Technique : revue industrielle = industrial review, 1 décembre 1928, Décembre

[" Mig; SUNN J I I I I I 7 I J I I I I I IRI = g J pet \u2014\u2014\u2014 J \u201can D J = = = N= =, SE D ges A = el ad D = = i | G D it tle * rampe animes SRO P= ii a Sa www: EOE 5 Ecole Techmque \u2014 MONTREAL \u2014 Technical School d 0 ell, = pas VoL.III MONTREAL No 10 SU tre Lon sf Cm TECHNIQUE mi 4 REVUE INDUSTRIELLE Li SITES INDUSTRIAL Visa ; (rd REVIEW te 0 = = © 5 ans h à or 3e l} = Ours q = D = D = y DECEMBRE + DECEMBER = MCMXXVIII Ne S al JE AE VE AE AE JE VAE SE VE A A AE AA A VE EE EE A EVE VE J I I I ZA J J J JI J { Na di Ee ! MN | X 7 ir NHN i aN N VAN D TN NNN DN DIINO, WINNT 5 PROVINCE DE QUEBEC, SECRETARIAT DE LA PROVINCE Ecole des Beaux Arts de Montréal 628, rue Saint-Urbain, près Sherbrooke (ouest) Directeur: CHARLES MAILLARD 2 a ena ÉTUDE D'UN ÉLÈVF DU COURS D'ART DÉCORATIF ENSEIGNEMENT GRATUIT L'école est ouverte aux jeunes gens et aux jeunes filles, avec ateliers séparés sauf pour les cours oraux, ainsi que pour les cours d'architecture et de composition décorative, où cependant les sections sont divisées.L\u2019Enseignement comprend : ARCHITECTURE, PEINTURE, SCULPTURE, ART DECORATIF .Architecture:\u2014Formation d'architectes diplômés (5 ans d'études) de dessinateurs pour entrepreneurs industriels, etc.Architecture pratique (cours du soir).Dessin et Peinture d\u2019Art, Aquarelle.Statuaire.Art Décoratif dans toutes ses applications (théorie et réalisations.) a) Adaptation architecturale, comprenant une section de sculpture ornementale et une section de peinture décorative.; ; b) Adaptation aux métiers; étude des différentes techniques\u2014bois, métaux, céramique, verre, etc.Cours Oraux et Spéciaux:\u2014Sciences appliquées à l\u2019architecture; perspective; anatomie artistique; histoire de l\u2019art.Formation de professeurs de Dessin à Vue, diplômés après 4 ans d'études.LES COURS ONT LIEU DU 1\u201c OCTOBRE A FIN MAI L'inscription des élèves commence le 15 septembre 1] PQ ELECTRICITY Montreal Technical School 200 SHERBROOKE STREET WEST Founded by the Government of the Province of Quebec Subsidized by the Provincial Government and the City of Montreal Prepares young men for positions in industrial life as experts, foremen, etc.DAY CLASSES 1.\u2014Regular three year Technical Course for boys and young men who have completed at least one year in a regular high school or its equivalent.2 \u2014Trades\u2019 School Course for boys and young men who have not the necessary preparation to follow Course No.1.3.\u2014Printing Course for young men who have completed one year of a regular high school course and who are at least 16 years of age.4.\u2014 Automobile Short Term Course (9 weeks) for young men who wish to learn the care and repair of the automobile.Applicants must be at least 18 years of age.EVENING CLASSES 5.\u2014All Trades and Technical Subjects.Ask for a Prospectus For further information, apply to Montreal Technical School Note: Regarding Courses 1 and 2 for worthy cases, pupils whose family conditions warrant the same, may receive a remission in part or in full of the fees required for these courses.Encouragez nos annonceurs SHAWINIGAN TECHNICAL INSTITUTE FOUNDED 1912 By Mr.J.E.ALDRED, President of Shawinigan Water & Power Co.INSTRUCTION IN FRENCH AND ENGLISH COURSE INCLUDES THE FOLLOWING SUBJECTS: Arithmetic, Algebra, Geometry, plane and solid, Trigonometry, Slide rule practice, Physics, Electricity, Chemistry, English, French, Drafting, Woodshop practice, Machine shop practice, Oxy-Acetylene Welding, and Automobile repairing.FOR FURTHER INFORMATION APPLY TO C.N.CRUTCHFIELD, Principal Automobile Salesman: \u2018\u201cThis controls the emergency brake.It is put to use very quickly in case of emergency.\u2019\u2019 Sweet Young Thing: \u201cI see; something like a | kimono.\u201d 1 Tourist: \u2018\u201cIs the water at this hotel pure?\u201d Guest: \u201cNot very.We frequently find traces of coffee and other substances in it.\u201d\u2019 LIMITED Genuine auto electrical GOODHUE parts for all makes of automobiles BELTING Quality, Service | \u201cEXTRA\u201d \u201c STANDARD\" \u201cACME\u201d A.E.L.\u201c WATERPROOF\" Storage Batteries 3475 PARK AVENUE J.L.GOODHUE & CO., Limited Montreal, Que.DANVILLE - QUE.Patronize our advertisers | I Ve [I t i Wabasso Prints \u201cLovely As Nature\u2019s Tints\u201d Recognizing the trend of the times, the Wabasso Cotton Company, Limited, has placed on the market a new line comprising WABASSO PRINTS.These include Wabas- so Printed Broadcloths, Wabasso Printed Shirtings, Wabasso Printed Dress Goods and Wabasso Printed Silks for lingerie and dresses.The very latest type of machinery has been installed for this purpose; and the range of Prints is unsurpassed for smartness, novel and attractive patterns and colourings.The Wabasso Cotton Company, Limited Three Rivers, Que.Makers of the famous Wabasso Cottons\u2014the best Cotton Fabrics Canada can produce; also Wabasso Silks\u2014pretty as the rainbow\u2014and made from Wabasso Combed Yarns and Rainbow Silks.Pour paraitre prochainement Dictionnaire Larousse Complet Edition Canadienne (303° Edition) avec Nouveau supplément canadien Nouvelle édition revue corrigée et considera- blement augmentée.ENNE : | CE\" IE = MN LIBRAIRIE BEAUCHEMIN LIMITÉE MONTREAL : .Le seul dictionnaire x | Dictionnaire ; : francais Renfermant les noms SSE i L arousse approuvé par le les plus nouveaux de la ir: ê Conseil de langue française.: Complet 3 l\u2019Instruction Publique TH SOND) de la Enrichie d'un nouveau supplément canadien Province de Québec revue et mis à jour.eee En vente chez tous les libraires Encouragez nos annonceurs 1 M pa 5 Os I: i Wi 73 RE fil ne, LL A I « L'ÉCOLE CHEZ SOI\u201d A tous ceux qui ne peuvent suivre ses cours du jour et du soir L Ecole des Hautes Etudes Commerciales de Montréal (Affiliée à l\u2019Université ) OFFRE SES Cours par Correspondance Comptables, employés de banque ou autres salariés du commerce, de l\u2019industrie et de la finance qui désirez améliorer votre sort, augmentez votre compétence professionnelle en suivant ces cours! Prospectus et renseignements sur demande Détachez ce coupon Ecole des Hautes Etudes Commerciales de Montréal, Coin Viger et St-Hubert, Montréal.Adressez-moi par retour du courrier voire brochure \u201cL'ECOLE CHEZ-SOI\" que je pourrai garder sans aucune obligation de ma part de SUIVTE VOS COUTS.[ ] Comptabilité [ ] Langue anglaise [ ] L\u2019anglais commercial [ ] Economie politique [ ] Le frangais commercial [ ] Le droit commercial Occupation Patronize our advertisers Ecole Polytechnique de Montréal FONDÉE EN 1873 Travaux Publics Industrie Toutes les Branches du Génie.PRINCIPAUX COURS D\u2019APPLICATION: Electricité Mécanique Chimie industrielle Machines Dessin Hydraulique Machines thermiques Métallurgie Chemins de fer Arpentage Mines Constructions civiles Béton Travaux publics Génie sanitaire Ponts L\u2019Ecole Polytechnique forme des ingénieurs susceptibles de diriger les grandes entreprises industrielles et les travaux publics.Laboratoire Provincial des Mines Laboratoire de Recherches et d\u2019Essais.1430, rue Saint-Denis - Montréal PROSPECTUS SUR DEMANDE Encouragez nos annonceurs J se iB 1 } Les Pompes Fairbanks-Morse avee coussinets a billes Nos nouveaux bulletins expliquent pourquoi ces pompes sont d\u2019un rendement de cing a dix pour cent plus élevé que les autres.Les pompes avec coussinets à billes sont fabriquées en trois modèles et en toutes grandeurs.Permettez à nos ingénieurs de discuter leurs avantages avec vous.Nous pouvons aussi fournir la force motrice \u2014 les moteurs Fairbanks-Morse avec coussinets, à billes et moteurs Diesel.Nous pouvons ainsi étudier intelligemment tous vos problèmes de pompage et contrôler tous les éléments qui rentrent dans la construction d\u2019une unité complète \u2014 la pompe et la force motrice.Ceci veut dire une responsabilité non divisée.\u201cJhe CANADIAN Ball-Bearing Motors The life of a motor is the life of its insulation.Hard brittle insulation, especially if oil soaked, sends motors to the repair shop or to the scrap pile.Fairbanks-Morse motors have insulation that will not harden and crack.Fairbanks - Morse ball bearing motors require greasing only once a year and eliminate oil soaked wind- ings, oil spotted products, oil slop on the floor and the cost of oil and oiling.Fairbanks-Morse motors have a liberal overload capacity and are now made in \u2018fully enclosed\u201d and \u201cventilated\u201d types, which can operate safely in the foulest acid fumes and in extremely damp and dirty places.Fairbanks-Morse COMPANY-Limited SL John - Quebec-Montreat-Ottawa - Toronto-Windsor-Winnipeg- Resina - Calgary-Väncouver -Viclona THE MAKERS OF FAIRBANKS SCALES AND VALVES vi Patronize our advertisers A\\N pt Ll M rl fer Di pédecté Ridactt 98 Distt! bE Ridact Directe _\u2014 Dee Fim oni \\ TECHNIQUE REVUE INDUSTRIELLE Paraît mensuelle - - excepté juillet et août Le Numéro - - - - - - - .10 Abonnement: Canada - - - = par année, $1.00 Etranger - - - - par année, 1.50 Publiée sous le patronage de L\u2019HON.ATHANASE DAVID et sous la direction de AUGUSTIN FRIGON Directeur Général de l\u2019Enseignement Technique dans la Province de Québec Rédacteur en chef\u2014Section française: GUSTAVE-H.CINQ-MARS Rédacteur en chef \u2014Section anglaise - IAN McLEISH Directeur de publicité - - - JEAN-M.GAUVREAU Trésorier - - - - - - - - LOUIS LARIN Région de Québec: Rédacteur - - - - - - - = Directeur de Publicité - - - .- A.