Materials science

"In the summer of 1884... the Syndics... placed in my hands the manuscript of the late Dr Todhunter's History of Elasticity, in order that it might be edited and completed..."

"[I]t was not till I had advanced... into the work that I felt convinced that... the... writer's terminology and notation must be abandoned and a uniform terminology and notation adopted for the whole book... to be available for easy reference, and not merely of interest to the historical student."

"[T]he notation and terminology will be found fully discussed in Notes B—D of the Appendix, which I would ask the reader to examine before passing to the text."

"[C]onsistency in [notation and terminology] will be found after the middle of the chapter devoted to Poisson."

"The symbols and terms used in the manuscript are occasionally those of the original memoirs, occasionally those of Lamé or of Saint-Venant... the memoirs being of historical rather than scientific interest, and their language often the most characteristic part of their historical value."

"Dr Todhunter's manuscript consists of two distinct parts, the first contains a purely mathematical treatise on the theory of the 'perfect' elastic solid; the second a history of the theory of elasticity. The treatise based principally on the works of Lamé, Saint-Venant and Clebsch is yet to a great extent historical, [i.e.,] many paragraphs are composed of analyses of important memoirs."

"The changes I have made in that manuscript are of the following character; the introduction of a uniform terminology and notation, the correction of clerical and other obvious errors, the insertion of cross-references, the occasional introduction of a remark or of a footnote. The remarks are inclosed in square brackets. With this exception any article in this volume the number of which is not included in square brackets is due entirely to Dr Todhunter."

"I... regret that I have not devoted special chapters to such elasticians as Hodgkinson, [Guillaume] Wertheim and F. E. Neumann; in the latter case the regret is deepened by the recent publication of his lectures on elasticity."

"I may appear to have exceeded the duty of an editor. For all the Articles in this volume whose numbers are enclosed in square brackets I am alone responsible, as well as for the corresponding footnotes, and the Appendix with which the volume concludes."

"The principle which has guided me throughout the additions I have made has been to make the work, so far as it lay in my power, a standard work of reference for its own branch of science."

"The use of a work of this kind is twofold. It forms on the one hand the history of a peculiar phase of intellectual development, worth studying for the many side lights it throws on general human progress. On the other hand it serves as a guide to the investigator in what has been done, and what ought to be done. In this latter respect the individualism of modern science has not infrequently led to a great waste of power; the same bit of work has been repeated in different countries at different times, owing to the absence of such histories as Dr Todhunter set himself to write. ...the various Jahrbücher and Fortschritte now reduce the possibility of this repetition, but besides their frequent insufficiency they are at best but indices to the work of the last few years; an enormous amount of matter is practically stored out of sight in the Transactions and Journals of the last century and of the first half of the present century."

"It would be a great aid to science, if, at any rate, the innumerable mathematical journals could be to a great extent specialised, so that we might look to any one of them for a special class of memoir. ...the would-be researcher either wastes much time in learning the history of his subject, or else works away regardless of earlier investigators. The latter course has been singularly prevalent with even some firstclass British and French mathematicians."

"Keeping the twofold object of this work in view I have endeavoured to give it completeness (1) as a history of developement, (2) as a guide to what has been accomplished."

"Taking the first chapter of this History the author has discussed the important memoirs of James Bernoulli and some of those due to Euler. The whole early history of our subject is however so intimately connected with the names of Galilei, Hooke, Mariotte and Leibniz, that I have introduced some account of their work."

"The labours of Lagrange and Riccati also required some recognition... [of] interest, whether judged from the special standpoint of the elastician or from the wider footing of insight into the growth of human ideas."

"With a similar aim I have introduced throughout the volume a number of memoirs having purely historical value which had escaped Dr Todhunter's notice."

"I have inserted... memoirs of mathematical value, omitted [by Todhunter] apparently by pure accident. For example all the memoirs of F. E. Neumann, the second memoir of Duhamel, those of Blanchet etc. I cannot hope that the work is complete in this respect even now, but I trust that nothing of equal importance has escaped..."

"My greatest difficulty arose with regard to the rigid line which Dr Todhunter had attempted to draw between mathematical and physical memoirs. Thus while including an account of Clausius' memoir of 1849, he had omitted Weber's of 1835, yet the consideration of the former demands the inclusion of the latter..."

"There has been far too much invention of 'solvable problems' by the mathematical elastician; far too much neglect of the physical and technical problems which have been crying out for solution. Much of the ingenuity which has been spent on the ideal body of 'perfect' elasticity ideally loaded, might I believe have wrought miracles in the fields of physical and technical elasticity, where pressing practical problems remain in abundance unsolved. I have endeavoured... to abrogate this divorce between mathematical elasticity on the one hand, and physical and technical elasticity on the other. With this aim in view I have introduced the general conclusions of a considerable body of physical and technical memoirs, in the hope that by doing so I may bring the mathematician closer to the physicist and both to the practical engineer. I trust that in doing so I have rendered this History of value to a wider range of readers, and so increased the usefulness of Dr Todhunter's many years of patient historical research on the more purely mathematical side of elasticity. In this matter I have kept before me the labours of M. de Saint-Venant as a true guide to the functions of the ideal elastician."

"To the late M. Barré de Saint-Venant I am indebted for the loan of several works, for a variety of references and facts bearing on the history of elasticity, as well as for a revision..."

"My colleague, Professor A. B. W. Kennedy, has continually placed at my disposal the results not only of special experiments, but of his wide practical experience. The curves figured in the Appendix, as well as a variety of practical and technical remarks scattered throughout the volume I owe entirely to him; beyond this it is difficult for me to fitly acknowledge what I have learnt from mere contact with a mind so thoroughly imbued with the concepts of physical and technical elasticity."

"The modern theory of elasticity may be considered to have its birth in 1821, when Navier first gave the equations for the equilibrium and motion of elastic solids, but some of the problems which belong to this theory had previously been solved or discussed on special principles, and to understand the growth of our modern conceptions it is needful to investigate the work of the seventeenth and eighteenth centuries."

"Galileo Galilei['s] second dialogue of the Discorsi e Dimostrazioni matematiche, Leiden 1638... both from its contents and form is of great historical interest. It not only gave the impulse but determined the direction of all the inquiries concerning the rupture and strength of beams, with which the physicists and mathematicians for the next century principally busied themselves."

"Galilei gives 17 propositions with regard to the fracture of rods, beams and hollow cylinders. ...[H]e supposed the fibres of a strained beam to be inextensible. There are two problems... discussed... which form the starting points of many later memoirs. They are the following:"

"A beam (ABCD) being built horizontally into a wall (at AB) and strained by its own or an applied weight (E), to find the breaking force upon a section perpendicular to its axis. This problem is always associated... with Galilei's name, and we shall call it... Galilei's Problem. The 'base of fracture' being defined as the section of the beam where it is built into the wall; we have the following results :— (i) The resistances of the bases of fracture of similar prismatic beams are as the squares of their corresponding dimensions. In this case the beams are supposed loaded at the free end till the base of fracture is ruptured; the weights of the beams are neglected. (ii) Among an infinite number of homogeneous and similar beams there is only one, of which the weight is exactly in equilibrium with the resistance of the base of fracture. All others, if of a greater length will break,—if of a less length will have a superfluous resistance in their base of fracture."

"The discovery apparently of the modern conception of elasticity seems due to Robert Hooke, who in his work De potentiâ restitutiva, London 1678, states that 18 years before... he had first found out the theory of springs, but had omitted to publish it because he was anxious to obtain a patent for a particular application of it. He continues:— About three years since His Majesty was pleased to see the Experiment that made out this theory tried at White-Hall, as also my Spring Watch. About two years since I printed this Theory in an Anagram at the end of my Book of the Descriptions of s, viz. ceiiinosssttuu, id est, Ut Tensio sic vis; That is, The Power of any spring is in the same proportion with the Tension thereof."

"By 'spring' Hooke does not merely denote a spiral wire, or a bent rod of metal or wood, but any "springy body" whatever. Thus after describing his experiments he writes: From all which it is very evident that the Rule or Law of Nature in every springing body is, that the force or power thereof to restore it self to its natural position is always proportionate to the Distance or space it is removed therefrom, whether it be by rarefaction, or separation of its parts the one from the other, or by a Condensation, or crowding of those parts nearer together. Nor is it observable in these bodies only, but in all other springy bodies whatsoever, whether Metal, Wood, Stones, baked Earths, Hair, Horns, Silk, Bones, Sinews, Glass and the like. Respect being had to the particular figures of the bodies bended, and to the advantageous or disadvantageous ways of bending them."

"The modern expression of the six components of stress as linear functions of the strain components may perhaps he physically regarded as a generalised form of ."

"Mariotte seems to have been the earliest investigator who applied anything corresponding to the elasticity of Hooke to the fibres of the beam in Galilei's problem. ...[H]is Traité du mouvement des eaux, Paris 1686... shows that Galilei's theory does not accord with experience. He remarks that some of the fibres of the beam extend before rupture, while others again are compressed. He assumes however without the least attempt at proof ("on peut concevoir" [we can conceive]) that half the fibres are compressed, half extended."

