbs. per cubic foot, and 164 x 5 = 820 lbs. per foot super of the roadway ; upon this there will be about 4 feet more of masonry, ballast, and paving at 140 lbs. per foot, 140 x 4 = 560 lbs., making the whole weight at this point 1,360 lbs., while the traffic will not exceed 120 lbs. per square foot, so that its variations will not sensibly affect the mass of the structure. From the peculiar conditions of the case a formula for the general thickness of abutments in relation to the span cannot be evolved, but one including all the varying quan- titles may be given. From ^ ^ — = — - — + — mo„ that f = J^^,; ^^^^i,^} *» side, and taking the square roots, f + + ( V = w.UB. ■ / wl \^ wl _ / ioPB. y ( wl ^ 4V.WA^V2W.A; ''"^2W;^~V 4.y. WA "^ \¥W7h) V 4rv."wrA + \2w:h) rm ^^^^^ ing this formula w must be multiplied by the factor of safety. K 3 202 MATERIALS AND CONSTRUCTION. The abutments of bridges may be strengthened by coun- terforts placed behind them, as described in connection with retaining walls. Of piers between arches (if the arches be not equal), it is to be observed that" their stability must be equal to sustaining the difference of the thrusts from either side. It is necessary to show that generally there is ample strength to resist the thrust coming upon the materials. I will take a case of an arch in brick, 40 feet span, 28 feet wide over all, 2 feet thick, carrying two lines of railway, the rise of the arch being 10 feet. Taking the brickwork and the ballast, of which there will be 2 feet in thickness, all at 1 cwt. per cubic foot, the load at the crown will be 1 x4 x 28 = 112 cwt. The average weight between the crown and the abutment may be taken at 140 cwt. per foot lineal. The load due to the railway may at a maximum be taken at 50 cwt. per lineal foot for the two lines of railway ; hence the load w will be 162 cwt. at the crown, and average 190' cwt. along the bridge ; the thrust on the abutment will be T = / (wiy (wl'V^ //162 X 40 X 40V , /190 X 40\ V (syj +(-2-)-v( 8x10 ) +(-2-> = 4,994 cwt. (nearly), or 249*7 tons. The sectional area at the abutment is 28 feet by 2 feet thick, or 56 square feet ; hence the thrust is 4-4 tons per sectional square foot. The weakest kind of brick given in our table (in chapter on Building Materials) does not begin to crack under 43 '4 tons per square foot, or practically ten times the maximum strain. In Kg. 83 is shown a buttress used to assist an abutment in resisting the thrust of an arch. The arch, of which half is shown at a h, producing a thrust too great for the abut- ment he, a, part of it is carried by the member / to the buttress d e. By increasing the height of the spire d, the stability of FLYING BUTTRESS. 203 the buttress deis increased, and at the same time an elegant appearance is given to the work. This kind of construction is to be found principally in church architecture. Fig. 83. In Gothic and other ornamental arches the curve of equilibrium can be determined by means of the parallelo- gram of forces, similarly to those already investigated. CHAPTEE XYII. PIERS AND FOUNDATIONS. The piers supporting a bridge or viaduct have two duties to perform : one to support the weight of the superstructure, the other to resist the attacks of the elements, either the wind on land, or water in rivers, estuaries, and on the sea- shore. When coming to the consideration of the forces exerted by the winds and waves, we are unfortunately stepping off that solid ground of fact which we have hitherto been treading, to find ourselves relying upon at best but doubt- ful bases. Notwithstanding the improved appliances adapted for the scientific investigation of meteorological conditions, the data furnished as to the actual energy of the elemental forces are in a very unsatisfactory state. The feeling must still exist that prompted Smeaton, when justifying his system of joggling the stones in the Eddy- stone Lighthouse, to write, "Where we have to do with, and to endeavour to control, those powers of nature that are subject to no calculation, I trust it will be deemed prudent not to omit in such a case anything that can without difiiculty be applied, and that would be likely to add to the security." It does not seem that the anemometers are to be relied upon, for their indications do not agree with the velocity of wind as shown by the speed of balloons. Of course there are two sides to this question, and it does not follow that WIND PRESSURE. 205 the balloon was throughout its journey in the same current that actuated the anemometers, but these instru- ments in the same localities also give different readings at the same time, which is certainly confusing. A pressure of 50 lbs. per superficial foot has been taken as the pressure during a tornado, and this has been stated to be the highest pressure occurring in this country ; but, again, people assert that still higher pressures have been recorded. In examining the effect of the wind upon a structure there is, moreover, the mode of action to be considered. Suppose, for example, the wind to be blowing not steadily, but in short gusts upon the surface opposed to it ; if one gust causes the structure to oscillate, and just as it has passed through this oscillation to and fro, and is about to commence another (and smaller one), a second gust strikes it, the energy of this will be added to what remains of the energy of the fixst, and by the continuation of such action, the amplitude of the oscillations may be so increased as to cause the structure to overturn, although it is quite stable enough to resist the steady, continuous pressure of the same wind at the same intensity. Increasing oscillation is then a more distinct warning than amplitude of oscillation ; for so long as the amplitude does not increase, we may consider the work safe, but when it increases regularly, the fate of the work will depend upon the duration of the storm. If the wind blow against a flat surface at right angles to its course, the whole effective pressure will be the pressure of the wind per square foot multiplied by the area acted on ; this will not, however, be the case with a round surface, such as one side of a cylindrical column. In Eig. 84, showing a horizontal section of a cylindrical column, let the wind be assumed to be blowing against it in the direc- tion shown by the arrow, and with a force equal p pounds 206 MATERIALS AND CONSTRUCTION. per superficial foot. At the point r the wind will exert its full force on the surface opposed to it ; but take two parts of the surface having their centres a and h at 45 degrees from r, and examine the effects of the wind blowing on these parts ; its force will be expended, partly in normal pressure at right angles to the surface of the column, and partly in continuing the motion of its particles, but in a direction at right angles to that pressure. Draw the radii ac, he, and at right angles to them the tangents ad,le. Equal sur- faces being taken, the wind forces will be equal : let 2-39 feet to scale, and erect a be the template for the intradosal notches. It may be made of thin wood or sheet iron, so that it will yield and adapt itself to the curve of the intrados when pressed against it for the lines indicating its boundaries to be marked. The length of the check on the extrados will be of the same length, but its height will be greater in the proportion that the radius of the extrados is greater than that of the intrados ; that is, in the ratio of the radius of intrados to that radius plus the thickness of the arch. From the point d draw (?/at right angles to al, then pro- duce it upwards to g, making (jf = the radius plus thick- j<- perpendicular 1 foot high to c ; join ca, then c« 5 = the intra- dosal angle; make ae — l-'lTl feet, the length of one check, and from e draw ed right angles to ac, then will ade Fig. 88. OBLIQUE ARCHES. 227 ness of arch divided by the radius ; join g a, g e, tlien age is the template for the notches on the extrados. Next as to the templates for the face voussoirs. We must deter- mine the elevation of the face of the arch, and ascertain how the face joints occur in it. Let ahc, Tig. 89, he an elevation of the arch square to its axis ; « c is the line of springing ; from a draw ae, so that if c e be at right an- gles to ac, the angle c ea\^ equal to the angle of skew of the bridge. Through the elevation ah c draw at right an- gles io ac any con- venient number of lines, such as g d, which produce until they meet ae in A ; and from h draw hj at right angles to a e, and making h i ~df, and hj — dg. By proceeding in the same manner ^ith the other lines a series of points is obtained, through which the natural elevation of the face can be drawn; its boundaries will be parts of an ellipse. Having got thus the intradosal and extradosal boundaries of the face, the next thing is to find the position of the joints. These may be found by developing the Fig. 89. 228 MATERIALS AND CONSTRUCTION. intrados and extrados, and marking the courses on them. But the simpler plan is to find the focus or point to which all the face joints converge, which point lies beloio the axis of the cylinder, of which the arch is a part, and in some cases below the periphery of that cylinder altogether. If we suppose the arch to be semicircular on the square, then on the square the joints at the springing will be horizontal. Not so, however, those at the springing on the face, and for this reason : looking at the plan of the springing E QI K, it does not stop square off at H I, but the extra- dosal spiral passes farther than the intradosal by the quantity H G, and during that passage it is rising ; there- fore at Q- it is above the springing at I by a quantity equal to the rate of inclination of the extradosal check multiplied by the length H Gr. We have found the inclination of the intradosal spiral to be 1 in 2-39. Let the thickness of the arch be 2-5 feet; its radius has been found to be 32-04 feet; hence the rate of inclination of the extradosal spiral wiU be 1 in 2-39 x — '^^^ — = 2-217. ^ 32-04 + 2-5 It is evident H Q- 1 is the angle of skew ; hence H G is to H I, the thickness, as the obliquity is to the square span of the bridge, Q- 1 being in the ratio of the skew span. In the elevation of the springing, D A represents the rise from Gr, A 0 being a horizontal line passing through the centre 0 of the cylinder ; this line is in the plane of the face of the arch. If D C be the joint at the springing, produce it to meet at B a vertical line 0 B let fall from the centre 0, then B wiU be the focus of face joints, and 0 B the excen- tricity. 0 B will be to 0 C (half the span) as AD is to the thickness measured on the face, and therefore as the radius T? is to the square thickness. OB = DA x — , if^ = the square thickness; but DA =JE-^, and H G = i5 x — 2-217 50 OBI JQUE ARCHES. 229 = 2-5 X — = 1-2; henceDA = -i^, andOB= ^"^ 50 ~ ' 2-217' 2-217 X ^1^'^^ = 6-94 feet. Adding this to the radius, 32-04 + 6-94 = 38-94 feet, the distance of the focus B from the intrados of the arch at the crown. Let h be the centre of the intrados aihl, and I the position of a joint at the intrados; draw at right angles to ae, and equal to 38-94 feet; then F will he the point from which all the face joints, as Im, wiR radiate, nqropis a perspective sketch of the springer. The formula for the excentricity may be simplified. Let 0 = 0 B ; S = square span ; U = obliquity ; X — rate of inclination of extrados ^as 2^^- because H Gr = IL>ii, and D A = HQ X X, then 0 = DA X ^ = HG S ^ ^ E Ux^ ^ E _ U X X X B X Ji. X — = -g— X X X ^ S If we follow the course of a joint along the intrados it is obvious that it will, commencing from the springing, run out somewhere in the face of the arch, and it is equally obvious that this point must be a face joint. Now it may, and most likely will, happen that the theoretical inclina- tion of the intradosal spiral will not hit a point in the face that win make a joint, and admit of the proper division of the face into equal voussoirs; then we must take the nearest inclination that will fit, and correct our quantities to suit it. Ill Fig. %1 gh must include an even number of face stones. First find the theoretical value oigh; it wiU be at right angles to fh, and will be to gf, the length of impost, as cf, the obliquity, is to fd, which last is called the head- ing spiral: fd = s/7l' + cj' = x/(57-28f + (24)^ = 62-1 feet. Suppose we wish the voussoirs to be about 230 MATERIALS AND CONSTRUCTION. 62'1 15 inches thick on the intrados, then = 50 will be the 1'25 nearest number; to get a keystone the number must be odd, say 51, then each stone will be 1-217 feet thick. 24 The theoretical divergence ^ ^ = 33-278 X =12-8. The nearest number of voussoirs to this quantity is 10, and the actual divergence 12-17 feet; hence the intradosal 12-8 rate of inclination as corrected is one in 2-39 X 'i2rl7 ~ 2-51 feet. To this value the other quantities must be corrected. The effect of this practical correction is to slightly alter the angle of the lines of strain to the joints, but this alteration is not of sufficient magnitude to be practically important. From the methods given above the various templates can be made, and the coursing lines marked on the centring of the arch to guide the builders ; the boards covering ^ the centres are called the laggings, and on these the lines are to be laid down. By means of stocks made to a proper angle the stones are worked to the shape of the intrados ; but we must show how to determine the di- mensions of the twisting rules for working the spiral beds. In Fig. 90 draw the rectangle fff i h to include the lines f'l and / h, drawn to the inclinations of the ex- tradosal and intradosal spirals respec- tively. Let I d\)Q the distance chosen for the masons' rules or strips on the intrados, draw lade to represent the rules, then a c will be the distance apart of the rules on the extrados, and these distances wiU vary OBLIQUE ARCHKS. 231 as fi io fh. X being the rate of inclination of tlie extra- dosal spiral, and Y that of the intradosal spiral, and fg h, f g i right-angled triangles, ~'Yh~ '^^ +X^H- \/r+~Y-; Y as corrected is and X = ; hence then the distance apart of the rules at J is 24 inches, the distance at 04 Wrought-iron rolled floor beams \ to ( 21,570,000 „ = 9,630 „ Single-webbed plate girder . . 14,316,000 „ =6,391 „ Double „ „ . . ,23,610,000 „ =10,641 „ Tubular (Conway Bridge) girder . 18,764,000 „ = 8,372 „ In the rolled floor beams there is noticed a variation of nearly 32 per cent. From a number of plate-webbed girders, made from iron guaranteed at 21 tons per sec- tional inch, the modulus of elasticity being calculated, ranged at about 7,000 tons. Experiments on the elasticity of materials enable us, however, to examine their molecular constitution. It is assumed that the resistances to extension and shortening are equal, and the alterations of length in simple ratio to EI.ASL1C1TY OF IRON. 241 the load. In a niimber of experiments on cast iron the ratio of weight to extension, between loads of 0-47 and 6-60 tons per square inch, ranged from 117,086 to 79,576, and the apparent limit of elasticity was -^rth the breaking weight. In compression from 0-92 to 16-56 tons per square inch that ratio varied between 110,120 and 90,304, the limit of elasticity being -Mh of the weight that permanently injured the bar. In compression at 1-84 tons, the elastic compression (re- covered on removing the load) was 0"03652 inch in a 10-foot bar ; the nearest load to this in the experiments on 1 "88 extension was 1-88 tons per square inch : 0-03652 x = 0-03731 inch ; the actual extension was 0-03735, or practically the same as that calculated from the compres- sion. At 3-68 tons the compression was 0-07234; this would give for 3-76 tons per square inch 0-07234 x = 0-07385 inch"; that observed in extension under this load was 0-07926 inch, showing a very considerable dif- ference. So in the compression corresponding to a load of 0-9217 ton, that calculated from the extensions is 0-0177, as against 0-0182 in the experiment ; but in these instances the elasticity is imperfect, for in the extension experiments permanent set occurred at 0-7 ton, and in compression at 0-92 ton per square inch. As to the uniformity of extension, aU we have practi- cally to deal with are those up to the highest strain used in practice — say up to 3 tons per sectional square inch — which is used in some hydraulic apparatus. Taking the first experimental number, the extensions corresponding to the increasing weights are calculated by the common formula for comparison with the actual extensions. In compression we take up to 9 tons in the same way ; the bars were 10 feet long. M 242 MATEllIALS AND CONSTRUCTION. Load — Tons per Sq. Inch. Extensions in Xnches. . — Calculated Extensions . Load — ; Tons per Inch. [ Compres- sions in Inches. Calculated Compres- sions. 0-47 0-00900 0-9217 0-01828 0-70 0-01348 0-01340 1-8400 0-03652 0-03648 0-94 0-01805 0-01800 2-7600 0-05578 0-05473 1-41 0-02763 0-02700 3-6800 0-07234 0-07297 1-88 0-03735 0-03600 4-6000 0-09097 0-09122 2-35 0-04735 0-04500 5-5200 0-10942 0-10946 2-82 0-05758 0-05400 6-4400 0-12758 0-12770 7-3600 0-14626 0-14595 8-2800 0-16454 0-16419 9-2100 0-18140 0-18263 From these tables the compressions follow more closely the generally received law than the extensions, and they may be regarded as fairly supporting the theory. The following results are found from experiments on wrought iron : — In 20 readings under loads from 0-56 tons to 11-26 tons per sectional square inch, the ratio of the weight to the extension varies from 219,459 to 242,665, the next highest being 234,982, so that the first is probably exceptional ; the mean is 230,760. Here, then, the extensions are tolerably regular. In the experiments on the cast-iron bars, the rods in compression were cased to prevent deflection. The modulus of elasticity will be seen to have varied in extension from 14,050,320 lbs. to 12,377,040 lbs., the mean of these two being 13,213,680 lbs.; in compression from 13,214,400 lbs. to 12,013,680, of which the mean is 12,614,040 lbs. The modulus of elasticity of wrought iron, correspond- ing to the mean ratio of weight to extension, as givea above, is 27,691,200 lbs. TABLES. 243 TABLE No. 1. Ultimate Tensile Kesistance of Timber in Lbs. per Square Inch of Section. Ash . Beech Elm . Fir . „ American. „ Memel „ Riga . „ Mar Forest Larch Hornbeam Mahogany Oak . „ English „ African „ Canadian „ Dantzic Teak 19,600 to 15,784 22,200 „ 11,500 14,400 „ 13,489 18,100 „ 7,000 12,000 11,000 12,600 12,000 10,200 20,240 to 4,263 21,800 „ 8,000 19,800 „ 9,000 16,000 14,400 12,000 14,500 16,000 to 8,200 TABLE No. 2. Ultimate Resistance ov Timber to Crushing in Lbs. per SauARE Inch of Section. Ash . Beech Elm . Fir . Hornbeam . Mahogany . Oak, English „ Dantzic Teak . 9,363 to 8,683 9,363 „ 7,733 10,331 6,819 „ 5,375 7,289 „ 4,533 8,280 10,058 „ 6,484 7,731 12,101 . 244 MATERIALS AISD CONSTRUCTION. TABLE No. 3. TuANSviiiiSE Kesistance of Timber. E, modulus of elasticity ; S, ultimate moment of resistance in incli lbs. E. s. Teak .... . 603,600 2,462 Poon .... . 422,400 2,221 English Oak . )5 )) • • • . 218,400 1,181 . 362,800 1,672 Canada „ . 536,200 1,766 Dantzic „ . . . . 297,800 1,457 Adriatic „ . . . . 243,600 1,383 Ash . 411,200 2,026 Beech .... . 338,400 1,556 Elm . 174,960 1,013 Pitch Pine . 306,400 1,632 Eed „ ... . 460,000 1,341 New England Fir . . 547,800 1,102 Eiga „ . 332,200 1,108 Mar Forest „ . 161,340 1,144 Larch .... . 154,080 853 Norway Spar . . 364,400 1,474 TABLE No. 4. Ultimate Tensile Resistance of Metals in Tons pkr StiUARE Inch of Section. Cast Iron, cast horizontally 8*48 „ „ vertically 8-70 Tilted Cast Steel 69-93 Hammered Blister Steel 59-43 Sheer Steel 56-97 Welsh Wrought Iron 29-30 Stafford „ 27-15 Swedish „ „ 29'00 Fagoted „ „ 29-00 Iron Wire • • 38-40 Hard Gun Metal 16-23 Hammered Wrought Copper 16-08 Cast Copper 8-51 Fine Yellow Brass 8-01 Cast Tin 2-11 Cast Lead 0-81 TABLES. 245 TABLE No. 5. Ultimate Resistance of various Cast Irons in Tons per SauARE Inch of Section. T, resistance to tensile force. C, crushing „ Low Moor, No. 1 No. 2 Clyde, No. 1 „ No. 2 „ No. 3 Blaenavon, No. 1 No. 2 . Calder, No. 1 Coltness, No. 3 • Brymbo, No. 1 No. 3 . Bowling, No. 2 . T. 5-667 6- 201 { 7- 198 J 7-949 { 10-477 6-222 I 6-380 I 6-131 I 44 41 41 39 49 45 (47 i 46 40 35 30 30 32 33 6-820 { 33 6-440 6-923 { 6-032 i { 33 C. 809 198 430 219 459 616 103 549 855 821 662 964 606 594 229 921 723 460 390 784 988 356 987 028 TABLE No. 6. Ultimate Eksistange of various Buildinu Materials to Crushing Force in Lbs. per Square Inch of Section. Portland Stone 1,284 Statuary Marble 3,216 Craigleith „ 8,688 Chalk 501 Pale Red Brick . 