-V.DUMAS - H TALBOT * Published monthly INDUSTRIAL REVIEW - except July and August One copy - - 0-0 == .10 Subscription: Canada - - - - = Other Countries - - - per annum, $1.00 per annum, 1.50 Published under the patronage of HON.ATHANASE DAVID and under the direction of AUGUSTIN FRIGON General Director of Technical Education in the Province of Quebec Chief Editor\u2014English Section - - Chief Editor\u2014French Section: GUSTAVE H.CINQ-MARS - JEAN M.GAUVREAU - IAN McLEISH Publicity Director - - - Treasurer - - - - - - - .LOUIS LARIN Quebec District Editor - - - .A V.DUMAS Publicity Director - - - - - - .H.TALBOT Adresser toute correspondance: 200, rue Sherbrooke Ouest, Montréal TECHNIQUE Address all correspondence to: 200 Sherbrooke St.West, Montreal Decembre, 1928 EDITORIAL STAIR BUILDING LE CALCUL GRAPHIQUE À L'USINE THE DRAMA OF THE LINOTYPE\u2014 PART II NOTIONS ÉLÉMENTAIRES DE MÉCANIQUE SPECIAL DEVICES USED IN CONJUNCTION WITH MACHINE-TOOLS LES PRINCIPALES NOTIONS DE LA GÉOMÉTRIE SOMMAIRE \u2014 SUMMARY December, 1928 PAGE E.Morgentaler 3 Alex.Bailey 7 .Edward Mott Woolley 11 Jules Hallé 16 G.Berthiaume 21 .Paul Cadotte 24 ELEMENTARY ALGEBRA FOR BEGINNERS WITH SOME PRACTICAL APPLICATIONS .GRADUATES\u2019 PAGE .Imprimé par la Section d' Imprimerie Ecole Technique de Montréal George Stevenson 32 36 Printed by the Printing Section Montreal Technical School >, 5 [1 8 vr mmm Et ne TRAVAUX D'ÉLÈVES FORGERONS ET SOUDEURS Ecole Technique de Québec Fondée par le Gouvernement Provincial.Subventionnée conjointement par le Gouvernement Provincial et la Cité de Québec.185, Boulevard Langelier SECTIONS FRANÇAISES ET ANGLAISES .ENGLISH AND FRENCH SECTIONS I.COURS REGULIERS (a) COURS TECHNIQUES dont la durée est de trois années.Ces cours sont organisés en vue des examens à subir pour obtenir le diplôme d'Etudes techniques du gouvernement provincial.Rétribution : $1.50 par mois en 1re année ; des bourses sont accordées aux élèves méritants en 2e et 3e années.II.COURS Ces cours peuvent commencer en tout temps de l\u2019année scolaire ; ils sont organisés en vue de permettre des études spéciales dans un des (à) COURS DES METIERS destinés à ceux qui sont incapables de s'assimiler toute la théorie que comporte le cours technique, mais qui sont quand même désireux de bénéficier d'un stage d\u2019une couple d'années à l'Ecole Technique.SPÉCIAUX métiers enseignés à l'Ecole Technique : (mécanique, forge, fonderie, menuiserie, modèlerie.) III.COURS D\u2019AUTOMOBILE Cours abrégé de mécanique d'automobile durant trois mois et se répétant trois fois durant l\u2019année scolaire.IV.COURS DU SOIR Comprenant de nombreux cours libres: Mathématiques, Dessin Industriel, Electri- cité, Mécanique d\u2019Ajustage, Mécanique d\u2019Automobile, Forge, Trempe, Soudure autogène, Menuiserie, Charpente, Modèlerie, Fonderie, Plomberie et Chauffage, Chauffeur et Ingénieur stationnaire, Maréchalerie, Pose de la Brique.Prospectus et Renseignements additionnels sur demande viii Patronize our advertisers hy mn A Tr \u201cen | dr Su i Bil à us i 7 TECHNIQUE REVUE INDUSTRIELLE \u2014 INDUSTRIAL REVIEW Vou.III DECEMBRE \u2014 DECEMBER N° 10 EDITORIAL ITHIN comparatively recent years, \\ \\ there has come into vogue in the educational field, a new system of teaching, which for want of a better term we will refer to as \u201cBook Training\u201d as distinguished from the old style or \u2018\u2018Demonstration by the Teacher\u2019.The former style of training, we believe, originated in the United States, where the book publishers, true to their commercial instincts, are seeking by all means to push the sale of text books of various kinds.In a discussion of the merits of the two different forms of training, naturally each side can bring arguments to bear in tavour of his own side of the question, and there is no doubt but that both forms have their advantages and disadvantages, a conclusion quite general in all matters of discussion.The proponents of the \u201cBook Training\u201d system claim that with the old system there is a danger of \u2018\u201c\u201cSpoon-feeding\u2019\u2019 the student; in other words, there is a great tendency for the teacher to do all the thinking, while all the student has to do is to sit tight and take it in.We admit this possibility.We will not admit, however, that a slavish adherence to the other form of training will be productive ot much better results, because in this instance it is the teacher who sits tight and simply watches the student as he sucks in his own knowledge, 1f he can.We will admit that the \u2018book\u2019 method training is far easier tor the teacher, but carried to its ultimate conclusion, why go to school at all?Why not correspondence schools for everyone?It would save tremendous expense in teaching staffs, school buildings and equipment.Like most other propositions of its kind, experience proves that while very beautiful in theory, it falls down in practice,%if carried to extremes.The writer can remember in his own student days, being given a certain model to sketch, with the object of making a workshop drawing therefrom.He never really did know what was expected of him for the instructor seemed to think that all he was there for was to sit at his desk and watch the students work.A little hint here and there on the part of the teacher may open up vistas to the pupil which he might otherwise never realize it left to his own devices, and before a boy can be left to himself to worry out his own problems, he must first of all be trained to think and this is where the teacher comes in.No book can adequately teach a student how to think, except in perhaps exceptional cases.At the Montreal Technical School neither of these methods is used exclusively, but rather a combination of both.That is, a student is first shown how to reason things out for himself and then is given a chance by the \u201cbook\u201d method to see if he is capable of working alone.But to assume that the average student can work all alone without any help on the part of his instructor is contrary to all experience and absolutely erroneous.The teacher should be available at all times to help the student over difficult passages.A NOS LECTEURS OICI l\u2019approche des fêtes et nous en \\ profitons pour offrir à nos lecteurs, nos souhaits de paix, de santé, et de prospérité pour l\u2019année qui va bientôt commencer.TECHNIQUE entre déjà dans sa quatrième année.Quatre ans, c\u2019est l'âge encore tendre où l\u2019enfant commence à extérioriser les connaissances qu\u2019il a acquises depuis son apparition en ce monde; déjà il rend des services, il fait de petites commissions, et pour cela il s\u2019expose à des dangers, des chutes, des maladies.S'il est bien constitué, s\u2019il a de bons parents qui en prennent bien soin, il traversera tout cela triomphalement.En sera-t-il ainsi de TECHNIQUE, passera-t-elle à travers les différentes épreuves qui l\u2019assaillent.La réponse dépend de nos lecteurs, de l'attachement qu\u2019ils ont pour leur revue, du zèle qu'ils déploient à accroître son champ d'action en la faisant connaître à leur entourage, en [1] Décembre TECHNIQUE December engageant leurs amis ou compagnons de travail à s\u2019y abonner.S\u2019abonner et faire abonner les autres, voilà le mot d\u2019ordre de cette année pour nos lecteurs.TECHNIQUE est composée et imprimée pour eux, pour leur seul bénéfice, qui est l'instruction, et non pas pour le profit des collaborateurs de la revue, car tout cela est fait gratuitement.Les techniciens se doivent donc de soutenir par tous les moyens cette œuvre importante Pour nous, nous offrons notre dévouement dans la mesure de nos forces et du temps dont nous disposons, et nos lecteurs peuvent Être assurés que nous aussi avons un mot d'ordre qui est: progrès.To our Readers On the approach of the festive season, we desire to express our appreciation of the kind cooperation we have received from all sides towards the making of TEcH- NIQUE a success.We wish to thank our advertisers and our readers, as well as those who, by contributing articles, have enabled us to produce a review which seems to fill a long- felt need in this Province.To each and every one then, without exception, who have taken the least interest in our magazine, we wish a Merry Christmas and we trust that for them the coming year will be a very happy one indeed.Five Kinds of \u201cSand\u201d There are five different materials used as abrasives in the manufacture of abrasive papers and cloths.First of all comes flint, the crushed quartz or \u2018\u2018sand\u2019\u2019 with which most individuals are acquainted, and from which the common term \u2018\u2018sandpaper\u2019 is derived.Then there is garnet, the precious gem of the jeweler, which is used in this business in its impure, mined state.The upper reaches of the Hudson River Valley in the Adirondacks produce the best American grades; another variety is imported from Spain.It is much in demand as an industrial abrasive in woodworking and furniture factories.Emery is a third material, used principally in the metal trades.Turkey supplies the best grades, with Greece and America supplementing the supply.Emery is being rapidly supplanted by an artificial abrasive, aluminum oxide, which is sold under the names of \u2018garalun\u2019\u201d and \u201c\u2018alundum.\u201d It is obtained by fusing bauxite clay, the ore of aluminum, in an electric furnace, then crushing and grading the resulting crystals.This abrasive is employed in working on metals of high tensile strength.The fifth abrasive is silicon carbide, another artificial abrasive obtained by high-temperature fusing of sand (silicon) and charcoal (carbon) in an electric furnace.It is used principally on leather, and on metals of low tensile strength.Don\u2019t Stay in a Rut Two business women were talking, and when I say that they were employed in offices on an important railway I give away no secret.They were both ambitious, I should judge, and yet, there they stood, yawning.\u201cI'm tired to death,\u201d one said, of everything.\u201cSo am I,\u201d the other added, \u201cbut I'm just lazy, I think.Stay that way all the time.Never feel like reading, or studying, or working.I hate everybody.Don\u2019t know what is the matter.