"G. W. Leibniz: Demonstrationes novae de Resistentiâ solidorum. Acta Eruditorum Lipsiae July 1684. The stir created by Mariotte's experiments... seem to have brought the German philosopher into the field. He treats the subject in a rather ex cathedrâ fashion, as if his opinion would finally settle the matter. He examines the hypotheses of Galilei and Mariotte, and finding that there is always flexure before rupture, he concludes that the fibres are really extensible. Their resistance is, he states, in proportion to their extension. ...[i.e.,] he applies " Hooke's Law" to the individual fibres. As to the application of his results to special problems, he will leave that to those who have leisure for such matters. The hypothesis... is usually termed by the writers of this period the Mariotte-Leibniz theory."

"Varignon: De la Résistance des Solides en général pour tout ce qu'on peut faire d'hypothèses touchant la force ou la ténacité des Fibres des Corps à rompre; Et en particulier pour les hypothèses de Galiée & de M. Mariotte. Memoires de l'Académie, Paris 1702... considers that it is possible to state a general formula which will include the hypotheses of both Galilei and Mariotte, but... it will [in most practical cases] be necessary to assume some definite relation between the extension and resistance of the fibres. ...Varignon's method ...[is] generally adopted by later writers (although in conjunction with either Galilei's or the Mariotte-Leibniz hypothesis), we shall briefly consider it here ..."

"Let ABCNML be a beam built into a vertical wall at the section ABC, and supposed to consist of a number of parallel fibres perpendicular to the wall... and equal to AN in length. Let H' be a point on the 'base of fracture,' and H'E [which is perpendicular to AC] = y, AE= x. Then if a weight Q be attached by means of a pulley to the extremity of the beam, and be supposed to produce a uniform horizontal force over the whole section NML, \; Q = r \cdot \int ydx where r is the resistance of a fibre of unit sectional area and the integration is to extend over the whole base of fracture. Q is by later writers termed the absolute resistance and is given by the above formula. Now suppose the beam to be acted upon at its extremity by a vertical force P instead of the horizontal force Q. All the fibres in a horizontal line through H' will have equal resistance, this may be measured by a line HK drawn through H in any fixed direction where H is the point of intersection of the horizontal line through H and the central vertical BD of the base. As H moves from B to D, K will trace out a curve GK which gives the resistance of the corresponding fibres. Take moments for the equilibrium of the beam about ACP \cdot l = \iint uydxdywhere l = length of the beam DT and u = HK."

"This quantity \iint uydxdy was termed the relative resistance of the beam or the resistance of the base of fracture. ...it is necessary to know u before we can make use of it. He then proceeds to apply it to Galilei's and the Mariotte-Leibniz hypotheses."

"In Galilei's hypothesis of inextensible fibres u is supposed constant = r and the resistance of the base of fracture becomesr \int ydxdy = \frac{r}{2} \cdot \int y^2dx.On the supposition that the fibres are extensible we ought to consider their extension by finding what is now termed the neutral line or surface. Varignon however, and he is followed by later writers, assumes that the fibres in the base ACLN are not extended; and that the extension of the fibre through H' varies as DH, in other words he makes the curve GK a straight line passing through D. Hence if r' be the resistance of the fibre at B, and DB = a, the resistance of the fibre at H = r'y/a or the resistance of the base of fracture on this hypothesis becomes\frac{r'}{3a}\int y^3dxThis resistance in the case of a rectangular beam of breadth b and height a becomes on the two hypotheses\frac{ra^2b}{2} and \frac{r'a^2b}{3}...his results are practically vitiated when applying the true ( Leibniz-Mariotte) theory by his assumption of the position of the neutral surface, but in this error he is followed by so great a mathematician as Euler himself."

"The first work of genuine mathematical value on our subject is clue to James Bernoulli... Véritable hypothèse de la résistance des Solides, avec la démonstration de la Courbure des Corps qui font ressort... 12th of March 1705... begins by brief notices of what had been already done with respect to the problem by Galilei, Leibniz, and Mariotte; James Bernoulli claims for himself that he first introduced the consideration of the compression of parts of the body, whereas previous writers had paid attention to the extension alone."

"Three Lemmas which present no difficulty are given and demonstrated [by James Bernoulli]: I. Des Fibres de même matière et de même largeur, ou épaisseur, tirées ou pressées par la même force, s'étendent ou se compriment proportionellement à leurs longueurs. [Fibers of the same material and of the same width, or thickness, drawn or pressed by the same force, extend or compress proportionally to their lengths.] II. Des Fibres homogènes et de même longueur, mais de différentes largeurs ou épaisseurs, s'étendent ou se compriment également par des forces proportionelles à leurs largeurs. [Fibers homogeneous and of the same length, but of different widths or thicknesses, extend or are also compressed by forces proportional to their widths.] III. Des Fibres homogènes de même longueur et largeur, mais chargées de différens poids, ne s'étendent ni se compriment pas proportionellement à ces poids; mais l'extension ou la compression causée par le plus grand poids, est à l'extension ou à la compression causée par le plus petit, en moindre raison que ce poids—là n'est à celui—ci. [Homogeneous fibers of the same length and width, but charged with different weights, neither extend nor compress proportionally to these weights; but the extension or the compression caused by the greatest weight, is to the extension or to the compression caused by the smaller, in less reason...]"

"The fourth Lemma... may be readily understood by reference to Varignon's memoir. ...Varignon supposed the neutral surface to pass through... the so-called 'axis of equilibrium'... James Bernoulli... recognises the difficulty of determining the fibres which are neither extended nor compressed, but he comes to the conclusion that the same force applied at the extremity of the same lever will produce the same effect, whether all the fibres are extended, all compressed or part extended and part compressed about the axis of equilibrium. In other words the position of the axis of equilibrium is indifferent. This result is expressed by the fourth Lemma and is of course inadmissible."

"Saint-Venant remarks in his memoir on the Flexure of Prisms in Liouville's Journal, 1856: On s'étonne de voir, vingt ans plus tard, un grand géomètre, auteur de la première théorie des courbes élastiques, Jacques Bernoulli tout en admettant aussi les compressions et présentant même leur considération comme étant de lui commettre sous une autre forme, précisement la même méprise du simple au double que Mariotte dans l'évaluation du moment des résistances ce qui le conduit même à affirmer que la position attribuée à l'axe de rotation est tout à fait indifférente. [It is surprising to see, twenty years later, a great geometer, author of the first theory of elastic curves, Jacques Bernoulli... commit precisely the same mistake of... Mariotte in the evaluation of moment of resistance which leads him... to assert that the position attributed to the axis of rotation is entirely indifferent.]"

"Bernoulli... rejects the Mariotte-Leibniz hypothesis or the application of Hooke's law to the extension of the fibres. He introduces rather an idle argument against [it], and quotes an experiment of his own which disagrees with Hooke's Ut tensio, sic vis."

"James Bernoulli next takes a problem which he enunciates thus: "Trouver combien il faut plus de force pour rompre une poutre directement, c'est-à-dire en la tirant suivant sa longueur, que pour la rompre transversalement." [Find out how much more force is needed to break a beam directly... by pulling it along its length in order to break it transversely.] The investigation depends on the fourth Lemma, and is consequently not satisfactory."

"The method of James Bernoulli with improvements, has been substantially adopted by other writers. The English reader may consult the earlier editions of Whewell's Mechanics. Poisson says in his Traité de Mécanique... Jacques Bernoulli a déterminé, le premier, la figure de la lame élastique en équilibre, d'après des considérations que nous allons développer, . . .[Jacques Bernoulli has determined, the first, the figure of the elastic blade in equilibrium, according to considerations that we will develop...]"

"Sir Isaac Newton : Optics or a Treatise of the Reflections, Refractions and Colours of Light. 1717. ...The Query [XXXIst, termed 'Elective Attractions,'] commences by suggesting that the attractive powers of small particles of bodies may be capable of producing the great part of the phenomena of nature:—For it is well known that bodies act one upon another by the attractions of gravity, magnetism and electricity; and these instances shew the tenor and course of nature, and make it not improbable, but that there may be more attractive powers than these. For nature is very consonant and conformable to herself. ... The parts of all homogeneal hard bodies, which fully touch one another, stick together very strongly. And for explaining how this may be, some have invented hooked atoms, which is begging the question; and others tell us, that bodies are glued together by Rest: that is, by an occult quality, or rather by nothing: and others, that they stick together by conspiring motions, that is by relative Rest among themselves. I had rather infer from their cohesion, that their particles attract one another by some force, which in immediate contact is exceeding strong, at small distances performs the chemical operations above-mentioned, and reaches not far from the particles with any sensible effect."

"Newton supposes all bodies to be composed of hard particles, and these are heaped up together and scarce touch in more than a few points.And how such very hard particles, which are only laid together, and touch only in a few points can stick together, and that so firmly as they do, without the assistance of something which causes them to be attracted or pressed towards one another, is very difficult to conceive."

"After using arguments from capillarity to confirm these remarks he continues:Now the small particles of matter may cohere by the strongest attractions, and compose bigger particles of weaker virtue; and many of these may cohere and compose bigger particles, whose virtue is still weaker; and so on for divers successions, until the progression end in the biggest particles, on which the operations in chemistry, and the colours of natural bodies depend; and which by adhering, compose bodies of a sensible magnitude. If the body is compact, and bends or yields inward to pression without any sliding of its parts, it is Hard and Elastick, returning to its figure with a force rising from the mutual attractions of its parts."

"The conception of repulsive forces is then introduced [by Newton] to explain the expansion of gases.Which vast contraction and expansion seems unintelligible, by feigning the particles of air to be springy and ramous, or rolled up like hoops, or by any other means than a Repulsive power. And thus Nature will be very conformable to herself, and very simple; performing all the great motions of the heavenly bodies by the attraction of gravity, which intercedes those bodies; and almost all the small ones of their particles, by some other Attractive and Repelling powers."

