BORACe c c 1111 ORNELL 画 UNIVERSIT 111111111 L 旧 RAF _lll »Y III 1111 31 924 103 137 8 77 MEMOIRS OF THE TOKIO D AIGAKU . (UNIVERSITY OF TOKIO) No. 11. A SYSTEM O'F IRON RAILROAD BRIDGES FOR JAPAN BY J. A. L. WADDELL, C.E., B.A.Sc., Ma.E.， PROFESSOR op CIVIL ENGINEERING IN THE UNIVERSITY OP TOKIO, JAPAN : CONSULTING ENGINEER POR THE FIRM OF RAYMOND AND CAMPBELL, BRIDOE-BUILDEBS OF COUNCIL BLUFFS, IOWA : MKMBER OP THE AMERIC\N fiOCIETY OP CIVIL KNQINEER8, RKN8FELAER SOCIETY OP ENGINEERS, ENOINKKRS* CLUB OF PHILADELPHIA, AND WESTERN 80CIKTT OF ENGINKEKB； A8BOCIATE MEMBER OP THK INSTITUTION OF CIVIL KNQINKKR8, LONDON : AUTHOR OF THK DESIGNING OF OKDINAUT IKON HIGHWAY BRIIHJK8. (TEXT.) PUBLISHED BY TOKIO DAIGAKU TOKIO: 2545 (jAPANEßE ^Ry\) 1885 A. D. MEMOIRS OF THE TOKIO D A I G A K U (UNIVERSITY OF TOKIO) No. 11. ■ ♦ _ • 山 ♦ "I - A SYSTEM OF IRON RAILROAD BRIDGES FOR JAPAN BY J." A. L. WADDELL, C.E., B.A.Sc., Ma.E., PROFESSOR OF CIVIL ENGINEERING IN THE UNIVERSITY OF TOKIO, JAPAN : CONSULTING ENGINEER FOR THE FIRM OF RAYMOND AND CAMPBELL, BRIDGE-BUILDERS OP COUNCIL BLUFFS, IOWA: MEMBER OF THE AMERICAN SOCIETY OF CIVIL ENGINEERS, RENSSELAER BOCIETY OF ENGINKER8, ENGINEERS* CLUB OF PHILADELPHIA, AND WESTERN SOCIETY OF ENGINEERS； ASSOCIATE MEMBER OP THE INSTITUTION OP CIVIL ENGINEER8, LONDON： AUTHOR OF THE DESIGNING OF ORDINARY IRON HIGHWAY BRIDGES. (TEXT.) 螭 ♦知 _ _ PUBLISHED BY TOKIO DAIGAKU TOKIO: 2545 QAPANEßE Er/) 1885 A. D. Printed by “ SUISHI-BUNSIIA»” Tokio Japan. しも Gzn グ CORNELL、 Uf\JVER82TY k ÜBRÄRY メ TABLE OF CONTENTS. Chapter X • Introduction. ••.••••••••••.•••••.•••••••••.•••.•••••••..き XX« Sections of Xi^ou* ••• ••• ••• ••• ••• ••• ••• ••• ••• ••• ••• • • • •• • III. List of ^RXönib©i*s« ••• ••• ••• ••• ••• ••• ••• ••• ••• ••• ••• ••• IV. General Description and Remarks V. Floor System Proper, Re-railing and Ditching Apparatus VI. General Specifications VII. LAve and Dead Loads, Wind Pressure. Stresses iti n^russ6s* ••• ••• ••• ••• ••• ••• ••• ••• ••• ••• ••• ■LX. Stresses in Lateral Systems and Sway Bracing vetting« ••• • • • ••• ••• ••• ••參 ••癱 _參* «•參 • § • ••• ••• XI. Proportioning of Main Members of Trusses, Lateral Systems and Sway •BrSiCin ••• ••• ••• ••• ••• ••• • • • ••• ••• XII. Proportioning of Track stringers, Plate Girders, Floor Beams and Beam ^3 9>I3^6P8» ••• ■»看 ««■ •«* •• • ••• 翁** ••• ••• ••• •• • XIII. Theory and Practice of Pin Proportioning XIV. Proportioning- of Other Details XY. Double Track Bridges. ... Economy. ••• ••• ••• ••• ••• ••• ••• •》• ••• ••• ••• ••• XVII. Bills of Materials and Estimates of Cost.. XVin. Complete Design for a Bridge. ••• … XIX. Working* Drawings * XX. Approximate Method of Designing1 a Single Track Bridge XXI. Order Bills and Shipping- Bills - … XXII. Erection and Maintenance XXIII. Effect of Brakes on Bottom chords * XXIV. Recapitulation. Addenda 01088 ary of Terms. Index 13 46 61 69 63 81 86 104 113 115 122 129 139 144 145 149 155 182 203 209 221 236 239 240 243 251 Table. » y> xt ” » ” » » ，， » ft ” ，， ” ，， » if ” » >» ” » LIST OF TABLES. I. Weights of Iron and Dead Loads for single Track Through and Pony Truss Bridges II. Natural Sines, Tangents and Secants • III. Stresses in Single Intersection Trasses. ♦♦參 ••• ••• • • • ••• ■癱 着 •争* IY. Stresses in Doable Intersection Trusses Y. Wind and Curvature Stresses in Chords and Lateral Systems YI. W orking^ Tensile Stresses and Initial Tensions for Round and Square Bars. VIT. Sizes of Hip Verticals and Beam Hangers for Single Track Bridges. ... VIII. Intensities of Working- ( Compressive Stress for Channel Struts in trusses. IX. Intensities of Working- Compressive Stress for Channel Struts in Lateral Systems and Sway Bracing X. Working Loads for I Beam Struts in Lateral Systems and Vertical Sway 1 •!* flmTl ぎ. ■•攀 秦» _ ••• ■•鲁 mm m ••• • • • XI. Dimensions and Weights of Tmek Stringers XII. Dimensions and WeigTits of Floor Beams for Single Track Bridges. ... XIII. Dimensions of Members of Lateral Systems, Portal Bracing and Vertical Sway Bracing for Single Track Through and Pony Truss Bridges XIV. Bending Moments for Iron and Steel Pins. ••• ••• »»■ Pm BG3»riDg&_ ■■審 • ••• • ••• ••• •• • ••• ••• •• • ••• XYI. Dimensions oi Union Iron Mills’ Channel Bars 、 XVII. Permissible Pressures on Rollers XVIII. Working Bearing Stresses and Bending Moments for Rivets ... XIX. Lengths of Lattice Bars &e XX. Sizes of Lattice Bars. ••• _»■ •奉* 瓤 》鲁 »»參 》•拳 •■參 Sxzos of T ■ぎ • "• ••• XXII. Sizes of Stay Plates used with Latticing and Double Kivetted Lacing •… XXIII. Sizes of Stay Plates used with Single Rivetted Lacing. XX£V*. Working Loads for Pute FalsGWort jPillars . • • • ••• ••• LIST OF PLATES. Plate. I. Isometric Projection of a Bridge, ••• •** … … … »» II. Descriptive Plate of Details … … … … … … >y III. Floor System with Wooden Shims …. •• »> IV. Floor System without Wooden Shims. .. … … ••- Y. Ee-ßailing Apparatus. y> YI. Ditching Apparatus. •«籲 ••鲁 «• … … … … … » VII. Plate Girder Span. ... »> VIII. Detaüs for Lateral Systems, Portal Bracmor and Vertical Sway Bracing.... ... … … •• — • — • … … ，》 IX. Details for Trusses. • • • ■ ■ _ • • ••奉《' • • ••一 •- … » X. Working Drawings. … … » XI. Falsework. • • • • • • • *••• • • •** >r XII. Tools. ... … >» XIII. Complete Diagram of