\u201d They are in a rut, that is the answer to their problem.And if they are not careful the rut will grow deeper and it will become more difficult for them to escape.Inertia has dragged them there, and nobody in its relentless grip amounts to much no matter what their natural abilities may be.I should advise that they turn sharply and get some decided interest in life, especially in their work, or they will end in overwhelming failure.It is easy to tell when the rut is engulfing us, and it isn\u2019t a matter of years, either.It is a matter of inner awareness, so L.D.Stearns says.It is not necessary for us to leave our home, our work, our office, or wherever we happen to be, and roam to far distant places, in order to get out of our rut.We must just swing to higher ground.We can learn how.Let us do something occasionally that takes downright grit and moral will-force to achieve, something that makes us shut our teeth hard and say, \u201cI will.\u201d Let us learn every day something new, something outside of our own particular line, as well as something especially to do with our job, no matter how well informed we are.À book that will teach us rather than amuse us, let us read.Let us do something kind, a lift of some sort given to some one where we know it is needed, but that we do not have to give.There are so many ways in which we can grow.There are unknown, mighty powers of growth waiting to be unlocked in every life, if we but find the key.And let us remember always, that \u201cOut of the heart are the issues of life.\" Let us look outward, over our own individual | problems for a few moments each day.Let us note the beauties of other lives and of other places, and | if restless we come to our jobs, let us consider the opportunities for growth and still more growth surely there for us, if we have the grit to avail | ourselves of them.If we do this, we will mount, before we know it, toward the skies, and our jobs will give us outlet for our ambitions.THE FACE THAT MEN FORGET Two faces were close together, the hardware | salesman\u2019s, grim and tense; the other face was smal and white, with two slender hands pressed tightly against it.It was those frail hands that riveted } the man\u2019s horrified gaze.\u201cHeavens!\u201d he said, still staring; and his voice was tragic, for that other face was the face of his watch, and those little hands told him that he had missed the last train home.IN YE OLDEN TIMES It was back in medieval times.\u201cIt\u2019s no fun trying to live in this coat of mail,\" complained a cootie.\u201cNo,\u2019\u2019 agreed the second parasite.\u2018Heaven help a fellow on a knight like this.\u201d [2] Tw We shall fee: a new, vibrant force | sweeping into our veins when this is accomplished.| i) \" Î si vir; Te lo en, Zh Décembre TECHNIQUE December : Wg.e e .os Stair Building = de Fe By E.MORGENTALER \u201cie Instructor in Building Construction, Montreal Technical School.Sa 08 fy Part II Sie, oh N the September, 1927, issue of TECH- as possible of a uniform width on an estab- he NIQUE, a study of the planning and lished \u201cline of travel\u201d which is approxi- ul balancing of circular stairs was pre- matly 14\u201d io 18\u201d from the front stringer 2 sented to the reader.We are reproducing as shown in Fig.1.\u201cmg here in Fig.1, the plan of the stairs shown In making a plan of the stairs, the first oh as Fig.5 in that number, and will explain thing to be determined is the wall lines a how to lay out the stringers.A B C D.Next, the width of the body of 8, 5 I 8- 0\" = latte \u2014 > \u201cour AE at B C C 2 | - 26% 20 20 \u2014\u201d 262 15 waLe sgRINGER || : 9 3 1 cincud 0 ni af > bé p ser lo\u201d y 2 ped \\ Cine OF TRAVEL ' È | | - 2 7 | D f J A LadoinG STEP Le \u2014+-_\u2014 _ - \u2014\u2014 \u2014 H \u2014- OSITION OF THE ELOOR HEADER Fic.1\u2014Plan of a Stair It is important in planning winding stairs of various forms, and this example will serve for all, to make the treads as nearly the stairs from the wall to the front stringer.The width of the hall in this staircase Décembre TECHNIQUE December is 8-0\" between rough walls and 3'-6\u201d the width of the stairs with 12\" diameter of cylinder.The line of travel is drawn in position as before mentioned; the starting or first, and top of landing riser lines are now drawn as required.Between the starting and landing risers, on the line of travel, equal spaces are marked for the width and number of treads required.Next the treads in the cylinder and along the line of the front string are marked as shown and explained in the September issue of TECHNIQUE.The lines for the risers are now drawn from the points of division on the cylinder and front string through the points of division on the line of travel.This completes the plan.The plan should be drawn to as large a scale possible.An important point, in framing the staircase opening in the floor, is the head room.It is not necessary to set up an elevation of a staircase to determine this.The head room may be found, as well as the length of the well hole, by estimating how many risers down from the top, after subtracting the depth of tioorbeam, flooring and plaster, would equal in height seven feet or as close to seven feet as possible.The stair shown in Fig.1 is a continuous one, each flight being superimposed.The FIGURE 2 floor header should be placed as shown in dotted lines.LAYING OUT THE FRONT STRINGER AND CYLINDER The distance G H on the front stringer (Fig.2) must equal altogether the depth of timber, thickness of plaster and thick- § ness of riser.The cylinder is spliced to the stringers on the lines O P and (R S).The treads as given in the cylinder and stringers agree with the plan Fig.1.The depth of the cylinder is found as shown by describing arcs of a radius equal to G H trom the angles of tread and rise as shown at (U V).It is better to join the cylinder as at R on the straight line R S even if it has 2\u201d or 3\u2019 more depth at that point than G H.Cylinders are sometimes, particularly in the best work, laid out with the straight string in one plank as here shown, and the whole of that portion for forming the cylinder up to the line (O P) and (RS) is cut away at the back leaving only a thin veneer at the face, which is bent over a convex cylinder and filled out with staves, as shown in Figures 7, 9, and 10.WALL STRINGER Fig.3 shows the starting portion marked A B on the plan (Fig.1).In preparing F FLOOR FIGURE y Too FIGURE 4 idl fis § cons the s is be ma Ie - tie marke] gi | Décembre TECHNIQUE December | this stringer to join the floor base, the curve (S L) eases off the angle of stringer to the level of the base.The stringer may be mitred to the base | as at Y O, R Y being equal to V S.The | height of stringer M N above the angle step must be the same as the step M N \u2018& on the next stringer (Fig.4) also the stringer : connecting these angles may be brought to a level by curving as shown or it may be left angular.They must in all cases be | brought to a level, so that the base mould- | ings will connect properly.The wall stringer B C Fig 1 is shown in | detail in Fig.4.The height of the stringer ; at O P must be the same as the angle step | at O.P.in Fig.5.The wall stringer C D i 1s shown in Fig.5.A good way to lay out winder stringers | from a scale drawing is to set up to a scale | of 114\"\"=1\"-0\"\" an elevation of treads and | risers as shown in Fig.6 and draw a line | touching the outermost points of the lower edge of the stringer as at (X E O) then with F a bevel set to the angle O S, a stringer may be laid out full size whose points X and E will touch the edge of the plank.Begin laying out with the line O S and make U S | as many inches full size as it measures on the scale.CONSTRUCTION OF CYLINDER Different methods of bending cylinders are practised.In Fig.7 is shown the construction of a circular form over which the saw kerfed material as above explained is bent in position.E F G is the plank rib FIGURE 7 .(made of 3 pieces) of which 2 or more are required according to the work to be done.H represents the staves which are nailed to the ribs and so complete the circular form.The wood is removed from the back of the stuff as at XXX etc., leaving the thickness of a veneer at the face after bending.The grooves XXX are filled with tightly fitted strips of wood (glued in) called keys as at SSS.It greatly adds to the strength of this bent keyed work to glue on three strips of veneer, one at each edge of the keyed stuff and one in the middle.The glue should be perfectly dry before the work is removed from the form.The spaces between the keys may be determined by the following method: To find the correct distance between saw kerfs for any required radius of curvature, select a piece of stuff of suitable length and equal to the thickness of the material to be bent (see Fig.8) let A B equal the thickness of stuff and A C the radius of the ey THIS dustance is equal kb D.C FIGURE.8 required curve; make a saw kerf at B O leaving a thin veneer A O uncut, nail the cut piece at S K and move 1t from C to D or just enough to close the saw kerf at B; then C D being the distance moved will also be the exact space between each saw kerf.The same thickness of veneer À O must be maintained and the same saw used throughout.