562 Gloucester Roe Stone 644 Red Brick 808 Fire Brick 1,717 246 MATERIALS AND CONSTKUCTION. Derby Grit ..... . . . 3,142 Killaly White Freestone 4,566 Portland „ 4,571 Craigleith „ 5,487 York Paving 5,714 White Statuary Marhle 6,059 Bramley Fall Sandstone 6,059 Cornish Granite 6,364 Dundee Sandstone 6,630 Craigleith „ 6,916 Devon Eed Marble 7,428 Compact Limestone 7,713 Peterhead Granite 8,283 Black Compact Limestone 8,855 Purbeck 9,160 Black Brabant 9,219 Blue Aberdeen Granite ...... 10,914 TABLE No 7. Modulus of Elasticity and Limit of Elastic Resistance of VARIOUS Materials in Lbs, per Square Inch op Section. Material. Brass . . . Gun Metal . Cast Iron Wrought Iron Lead . . Steel . . . Tin ... Zinc . . . Marble . . Slate . . . Portland Stone Ash ... Beech . . . Ehn . . . Fir (Eed) . Larch . . Mahogany . Oak . . . Modulus. 8,930,000 9,873,000 18,400,000 24,920,000 720,000 29,000,000 4,608,000 13,680,000 2,520,000 15,800,000 1,633,000 1,640,000 1,345,000 1,540,000 2,016,000 1,074,000 1,596,000 1,700,000 Limits. TABLES. 247 TABLE No. 8. "Summary of Ultimate and Working Resistances of VAmors Materials in Tons per Square Inch of Section. Material. Ultimate Strength. Working Strengt!;. Ten- sion. Com- pression. Shear- ing. Ten- 1 sion. Compres- sion. Shear- ing. Steel Bars .... 45 70 30 9 9 6 j9 L iciieb .... 40 : 8 Wrought-iron Bars 25 17 22 5 Si- 4^ Plates . Iron Wire Cable . . . 22 17 20 4 4 40 8" Cast Iron 71 45 15 ]^ i 9 3 Ash Beech 7* 5 4 4 Of 0,1 Ot 0,1- Elm Fir 6 5 4* 2| Of Oi Of 0^ H OA Oak oj Tealc 5 1 Granite 3i 0| Sandstone l| 0.^ INDEX. i BUTMENTS, 199 J\. Adventitious bracing, 80 Anchorage, 110 Angle and tee-iron struts, 116 Angle-iron covers, 160 Arches, iron, 97 Arch, tied, 89-100 Arches, masonry, 199 Arches, oblique, 222 Auxiliary girder, 139 BEAMS, moment of resistance of, 22 Beams, supported at both ends, 32-38 Beams, triangular loads, 39 Bedstones, 162 Bending stress, 5-18 Bolts, proportions of, 129 Bowstring girder, 73 Bracing, adventitious, 80 Brick bonding, 221 Bricks, strength of, 214 Butt joints, 128 CAMBER of girders, 96 Cantilever, shearing strain, 52 Cantilevers, 29 Cast iron, quality of, 168 Cast-iron columns, 11-5 Centre of gravity, 18 Coefficients of friction, 182 Columns and struts. 111 Combinations of girders, 137 Concrete, 215 Counter-bracing, 89 Counterforts, 195 Cover-joint plate, 122 Crescent girder, 77 Cross girders, 148 Crushing stress, 7 Curved retaining walls, 191 Curve of strain, 42 DAMS, 184 Deflection of girders, 51, 92- 94 Distributing girder, 142, 153 ECONOMICAL proportions of girders, 172 Elasticity, modulus of, 4, 240; limit of, 8 ; range of, 9 Expansion rollers, 167 External forces, 5 FIXED girders, 43-46 Flying buttress, 203 Footings, 232 Forces, external, 5 ; parallelogram of, 14 ; of waves, 183 ; inclined, 14; tangential, 49 ; moment of, 12 ; internal, 3 Foundations, 209 Framed structures, 56 Framed cantilevers, 60 Friction, 10, 180, 181; limiting angle of, 181 ; coefficients of, 182; stability of, 180 GIB and cotter, 130 Girder, auxiliary, 139; bed- stones, 162 ; bowstring, 73 ; camber of, 96 ; combinations of, 137 ; crescent, 77 ; cross or I^'I)Ex. 249 transverse, 148; deflection of, 51 ; distributing, 142-153; fixed one end, 46 ; fixed both ends, 43 ; main, 155 ; triangular, 65 Granites, 212 Gravity, centre of, 18 Gussets, 87 INCLINED force, U j. Initial strain, 83 Internal forces, 3 Iron roof joints, 134 Iron arches, 97 JOINTS and connections, 117 Joints, timber, 118 LEVER, 13 Limit of elasticity, 8 Limestones, 213 Limiting angle of friction, 181 MAIN girders, 155 Masonry arches, 199; abut- ments, 199 Matter, molecules of, 2 Modulus of elasticity, 4, 240 Moleciiles of matter, 2 Moment of resistance of beams, 22 Moment of force, 12 ^EUTEAL axis, 21, 53 QBLIQUE arches, 222 pARALLELOGRAM of forces. Permanent set, 8 Pierpoints, 222 Piers, wind pressure on, 204 ; bracing, 84 Portlajid cement, 215 RADIAL pressure, 50 Range of elasticity, 9 Reservoir walls, 184 Retaining walls, 184; for earth, 188 ; curved, 191 Rivets, 123 Rivet holes, 125 Ri\;cts, proportions of, 124 Rollers, expansion, 167 Roof trusses, 77 QANDSTONES, 213 D Screw piles, 210 Screw bolts, 129 Semi-chain bridges, 108 Semi-beams, 29 Shearing stress, 6 Stability, 178; frictional, 180 Steel columns, 116 Stifi'eners, 87 Strain, curve of, 42 ; initial, 83 Strength of materials, 236 ; timber columns, 115; cast iron, 115; wrought iron, 116; L and T- iron, 116 ; steel, 116 Struts and columns. 111 ■ Suspension-bridges, 106 ; chains, 107 TANGENTIAL forces, 49 Tee-iron stitFeners, 163 Testing structures, 170 Tied arch, 89, 100 Timber columns, strength of, 115 ; joints, 118 Transverse girders, 148 Triangular load on beams, 39 Triangular girder, 65 WAVES, force of, 183 Web, 163 Winding beds, 223 Wind pressure, 84, 183, 204, 206 Wrought-iron columns, 116; girders, weight of, 147 Wrought iron, quality of. 169 t . t ■ • • ! • •• r««*i •• • • .•••*•.•.*. I.* *,.* Stationers' Hall Coort, Londov, E.C. Crosby Lockwood & Son^s CATALOGUE OF SCIENTIFIC TECHNICAL AND INDUSTRIAL BOOKS PAQE MECHANICAL ENQINEERINQ . 1 CIVIL ENQINEERINQ .... 11 MARINE ENQINEERINQ. Ao. . 20 MINING & METALLURGY . . 28 COLLIERY WORKING, &c. . . 26 ELECTRICITY 28 ARCHITECTURE & BUILDING . 31 SANITATION & WATER SUPPLY 86 CARPENTRY & TIMBER ... 87 PAQE DECORATIVE ARTS 89 NATURAL SCIENCE 41 CHEMICAL MANUFACTURES . 42 INDUSTRIAL ARTS .... 44 COMMERCE, TABLES, &o. . 50 AGRICULTURE & GARDENING. 52 AUCTIONEERING, VALUING, i»o. 57 MATHEMATICS & ARITHMETIC 59 LAW & MISCELLANEOUS . . 62 MECHANICAL ENGINEERING, ETC. THE MECHANICAL HANDLING OF MATERIAL. A Treatise on the Handling of Material such as Coal, Ore, Timber, &c., by Automatic or Semi-Automatic Machinery, together with the Various Accessories used in the Manipulation of such Plant, and Dealing fully with the Handling, Storing, and Warehousing of Grain, By G. F. Zimmer, A.M. Inst. 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Net 1 2/6 L, A CROSBY LOCK WOOD S- SON'S CATALOGUE. MODERN MACHINE 5H0P TOOLS. A Practical Treatise describing in every detail the Construction, Operation and Manipulation of both Hand and Machine Tools ; being a work of Practical Instruction in all Classes of Machine Shop Practice, including Chapters on Filing, Fitting and Scraping Surfaces ; on Drills, Reamers, Taps and Dies ; the Lathe and its Tools ; Planers, Shapers and their Tools ; Milling Machines and Cutters ; Gear Cutters and Gear Cutting ; Drilling Machines and Drill Work; Grinding Machines and their Work; Hardening and Tempering, Gearing, Belting, and Transmission Machinery; Useful Data and Tables. By William H. Van Dervoort.M.E. Fourth Edition. Illustrated by 673 Engravings. Medium 8vo, cloth JVet 2 1 /O TOOLS FOR ENGINEERS AND WOODWORKERS. Including Modern Instruments of Measurement. By Joseph Horner, A.M. Inst. M.E., Author of "Pattern Making," &c. Demy 8vo, with 456 Illustrations. [Just Publtshed. Q/Q net. " As an all-round practical work on tools it is more comprehensive than any with which we are acquainted, and we have no doubt it will meet with the large measure of success to which its merits fully entitle it." — A/echanical IVorld. SUMMARY OF CONTENTS ;— INTRODUCTION.— GENERAL SURVEY OF TOOLS.— TOOL Angles.— SEC. I. chisel group.— Chisels and Applied Forms for Woodworkers. —Planes.— Hand Chisels and Applied Forms for metal Working.— Chisel-like Tools for Metal Turning, planing, &c.— Shearing Action and Shearing Tools.— Sec. II. Examples of Scraping Tools.— Sec. Ill Tools— Relating to Chisels and Scrapes.— Saws.— Files.— milling Cutters.— Boring Tools for wood and Metal. -^Taps and Dies.— Sec. IV. Percussive and Moulding Tools.— punches, Hammers and Caulking Tools.— Moulding and modelling Tools.— Miscellaneous Tools. —Sec. V. Hardening, Tempering, Grinding and Sharpening.— Sec. 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III. work supported at One End.— Face Plate Turning.— Angle Plate Turning.— Independent Jaw chucks.— Concentric, Universal, Toggle, and applied Chucks.— Sec. IV. Internal Work.— Drilling, Boring, and allied Operations.— Sec. V. Screw cuttings and Turret Work, —sec. VI Miscellaneous. — special Work. — Measurement, Grinding. — Tool Holders— Speed and Feeds, Tool steels.— Steel makers' Instructions. THE MECHANICAL ENUINEER'S REFERENCE BOOK. For Machine and Boiler Construction. In Two Parts. Part I. General Engineering Data. Part II. Boiler Construction. Witn 51 Plates and numerous Illustrations. By Nelson Foley, M.I.N. A. Second Edition, Revised throughout and much Enlarged. Folio, half-bound . JVei £3 Ssi PART I.— measures.— circumferences and areas, &c.— squares. Cubes, Fourth powers.— square and Cube Roots.— Surface of tubes.— reciprocals.— Logarithms. — Mensuration. — specific Gravities and weights.— work and power. — Heat. — Combustion. — Expansion and contraction. — Exp.^nsion op Gases.— Steam.— Static forces.— gravitation and attraction.— motion and Computation of Resulting forces.— accumulated Work.— Centre and Radius of gyration.— Moment of Inertia.— Centre of Oscillation.— Electricity.— .strength of Materials.— Elasticity.— Test Sheets of metals.— Friction.— Transmission of Power.— Flow of Liquids.— Flow of G.\sf-S.— air Pumps, Surface Condensers, &c.— Speed of steamships.— propellers.— Cutting Tools.— Flanges, —copper sheets and tubes -screws, Nuts, Bolt Heads, &c.— Various Recipes ,/«A TABLES AND MEMORANDA FOR ENGINEERS, MECHANICS, ARCHITECTS, BUILDERS, &c. Selected and Arranged by Francis Smith. Seventh Edition, Revised, including Electrical Tables, FoRMULiK, and Memoranda. Waistcoat-pocket size, limp leather -J /g " It -would, perhaps, be as difficult to make a small pocket-book selection of notes and formulae to suit ALL engineers as it would he to make a universal medicine ; but Mr. Smith's waistcoat- pocket collection may be looked upon as a successful attempt." — Hn^ineer, " The best example we have ever seen of 270 pages of useful matter packed into the dimen- sions of a ciLiA-case." —Building- News. " A veritable pocket treasury of knowledge."— /rtfn. THE MECHANICAL ENGINEER'S COMPANION. Of Areas, Circumferences, Decimal Equivalents, in inches and feet, millimetres, squares, cubes, roots, &c. ; Strength of Bolts, Weight of Iron, &c. ; Weights, Measures, and other Data. Also Practical Rules for Engine Prof>ortions. By R. Edwards, M.Inst.C.E. Fcap. 8vo, cloth 3/3 "A very useful little volume. It contains many tables, classified data and memoranda generally useful to engineers," — Enpinetr. " What it professes to be, ' a handy office companion,' giving in a succinct fonn a variety of information likely to be required by mechanical engineers in their everyday office work."— Aa/i-. TOOTHED GEARING. A Practical Handbook for Offices and Workshops. By J. Horner, A.M.I.M.E. Second Edition, with a new Chapter on Recent Practice. With 184 Illustra- tions. Crown Bvo, cloth 6/0 " We give the book our unqualified praise for its thoroughness of treatment, and recommend it to all interested as the most practical book on the subject yet vAtK&Si. "— Mechanical V/orld. MODERN WORKSHOP PRACTICE, As applied to Marine, Land, and Locomotive Engines, Floating Docks, Dredging Machines, Bridges, Shipbuilding, &c. By J. G. Winton. Fourth Edition, Illustrated. Crown Svo, cloth 3/6 "Whether for the apprentice determined to master his profession, or for the artisan bent upon raising liimself to a higher position, this clearly-written and practical treatise will be a great help." — ScoCsjnan. DETAILS OF MACHINERY. Comprising Instructions for the Execution of various Works in Iron in the Fitting Shop, Foundry, and Boiler Yard. By Francis Campin, C.E. Crown Bvo, cloth 3/0 "A sound and practical handbook for all engaged in the engineering UaAss."— Building World. ENGINEERING ESTIMATES, COSTS, AND ACCOUNTS. A Guide to Commercial Engineering. With numerous examples of Estiraates and Costs of Millwright Work, Miscellaneous Productions, Steam Engines and Steam Boilers ; and a Section on the Preparation of Costs Accounts. By A General Manager. Second Edition. Svo, cloth 1 2/0 " This Is an excellent and very useful book, covering subject-matter In constant requisition In every factory and workshop. . . . The book is invaluable, not only to the young engineer, but also to the estimate department of every works- " — Builder. " We accord the work unqualified praise. The Information Is given In a plain, straightforward manner, and bears throughout evidence of the intimate practical acquaintance of the author with every phase of commercial engineering."— A/lE<:Aan»c:e done, but who also kiiows how to do it, and how to convey his knowledge to others. To all turners this book would i3e valuable."— En/fineering. " We can safely recommend the work to young engineers. To the amateur it wiU simply be invaluable. To the student it will convey a great deal of useful Information "—Eii^ ineer. SCREW-THREADS, And Methods of Producing Them. With numerous Tables and complete Directions for using Screw-Cutting Lathes. By Paul N. Hasluck, Author of " Lathe- Work, " &c. Sixth Edition. Waistcoat-pocket size . .1/6 " Full of useful information, hints and practical criticism. Taps, dies, and screwing tools generally are illustrated and their action i&scx&eii."— Mechanical World, CROSBY LOCK WOOD &- SON'S CATALOGUE. CONDENSED MECHANICS. A Selection of Formulae, Rules, Tables, and Data for the Use of Engineering Students, &c. By W. G. C. Hughes, A.M.I.C.E. Crown 8vo, cloth . 2/6 "The book is well fitted for those who are preparing" for examination and wish to refresh their knowledge by going through their formulae again."— Marine E'ngineer. MECHANICS OF AIR MACHINERY. By Dr. J. Weiseach and Prof. G. Herrmann. Authorized Translation with an Appendix on American Practice by A. Trowbridge, Ph.B., Professor of Engineering, Columbia University. Royal 8vo, cloth. . . Net 1 Q/O PRACTICAL MECHANISM, And Machine Tools. By T. Bakkr, C.E. With Remarks on Tools and Machinery by J. Nasmyth, C.E. Crown 8vo, cloth .... 2/6 MECHANICS. Being a concise Exposition of the General Principles of Mechanical Science and their Applications. By C. Tomlinson, F.R.S. Crown 8vo,'cloth 1/6 FUELS: SOLID, LIQUID, AND GASEOUS. Their Analysis and Valuation. For the use of Chemists and Engineers. By H. J. Phillips, F.C.S., formerly Analytical and Consulting Chemist to the Great Eastern Railway. Fourth Edition. Crown 8vo, cloth . . 2/0 "Ought to have its place in the laboratory of every metallurgical establishment, and where- ever fuel is used on a large scale." — Che7nical Neivs. FUEL, ITS COMBUSTION AND ECONOMY. Consisting of an Abridgment of " A Treatise on the Combustion of Coal and the Prevention of Smoke." By C. W. Williams, A. Inst. C.E. With extensive Additions by D. Kinnear Clark, M.Inst. C.E. Fourth Edition. Crown Svo, cloth 3/6 *' Students should buy the book and read it, as one of the most complete and satisfactory treatises on the combustion and economy of fuel to be had." — Eni^incer. STEAM AND THE STEAM ENGINE, stationary and Portable. Being an Extension of the Treatise on the Steam Engine of Mr. J. Sewell. By D. K. Clark, C.E. Fourth Edition. Crown Svo, cloth 3/6 " Every essential part of the subject is treated of competently, and in a popular style." — Irmi. PUMPS AND PUMPING. A Handbook for Pump Users. Being Notes on Selection, Construction, ar.d Management. By M. Pov/is Bale, M.Inst. C.E. , M.I.Mech.E, Fourth Edition. Crown Svo, cloth 3/6 " The matter is set forth as concisely as possible. In fact, condensation rather than diffuse- ness has been the author's aim throughout ; yet he does not seem to have omitted anything likely to be of use." — journal of Gas Lighting. REFRIGERATION, COLD STORAGE, & ICE-MAKING: A Practical Treatise on the Art and Science of Refrigeration. By A. J. Wallis-Tayler, A.M.Inst.C.E., Author of " Refrigerating and Ice-Making Machinery." 600 pp., with 360 Illustrations. Medium Svo, cloth. Net 1 6/0 ** The author has to be congratulated on the completion and production of such an impor- tant work and it cannot fail to have a large body of readers, for it leaves out nothing that would in any way be of value to those interested in the subject." — Stca^nship. " No one whose duty it is to handle the mammoth preserving installations of these latter days can afford to be without this valuable book." — Glasgow Herald. THE POCKET BOOK OF REFRIGERATION AND ICE- MAKING. By A. J. Wallis-Tayler, A.M.Inst.C.E. Author of " Refrigerating and Ice- making Machinery," &c. Third Edition, Enlarged. Crown Svo, cloth Net 3/6 REFRIGERATING & ICE-MAKINQ MACHINERY. A Descriptive Treatise for the Use of Persons Employing Refrigerating and Ice-Making Installations, and others. By A. J. Wallis-Tayler, A.M.Inst.C.E. Third Edition, Enlarged. Crown Svo, cloth . . 7/6 " We recommend the book, which gives the cost of various systems and illustrations showing details of parts of machinery and general arrangements of complete installations."— £KjV!e«r. "The publishers have rendered a substantial service to the profession, especially to the youriger members, by bringing out the present edition of Mr. Simms's useful •wotls.." —Engineering . TABLES OF TANGENTIAL ANGLES AND MULTIPLES. For Setting-out Curves from 5 to 200 Radius. By A. Beazeley, M.Inst.C.E. 7t£i Edition, Revised. With an Appendix on the use of the Tables for Measurmg up Curves. Printed on 50 Cards, and sold in a cloth box, waistcoat- pocket size . . I . ■ 3/a " Each table is printed on a small card, which, placed on the theodolite, leaves the hands free to manipulate the instrument— no smaU advantage as regards the rapidity of work."— ^Kf-^ineer. " Very handy ; a man may know that all his day's work must fall on two of these cards, which he puts into hLs own card-case, and leaves the rest \xiiiiiA. "—Athenaum, PIONEER ENGINEERING. A treatise on the Engineering Operations connected with the Settlement of Waste Lands in New Countries. By E. Dobson, M.Inst.C.E. Second Edition. Crown 8vo, cloth 4/6 " Mr. Dobson is familiar witli the difficulties which have to be overcome in this class of work, and much of his advice will be valuable to young engineers proceeding to our colonies."— TUNNELLING. A Practical Treatise. By Charles Prelini, C.E. With additions by Charles S. Hill, C.E. With 150 Diagrams and Illustrations. Royal 8vo, cloth •'VeM 6/0 PRACTICAL TUNNELLING. Explaining in detail Setting-out the Works, Shaft-sinking, and Heading-driving, Ranging the Lines and Levelling underground, Sub-Excavating, Timbering and the Construction of the Brickwork of Tunnels. By F._ W. Simms, M.Inst.C.E. Fourth Edition, Revised and Further Extended, including the most recent (1895) Examples of Sub-aqueous and other Tunnels, by D. Kinnear Clark, M.Inst.C.E. With 34 Folding Pl.-ites. Imperial 8vo, cloth £2 2s. •' The present (1896) edition has been brought right up to date, and is a work to which civil engineers should have ready access, and engineers wlio have construction work can hardly afford to be without, but which to the younger meniDers of the profession is invaluable, as from its pages they can learn the state to whicli the science of tunnelling has aXtam^A." —Railway News. EARTH AND ROCK EXCAVATION. A Practical Treatise, by Charles Prelini, C.E. 365 pp., with Tables, manv Diagrams and Engravings. Royal Svo, cloth. ^ [Just Published. Net 1 6/0 CONSTRUCTION OF ROADS AND STREETS. By H. Law, C.E., and D. K. Clark, C.E. Sixth Edition, revised, with Additional Chapters by A. J. Wallis-Tayler, A. M.Inst. C.E. Crown Svo, cloth ■ ; 6/0 " A book which every borough surveyor and engineer must possess, and which will be of considerable service to architects, builders, and property owners ge-ne-aWy."— Building News. i6 CROSBY LOCK WOOD S- SON'S CATALOGUE. TRAMWAYS: THEIR CONSTRUCTION AND WORKING. Embracing a Comprehensive History of the System ; with an exhaustive Analysis of the Various Modes of Traction, including Horse Power, Steam, Cable Traction, Electric Traction, &c. ; a Description of the Varieties of Rolling Stock ; and ample Details of Cost and Working Expenses. New Edition, Thoroughly Revised, and Including the Progress recently made in Tramway Construction, &c., &c. By D. Kinnear Clark, M.Inst.C.E. With 400 Illustrations. 