Stresses and Sections … … ••- 99 XIV. Truss Diagram for a GO' span, pony. ... ••- … •- … i> W. ,, „ 99- 阶 »» » »> • • … •一 •- … i> XVI. •， » ff 70, a > »r • • • •• … •— ” XYII. ,, „ y> 70 „ , through. … 一 »» XYin. „ „ y* 80, ”， ” ••• … … … … ' 9i XIX. „ ” yy 90产 a » yy- … … ”备 » XX. ，， ，， >r 獅 ”》 ** … ... … … … if xxr. „ „ 99 no. »» f »• … - … … … … ，》 XXII. „ ，， ” 120, ” j ” ••• … … … 9» XXIII. ” „ »i 130 产 f» r r» … … ” XXIV. ,， „ tr 140^ ft t f* … … — - … … » XXV. ,, „ ” 150' yy > - … — 一 ••- a XXVI. „ ,， a 肅 a » »• ••• ••• … … … . » XXVII. „ „ a !7Ü' >j * f*' ••• … … a XXVIII. „ 炒 a ISO, ” » ft- Single Int. … … … ，， XXIX. ” ，， ，， iscy »» t ，， Doub. Int- … … » XXX. „ ” 190, ”》 ” Single Int^ … … »» XXXI. ，， „ fy 190f fi > . ” Dcmb. Int* … … ••- »> XXXII. „ ” y> 200, y> t » »f ff … … … » XXXIII. ” ” >> 210, ”， ” tr ，， **• »> XXXIV. „ „ ，》 220, it 沙 … … … ” XXXT. „ „ jr 230, >t > ” yy •• • >» XXXVI. „ ” ” 240^ » 9 » >* » … … » XXXVII. ,， ，， ” 公 50, » » ” 99 … ••拳 ，》 XXXVIII. ” ” 260, ”》. ” ” » … … ••- >3 • XXXIX. „ ” 270, ” > ”. t9 … » >» 280' ”， *• 99 y* … i> 乂 LI. ” ” ” 290, >» » »» ” >t … J> XLII. „ ,> 300 XX > y> M- … … … … CHAPTER I. INTRODUCTION. To the Civil and Mechanical Engineers of Japan. Gentlemen, Before entering upon tlie subject of this treatise, it will be necessary to make so many explanations and statements of facts that it will be much better to address you directly； I hope therefore, that you will pardon me for writing this chapter in tlie first person. Probably tlio first question which enters tlie mind of 0110 wlio is about to road a technical work is “for wliat purpose aiul in whoso interest is this book written. The Japanese arc generally, and perhaps with reason, suspicious of any proposed innovation by a foreigner, tl linking that tlio proposer may have an ** axe to grind. Oil this account they occasionally fail to profit by tho experience and advice of those wlio really have the interests of Japan at heart. But as nothing is clone without a reason, it may be as well to explain, before going any further, why this book was written. In the first place let me assure you, gentlemen, that 1 have not an axe tv jrind ; because my stay in this country is for various reasons necessarily limited to a little over a year longer ; indeed, it lias been with difficulty tliat I have so arranged my family affairs as to be able to comply with tlie request of tlie University authorities to remain a year longer than my original contract stipulated ; consequently I can in no way bo pecuniarily benefitted by your adopting the system of bridges herein pro- posed. My reason for preparing tlie treatise is simply tliis. I carae some two years and a half ago to Japan, hoping not only to be at the head of a large department, but also to be able to occupy my spare time iu attend- ing to practical engineering work. Instead, I liayo found that there is no work in the country for foreign ongineors ; and, wliat is worse, that there are never more than a dozen students in tlio engineering department. Now as I am unwilling to depart from Japan after a sojourn of three or four years without leaving behind me some professional record of my stay, I have devoted a twelvemonth of my spare time to tlie preparation of tliis work, which I hope will meet with your approval. Iu suggestmg that you change your present style of bridge designing to that ex- pounded in tlio following pages, it is no untried experiment timt I am asking you to make ; for th G system proposed is essentially iu agreement witli tlie best Americau piactice iu bridge construction. That the United States of America lead the world in bridge building is a fact undisputed even in Europe. It is no wonder that such is the case, for owing to iho immense extent of territory and tlio rapid progress in railroad building of late years, there have been moi’Q iron bridges built there than in any other country. Then again the amount of capital available for railroad purposes or any other engineering work being much less in the United States than that which could bo obtained in older and richer countries, and tho cost of all kinds of labour being very high, it has been fouud necessary iu all brauchos of construction to study economy. In no department of engineering is tliis fact moro evident than in bridge building, for not only is it made a specialty by many companies, but what is more, when American bridges are put in competion with those of other countries, the American bridges are cliosen, notwithstanding the higher price« of American labour aud materials. In this connection let mo quote a little from an article which appeared some eight months ago in the New York Times upon M Bridge Building in America.” “If there is anything in which the United States can justly claim procedence over all other countries it is for the simplicity, mechanical construction and boldness of de- sign of their bridges.” This remark was made to a Times’ reporter, and with a good deal of pride, by Mr. Thomas C. Clarke, of the Union Bridge Company, and one of tho veteran bridge-builders of tlie company. “ The Brooklyn bridge/* lie added, ^lia s tlic largest span and is considered the largest bridge in the world. But we will soon be obliged to yioid tho palm of