| A method of bending a veneer facing and filling out the thickness with staves is shown in Fig.9.The wood is removed FIGURE 9 Décembre TECHNIQUE December wholly from the back of the stuff between the points required, leaving a veneer facing which is bent over the form and then staves ZZ Z are fitted and glued on, as shown in drawing.The laminated work method is shown in Fig.10.Bending several thicknesses of veneer together is defined as laminated work.The whole of the veneer required should be heated and bent over the form together and secured in place; then releasing and applying glue to one half, put it back in position again, and proceed with the other half in the same way, pressing and binding solidly the whole together and to the surface of the form.To ascertain what thickness of white pine will bear bending without injury to its elasticity, multiply the radius of curvature in feet by the decimal .05 and the product will be the thickness in inches.For Mours SUILT To VENEER THE CURVED SYRIMGER FIGURE 11 example, multiply a 2 feet radius of curvature by the decimal given and you obtain 20\" X .05=.10 equals one tenth of an in.thickness.This wou!d bend without fracture.The construction of an ordinary form for bending stair stringer is shown in Fig.11 where the correct position of a stair stringer bent in position is indicated.The § ribs of this form are quarter circle and are set parallel to each other.A method used where a strong stringer is required, is shown in Fig.12.This drawing shows the plan, elevation and rabattement of a stringer on a quarter turn.The construction is as follows: THICKHE// OF THE PLANK / DEPTH OF THE J GER FIGURE.12 A B C D represents the plan of cylinder string.The plan is divided into three equal segments by lines radiating from center 0 and passing through the points k 1 and m n.These points of intersection should always F coincide with the riser lines, as shown in plan in Fig.1.Join A D and from B A, 3.4.5.6.7.D.9 the projections of the points of equal division on the horizontal line A D project vertical lines to intersect horizontal lines from M N O P which are separated by a distance equal to the height of a riser in each case.(Continued on page 20) [6] pie i qu fon ie and uct | la dy ' fon Up I SEE ET Décembre TECHNIQUE December Le Calcul Graphique à l\u2019Usine Par ALEX.BAILEY Professeur à l'Ecole Technique de Montréal \u201cSavoir c\u2019est pouvoir\u201d est un vieil adage qui ne cesse d'être vrai.Mais sa justification exige plus que la connaissance superficielle d\u2019un fait, l\u2019observation des circonstances qui l\u2019entourent, voire même la déduction des causes immédiates, médiates ou premières qui peuvent l\u2019engendrer.Il faut encore, et surtout, le moyen d\u2019apprécier la justesse des observations et analyses que comporte l'étude détaillée de ce fait: à cette seule condition, le savoir devient une réelle philosophie des choses, une source vraiment féconde de réalisation même matérielle.L'ouvrier est-il toujours entrainé à la solution de ce problème?A cette question nous répondrons que l\u2019écueil qui se dresse presque constamment sur sa route est son inaptitude à saisir cette philosophie des choses, conséquence du défaut de concentration, et de sa répugnance plutôt proverbiale pour l'étude des sciences exactes qui lui semblent quelque peu austères et stériles.Cependant il lui est impérieux de faire large la part de la méditation, celle de la lecture appropriée et d\u2019une étude parfois théorique, abstraite\u2026 Car, ne l\u2019oublions pas, ce n\u2019est qu\u2019au prix de tels efforts qu\u2019il développera en lui cette curiosité scientifique qui n\u2019est autre que le ferment des grandes énergies industrielles.Ainsi, l'assimilation des principes basiques des mathématiques élémentaires (arithmétique, algèbre, géométrie, trigonométrie) et la manipulation facile du mécanisme des formules fondamentales qui en dérivent seront, de tout temps, choses indispensables au praticien qui escompte le succès.Plus encore, nous sommes d\u2019avis\u2014 et c\u2019est là une opinion passée à l\u2019état de lieu commun\u2014que la faculté de contrôler, de titrer l'exactitude dans l'emploi de ces mémes formules ainsi que celle des résultats obtenus en application, constitue une autre assise très importante dans l\u2019édification de son éducation technique.Or la science moderne, aidée du dessin, a conçue une méthode permettant de substituer la simple lecture par l\u2019échelle d\u2019un \u201cLa vraie règle de bien juger est de ne juger que lorsqu\u2019on voit clair\u201d\u2019.\u2014 Bossuet.système d\u2019abaques à l'élaboration des calculs numériques: c\u2019est là le principe essentiel de la nomograpme, communément appelée calcul graphique.Cette nouvelle science d'application, nonobstant le vif intérêt qu\u2019elle provoque, ne saurait ralentir la culture des.mathématiques théoriques; elle deviendra plutôt, pour ces dernières, un appoint de vérification tout particulièrement précieux durant la période pleine d\u2019incertitudes et d\u2019hésitations des études primaires.C\u2019est surtout en cela qu\u2019elle intéresse directement l\u2019apprenti soucieux de son avenir, ainsi que l\u2019ouvrier chez qui une connaissance mal coordonnée ou insuffisante des données mathématiques fondamentales entrave le progrès.Loin de nous proposer de couvrir entièrement le champ actuel de cette science toute moderne, nous voulons simplement indiquer en substance certains procédés dont elles dispose pour la vérification de la plupart des calculs de l'usine, et dont nous donnerons un bref exposé sous forme de problèmes gradués, mentionnant au passage les possibilités d'applications.PROBLÈME 1.Obérer graphiquement l\u2019addition de deux quantités données \u201ca et \u201cD\u201d Solution: (Voir Fig.I).a L 4 C 0 __ Ê | X Fig re A une échelle convenablement choisie portons, bout a bout, et dans une méme direction arbitraire \u201cO X\u2019\u2019 les deux segments rectilignes qui correspondent aux quantités \u2018\u2019a\u2019\u2019 et \u2018b\u2019\u2019: la longueur totale résultante \u2018\u201cO C\u2019\u2019, évaluée à la même échelle, donnera le résultat cherché.Le même procédé servira aussi à établir la somme de plusieurs quantités entières, fractionnaires, décimales.PROBLÈME II.Opérer graphiquement la def frence de deux quantités données \u2018\u201cc\u2019\u2019 et Solution: (Voir Fig.IT).[7] Décembre Sur une direction arbitrairement choisie \u201cOX\u201d portons\u2014à une même échelle con- venable\u2014l\u2019une des quantités données \u2018\u2018c\u2019 : id Ia > , ce ,, suivant \u201cOA\u201d, puis l'autre \u2018\u201cd\u2019\u2019\u201d en sens inverse suivant \u2018AB\u2019: le segment différentiel résultant \u2018OB\u2019\u2019, évalué à la même Cc A B| d 1 X Fig.\u2018I: échelle, résoudra le problème.L'utilité de ce procédé graphique devient plus évidente surtout dans le cas des nombres complexes décimaux ou fractionnaires.PROBLÈME ITIa.Opérer graphiquement le produit de deux quantités données.Nous donnerons aux diverses solutions de ce problème la facture d\u2019une proportion simple X B A 1 nous basant sur le fait que la mesure d'une grandeur résulte de sa comparaison avec une autre prise pour unité, ce qui entraîne que l'inconnue cherchée est une quatrième proportionnelle à trois quantités données \u201cA\u201d, \u201cB\u201d, et l'unité.Solution 1: Soient \u2018\u201ce\u2019\u201d et \u201c\u2018f\u2019 (Voir Fig.IIT), les quantités données.A une échelle - convenablement A choisie, tragons p i NR l\u2019unité et la lon- 7 AN gueur \u2018\u2018e\u2019\u2019 A pari EN tir d'un même e Fig II.> point \u201c0\u201d et en J LS recouvrement = ~7\" l\u2019une de l\u2019autre, puis la longueur \u201cf\u201d à l'extrémité de l\u2019unité et perpendiculaire à cette dernière.Une parallèle à \u201cf'\u2019 issue de \u2018s\u2019 rencontrera \u201cO R\u2019\u201d\u2019 prolongée en \u201cPF, Deux triangles rectangles semblables \u201cOPR\u2019et OS\u201d seront ainsi déterminés, donnant la relation \u2014] ba \u2014I d\u2019où xX1 = eXf.x\u201d évaluée à l'échelle usitée correspondra donc au produit cherché.Solution 2: Soient \u2018\u201cg\u2019\u2019 et \u2018\u201ch\u2019\u2019 les nombres donnés (voir Fig.IV).Ayant choisi l'unité de longueur traçons les segments rectilignes représentatifs de TECHNIQUE [8] December ce.» l'unité, de \u2018\u2018g\u2019\u2019 (ces deux derniers en recouvrement l\u2019un de l\u2019autre) et de \u201ch\u201d (la position de ce dernier ne sera près avoir élevé une perpendiculaire \u201cp R\u2019 à \u201cOS\u201d), tels que l'indique la graphique ci-contre, puis complétons les triangles rectangles semblables \u201cO S T\u201d\u2019 et OP R\u2019\u201d\u2019 qui donnent la proportion i x_8 h 1 d\u2019où xX1= gxh cr Ici encore, \u2018x\u2019\u2019 mesurée à la même échelle établira le produit demandé.Contrairement au cas de la solution \u2018\u2018l\u2019\u201d\u2019 qui est toujours réalisab'e, ce procédé-ci ne sera possible qu\u2019à la condition h> 1.Soluhon 3: Soient \u2018\u2018j\u201d et \u2018k\u2019\u2019 les quantités imposées (voir Fig.V).J / Q 4%\u2019; d= mp Xx 2 Une fois l\u2019échelle choisie, traçons les segments linéaires correspondant aux nombres \u2018\u201c1\u2019\u2019, \u2018\u201cj\u2019\u2019 (ces deux derniers en recouvrement l\u2019un de l\u2019autre) et \u2018Kk,\u2019 dans des directions arbitraires convenables, tels que représentés, et complétons les deux triangles semblables quelconques \u201cO S T\u201d et \u201cO P R\u201d\u2019 qui fournissent la relation x_} k 1 d\u2019où xX1=kX1 \u2018x\u2019 donnera encore, à la même échelle, le produit cherché.Solution 4: Soient \u2018\u201cm\u2019\u2019et \u2018\u2018n\u2019\u2019 les nombres donnés (voir Fig.VI).L'échelle étant déterminée traçons, bout à bout, les segments recti- iignes \u201cOS\u201d et \u201cOP\u201d représentatifs des nombres \u201cm\u2019 et \u2018\u201cn\u2019\u2019, puis \u201cO R\u2019\u2019 correspondant à I'unité et dans une direction appropriée.Si l\u2019on décrit ensuite la circonférence de déterminée qu'\u2019a- y { utr aren pint qe sles liq Décembre cercle qui passe par les trois points \u2018\u2018P\u201d \u201cR\u2019\u201d\u2019 et \u201cS\u201d, on aura alors deux cordes \u201cPS\u201d et \u201cR T\u201d qui se coupent en donnant la relation d\u2019où Le segment \u2018\u2018x\u2019\u2019 évalué à l\u2019échelle, correspondra au produit cherché.Solution 5: Soient \u2018\u201cp\u201d et \u2018\u201cq\u2019 les quantités considérées (voir Fig.VIT).Choisissons une échelle convenable, et à partir d'un même point \u2018\u201c\u201cO\u201d\u2019 traçons le segment rectiligne unitaire \u2018\u201cO P\u201d\u2019, puis \u201cOR\u201d et \u201cOT\u201d\u2019repré- : sentatifs des nombres et en recouvrement l\u2019un de l\u2019autre.Si, maintenant, on décrit une circonférence de cercle passant par les trois points \u201cP\u201d\u2019, \u201cR\u201d\u2019 et \u201cT\u201d\u2019, on se rappellera que les deux sécantes \u201cO T\u201d et \u201cO S\u201d issues du même