"A suggestive paragraph... occurs... which is sometimes not sufficiently remembered when gravitation is spoken of as a cause :—These principles—i.e. of attraction and repulsion—I consider not as occult qualities, supposed to result from the specifick forms of things, but as general laws of Nature, by which the things themselves are formed; their truth appearing to us by phenomena, though their causes be not yet discovered."

"This seems to be Newton's only contribution to the subject of Elasticity, beyond the paragraph of the Principia on the collision of elastic bodies."

"[W]hile the mathematicians were beginning to struggle with the problems of elasticity, a number of practical experiments were being made on the flexure and rupture of beams, the results of which were of material assistance to the theorists."

"Petris van Musschenbroek: Introductio ad cohaerentiam corporum firmorum.... commences at of the author's Physicae experimentales et geometricae Dissertationes. Lugduni 1729. It was held in high repute even to the end of the 18th century. ...[The] historical preface,... has been largely drawn upon by Girard. [Van Musschenbroek] describes the various theories which have been started to explain cohesion, and rejects successively that of the pressure of the air and that of a subtle medium. ...He laughs at Bacon 's explanation of elasticity, and another metaphysical hypothesis he terms abracadabra. ...[H]e falls back... upon Newton's thirty-first Query... and would explain the matter by vires internae [internal forces]. Musschenbroek assumes... we may determine them in each case by experiment. ...The source of elasticity is a vis interna attrahens... drawn directly from Newton's Optics."

"Musschenbroek... treats of the extension (cohaerentia vel resistentia absoluta) and of the flexure (cohaerentia respectiva aut transversa) of beams, but does not seem to have considered their compression. His experiments are... on wood, with a few... on metals. ...Anything of value in his work is however reproduced by Girard."

"Musschenbroek discovered by experiment that the resistance of beams compressed by forces parallel to their length is... in the inverse ratio of the squares of their lengths; a result afterwards deduced theoretically by Euler."

"Pere Maziere: Les Loix du choc des corps à ressort parfait ou imparfait, déduites d'une explication probable de la cause physique du ressort. Paris, 1727... carried off the prize of the Acadimie Royale des Sciences... 1726. Pere Maziere, Pretre de I'Oratoire... brings out clearly the union of those theological and metaphysical tendencies of the time, which so checked the true or experimental basis of physical research. It shews us the evil as well as the good which the Cartesian ideas brought to science. It is startling to find the French Academy awarding their prize to an essay of this type, almost in the age of the Bernoullis and Euler. Finally it more than justifies Riccati' s remarks as to the absurdities of these metaphysical mathematicians. Pere Maziere finds a probable explanation of the physical cause of spring in that favorite hypothesis of a 'subtile matter' or étherée. ...Mazière ...applies the Cartesian theory of vortices to the aether ..."

"G. B. Bülfinger: De solidorum Resistentia Specimen, Commentarii Academiae Petropolitanae... is a memoir of August 1729... first published... 1735. [It] commences with a reference to the labours of Galilei, Leibniz, Wurtz, Mariotte, Varignon, James Bernoulli and Parent... [His following] sections are concerned with the breaking force on a beam when it is applied longitudinally and transversally. Galilei's and the Mariotte-Leibniz hypotheses are considered. It is shewn that the latter is the more consonant with... fact, but... is not exact because it neglects the compression (i.e. places the neutral line in the lowest horizontal fibre of the beam)."

"Bülfinger... suggests a parabolic relation of the formtension ∝ (distance from the neutral line) m, where the [exponent m] power is a constant to be determined by experiment."

"[On] the question of extension and compression of the fibres of the beam under flexure... [Bülfinger] cites the two theories... that of Mariotte, that the neutral line is the 'middle fibre' of the beam, and that of Bernoulli that its position is indifferent. He... rejects both theories, and gives... sufficient reasons... [N]ot having accepted Hooke's principle... he holds that till the laws of compression are formulated, the position of the neutral line must be found by experiment."

". ...first is a memoir entitled Verae et germanae virium elasticarum leges ex phaeiwmenis demonstratae, 1731... printed in the De Bononiensi scientiarum Academia Commentarii, 1747. ...[I]t marks the first attempt since Hooke to ascertain by experiment the laws which govern elastic bodies."

"[T]he state of physical investigation with regard to elasticity in Riccati's time... [is indicated by the] remark of Bernoulli... in the corollary to his third lemma: "Au reste, il est probable que cette courbe" (ligne de tension et de compression) "est différente de différens corps, à cause de la différente structure de leurs fibres." [Moreover, it is probable that this curve (line of tension and compression) is different for different bodies, because of the different structure of their fibers.] It struck Riccati... to consider the acoustic properties of bodies. For, he remarks, the harmonic properties of vibrating bodies are well known and must undoubtedly be connected with the elastic properties—("canoni virium elasticarum" canon elastic forces])."

"Riccati... has no clear conception of , nor does [his] theory... of acoustic experiments lead him to discover that law. In his third canon he states that the 'sounds' of a given length of stretched string are in the sub-duplicate ratios of the stretching weights. The 'sounds' are to be measured by the inverse times of oscillation. ...from this ...he deduces ...that, if u be a weight which stretches a string to length x and u receive a small increment \partial u corresponding to an increment \partial x of x, then the law of elastic force is that \frac{\partial u}{u} is proportional to \frac{\partial x}{x^2}. Hence according to Riccati we should have instead of Hooke's Law: \boldsymbol{u = Ce^{-\frac{1}{x}}}, where C is constant. For compression the law is obtained by changing the sign of x. Riccati points out that James Bernoulli's statements... do not agree with this result...He notes that the equation du/u = \pm dx/x^2 has been obtained by Taylor and Varignon for the determination of the density of an elastic fluid compressed by its own weight"

"Riccati... attempt[s]... a general explanation of the character of elasticity... in his Sistema dell' Universo [System of the Universe]... written before 1754... [and] first published in the Opere del Oonte Jacopo Riccati... 1761. [Two chapters] are respectively entitled: Delle forze elastiche and Da quali primi principi derivi la forza elastica... display... dislike... of any semi-metaphysical hypothesis introduced into physics; and desire to discover a purely dynamical theory for physical phenomena."

"[Riccatti states that] the physicists of his time had troubled themselves much with the consideration of elasticity: E si può dire, che tante sono le teste, quante le opinioni, fra cui qual sia la vera non si sa, se pure non son tutte false, e quale la più verisimile, tuttavia con calore si disputa. [And it can be said that so many are the thinkers, how many opinions, among which the true is not known, even if they are not all false, and which is the most verisimilar, nevertheless, it is hotly disputed.]"

"Riccati... sketches briefly some [current] theories... Descartes... supposed [that] elasticity to be produced by a subtle matter (aether) which penetrates the pores of bodies and keeps the particles at due distances; this aether is driven out by a compressing force and rushes in again with great energy on the removal of the compression. ...John Bernoulli... supposes the aether enclosed in cells in the elastic body and unable to escape. In this captive aether float other larger aether atoms describing orbits. When a compressing force is applied the cells become smaller, and the orbits of these atoms are restricted, hence their centrifugal force is increased; when the compressing force is removed the cells increase and the centrifugal forces diminish. Such is... how the forza viva [live force] absorbed by an elastic body can be retained for a time as forza morta [dead force]. (This theory of captive aether was at a later date adopted by Euler although in a slightly more reasonable form...)"

"Riccati gives a characteristic paragraph with regard to the English theorists:...Non ci ha fenomeno in Natura, ch' eglino non ascrivano alle favorite attrazioni, da cui derivano la durezza, la fluidità, ed altre proprietà de' composti, e spezialmente la forza elastica ... [There is no phenomenon in Nature, which is not ascribed to the favorite attractions, from which is derived hardness, fluidity, and other properties of the compounds, and especially the elastic force. ...]"

"Riccati... will not enter into these disputes [as to current hypotheses as to the nature of elasticity]... For [in] his own theory he will not call to his assistance the aether of Descartes or the attractions of Newton. ...[H]e ...seems ignorant of and quotes Gravesande [Physices elementa mathematica experimentis confirmata, 1720.] to shew that the relation of extension to force is quite unknown... curious as he elsewhere cites Hooke..."

"Riccati states la mia novella sentenza [my new sentence]... Every deformation is produced by forza viva and this force is proportional to the deformation produced. ...The forza viva spent in producing a deformation remains in the strained body in the form of forza morta; it is stored up in the compressed fibres. Riccati comes to this conclusion after asking whether the forza viva so applied could be destroyed? That... he denies, making use strangely enough of the argument from design, a metaphysical conception such as he has told us ought not to be introduced into physics!La Natura anderebbe successivamente languendo, e la materia diverrebbe col lungo girare de' secoli una massa pigra, ed informe fornita soltanto d' impenetrabilità, e d' inerzia, e spogliata passo passo di quella forza (conciossiachè in ogni tempo una notabil porzione se ne distrugge) la quale in quantità, ed in misura era stata dal sommo Facitore sin dall' origine delle cose ad essa addostata per ridurre il presente Universo ad un ben concertato Sistema. [Nature would then be languishing, and matter would become a lazy, unformed mass with the long passage of centuries, and only provided impenetrability, and inertia, and stripped step by step of that force (because at any time a notable portion destroys it) which in quantity, and to an extent had been from the supreme Authority since the origin of the things, subjected to, in order to reduce the present Universe to a well-organized System.]"