8vo, 780 pp., buckram 28/0 *' The new volume is one which will ranlc, among tramway engineers and those interested in tramway working, with the Author's world-famed book on railway machinery." — T/ie Engineer. HANDY GENERAL EARTH-WORK TABLES. Giving the Contents in Cubic Yards of Centre and Slopes of Cuttings and Embankments from 3 inches to 80 feet in Depth or Height, for use with either 66 feet Chain or 100 feet Chain. By J. H. Watson Buck, M.Inst.C.E. On a Sheet mounted in cloth case 3/6 EARTHWORK TABLES. Showing the Contents in Cubic Yards of Embankments, Cuttings, &c., of Heights or Depths up to an average of 80 feet. By Joseph Broadbent, C.E., and Francis Campin, C.E. Crown 8vo, cloth 6/0 " The way In which accuracy is attained, by a simple division of each cross fection into three elements, two in which are constant and one variable, is Ingenious." — Athenaum. A MANUAL ON EARTHWORK. By Alex. J. Graham, C.E. With numerous Diagrams. Second Edition. i8mo, cloth 2/6 THE CONSTRUCTION OF LARGE TUNNEL SHAFTS. A Practical and Theoretical Essay. By J. H. Watson Buck, M.Inst.C.E., Resident Engineer, L. and N. W. R. With Folding Plates, 8vo, cloth 1 2/0 " Many of the methods given are of extreme practical value to the mason, and the observa- tions on the form of arch, the rules for ordering the stone, and the construction of the templates, will be found of considerable use. We commend the book to the engineering profession."— Building News. " Will be regarded by ci-rfl engineers as of the utmost value and calculated to save much time and obviate many mistakes." — Colliery Guardian. ESSAY ON OBLIQUE BRIDGES (Practical and Theoretical). With 13 large Plates. By the late George Watson Buck, M.Inst.C.E. Fourth Edition, revised by his Son, J. H. Watson Buck, M.Inst.C.E. ; and with the addition of Description to Diagrams for Facilitating the Construction of Oblique Bridges, by W. H. Barlow, M.Inst.C.E. Royal 8vo, cloth 1 2/0 " The standard text-book for all engineers regarding skew arches is Mr. Buck's treatise, and it would be impossible to consult a better." — Engineer. " Mr. Buck's treatise is recognised as a stanclard text-book, and his treatment has divested the subject of many of the intricacies supposed to belong to it. As a guide to the engineer and architect, on a confessedly difficult subject, Mr. Buck's work is UDSutpasssd."— Building Nevis. CAST & WROUGHT IRON BRIDGE CONSTRUCTION (A Complete and Practical Treatise on), including Iron Foundations. In Three Parts. — Theoretical, Practical, and Descriptive. By William Humbkr, A.M.Inst.C.E., and M.Inst.M.E. Third Edition, revised and much im- proved, with 115 Double Plates (20 of which now first appear in this edition, and numerous Additions to the Text. In 2 vols., imp. 410, half-bound in morocco £6 168. 60. " A very valuable contribution to the standard literature of civil engineering. In addition to elevations, plans, and sections, large scale details are given, which very much enhance the instructive worth of those illustrations." — Civil Engineer and Arihitecfs yournal. "Mr. Humber's stately volumes, lately issued — in which the most important bridg"*s erected during the last five years, under the direction of the late Mr. Brunei, Sir Vi. Cubrtt, Mr. Hawkshaw, Mr. Page, Mr. Fowler Mr. Hemans, and others among our most eminent engineers, are drawn and specified in great detail." — Enginner. CIVIL ENGINEERING, SURVEYING. Sc. IRON BRIDGES OF MODERATE SPAN: Their Construction and Erection. By H. W, Pendred, With 40 illustra- tions. Crown 8vo, cloth 2/0 " Student;, and engineers should obtain tliis book for constant and practical use."— CcUiety Guariiiatt. IRON AND STEEL BRIDGES AND VIADUCTS. A Practical Treatise upon their Construction. For the use of Engineers, Draughtsmen, and Students. By Francis Campin, C.E. Crown 8vo, cloth 3/6 TUBULAR AND OTHER IRON GIRDER BRIDGES, Describing the Britannia and Conway Tubular Bridges. With a Sketch of Iron Bridges, &o. By G. D. Dempsey, C.E. Crown 8vo, cloth . 2/0 GRAPHIC AND ANALYTIC STATICS. Ill their Practical Application to the Treatment of Stresses in Roofs, Solid Girders, Lattice, Bowstring, and Suspension Bridges, Braced Iron Arches and Piers, and other Frameworks. By R. Hudson Graham, C.E. Containing Diagrams and Plates to Scale. With numerous Examples, many taken from existing Structures. Specially arranged for Class-work in Colleges and Universities. Second Edition, Revised and Enlarged. 8vo, cloth . 1 6/0 " Mr. Graham's book will find a place wherever graphic and analytic statics are used or studied. " — Eng inter. " The work is excellent from a practical point of view, and has evidently been prepared with much care. The directions for working are ample, and are illustrated by an abundance t f well-selected examples. It is an excellent text-book for the practical draughtsman. " — W^/f«ni7wm WEIGHTS OF WROUGHT IRON & STEEL GIRDERS. A Graphic Table for Facilitating the Computation of the Weights of Wrought Iron and Steel Girders, &c., for Parliamentary and other Estimates. By J. H. Watson Buck, M.Inst.C.E. On a Sheet 2/6 GEOMETRY FOR TECHNICAL STUDENTS. An Introduction to Pure and Applied Geometry and the Mensuration of Surfaces and Solids, including Problems in Plane Geometry useful in Drawing. By E. H. Sprague, A.M.Inst.C.E. Crown 8 vo, cloth. . . . Net\lO PRACTICAL GEOMETRY. For the Architect, Engineer, and Mechanic. Giving Rules for the Delineation and Application of various Geometrical Lines, Figures, and Curves. By E. W. Tarn, M.A., Architect. Svo, cloth 9/0 *' No book with the same objects in view has ever been published in which the clearness of the rules laid down and the illustrative diagrams have been so satisfactory." — Scotsman. THE GEOMETRY OF COMPASSES. Or, Problems Resolved by the mere Description of Circles and the Use of Coloured Diagrams and Symbols. By Oliver Byrne. Coloured Plates. Crown Svo, cloth 3/6 MENSURATION AND MEASURING. With the Mensuration and Levelling of Land for the purposes of Modern Engineering. By T. Baker, C.E. New Edition by E. Nugent, E.C. Crown Svo, cloth .1/6 HANDY BOOK FOR THE CALCULATION OP STRAINS In Girders and Similar Structures and their Strength. Consisting of Formulae and Corresponding Diagrams, with numerous details for Practical Applica- tion, &c. By William Humber, A. M.Inst.C.E., &c. Sixth Edition. Crown Svo, with nearly 100 Woodcuts and 3 Plates, cloth . . . 7/6 "The formulae are neatly expressed, and the diagrams good." — Alkenaum. *' We heartily coramena this really handy book to our engineer and architect readers."— English Mechanic. THE STRAINS ON STRUCTURES OF IRONWORK. With Practical ^Remarks on Iron Construction. By F. W. Shkiles, M.Inst.C.E. Svo, cloth 5/0 L. B i8 CROSBY LOCKWOOD * SON'S CATALOGUE. CONSTRUCTIONAL IRON AND STEEL WORK, As applied to Public, Private, and Domestic Buildings. By Francis Campin, C.E. Crown 8vo, cloth 3/6 " This practical book may be counted a most valuable work." — British Architect, MATERIALS AND CONSTRUCTION. A Theoretical and Practical Treatise on the Strains, Designing, and Erection of Works of Construction. By F. Campin. Cloth .... 3/0 EXPERIMENTS ON THE FLEXURE OF BEAMS. Resulting in the Discovery of New Laws of Failure by Buckling. By Albert E. Guv. Medium 8vo, cloth iVe/ 9/0 TRUSSES OF WOOD AND IRON. Practical Applications of Science in Determining the Stresses, Breaking Weights, Safe Loads, Scantlings, and Details of Construction. With Complete Working Drawings. By W. Griffiths, Surveyor. Oblong 8vo, cloth 4/6 "This handy little book enters so minutely into every detail connected with the con- struction of roof trusses that no student need be ignorant of these m-axx^ts." —Practical Eng'ineer. CONSTRUCTION OF ROOFS, OF WOOD AND IRON: Deduced chiefly from the Works of Robison, Tredgold, and Humber. By E. W. Tarn, M.A., Architect. Fourth Edition. Crown 8vo, cloth . 1 /6 " Mr. Tarn is so thoroughly master of his subject, that although the treatise was founded on the works of otliers he has given it a distinct value of his own." — Builder. A TREATISE ON THE STRENGTH OF MATERIALS. By p. Barlow, F.R.S., P. W. Barlow, F.R.S., and W. H. Barlow, F.R.S. EditedbyWM. Humber, A.M.Inst.C.E. 8vo, cloth . . . . 18/0 " Valuable alike to the student, tyro, and the experienced practitioner, it will always rank in future as it has hitherto done, as the standard treatise on that particular subject."— £«£«ne«r. EXPANSION OF STRUCTURES BY HEAT. By John Keily, C.E. Crown 8vo, cloth 3/6 " The aim the author has set before him, viz., to show the effects of heat upon metallic and other structures, is a laudable one, for this is a branch of physics upon which the engineer or ar:httect can find but little reliable and comprehensive data in \X)0)l%." — Builder. CIVIL ENGINEERING. By Henry Law, M.Inst. C.E. Including a Treatise on Hydraulic Engi- neering by G. R. Burnell, M.Inst. C.E. Seventh Edition, revised, v^-ith Large Additions on Recent Practice by D. Kinnear Clark, M.Inst. C.E. Crown 8vo, cloth 6/6 "An admirable volume, which we wannly recommend to young engineers." — Bitildcr. THE PROGRESS OF ENGINEERING (1863=6). By Wm. Humber, A. M Inst. C.E. Complete in Four Vols. Containing 148 Double Plates, with Portraits and Copious Descriptive Letterpress. Impl. 410, half-morocco. Price, complete, £1 2 1 2s. \ or each Volume sold separately at £3 3s. per Volume. Descriptive List of Contents on application. GAS WORKS, Their Construction and Arrangement, and the Manufacture and Distribution of Coal Gas. By S. Hughes, C.E. Ninth Edition. Revised, with Notices of Recen: Improvements by Henry O'Connor, A.M.Inst.C.E. Crown 8vo, cloth 6/- PNEUMATICS, Including Acoustics and the Phenomena of Wind Currents, for the use of Beginners. By Charles Tomlinson, F.R.S. Crown 8vo, cloth . 1 /6 FOUNDATIONS AND CONCRETE WORKS. With Practical Remarks on Footings, Planking, Sand, Concrete, B6ton, Pile-driving Caissons, and Cofferdams. By E. DoBSON.^Crown 8vo. 1/6 CIVIL ENGINEERING, SURVEYING, *c. 19 BLASTING AND QUARRYING OF STONE, For Building and other Purposes. With Remarks on the Blowing up of Bridges. By Gen. Sir J. Burgoyne, K.C.B. Crown 8vo, cloth . . 1/6 SAFE RAILWAY WORKING. A Treatise on Railway Accidents, their Cause and Prevention ; with a De- scription of Modern Appliances and Systems. By Clement E. Stretton, C.E. Third Edition, Enlarged. Crown 8vo, cloth .... 3/6 ENGINEERING STANDARDS COM- MITTEE'S PUBLICATIONS. The Engineering Standards Committee is the outcome of a Committee appointed by the Institution of Civil Engineers at the instance of Sir John Wolfe Barry, K.C.B., to inquire into the advisability of Standardising Rolled Iron and Steel Sections. The Committee is supported by the Institution of Civil Engineers, the Institution of Mechanical Engineers, the Institution of Naval Architects, the Iron and Steel Institute, and the Institution of Electrical Engineers ; and the value and importance of its labours has been emphatically recognised by His Majesty's Government, who have made a liberal grant from the Public Funds by way of contribution to the financial resources of the Committee. Reports already Published : — 1. BRITISH STANDARD SECTIONS (9 lists). Angles, Equal and Unequal. — Bulb Angles, Tees and Plates.— Z and T Bars.— Channels.— Beams. JVei 1/0 2. TRAMWAY RAILS AND FISH=PLATES. ^et 21/0 3. REPORT ON THE INFLUENCE OF GAUGE LENGTH. By Professor W. C. Unwin, F.R.S. 2/6 4. PROPERTIES OF STANDARD BEAMS. {Included in No. 6.) Net 1 /O 5. STANDARD LOCOMOTIVES FOR INDIAN RAIL= WAYS. ^''^i 1 0/6 6. PROPERTIES OF BRITISH STANDARD SECTIONS. Diagrams, Definitions, Tables, and Formulae. Net S/0 7. 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'iO/G Net. 25. ERRORS IN WORKMANSHIP. Based on Measurements carried out by the National Physical Laboratory. * Net 1 0/6 27. STANDARD SYSTEMS FOR LIMIT GAUGES. (Running Fits) Net 2/6 28 NUTS, BOLT-HEADS, AND SPANNERS. Net 2/6 31 STEEL CONDUITS FOR ELECTRICAL WIRING. Net 2/6 MARINE ENGINEERING, SHIPBUILDING, NAVIGATION, ETC. MARINE ENGINES AND BOILERS. Their Design and Construction. A Handbook for the Use of Students, Engineers, and Naval Constructors. Based on the Work " Berechnung und Konstruktion der Schiffsmaschinen und Kessel," by Dr. G. Bauer, Engineer- in-Chief of the Vulcan Shipbuilding Yard, Stettin. Translated from the Second German Edition by K. M. Donkin, and S. Bryan Donkin, A.M.LC.E. Edited by Leslie S. Robertson, Secretary to the Engineering Standards Committee, M.LC.E., M.LM.E., M.LN.A.,&c. With numerous Illustrations and Tables. Medium 8vo, cloih. ijust Published. QBI- A'ei. SUMMARY OF CONTENTS :— PA liT I.— MAIN ENGINES.— DETERMINATION OF CYLIN- DER Dimensions.— The Utilisation of Steam in the Engine.— Stroke of piston. —NUMBER OF Revolutions.— TURNING Moment.— Balancing of the Moving Parts —Arrangement of Main Engines.— Details of Main Engines.— The Cylindfr _ Valves.— Various Kinds of Valve Gear. -Piston Rods.— Pistons.— Connecting Rod and Crosshead. —Valve Gear Rods.- bed Plates. — Engine Column^; — Rever'^ing AND Turning Gear, part II.— pumps.— Air, Circulating Ffed, and AUXILIARY Pumps, part III.— shafting, RESISTANCE OF SHIPS, PROPELLERS. —Thrust Shaft and thrust Block.— tunnel Shafts and plummer Blocks — SHAFT Couplings.— Stern TUBE.— THE Screw propeller.— construction of the Screw. part IV.— pipes and connections.— general remarks, Fn..\GfcS, Valves, &c.— Under Water Fittings.— Main steam, auxiliary steam and Exhaust Piping —Feed Water, bilge, Ballast and Circulating pipes. PART V — STEAM boilers.— Firing and the Generation of stf am.— cylindrical boii frs — Locomotive Boiler.'^. — Water-Tube Boilers. — Small Tube Water-Tube Boilers.— Smoke Box.— Funnel and Boiler Lagging.— Forced Draught.- boiler Fittings and mountings, part VI.— MEASURING INSTRUMENTS PART VII — VARIOUS DETAILS.— Bolts, Nuts, Screw threads, &c.— platforms, Gratings Ladders. — Found ^tions. — Seatings. — Lubrication Ventilation of Engine Rooms.— RULES for Spare Gear. PART Vlll.— ADDITIONAL TABLES. "This handsome voUiine contains a comprehensive account of the design and construction of modern marine engines and boilers. Its arrang:ement is excellent, and the numerous illustrations represent recent practice for all classes of warships and vessels of the mercantile marine. His position as Engineer-in-Chief of the great Vulcan Works at Stettin gave the author special facilities for selecting illustrations from the practice of that firm, which has built many of the swiftest types of steamships for both war and conmierce. Other German firms and the German Admiralty have been euually generous in contributing information, while a large proportion of the illustrations is drawn from English technical journals and the proceedings of our engineering societies. American practice is also represented. The compilation has been laborious, no doubt, but it constitutes a valuable book of reference and a treasury of information. The English editor and his assistants have done their work well, both in translation and in the conversion of metric to English measures." — The TimeSt MARINE ENGINEERING, NAVIGATION, *c. 21 THE NAVAL ARCHITECT'S AND SHIPBUILDER'S POCKET-BOOK Of Formulae, Rules, and Tables, and Marine Engineer's and Surveyor's Handy Book of Reference. By Clement Mackrow, M.I.N. A. Eighth Edition, carefully Revised and Enlarged. Fcap., leather . . , JVei 12/6 Summary of Contents :—S:gns and symbols, Decimal Fractions.— Trigo- nometry.— practical Geometry.— Mensuration.— Centres and Moments op Figures. —MOMENTS of inertia and Radii Gyration.— Algebraical Expressions for Simpsons Rules.— Mechanical Principles.— Centre of Gravity.— Laws of Motion. -Displacement, Centre of Buoyancy.— Centre of Gravity of Ship's Hull.— stability Curves and Metacentres.— Sea and Shallov/-water Waves. —Rolling of Ships.— propulsion and Resistance of Vessels.— Speed Trials.— Sailing, cf.ntre of Effort.— Distances down Rivers, Coast Lines.— Steering and Rudders of Vessels.— Launching Calculations and velocities.— Weight op Material and Gear. —Gun Particulars and weight.— Standard Gauges.— Riveted Joints and Riveting.— Strength and Tests of Materials.— Binding AND Shearing stresses. —Strength of Shafting, Pillars, wheels, &c. — Hydraulic Data, &c. — Conic Sections, Catenarian Curves. — Mechanical Powers, Work.— Board of Trade Regulations for Boilers and Engines.— Board OP trade Regulations for Ships.— Lloyd's Rules for boilers.— Lloyd's Weight OF Chains.— Lloyd's scantlings for Ships.— Data of Engines and Vessels.— Ships' Fittings and Tests.— Seasoning preserving Timber.— Measurement op Timber.— ALLOYS, Paints, Varnishes.— Data for Stowage.— Admiralty Trans, port Regulations. — Rules for Horse-power, Screw Propellers, &c.— Per- centages for Butt straps.— particulars of Yachts.— Masting and Rigging. — Distances of Foreign ports. —Tonnage Tables.— Vocabulary of French and English Terms.— English Weights and Measures.— Foreign weights and Mea- sures.— Decimal equivalents.— Useful Numbers.— Circular Measures.— Areas OF AND Circumferences of Circles.— Areas of Segments cf Circles.— Tables op Squares and cubes and Roots of Numbers.— Tables of Logarithms of Num- bers.— Tables OF Hyperbolic Logarithms.— Tables op Natural Sines, Tangents, —Tables of Logarithmic Sines, Tangents, &c. "In these days of advanced knowledge a work like this Is of the greatest value. It contains a vast amount of information. We unhesitatingly say that it is the most valuable compilation for its specific purpose that has ever been printed. No naval architect, engineer, surveyor, seaman, wood or iron shipbuilder, can afford to be without this work." — I^auiicaL Magazine. " Should be used by all whr are engaged in the construction or design of vessels. . . . Will be found to contain the most useful tables and formulae required by shipbuilders, collected from the best authorities, and put together in a popular and simple form. It is of exceptional merit."— Engineer. "A pocket-book of this description must be a necessity in the shipbuilding trade. It con- tains a mass of useful information clearly expressed and presented in a handy form." — Marine Engineer. WANNAN'S MARINE ENGINEER'S QUIDE To Board of Trade Examinations for Certificates of Competency. Containing all Latest Questions to Date, with Simple, Clear, and Correct Solutions ; 302 Elementary Questions with Illustrated Answers, and Verbal Questions and Answers ; complete Set of Drawings with Statements completed. By A. C. Wannan,C.E., Consulting Engineer, and E. W. I. Wannan, M.I.M.E., Certificated First Class Marine Engineer. With numerous Engravings. Fourth Edition, Enlarged. 500 pages. Large crown 8vo, cloth . . Net 1C/6 '*The book is clearly and plainly written and avoids unnecessary explanations and formulas, and we consider it a valuable book for students of marine engineering." — Nautical Magazine. WANNAN'S MARINE ENQINEER'5 POCKET-BOOK. Containing Latest Board of Trade Rules and Data for Marine Engineers. By A. C. Wannan. Third Edition, Revised, Enlarged, and Brought up to Date. Square iSmo, with thumb Index, leather . , . , , 6/0 "There is a great deal of useful information in this little pocket-book. It is of the rule-of thumb order, and is, on that account, well adapted to the uses of the sea-going engineer."— Efigineer. MARINE ENGINES AND STEAM VESSELS. By R. Murray, C.E. Eighth Edition, thoroughly Revised, with Additions by the Author and by George Carlisle, C.E. Crown 8vo, cloth . 4 6 ".\n indispensable manual for the student of marine e.x\^m&t^ yoKrwa/. ^ GOLD ASSAYING. A Practical Handbook, giving the Modus Operandi for the Accurate Assay of Auriferous Ores and Bullion, and the Chemical Tests required in the Processes of Extraction by Amalgamation, Cyanidation, and Chlorination. With an Appendix of Tables and Statistics. By H. Joshua Phillips, F.I.C., F.C S., Assoc.Inst.C.E., Author of " Engineering Chemistry," &c. With Numerous Illustrations. Large Crown 8vo, cloth Net "J IQ FIELD TESTING FOR GOLD AND SILVER. A Practical Manual for Prospectors and Miners. By W. H. Merritt M.N.E.Inst.M.E., A.R.S.M., &c. With Photographic Plates and other Illustrations. Fcap. Svo, leather Jifet B/0 "As an instructor of prospectors' classes Mr. Merritt has the advantage of knowine exactly the information likely to be most valuable to the miner in the field. ThI contents cover ^t ^lm^^l/yfu'^^laT """'"^ ^ ^"'^ ^ addition to a prospector" THE PROSPECTOR'S HANDBOOK. A Guide for the Prospector and Traveller in search of Metal-Bearing or other Valuable Minerals. By J. W. Anderson, M.A. (Camb.), F.R.G.S. Tenth Edition. Small crown Svo, 3/6 cloth ; or, leather . . . . 