point \u2018O\u2019 fournissent l\u2019équation d\u2019où x X Le segment rectiligne \u2018x\u2019 mesuré à l\u2019échelle correspondra donc au produit demandé.Les divers procédés employés dans la solution du problème IIIa, sont fort commodes pour le calcul de circonférences, de surfaces simples ou encore dans .a vérification du partage parfois complexe de certaines quantités.PROLÈME IIb: Opérer graphiquement un produit de plusieurs facteurs.En d\u2019autres termes, i' s\u2019agit ici de généraliser \u2018e problème IITa.Deux solutions sont fort en usage.Solution 1: Soient \u2018\u2018r\u2019\u2019, \u2018\u2018s\u201d, \u201ct\u201d, \u201cu\u201d, \u201cv\" et \u2018\u201cW\u2019 les facteurs donnés tels que l\u2019on doit avoir x=rXsXtXuXvXw A une échelle convenablement choisie (voir Fig.8), on porte, à partir d\u2019un même point \u201cO\u201d et en recouvrement l\u2019un de l\u2019autre, les segments \u201cO R\u201d et \u201cO P\u201d représentatifs des nombres \u2018\u2018r\u2019\u201d et \u201817, puis on trace en \u201cP\u201d\u2019 une perpendiculaire à \u201cO R\u201d.Enfin traçons à partir de \u201cO\u201d comme centre, avec une ouverture de com- x pas \u201cO M\u2019 représentative de \u2018\u2018s\u201d\u2019 à l'échelle TECHNIQUE December choisie, un arc de cercle qui donnera le point \u201cM\".La droite \u201cO M\u2019 prolongée et la perpendiculaire \u201cR N\u201d à \u201cO R\u201d détermineront, par leur intersection, deux triangles rectangles \u201cO R N\u201d et \u201cOP M\u201d semblables qui permettront d'écrire les rapports égaux d\u2019où S1 maintenant on imagine que \u201cON =x\"\", tourne autour de \u2018O\u2019 comme charnière pour se coucher en \u2018\u201cO S\u2019\u2019, une construction semblable à la première (en y faisant intervenir la valeur \u2018\u2018t\u2019\u2019) donnera X2 Xr t 1 d\u2019où x,X1= x Xt=rXsXt.Par une série de constructions géométriques semblables, découlant toutes les unes des autres, on pourra faire les déductions suivantes : X3 \u2014 Xa u 1 d\u2019où x; X1=x,Xu=rXsXtXu; v 1 d\u2019où X,X1=x,Xv=rXsXtXuXv; d\u2019où X,X1=x,Xw=rXsX1Xu xXvXw.Solution 2: Soient \u2018a\u2019, \u201cb\u201d, \u201cc\u2019\u2019 et \u2018\u201cd\u201d\u2019 les facteurs que l\u2019on considère tels que l\u2019on veut avoir x=aXbXcXd (Voir Fig.IX).[9] Décembre TECHNIQUE December | spot ee Choisissons une échelle convenable et, à partir d\u2019un même point \u2018\u201cO\u201d, traçons en direction arbitraire mais appropriée les segments \u2018\u201cO P\u201d et \u201cO S\u201d\u2019 représentatifs de l'unité et du facteur \u2018a\u2019 (en recouvrement l\u2019un de l\u2019autre), ainsi que le segment \u201cO R\u2019' correspondant au facteur \u2018\u2018b\u201d\u2019, puis complétons les triangles semblables quelconques \u201cO PR\u201d et \u201cOST\u201d qui établiront la proportion.\u201ca b 1 d\u2019où x, X1=aXb.Alors on couchera OT=x, en \u201cO U\u2019, et comme dans le cas de la solution \u2018\u201c1\u201d\u2019 une série de constructions semblables subséquentes nous permettront d'écrire X2 Xi e 1 d\u2019où X, X1=x,Xc=aXbXc; X; _X2 d 1 d\u2019où x; X1=x,Xd=aXbXcXd.Les procédés en usage dans les solutions du problème IITb sont de ces plus utiles pou la vérification des surfaces plutôt complexes (surtout dans le cas du cercle et de l\u2019ellipse), des volumes, et de tout autre calcul impliquant l'élaboration du produit de plusieurs facteurs entiers, décimaux, fractionnaires, etc.PROBLÈME IV : Opérer graphiquement le quotient de deux nombres donnés.Tout comme dans le cas de la multiplication on fera appel au principe des proportions interprêtant comme comparaison à une unité choisie la mesure d\u2019une grandeur considérée.L'inconnue cherchée sera, ici de même, une quatrième proportionnelle à [10] la relation y x_ À 1 B Trois solutions principales sont en usage.Solution 1: Solent \u2018a\u2019 et \u2018b\u201d\u2019 les quantités dont on veut établir graphiquement | le quotient (voir Fig.\u201cX\").0 Choisissons une échel- # le convenable et traçons, J a partir d'un même / point \u201c0\u201d en recouvre- segments \u2018\u201cOS\u201d\u2019 et \u201cOP\u201d représentatifs des nombres donnés puis le segment unitaire \u201cP Fig x a I= section avec \u2018S T\u201d\u2019 parallèle à deux triangles rectangles semblables \u2018\u2018OPR\u201d et \u201cOS T\u201d\u2019 nous permettront d\u2019écrire x a 1 b c\u2019est-à-dire que le segment \u2018x\u2019\u2019 mesuré à | l\u2019échelle établira le quotient cherché.Solution 2: Soient \u201cc\u2019\u201d\u2019 et \u2018\u2018d\u2019\u2019 les nombres à diviser graphiquement l\u2019un par l\u2019autre M (voir Fig.XI).L'échelle étant # choisie, opérons com- | me dans le cas pré- > présentatifs de \u2018\u201cc\u2019\u2019 et de \u201cd\u201d en \u201cO S\u201d et \u201cO P\u201d\u2019.L'intersection de cette dernière avec un arc de circonférence décrit de \u2018\u201cO B\u2019 comme centre et comme noyau permettra de compléter deux triangles rectangles semblables \u2018O P R\u201d et OS T\u201d qui donnent l'égalité de rapports.Le segment \u2018x\u2019 évalué à l'échelle, correspondra au quotient demandé.Solution 3: Soient \u2018\u2018e\u2019\u2019 \u2018f\u2019\u2019 les quantités e\u2019et imposées dont on veut établir graphiquement P e 5 c= © Cf (Voir Fig.XII).A une échelle convenable traçons, à (Suite à la page 31) trois quantités connues, et s\u2019obtiendra par | ment l\u2019un de l'autre, les | R\u2019 i perpendiculaire 3 O P.|§ Si l\u2019on prolonge \u201c\u201cO R\u201d\u2019 jusqu'à son inter- \u201cP R\u201d les a cédent a partir d'un § point \u2018\u201cO\u2019 pour cou- # cher les segments re- Sry ~_ li i SF Décembre hy I | 8 lg ig, | | Ù ji fi > Même | .Je ke : Ep 5 Roms Lt \u201cPA 008 hs gr au UMR Ï TECHNIQUE December The Drama of the Linotype Part II By Epwarp MOTT WooLLEY (Reprinted from the American Printer) dreams of many a man into money.If the average yearly output of all the 55,000 Linotypes were set by hand, and the compositors\u2019 arms could be attached to automatic recording devices,amost amazing chart would result.If extended in a tangent, the line would go straight to the sun, To Linotype has, indeed, turned the } and would curve around that fiery body and come back to earth.Or, to emphasize the point in another way, you could follow that line on more than two hundred round trips to the moon.If you could gather all the Linotypes and put them side by side, you would have the most amazing printing office one could imagine, reaching more than sixty-two miles.If all of them together were put at work some morning on book composition they could flood the market by night with nearly 6,000 books.If you imagine Linotype machines doing acrobatic stunts, these 55,000 would make a column seventy miles high.The Linotype holds within itself unknown possibilities for speed.No operator ever yet found its limit in a race against time, for, no matter how fast the operator worked, the machine was always ahead.Many extraordinary records have been established.One brilliant operator set 16,000 ems in an hour, which in plain English means about 5,500 words, or over two newspaper columns of six-point type.Another operator on a run of eight hours averaged 12,151 ems an hour.Ordinarily the average Linotype operator sets from six to seven times as much matter as a hand compositor, or from 5,000 to 7,000 ems per hour.Daily records have been made, however, in excess of this amount.In a year the usual Linotype operator composes a column of type 8,600 feet long.The hand compositor will average perhaps 800 ems an hour.In the old-fashioned way the hand printer will distribute somewhere around 5,000 ems an hour, but the Linotype automativally distributes more than 16,000 ems in sixty minutes\u2014and rarely, if ever, makes a mistake.Time is the essence of success in these modern days.The printer, as well as the merchant and manufacturer, must realize this and seek to get as many turnovers as possible.The trend of the times is toward speed and the conservation of labor, material, and space.The tactics of past years will not keep a printing shop going now.The Linotype has made possible the very existence of thousands of printing plants.The shop with a Linotype gets the job through while the shop of obsolete methods is getting ready.Quick service to customers is the first consideration of business- building, and by increasing the number of sales the Linotype enables a shop to increase its earnings.Then, too, the Linotype enables the printer to meet unusual demands.He need not say to customers, \u201cI can\u2019t do the job.