"This paragraph... unit[es] the old theologico-mathematical standpoint, with the first struggling towards the modern conception of the . It is this principle of energy which la mia novella sentenza endeavours so vaguely to express, namely that the mechanical work stored up in a state of strain, must be equivalent to the energy spent in producing that state."

"Riccati... tells us that the forza viva must be measured by the square of the velocity. The consideration of the impact of bodies is more suggestive; the forza viva existing before impact is converted at the moment into forza morta and this re-converted into forza viva partly in the motion of either body as a whole, and partly in the vibratory motion of their parts, which we perceive in the sound vibrations they give rise to in the air."

"The importance of Riccati's work lies not in his practical results, which are valueless, but in his statement of method, and his desire to replace by a dynamical theory semi-metaphysical hypotheses. ...[H]is writings remind us... of Bacon, who in like fashion failed to obtain valuable results, although he was capable of discovering a new method. Euler's return to the semi-metaphysical hypothesis... is a distinct retrogression on Riccati's attempt, which had to wait till George Green's day before it was again broached."

"Gravesande in his Physices Elementa Mathematica [Vol.1; Vol. 2], 1720, explains elasticity by Newtonian attractions and repulsions. The... chapter... entitled De legibus elasticitatis [The laws of elasticity].... is of opinion that within the limits of elasticity, the force required to produce any extension is a subject for experiment only. ...he considers elastic cords, laminae and spheres (supposed built up of laminae), and finds the deflection of the beam in Galilei's problem proportional to the weight. He makes... no attempt to discuss the elastic curve."

"The direct impulse to investigate elastic problems... came to Euler from the Bernoullis."

"Galilei's problem had determined the direction of later researches... while James Bernoulli solved the problem of the elastic curve his nephew Daniel first obtained a differential equation which really does present itself in the consideration of the transverse vibrations of a bar."

"[In an Oct. 20, 1742 letter, Daniel Bernoulli] suggests for Euler's consideration the case of a beam with clamped ends, but states that the only manner in which he has himself found a solution of this "idea generalissima elasticarum" is "per methodum isoperimetricorum." He assumes the "vis viva potentialis laminae elasticae insita" must be a minimum, and thus obtains a differential equation of the fourth order, which he has not solved, and so cannot yet shew that this "aequatio ordinaria elasticae" is general.Ew. reflectiren ein wenig darauf ob man nicht konne sine interventu vectis die curvaturam immediate ex principiis mechanicis deduciren. Sonsten exprimire ich die vim vivam potentialem laminae elasticae naturaliter rectae et incurvatae durch \int ds/R^2, sumendo elementum ds pro constante et indicando radium osculi per R. Da Niemand die methodum isoperimetricorum so weit perfectionniret als Sie, werden Sic dieses problema, quo requiritur ut \int ds/R^2 faciat minimum, gar leicht solviren. [Ew. reflect a little on whether one can not deduce the curvature of the bar directly from the principles of mechanics. In the first place I express the actual elastic laminar potential, naturally right and yet curving, by \int ds/R^2, summing the element ds per constant radius of curvature R. Since no one has perfected the isoperimetric method as much as You, So this problem, which requires that \int ds/R^2 be minimum, might be easily solved.]"

"Bernoulli writes... to Euler... Sept. 1743 [and] extends his principle of the 'vis viva potentialis laminae elasticae' to laminae of unequal elasticity, in which case \int E ds/R^2 is to be made a minimum. The... letter...in... April or May 1744... expresses his pleasure that Euler's results on the oscillations of laminae agree with his own."

"The celebrated work of Euler relating to... the Calculus of Variations appeared in 1744 under the title of Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes. ...an appendix called Additamentum I. De Curvis Elasticis ...commences with a statement... shewing the theologico-metaphysical tendency... so characteristic of mathematical investigations in the 17th and 18th centuries. It was assumed that the universe was the most perfect conceivable, and hence arose the conception that its processes involved no waste, its 'action' was always the least required to effect a given purpose. ...Thus we find Maupertuis' extremely eccentric attempt at a principle of Least Action. ...[I]t is... probable that physicists have to thank this theological tendency in great part for the discovery of the modern principles of Least Action, of Least Constraint, and perhaps even of the Conservation of Energy."

"[S]tating that Daniel Bernoulli... had discovered... that the vis potentialis represented by \int ds/R^2 was a minimum for the elastic curve, Euler proceeds to discuss the inverse problem... The curve is to have a given length between two fixed points, to have given tangents at those points, and to render \int ds/R^2 a minimum... No attempt is made to shew why... By the aid of the principles of his book Euler arrives at the following equations where a, \alpha, \beta, \gamma are constants,dy = \frac{(\alpha + \beta x + \gamma x^2)}{\sqrt{a^4 - (\alpha + \beta x + \gamma x^2)^2}}from this we obtainds = \frac{a^2 dx}{\sqrt{a^4 - (\alpha + \beta x + \gamma x^2)^2}}"

"Euler gives... his investigation of the elastic curve in what he has just called an a priori manner. But this method is far inferior to that of James Bernoulli; for Euler does not attempt to estimate the forces of elasticity, but assumes that the moment of them at any point is inversely proportional to the radius of curvature: thus he... writes... an equation like... Poisson's Traite de Mecanique, Vol. I., without giving any of the reasoning by which Poisson obtains the equation."

"Euler... has hitherto considered the elasticity constant, but he will now suppose that it is variable... S, which is supposed a function of the arc s; \rho is the radius of curvature. He proceeds to find the curve which makes \int S ds/\rho^2 a minimum; and... finds for the differential equation of the required curve\alpha + \beta x -\gamma y = S/\rho where \alpha, \beta, \gamma are constants."

"Euler takes the case in which forces act at every point of the elastic curve; and he obtains an equation like the first volume of Poisson's Traiti de Mecanique."

"Euler devotes his attention to the oscillations of an elastic lamina; the investigation is some what obscure for the science of dynamics had not yet been placed on the firm foundation of : nevertheless the results obtained by Euler will be found in substantial agreement with those in Poisson's Traite de Mecanique, Vol. II."

"1757. Sur la force des colonnes, Mémoires de l'Académie de Berlin, Tom. XIII. 1759... is one of Euler's most important contributions to the theory of elasticity. The problem... is the discovery of the least force which will suffice to give any the least curvature to a column, when applied at one extremity parallel to its axis, the other extremity being fixed. Euler finds that the force must be at least = \pi^2 \cdot \frac{Ek^2}{a^2}, where a is the length of the column and Ek^2 is the 'moment of the spring' or the 'moment of stiffness of the column' (moment du ressort or moment de roideur)."

"If we consider a force F perpendicular to the axis of a beam (or lamina) so as to displace it from the position AC to AD, and \delta be the projection of D parallel to AC on a line through C perpendicular to AC, Euler finds by easy analysis D \delta = \frac{F\cdot a^3}{3\cdot Ek^2}, supposing the displacement to be small. This suggests to him a method of determining the 'moment of stiffness' Ek^2, and he makes various remarks on proposed experimental investigations. He then notes the curious distinction between forces acting parallel and perpendicular to a built-in rod at its free end; the latter, however small, produce a deflection, the former only when they exceed a certain magnitude. It is shewn that the force required to give curvature to a beam acting parallel to its axis would give it an immense deflection if acting perpendicularly."

"Euler deduces the equation for the curve assumed by the beam AC fixed but not built in at one end A and acted upon by a force P parallel to its axis. If RM be perpendicular to AC and y=RM, x = AM, he finds\frac{y}{\theta}\cdot \sqrt{\frac{P}{Ek^2}} = sin(x \sqrt{\frac{P}{Ek^2}}),where \theta = \angle RCM. Hence since y = 0, when x = a the length of the beam, a \sqrt{\frac{P}{Ek^2}} must at least = \pi, whence it follows that P must be at least = \pi^2 \cdot \frac{Ek^2}{a^2}. This paradox Euler seems unable to explain."

"If Q be the total weight of the beam the differential equationEk^2 ad^3 y + Pa (dx)^2 dy + Qx(dx)^2 dy = 0is obtained... This is reduced by a simple transformation to a special case of Riccati's equation, which is then solved on the supposition that \frac{Q}{P} is small. Euler obtains finally for the force P, for which the rod begins to bend, the expressionP = \pi^2 \cdot Ek^2/a^2 - Q \cdot (\pi^2 - 8)/2\pi^2;which shews that the minimum force is slightly reduced by taking the weight of the beam into consideration."

"Determinatio onerum quae columnae gestare valent. Examen insignis paradoxi in theoria columnarum occurrentis. De altitudine columnarum sub proprio pondere corruentium. [all in] Acta Academiae Petropolitanae [1778, 1780]. The first memoir... points out that vertical columns do not break under vertical pressure by mere crushing, but that flexure of the column will be found to precede rupture. ...[Euler] proposes to deduce a result which is now commonly in use... to find an expression connecting Ek^2 with the dimensions of the transverse section of the column. Euler finds Ek^2 = h \cdot \int x^2 ydx, where x and y... Euler appears however to treat the unaltered fibre or 'neutral line' without remark as the extreme fibre on the concave side of the section of the column made by the central plane of flexure. Thus for a column of rectangular section of dimensions b [with]in, and c perpendicular to the plane of flexure, he finds...Ek^2 = \frac{1}{3} b^3 ch, and the like method is used in the case of a circular section."