4/g " Will supply a much-felt want, especially among Colonists, in whose way are so often thrown many mmeralogical specimens the value of which it is difficult to determine. How to find commercial minerals, and how to identify them when they are found, are the leading points to which attention is directed."— Aftmn^- Journa.!, ■o""u, ire cne THE METALLURGY OF SILVER. A Practical Treatise on the Amalgamation, Roasting, and Lixiviation of Silver Ores. Including the Assaying, Melting, and Refining of Silver Bullion. By M. Eissler, M.Inst.M.M. Fifth Edition. Crown Svo, cloth . 10/6 " A practical treatise, and a technical work which we are convinced wiU supply a long-felt want amongst prac ical men, and at the same time be of value to students and others Indirlctlv connected with the industries. '—Aft«i«^ Journal. uiuoi» uiuirecuy THE HYDRO=METALLURGY OF COPPER. Being an Account of Processes Adopted in the Hydro-Metallurgical Treat- ment of Cupriferous Ores, Including the Manufacture of Copper Vitriol, with Chapters on the Sources of Supply of Copper and the Roasting of Copper Ores. By M. Eissler, M.Inst.M.M. Svo, cloth .... Nei12lB .1 f ii.^^" this volume the various proc-esses for the extraction of copper by wet methods are fuU v detailed. Costs are given when available, and a great deal of useful information about the copped industry of the world is presented in an interesting and attractive manner. "-Afjm«r Journal MINING, METALLURGY. * COLLIERY WORKING. 25 THE METALLURGY OF ARGENTIFEROUS LEAD. A Practical Treatise on the Smelting of Silver-Lead Ores and the Refining of Lead Bullion. Including Reports on various Smelting Establishments and Descriptions of Modern Smelting Furnaces and Plants in Europe and America. By M. EissLER, M.Inst.M.M. Crown 8vo, cloth .... 12/6 " The numerous metaUurgfical processes, which are fully and extensively treated of, embrace all the stages experienced in the passage of the lead from the various natural states to its Issue from the refinery as an article of commerce." — Practical Engineer. METALLIFEROUS MINERALS AND MINING. By D. C. Davies, F.G.S. Sixth Edition, thoroughly Revised and much Enlarged by his Son, E. Henry Davies, M.E., F.G.S. 600 pp., with 173 Illustrations. Large crown 8vo, cloth Net 1 2/6 " Neither the practical miner nor the general reader, interested in mines, can have a better book for his companion and his guide." — Mining; Joumai. EARTHY AND OTHER MINERALS AND MINING. By D. C. Davies, F.G.S., Author of " Metalliferous Minerals," &c. Third Edition, Revised and Enlarged by his Son, E. Henry Davies, M.E., F.G.S. With about 100 Illustrations. Crown 8vo, cloth 12/6 " We do not remember to have met with any English work on mining matters that contains the same amount of information packed in equally convenient form." — Academy. BRITISH MINING. A Treatise on the History, Discovery, Practical Development, and Future Prospects of Metalliferous Mines in the United Kingdom. By Robert Hunt, F.R.S., late Keeper of Mining Records. Upwards of 950 pp., with j^o Illustrations. Second Edition, Revised. Super-royal 8vo, cloth £2 28. POCKET-BOOK FOR MINERS AND METALLURGISTS. Comprising Rules, Formulas, Tables, and Notes for Use in Field and Office Work. By F. Danvers Power, F.G.S., M.E. Second Edition, Corrected. Fcap. 8vo, leather 9/0 " This excellent book is an admirable example of its kind, and ought to find a large sale amongst English-speaking prospectors and mining eagm&exs."— Engineering, THE MINER'S HANDBOOK. A Handy Book of Reference on the subjects of Mineral Deposits, Mining Operations, Ore Dressing, &c. For the Use of Students and others interested in Mining Matters. Compiled by John Milne, F.R.S., Professor of Mining in the Imperial University of Japan. Third Edition. Fcap. 8 vo, leather 7/6 " Professor Milne's handbook is sure to be received with favour by all connected with mining, and will be extremely popular among students." — Athenieum. IRON ORES of GREAT BRITAIN and IRELAND. Their Mode of Occurrence, Age and Origin, and the Methods of Searching for and Working Them. With a Notice of some of the Iron Ores of Spain. By J. D. Kendall, F.G.S., Mining Engineer. Crown Svo, cloth , . 16/0 METALLURGY OF IRON. Containing History of Iron Manufacture, Methods of Assay, and Analyses of Iron Ores, Processes of Manufacture of Iron and Steel, &c. By H. Bauermak, F.G.S., A.R.S.M. With numerous Illustrations. Sixth Edition, revised and enlarged. Crown Svo, cloth .... 5/0 " Carefully written, it has the merit of brevity and conciseness, as to less important points; while all material matters are very fully and tlioroughly entered into." — Standards MINE DRAINAGE. A Complete Practical Treatise on Direct-Acting Underground Steam Pumping Machinery. By Stephen Michell. Second Edition, Re-written and Enlarged. With 250 Illustrations. Royal Svo, cloth . A'e/ 25/0 HORIZONTAL PUMPING ENGINES.— ROTARY AND NON-ROTARY HORIZONTAL engines.— Simple AND Compound Steam pumps.— VERTICAL PUMPING ENGINES.- rotary and non-rotary vertical engines.— simple and compound steam pumps. — triple-expansion steam pumps. — pulsating steam pumps. — pump Valves.— Sinking pumps, &c., &c. "This volume contains an Immense amount of Important and Interesting new matter. The book should undoubtedly prove of great use to all who wish for information on the sub- ject." — The Engineer, 26 CROSBY LOCKWOOD * SON'S CATALOGUE. PRACTICAL COAL-MINING. An Elementary Class-Book for the Use of Students attending Classes in Pre- paration for the Board of Education and County Council Examinations, or Qualifying for First or Second Class Colliery Managers' Certificates. By T. H. CocKiN, Member of the Institution of Mining Engineers, Certificated Colliery Manager, Lecturer on Coal-Mining at Sheffield University College. With Map of the British Coal-fields and over 200 Illustrations specially Drawn and Engraved for the Work. 440 pages, Crown 8vo, cloth . . Nei 4-IQ " Tlie style of exposition is lucid, the diagrams are clear, and as a 'first-book' to put into the hands of an embryonic colliery m.inager, the volume is an unquestionable success." — Mining- Journal. FIRST LESSONS IN COAL MINING. For Use in Primary Schools. By William Glover, Headmaster of the Higher Standards School, Maesteg, Glamorgan. With Diagrams and other Illustrations, and Introductory Note by H. F. Bulman, Member of the Institution of Mining EngineerSk Crown 8vo. {Just Published. Net 1 /O ELECTRICITY AS APPLIED TO MINING. By Arnold Lupton, M.Inst.C.E., late Professor of Coal Mining at the Yorkshire College, Victoria University ; G. D. Aspinall Parr, M.I.E.E., A.M.I.M.H, Head of the Electrical Engineering Department, Yorkshire College, Victoria University; and Herbert Perkin, M.I.M.E., Certificated Colliery Manager, Assistant Lecturer in the Mining Department of the Yorkshire College, Victoria University, With about 170 Illustrations, Second Edition, Revised and Enlarged. Medium 8vo, cloth, \J^^i Published. Net 1 2/0 " The work is well written, and exactly suited for rapid reference by men to whom time is an object of the first importance." — Athen^um. " Ought to find a place in the library of all who are interested in the latest development of this branch of mining engineering." — Electrical Review, THE COLLIERY MANAQER'5 HANDBOOK. A Comprehensive Treatise on the Laying-out and Working of Collieries, Designed as a Book of Reference for Colliery Managers, and for the Use of Coal- Mining Students preparing for First-class Certificates, By Caleb Pamely, Member of the North of England Institute of Mining and Mechanical Engineers, and the South Wales Institute of Mining Engineers. With over 1,000 Diagrams, Plans, and other Illustrations. Fifth Edition, Carefully Revised and Greatly Enlarged. 1,200 pp. Medium 8vo, cloth Net £1 Qs. Geology.— Search for coal.— Mineral Leases and other Holdings.— Shaft Sinking.— Fitting up the Shaft and Surface Arrangements.— Steam Boilers and their Fittings.— Timbering and Walling.— Narrow work and Methods of Working. — Underground Conveyance. - Drainage.— the Gases met with in Mines ; Ventilation. — On the Friction op Air in Mines. — the Priestman Oil Engine; Petroleum and Natural Gas. — Surveying and Planning.— Safety I^amps and Firedamp Detectors.— St ndrv and Incidental Operations.— Colliery Explosions.— Miscellaneous Questions .\nd Answers.— Summary op Report op H.M. Commissioners on accidents in Mines, ' ' Eminently suited to the purpose for which it Is intended, bein^ clear interesting, exhaustive, rich in detail, and up to date, giving descriptions of the latest machines Ir every department. A mining engineer could scarcely wrong who followed this work." — Colliery (ruavdian. "This Is the most comj-lcte 'all-round' work on coal-mining puDllshetl in the English language. . , . No library of coal-mlnlng books Is complete without It. "- Colliery Engitieer (Scranton, Pa., U.S.A.). COLLIERY WORKING AND MANAGEMENT. Comprising the Duties of a Colliery Manager, the Superintendence and Arrangement of Labour and Wages, and the different Sj'Stems of Working Coal Seams. By H. F. Bulman, F.G.S., Member of the Institution of Mining Engineers, and R. A, S. Redmayne, M.Sc, F.G.S., Professor of Mining in the University of Birmingham. 450 pp., witt 28 Plates and other Illustrations, including Underground Photographs. Medium 8vo, cloth. \. Just published. Net 18 '0 '*Thls Is, Indeed, an admirable Handbook for Colliery Managers, in fact It Is an indispensable adjunct to a Colliery Manager's education, as well as being a most useful and interesting work on the subject for all who in any way have to do with coal mining," — Colliery Guardian, MINim. METALLURGY. S- COLLIERY WORKING. 27 NOTES AND FORMUL/E FOR MINING STUDENTS. By John Herman Merivalk, M.A., Late Professor of Mining in the Durham College of Science, Newcastle-upon-Tyne. Fourth Edition, Revised and Enlarged. By H. F. Bulman, A.M.Inst.C.E. Small crown 8vo, cloth. 2/6 "The author has done his work in a creditable manner, and has produced a book that will be of service to students and those who are practically engaged in mining operations."— Enfz/teer. PHYSICS AND CHEMISTRY OF MINING. An Elementary Class-Book for the use of Stiidents preparing for the Board of Education and County Council Examinations in Mining, or qualifying for Colliery Managers' Certificates. By T. H. Byrom, Chemist to the Wigan Coal and Iron Co., Ltd., &c. With Illustrations. Crown 8vo, cloth. [/usf Published. Net 3/6 MINING CALCULATIONS. For the use of Students Preparing for the Examinations for Colliery Managers' Certificates, comprising Numerous Rules and Examples in Arithmetic, Algebra, and Mensuration. By T. A. O'Donahue, M.E., First- class Certificated Colliery Manager. Crown 8vo, cloth . . . 3/6 COAL AND COAL MINING, By the late Sir Warington W. Smyth, M.A., F.R.S. Eighth Edition, Revised and Extended by T. Forster Brown, Chief Inspector of the Mines of the Crown and of the Duchy of Cornwall. Crown 8vo, cloth . 3/6 " Every portion of the volume appears to have been prepared with n\uch care. The book will doubtless interest a very large number of readers."— Journal. INFLAMMABLE GAS AND VAPOUR IN THE AIR (The Detection and Measurement of). By Frank Clowes, D.Sc, Lond., F.I.C. With a Chapter on The Detection and Measurement or Petro- leum Vapour, by Boverton Redwood, F.R.S.E. Crown 8vo, cloth. Net 5/0 " Professor Clowes has given us a volume on a subject of much industrial Importance . . Those Interested in these matters may be recommended to study this book, which is easy of compre- hension and contains many good things."— rA< Engineer. COAL & IRON INDUSTRIES of the UNITED KINGDOM. Comprising a Description of the Coal Fields, and of the Principal Seams of Coal, with Returns of their Produce and its Distribution, and Analyses of Special Varieties. Also, an Account of the Occurrence of Iron Ores in Veins or Seams ; Analyses of each Variety ; and a History of the Rise and Progress of Pig Iron Manufacture. By Richard Meade. 8vo, cloth . . £1 8s. MINING TOOLS, , , . Manual of. By W. Morgans, Lecturer on Mining at the Bristol School of Mines. Crown Svo, cloth 2/6 Atlas of Engravings to the above, containing 235 Illustrations drawn to Scale. 4to 4/6 " Ktudents, Overmen, Captains, Managers, and Viewers may gain practical knowledge and useful hints by the study of .Vlr. Morgans' ^\;\\\wa\." —Colliery Gtiardian. SLATE AND SLATE QUARRYING. Scientific, Practical, and Commercial. By D. C. Davies, F.G.S., Mining Engineer, &c. With numerous Illustrations and Folding Plates. Fourth Edition. Crown 8vo, cloth 3/0 " One of the best and best-balanced treatises on a special subject that we have met with."— Ensineer. A FIRST BOOK OF MINING AND QUARRYING. By J. H. C0LLIN.S, F.G.S. Crown 8vo, cloth 1/6 ASBESTOS AND ASBESTIC. Their Properties, Occurrence, and Use. By Robert H. Jones, F.S.A., Mineralogist, Hon. Mem. Asbestos Club, Black Lalte, Canada. With Ten Collotype Plates and other Illustrations. Demy Svo, cloth. . Net 1 6/0 " An Interesting and invaluable work."— Co/Ziery Guardiar, 28 CROSBY LOCKWOOD * SON'S CATALOGUE. QRANITE5 AND OUR GRANITE INDUSTRIES. By George F. Harris, F.G.S. With Illustrations. Crown 8vo. cloth 2/6 MINERAL SURVEYOR AND VALUER'S GUIDE. Comprising a Treatise on Improved Mining Surveying and the Valuation of Mining Properties, vfith New Traverse Tables. By W. Lintern, C.E., Fourth Edition, enlarged. Crown 8v6, cloth 3/6 " Cont.-iiTi.s much valuable information, and is thoroughly trustworthy."— and Coal Trades Review. TRAVERSE TABLES. For use in Mine Surveying. By William Lintern, C E With two plates. Small crown 8vo, cloth Q/Q SUBTERRANEOUS SURVEYING. By T. Fenwick. Also the Method of Conducting Subterraneous Surveys without the use of the Magnetic Needle, &c. By T. Baker. Cr. 8vo. 2/6 MINERALOGY, Rudiments of. By A. Ramsay, F.G S. Fourth Edition. Woodcuts and Plates. Crown 8vo, cloth g/g PHYSICAL GEOLOGY, Partly based on Major-General Portlock's " Rudiments of Geology." By Ralph Tate, A.L.S., &c. Woodcuts. Crown 8vo, cloth . , . 2'0 HISTORICAL GEOLOGY, Partly based on Major-General Portlock's "Rudiments." By Ralph Tate. Crown 8vo, cloth 2/6 GEOLOGY, Physical and Historical Consisting of the above two volumes bound together. Crown 8vo, cloth 4/g ELECTRICITY, ELECTRICAL ENG INEERING, ETC. THE ELEMENTS OF ELECTRICAL ENGINEERING. A First Year's Course for Students. By Tyson Sewell, A.I.E.E., Assistant Lecturer and Demonstrator in Electrical Engineering at the Polytechnic, Regent Street, London. Third Edition, Revised and Enlarged, including an Appendix of Questions and Answers. 460 pages, with 274 Illustrations. Demy 8vo, cloth. [Just Published. Net 7/6 Ohm's Law.— Units Employed in Electrical Engineering. -Series and Parallel Circuits; Current Density and potential Drop in the Circuit — The Heating Effect of the Electric Current.— the Magnetic Effect of an Electric Current.— The Magnetisation ofIron.— electro-Chemistry; primary Batthries.—Accumulators.— Indicating Instruments Ammeters, Voltmeters, Ohmmeters.— Electricity Supply Meters. —Measuring Instruments, and the Measurement of Electrical Resistance. — Measurement of Potential Dif- ference, Capacity Current Strength, and Permeability.— arc Lamps.— incan- descent Lamps, Manufacture and installation ; Photometry. — the con- tinuous Current Dynamo.— Direct Current Motors.— alternating Currents. —Transformers, Alternators, Synchronous Motors.— Polyphase working — Appendix of Questions and Answers. » "An excellent treatise for students of the elementary facts connected with electrical engineering." — The Electrician, " One of the best books for those commencing- the study of electrical engineering. Every- thing is explained in simple langu ge which even a beginner cannot fail to understand."— En^neer. " One welcomes this book, which is sound in its treatment, and admirably calculated to give students the knowledge and information they most reauire." — Nature. ELEMENTARY ELECTRICAL ENGINEERING In Theory and Practice. A Class-book for Junior and Senior Students, and Working Electricians. By J. H. Alexander, M.B., A.I.E.E. With 181 Illustrations. Crown 8vo, cloth. [Just Published. Net 3/6 THE ELECTRICAL TRANSMISSION OF ENERGY. A Manual for the Design of Electrical Circuits. By Arthur Vaughan Abbott C.E., Member American Institute of Electrical Engineers, Member American Institute of Mining Engineers, Member American Society of Civil Engineers, Member American Society of Mechanical Engineers, &c. With Ten Folding Diagrams and Sixteen Full-page Engravings. Fourth Edition, entirely Re-Written and Enlarged. Royal Svo, cloth . . Net 30/0 ELECTRICITY. ELECTRICAL ENGINEERING, S'C. 2g ELECTRICITY AS APPLIED TO MINING. By Arnold Lopton, M.Inst C.E., M.I.M.E., M.I E E., late Professor of Coal Mining at the Yorkshire College, Victoria University, Mining Engineer and Colliery Man.iger ; G. D. Aspinall Parr, M.I. E E., A M.I.M.E., Associate of the Central Technical College, City and Guilds of London, Head of the Electrical Engineering Department, Yorkshire College, Victoria University; and Herbert Perkin, M.I.M.E., Certificated Collierj' Manager, Assistant Lecturer in the Mining Department of the Yorkshire College, Victoria University. With about 170 Illustrations Second Edition, Revised and Enlarged. Medium 8vo, cloth. [/^st P-ublisheA. Net 1 2/0 ELECTRIC=WIRlNO, DIAGRAMS «& SW1TCH=B0ARDS. A Work on the Theory and Design of Wiring Circuits. A Practical Guide for Wiremen, Contractors, Engineers, Archilects, and others interested in the application of Electricity to Illumination and power. By Newton Harrison, E.E., Instructor in Electrical Engineering in the Newark (U.S.) Technical School. With 105 Illustrations. Crown Svo, cloth. \J-ust Published. Net 5/0 CONDUCTORS FOR ELECTRICAL DISTRIBUTION. Their Materials and Manufacture, The Calculation of Circuits, Pole-Line Construction, Underground Working, and other Uses. By F. A.C.Perrine, A.M., D.Sc- ; formerly Professor of Electrical Engineering, Leland Stanford, Jr., University ; M.Amer.I.E.E. Svo, cloth .... Net 20/0 Conductor Materials— alloyed conductors— Manufacture of Wire— Wire-Finishing— Wire insulation— Cables— Calculation of circuits— Kelvin's Law of Economy in Conductors— Multiple Arc Distribution— alternating Current Calculation— Overhead Lines— Pole Line— Line Insulators— Under. GROUND Conductors. DYNAMO ELECTRIC MACHINERY: its CONSTRUC- TION, DESIQN, and OPERATION. By Samuel Sheldon, A.M., Ph.D., Professor of Physics and Electrical Engi- neering at the Polytechnic Institute of Brooklyn, assisted by H. Mason, B.S. In two volumes, sold separately, as follows : — Vol. I.— DIRECT CURRENT MACHINES. Fifth Edition, Revised. Large crown Svo. 280 pages, with 200 Illustrations . . Net 1 2/0 Vol. II.— ALTERNATING CURRENT MACHINES. Large crown Svo. 260 pages, with 184 Illustrations Net 12/0 Desigrned as Text-books for use in Technical Educational Institutions, and by Engineers whose worlc includes the handling- of Direct and Alternating Current Machines respectively, and for Students proficient in mathematics. DYNAMO, MOTOR AND SWITCHBOARD CIRCUITS FOR ELECTRICAL ENGINEERS. A Practical Book dealing with the subject of Direct, Alternating and Poly- phase Currents. By William R. Bowkkr, C.E., M.E., E.E., Consulting Tramway Engineer. Svo, cloth Net 6/0 " Mr. Bowker's book consists chiefly of diagrams of connections, with short explanatory notes, there are over 100 diagrams, and the cases considered cover all the more important circuits, whether in direct current, single-phase or polyphase work." — Nature. ARMATURE WINDINGS oP DIRECT CURRENT DYNAMOS. Extension and Application of a General Winding Rule. By E. Arnold, Translated from the German by F.B. De Gress. Svo, cloth . Net 12/0 POWER TRANSMITTED BY ELECTRICITY, And applied by the Electric Motor, including Electric Railway Construction. By P. Atkinson, A.M., Ph.D. Third Edition, Fully Revised, and New Matter added. With 94 Illustrations. Crown Svo, cloth . . Net 9/0 THE MANAGEMENT OF DYNAMOS. A Handybook of Theory and Practice for the Use of Mechanics, Engineers, Students, and others in Charge of Dynamos. By G. W. Lummis-Patkrson. Third Edition, Revised. Crown Svo, cloth 4/6 " The subject is treated In a manner which any intelligent man who Is fit to be entrusted with charge of an engine should be able to understand. It is a useful boot to all who make, tend, or employ electric machinery." — Architect. CROSBY LOCK WOOD SOiTS CATALOGUE. DYNAMO CONSTRUCTION. A Practical Handbook for the Use of Engineer-Constructors and Electricians- in-Charge. By J. W. Urquhart. Second Edition, Enlarged, with 114 Illustrations. Crown 8vo, cloth . 