\u201d Yet when the Linotype was first put on the market it brought consternation to compositors.Naturally, they looked on it as a device to take away their living.Instead, it has immensely raised the plane of the printer.The old days of the journeyman typesetter, with his perennial quest for work, are gone.The Linotype instead of being his enemy is his best friend.It has led him up out of primitive things, and from scanty and irregular income, into what is perhaps the highest plane of labor today.The Linotype operator is in the limelight of artisanship.In brains and distinction he ranks with every other skilful worker.He is the intermediary between creative human brains and the Linotype-\u2014which, figuratively, is the brainy aristocrat of machines.There are now 70,000 Linotype operators and machinists in the United States, and with the owners you have an army of 80,000 men.Their product goes into practically every home in the land, no matter whether English is spoken or some other language.The Linotype serves all printers alike, big and little.In the composing rooms of the great dailies you find long batteries of these machines, and more than 6,000 printing shops in the United States alone have only one Linotype apiece.Hundreds [11] le ee ere ee Le il ni Décembre TECHNIQUE December of hand-composing shops change to the Linotype every year.No matter whether a shop does everyday commercial printing or produces the most artistic and difficult work, the Linotype does it.Whether the printer sets ordinary reading matter or advertising, he is served by this machine\u2014so nearly human.It has taken possession of many an advertising department, where its range is from 5 to 60-point type.Headline setting, and getting ads out on time, are now functions of the many-sided Linotype.The early inventors never contemplated such fields for it.Recently the use of these machines enabled a shop to take four men from the ad room and place them in other departments of the composing room.Twelve tons of metal were released and 500 cases of type discarded, along with six type-racks.The space occupied was reduced one-half, and two men in a night were able to handle all the display for 210 columns of advertising.All along the line this machine eliminates time and sidetracks disaster.For one thing, Linotype matter is never considered.One night the first page of a New York daily was pied on its way to the stereo- typers, but in thirty-one minutes it was restored.Not a single reader suffered a delay in getting his paper.And the composing room devil who caused the accident was forgiven.In the old days his career in that particular shop would have been ended.With the Linotype always printing from new slugs, make-ready is reduced almost beyond belief, and for the proofreader it dispenses with many time-honored hieroglyphics of the craft.It is impossible to get a letter upside down, and a wrong font seldom gets past the font-distinguisher.In other directions, too, the Linotype has been the inspiration that has given the world scores of inventions for machines in the printing line.But the company has followed a policy not to use ideas until satisfactory arrangements are made with the inventors.It constantly calls for suggestions, and Linotype operators, machinists, and others are invited to submit ideas for improvements.There is no department in any of the mechanical trades that is of such ultimate importance to the buyer as that of engineering and research.There is hardly a concern in the country that devotes so much time, spends so much money, and gives such a large proportion of its floor space and its supervision for experimental and development work.In this way there is being worked out a constant succession of practical improvements that effect operating advantages and reduce the cost |: of the Linotype'\u2019s product.And the company aims to contrive these improvements in such a way that they may be used on older models.In this service it stands unique.Although Linotype-users may charge off a theoretical ten per cent.every year for depreciation, their machines may be in use fifteen or twenty years\u2014because of innate stability and the use of these attachable improvements.In 1892 a large eastern newspaper installed a battery of Linotypes which rendered continuous service, three shifts daily, for twenty-four years.In the office, and in countless other establishments, the Linotype is known as the machine that lasts.The Linotype has worked into every form of composition, including dictionaries, encyclopedias, catalogues, directories, editions de luxe, books, magazines, and tabular work of intricate kinds.In versatility it À amazes us.In some shops you find Linotypes working patiently and correctly on great freight-rate sheets with so many columns of figures that your head swims; or you find a Linotype composing a comparative summary of costs\u2014drawing the lines, filling in the totals, and doing the whole job with infinite neatness.Nor does it balk at statistical charts that } look like the skyline of a great city.In election time it works on ballots, and here you find the same expert results.In many printing offices in summer you see Linotypes rapidly working out the baseball scores, and accommodating themselves gracefully to the unplayed innings.The more you look into the adaptability of this machine, the greater does your admiration become.With the aid of over 1,500 different faces it accepts without § protest almost any special job.It works mathematical, algebrical, geometrical, and trigonometrical problems, using all the} technical characters.You can make it do almost any sort of work that calls for unusual commercial characters, piece fractions, logotypes, Roman numerals, box rules, or reference marks of wide variety.It handles tariff, medical, ecclesiastical, [12] Sète i ; ear yg a lng achat = Castor otrrag 8 thre j \u201ché stabs su J ie Inne Te ed Lah tly i 1 Lin eetiy I À sv 2 4 COM ing ing fh arte fhe ary.ln xd hen [1 mam æ Lino seh see peli # You of veg thous ork aa dt ai ru A frat gs, 08 arf | Décembre | astronomical, TECHNIQUE December and similar composition.Originally the Linotype's range of cha- | racters was limited to ninety, but printers ef.speedily demanded more.From decrying : the machine they began to grasp its possi- ~ bilities.Then came the two-letter matrices, with 180 characters.By this time the I printer's imagination was aroused, and the 4 company evolved the two-magazine machine, bringing into use 560 characters.But still the printer was unsatisfied, and : the company continued to measure up to the quickening market.It became possible to use 540 characters, and then 720, and today in the modern newspaper shop the text, heads, and advertisements may be set on the Linotype without changing the magazines.As a linguist the Linotype has an astonishing capacity, for it speaks fifty languages.If you know how, you may converse with it in all the modern tongues of Europe, in Albanian, Arabic, Armenian, Burmese, Hebrew, Icelandic, Roumanian, Ruthenian, Servian, Slavic, Esperanto, Welsh, Bulgarian Estrangela, Nestorian, Jacobite, Portuguese, and so on.You would scarcely expect to see Linotypes a thousand miles up the Amazon, almost on the equator, yet you will find twelve machines there, and some of them have been in operation for years\u2014in a climate extraodinarily damp and trying.There are Linotypes, too, 1,100 miles up the Paraguay River from Buenos Aires; and in the mountains of Peru, more than 20,000 feet above the sea, Linotypes have been working faithfully through a series of years\u2014in a wonderfully rarefied atmosphere.These abnormal climates are a severe test, indeed, and if the machines can be used successfully in such countries\u2014 and far from supply stations\u2014they can be used anywhere.In Brazil, Columbia, Bolivia, Chile, Venezuela, and British Guiana you find batteries of them; and elsewhere in South America.At the time this is written there are more than 2,000 Linotypes on the South American continent.There are several hundred in Central America, Mexico and the West Indies.All across Siberia, withstanding the arctic cold, there is a string of them, and some are 6,000 miles from an agency or supply warehouse.Yet these machines run every day without inconvenience or delay, just as the Linotypes do in the cities of the United States or of England; and in various parts [13] of the world such instances are repeated.Durability and simplicity of operation make these things possible.Two Linotypes at Reykjavik, Iceland, are used daily in setting the newspaper \u201cLogrjetta.\u201d Finland uses them also.In Honolulu, Linotypes have been used more than twenty years.In 1910 in Alaska there were only nine men setting type\u2014 all by hand; today a score or more of newspapers in Alaska depend wholly on the Linotype.In the Fiji Islands you will find them, too; and in the Philippines more than forty are operated.South Africa, Australia, and all those far countries have the Linotypes on every-day duty.In Tokyo the Japan \u2018Advertiser\u2019 is published in English, and the composition is done on Linotype machines by Japanese printers who do not know our language.They simply follow copy, and set about a galley an hour.Almost anywhere you go the Linotype has gone ahead.If you could open the door of a certain printing office in Rangoon, India, the click of three machines, operated by natives and talking the language of the country, would greet you.You would hear the same cheerful sound, too, in Singapore Calcutta, Bombay, and Allahabad, the latter in the heart of India.One Linotype job, for instance, was to speak three languages at once, which it did in setting an English, Turkish and Armenian dictionary.The Linotype is strong on diplomacy and court life.Long ago it secured its credentials to the inmost circles of almost every capital in the world.You will find it in the government printing offices in Washington, London, Ottawa, Rome, Madrid, Lisbon, Prague, The Hague, Athens, Sofiia, Calcutta, Rio de Janeiro, Santiago, Quito, Lima, Guatemala, Montevideo, Bogota, Pretoria, Tokyo, Manila, City of Mexico, Havana, Melbourne, Wellington, and Sydney.Nor do I attempt to give the full list.Then the Linotype is used in state printing offices in every state of the Union.The lingual abilities of the Linotype are many and curious.It is often necessary in printing shops to set up foreign-language composition not in line with their regular practice, and supplementary keyboards are placed on top of the ordinary ones.Thus Russian, for example, can be set on an English-speaking Linotype. Décembre TECHNIQUE December Just a little more of its ancient history.If there had never been a typewriter, there never would have been a Linotype.It was when the writing machine came along and began to be talked about, somewhere around 1876, that those five shorthand writers in Congress\u2014Moore, Warburton, Clephane, Murphy, and Devine\u2014were immensely interested.Their calling was a strenuous one.Each of the five would work perhaps an hour in the laborious longhand transcription.One of these men\u2014it is usually attributed to Moore, though Clephane also claimed it \u2014conceived the idea of doing away altogether with the intermediate transcription and of inventing a machine that would set type direct from the notes.It was Moore, however, who really began to experiment, and among them the five contributed a