"Euler... calculate[s] the flexure which may be produced in a column by its own weight. If y be the horizontal displacement of a point on the column at a distance x from its vertex, the equation Ek^2 \cdot \frac{d^2y}{dx^2} + b^2 \int_0^y xdy = 0 is found, where the weight of unit volume of the column is unity and its section a square of side b. ...[I]f a be the altitude of the column and m = Ek^2/b^2, it is found that the least altitude for which the column will bend from its own weight is the least root of the equation,0 = \frac{1 \cdot a^3}{4! m} + \frac{1 \cdot 4 \cdot a^6}{7! m^2} - \frac{1 \cdot 4 \cdot 7 \cdot a^9}{10! m^2} + \frac{1 \cdot 4 \cdot 7 \cdot 10 \cdot a^{12}}{13! m^2} - \mathrm{etc.}Euler finds that this equation has no real root, and thus arrives at the paradoxical result, that however high a column may be it cannot be ruptured by its own weight. <!--(77-78.)p.45"

"P. S. Girard. Traite Analytique de la Resistance des solides, et des solides d'e'gale Resistance, Auquel on a joint une suite de nouvelles Experiences sur la force, et Velasticite specifique des Bois de Chine et de Sapin. Paris, 1798. ...This work very fitly closes the labours of the 18th century. It is the first practical treatise on Elasticity; and one of the first attempts to make searching experiments on the elastic properties of beams. It is not only valuable as containing the total knowledge of that day on the subject, but also by reason of an admirable historical introduction... The work appears to have been begun in 1787 and portions of it presented to the Academie in 1792. Its final publication was delayed till the experiments on elastic bodies, the results of which are here tabulated, were concluded at Havre. ...We are... considering the period of the French Revolution."

"The book... introduction is occupied with an historical retrospect of the work already accomplished in the field of elasticity... [and] concludes with an analysis of Girard's own work."

"The first section of Girard's treatise is concerned with the resistance of solids according to the hypotheses of Galilei, Leibniz and Mariotte. He notes Bernoulli's objections to the Mariotte-Leibniz theory; but remarks that physicists and geometricians have accepted this theory... [H]e thinks it probable that Galilei's hypothesis of non-extension of the fibres may hold for some bodies—stones and minerals—while the Mariotte-Leibniz theory is true for sinews, wood and all vegetable matters (cf. p. 6). As to Bernoulli's doubt with regard to the position of the neutral surface, Girard accepts Bernoulli's statement that the position of the axis of equilibrium is indifferent, and supposes accordingly that all the fibres extend themselves about the axis AC..."

"[Girard's] book forms... a most characteristic picture of the state of mathematical knowledge on the subject of elasticity at the time and marks the arrival of an epoch when science was to free itself from the tendency to introduce theologico-metaphysical theory in the place of the physical axiom deduced from the results of organised experience."

"General summary. As the general result of the work... previous to 1800... while a considerable number of particular problems had been solved by means of hypotheses more or less adapted to the individual case, there had as yet been no attempt to form general equations for the motion or equilibrium of an elastic solid. Of these problems the consideration of the elastic lamina by James Bernoulli, of the vibrating rod by Daniel Bernoulli and Euler, and of the equilibrium of springs and columns by Lagrange and Euler are the most important. The problem of a vibrating plate had been attempted, but with results which cannot be considered satisfactory."

"A semi-metaphysical hypothesis as to the nature of Elasticity was started by Descartes and extended by John Bernoulli and Euler. It is extremely unsatisfactory, but the attempt to found a valid dynamical theory by did not lead to any more definite results."

"In the appendix Mr. Pearson has carefully analysed the conflicting notations of different writers, and proposed a very convenient terminology and notation, which would save great trouble if universally adopted. He has also given an account of experiments carried out by Prof. Kennedy in his mechanical laboratory, which have an important bearing on the limitations of the truth of Hooke's law, or in the language of elasticity, the constancy of the ratio of stress to corresponding strain. The present volume is an indispensable hand-book of reference for the mathematician and the engineer, and in the editing and printing must be considered a very fitting tribute to the wonderful industry and application of its projector, the late Dr. Todhunter."

"At Mr Webb's suggestion, the exposition of the theory is preceded by an historical sketch of its origin and development. Anything like an exhaustive history has been rendered unnecessary by the work of the late Dr Todhunter as edited by Prof. Karl Pearson, but it is hoped that the brief account given will at once facilitate the comprehension of the theory and add to its interest."

"My invention shows a new product which helps to replace timber where it is endangered by wetness, as in wood flooring, water containers, plant pots, etc. The new substance consists of a metal net of wire or sticks which are connected or formed like a flexible woven mat. I give this net a form which looks in the best possible way, similar to the articles I want to create. Then I put in hydraulic cement or similar bitumen tar or mix, to fill up the joints."

"[W]elded wire reinforcement (WWR) [was] formerly known as welded wire mesh or fabric. Welded steel wire reinforcement is the predominant form... A grid of orthogonal longitudinal and transverse cold-drawn steel wires is welded together at every wire intersection... The size and spacing of the wires can vary... based on the requirements... Welded wire reinforcement can be epoxy coated or zinc coated (galvanized). ...Plain and deformed welded wire reinforcement is covered in... ASTM A1064... Stainless steel wires are specified according to ASTM A1022... Epoxy-coated WWR... in accordance with ASTM A884... Galvanized WWR... with ASTM A1060... Even plain wire used in welded wire reinforcement has both chemical bond and mechanical bond to the concrete. The mechanical bond results from bearing of the welded cross wires against the concrete in the grid of reinforcement."

"A thin shell is a special kind of vault whose geometry may include many shapes. ...a three-dimensional form made thicker than a membrane, so that it can not only resist tension as membranes do, but also compression. On the other hand, a thin shell is made thinner than a slab, which makes it unable to resist bending, as a slab does. In short, thin shells are structures thicker than membranes, but thinner than slabs. Thin shells are made possible by the use of materials that work well under tension and compression. Masonry has no tensile strength... Only the availability of and made a thin shell possible."

"RECOMMENDATION 6: Ferrocement in Disaster Relief. After fires, floods, droughts, and earthquakes... [t]ransportation is often disrupted... Supplies of bulky conventional building materials may be stranded outside the disaster area, whereas the basic ingredients of ferrocement may be available on the site or easily transported. The versatility of ferrocement also reduces logistical supply problems: wire mesh, cement, sand, and water can be substituted for the metal used for roofing, woods or plastic for shelters and clinics, asphalt for helipads, steel for bridges, and so on. Moreover, most ferrocement structures, though built for an emergency, will last long after the emergency is over. ...[F]errocement could be used at a disaster site for many purposes: Transport facilities, from simple boats to barges, docks, marinas, helipads, and simple floating bridges or short footbridges as well as road repairs. ...Food-storage facilities, quickly designed to local needs and quickly built, to preserve emergency food supplies. ...Emergency shelters such as, for example, the quonset type of roof, which is easy to erect and highly efficient. ..Public health facilities, such as latrines and clinics, built with ferrocement roofs and stucco-type walls of the same wire mesh and mortar. ...[C]adres of ferrocement workers could be trained in emergency applications and the supervision of local laborers at the disaster site."

"[Ferrocement defined:] A thin walled construction, consisting of rich cement mortar with uniformly distributed and closely spaced layers of continuous and relatively small diameter mesh (metallic or other suitable material)."

"The construction method chosen was the inverted wooden mold. For hulls up to 50 feet in length, and for utilizing unskilled labor, this method has been shown to be most efficient. ...The shape and fairness of the hull is first established and checked with the quick and easy-to-build wooden mold. ..The use of air-powered staple guns to fasten mesh and rods to the hull mold is a quick and efficient method and can be performed with unskilled labor. ..Lamination of the concrete skin is eliminated as the mortar is applied from one side only and vibrated through the hull shell reinforcing. ...Sagging of large unsupported areas is avoided. The men work from the outside of the hull and downwards."

"One inch (25 mm), 21 gauge, hexagonal galvanized mesh was used. This mesh was the type manufacturers describe as "reverse twist," galvanized after weaving. Ten layers were applied... Four layers of mesh were stapled to the mold over 4-mil plastic sheathing. Two more layers of mesh were stapled over 1/4-inch (6.4 mm) diameter vertical reinforcing bars which had been stapled on at 6-inch (152 mm) centers. 1/4-inch (6.4 mm) diameter reinforcing bars were then stapled longitudinally over this second layer of mesh. This layer of reinforcing bar was spot-welded to the first layer at approximately every second joint. This second layer of horizontal rods was applied on 3-inch (76 mm) centers. The last four layers of mesh were hogring fastened to the outside of this last layer of rods."

"Clear plastic 4-millimeter sheathing was hand-stapled to the mold for two reasons: ...To stop the moist mortar from falling through the joints and gaps between the wooden battens planking the mold. ...To form a barrier between the wooden mold and the fresh mortar. If no barrier were placed the wood would draw moisture from the new mortar and reduce its final strength."

"The first four layers of mesh were stapled to the mold over the plastic sheeting. Each length of mesh, already folded double, formed two layers. This first layer of mesh strips, 1-1/2 feet (457 mm) wide, was butted together. The second layer of mesh strips was laid out so as to cover the joints where the first layer was butted together, making a total of four layers of mesh."

"The vertical rods were stapled firmly to the hull. An air-powered staple gun was used..."