7IS HOW TO MAKE A DYNAMO. A Practical Treatise for Amateurs. Containing Illustrations and Detailed Instructions for Constructing a Small Dynamo to Produce the Electric Light. By Alfred Crofts. Seventh Edition. Crown 8vo, cloth . . . 2/0 WIRELESS TELEGRAPHY; Its Origins, Development, Inventions, and Apparatus. By Charles Henry Skwall. With 85 Diagrams and Illustrations. Svo, cloth . Net 1 0/6 SUBMARINE TELEGRAPHS. Their History, Construction, and Working. Founded in part on WCnschkn- dorff's " Traite de T^legraphie Sous-Marine," and Compiled from Authorita- tive and Exclusive Sources. By Charles Bright, F.R.S.E., A.M.Inst.C.E., M.I.E.E. 780 pp., fully Illustrated, including Maps and Folding Plates. Royal Svo, cloth JVet £3 Ss. " This admirable volume must, for many years to ccme, hold the position of the English classic on submarine telegraphy." — Eng^ineer. ELECTRICAL AND MAGNETIC CALCULATIONS. For the Use of Electrical Engineers and Artisans, Teachers, Students, and all others interested in the Theory and Application of Electricity and Magnetism. By Prof. A. A. Atkinson, Ohio University. Crown 8vo, cloth Net 9/0 " To teachers and those who already possess a fair knowledge of their subject we can recom- mend this book as being useful to consult when requiring data or formulae which it is neither con- venient nor necessary to retain by memory." — Tke Electrician. THE STANDARD ELECTRICAL DICTIONARY. A Popular Encyclopaedia of Words and Terms Used in the Practice of Electrical Engineering. Containing upwards of 3,000 definitions. By T. O'Conor Sloane, A.m., Ph.D. Third Edition, with Appendix. Crown 8vo, 6qo pp., 3QO Illustrations, cloth Net 7/6 " The work has many attractive features in it, and Is, beyond doubt, a well put together and useful publication. The amount of ground covered may be gathered from the fact that in the index about 5,000 references will be io\md."— Electrical Review. ELECTRIC LIGHTING (ELEMENTARY PRINCIPLES OF). By Alan A. Campbell Swinton, M.Inst.C.E., M.I.E.E. Sixth Edition. With 16 Illustrations. Crown 8vo, cloth 1/6 ELECTRIC LIGHT. Its Production and Use, Embodying Plain Directions for the Treatment of Dynamo-Electric Machines, Batteries, Accumulators, and Electric Lamps. By J. W. Urquhart, C.E. Seventh Edition. Crown 8vo, cloth . 7/6 " The whole ground of electric lighting is more or less covered and explained In a very clear and concise manner, "—Elect} ical Review. ELECTRIC LIGHT FOR COUNTRY HOUSES. A Practical Handbook on the Erection and Running of Small Installations, with Particulars of the Cost of Plant and Working. By J. H. Knight. Fourth Edition, Revised. Crown Svo, wrapper 1/0 ELECTRIC LIGHT FITTING. A Handbook for Working Electrical Engineers, embodying Practical Notes on Installation Management. By J. W. Urquhart. With numerous Illustra- tions. Fourth Edition, Revised. Crown Svo, cloth S/O " This volume deals with the mechanics of electric lighting, and is addressed to men who are already engaged in the work, or are training for it. The work traverses a great deal of ground, and may be read as a sequel to the author's useful work on 'Electric U^ht.' "—Electrician. ELECTRIC SHIP-LIGHTING. A Handbook on the Practical Fitting and Running of Ships' Electrical Plant. For the Use of Shipowneis and Builders, Marine Electricians, and Seagoing Engineers-in-Charge. By J. W. Urquhart, C.E. Crown Svo, cloth 7/6 " Mr. Urquhart Is to be highly complimented for placing such a valuable work at the service of marine electricians." — The Steamskif. DYNAMIC ELECTRICITY AND MAGNETISM. By Philip^ Atkinson, A.M., Ph.D., Author of "Elements of Static Electricity," &c. Crown Svo, 417 pp., with 120 Illustrations, cloth . ■|0/'6 THE STUDENT'S TEXT-BOOK OF ELECTRICITY. By H. M. NoAD, F.R.S. 650 pp., with 470 Illustrations. Crown Svo, cloth. 9yo ARCHITECTURE, BUILDING, &'C. 31 ARCHITECTURE, BUILDING, ETC. PORTFOLIO OF MEASURED DRAWINGS. Issued by the School of Architec ure of the University of Liverpool. To be published annually under the direction of Professor C. H. Reii.i.y. Con- taining measured drawings (including detailed _ drawings and contours ot mouldings) of notable buildings in Great Britain and Ireland, and on the Continent. Each volume will be produced in folio, with about 30 full-page plates and descriptive letterpress. . , ., ,. , , ^ Vol I. contains a complete External Survey of the following buildings with detail drawing-! to a large scale THE TOWN HALL, 7.IVERPOOL, 7 PLATES.-THE PALACE OE THE PETIT TRIANON. Versailles, 5 Pl.-\tes.-The Palace of the Grand Trianon, Versailles, 4 Plates,— THE Custom House, Dublin, 4 plates.-The Orangery, Kensington Palace % plates.— The Senate House, Cambridge, 3 Plates.— The House of Providence, dingle Lane, Liverpool, i plate.-Lodge to the House of Provi- dence I Plate —Main Doorway under Colonnade, St. George's Hall, Liverpool, I Plate.— Jacobean Oak Chimney Piece, hall-i'-th'-Wood museum, Bolton, i Plate. Either loose in a cloth Portfolio or bound in cloth. Net 21/0 SPECIFICATIONS IN DETAIL. By Frank W. Macey, Architect, Author of " Conditions of Contract. Second Edition, Revised and Enlarged, containing 644 pp., and 2,000 Illustra- tions. Royal 8vo, cloth Net ^MO Summary of contents :— General Notes.— Specification of works and List of general conditions.— preliminary Items (including Shoring and house Breaker).— Drainage (including Rain-water Wells and reports.— Excavator (including Concrete Floors, roofs. Stairs and Walls) - Pavior.— Bricklayer (including Flintwork, River and other Walling. Spring- water Wells, Storage TA^KS, Fountains, Filters, Terra Cotta and Faience).— Mason —Carpenter, Joiner and ironmonger (including Fencing and piling).— Smith and founder (including Heating, Fire Hydrants, stable and Cow-housk FITTINGSI.-SLATER (including slate MAS0N).-TILHR.— stone TILER.-SHINGLER.- THATCHER - plumber (including hot-water WORK). - ZINCWORKER. — copper- smith — Plasterer - Gasfitter. — Bellhanger. — Glazier. — painter. — paper HANGKR. — GENERAL REPAIRS AND ALTERATIONS. —VENTILATION. — ROAD-MAKING. - ELECTRIC Light.— Index. "We strongly advise every student to purchase the volume and carefully study it, while to the older practitioner we would say, have it by you as a most useful work of reference. —A rchitectural Associaiiofi Notes. LOCKWOOD'S BUILDER'S PRICE BOOK for 1906. A Comprehensive Handbook of the Latest Prices and Data for Builders, Architects, Engineers, and Contractors. Re-constructed, Re-written, and Greatly Enlarged. By Francis T. W. Miller. 800 closely-prmted pages, crown 8vo, cloth. \Jusi Published 4/0 "An excellent book of reference."— ^r<;A«y ,. > •' Comprehensive, reliable, weU arranged, legible and well bound. —British Archtiect. PRACTICAL BUILDING CONSTRUCTION. A Handbook for Students Preparing for Examinations, and a Book of Reference for Persons Engaged in Building. By John Parnell Allen, Surveyor, Lecturer on Building Construction at the Durham College of Science, Newcastle-on-Tyne. Fourth Edition, Revised and Enlarged. Medium 8vo, 570 pp., with over 1,000 Illustrations, cloth . . NetTlQ " The author depends nearly as much on his diagrams as on his type. The pages suggest the hand of a man of experience in buUding operations-and the volume must be a blessmg to many teachers as well as to students." — The Architect. A HANDBOOK ON REINFORCED CONCRETE. For Architects, Engineers and Contractors. By F. D. Warren, Massa- chusetts Institute of Technology, with Illustrations, 271 pages. Crown 8yo, cloth published. Net 1 0/6 EXTRACT from PREFACE. The bjok is divided into four parts. Part I. gives a gf neral but concise xi%w\i. of the subject from a practical standpoint, bringing out some of the difficulties met with in practice and suggesting remedie-. Under Part 11. is cimpiled a series of tests justifying the use of various constants and co-efficients in preparing the tables under Part 111. Part HI. contains a series of Tables from which it is hoped the designer may obtain all necessary information to meet the more common cases in practice. Part IV. treats of the design of trussed roofs from a practical standpomt. 32 CROSBY LOCKWOOD * SON'S CATALOGUE. SPECIFICATIONS FOR PRACTICAL ARCHITECTURE. A Guide to the Architect, Engineer, Surveyor, and Builder. Upon the Basis of the Work by A. Bartholomew, Revised, by F. Rogers. 8vo, cloth 1 5/O " Oneot the books with which every young architect must be equipped."— ^rtAtVerf. SCIENCE OF BUILDING: An Elementary Treatise on the Principles of Construction. By E. Wynd- HAM Tarn, M.A. Lond. Fourth Edition. Crown 8vo, cloth . . 3/6 ART OF BUILDING, Rudiments of. General Principles of Construction, Character, Strength, and Use of Materials, Preparation of Specifications and Estimates, c&c. By Edward Dobson, M.Inst.C.E. Fifteenth Edition, revised by J. P. Allen, Lecturer on Building Construction at the Durham College of Science. Crown 8vo, cloth 2/0 " A good book for practical knowledge, and about the best to be obtained."— ^Kz'/rfiw.i'- News. BOOK ON BUILDING, Civil and Ecclesiastical. By Sir Edmund Beckett, Bart., LL.D. Second Edition. Crown 8vo, cloth 4/6 " A book whicli' is always amusing and nearly always instructive." — Times. BUILDING ESTATES: A Treatise on the Development, Sale, Purchase, and Management of Building Land. By F. Maitland. Fourth Edition. Crown 8vo, cloth 2/0 " This book should undoubtedly be added to the library of every professional man dealing with building land.' ' — Land Agent's Record. COTTAGE BUILDING. By C, Bruce Allen. Twelfth Edition, with Chapter on Economic Cottages for Allotments by E. E. Allen, C.E. Crown 8vo, cloth . 2/0 DWELLING=HOUSES, Erection of, illustrated by a Perspective View, Plans, Elevations, and Sections of a Pair of Villas, with the Specification, Quantities, and Estimates. By S. H. Brooks. Crown 8vo, cloth 2/6 FARM BUILDINGS: Their Arrangement and Construction, with Plans and Estimates. By Pro- fessor J. Scott. Crown 8vo, cloth 2/0 " No one who is called upon to design farm buildings can afford to be without this work."— Builder. SHORING, And its Application. By G. H. Blagrove. Crown 8vo, cloth . .1/6 " We recommend this valuable treatise to all students." — BtiiUhjig News. ARCHES, PIERS, BUTTRESSES. By William Bland. Crown 8vo, cloth -| /6 PRACTICAL BRICKLAYING. General Principles of Bricklaying ; Arch Drawing, Cutting, and Setting, Pointing; Paving, Tiling, Sic. By Adam Hammond. With 68 Woodcuts. Crown 8vo., cloth ■( /g " The young bricklayer will find it infinitely valuable to \ma." —Glasgow Herald. ART OF PRACTICAL BRICK=CUTTING AND SETTING. By Adam Hammond. With 90 Engravings. Crown 8vo, cloth . 1 /6 BRICKWORK : Embodying the General and Higher Principles of Bricklaying, Cutting and Setting; with the Application of Geometry to Roof Tiling, &c. By F. Walker. Crown 8vo, cloth 1/6 " Contains all that a student needs to learn from \>ooY%."— Building News. BRICKS AND TILES, Rudimentary Treatise on the Manufacture of. Containing an Outline of the Principles of Brickmaking. By E. Dobson, M.R.LB.A. Additions by C. ToMLiNSON, F.R.S. Illustrated. Crown 8vo, cloth . . , 3/0 " The best handbook on the subject. We can recommend it as a good investment." -Builder. ARCHITECTURE, BUILDING, &-c. 33 PRACTICAL BRICK AND TILE BOOK. Comprising: Brick and Tile Making, by E. Dobson, M.Inst.C.E. ; Practical Bricklaying by A. Hammond, Brick-Cutting and Setting, by A. Hammond. 550 pp., with 270 Illustrations, strongly half-bound .... 6/0 PRACTICAL MASONRY. A Guide to the Art of Stone Cutting. Comprising the Construction, Setting- Out, and Working of Stairs, Circular Work, Arches, Niches, Domes, Penden- tives. Vaults, Tracery Windows, &c. ; to which are added Supplements relating to Masonry Estimating and Quantity Surveying, and to Building Stones and Marbles, and a Glossary of Terms. For the Use of Students, Masons, and Craftsmen. By W. R. Purchase, Building Inspector to the Borough of Hove. Fifth Edition, Enlarged. Royal 8vo, 226 pp., with 52 Plates, comprising over 400 Diagrams, cloth ..... Net 7/6 " The book Is a practical treatise, Most of the examples given are from actual work carried out. It should be found of general utility to architectural students and others, as well as to those to whom it is SDecially addressed." — jfournal o/the Royal Institute 0/ British Architects, MASONRY AND STONECUTTINQ, The Principles of Masonic Projection, and their Application to Construc- tion. By E. Dobson, M.R.I. B. A. Crown 8vo, cloth . . . . 2/6 MODERN LIGHTNING CONDUCTORS. An Illustrated Supplement to the Report of the Lightning Research Com- mittee of 1905, with Notes as to the Methods of Protection, and Specifica- tions. By KiLLiNGWORTH HEDGES, M.Inst.C.E., M.I.E.E., Honorary Secretary to the Lightning Research Committee, Author of " American Street Railways." Medium 8vo, cloth. {Juit Published. Net 6/6 " The illustrations are very interesting" and give one a clear idea of what is likely to happen when a building is struck by liglitning. Mr. Hedges' suggestions of possible reasons why certain protected buildings were struck are instructive. He also explains the modern methods of fitting buildings with lightning conductors. To the ordinary reader the book will be of interest, and to anyone who lias to design a system for protecting a building from lightning strokes it will be helpluV—SuMer. "The damage done by lightning to various buildings throughout the country is shown. by sketches and photograplis which make the path of the lightning clear. In the book will be found the suggestions and rules of tlie Research Connnittee, which were drawn up after a consideration of the reports on a large number of lightning strokes. These are commented on by the author, who gives also some specifications which will guide surveyors and architects in the right direction. . . . The information given in the volume is mos v3.\ua.b\e."~£lectrical JEji^i^ijieer. MODERN PLUMBING, STEAM AND HOT WATER MEATINQ. A Work for the Plumber, the Heating Engineer, the Architect, and the Builder. By J. J. Lawler. With 284 Illustrations. 4to, cloth . . Net 21/- PLUMBING : A Text-Book to the Practice of the Art or Craft of the Plumber. With Chapters upon House Drainage and Ventilation. By Wm. Paton Buchan. Ninth Edition, with 512 Illustrations. Crown bvo, cloth . . . 3/6 " A text-book which may be safely put into the hands of every young plumber, and whicli will ;il.;o be found useful by architects ancf medical professors." — Builder. HEATING BY HOT WATER, VENTILATION AND HOT WATER SUPPLY. By Walter Jones, M.I.M.E. 360 pages, with 140 Illustrations. Medium 8vo, cloth Net 6/0 THE PRACTICAL PLASTERER: A Coinpendium of Plain and Ornamental Plaster Work. By W. Kemp. Crown 8vo, cloth 2/0 CONCRETE: ITS NATURE AND USES. A Book for Architects, Builders, Contractors, and Clerks of Works. By G. L. SuTCLiFFE, A.R.I.B.A. Second Edition, Revised and Enlarged. 396 pp., with Illustrations. Crown 8vo, cloth. [Just Publislied. Net 9/0 " The manual fills a long-felt gap. It Is careful and exhaustive ; equally useful as a studeLt's gruide and an architect's book of reference."— yo«>«a^ 0/ the Royal Institute 0/ British Architecu. L. 34 CROSBY LOCKWOOD & SON'S CATALOGUE. PORTLAND CEMENT FOR USERS. By the late Henry Faija, M.Inst.C.E. Fifth Edition. Revised and Enlarged by D. B. Butler, A. M.Inst.C.E. Crown 8vo, cloth . . 3/0 " Supplies in a small compass all that is necessary to bo known by users of cement." — Buildin,:; News. LIMES, CEMENTS, MORTARS, CONCRETES, MASTICS, PLASTERING, &c. By G. R. BuRNELL, C.E. Fifteenth Edition. Crown 8vo, cloth . 1/6 MEASURING AND VALUING ARTIFICERS' WORK (The Student's Guide to the Practice of). Containing Directions for taking Dimensions, Abstracting the same, and bringing the Quantities into Bill, with Tables of Constants for Valuation of Labour, and for the Calculation of Areas and Solidities. Originally edited by E. Dobson, Architect. With Additions by E. W. Tarn, M.A. Seventh Edition, Revised. Crown 8vo, cloth. 7/6 "The most complete treatise on the principles of measuring and valuing artificers' work," —Building News. QUANTITIES AND MEASUREMENTS, In Bricklayers', Masons', Plasterers', Plumbers', Painters', Paperhangers', Gilders', Smiths', Carpenters' and Joiners' Work. By A. C. Beaton, Surveyor. Crown 8vo, cloth 1/6 " This book is indispensable to builders and their quantity clerks." — English Mechanic. TECHNICAL GUIDE, MEASURER, AND ESTIMATOR. For Builders and Surveyors. Containing Technical Directions for Measuring Work in all the Building Trades, Complete Specifications for Houses, Roads, and Drains, and an Easy Method of Estimating the parts of a Building collectively. By A, C. Beaton, Tenth Edition. Waistcoat-pocket size. 1 /6 " No builder, architect, surveyor, or valuer should be without his ' Beaton.' "—Building News. COMPLETE MEASURER; Setting forth the Measurement of Boards, Glass, Timber, and Stone. By R. HoRTON. Sixth Edition. Crown Bvo, cloth 4/0 THE HOUSE-OWNER'S ESTIMATOR. Or, What will it Cost to Build, Alter, or Repair? A Price Book for Un- professional People as well as the Architectural Surveyor and Builder. By J, D. Simon. Edited by F. T. W. Miller, A.R.LB.A. Fifth Edition. Carefully Revised. Crown 8vo, cloth JVei 3/6 *' In two years it will repay its cost a hundred times over." — Field. HANDBOOK OF HOUSE PROPERTY. A Popular and Practical Guide to the Purchase, Tenancy, and Com- pulsory Sale of Houses and Land, including Dilapidations and Fixtures : with Examples of all kinds of Valuations, Information on Building and on the right use of Decorative Art. By E. L. Tahbuck, Architect and Surveyor. Seventh Edition. lamo, cloth ........ 6/0 " The advice is thoroughly practical."— Aaa/ jfo " For all who have dealings with house property, this is an Indispensable guide." — Decoration. " Carefully brought up to date, and much improved by the addition of a division on Fine Art. A well-written and thoughtful work." — Land Agents' Record. ARCHITECTURAL PERSPECTIVE. The whole Course and Operations of the Draughtsman in Drawing a Large House in Linear Perspective. Illustrated by 43 Folding Plates. By F. O. Ferguson. Third Edition. 8vo, boards 3/6 " It is the most intelligible of the treatises on this ill-treated subject that I have met with."— E. INGRESS Bhll, Esq., inthe -R./.B.y^. Journal. PERSPECTIVE FOR BEGINNERS For Students and Amateurs in Architecture, Painting, &c. By G. Pvne. Crown 8vo, cloth 2/0 PRACTICAL RULES ON DRAWING. For the Builder and Young Student in Architecture. By G Pynb. 410 7/6 ARCHITECTURE, BUILDING, &'C. 35 THE MECHANICS OP ARCHITECTURE. A Treatise on Applied Mechanics, especially Adapted to the Use of Architects. By E. W. Tarn, M.A., Author of " The Science of Building," &c. Second Edition, Enlarged. Illustrated with 125 Diagrams. Crown 8vo, cloth 7/6 "The book Is a very useful and helpful manual of architectural mechanics."— Builder. A HANDY BOOK OF VILLA ARCHITECTURE. Being a Series of Designs for Villa Residences in various Styles. With Outline Specifications and Estimates. By C. Wickks, Architect, Author of "The Spires and Towers of England," &c. 61 Plates, 4to, half-morocco, gilt edges £1 11s. 6d. DECORATIVE PART OF CIVIL ARCHITECTURE. By Sir William Chambers, F.R.S. With Portrait, Illustrations, Notes, and an Examination of Grecian Architecture, by Joseph Gwilt, F.S.A. Revised and Edited by W. H. Leeds. 66 Plates, 4to, cloth . . 2 I/O HINTS TO YOUNG ARCHITECTS. By George Wightwick, Architect, Author of "The Palace of Architec- ture," &c., &c. Sixth Edition, revised and enlarged by G. Huskisson GuiLLAUME, Architect. Crown 8vo, cloth 3/6 " Ought to be considered as necessary a purchase as a box of instruments."— ^ri;/wV«<3*. THE ARCHITECT'S GUIDE. Being a Text-book of Useful Information for Architects, Engineers, Surveyors, Contractors, Clerks of Works, &c. By F. Rogers. Crown 8vo. . 