having tlie biggest bridge to another country. There is now building over the Firtli of Forth, iu Scotland, a bridge of two spans, each of which is as long as tlio Brooklyn bridge. This is the greatest bridge over designed anywhere. Wo are up to nothing of the kind in Amorica, and we haven't money enough for U.” “ There are probably 300 miles of iron bridges in tlie country now, and perhaps in the neighborhood of 700 miles of wooden bridges. I am speaking now of railway bridges, Tlie construction of road bridges is quite a separate and distinct industry. It is the price of iron that regulates the cost of a bridge ; the cost of labor has very little to do witli it.” “To come back to bridges/* continued Mr. Clarke, all, or nearly all, tlio steel used in railway bridges is made here, very little being imported. That now bridge at Bondout, on tlio west Shore, if built ten years ago, would have been the subject of a book. Now it is simply a railroad bridge, and not one traveller in ten even looks at it as lie goes over it. It is very light, yet perfectly secure. That is a great point where American engineers excel — in having lightness combined with perfect security. It is a saving to the railways, too, for bridges are paid for by tho pound. Now an order is given for a br'ulge just as it is for a locomotive — it is mero matter of com- mercial mannfacture. When I was iu England some years ago I wanted to go and see the Tay bridge, bub the civil engineers said : * 0, tlmt’s nob much good ; it，s not worth going to see.* I didn't see tho bridge. But I know its construction was so palpably erroneous that a common house carpenter could have seen its unsafe condi- tion. Our American railway history shows nothing the equal of that great disaster, tliougli tlie Ashtabula horror came near euougli.” “The bridges built in the last five or six years are perfectly safe, unless two trains should meet or a train run off the edge. Both of these accidents are extremely im- probable. The railroad companies allow no iron bridges, improperly constructed, to remain. There are, to be suit — or so I have hoard — a good many unsafe bridges, probably hundreds of them. Ifc will take timo for these to be replaced by iron or steel ones. The great danger with wooden bridges is from cinders and sparks. Theso drop on the wood, cliar in a little, and weaken tho s true bur o until an unusually heavy train or sudden jar causes ft crash. Tlicro liavo been lmiulreds of accidents from this cause. So the wooden bridges must go. An iron bridge costs little more. We’ve always been ahead of the world in bridge building, and wo intend to stay there. M Tho following extract from the 14 Delaware Bridge Company’s Album ’’ boars upon wliat I have already said concerning bridge designing in America being a specialty. “ The construction of wrought iron bridges has attained such development "witliin tho past 10 years as to be now recognized as a separate and important braucli of constructive engineering, essentially depending for its succoss upon tho skill, ex- perience ami integrity of the engineer, who lias specially devoted bimseU* to the study find practice of tbo subject. Good iron bridges are occasionally built by engineers in general practice, and thero aro still a few railroad companies which li.avo a bridge construction depavt- mon^ I but as a rule, bridges are builfc to-day by men who have onileavorccl to acquaint themselves with the intricate questions involved in the application of tlio general theory of skeleton structures to practice, and who have found that tbo subject was capable of a sufficient development to absorb their exclusive attention. In other words, bridges are built to-day by bridge-builders, ami to become a britlge-builtler demands such an amount of technical knowledge, coupled with, and partly the result of， largo experience in design, and in tlio manipulation of materials, as will ensure tlio erection of structures which are not only scientifically sound in principle, but at the samo time economical and durable. M The following from an article in tlio Chicago Railroad Gazette of J uly 1870 wp- “ English and American Iron Bridges n will also couiinn sonic of my state uiouts. “ Some two months ago tenders were solicited for tho construction of iron rail- w«iy bridges of spans of 100 and 200 feet, by the Intercolonial Railway of Canada, connecting Quebec and Halifax. This call was very generally rosponded to, tlicn.o being tenders put in by nine fee en English, ono Belgian, aiul sixfcoeu Americ.an Lritlgc- builders. Tlie specification, wliicli was a rigid ono, called for uniformity of strength， hut the design open to each person. The bridges wero all to be of wrought iron, capablo of bearing 1 \ gross tons per lineal foot, in additiou to their own weight, straining the iron in tension to over 10,000 poumls per square inch, riio 】 rou of* the 200 fee fc spans was to be capable of bearing 00,000 poiuuls per square iuch before breaking, and that of the 100 feet spans 50,000 pouiula per square incli. Much interest was felt as to the result of this competition, which was viftaally one between English and American systems of bridge building. The decision was that the long spans woro awarded to an American