"Two more layers of mesh were stapled over the mold. Again 1" x 2" (25.4 mm x 51 mm) wide staples were used. The folded mesh was not lapped but just butted."

"The horizontal rods were welded on. Where a rod terminated on the hull it was lapped for six inches (152.4 mm) with another rod and spotwelded. All the rod joints were treated in this same way. The rods were stapled at approximately three-inch (76 mm) centers. Every second intersection of horizontal with vertical rods was spot welded. As there were two layers of mesh between the vertical and horizontal rods, the mesh was faired smooth in this small area. Care was taken not to burn too large a hole in the plastic sheeting where the rod welding took place."

"Wooden plugs of the same diameter as each through-hull fitting were cut out and placed on the mold in the exact position where the future through-hull fitting was to be installed later. These were cut from doweling and made one inch (25.4 mm) deep. A hole was drilled in the center of the doweling to ensure that the plug did not split when nailed to the mold. The mesh was cut away under the plug and trimmed neatly at the edges. Some attempt was made to place the doweling in a position clear of the intersecting rods."

"Starter rods for the stem, webs, bulkheads, bilge stringers, and engine beds were welded in place. These starter rods were placed at approximately six-inch (152 mm) centers. They were six inches (152 mm) long where they extended through the hull. Quarter-inch (6.4 mm) holes were drilled for these... The starter rods were lap-welded to either the vertical rods or the horizontals, depending on their position."

"One-inch (25.4 mm) chain links were welded to the hull reinforcing cage where scuppers were to be placed. These links were aligned and welded in at deck level. ...[E]xposed steel pieces such as scuppers or screeds which require welding... should always be cleaned and protectively coated."

"The last four layers of mesh were stapled to the hull mold. They were laid in the same way as the first layers. The mesh was fastened... as smoothly and as tightly as possible. It was clipped onto the horizontal rods with 3/4-inch (19 mm) hog rings. ...One-half inch (12.7 mm) hog ring staples which do a neater job could not be located ...All edges of the mesh were stapled down tightly so that no stray ends of mesh would penetrate later through the fresh mortar and thus interfere with the plasterers' work... Mesh over the chain link scuppers was clipped away and the ends fastened down neatly."

"The mortar used for the hulls was a mixture of clean, graded silica sand, ...Portland Cement Type II, and drinking-type water. This silica sand, of the grading and particle shape used in high-strength structures... The sand content used was... one 50-pound (22 Kg) bag of coarse grade, one 100-pound (44 Kg) bag of medium grade and one 50-pound (22 Kg) bag of fine grade. To this graded sand was added two 80-pound (31 Kg) bags of Portland Cement Type II and just sufficient water to make the mortar workable into the hull mesh reinforcing. ...There was one plasterer for roughly every 100 square feet (9 m2) ...Retarders or additives were not used. The sun shelters were moved into place ..."

"First a heavy coat was applied all over the hull. Men stationed inside the hull mold began systematically vibrating the mold planking and checking the gaps between the planking for mortar penetration. Once the mortar had all been applied to the satisfaction of the men vibrating and checking, the excess mortar was then scraped back to the mesh. ...A new thin coat was troweled over the hull and allowed to start setting. When it started to set the hull was sponge troweled, the sponge trowel being used in a circular motion to smooth out surface irregularities. As soon as the sponge troweling was finished, the final steel troweling began. This was carried on until the hull surface had set up too hard to be worked on any further, and was as smooth and fair as the plasterers could make it."

"The hulls were steam cured for 24 hours at a temperature of 150°F (66° C). A steam pipe, perforated for its entire length, was placed under the inverted hull and a rubberized canvas steam tent drawn completely over. The temperature was carefully brought up to 150°F (66°C) in a period of four hours. Twenty-four hours were then maintained at this prescribed temperature until, finally, it was allowed to drop slowly to ambient temperature of 85° F (30°C)."

"The hull was left untouched for 18 hours after the plaster finishing work had ceased. This allowed the hull to set-up hard enough for the men to drag the steam tent over it. It is not advisable to start steam curing too soon, as the jets of hot water from the steam pipe may wash some of the mortar off the hull while it is still green. Before steam curing began the wooden screeds were removed from around the hull sheer."

"[These] low cost, easily built, high quality ferrocement roofings... offer an innovative solution to the serious dwelling problem affecting large numbers of people, especially in the marginal urban areas and rural zones of developing countries..."

"Ferrocement was chosen as the material for the proposed roofing because of its physical properties (strength in compression and tension, impact, permeability, etc.) and because it is cheap and easy to build."

"[I]t was decided to develop a type of roofing based on prefabricated sections. ...With the partial results obtained in this stage, another part of the study could be initiated, i.e. to build this same type of element "in situ"... thus providing solutions for situations in which prefabrication is not appropriate..."

"The adaption of ferrocement precast roofings in self-help construction projects... permits the use of standard components which are easily erected without sophisticated equipment."

"The construction of the mold simply consists of making a dome of well compacted earth, covered by a layer of well-finished concrete having a thickness of 8 cm [3.15 inches], with the shape defined by the trusses... used to [shape] the mold."

"The reinforcement consists of two no. 2 bars along the edges, one of them straight and the other one with the necessary bends to provide the handles to lift and fix the dome to the structure. ...[T]wo layers of galvanized chicken wire, guage 22 with a separation of 13 mm are attached to the bars and directly mounted over the mold, one perpendicular to the other. ...[E]nsure a minimum overlap of 5 cm... and... ensure that these are stretched... to achieve the thinnest section possible."

"The mortar used for the mix is made (using a mixture) of normal or ic cement and sand in a proportion of 1:1.5 by volume and with a water-cement ratio of 0.55."

"After a couple of hours, the desired finish is applied (polishing or brushing), with the object of sealing the cracks or faults that may appear on the surface of the dome."

"The curing of the shell is achieved by covering the surface with wet sand for a period of 72 hours."

"An alternative construction method was also developed which did not require the use of any type of mold or form."

"The best solution found was to form a double curvature surface... The curvature does not necessarily follow a pre-determined law, so that it may be checked roughly "with the naked eye"."

"[T]he smaller the thickness of the cover, the better will be its quality, which is why at the time of pouring, the meshes of the wire should be well stretched. Care should be taken that only enough mortar to cover the reinforcement is used."

"One worker on one of the supports... either manually or with a trowel distributes the mortar over the chicken wire... Simultaneously, another worker from within the room... holds the mortar which is applied from the outside with a metal float or trowel in order that the mortar does not fall. Once this operation is completed, the required finish is applied both from the outside and the inside."

"The central part remains [bare wire] and will be completed after 72 hours. ...[T]he worker can [then] climb on the previously cast portion, carrying out the same process ...[S]upport the dome until the mortar has cured in order to avoid deformations caused by the weight of the mortar and to guarantee curvature of the shell."

"As eight of the shells tested failed as a result of the failure of the supporting concrete ties on the walls, it was decided to build samples which were very well reinforced... The ultimate load increased by 1.7 times for these shells..."

"The domes were very easily repaired by replacing the damaged mortar or mesh..."

"[T]he ferrocement roofings are practically waterproof and that they do not need any special treatment."

"[T]o increase the load capacity of the domes and to avoid excessive deformations, it is necessary to provide the best possible anchoring at the edges."

"[A] dome of any shape will amply comply with safety requirements. Because of this it is believed that it is possible to build domes in situ without specifying the shape of the dome, which makes skilled labor unnecessary."

"Chicken wire mesh was recommended because of its ductility. It shows no oxidation problems as it is made with galvanized wire. It has reliable properties and is low in cost."

"The purpose of this book is to match an existing resource with an existing need. The need is shelter... simpler structures... that can be assembled quickly in the wake of a hurricane or flood... that can be built economically in undeveloped countries... that... provides pleasure in the form of self-made personal retreats..."

"This highly specialized, but by no means highly complicated building technique had been almost forgotten after its first use... in the middle of the nineteenth century until it was virtually reinvented in the 1940s by... ."

"Ferrocement is used relatively little in the housing field because it is regarded as a labor-intensive... building technique. ...It is true that considerable labor is required to put together... sand, cement, and wire mesh... However, the elaborate temporary framework which consumes most of the labor in conventional work is often entirely eliminated... Even if we concede that ferrocement is impractical where labor is expensive... its use requires only time, not skill..."

"All ferrocement can be said to be , but all types of reinforced concrete are not ferrocement."

"[F]erroconcrete would be a more accurate term for our material, but that term is already in common use to describe... reinforced concrete work."

"[F]errocement ...uses wire mesh, rather than heavy rods or bars, as the primary part of its metal reinforcement and which uses sand [in a mortar mixture] rather than a mixture of sand and stone ...as the aggregate in its concrete mix. ...The resultant product can be a shell of surprising thinness, durability, resilience, and, when properly shaped, strength."

"The structural effectiveness of any reinforced concrete, including ferrocement, depends on the almost miraculously fortuitous fact (first discovered in 1870 by ) that steel and concrete have close to identical coefficients of expansion, swelling at exactly the same rate when heated, shrinking at exactly the same rate when cooled. Thus they may be permanently bonded together as a single material, utilizing the best structural characteristics of each: steel has the tensile strength... while concrete has the ..."

"Ferrocement... often acts more like steel than like a standard reinforced concrete. Hit with a hammer, it rings like a bell."

"[F]errocement... may eliminate the need for separate layers of waterproofing."