3/6 ARCHITECTURE— ORDERS. The Orders and their Esthetic Principles. By W. H. Leeds. Cr. 8vo. 1 /6 ARCHITECTURE— STYLES. The History and Description of the Styles of Architecture of Various Countries, from the Earliest to the Present Period. By T. Talbot Bury, F.R.LB.A., &c. Illustrated. Crown 8vo, cloth 2/0 "Orders and Styles of Architecture," tn Oh£ l/o/. . . , 3/6 ARCHITECTURE-DESIGN. The Principles of Design in Architecture, as deducible from Nature and exemplified in the Works of the Greek and Gothic Architects. By Edw. L. Garbett, Architect. Crown Svo, cloth 2/6 "We know no work that we would sooner recommend to an attentive reader desirous 10 obtain clear views of the nature of architectural art. The book is a valuable one."— Builder. *** The three preceding Works in One handsome Vol., half-bound, entitled "Modern ARCHiTECTURi'," price QIQ. ARCHITECTURAL MODELLING IN PAPER, The Art of. By T. A. Richardson. Crown Svo, cloth . . .1/6 " A valuable aid to the practice of architectural modelling."— Btiilder's U'eekly Reporter. VITRUVIUS.— THE ARCHITECTURE OF MARCUS VITRUVIUS POLLIO. In Ten Books. Translated from the Latin by J. Gwilt. With 23 Plates. Crown Svo, cloth 5/0 N.B.—This is the only Edition of Vitruvius procurable at a moderate price. GRECIAN ARCHITECTURE, An Inquiry into the Principles of Beauty in ; with an Historical View of the Rise and Progress of the Art in Greece. By the Earl of Aberdeen 1 IQ *** The two preceding Works in One handsome Volume, half-bound, entitled "Ancient Architecture," price 6/0- ACOUSTICS OF PUBLIC BUILDINGS: The Laws of Sound as applied to the Arrangement of Buildings By Professor T. Roger Smith, F.R.I.B.A. New Edition revised. With numerous Illustrations. Crown Svo, cloth 1/6 LIGHT: An introduction to the Science of Optics. Designed for the Use of Students of Architecture, Engineering, and other Applied Sciences, By E, W, Tarn, ■M.A. Crown Svo, cloth 1/6 c 2 36 CROSBY LOCK WOOD *• SONS CATALOGUE. SANITATION AND WATER SUPPLY. THE HEALTH OFFICER'5 POCKET-BOOK. A Guide to Sanitary Practice and Law. For Medical OflScers of Health, Sanitary Inspectors, Members of Sanitary Authorities, &c. By Edward F. WiLLOUGHBY, M.D. (Lond.), &c. Second Edition, Revised and Enlarged. Fcap. 8 vo, leather iV^f 10/6 •• A mine of condensed information of a pertinent and useful kind. The various subjects of which it treats being succinctly but fully and scientifically dealt with."— The Lancet. " We recommend a'l those engaged in practical sanitary work to furnish themselves with a copy for reference."— 5o«rtoo' Journal. THE WATER 5UPPLY OF TOWNS AND THE CON- STRUCTION OF WATER-WORKS. By Professor W. K. Burton, A.M. Inst.C.E. Second Edition, Revised and Extended. Royal 8vo, cloth. (See page i2.) .... £1 Ss. THE WATER SUPPLY OF CITIES AND TOWNS. By William Humber, A.M.Inst.C.E., and M.Inst.M.E Imp. 410, half- bound morocco. (See page 12.) iV^e^ £6 OS. WATER AND ITS PURIFICATION. A Handbook for the Use of Local Authorities, Sanitary Officers, and others interested in Water Supply. By S. Rideal, D.Sc. Lond., F.I.C. Second Edition, Revised, with Additions, including numerous Illustrations and J-ables. Large Crown 8vo, cloth 9/0 RURAL WATER SUPPLY. A Practical Handbook on the Supply of Water and Construction of Water- works for Small Country Districts. By Allan Grkenwell, A.M. I.C.Em andW. T. Curry, A.M.I.C.E. Revised Edition. Crown 8vo, cloth 5/0 WATER ENQINEERINQ. A Practical Treatise on the Measurement, Storage, Conveyance, and Utilisa. tion of Water for the Supply of Towns. By C. Slagg, A.M.Inst.C.E. 7/6 THE PURIFICATION OF SEWAGE. Being a Brief Account of the Scientific Principles of Sewage Purification, and their Practical Application. By Sidney Barwise, M.D. (Lond.), B^c., M R C S , D P.H. (Camb.), Fellow of the Sanitary Institute, Medical Officer of Health to the Derbyshire County Council. Second Edition, Revised and Enlarged, with an Appendix on the Analysis of Sewage and Sewage Effluents. With numerous Illustrations and Diagrams. Demy 8vo, cloth. ISet 10/6 SUMMARY OV CONTENTS: — SEWAGE : ITS NATURE AND COMPOSITION. — THE CHEMISIW OF SEWAGE.-VARIETIES OF SEWAGE AND THE CHANGES IT UNDERGOES -- rVveR POLLUTION AND ITS EFFECTS.-THE LAND TREATMENT OF SEWAGE -PRECIPI- ?lTfoN l^EcIrriANT^^ TANKS.-THE LIQUEFACTION OF SEWAGE.-PRINCIPLES INVOLVED IN THE OXIDATION OF SEWAGE.-ARTIFICIAL PROCESSES OF PURIFICATION - A^UTOMATIC DISTRIBUTORS AND SPECIAL FILTERS.-PARTICULARS OF SEWERAGE AND SEWAGE DISPOSAL SCHEMES REQUIRED BY LOCAL GOVERNMENT BOARD - V,K-XK-At*mdix- THE APPARATUS REQUIRED FOR SEWAGE ANALYSIS.-ST ANDARD SOLUTIONS USED IN THE METHOD OF SEWAGE ANALYSlS.-raWw : LSTIMATTON OF AMMONIA.-Nn-ROGEN AS NiTRATES.-INCUBATOR TEST, OXYGEN ABSORBHD.-TO CONVERT GRAINS PER GALLON TO PARTS PER 100,000. "The book will be of use to those who are responsible for directing and advising on the tientnient of sewage. The information furnished, as a whole, is reasonably accurate and up-to-date. —Nature. SANITARY WORK IN SMALL TOWNS AND VILLAGES. By Charles Slagg, A.M.Inst.C.E. Third Edition, Enlarged. Crown 8vo, cloth ^ • 3'P "This is averj. useful book. There is a great deal of work required to be done in the smaller towns and villages, and this little volume will help those who are willing to do it. -builder . VENTILATION: A Text-Book to the Practice of the Art of Ventilating Buildings. By W. P. BucHAN. With 170 illustrations. Crown 8vo, cloth .... 3/0 CARPENTRY, TIMBER, 37 CARPENTRY, TIMBER, ETC. PRACTICAL FORESTRY. And its Bearing on the Improvement of Estates. By Charles E. Curtis, F.S.I. , Professor of Forestry, Field Engineering, and General Estate Management, at the College of Agriculture, Downton. Second Edition, Revised. Crown 8vo, cloth 3/6 PREFATORY REMARKS. — OBJECTS OF PLANTING. — CHOICE OF A FORESTER. — choice of soil and site.— laying out of land for plantations.— preparation of the ground for planting. —drainage.— planting.— distances and distri- bution of trees in plantations.— trees and ground game.— attention after planting.— thinning of plantations — pruning of forest trees.— realization. —Methods of Sale.— Measurement of Timber.— Measurement and Valuation OF LARCH Plantation.— Fire Lines.— Cost of Planting. " Mr. Curtis has in the course of a series of short pithy chapters afforded much informa- tion of a useful and practical character on the planting and subsequent treatment of trees."— Illustrated Carpenter and Builder. WOODWORKING MACHINERY. Its Rise, Progress, and Construction. With Hints on the Management of Saw Mills and the Economical Conversion of Timber. Illustrated with Examples of Recent Designs by leading English, French, and American Engineers. By M. Powis Bale, M.Inst.C.E., M.I.Mech.E. Second Edition, Revised, with large Additions, large crown 8vo, 440 pp., cloth .... 9/0 " Mr Bale Is evidently an expert on the subject, and he has collected so much Information that his book is all-sufficient for builders and others engaged in the conversion of timber."— vif-cAiVnt.'. "The most comprehensive compendium of wood-working machinery we have seen. The author is a thorough master of his subject."— S««7rfi«£-iV;«7a'cr. TIMBER IMPORTER'S, TIMBER MERCHANT'S, AND BUILDER'5 STANDARD GUIDE. By R. E. Grandy. Crown 8vo, cloth 2/0 " Everything it pretends to be : built up gradually, it leads one from a forest to a treenail, and throws in, as a makeweight, a host of material concerning bricks, columns, cisterns, &c." — English Mechanic. TIMBER MERCHANT'S and BUILDER'S COMPANION. Containing New and Copious Tables of the Reduced Weight and Measure ment of Deals and Battens, of all sizes, and other Useful Tables for the use of Timber Merchants and Builders. By William Dowsing. Fifth Edition, Revised and Corrected. Crown 8vo, cloth 3/0 "We are glad to see a fourth edition of these admirable tables, which for correctness and simplicity of arrangement leave nothing to be desired." — Timber Trades Jcmrnal. THE PRACTICAL TIMBER MERCHANT. Being a Guide for the Use of Building Contractors, Surveyors, Builders, &c., comprising useful Tables for all purposes connected v/ith the Timber Trade, Marks of Wood, Essay on the Strength of Timber, Remaiks on the Growth of Timber, &c. By W. Richardson. Second Edition. Fcap. Svo, cloth . 3/6 "This handy manual contains much valuable information for the use of timber merchants, builders, foresters, and all others connected with the growth, sale, and manufacture of timber."— yournal of Forestry. PACKING-CASE TABLES. Showing the number of Superficial Feet in Boxes or Packing-Cases, from six inches square and upwards. By W. Richardson, Timber Broker. Fourth Edition. Oblong 410, cloth 3/6 " Invaluable labour-saving \.3\Jies."— Ironmonger. "Will save much labour and calculation." — Grocer. GUIDE TO SUPERFICIAL MEASUREMENT. Tables calculated from i tolaoo inches in length, by i to 108 inches in breadth. For the use of Architects, Surveyors, Engineers, Timber Merchants, Builders, &c. By J. Hawkings. Fifth Edition. Crown 8vo, cloth . 3/6 " These tables will be found of great assistance to all who require to make calculations of superficial measurement."— Mechanic. DECORATIVE ARTS, S-c. 39 DECORATIVE ARTS, ETC. SCHOOL OF PAINTING FOR THE IMITATION OF WOODS AND MARBLES. As Taught and Practised by A. R. Van der Burg and P. Van der Burg, Directors of the Rotterdam Painting Institution. Royal folio, i8J by izj in., Illustrated with 24 full-size Coloured Plates ; also 12 plain Plates, comprising 154 Figures. Fourth Edition, cloth iWif £1 5s. List of Plates. i. various tooi-s requirbd for wood painting.— s, 3. walnut: preliminary Stages or graining and Finished Specimen. — 4. Tools used for Marble Painting and Method of Manipulation.— 5, 6. St. Remi marble; Earlier Operations and finished Specimen. — 7. Methods of Sketching Different Grains, Knots, &c.— 8, 9. Ash: preliminary Stages and Finished Speci- men. — 10. Methods of Sketching Marble Grains. — n, 12. breche Marbles Preliminary Stages of Working and Finished Specimen.— 13. Maple ; Method. OF producing the Different Grains.— 14, 15. Bird's-Eye Maple; Preliminary Stages and Finished Specimf.n.— 16. methods of Sketching the Different Species of White marble.— 17, 18. white Marble ; Preliminary Stages of Process and Finished Specimen —19. Mahogany: Specimens of Various Grains AND methods of MANIPULATION. —20, 21. MAHOGANY ; EARLIER STAGES AND FINISHED SPECIMEN.— 22, 23, 24 SlENNA MARBLE ; VARIETIES OF GRAIN, PRELIMINARY STAGES AND FINISHED SPECIMEN —25, 26, 27. JUNIPER WOOD; METHODS OF PRO- DUCING GRAIN, &c. ; PRELIMIN.A.RY STAGES AND FINISHED SPECIMEN.— 28, 29, 30. VERT DE MER MARBLE; VARIETIES OF GRAIN AND METHODS OF WORKING, UNFINISHED AND FINISHED SPECIMENS.— 31, 32, 3.3. OAK ; VARIETIES OF GRAIN, TOOLS EMPLOYED AND METHODS OF M.4.NIPULATION, PRELIMINARY STAGES AND FINISHED SPECIMEN.— 34. 35, 36. WAULSORT MARBLE; VARIETIES OF GRAIN, UNFINISHED AND FINISHED SPECIMENS. "Those who desire to attain skill in the art of painting woods and marbles will find advantage in consulting this book. . . . Some of the Working Men's Ciubs should give their young men the opportunity to study it." — Buiider. " A comprehensive guide to the art. The explanations of the processes, the manipulation and management of the colours, and the beautifully executed plates will not be the least valuable to the student who aims at making his work a faithful transcript of nature."— S««Vift«^ News. " Students and novices are fortunate who are able to become the possessors of so noble a work." — The Architect, HOUSE PAINTING, GRAINING, MARBLING, AND SIGN WRITING: With a Course of Elementary Drawing, and a Collection of Useful Receipts. By E. A. Davidson. Ninth Edition. Coloured Plates. Cr. 8vo, cloth . 5/0 *^5* The above, in cloth boards, strongly bound, 6/0- " A mass of information of use to the amateur and of value to tlie practical man."— £u£l!sh Mechanic. ELEMENTARY DECORATION: As Applied to Dwelling-Houses, &c. ByJ.W. Facey. Cr. 8vo, cloth 2/0 "The principles which ought to guide the decoration of dwelling-houses are clearly set forth, and elucidated by examples ; while full instructions are given to the learner." — Scotsman. PRACTICAL H0U5E DECORATION. A Guide to the Art of Ornamental Painting, the arrangement of Colours in Apartments, and the Principles of Decorative Design. By James W. Facey. Crown 8vo, cloth 2 '6 * * The last two works in One handsome Vol., half-bound, entitled "House Decoration, Elementary and Practical," price 5/0- ORNAMENTAL ALPHABETS, ANCIENT & MEDI/EVAL. From the Eighth Century, with Numerals ; including Gothic, Church-Text large and small, German, Italian, Arabesque, Initials for Illumination Monograms, Crosses, &c., for the use of Architectural and Engineering Draughtsmen, Missal Painters, Masons, Decorative Painters, Lithographers, Engravers, Carvers, &c., &c. Collected and Engraved by F. Delamotte, and printed in Colours. New and Cheaper Edition. Royal 8vo, oblong, ornamental boards 2/6 ** For those who insert enamelled sentences round gilded chalices, who blazon shop legends over shop-doors, who letter church walls with pithy sentences from the Decalogue, this book will be useful." — A thenaum . CROSBY LOCK WOOD &- SON'S CATALOGUE. MODERN ALPHABETS, PLAIN AND ORNAMENTAL. Including German, Old English, Saxon, Italic, Perspective, Greek, Hebrew, Court Hand Engrossing, Tuscan, Riband, Gothic, Rustic, and Arabesque ; with several Original Designs, and an Analysis of the Roman and Old English Alphabets, large and small, and Numerals, for the use of Draughtsmen, Surveyors, Masons, Decorative Painters, Lithographers, Engravers, Carvers, &c. Collected and Engraved by F. Delamotte, and printed in Colours. New and Cheaper Edition. Roval 8vo, oblong, ornamental boards . 2/6 " There is comprised in It every possible shape into which the letters of the alphabet and numerals can be formed, and the talent which has Deen expended in the conception of the various plain and ornamental letters is wonderful." — Standard. MEDI/EVAL ALPHABETS AND INITIALS. By F. G. Delamotte. Containing 21 Plates and Illuminated Title, printed in Gold and Colours. With an Introduction by J. Willis Brooks. Fifth Edition. Small 4to, ornamental boards JVei S/O "A volume in which the letters of the alphabet come forth glorified In gliding and all the colours of the prism interwoven and intertwined and intermingled."— A PRIMER OF THE ART OF ILLUMINATION. For the Use of Beginners ; with a Rudimentary Treatise on the Art, Practical Directions for its Exercise, and Examples taken from Illuminated MSS., printed in Gold and Colours. By F. Delamotte. New and Cheaper Edition. Small 410, ornamental boards . 6/0 " The examples of ancient MSS. recommended to the student, which, with much good sense, the author chooses from collections accessible to all, are selected with judgment and knowledge as well as taste."— A thenaum. THE EMBROIDERER'S BOOK OF DESIGN. Containing Initials, Emblems, Cyphers, Monograms, Ornamental Borders, Ecclesiastical Devices, Medissval and Modern Alphabets, and National Emblems. Collected by F. Delamotte and printed in Colours. Oblong royal 8vo, ornamental wrapper JVei 2/0 " The book will be of great assistance to ladies and young children who are endowed with the art of plying the needle in this most ornamental and useful pretty work." — East Ang^lian Times. MARBLE DECORATION And the Terminology of British and Foreign Marbles. A Handbook for Students. By George H. Blagrove, Author of " Shoring and its Applica- tion," &c. With 28 Illustrations. Crown 8vo, cloth , . . , 3/6 " This most useful and much wanted handbook should be iu the bands of every architect and builder."— £K«Virt«f World. "A carefully and usefully written treatise ; the work is essentially jiractical. ' — Scotsman. THE DECORATOR'S ASSISTANT. A Modern Guide for Decorative Artists and Amateurs, Painters, Writers, Gilders, &c. Containing upwards of 600 Receipts, Rules, and Instructions ; with a variety of Information for General Work connected with every Class of Interior and Exterior Decorations, &c. Eighth Edition. Cr. 8vo . 1 /O " Full of receipts of value to decorators, painters, gilders, &c. The book contains the gist of larger treatises on colour and technical processes. It would be difhcult to meet with a work so full of varied information on the painter's art." — Building News. GRAMMAR OF COLOURING. Applied to Decorative Painting and the Arts. By G. Field, New Edition, enlarged by E. A. Davidson. With Coloured Plates. Crown 8vo, cloth 3/0 " The book is the most useful resume oi the properties of pigments." — Builder. ART OF LETTER PAINTING MADE EASY. By J. G. Badenoch. With 12 full-page Engravings of Examples. Cr. 8vo 1 /6 '* Any intelligent lad wlio fails to turn out decent work after studying this system has mistaken Ins vocation." — H?t<;lish Mechanic. DECORATIVE ARTS, &c. 41 PAINTING POPULARLY EXPLAINED. By Thomas John Gullick, Painter, and John Timbs, F.S.A. Including Fresco, Oil, Mosaic, Water Colour, Water-Glass, Tempera, Encaustic, Miniature, Painting on Ivory, Vellum, Pottery, Enamel, Glass, &c. Sixth Edition. Crown 8vo, cloth 5/0 *i* Adopted as a Prize Book at South Kensington. " Much may be learned, even by tliose who fancy they do not require to be taught, from the careful perusal of this unpretending but comprehensive treatise." — Art Journal. GLASS STAINING, AND PAINTING ON GLASS. From the German of Dr. Gessert and Emanuel Otto Fromberg. With an Appendix on The Art of Enamelling. Crown 8vo, cloth . . 2/6 WOOD-CARVINQ FOR AMATEURS. With Hints on Design. By A Lady. With 10 Plates. New and Cheaper Edition. Crown 8vo, in emblematic wrapper 2/0 " The handicraft of the wood-carver, so well as a book can impart it, may be learnt from ' A Lady's' publication. "—^4 NATURAL SCIENCE, ETC. THE VISIBLE UNIVERSE. Chapters on the Origin and Construction of the Heavens. By J. E. Gore, F.R.A.S., Author of " Star Groups," &c. Illustrated by 6 Stellar Photographs and 12 Plates. Demy 8vo, cloth 1 6/0 STAR GROUPS. A Student's Guide to the Constellations. By J. Ellard Gore, F.R.A.S., M.R.I. A., &c., Author of "The Visible Universe," "The Scenery of the Heavens," &c. With 30 Maps. Small 410, cloth 5/0 AN ASTRONOMICAL GLOSSARY. Or, Dictionary of Terms used in Astronomy. With Tables of Data and Lists of Remarkable and Interesting Celestial Objects. By J. Ellard Gore, F.R.A.S., Author of " The Visible Universe," &c. Small crown 8vo, cloth. 2/6 ASTRONOMY. By the late Rev. R. Main, M.A., F.RS. Third Edition, revised by William Thynne Lynn, B.A.,F.R.A.S. Crown 8vo, cloth . . 2/0 "A sound and simple treatise, very carefully edited, and a capital book for beginners."— KficnvUdge. THE MICROSCOPE. Its Construction and Management. Including Technique, Photo-nucrography, and the Past and Future of the Microscope. By Dr. Henri van Heurck. Re-Edited and Augmented from the Fourth French Edition, and Translated by WvNNB E. Baxter, F.G.S. Imp. 8vo, cloth .... 1 8/0 MANUAL OF THE MOLLUSCA : A Treatise on Recent and Fossil Shells. By Dr. S. P. Woodward, A.L.S. With Appendix by Ralph Tate, A.L.S., F.G.S. With numerous Plates and 300 Woodcuts. Crown Bvo, cloth 7/8 " A storehouse of concliological and geological information."— //aJ-^fJf/te'i- Science Gossip. THE TWIN RECORDS OF CREATION. Or, Geology and Genesis, their Perfect Harmony and Wonderful Concord. By G. W. V. LE Vaux. Bvo, cloth 5/0 LARDNER'S HANDBOOKS OF SCIENCE. HANDBOOK OF MECHANICS. Enlarged and re-written by B. Loewv, F.R.A.S. Post 8vo, cloth . 6/0 HANDBOOK OF HYDROSTATICS AND PNEUMATICS. Revised and Enlarged by B. Loewy, F.R.A.S. Post 8vo, cloth . 6/0 HANDBOOK OP HEAT. Edited and re-written by B. Loewy, F.R.A.S. Post Svo, cloth . 6/0 CROSBY LOCK WOOD «• SON'S CATALOGUE. LARDNER'S HANDBOOKS OF SCIENCE— continued. HANDBOOK OF OPTICS. New Edition. Edited by T. Olver Harding, B. A. Small 8vo, cloth S/0 ELECTRICITY, MAGNETISM, AND ACOUSTICS. Edited by Geo. C. Foster, B.A. Small 8vo, cloth .... 5/0 HANDBOOK OF ASTRONOMY. Revised and Edited by Edwin DuNKiN, F.R.A.S. 8vo, cloth . . 9/6 MUSEUM OF SCIENCE AND ART. With upwards of 1,200 Engravings. In Six Double Volumes, £1 1 s. Cloth, or half-morocco £1 11b. 6d. NATURAL PHILOSOPHY FOR SCHOOLS . . 3/6 ANIMAL PHYSIOLOGY FOR SCHOOLS . . 3/6 THE ELECTRIC TELEGRAPH. Revised by E. B. Bright, F.R.A.S. Fcap. Bvo, cloth . . . 