firm, Messrs. CLAEKE, EE- EVES & CO. , of Plioenixville, Pa. , and the short spans to English bridge-builders, tlio Fairbairn Manufacturing Company, of Manchester. Of the thirty-six plans submitted, only three or four were rejected on account of not coming up to special strength. The bridges of Clavko, Ecoves & Co. were selected for the long spans, not only as being unclonbtedly first-class, both in material and workmanship, but also as be- ing the lowest responsible tender. Somo curiosity lias been expressed to know how American bridgo-builders, using liigh-priced iron, and paving higlicr wages for labor than their English competitors, could jet build a less costly bridge. While it is to some extent true that the specifications allowed of a lower quality find loss expensive iron for tlio 100 than for tlio 200 foot span, yet one of tlio prin- cipal reasons why an American firm was lowest on the long and an English firm on tho short spans is owing to the less weight of iron roquiretl by tlio American system of bridge, an^l this is more apparent the longer tlio span. Somo persons erroiiGously suppose that tlio raoro iron thcro is in a bridge the stronger it will be. But a little reflection will show that it is only tlio iron that is working, or, in other words, that is actually strained by thd load, that contributes to the strength of the structure. All the rest is cload weight, and merely weighs down the bridge. 111 very short spans this ia not disadvantageous, as it tends to diminish vibration, but in long spans where the weight of the bridge much exceeds that of the load passing over it, every pound of iron that does not contribute to the strength of the bridge is a positive injury. To illustrate tliis more clearly : if one bridge weighs 125 tons and another 250, and both are strained by the rolling load 10,000 pounds per square inch, tlio lighter is the stronger of the two. But if the 125 ton bridge be strained 10,000 pounds per square inch, wliile the 250 ton bridge is strained only 0000 pounds per square inch, then tno latter has really double the strength and double the lifo of the former ; for half the iron may corrode away, and thon the worldng area of tlio bar will bo oqual. It is noi clearly perceiving this fnot — that the streng- th of the bridge depends upon tlio working area of each part — tliat has led our English friends to make such heavy bridges. In several plans, if the strains per square inch are alike for similar loads they must all bo of tlio same strength, providing the connections aro equally perfect. - Some take more iron than others to effect the result, but the result is the same. The lightness of American bridges is due — 1st, to tlio concentration of material along the lines of strain, which enabled a lighter web system to be used, and hence a higher truss ; 2d, to this greater lieiglit of truss, wlncli throws less leverage on tlio upper and lower chord system, and lienee requires loss iron in tlieir members ； 3d, to the use of eye and pin connections instead of rivets, by which there is no waste of metal to compensate for tlio doduotion of rivet- liolos. American bridges are stiffer vertically and better braced laterally than English bridges, tlieir greater hoiglit giving less deflection under a load, ancl allowing of overhead bracing as well as that below the track. But tlie less quantity of iron required to do tlio worlds not tho wliolo explanation of tlie less cost of American as compared with English bridges. A second and equally important reason is tlie less amount of manual labor required to construct and ereot tliem — owing to tlie general use of machinery in forming all tlie parts. English bridges are made of low-price iron and require a groat deal of it-, and a great deal of hand-labor in constructing and erecting. American bridges have all tlieir principal parts formed by machinery. They are of exact uniform dimensions, in similar spans, and lienee perfectly interchangeable, like tlie parts of tlio locks of tlie American rifles, or of sewing-machines. Hence machino-labor can be applied to thoir manufacture, and tho cost at tho works rc- (liiCGd to a minimum. But American bridges have still auotlier advantage. They arc so made that nearly all tlie work is clone at tho sliopg, and they can bo croctod with tlio least pos- 8ル1〇 amount of labor, and that unskilled. In fact, tlie cost of erecting tlio staging tho principal expense ; after that a 200 foot span can be orcctod and made self-sus- taining in tlio space of two days, if necessary. But the English bridge is only about half clone when the scaffolding is built and tlio iron placed upon it. It has then to be riveted together, which is expensive, as tlie conveniences for such work at the site of a bridge are not often groat. It is slow anti tedious, requiring from two to three weeks to put together a 200 feet span. Taking all these tilings into account, ifc will bo seon liow American bridge-build- ei’s liave been able to compete with English firms on the large bridge at Buffalo, and iu tlio recent case of tlie long span bridges of tlio Intercolonial Eailroad of Canada. M I have dwelt at length upon tlio comparison of American and European bridges, for the reason that the Japanese railroad