"[A]t the new ... [the] famous sail-shaped roofs (built of conventional reinforced concrete) have been covered with tile-surfaced panels of ferrocement which serve as waterproofing..."

"[B]ecause of its intrinsic hardening process which continues indefinitely, good concrete gets better and better, imperfect concrete (with flaws that invite erosion and corrosion) gets worse and worse."

"[B]efore... crude beginnings of work with conventional reinforced concrete, work with ferrocement had already begun. ...The ferrocement technique seems to have been first used by ... and, apparently... independently, by ...Jean-Louis Lambot. ...Lambot called his invention "ferciment" and used it to build boats... He constructed his first boat in 1848..."

"Although... two of the first patents for reinforced concrete of any type... were for ferrocement, that particular type of reinforced concrete was generally underutilized—in fact, forgotten—until 's work of the 1940s. ...The turning to ferrocement... was based on the logical use of a known fact: the structural behavior of reinforced concrete is most effective near the points of its reinforcement. ...Nervi was first to ask the question... why not distribute the metal reinforcement so evenly that all the concrete is in immediate proximity to it? On this theoretical foundation Nervi performed the experiments which led to his establishment of ferrocement building technique as we know it today."

"[B]y the end of 1943 Nervi's firm was at work on three 150-ton transport boats, their hulls completely of ferrocement, and one 400-ton vessel, largely of ferrocement. The first construction was interrupted by the war, and it was not until 1945 that Nervi's method resulted in... [t]he Irene... a motor boat with a 165-ton displacement. On a supporting frame of 1/4" steel rods spaced about 4" apart, Nervi spread eight layers of wire mesh, four on each side of the rods, which were tied tightly together and plastered by hand with a rich cement mortar. The resultant ferrocement was 1 3/8" thick (about the same thickness as Lambot's boat). Other than the rods sandwiched into the mesh, no formwork was needed."

"In 1947 [Nervi] built his first ferrocement structure on land, a storage warehouse... 35' x 70' and all four... walls [and] roof were of ferrocement 1 3/16" thick, their thinness made structurally feasible by their corrugated shapes."

"The following year Nervi designed and built a 41' ... the Nennele... the hull's total thickness was less than 1/2"."

"Nervi's first used of ferrocement in an important public structure was in the 1948 Exposition Hall in Turin. ...The great corrugated roof is... ferrocement panels 1 1/2" thick tied together by ribs of conventional poured concrete..."

"In the 1953 Milan Fair building and in the 1959 Flaminio stadium... Nervi used ferrocement corrugations... in strikingly cantilered roofs. A further use by Nervi of the material has been in... smooth, lightweight forms into which conventional poured concrete could be molded..."

"Most of the more recent use of ferrocement have been by others, but it is to the insight and pioneering work of that they owe their successes."

"Ferrocement is a form of reinforced concrete... [utilizing] closely spaced multiple layers of mesh or fine rods completely embedded in cement mortar. It can be formed into thin panels or sections, mostly less than 1 in. (25 mm) thick... Unlike conventional concrete, ferrocement reinforcement can be assembled into its final desired shape and the mortar... plastered directly in place without the use of a form."

"[T]he early work of Lambot... was one of the first applications of , but [was] also... a form of . His patent on wire-reinforced boats that was issued in 1847... This was the birth of reinforced concrete, but subsequent development differed from Lambot’s concept. The technology of the period could not accommodate the time and effort needed to make mesh of thousands of wires. Instead, large rods were used to make what is now called conventional reinforced concrete, and the concept of ferrocement was almost forgotten for 100 years."

"Portland cement is generally used, sometimes blended with a . The filler... is usually a well-graded sand capable of passing a 2.36 mm (No. 8) sieve. However, depending upon the... reinforcing material (mesh opening, distribution, etc.), a mortar containing some small-size gravel may be used. ...Addition of short and discrete fibers of different types favorably affects the control of cracking and the capacity... to resist tensile loads. ...[R]elatively short and slender (l/d = 100) steel fibers may be randomly distributed in hydraulic cement mortars... the overall effect being to increase tensile strength and improve the shear resistance..."

"Peter Venkman: Ray, for a moment, pretend that I don't know anything about metallurgy, engineering, or physics, and just tell me what the hell is going on."

"Say, any of you boys smithies? Or, if not smithies per se, were you otherwise trained in the metallurgic arts before straitened circumstances forced you into a life of aimless wanderin'?"

"The export of into Italy was strictly forbidden; but aluminium was almost the only metal that Italy produced in quantities beyond her own needs. The importation of scrap iron and into Italy was sternly vetoed in the name of public justice. But as the Italian metallurgical industry made but little use of them, and as steel billets and were not interfered with, Italy suffered no hindrance. Thus, the measures pressed with so great a parade were not real sanctions to paralyse the aggressor, but merely such half-hearted sanctions as the aggressor would tolerate, because in fact, though onerous, they stimulated Italian war spirit. The League of Nations, therefore, proceeded to the rescue of Abyssinia on the basis that nothing must be done to hamper the invading Italian armies. These facts were not known to the British public at the time of the election. They earnestly supported the policy of the sanctions, and believed that this was a sure way of bringing the Italian assault upon Abyssinia to an end."

"As the silversmith removes Impurities from silver So the wise man from himself One by one, little by little, again and again"

"Ramsey: At the Naval War College it was metallurgy and nuclear reactors, not 19th-century philosophy."

"Between the years 1942 and 1954, the obtained thousands of pages of technical information about the Manhattan Project. Sergei Leskov reports that this information included: calculations for the construction of the charge; calculations for the of ; information on detonation devices; information on the gaseous diffusion factory that produced U-235; information about a plutonium production report; a report on the study of secondary s; a report on the metallurgy of and plutonium; and information on the kinetics of atomic reactions. Such information would have been unfathomably important to the development of a bomb. Thus, energy could be focused along the successful lines of the American project rather than approaching the situation blindly and attacking all possible avenues. Kurchatov admitted in a memo of March 4, 1943, that certain information "came as a surprise to our physicists and chemists," such as the centrifugal method of isotope separation. The Soviets also had reached an impasse on the "problem of nuclear explosion and combustion." Stolen documents revealed that this problem could be rectified by mixing and together—a method the Soviet scientists thought was impossible. Moreover, the Soviets were provided with information on the “physical process” of the inner workings of the uranium bomb, which Kurchatov said "revised views on many problems," and, most importantly, told the Russians that an atomic bomb was a realistic possibility."

"For my financial interest in the greatest metallurgical concern in Germany, the United Steel Works, instead of being transferred to the Reich, has been seized by . Goering may have certain ideas in this connection. Indeed, a large share ownership in these steel works might save the Hermann Goering Works from bankruptcy."

"There are only two ores of tin: the peroxide, tin-stone, or Cassiterite; and tin pyrites, sulphide of tin, or Stannine: the former of which alone has been found in sufficient abundance for metallurgical purposes."

"While Paracelsus was pressing his doctrines on all sides, and endeavouring to lead chemistry into a new channel, another, Agricola, was quietly at work among the mines of Saxony, utterly indifferent to all but the advance of his science. It is to Agricola's systematic observations that we trace the beginnings of the science of mineralogy. In metallurgy, also, he was a pioneer, the first to give a clear and succinct account of the preparation of many metals. He taught the condensation and purification of sulphur given off during the roasting of many s, the separation of silver from gold by means of nitric and sulphuric acid, the preparation of such bodies as salt, , and saltpetre on a large scale. The apparatus described by Agricola and employed by him for the and testing of ores were still in use at the end of the eighteenth century. Agricola stands out solitary among the men of his time as one pursuing chemistry from pure love of the science; his work had no other aim than the increase of knowledge."

"Chemistry is not a primitive science, like geometry or astronomy; it is constructed from the debris of a previous scientific formation; a formation half chimerical and half positive, itself founded on the treasure slowly amassed by the practical discoveries of , medicine, industry, and domestic economy. It has to do with alchemy, which pretended to enrich its adepts by teaching them to manufacture gold and silver, to shield them from diseases by the preparation of the , and finally to obtain for them perfect felicity by identifying them with the soul of the world and the universal spirit."

"In the new College he occupied the Chair of Chemistry, and found a fresh field of work in organising the duties of the Chair, and planning and equipping the classrooms and laboratories which were essential for their performance. The Chemical Laboratories were built in 1884 and extended two years later, while in 1896-7 the Wilham Gossage Laboratory was opened and rooms were added for Metallurgy, Electro-Chemistry, and Gas Analysis. The whole forms one of the most perfect installations for the teaching of chemistry, which is to be found in this country."

"The Egyptians built an empire and ran it with a handful of technology... the wheel, irrigation canals, the loom, the calendar, pen & ink, some cutting tools, some simple metallurgy, and the plough, the invention that triggered it all off. And yet look how complex and sophisticated their civilisation was. And how soon it happened, after that first man-made harvest. The Egyptian plough and those of the few other civilisations sprang up around the world at the same time... Gave us control over nature... And at the same time, tied us for good, to the things that we invent so that tomorrow will be better than today. The Egyptians knew that. That's why they had gods. To make sure that their systems didn't fail."

"The only processes which can be called chemical, known to the civilized nations of antiquity, belonged to certain arts, such as metallurgy, dyeing, and the manufacture of glass or porcelain; but these processes appear to have been independent of each other, pursued in the workshop alone, and unconnected with general knowledge."