2/6 CHEMICAL MANUFACTURES, CHEMISTRY, ETC. THE OIL FIELDS OF RUSSIA AND THE RUSSIAN PETROLEUM INDUSTRY, A Practical Handbook on the Exploration, Exploitation, and Management of Russian Oil Properties, including Notes on the Origin of Petroleum in Russia, a Description of the Theory and Practice of Liquid Fuel, and a Translation of the Rules and Regulations concerning Russian Oil Properties. By A. Beeby Thompson, A.M.LM.E., late Chief Engineer and Manager of the European Petroleum Company's Russian Oil Properties. About 500 pp., with numerous Illustrations and Photographic Plates, and a Map of the Baiakhany- Saboontchy-Romany Oil Field. Super-royal 8vo, cloth . . A''e( £3 3s. " A careful and comprehensive study of the conditions of the inciustry. The v. ork is very vahiable, and sliould undoubtedly be the standard authority on Baku for some time to come." — j\finiH!^ Journal. THE ANALYSIS OF OILS AND ALLIED SUBSTANCES. By A. C. Wright, M.A.Oxon., B.Sc.Lond., formerly Assistant Lecturer in chemistry at the Yorkshire College, Leeds, and Lecturer in Chemistry at the Hull Technical School. Demy 8vo, cloth A?«i 9/0 A HANDYBOOK FOR BREWERS. Being a Practical Guide to the Art of Brewing and Malting. Embracing the Conclusions of Modern Research which bear upon the Practice of Brewing. By Herbert Edwards Wright, M.A. Second Edition, Enlarged, Crown 8vo, 530 pp., cloth 1 2/6 " May be consulted with advantage by the student who is preparing himself for examinational tests, while the scientific brewer v/iU find in it a r^sum^ of all the most important discoveries oi modern times. Written throughout in a clear and concise manner, and the author takes great care to discriminate between vague theories and well-established facts." — Brezverr yjwi-nal. ""We have no hesitation in saying that It is one of the best — if not the best book— wliich has yet been written on the subject of beer-brewing in this country." — Ere-wers Guardian. A POCKET-BOOK OF MENSURATION AND GAUGING. Containing Tables, Rules, and Memoranda for Revenue Otricers, Brewers, Spirit Merchants, &c. By J. B. Manx Inland Revenue. Second Edition. Revised. i8mo, leather 4/0 " Should be in the hands of every practical brewer." — Brewers' yournat. CHEMICAL MANUFACTURES. CHEMISTRY, S-c. 43 LIOHTINQ BY ACETYLENE Generators, Burners, and Electric Furnaces. By William E. Gibbs, M.E. With 66 Illustrations. Crown 8vo, cloth 7/9 THE GAS ENGINEER'S POCKET-BOOK. Comprising Tables, Notes and Memoranda relating to the Manufacture, Distribution and Use of Coal Gas and the Construction of Gas Works. By H. O'Connor, A.M. Inst.C.E. Crown Svo, leather .... 10/6 " The book contains a vast amount of Information. The author goes consecutively through the engineering details and practical methods involved In each of the different processes or parts of a gas-works." — Gas World. ENGINEERING CHEMISTRY. A Practical Treatise for the Use of Analytical Chemists, Engineers, Iron Masters, Iron Founders, Students and others. Comprising Methods of Analysis and Valuation of the Principal Materials used in Engineering Work, with numerous Analyses, Examples and Suggestions. By H. Joshua Phillips, F.I.C., F.C.S. Third Edition, Revised and Enlarged. Crown Svo, 420 pp., with Plates and other Illustrations, cloth. .... Net "{QjQ " In this work the author has rendered no small service to a numerous body of practical men. . . . The analytical methods may be pronounced most satisfactory, being as accurate as the despatch'requiredof engineering chemists pennits.''—CA«?Kii:FSTS AND FUNGOID DISEASES.- COLLECTING THE RUBBER: "vApmn^ METHODS EM^ IN TAPPING RUBBER TREES. - FLOW OF LATEX — VARIOUS MEl"""^,,^"^'!,^^^ T-RPH _HOW TO TAP.— THE PREPARATION OF RUBBER IpHM tI^F^I AT^X lI?fX -^ METHODS EMPLOYED IN THE PREPARATION OF P w«uBB S^frrF^l^D METkoD^^^^^ PREPARING RUBBER.-SCRAP RUBBER -YIELD OF f l^i'^RBR FROM CUI^^^^ :_CEYLON.-MALAY PENINSULA.-GOLD COAST, PARA RUHBER I^g^ nVA rED ^ ^^^,^.,^^j,t,cR OF A PARA RUBBER PLANTATION CEYLON -MALA? PENI^^^^^^^^^ VALUE OF THE OIL IN HEVEA SEEDS. " The Author does not claim that the book is more tlian a collection of inforniation gathered fron. various sources; as such it is exceUent. and will undoubtedly serve a very usetul purpose. - India Kudlier Journal. RUBBER HAND STAMPS And the Manipulation of Rubber. A Practical Treatise on the Manufacture of Indiarubber Hand Stamps, Small Articles of Indiarubber, The Hektograph, SpecTal Inks, Cements, and Allied Subjects. By T. O'CoNOR Sloane, A Ph.D: With numerous Illustrations. Square 8vo, cloth. . . . O/O PRACTICAL TANNING. A Handbook of Modern Processes, Receipts, and Suggestions for the Treatment of Hides, Skins, and Pelts of every Description. By L. A. Flemming, American Tanner. 472 pages. 8vo, cloth iv« ,«*ertf/CDCTW«»-«yo!i^&x." —Saturday Review. 48 CROSBY LOCKWOOD «• SON'S CATALOGUE. PASTRYCOOK & CONFECTIONER'5 GUIDE. For Hotels, Restaurants, and the Trade in general, adapted also for Familv Use, By R. Wells, Author of " The Bread and Biscuit Baker " . .1/0 ' ' We cannot speak too highly of this really excellent work. In these days of keen competition our readers cannot do better than purchase this book." — Baker's Times, MODERN FLOUR CONFECTIONER. Containing a large Collection of Recipes for Cheap Cakes, Biscuits, &c. With remarks on the Ingredients Used in their Manufacture. By R. Wells 1 /O " The work Is of a decidedly practical character, and In every recipe regard Is had to economical workiag."— A'or/A British Daily Mail. SAVOURIES AND SWEETS Suitable for Luncheons and Dinners. By Miss M. L. Allen (Mrs. A. Macaire), Author of " Breakfast Dishes," &c. Thirtieth Edition. F'cap 8vo, sewed -J /O BREAKFAST DISHES For Every Morning of Three Months. By Miss Allen (Mrs. A. Macaire) Author of " Savouries and Sweets," &c. Twenty-second Edition. F'cap 8vo, sewed -J /O MOTOR CARS OR POWER CARRIAGES FOR COMMON ROADS. By A. J. Wallis-Tavler, A.M.Inst. C.E. Crown Svo, cloth . . 4/6 "A work that an engineer, thinking of turning his attention to motor-carriage work, would do well to read as a preliminary to starting operations." — Engineering. FRENCH POLISHING AND ENAMELLING. A Practical Book of Instruction, including numerous Recipes for making Polishes, Varnishes, Glaze Lacquers, Revivers, &c. By R. Bitmead. Crown Svo, cloth "[ IQ CEMENTS, PASTES, GLUES, AND GUMS. A Guide to the Manufacture and Application of Agglutinants for Workshop Laboratory, or Office Use. With goo Recipes and Formulae. By H. C Standage. Grown Svo, cloth 2/0 "As a revelation of what are considered trade secrets, this book will arouse an amount of curiosity among the large number of industries it touches."— Daily Chronicle. PRACTICAL ORGAN BUILDING. By W. E. Dickson, M.A., Precentor of Ely Cathedral. Second Edition, Revised. Crown Svo, cloth 2/6 " The amateur builder will find in this book all that is necessary to enable him personally to construct a perfect organ witli his own hands." — Academy. COACH=BUILDING: A Practical Treatise, Historical and Descriptive. By J. W. Burgess. Crown Svo, cloth 2/6 "This handbook will supply a long-felt want, not only to manufacturers themselves, but more particularly apprentices, and others connected with the trade oi codiC\\-h\xMu\g."—EuroJ:caii Mail. SEWING MACHINERY. Construction, History, Adjusting, &c. By J. W. Urquhart. Cr. Svo 2/0 WOOD ENGRAVING: A Practical and Easy Introduction to the Study of the Art. By W. N. Brown. Crown Svo, cloth 1/6 LAUNDRY MANAGEMENT. A Handbook for Use in Private and Public Laundries. Cr. Svo, cloth 2/0 " This book should certainly occupy an honoured place on the slielves of all housekeepers who wish to keep themselves au courant of the newest appliances and methods."— 77i« Queen. INDUSTRIAL AND USEFUL ARTS. 49 HANDYBOOKS FOR HANDICRAFTS. BY PAUL N. HASLUCK. Author of " Lathe Work," &c. Crown 8vo, 144 pp., price is. each. iSr These Handybooks have been written to supply information /oy Workmen, Students, and Amateurs in the several Handicraj ts, on the actual Practice o/ the Workshop, and are intended to convey in plain language Technical Know- ledge 0/ the several Crafts. In describing the processes emploved, and the manipu- lation of material, workshop terms are used ; workshop practice is fully explained ; and the text is freely illustrated with drawings of modern tools, appliances, and processes. METAL TURNER'5 HANDYBOOK. A Practical Manual for Workers at the Foot-Lathe. With 100 Illustrations. 1/0 " The book will be of service alike to the amateur and the artisan turner. It displays thorough knowledge of the svib)ect."—Scotsman. WOOD TURNER'S HANDYBOOK. A Practical Manual for Workers at the Lathe. With over 100 Illustrations. 1/0 " We recommend the book to young turners and amateurs. A multitude of workmen have hitherto sought in vain for a manual of this special mimiry. "—Meckanicai IVorld. WATCH JOBBER'S HANDYBOOK. A Practical Manual on Cleaning, Repairing, and Adjusting. With upwards of 100 Illustrations 1/0 " We strongly advise all young persons connected with the watch trade to acquire and study this nexpensive work." — CUrkeniuell Chronicle. PATTERN MAKER'S HANDYBOOK. A Practical Manual on the Construction of Patterns for Founders. With upwards of 100 Illustrations 1/0 "A most valuable, if not indispensable, manual for the pattern maker."— A'««*/«<oo)i." —Buildtr. CLOCK JOBBER'S HANDYBOOK. A Practical Manual on Cleaning, Repaiting, and Adjusting. With upwards of 100 Illustrations 1/0 " It is of inestimable service to those commencing the \.td.Ae." —Coventry Standard. CABINET WORKER'S HANDYBOOK. A Practical Manual on the Tools, Materials, Appliances, and Processes employed in Cabinet Work. With upwards of 100 Illustrations . .1/0 '• Mr. Hasluck's thorough-going little Handybook Is amongst the most practical guides we have seen for beginners in cabinet-work." — Saturday Review, WOODWORKER'S HANDYBOOK. Embracing Information on the Tools, Materials, Appliances and Processes Employed in Woodworking. With 104 Illustrations . . . .1/0 " Written by a man who knows, not only how work ought to be done, but how to do It, and how to convey his knowledge to others."— Engineering. " Mr. Hasluck writes admirably, and gives complete Instructions."— fin^^ncer, " Mr. Hasluck combines the experience of a practical teacher with the manipulative ^kill and scientific knowledge of processes of the trained mechanicicm, and the manuals are trarvels of what can be produced at a popular price." — Sckooimaster. " Helpful to workmen of all ages and degrees of experience."— Dai/y Chronicle " Concise, clear, and practical." — Saturday Review. 50 CROSBY LOCK WOOD S' SON'S CATALOGUE. COMMERCE, COUNTING-HOUSE WORK, TABLES, ETC. LESSONS IN COMMERCE. By Professor R. Gambaro, of the Royal High Commercial School at Genoa. Edited and Revised by James Gault, Professor of Commerce and Commercial Law in King's College, London. Fifth Edition. Crown 8vo, cloth . 3/6 " The publishers of this work have rendered considerable service to the cause ol commercial education by the opportune production of this volume. . . . The worlc is peculiarly acceptable to English readers and an admirable addition to existing class books. In a phrase, we think the work attains its object in furnishing a brief account of those laws and customs of British trade with which the commercial man interested therein should be familiar."— CAa?«A«»- n/ Commerce youmal. " An invaluable guide in the hands of those who are preparing for a commercial career, and, in fact, the information it contains on matters of business should be Impressed on every one."— Coimting House, THE FOREIGN COMMERCIAL CORRESPONDENT. Being Aids to Commercial Correspondence in Five Languages— English, French, German, Italian, and Spanish. By Conrad E. Baker. Third Edition, Carefully Revised Throughout. Crown 8vo, cloth . . . 4/6 " Whoever wishes to correspond In all the languages mentioned by Mr. Baker cannot do better than study this work, the materials of which are excellent and conveniently arranged. They consist not of entire specimen letters, but— what are far more useful— short passages, sentences, oi plirases expressing the same general idea in various forms.' —Athenaum, " A careful examination has convinced us that it Is unusually complete, well arranged and reliable. The book is a thoroughly good one." — ScHodmaster. FACTORY ACCOUNTS: their PRINCIPLES & PRACTICE. A Handbook for Accountants and Manufacturers, with Appendices on the Nomenclature of Machine Details; the Income Tax Acts; the Rating of Factories ; Fire and Boiler Insurance ; the Factory and Workshop Acts &c., including also a Glossary of Terms and a large number of Specimen Rulings. By Emilk Garcke and J. M. Fells. Fifth Edition, Revised and Enlarged. Demy 8 vo, cloth flQ "A very Interesting description of the requirements of Factory Accounts. . . . The principle of assimilating the Factory Accounts to the general commercial books Is one which we thoroughly agree -Kith."— Accountants' journal. " Characterised by extreme thoroughness. There are few owners of factories who would not derive great benefit from the perusal of this most admirable viotk."— Local Government Chronicle. MODERN METROLOGY. A Manual of the Metrical Units and Systems of the present Century. With an Appendix containing a proposed English System. By Lewis d'A. Jackson, A. M. Inst. C. E., Author of " Aid to Survey Practice," &c. Large crown 8 vo, cloth 12/8 "We recommend the work to all interested In the practical reform of our weights and measures." — Naturt. A SERIES OF METRIC TABLES. In which the British Standard Measures and Weights are compared with those of the Metric System at present in Use on the Continent. By C. H. Dowling, C.E. 8 vo, cloth 10/6 "Mr. Dowhng's Tables are well put together as a ready reckoner for the conversion of one system Into the a'Caat."— Athenaum. IRON AND METAL TRADES' COMPANION. For Expeditiously Ascertaining the Value of any Goods bought or sold by Weight, from is. per cwt. to 112s. per cwt., and from one farthing per pound! to one shilling per pound. By Thomas Downie. Strongly bound in leathier, 396 pp 9 /0 " A most useful set of tables, nothing like them before CjisXxA."— Building News. " Although specially adapted to the iron and metal trades, the tables wlu be found usefuil In every uiber business in which merchandise is bought and sold by weight."— Xoi^woy Nev/s, COMMERCE, COUNTING-HOUSE WORK, TABLES, S<. 51 NUMBER, WEIGHT, AND FRACTIONAL CALCULATOR. Containing upwards of 250,000 Separate Calculations, showing at a Glance the Value at 422 Different Rates, ranging from y^th of a Penny to 20s. each, or per cwt., and £20 per ton, of any number of articles consecutively, from i to 470. Any number of cwts., qrs., and lbs., from i cwt. to 470 cwts. Any number of tons, cwts., qrs., and lbs., from i to 1,000 tons. By William Chadwick, Public Accountant. Fourth Edition, Revised and Improved. 8vo, strongly bound 1 8/0 " It is as easy of reference for any answer ot any number of answers as a dictionary. For making up accounts or estimates the book must prove mvaluable to all who have any considerable quantity of calculations involving price and measure in any combination to do."— Engineer. "The most perfect work of the kind yet prepared."— G/aJfoa' Herald. THE WEIGHT CALCULATOR. Being a Series of Tables upon a New and Comprehensive Plan, exhibiting at one Reference the exact Value of any Weight from i lb. to 15 tons, at 300 Progressive Rates, from xd. to i68s. per cwt., and containing 186,000 Direct Answers, which, with their Combinations, consisting of a single addition (mostly to be performed at sight), will afford an aggregate of 10,266,000 Answers ; the whole being calculated and designed to ensure correctness and promote despatch. By Henry Harben, Accountant. Sixth Edition, carefully Corrected. Royal 8vo, strongly half-bound £1 6s. " A practical and useful work of reference for men of business genetaSly."— Ironmonger . " Of priceless value to business men."- Sheffield Independent. THE DISCOUNT GUIDE. Comprising several Series of Tables for the Use of Merchants, Manufacturers, Ironmongers, and Others, by which may be ascertained the Exact Profit arising from any mode of using Discounts, either in the Purchase or Sale of Goods, and the method of either Altering a Rate of Discount, or Advancing a Price, so as to produce, by one operation, a sum that will realise any required Profit after allowing one or more Discounts : to which are added Tables of Profit or Advance from ij to 90 per cent.. Tables of Discount from ij to gSf per cent., and Tables of Commission, &c., from \ to 10 per cent. By Henry Harben, Accountant. New Edition, Corrected. Demy 8vo, half-bound . £1 6s. " A book such as this can only be appreciated by business men, to whom the saving ot time means saving of money. The work must prove of great value to merchants, manufacturers, and general traders."— 5»-««. k s v THE FORCING GARDEN; Or, How to Grow Early Fruits, Flowers and Vegetables. With Plans and Estimates for Building Glasshouses, Pits and Frames. With Illustrations By Samuel Wood. Crown 8vo, cloth 3/g "A good book, containing a great deal of valuable teaching.' —Gardeners' Magazine. KITCHEN GARDENING MADE EA5Y. Showing the best means of Cultivating every known Vegetable and Herb &c., with directions for management all the year round. By Geo M f' Glenny. Illustrated. Crown 8vo, cloth -j /g " This book will be found trustworthy and u^ehiV —Nort/t Rritish Agriculturist. COTTAGE GARDENING; Or, Flowers, Fruits, and Vegetables or Small Gardens. By E. Hobday, Crown 8vo, cloth 1/6 " Definite instructions as to the cultivation of small gardens."— 5fo/j-?«a«. GARDEN RECEIPTS. Edited by Charles W. Quin. Fourth Edition. Crown Svo, cloth . 1 /6 "A singularly complete collection of the principal receipts needed by gardeners."— y^arwo-. MULTUM-IN-PARVO GARDENING ; *^/> How to Make One Acre of Land produce £i,io a year, by the Cultivatior, of i ruits and Vegetables ; also, How to Grow Flowers in Three Glass Houses to reali.se per annum clear Profit. By Samuel Wood, Author of Good Gardening," &c. Sixth Edition, Crown Svo, sewed , . .1/0 THE LADIES' MULTUM-IN-PARVO FLOWER GARDEN. An! Ama.eur's Complete Guide, By S. Wood, Crown Svo, cloth . 3/6 AGRICULTURE, FARMING. GARDENING, cS-c. 57 FRUIT TREES, The Scientific and Profitable Culture of. From the French of M. Du Breuil. Fifth Edition, carefully Revised by George Glenny. With 187 Woodcuts. Crown 8vo, cloth 3/6 *' The book teaches how to prune and train fruit trees to perfection." — Field. ART OF GRAFTING AND BUDDING. By Charles Baltet. With Illustrations. Crown 8vo, cloth . . 2/6 " The one standard work on this subject." — Scots?na7t. TREE PRUNER: Being a Practical Manual on the Pruning of Fruit Trees, including also their Training and Renovation, also treating of the Pruning of Shrubs, Climbers, and Flowering Plants. With numerous Illustrations. By Samuel Wood, Author of " Good Gardening," &c. Crown 8vo, cloth 1 /6 " A useful book, written by one who has had great experience." — Mark Lane Express. TREE PLANTER AND PLANT PROPAGATOR: With numerous Illustrations of Grafting, Layering, Budding, Implements, Houses, Pits, &c. By S. Wood. Crown 8vo, cloth .... 2/0 " Sound in its teaching; and very comprehensive in its aim. It is a ."— Globe. "Admirably done, admirably arranged, and admirably cheap." — Leeds Mercury. " A concise, cheap, and complete epitome of the English law. So plainly written that he wfc o ■ ilms may read, and he who reads may understand." — Figaro. " A dictionary of legal facts well put together. The book is a very useful one."— Spectator. LABOUR CONTRACTS. A Popular Handbook on the Law of Contracts or Works and Services. By David Gibbons. Fourth Edition, with Appendix of Statutes by T. F, Uttlev, Solicitor, Fcap. 8vo, cloth 3/S* LAW AND MISCELLANEOUS. 63 HANDBOOK FOR SOLICITORS AND ENGINEERS Engaged in Promoting Private Acts of Parliament and Provisional Orders for the Authorisation of Railways, Tramways, Gas and Water Works, &c. By L, L. Macassev, of the Middle Temple, Barrister-at-Law, M.I.C.E. Svo, cloth dBI Ss. PATENTS for INVENTIONS, HOW to PROCURE THEM. Compiled for the Use of Inventors, Patentees and others. By G. G. M. Hardingham, Assoc. Mem. Inst. C.E., &c. Demy Svo, cloth . .1/6 CONCILIATION & ARBITRATION in LABOUR DISPUTES. A Historical Sketch and Brief Statement of the Present Position of the Question at Home and Abroad. By J. S. Jeans. Crown Svo, 200 pp., cloth 2/6 MODERN JOURNALISM. A Handbook of Instruction and Counsel for the Young Journalist. By John B. Mackie, Fellow of the Institute of Journalists. Crown Svo, cloth . 