bridges are of the latter type. It will now be necessary for me to criticize tlie railroad bridges of this country, and I hope you will excuse me for so doing. I have little hesitation in expressing my opinion tbereou, knowing that tlie designs are not yours, but arc the work of some of the present and former foreign employees of the Eailway Department. llie first grave error to which I would call your attention is that both for economical and prudential reasons the spans are too short, tlie superior limit being 0116 hundred feet. For any locality that bridge is tlio most economical, for which tlie total cost of both superstructure and foundations is a minimum, provided that tli デ waterway be not so lessened as to endanger tlie structure from washout or to raise t]ie flood level of tlio river enough to injur o the surrounding country. Now as the cost of foundations is always very uncertain and in most cases exce- ocls tho estimate, ifc is clear that long spans, especially over tho deepest part of tho llver, ave liable to be more economical than short ones, and no one will deny that a 8Pan of one liumlred feet is a short one. Agaiu, for such spans tbo contraction of waterway is least ten per cent, which, in addition to tlie piling np of the water by 10 irupn；ct of tlio current against the piers, ■will cause a decided increase in the flood level. If an American engineer were sent to inspect and pass judgment upon a Japanese railroad truss bridge, ho would condemn it before getting within a hundred- yards of the structure, for all such bridges have pony trusses without any side brae ing. This is objectionable for two very important reasons : first there is nothing to resist the wind pressure upon the top chord, and to prevent its overturning the truss; and second, when the top chord is not held laterally at the panel points or other places, its true length as a column must be about equal to the total length of span, when considered in respeefc to lateral deflection under load. Ifc is quito evident that no pony trusses in this country have their top chorda proportioned for tho number of diameters found by dividing the length of span by the width of top chord plate. As tho before montioned inspector would approach tlio bridge I10 would bo struck, in fact liorrified, by tho nbsoluto lack of laterfil bracing j for one oannofc im- ftgme that tho n vetting of the floor beams to the lower chords by four rivets at each end can give any lateral strength to tlio bridgo wlion subjected to wind pressure. Ther“8 iust as much reason in this arrangement as there would ba in omitting the diago- nals from the trusses and rivet ting the vevticcil posts to the outside of the top and bottom chords. Such an arrangement might sustain a small balancod load, but an unevenly distributed load would certainly destroy the structure. The Japanese truss bridges file therefore wholly unfit tod to resist the strossos produced by a wliirlwind. ThG next thing that would catch tho inspector’s eye would be the inclined struts of tlie Warren girder, formed by trussing, in the most inefficient manner possible, two very thin, wide bars. Such struts were experimented upon years ago in Ame- lica and were unhesitatingly condemnod. It needs no experiment, though, to show their inefficiency ; for theory teaches that tlio strength of a strut increases with tho radius of gyration of its section in respeefc to the neutral axis of that section； audit is evident to all that a flat bar lias a very small radius of gyration. The next parts that tlie inspector would notice would be the chords. In tho upper there is a waste of material at all points except the centre ； and the box form of the lower would condemn it immediately in hia eyes. Concerning this point let me give you the opinion of A. P. Boiler, Esq. C. E. , a well known American engin- es of acknowledged ability, as expressed in liis treatise on “Iron Highway Bridges." “In continuous box-shaped chords, the pin holes must be reinforced with thick- ening plates, not only to increase pin-bearing, but also to distribute the pressuro de- livered to tlie chord at each panel point over as much surface as possible. Further it is advisable that the increased nectional area required at each panel point, in ap- proaching the centre, be placed in the sides of the box. as it is through the sides that the pin passes. It is not one of tho least excellencies of the pin-connection system that the chords, posts and tension-members may be made to unite at the centre of their several sections, and by proportioning the box cliorcl as above this may be ac- complished very fully This principle is about as far lost sight of in rivet. ted work as ifc is possible to be. In such work tlio chords have no stiffening along the inner edges of the vertical plates or sides to which tho web system is rivetted, and the increase of area is made by rivet ting on plates to the upper side of the top chord, or lower side of the bottom. The centre of section is not at the middle of the sides, as usually assumed, but approaches the top or bottom plates, and in largo spans, where the strains are great, necessitating a large area of section ( placed mostly in the above plates ) the centre of section approaches the plates very rapidly. 