"Beccher, ...after having studied with minute attention, the operations of , and the phænomena of the kingdom, formed the bold idea of explaining the whole system of the earth by the mutual agency and changes of a few elements. And by supposing the existence of a vitrifiable, a metallic, and an inflammable earth, he attempted to account for the various productions of rocks, crystalline bodies, and metallic veins, assuming a continued interchange of principles between the atmosphere, the ocean, and the solid surface of the globe, and considering the operations of nature as all capable of being imitated by art."

"Medieval Islam was technologically advanced and open to innovation. It achieved far higher literacy rates than in contemporary Europe; it assimilated the legacy of classical Greek civilization to such a degree that many classical books are now known to us only through Arabic copies. It invented s, , sails and made major advances in metallurgy, mechanical and chemical engineering and methods. In the middle-ages, the flow of technology was overwhelmingly from Islam to Europe rather from Europe to Islam. Only after the 1500s did the net direction of flow begin to reverse.""

"The art of tempering and casting iron developed in India long before its known appearance in Europe; , for example, erected at Delhi (ca. 380 A.D.) an iron pillar that stands untarnished today after fifteen centuries; and the quality of metal, or manner of treatment, which has preserved it from rust or decay is still a mystery to modern metallurgical science. Before the European invasion the smelting of iron in small charcoal furnaces was one of the major industries of India. The Industrial Revolution taught Europe how to carry out these processes more cheaply on a larger scale, and the Indian industry died under the competition. Only in our own time are the rich mineral resources of India being again exploited and explored."

"All through our history, we have been changing the world with our technology. Our technology has been of two kinds, green and grey. Green technology is seeds and plants, gardens and vineyards and orchards, domesticated horses and cows and pigs, milk and cheese, leather and wool. Grey technology is and steel, spears and guns, and oil and ectricity, automobiles and airplanes and rockets, telephones and computers. Civilization began with green technology, with agriculture and animal-breeding, ten thousand years ago. Then, beginning about three thousand years ago, grey technology became dominant, with mining and metallurgy and machinery. For the last five hundred years, grey technology has been racing ahead and has given birth to the modern world of cities and factories and supermarkets. The dominance of grey technology is now coming to an end."

"There is a beautiful tale among the Australian aborigines which says that the bow and arrow were not man's invention, but an ancestor God turned himself into a bow and his wife became the bowstring, for she constantly has her hands around his neck, as the bowstring embraces the bow. So the couple came down to earth and appeared to a man, revealing themselves as bow and bowstring, and from that the man understood how to construct a bow. The bow ancestor and his wife then disappeared again into a hole in the earth. So man, like an ape, only copied, but did not invent, the bow and arrow. And so the smiths originally, or so it seems from Eliade's rather plausible argument, did not feel that they had invented metallurgy; rather, they learned how to transform metals on the basis of understanding how God made the world."

"At the present time administration is more an art than a science; in fact there are those who assert dogmatically that it can never be anything else. They draw no hope from the fact that metallurgy, for example, was completely an art several centuries before it became primarily a science and commenced its great forward strides after generations of intermittent advance and decline."

"Tradition has it that not only concerned himself with the unification of Egypt but also with the control of the river: to him is attributed the first damming of the Nile, the digging of dikes for agricultural purposes and indeed the first attempt to control and apportion the waters of the river. The wealth of Egypt was thus, with , based upon its agricultural output. However, unlike Mesopotamia, the Egyptians had on their doorstep a number of mineral resources that they were able to exploit with little effort, including copper ores, gold and a wide range of rocks suitable for building and the making of a wide variety of ornaments. [S]hortly before the year 3000 metallurgists made a discovery that was to transform the entire "industry." ...by mixing a small quantity of tin ore with the copper ores when... smelted... they discovered the alloy . The occurrence of tinstone... does not occur in the same type of deposit as do the ores of copper, but rather, [near] veins of gold. ...Thus tinstone ...may well have been noticed during washing for gold... finding that the little black lumps of ore were relatively heavy, presumably made various attempts at smelting them until they arrived empirically at a suitable alloy... [T]he effect is to reduce the melting point... they had a far more fluid metal that was much easier to cast. ...the quality of casting improved dramatically."

"Why would the oldest tree on earth be less than 4,400 years old (and still growing)? Why would the oldest coral reef on earth ( in Australia) be less than 4,400 years old? Why would the largest cave formations be dated at less than 4,400 years old? Why would the oldest records of capital punishment, farming, writing, husbandry, and metallurgy be less than 4,400 years old? Why would the oldest known civilizations be advanced and appear to have sprung up out of nowhere? It’s almost as if very intelligent people coming from a stock of people getting off Noah’s ark who already had knowledge of scores of things just moved into an area and developed a civilization in a short time. There is no evidence of "upward advancement from apelike creatures to hunter-gatherers," as books often teach. After the Flood it was sort of like a situation. The people were very smart, but it would take a while to rebuild civilization after a global flood. The first settlers coming off the ark would be in an automatic "Stone Age" because it’s faster to make stone tools than steel ones."

"The history of utopias is no less fascinating than the history of metallurgy or of chemical engineering."

"Indians living near the old Santa Clara Mission, about fifty miles from the present city of San Francisco... used to apply red and yellow pigments from the "Cave of the Red Earth" near there for personal adornment. In 1845 Captain Andres Castillero of the [, who had studied chemistry and metallurgy at the College of Mines in Mexico City, discovered near the Santa Clara Mission an in which he easily detected metallic mercury. When Don Manuel Herrera of that College of Mines analyzed specimens of this ore he found an average mercury content of 35.5 per cent and reported that some pieces were practically pure ."

"Mercury was known to the ancient Chinese and Hindus, and has been found in Egyptian tombs dating back to 1500 or 1600 B.C. Dioscorides mentioned its preparation from cinnabar, while Pliny gave a method of purifying it by squeezing it through leather, and stated that it is poisonous. Earle R. Caley has shown by quotations from Aristotle, Theophrastus, Dioscorides, Pliny the Elder, Vitruvius, and the Leyden Papyrus of the third century A.D. that mercury has been known much longer than most persons realize. He states that cinnabar was probably the only mercury compound known to the ancients and that they used it both as a pigment and as a source of the metal. In his "Metallurgic Chemistry," C. E. Gellert (1713-1795) stated that “The only ore of mercury hitherto known is native cinnabar". The most ancient specimen of quicksilver known is probably that which H. Schliemann found in a little cocoanut-shaped in an Egyptian tomb at Kurna dating from the fifteenth or sixteenth century B.C."

"In the history of war and society we single out three main innovations to describe significant changes before 1800: the introduction of metal, when humans abandoned stone weapons for ones made from bronze and iron; the domestication of the horse, which gave warriors greater mobility and speed; and the introduction of gunpowder, which transformed war on land and at sea. (Since other parts of the world, such as the Americas, did not have horses until the Europeans brought them in the sixteenth century and some parts of the world, such as Australia, never developed metal weapons, not all human societies have experienced change at the same time.) In each case, of course, many other things were happening both to technology and to society. Metal weapons were only a part of the story: societies had to develop the soldiers and the infrastructures to make use of them. Horses were more formidable when the wheel enabled them to pull chariots or later on when they could carry armed warriors. The introduction of gunpowder too was accompanied by other important developments: in metallurgy, for example, so that guns did not explode when they were fired, or in the design and navigation of ships, so that they could make use of the new cannon."

"Before the Industrial Revolution all techniques in use were supported by very narrow epistemic bases. That is to say, the people who invented them did not have much of a clue as to why and how they worked. The pre-1750 world produced, and produced well. It made many path-breaking inventions. But it was a world of engineering without mechanics, iron-making without metallurgy, farming without soil science, mining without geology, water-power without hydraulics, dye-making without organic chemistry, and medical practice without microbiology and immunology. The main point to keep in mind here is that such a lack of an epistemic base does not necessarily preclude the development of new techniques through trial and error and simple serendipity. But it makes the subsequent wave of micro-inventions that adapt and improve the technique and create the sustained productivity growth much slower and more costly. If one knows why some device works, it becomes easier to manipulate and debug it, to adapt to new uses and changing circumstances. Above all, one knows what will not work and thus reduce the costs of research and experimentation."

"In Alexandria two streams of knowledge met and fused together... The ancient Egyptian industrial arts of metallurgy, dyeing and glass-making... and... the philosophical speculations of ancient Greece, now tinged with ancient mysticism, and partly transformed into that curious fruit of the tree of knowledge which we call Gnosticism. ...the result was the "divine" or "sacred" art (...also means sulphur) of making gold of silver. ...during the first four centuries a considerable body of knowledge came into existence. The treatises written in Greek... in Alexandria, are the earliest known books on chemistry. ...The treatises also contain much of an allegorical nature... sometimes described as "obscure mysticism." ...the Neoplatonism which was especially studied in Alexandria... is not so negligible as has sometimes been supposed. ...The study of astrology was connected with that of chemistry in the form of an association of the metals with the planets on a supposed basis of "sympathy". This goes back to early Chaldean sources but was developed by the Neoplatonists."

"It was comparatively late in the metallurgical history of copper that was produced by knowingly adding tin to the metal."

"The swords made in India were prized all over the world. The sword of Tipu Sultan is almost a legend. These facts have rarely been mentioned or brought to the notice in the publications on history of metallurgy..."

"[T]he ancients... had a sort of practical or technical chemistry. In certain branches of metallurgy, in glass-making, dyeing, and tanning, they attained decided proficiency."