2/0 '* This invaluable guide to journalism is a work which all aspirants to a journalistic career will read with advantage." — youmalist. DICTIONARY OF PAINTERS, And Handbook for Picture Amateurs ; being a Guide for Visitors to Public and Private Picture Galleries, and for Art Students, including Glossary ot Terms, &c. By Philippe Daryl, B.A. Crown Svo, cloth . . 2/6 "Considering its small compass, really admirable. We cordially reconnnend tlie book." — Builder. DICTIONARY OF TERMS USED IN ARCHITECTURE, Building, Engineering, Mining, Metallurgy, Archaeology, the Fine Arts, &c. By John Weale. Sixth Edition. Edited by Robt. Hunt, F.R.S., Numerous Illustrations, Crown Svo, cloth 6/0 "The best small technological dictionary in tlie language." — Architect. NATURAL PHILOSOPHY, For the Use of Beginners. By C. Tomunson, F.R.S. Cr. Svo, cloth 1/6 HANDBOOK OF FIELD FORTIFICATION. By Major W. W. Knollys, F.R.G.S. Crown Svo, cloth . . . 3/0 " A well-timed and able contribution to our military literature . . . The author supplies, in clear business style, all the information likely id be practically useful." — Chambers 0/ Connncrce Chronicle. COMPENDIOUS CALCULATOR (Intuitive Calculations') ; or Easy and Concise Methods of performing the various Arithmetical Operations required in Commercial and Business Transactions; together with Useful Tables, &c. By Daniel O'Gorman. Twenty-eighth Edition, revised by C. Norris. Crown Svo, cloth . 2/6 "It would be difficult to exaggerate the usefulness of this book to every one engaged in commerce or manufacturing industry. It is crammed full with rules and formulo^ for shortening and employing calculations in money, weights and measures, &c., of every sort and description." — X>wwled£^e. MEASURES, WEIGHTS, AND MONEYS OF ALL NATIONS, And an Analysis of the Christian, Hebrew, and Mahometan Calendars. By W. S. B. WooLHOusE, F.R. A.S. Seventh Edition. Cr. Svo, cloth 2/6 A work necessary for every mercantile office." — Building Trades Journal 64 CROSBY LOCKWOOD &■ SON'S CATALOGUE. SPANISH GRAMMAR. In a Simple and Practical Form. With Exercises. By Alfred Elwes. Crown 8vo, cloth ■) /g SPANISH=ENQUSH AND ENQLISH=SPANISH DIC= TIONARY. Including a large number of Technical Terms used in Mining, Engineering, &c., with the proper Accents and the Gender of every Noun. By Alfred Elwes. Crown 8vo, cloth 4/0 PORTUGUESE GRAMMAR. In a Simple and Practical Form. With Exercises. By Alfred Elwes. Crown 8vo, cloth -j/g PORTUGUESE=ENQUSH AND ENGLISH=PORTU= OUESE DICTIONARY. Including a large number of Technical Terms used in Mining, Engineering, &c., with the proper Accents and the Gender of every Noun. By Alfred Elwes. Fourth Edition, revised. Crown 8vo, cloth .... 5/0 ANIMAL PHYSICS, Handbook of. By Dionysius Lardner, D.C.L. With 520 Illustrations. In One Vol. (732 pages). Crown 8vo, cloth . . . . .7/6 MUSIC, A Rudimentary and Practical Treatise on. By C. C. Spencer. Crown 8vo. 2/6 " Mr. Spencer has marshalled his infonuation with iiiiich sliill, and yet witli a simplicity that lid his works to all who wisli to thoroughly understand music." — Weekly Times. PIANOFORTE, The Art of Playing the. With Exercises and Lessons. By C. C. Spencer. Crown Svo, cloth 1/6 " A sound and excellent work, written with spirit, and calculated to inspire the pupil witli a desire to aim at high accomplishment in the art." — School Board Chronicle INDEX OF SUBJECTS. Acetylene Gas, Gibbs, 43 Acoustics, Smith, 35 Aerial Navigation, Walkei-, 11 Tramways, Tayler, i Agricultural Geology, McCon- nsll, 53 Note Book, McConnell, 55 Surveying, Scott, 54 Surveyor, Bright, 58 Valuing, Bright, 58 Air Machinery, Weisbach, 10 Algebra, Haddon, 60 Alkali Trade, Lomas, 43 Alphabets, Delamotte, 39, 40 Alternating Current Machines, Sheldon and Mason, 29 Angles, Tees, Plates, Beams, &c., 19 Animal Physics, Lardner, 64 Physiology, Lardner, 42 Appraiser's Assistant, Wheeler, 58 Arches, Piers, &c., Bland, 32 Architect's Guide, Rogers, 35 Architectural Drawings, Reilly, 31 Modelling, Richardson, 35 Architecture, Ancient, 35 Civil, Chambers, 35 • Design, Garbett, 35 Grecian, Aberdeen, 35 Mechanics of. Tarn, 35 Modern, 35 of Vitruvius, Gwilt, 35 Orders, Leeds, 35 Orders and Styles, 35 Styles, Bury, 35 Arithmetic, Haddon, 59 Young, 60 Equational, Hipsley, 60 Armature Wifidings, Arnold^ 29 Artists' Pigments, Standage, 44 Asbestos, Jones, 27 Astronomical Glossary, Gore, 41 Astronomy, Lardner, 42 Main and Lynn, 41 Auctioneers, Squibbs, 58 I Barn Implements, Scott, 54 Beams, Flexure of, Guy, 18 ! Properties of, 19 Bees, Samson, 57 Blast Furnaces, Stevenson, 11 Blasting, Burgoyne, 19 Blowpipe, Ross, 43 Boiler and Factory Chimneys, Wilson, 3 Boilers, Armstrong, 4 Bauer, 20 Courtney, 3, 4 FoZijy, 2 Horner, 3 Hutton, 3, 4 Wilson, 3 Book-keeping, Haddon, 60 for Farmers, Woodman, 56 Boot and Shoe Making, L^wo, 45 Brass Founding, Graham, js^j Bread and Biscuit Baker, Wells, 47 Breakfast Dishes, Allen, 48 Brewing and Malting, Wright, 42 Brick and Tile Book, 33 Making, Dobson, 32 Brick-cutting, Hammond, 32 Bricklaying, Hammond, 32 Brickwork, Walker, 32 Bridges, Iron, Humber, 16 Iron, Pendred, 17 Oblique, iJi^rA, 16 Tubular, Dempsey, l'j B 66 INDEX TO CATALOGUE. Bridges and Viaducts, Campin, British Mining, Hunt, 25 British Standard Sections (Dia- grams, Definitions, &c.), 19 Builder's Price Book, Lockwood, 31 Measuring, Beaton, 34 Quantities, Beaton, 34 Building, a Book on, Beckett, 32 Art of, Dobson, 32 Construction, Allen, 31 Cottage, Allen, 32 Dwelling Houses, Brooks, 32 Estates, Maitland 32 Science of, Tarn, 32 Cabinet-Making, Bitmead, 38 Working, Hasluck, 49 Calculator, O'Gorman, 63 Chadwick, 51 Concise Interest, Campbell, 51 Weight, Harben, 51 Calculus, Differential, Woolhouse. 60 Integral, Cox, 60 Carpenter's Guide, Nicholson, 37 Carpentry and Joinery, Trcdgold and Tarn, 37 Tredgold, 37 Cattle, Sheep, &c. , Burn, 52 Cements, &c., Standage, 48 Chain Cables, Traill, 22 Chemistry of Mining, Byrom, 27 Chimneys, Wilson, 3 Circular Work, Collings, 38 Civil Engineering, Law, 18 Clock Jobbing, Hashick, 49 Clocks, Watches, and Bells, Beckett, 46 Coach-Building, Burgess, 48 Coal & Iron Industries, Mm^f^, 27 Mining, Cochin, 26 Glover, 26 Smyth, 27 Colliery Manager, Pamely, 26 \Vorking, Bulman and Red- mayne, 26 Colouring, Field & Davidson, 40 Colours & Dye Wares, Slater, 44 Commerce, Gambaro, 50 Commercial Correspondence, Baker, 50 Compound Interest, Thoman, 59 Concrete, Sutcliffe, 33 Reinforced, Warren, 31 Confectioner, Flour, Wells, 48 Confectionery, Wells, 47, 48 Constructional Ironwork, Campin, 18 Copper Conductors, &c., ig Metallurgy of, Eissler, 24 Cottage Building, Allen, 32 Gardening, Hobday, 56 Cotton Manufacture, Lister, 45 Cranes, Glynn, 11 Creation, Records of, Le Vaiix, Curves, Tables of, Beazeley, 15 Cyanide Process, Eissler, 24 Dairying, British, Sheldon, 53 Dairy, Pigs, and Poultry, Burn, 53 Dangerous Goods, Phillips, 43 Decoration, Facey, 39 House-Painting, Graining, &c. , 39 Imitation of Woods and Marbles, 39 Marble, Blagrove, 40 For other works see pages 39. 40 Decorator's Assistant, 40 Deep Level Mines of the Rand, Denny, 23 Diamond Drilling, Denny, 24 Dictionary of Architecture, Weale and Hunt, 63 Painters, Daryl, 63 Direct Current Machines, Sheldon and Masi.n, 29 Discount Guide, Harben, 51 Drainage of Lands, Clark, 13 (Mine), Michell, 25 Draining & Embanking, So. '!, .54 Drawing Instruments, Heat}.:f, i'S. Rules on, Pyne, 34 Dwelling Houses, Brooks, 32 INDEX TO CATALOGUE. 67 Dynamic Electricity, Atkinson, 30 Dynamo Construction, Urquhart, 30 Electric Machinery, SA^Mow and Mason, 29 How to Make, Crofts, 30 Management, Paterson, 29 Motor and Switchboard Circuits, Bowker, 29 Earthwork, Graham, 16 Tables, Broadbent & Cam- pin, 16 Tables, Buck, 16 Earthy Minerals, Davies, 25 Electrical Calculations, ^;Ai«50«, 30 Conductors, Perrine, 29 Dictionary, Sloane, 30 Engineering, Alexander, 28 Sewell, 28 Machinery, Sheldon and Mason, 29 (Report on), 20 Transmission, Abbott, 28 Electricity Applied to Mining, Liipton, Parr, & Perkin, 26, 29 Lardner and Foster, 42 Text-Book, Noad, 30 Electric Light Fitting, Urquhart, 30 Light, Knight, 30 Light, Urquhart, 30 Lighting, Swiiiton, 30 Ship-Lighting, Urquhart, Telegraph, Lardner, 42 Wiring, Diagrams and Switchboards, Harrison, 29 Electro-Metallurgy, Watt, 46 Plating, Urquhart, 46 Plating, Watt and Philip, 46 ■ Typing, Urquhart, /\j Embroiderers Design, Delamotte, 40 Engine-Driving Life, Reynolds, 6 Engineering Chemistry, Phillips, 43 Drawing, Maxton, 8 Estimates, 9 Progress, Humber, iS Standards' Committee, 19, 20 Engineering Tools, Horner, 2 Engineer's Assistant, Templeton, 8 Companion, Edwards, 8 Field Book, Haskoll, 14 Handbook, Hutton, 4 Pocket-Book, Clark, 7 Reference Book, Fo'ey, 2 ■ Year Book, Kevipe, 7 Engineman's Companion, Rey- nolds, 6 Errors in Workmanship, 20 Estate Tables, Inwood, 57 Euclid, Laiv, 59 Every Man's Own Lawyer, 62 Excavating, Prelini, 15 Explosives, Eissler, 43 Nitro, Sanford, 43 Factory Accounts, Garcke S- Fells, 50 Farm Acct. Book, Woodman, 56 Buildings, Scott, 32, 54 Engineering, Scott, 54 Management, Burn, 54 Roads, &c., Scott, 54 Farmers' Tables, Francis, 55 Farming Economy, Burn, 55 * ■ Outlines, Burn, 54 Practical, Shepherd, 53 Small, Burn, 53 Fertilisers, &c., Dyet, 53 Field Coils (Electrical), 20 Fortification, Knollys, 63 Implements, Scott, 54 Fields of Gt. Britain, Clenents, 54 Fires & Fire Engines, Young, 11 Flour, Kick and Powles, 47 Forestry, Curtis, 37 Foundations, &c., Dobson, 18 French Polishing, Bitmead, 48 French and English Technical Terms, Fletcher, 8 Fruit Trees, Du Breuil, 57 Fuel, Williams and Clark, 10 Fuels, Phillips, 10 Garden, Forcing, Wo:d, 56 Receipts, Quin, 56 68 INDEX TO CATALOGUE. Gardening, Good, Wood, 56 Ladies', Wood, 56 Miiltum-in-Parvo, Wood, 56 Gas and Oil Engines, Bale, 6 Engines, Goodeve, 6 Engines, Mathot, 6 Engine Handbook, Roberts, 6 — — Engineer's Pocket Book, O'Connor, 43 Fitting, Black, 47 Producer Plants, Mathot, 6 Works, Hughes, 18 Gauge Length, Unwin, ig Gauges, Limit, 20 Geology, Historical, Tate, 28 Physical, Tate, 28 ■ Tate, 28 Geometry, Tarn, 17 Analytical, Hann, 60 Descriptive, Heather, 60 Technical, Sprague, 17 of Compasses, iJjv^'w^, 17 Plane, Heather, 60 Girders (Iron), Buck, 17 '-^ss Staining, Gessert and rmberg, 41 c !■ .1 V of French and English .Teciii.'cal Terms, Fletcher, 8 Gold As;:, tying, Phillips, 24 and Silver, Merritt, 24 Metallurgy of, Eissler, 24 Mining Machinery, Tinney, 23 i'rospecting, Rankin, 23 Goldsmith's Handbook, Gee, 46 ■ and Silversmith, Gee, 46 Grafting and Budding, Baltet, 57 Granites, Harris, 28 Grazier, Complete, Freatn, 52 Hall Marking Jewellery, Gee, 46 Handrailing, Collings, 38 — — Goldthorp, 38 Hay & Straw Measurer, Steele, 55 Health Officer, Willoughby, 36 Heat (Expansion by), Keily, 18 1 lont. Lardtier and Loewy, 41 ile^LUng by Hot Water, Jones, 33 Hints to Architects, Wight nick and Guillaume, 35 Hoisting Machinery, Horner, i Hoisting & Conveying Ma- chinery, Zimmer, i Horology, Saunier, 45 Horticulture, Neivsham, 56 House Decoration, Facey, 39 Owner's Estimator,S/wo«, 34 Painting, Davidson, 39 — — Property, Tarbuck, 34 Hydraulic Manual, Jackson, 13 Engineering, Marks, 13 Tables, Neville, 13 Hydrostatics, Lardner, 41 Illumination, Delamotte, 40 India Rubber, Johnson, 45, 57 Indian Railway Locomotives, 19 Inflammable Gas, Clowes, 27 Insulating Materials (Elec- trical), 20 Interest Calculator, Campbell, 51 Inwood's Estate Tables, 57 Iron Trades Companion, Downie, 50 and Steel, Hoare, 8 Metallurgy of, Bauerman, 25 — — Ores, Kendall, 25 Plate Weight Tables, Burlinson and Simpson, 51 Irrigation, Mawson, 11 and Water Supply, Scott, 54 Jeweller's Assistant, Gee, 46 Joints (Builders'), Christy, 38 Journalism, Mackie, 63 Key to Haddon's Algebra, 60 to Young's Arithmetic, 60 Kitchen Gardening, Glenny, 56 Labour Contracts. Gibbons, 62 Disputes, Jeans, 63 Land Improving, Ewart, 58 Ready Reckoner, An,. : , 50 (Reclamation of), Beazelc, Land, Valuing and Improving, Hudson and Ewart, 59 INDEX TO CATALOGUE. eg Land Valuing, Hudson, 59 Landed Estates, Bum, 55 Lathe Work, Hasluch, 9 Laundry Management, 48 Lawyer, Every Man's Own, 62 Lead (Argentiferous), Eissler, 25 Leather Manufacture, Watt, 45 Flemming, 45 Letter Painting, Badenoch, 40 Levelling, Simms, 15 Light, Tarn, 35 Light Railways, Calthrop, 11 Lightning Conductors, Hedges, 33 Limes, Cements, Burnell, 34 Limit Gauges, 20 Locomotive Engine, Stretton, 5 Engine, Weatherburn, 5 Engine Driving, Reynolds, 5 Engineer, Reynolds, 5 — — Engines, Dempsey, 5 Locomotives for Indian Rail- ways, 19 Logarithms, Law, 59 Machine Shop Tools, Van Dervoort, 2 Machinery, Details, Campin, 9 Marble Decoration, Blagrove, 40 Marine Engineer, Wannan, 21 Engineer's Pocket Book, Wannan, 21 Engineering, Brewer, 21 Engines, Murray, 21 and Boilers, Bauer, Donldn and Robertson, 20 Market Gardening, Shaw, 56 Masonry, Purchase, 33 and Stone-Cutting, Dob- son, 33 Dams, Courtney, 13 Masting and Rigging, Kipping,22 Materials, Campin, 18 Handling of, Zivimer, i (Strength oP), Barlow, 18 Mathematical Insts., Heather, 61 Heather &■ Walmisley, 61 Tables, Law and Young, 23, 59 Mathematics, Campin, 59 Measured Drawings, Reilly, 31 Measures, Weights, &c.. Wool- house, 63 Measuring Builders' Work, Dobson and Tarn, 34 Timber, &c., Horton, 34 Meat Production, Ewart, 52 Mechanical Dentistry, Hunter, 47 ■ Engineering, Campin, 9 Handling of Material, Zimmer, i • Terms, Lockwood, 8 Mechanics, Hughes, 10 Lardner and Loewy, 41 Tomlinson, 10 of Air Machinery, Weisbach, 10 (Tables for). Smith, 8 Mechanics' Companion, Tem- pleton and Hutton, 7 Workshop, Hasluck, 49 Mechanism, Baker, 10 Mensuration & Gauging, Mant, 42 and Measuring, Baker, 17 Metal Turning, Hasluck, 49 Horner, 2 Metalliferous Minerals, Davies, 25 Mining Machinery, Davies, 23 Metric Tables, Dowling, 50 Metrology, Jackson, 50 Microscope, Van Heurck, /^i Milk, Cheese, &c., Oliver, 53 Millers' Ready Reckoner, Hutton, 55 Milling Machines, Horner, i Mine Drainage, Michell, 25 Mines of the Rand, Denny, 23 Mineral Surveyor, Lintern, 28 Mineralogy, Ramsay, 28 Miners' Handbook, M«7w(?, 25 Pocket Book, Power, 25 Mining, British, Jf?««i, 25 Calculations, 0' Donahue, 27 Chemistry of, Byrom, 27 Students, Notes for, ilf^n- vale, 27 Tools, Morgans, 27 and Quarrying, Collins, 27 Model Engineer, Hasluck, 49 MoUusca, Woodward, 41 Motor Cars, Tayler, 11, 48 — — Vehicles, Tayler, 11 70 INDEX TO CATALOGUE Museum of Science and Art, Lardner, 42 Music, Spencer, 64 Natural Philosophy, Tomlinson, 63 for Schools, Lardner, 42 Naval Architect's Pocket Book, Mackrow, 21 — — Architecture, Peahc, 22 Navigation, Young, 23 Greenwood and Rosser, 22 Practical, 23 Nuts, Bolt Heads, and Spanners, 20 Oil Fields of Russia, Thompson, 23. 42 Oils, Analysis of, Wright, 42 Optical Instruments, Heather, 61 Optics, Lardner &• Harding, 42 Organ Building, Dickson, 48 Oriental Manuals and Text- books, 51 Packing Case Tables, Richard- son, 38 Painting, Gullick &' Tiriibs, 41 Paper Making, Clapperton, 44 Watt, 44 Pastrycook's Guide, Wells, 48 Patents, Hardinghatn, 63 Pattern Making, Barrows, 9 — Hasluck, 49 Horner, 8 Perspective, Ferguson, 34 Pyne, 34 Pianoforte, Spencer, 64 Pioneer Engineering, Dobson, 15 Pipe Flanges, 19 Threads, 20 Plastering, Kemp, 33 Plating & Boilermaking, Hoi'^ ner, 3 Plumbing, Buchan, 33 Laivler, 33 Pneumatics, Tomlinson, 18 Pocketbook, Agriculturist's, Bright, 58 Ewart, 58 Francis, 55 Hudson, 59 Pocketbook, Agriculturist's, McConnell, 55 — — Auctioneer's, Wheeler, 58 Builder's, Beaton, 34 Engineer's, Clark, 7 Edwards, 8 Fletcher, 8 Hasluck, 9 Kempe, 7 Smith, 8 Templeton, 7 Engineman's, Reynolds, 6 Gas Engineer's, O'Connor, 43 Health Officer's, Willoiighby, 36 Marine Engineer's, Mack- row, 21 Wannan, 21 Mensuration and Gauging, Mant, 42 Miner's, Milne, 25 Power, 25 Mining Prospector's, Anderson, 24 Merritt, 24 • Rankin, 23 Refrigeration, Tayler, 10 Pole Plantations, Bright, 58 Portable Engine, Wansbroiigh, 5 Portland Cement, jFaya fl«i Butler, 34 Specification, ig Portuguese Dictionary, Etwes, 64 Grammar, Elwes, 64 Potatoes, PmA, 57 Private Bills, Macassey, 63 Producer-Gas Plants, Mathot, 6 Prospector's Handbook, Ander- son, 24 Pumps and Pumping, id Quantities (Bui'ders'), B^aA «, 34 Railway Brakes, Reynolds, 5 Rails, Bull-headed, 19 Flat Bottomed, 19 Rolling Stock, 20 Working, Stretton, 19 Reclamation of Land, Beazeley, 11 INDEX TO CATALOGUE. 71 Refrigerating Machinery, Tay- ler, 10 Refrigeration, Tayler, 10 (Pocket Book), Tayler, 10 ' Reinforced Concrete, Warren,^! River Bars, Mann, 13 Roads and Streets, Law, 15 Rolling Stock (Railway), 20 Roof Carpentry, Collings, 38 Roofs, Construction of. Tarn, 18 Rothamsted Experiments, Tipper, 53 Rubber Hand Stamps, Shane., 45 Sailmaking, Kipping, 22 Sadler, 22 Sanitary Work, Slagg, 36 Savouries and Sweets, Allen, 48 Saw Mills, Bale, 37 Screw Threads, 20 Hasluck, g Sea Terms, Pirrie, 22 Sewage, Irrigation, Burn, 55 Purification, Barwise, 36 Sewing Machinery, Urquhart, 48 Sheep (The), Spooner, 52 Sheet-Metal Work, Crane, 47 Work, Warn &> Horner, 47 Shoring, Blagrove, 32 Ship Building, Sommerfeldt, 22 German, Felskowski, 22 Ships and Boats, Bland, 22 Silver, Metallurgy of, Eissler, 24 Silv'ersmith's Handbook, G££, 46 Sla.e Quarrying, Davies, 27 Sl'de Rule, Hoare, 59 Smithy and Forge, Crane, 9 Soap Making, 44 Soaps, Modern, Lamborn, 44 Soils, Burn, 53 Spanish Dictionary, Elwes, 64 • Grammar, Elwes, 64 Specifications, Bartholomew, 32 in Detail, Mirt^y, 31 Star Groups, Gore, 41 Statics, Graham, 17 and Dynamics, Baker, 61 Stationary • Engine Driving, Reynolds, 5 Steam Engines, Hurst, 6 Steam and Machinery Manage- ment, Bale, 6 ■ and Steam Engine, Clark, 10 Steam Boiler Construction, Hiitton, 3 Boilers, Armstrong, 4 Wilson, 3 Engine, Baker, 5 Goodeve, 4 Haeder and Powles, 5 Lardner, 5 Safe Use of, 6 Steel Conduits for Electrical Wiring, 20 (Structural) Specifications, 19 Stone Working Machinery, Bale, II Strains in Girders, Humher, 17 on Ironwork, Shields, 17 Structural Steel for Bridges and Building, 19 Marine Boilers, 19 Shipbuilding, 19 Submarine Telegraphs, Bright, 30 Superficial Measurement, HawUngs, 38 Survey Practice, Jackson, 14 Surveying, Baker and Dixon, 14 ■ Frome and Warren, 15 Instruments, Heather, 61 Land & Marine, Haskoll, 14 Subterraneous, Fenwick, 28 Usill, 14 Whitelaw, 14 with Tacheometer, Ken- nedy, 14 Tanning, Flenming, 45 Watt, 45 Tea Machinery Tayler, 47 Technical Guide, Beaton, 34 Terms, Fletcher, 8 Telegraph Material, 19 Temperature Experiments on Electrical Machines, 20 Temperatu 'e Experiments on Insulating Materials, 20 Timber Importer, Grandy, 38 Merchant, Dowsing, 38 Richardson, 38 Toothed Gearing, Horner, 9 Tramway Poles, 19 Rails and Fish Plates, ig Tramways, Clark, 16 7.2 INDEX TO CATALOGUE. Transmission by Electricity, Atkinson, 29 Traverse Tables, Lintern, 28 Tree Planter, Wood, 57 Pruner, Wood, 57 Trigonometry, Plane, Hann, 60 Spherical, Hann, 60 Trolley Groove and Wire, 20 Trusses, Griffiths, 18 Tunnelling, Prelini and Hill, 15 Simms and Clark, 15 Tunnel Shafts, Buck, 16 Turning Lathe, Hasluck, 9 Metal, Hasluck, 49 Horner, 2 Wood, Hasluck, 49 Ventilation of Buildings, Btichan, 36 Villa Architecture, Wickes, 35 Visible Universe, Gore, 41 Vitruvius'Architecture, Gwilt, 35 Wages Table, Garbutt, 51 Watch Jobbing, Hasluck, 49 Maker, Saunier, 46 Repairing, Garrard, 45 Watches, History of, Kendal, 46 Water Purification, Rideal, 36 Engineering, 12, 36 Power of, Glynn, 13 Supply, Humber, 12, 36 Green well and Curry, 12,36 Supply of Towns, Burton, 12, 36 Waterworks, Hughes, 13 Well-Sinking, Sivindell, 13 Wireless Telegraphy, Sewall, 30 Wood Carving for Amateurs, 41 Engraving, Brown, 48 Turning, Hasluck, 49 Woods and Marbles, Imitation of. Van der Burg, 39 Woodworking, Hasluck, 49 Machinery, 37 Workmanship, Errors in, 20 Workshop Practice, Winton, g Works' Manager, Hutton, 3 PRAPPURV, AGNKW, & CO. LPi, PRINTERS, LONDON ANP TONBBJDGEi [58.8.II.016. WEALE'S SCIENTIFIC & TECHNICAL SERIES. MATHEMATICS, ARITHMETIC, &c. Geometry, Descriptive. J. F. Heather . . • 2/- Practical Plane Geometry. J. F. Heathkb. . . 2/- Anaiyticai Geometry. J. Hann & J. R. YouNO. . 2/- Geometry. Part I. (Euclid, Bks. I.— III.) H. Law 1/6 Part II. (Euclid, Books IV., V., VI., XL, XII.). H. Law 1/6 Geometry, in i vol. (Euclid's Elements) . . . . 2/6 Plane Trigonometry. J. Hann . . . .1/6 Spherical Trigonometry. J. Hann . . . . i/- The above 2 vols., bound together . . . .2/6 Differential Calculus. W. S. B. Woolhouse . . 1/6 Integral Calculus. H. Cox i/- Algebra. J. Haddon 2/- Key to ditto 1/6 Book-keeping. J. Haddon 1/6 Arithmetic. J. R. Young 1/6 Key to ditto .1/6 Equational Arithmetic. W. Hipsley . . . . 1/6 Arithmetic. J. 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