few dollars a week out of their salaries\u2014which ran around thirty dollars a week from the government.A little shop was established in Washington.The primitive printing machine of Moore looked something like a typewriter.It had a cylinder bearing the characters, which were printed in lithographic ink on a strip of paper which was afterwards cut into lengths, arranged in the form of a page, and justified by cutting between the words and separating them.A transfer was then made to a lithographic stone, from which the print was made.In this queer device, nevertheless, those shorthand men saw, even if vaguely, immense possibilities.The time was ripe, and they knew it, for a revolution in printing procedures.Many of these first machines were built and used in Washington and New York.At the beginning the promotors thought they saw an immense fortune in the immediate future, but so many mechanical difficulties were encountered that they looked around for an expert to improve the device.They applied to a man named Hahl, in Baltimore, who was a maker of instruments of precision, such as chronometers.Hahl had no time for the work, but suggested his cousin, Ottmar Mergenthaler, who was a watchmaker.He was hired at five dollars a day and went to work in Hahl\u2019s shop, little dreaming that he was starting out on an enterprise destined to revolutionize the whole art of printing.Mergenthaler, putting his very life into the work, speedily exhausted the small fund available, and fresh means had to be provided.The same thing was repeated over and over for years.If the investors could have foreseen all this they might never have undertaken it.Yet the fight, with all its heartbreaking disappointments, was alluring.They stayed in because Mer- genthaler was always on the verge of some new and greater invention.Yet Mergenthaler himself was completely discouraged at one stage of the enterprise.He abandoned all experiments and severed his connection with the embryo machine, declaring that the strain of bearing the blame was wearing him out.Clephane, however, and perhaps some of the others, refused to quit.The machine on which Mergenthaler had been working was removed from the Hahl shop in Baltimore to a little experimental place in Washington where for several years Clephane and his associates continued to attempt its development.Meanwhile Mergenthaler, finding himself quite unable to let it alone, took up the problem on his own account in Baltimore, and finally produced important improvements.Then he returned to his former connections.It was about this time that the factory was established in better quarters in Washington, and additional capital secured.In this brief outline no attempt is made to record events in their close sequence.The machine finally developed into one which indented the characters on a strip of paper-mache, which was cut up and justified in lines on a flat surface and then used for casting the type in metal.From this machine were evolved others, all part of an evolution that resulted in the brass matrix.This was hailed with delight by the company, which by this time comprised many stockholders.In the new machine each matrix dropped in response to a touch of the keys.It looked as if success had been reached, and the company went out after more money to build machines.This was a difficult job, but another one loomed even bigger\u2014how to persuade the shop owners and printers to use this invention.In the newspaper field the traditions were centuries old.Not since the days of Gutenberg had any real change been made in the method of setting type.In the face of all opposition and incredulity, a number of newspaper owners determined to make a trial.The leaders of this group were Whitelaw Reid, of the New York [14] ph rd of tne Décembre TECHNIQUE December Tribune; Melville E.Stone, and Victor F.Lawson, both of the Chicago Daily News; Ti A ® Walter N.Haldeman, of the Louisville PB Courier-Journal; Henry Smith, of the Chi- § cago Inter-Ocean; W.H.Rand, of Rand, 8 McNally & Company, Chicago; and Stilson Hutchins, of the Washington Post.To Whitelaw Reid belongs the credit of inventing the name \u2018Linotype\u2019, and of using the machine first for regular newspaper composition.His selection of the name was a dramatic contribution to the literature and nomenclature of industry.But this so-called Blower machine was so imperfect that it fell far short of its mission.Two hundred of these machines were built, but the bulk of them could not be sold.Discouragement settled over the group of backers, and the project was all but abandoned.Then out of the gloom Mergenthaler and his co-workers produced a new Linotype.Itshowed such advantages that more capital was secured and the machine was adopted perforce.In time the older machines in use were replaced.This was the dividing line between ancient and modern Linotype History.In 1890 the factory was moved to Brooklyn, where a little building now forming a tiny part of the present plant was rented, and in 1891 Philip T.Dodge became president of the company, which post he has continuously held.But no sooner was a real composing machine attained than other inventors remembered they had been thinking along the same lines, and so began a fight to maintain the Linotype rights\u2014well earned through these years of expense, work, and worry.The stockholders groaned under the burden of assessments, and many years elapsed before the company really did get over the top.From the beginning of the enterprise in Washington more than two million dollars was spent in perfecting the Linotype and building the organization before any of the stockholders got a dollar of profit.To set type by machinery seems to have been a peculiarly baffling problem for inventors, for at least $50,000,000 has been lost in this country alone in unsuccessful attempts to develop such machines.Mark Twain was one famous loser in such an enterprise.He dropped all his fortune into it.But perhaps if he hadn't met with such misfortune the world would never have known some of his best books\u2014written to pay off his debts and get on his feet [1 ) again.Itis said that the company in which he was interested built two machines that cost a million dollars apiece and proved unavailing.Success is an elusive thing, hard to lay hold of, and it was not attained by the Mer- genthaler Linotype Company until the value of the Linotype to the printer and the publisher and the public had become irresistible.And today the Linotype and the corporation back of it maintain their present relations to the printing and publishing interest of the entire world only because they represent the idealism of all business\u2014the maximum of service.Get a Hobby Every one, no matter what his job is, should have some hobby.It is one of the best things in the world for both mental and physical health unless it is allowed to grow to such proportions that it rides us instead of our riding it.Most of us feel that we have to use about all the time and strength we have in getting a living, but there is practically no one who cannot find time during the week for some other type of work for change and relaxation.To me there is nothing so enjoyable as gardening.I well realize that there are many to whom the growing of flowers or good vegetables seem like an awful chore, but healthful hobbies are not confined to digging in the dirt.A little while ago an important official who has spent his life since early boyhood in railroading, beginning at a time when a day\u2019s work was often 16 hours long, said \u201cIf only I had learned to do something else once in a while, if it had been no more than to chase butterflies, I would be a great deal happier.I have spent every waking hour on my job, and now that I have caved and cannot do this, I have nothing to turn to which interests me in the slightest.\u201d All of us are going to get old and slow up if we live long enough.Unless we have some hobby, which we enjoy\u2014be it postage stamps, butterflies radio or garden\u2014we are apt to find ourselves very much at a loss for a really enjoyable occupation.Wholly apart from the happiness which some hobby will bring to us, there is the underlying sound medical basis for its development.We shall live longer and happier and do our work more efficiently if we, for a time every week, turn our minds or our muscles into some other channel than that in which they run while we are chasing the elusive dollar.It will help get the cobwebs out of the brain, lower the blood pressure and improve the disposition.Therefore, I strongly prescribe that, while you are well and before you have to, you develop a healthy hobby, even if it is nothing more than \u2018chasing butterflies.\u201d\u201d Start today! DISCONTENT There are two kinds of discontent in this world: the discontent that works, and the discontent that wrings its hands.The first gets what it wants, and the second loses what it has.There's no cure for the first but success; and there\u2019s no cure at all for the second.\u2014Gordon Graham.| Décembre TECHNIQUE December 5 ° ° ° (1) site \u2019 Notions élémentaires de Mécanique = Par JuLEs HALLE qu Professeur à l'Ecole Technique de Québec sos a He = iH H sn i + i | 4: i i: 3 ! ORAS ov: FORCES PRINCIPE DE L\u2019INERTIE.\u2014 L'inertie est la propriété qu\u2019ont les corps de ne pouvoir d\u2019eux-mémes 1° passer de l'état de repos à l\u2019état de mouvement, 2° modifier leur état de mouvement.La première partie du principe est confirmée par l'observation directe; la 2ème partie peut se comprendre en observant par exemple qu\u2019une bille lancée horizontalement conserve son mouvement d\u2019autant plus longtemps que la surface de roulement est polie et que ce mouvement continuerait sans modifications s\u2019il était possible de supprimer complètement les aspérités de la bille et du chemin de roulement ainsi que la résistance de l'air qui sont les causes de la diminution de vitesse et de l'arrêt final de la bille.Forces.