27’¢ rivelted system has of necessity, so m'any inperfections of design } of workmanship an^ ma^rialf in contrast with the above [pin-connected], that, to obtain anything ap- pJOciching equal strength on the same specification t it should only he used with a higher factor of safety. It is probable that this difference is not less than 20 per cent; so tlmt when a pin bridge is called for, having a factor of five, a rivefcted bridge cannot bo considered as approaching the same strength unless it is proportioned with a fac- tor of siiv. The fact that a rivetted bridge is stiff or that its deflections may bo small under a test, is no evidence of strength, which last depends upon other considera- tions than those applying to stiffness n These remarks of Mr. Boiler's are intended for lattice bridges, in ■which the web members are rivettod to the chords, but they ai*c most of them applicable to the lower chords of the Japanese bridges, which are made continuous from end to end of span by rivefcting. Tlie Japanese truss bridges, although Warren girders, are not wliat may be properly termed pin-comiectetl bridges, for the office of the lower chord pins is merely to transfer the web stresses to the chords. The inspector would next turn Lis attention to details and would notice the apo- logies for stay plates containing one rivet at each end and spaced about three feet apart, which connect the opposite flanges ou the under sides of the top chords； the lieads on the main diagonals formed by rivet ting a piece of plate on each side of the bar at the eye ； aud the smallness of the connecting plates and the pancity of rivets at; tlie joints in the chords. There is one tiling that he would be sure not to overlook, and that is the absence ^ a Suarc^ rail or any arrangement to prevent a derailed car or locomotive from go- lno through the bridge. This is indeed a grave fault, for derailed cars have been lvnown to go long distances before the accident lias been found out : the reason that no Japanese bridge has as yet been destroyed in this way is probably due to the ex- cellent quality of the road bed and to the absence of severe frost. Tlie trouble with most English bridges and consequently with those of this country is tliat they aro designed by railroad engineers, wlio have not made a special study of bridge designing, and are therefore incompetent to do the work entrusted to them. Although I have made many inquiries I liavo been unablo to ascertain anything certain concerning the designing of the Japanese bridges, in respect to either the as- sumed loads or the intensities of working stress, tlio invariable answer to my ques- tions being that u the bridges are made according to designs prepared by foreigners.*5 One engineer did tell me that 4.110 assumed live load for all cases was one ton ( 2240 pounds ) per liueal foot. If sucli be the case, the short spans aro too weak. Thanks to tlio courtesy of Mr. Takanobu Köno. M. 1^, and Mr. Yoshimura of the ICöbu Daigaku, I have been able to obtain the actual weights of iron in a number of t lie «I apanese bridges. Of these I have chosen the following for tlie purpose of com- p arison "witii tlie bridges designed for this treatise. A single track lattice girder of sixty- seven feet span on tlie Kobe and Osaka line weighs 31.5 long tons or 70,500 pounds. Another single track lattice girder of ninety- four feet span between Kioto and Osaka weighs 47 long tons or 105,280 pounds. A double track truss bridge of one lmndi'ed feet span weighs 77.6 long tons or 178,824 pounds. By interpolating in Table I we find tho weight of iron per lineal foot for a 67^ span to bo about 800 poumls, and that for a 94r span 852 pounds, making the total weights for these cases respectively 58, G00 and 80,088 pounds. A special calculation gave tlie total weight of iron for a 100， span double track briclgo as 176,750 pounds. Now as the bridges of this treatise are provided with iron stringers and guard rails and oak ties, while the Japanese bridges have only wooüen stringers it is evi- dent that the former are at any rate the more economical ； and, I think, that if you will take tlio trouble to carefully read tlic following chapters, you will conclude that they are also muoli better designed. Tlie reason why the double track bridge that I designed is proportionately so much heavier than the single track bridges is that tlie overhead bracing for reasons, wliicli will appear further on, is necessarily very heavy. But to return to the subject of American railroad bridges ; I do not wish you to imagine that I consider them all perfect and in every way superior to tlie European. Unfortunately such is not the case, for many existing bridges in the United States are tho work of inferior bridge companies and engineers, who have failed to pay proper attention to detail. Then again tlie bridges of twenty years ago are not heavy enough for tlie rolling loads of to-day, and moreover tlie science of bridge de- signing has made great progress in tho last twenty years. But the lately erected bridges of the better class of Amoricau bridge companies are uncloubtedly good, and it is with these in view that I have prepared this treatise, endeavouring in every res- pect not only to equal tlietn in excellence of design but to improve upon them where- ever I saw the opportunity. The styles of truss adopted are those of tlie Pratt and Whipple systems, or the single and double quadrangular trusses. That these forms are both the best and most economical is proved by thoir being almost universally adopted by the leading bridge builders of tho United States ; besides, I have shown in a paper entitled “Economy in Struts and Ties,” by a method entirely practica], that vertical posts and inclined ties are more economical than any other arrange- ment ; and these are tlie essential features of the Pratt and Whipple trusses. You will notice that double track bridges and deck bridges have not been as fully treated as through and pony truss bridges*: deck bridges are applicable to only high grade crossings, few of which will be found necessary in tliis country ; while tlie double track bridges will not bo needed, in all probability, for tlie next twenty years, by which time steel will have replaced iron in bridge construction. Nevertheless you -will find that both these styles of structure have received sufficient attention to enable an engineer to design them with ease, the only difference being that lie will have no diagrams similar to those on Plates XIV 一 XLII to guide him. In referenco to tliese diagrams I would stato that tlie dead loads and wind pressures liad to be first assumed then checked, so that they do not agree exactly with those given in tho body of the work, the differences, however, are all within the limits allowed in good practice. Although tlie principles employed in designing plate girder spans have been fully elucidated, no examples have been worked out or diagrams given, for the reason that time and space do not permit ; and there is no necessity therefor, because you have many examples of existing plate girder spans, wliicli do not differ funda- mentally from tlioso which would be designed by tlio methods of this book. Never- theless you will find that tlie latter will exceed the former in weight and efficiency. No special treatment; has been given for skew bridges, for none is needed ; the methods for designing them being precisely the same as those for designing other bridges. Whenever it is convenient to do so tlie panel length of a skew bridge should be chosen so that the shoe of one truss comes opposite tlie first panel point of tlie other truss, in order that the floor beams may be at right angles to the planes of the trusses, both for economical reasons and to avoid using single beam liaugers. This arrangement can often be made by shortening the panel length a little, and, if ifc be allowable, slightly changing the angle of the skew. Even if it bo impracticable to make this arrangement, it is usually better in skew bridges to advance the ends of the floor beams at one side of the bridge by one or even two panel lengths, if by 80 doing the floor beams be shortened. The ton used m the following chapters is tho American or short ton of two thousand pounds: it will be found much more convenient tlian the long ton. It seems almost unnecessary to state, except for the benefit of foreign readers, that the gauge of track is 8^ 6^, that the distance between centre lines of inner rails, where there is a double track, is Gr 2J", and that the width of the head of a rail is 2士"， making the distance between centres of parallel tracks 9f 10i". In making the designs on Plates XIV — XLII American iron was employed, tlie reason being, as can be seen from the next chapter, that tlio European channel sections do not have the necessary range iu weight and are with a single exception, limited to a depth of twelve inches. Carnegie's sections have been exclusively used, because not only does his company roll more iron than any other company in tlie United States, but they are also tabulated in a more convenient form than are any otlier sections. On this account I have copied from bis il Pocket Companion, M with kind permission of the Company, all the tables that I think will be of any use to you. It would be well for each engineer in this country, who lias anything to do ^vith ironwork, to provide himself with the books of sections of all the manufactur- ing companies mentioned in Chapter II. Concerning tlie cost per pound of finished bridges of the American type I have made many inquiries both iu England and America. The American price is at present about 4 i cents f. o. b. : the English manufacturers with but one exception refuse to quote prices without seeing working drawings. This exceptional company halves the price about half a cent less or 4 cents gold. The freight charges from England and America differ only a few cents per ton. . As to where it is better to have bridges manufactured each engineer must judge for himself. My opinion is that for plate girder spans it would be more — 10 — economical and satisfactory to import the iron and manufacture them in this coun- try ; that for nil single track bridges ami all ordinary double track bridges it would be cheaper au 26.82 5.7! »» 8.05 17.59 ，， 24.74 5.28 ，， 7.42 17.59 t» 24.74 5.28 » 7.42 19.17 »» - 36.67 5.75 11.00 15.91 t» 26.87 4.17 »* 8.