\u2014 Les forces sont des causes capables de modifier l\u2019état de repos ou de mouvement des corps.On appelle généralement force motrice, celle qui favorise ou tend à favoriser le mouvement d'un corps et force résistante celle qui s'oppose ou tend à s'opposer à son mouvement.Ainsi pour une automobile montant une côte, la force motrice sera fournir par le moteur, et les forces résistantes par les frottements des organes de la machine, la résistance au roulement, la résistance de l'air et la pesanteur du véhicule.En mécanique, une force est complètement définie par sa direction, son sens, son intensité et son point d'application.La direction est la ligne droite que suivrait le corps si, partant du repos, il cédait à la force.Le point d'application est le point matériel où la force est directement appliquée.Le sens qui se représente par une flèche indique sur la ligne de direction, lequel des deux chemins prendrait le point d\u2019application s\u2019il cédait à la force.L'intensité est la grandeur de la force lorsqu'on la compare à une autre prise pour unité.L'unité généralement adoptée est la livre, et pour mesurer directement l'inten- (1) Pour le commencement de cet article voir le numéro d\u2019octobre, page 13.sité d\u2019une force on se sert d'instruments appelés dynamomètres.Ceux-ci sont basés sur l'élasticité des lames métalliques et le plus simple est le peson qui peut être à lame ou à hélice.Peson a lame: 11 se compose d\u2019une lame d\u2019acier recourbée en forme de V (voir fig.1) L\u2019extrémité C est suspendue à un point fixe À par l'intermédiaire de la tige en arc À C; l\u2019extrémité D est reliée au crochet B par l'intermédiaire de la tige B D.B Fig.1\u2014Peson à lame.On suspend au crochet B des poids de 1, 2, 3.4 livres, pour une charge donnée la lame subit une certaine déformation et pour graduer le peson, il suffit de marquer sur la branche B D en face d'un repére O sur la branche A C, des divisions correspondant aux charges.Peson à hélice: (voir fig.2): Ce peson se compose d\u2019un ressort hélicoïdal maintenu par une rondelle À à l'extrémité d\u2019une tige B.Le ressort est enfermé dans une enveloppe cylindrique C portant un crochet D.Des poids variables étant accrochés en D, le ressort s\u2019aplatit d\u2019autant plus que les poids sont plus grands, et il suffit de repérer sur la tige les déformations correspondant à des charges connues.Dans les deux systèmes de peson, les mêmes charges produisant les mêmes déformations, il suffira de lire directement [16] for Ten le \u201ctemp fr Décembre TECHNIQUE December sur les graduations pour connaître l\u2019intensité des forces agissant sur les crochets.Les deux appareils ont le défaut, à l'usage, de donner des indications inexactes par suite de l'altération de l\u2019élasticité des ressorts.REPRÉSENTATION GRAPHIQUE.\u2014 Une force est représentée graphiquement (fig.3) par un segment de droite terminé d\u2019une part par un point À représentant le point d'application et par une pointe de flèche B indiquant le sens.&- La longueur AB est portée ?proportionnellement à une échelle choisie arbitrairement; par exemple à une échelle de 1\u201d pour 100 livres, une force d\u2019une intensité de 200 livres sera représentée par une longueur de 2\u201d.COMPOSITION ET DECOMPOSITION DES FORCES.\u2014 On constate par expérience que lorsqu\u2019un corps est soumis à plusieurs forces et par conséquent sollicité à se mouvoir dans plusieurs directions, il ne se déplace que dans une seule direction et on conçoit que l\u2019on pourrait obtenir ce déplacement au moyen d\u2019une seule force.rg, Cette force unique qui peut remplacer les autres forces (composantes) prend le nom de résultante.V7 EAN \u2014 AU \\ D Fig.2\u2014Peson a hélice.A 25 ECHELLE DES Forces 4% = 400 LBS.Fig.3\u2014Force de 200 1bs.Echelle des forces 1\u2019 00 lbs.7 Déterminer la résultante de plusieurs forces est composer ces forces.Inversement une force unique peut être remplacée par plusieurs autres produisant le même effet, et déterminer ces forces s'appelle décomposer une force en plusieurs autres.Plusieurs forces agissant sur un corps peuvent être dans le même plan ou dans des plans différents; dans cette étude élémentaire on n\u2019envisagera que des forces situées dans le même plan, et celles-ci peuvent être: 1° De même direction.2° Concourantes.5° Parallèles.FORCES DE MÊME DIRECTION.\u2014 Des forces de même direction peuvent être de même sens ou de sens contraire.Lorsque des forces sont de même direction et de même sens, leur résultante est égale à leur somme.Ainsi plusieurs enfants tirant sur la même corde avec des forces respectivement égales à 25, 35 et 40 lbs peuvent être remplacés par un homme tirant avec une force e 25+35+40 = 100 livres Si deux forces de même direction agissent en sens contraire leur résultante est égale à leur différence et son sens est celui de la plus grande force.D'une manière générale on peut conclure que: La résultante de plusieurs forces agissant dans deux sens opposés sur un même corps est égale à la différence entre la somme des Jorces agissant dans un sens et la somme des forces agissant dans l'autre et que son sens est celui de la plus grande somme.Si deux forces agissant en sens contraire sont égales, leur résultante est nulle et ces deux forces se font équilibre.On voit donc que lorsqu'une force agit sur un corps sans modifier son état de repos il y a équilibre entre deux forces: l\u2019une d'elles est la force agissante, l\u2019autre est une force égale et directement opposée qui est appelée la réaction.Ainsi, lorsqu\u2019un corps pesant est posé sur une table, la table réagit avec une force d'intensité égale au poids du corps; lorsqu\u2019on tire un objet avec une corde, cet objet tire avec la même force sur la corde.FORCES CONCOURANTES.\u2014 Lorsqu'un corps en équilibre est parfaitement rigide, on peut transporter le point d'application d\u2019une force agissante sur le corps, en un point quelconque de sa direction, (voir fig.4).Les forces F\u2019 et F?agissant sur le corps rigide À pourront être déplacées le long de leur ligne de direction et si elles sont dans [17 ] i\" ig i h Bt Un i i Décembre un même plan, deviendront concourantes en B et pourront être remplacées par F\" et F?ayant toutes deux leur point d\u2019application en B.Fig.4 PRINCIPE.\u2014 La résultante de deux forces concourantes est représentée en grandeur et en direction par la diagonale du parallélogramme construit sur ces deux forces.VÉRIFICATION EXPÉRIMENTALE\u2014 Ce principe se vérifie expérimentalement au moyen de l'appareil ci-dessous (fig.5).P ; 0 Fig.5\u2014Détermination expérimentale de la résultante de 2 forces concourantes.Cet appareil est composé d'un parallélogramme articulé A B C D , aux extrémités A et C duquel sont attachées des cordes qui passent sur des poulies P et P\u2019.Le parallélogramme peut tourner autour du point B qui est fixe.Si l\u2019on accroche aux extrémités des cordes des poids proportionnels aux longueurs des côtés À D et C D on constate que: 1° Le point D se déplace suwvant la droite verhcale B D (direction de la résultante).TECHNIQUE December 2° pour que le point D ne bouge plus, 7 faut suspendre en D un poids qui est lui même proportionnel à la longueur de la dragonale B D.Le système étant en équilibre, le poids suspendu en D représente l'intensité d'une force directement opposée et d'intensité égale à la résultante R des forces agissant aux extrémités À et C du parallélogramme.SOLUTION MATHÉMATIQUE.\u2014 Deux forces concourantes F\u2019 et F* étant données ainsi que la grandeur de l'angle a que font ces forces entre elles, la valeur de la résultante est: R=VF;+F#+#2F,F* cos a Exemple: Si 2 forces de 75 et 125 lbs font entre elles un angle de 120° la résultante a pour valeur R=V75-125+2X75X125(\u2014.5) R=109 lbs approximativement.La direction de la résultante peut être également déterminée par calcul.SOLUTION GRAPHIQUE.\u2014 (Voir fig.6)\u2014 >> 0 BY Fig.6\u2014Détermination graphique de la résultante de 2 forces concourantes.Généralement on emploie la méthode graphique.Pour composer les forces données dans l\u2019exemple précédent, on trace les lignes ox et oy faisant entre elles un angle de 120° En adoptant l\u2019échelle des forces lg\u201d = 10 Ibs, on portera sur ox et oty des longueurs OA et OB respectivement égales à \"5/26\" et 19/6\u2019 et on construit le parallélogramme OACB.La diagonale OC donne la résultante en direction et en intensité.Sa longueur mesurée est 134\u201d correspondant à 110 lbs app.Pour trouver la résultante de plusieurs forces concourantes, on procéde en composant la résultante de deux forces avec une troisiéme force, et ensuite la nouvelle résultante avec une autre force et ainsi de suite jusqu\u2019à ce toutes les forces aient été composées.Exemple: Soit à composer les forces F\u2019 F?, F3 et F* (voir fig.7).[18] E fe @ ré gel peut oer rep) fr AUTH js Décembre TECHNIQUE December R\u2019 est la résultante des forces F\u2019 et Fz; R est la résultante de R* et F3 et enfin R la résultante de R?et F4 est la résultante des forces F*, F?, F3 et F4.RB D Fig.7 Remarque: Le polygone fermée OABCD peut être construit directement si l\u2019on observe que les lignes AB, BC et CD sont respectivement parallèles et égales aux forces F?, F3 et F4.DECOMPOSITION D'UNE FORCE EN DEUX AUTRES DE DIRECTIONS DONNÉES.(voir fig.8 Il suffit par l\u2019extrémité À de la force F de Fig.8&\u2014Décomposition d\u2019une force en 2 autres de directions données.mener des parallèles aux directions données ox et oy.Les points B et C limitent les forces F' et F?pui sont les composantes cherchées.Remarque: Lorsqu'il y a plus de deux directions données, le probléme a une quantité infinie de solutions.VARIATION DE LA RESULTANTE DE DEUX FORCES CONCOURANTES, FAISANT UN ANGLE VARIABLE (voir fig.9).\u2014 L\u2019angle des forces peut varier de 0° (forces de méme direction et de méme sens) a 180° (forces de méme direction et de sens contraire).En déterminant graphiquement ou algébriquement les valeurs de la résultante on peut observer que pour a =0° on a R=F14-F> 0°