〇6 17.50 ，， 25.62 5.25 >» 7.69 14.67 ，* 20.57 4-4° 6.17 16.67 »» 20.57 5-oo » 6.17 15,83 >» 19*53 4.78 » 5.86 15.83 i» 23.12 4.78 n 6.94 12.03 f» 23.12 3.61 »» 6.94 11.41 21.87 3.42 » 6.56 10.78 ，》 20.62 6.19 10.78 »t 20.6 a 3.23 ” 6.19 10.16 f» 19.37 3.05 9» 5.81 10.16 ，， 19.37 3.05 »» 5.8i 10.16 »f 19.37 3.05 ，， 5.8i 10.16 »» 19-37 3.05 5.8i 9.53 »， 18.12 2.86 ” 5.44 9.53 >， 18.12 a.86 ff 5.44 8.91 ，， 16.87 2.67 »i 5.06 8.91 »» 16.87 2.67 ” 5.06 8.28 »> 15,62 2.48 »* 4.69 8.28 »» 15.62 2.48 *> 4.69 6.97 15.62 2.09 it 4.69 6.45 ft 12.24 1.94 >i 3.67 6.45 ff 12.24 1.94 3.67 6.45 »> 12.24 1.94 ft 3.67 4.79 fi 11.20 1.44 »t 3.36 5.9^ »> 9.17 1.78 » 2.75 5.9 ュ »y 9.17 1.78 i» 2.75 4.57 »» 8.33 1.31 it 2.50 4.37 n 8.33 1.5! ” 2.50 3.01 t» 7.50 .90 2.25 3.01 » 7.50 •90 it 2.25 2.7〇 6.67 .81 » 2.00 2.7〇 ，， 6.67 .81 ft 2.00 2.38 5.83 .71 ” 了 .75 Size in Inches. 7x7 10 X 9 x „ 8 x 4i 6x6 8x5} 5iX 7 X 5i 6 含 x 4 6X4 5 x 5 7 X $ 6 x 3 蚤 4 各 X 功 6x3 4*X 4i 52X 3 5X3* 4 聲 X 3 聲 4X4 5 X 5 4iX3 4X3* 3 春 x 4x3 4 X 5 3iX 3i 3ix 5 4 X 鑄 3 X 3 4Xa 3iX ah 2 聲 x 2 聲 3 X 鸩 2ix 2 备 3X2 埒 X 2 全 a 备 X a 2x2 Sections of Iron manufactured by the Butterley Co. Silverclale, North Staffordshire. ANGLE IRON. 5 Ä — 15 — CHANNEL IRON. Dt：|)tu in Tuches. Weight > er foot in Ibs. Area of Section. Thickness of Web in laches. Width of Flange. Note ! The above sections can be slightly increased in the thicknöss of the wob, but will also be to the same extent wider in the Jiang es. In all probability the Butterley Co. rolls also tee irons and I beams. s_4 L9 la L2 La 44 0a4 334 2 2 2 31 fl lw ” f f Ä la ” * ” 0000000050 6 o 490-6 76 98 2 986 435 3 1 I 1 0 ” >J «» S ** 5:; 52 opooo 00003 o 4 CC 3 9 3 4 3 8 7 2 8 7 6 73 2«- 5 3 I I 1 13 2 0 8 342 9266 3 2 2 1111 t0.. ”：r : : S 4- 086 I »>13 16 5 4*220-1111 2 OOC 766 5 4 44 — 16 — Inches. 20 X 7 x 7 1 8 x6f x6f 17 X6^ x6l 16 x6 x6 15 X5 X5 14 X6 x6 13 X7 X7 12 音 X5+ X5i 12 X7l X7s 12 X6 x6 12 X5 X5 io x6 x6 ro x 5 x 5 io X4i X4i 9i X4 各 X4i 9i X 3¢ x $| 9 X6 x6 9 X4 を X4i 9 X4 X4 8 聲 X 2 聲 8 x6 x6 8 X5 X5 8 X4 X4 8 X2i n X3| 7 X6 x6 7 X 斗 X4 7X3 X3 7 X2^ 6i X3 士 xsi 6 去 xji x^i 6 x 5 X5 ö Xj X3 6 x 功 5i Xaf xaf 5^ X2 X2 5 X4J X4i 5 X3 X3 4 聲 X 2 XT. 4 XJ X5 4 X if X if lOH. lbs. 100 90 80 77 77 70 68. 57 67 50 64 54 65 65 60 45 8r 11\ 67 52 55 39 56 56 47 35 41 30 36 27 3^ a8 21 40 40 30 23 27 16J 37 33 37 29 30 21 22 14 な 4 18 36 35 科 i8 18 18 11 di i5l I5i 25 18^ i4i 叫 10 15 12 川 H 25 21 15 全 12 12 11 聲 The author is unable to state wlietlier Messrs Dunkerkley & Co. roll tee and angle irons or whether they make a specialty of channels and I beams. GIRDERS. Section Numbci*. Section. Weight. Maxm. Minm. per foot, per foot. Sections of Iron manufactured by C. C. Dunkerkley, & Co. Manchester. CHANNELS. Weight. Section N umber. Section. Maxm. Minm. per foot. per foot. Inches. lbs. lhs. D 51 ii 冬 X3 X3 30 26 D 54 叫 X3i X3i 27 D 9> 10 X3i X3i 31 ゾ 51 D 57 9 聲 X3i 27 聲 叫 D 63 9 金 X3-i X3 士 3i 22 ； D 60 畴 X3i 3〇 21 D 62 22 D 61 7 士 x 17 ェ3 D 65 6| X2 蚤 xri *9 1 斗 D 64 6 去 X2 或 X 2* 17 12 D % 6 Xif Xif 1 6 + I 4 D 59 5¢ X2| X2| 10^ D 58 4l X^4 X2i II D 56 4 蚤 X2j ni 9 D 55 4 X-2 X-2 9i Rolls turned for new Sections. GIEDEES KEPT IN STOCK. Ijen^tha tip Io 40 fieet. Sectionul DimenBions. Approxi- Number. Top Bottom Weight Flauge. Flange. per foot. Inches. InclioH. Inches. lbs. - B 30 20 7 7 100 D 3^ l6 6 6 62 D 8a 14 6 6 56 B 27 12 6 6 56 D 25 12 5 5 43 D ^3 IO 5 5 4〇 D ^ IO 4* 33 D 19 が 3 聲 25 D 17 8 5 5 3〇 D 15 8 4 4 24 D I? 7 3 聲 3 聲 20 D 6 7 “ I 斗 D 2a 6 5 5 29 D ii 6 3 3 i6 D 2 6 2 蚤 ii D 20 5 4* 4i バ D 18 5 3 3 13 D 7 4i Tf 4 8 D 16 4 3 3 n D 4 4 if Tf 7 0 3 4 2 5 2 56 7 7 56 3 I 0 9 3 7 » 4 56 7 58 3 4 9 36 7921 21 2 0 8 76 4 3 3 3 3 2JOO 00 75 3 2 2 00 2 2 4 I 4. 4 9 4 A— 4 11 4 I 9 48 00 2 1 4 4 2 1 I dddddddbdbddddddddddddddddbdddddbddddddddd Sections of iron sold by Measures, Bros. & Co., Southwark St. London. CHANNELS. 冲 X 3， 9H 5 か 9^x 3 A， 7ivX si， 十 4^X sA， MINIMUM. Sections. Thicks, of Web. Wt. per ft. MAXIMUM. Sections. Thiclis. of Web. Wt. per ft. GIRDERS- Depth. Width. Wt. per ft. Remarks. Depth. Width. Wt, per ft. Remarks. 1 6， 6r 62. In Stock. r ao* Iu Stock. 14 ヶ 6^ 6on » 6*- 5^ ” » I2r 6- 56s* ti »1 6^ i6tt a M 12* 5# 42* a »> 5^ 4i" ” a lO〃 5^ 36 券 i» ，， 4l" y 13* it ，， 10, 4V ” »» 4" r 12* i* 1» 9^ 4 ぐ ず ” »» r Rounded Flan ges 9 耙 か it »> 11* t» >* 8 - 5# 29* a t* 4 耙 i 聲, Zn a »» 8^ r 22n yy »» ぐ ir 7n a ” Measures, Bros. & Co. roll also a number of angle and tee irons, the weights and dimensions of which are not given iu tlieir book of sections. Ä • tt • sf. 3 0 7 5 4 1 4 * 韻 sg M ^ Jo r r 0-6 -A8 3S il f 5 3 3 3 2 2 X X X c X X 18 18 X4 f -*5 I 9 9 8 5 4 昼 TT 暑 普 * Ä ■ — 18 — Sections of iron manufactured bv Philip Williams and Sons, Wednesbury Oak Ironworks, Tipton, Staffordshire. FLATS. i 基 inch wide， X i¥ to 1} inch thick 4* inch wide, X ^ to I inch thick if X fy 9» 4各 ” X ,， » ” if ” X* yy »» 4f ” X >» 3» » X „ I5 ff 5 »» X ” n if ” X ,, i» ff 5i ” X ff ，， y> 2 »> Xvs I 聲 ” 6 f» X >» ” a X 士 I »> » X i ” 2 + »> X „ 2 » H >» X 1 聲 y> »t X „ i » 7 »y X ，， i >y 2 -2 n X „ 分 ” 7 聲 » X ” if » » X „ 2 蚤 8 >y X if 2 ，， n X ” 2¢ » 81 » X ，， >y 3 n X „ ，， ” 3i- >» X „ 2音 » ，， X „ 2 »t 3f 9» X „ ff ，， 4 ” X „ ” a ROUNDS- h lh Ii， If, Ii， I|, if, i|, 2, 2j, a|, 2h 2f, h ih and 3^ inch. SQUARES- 聲， Ü， 4, 技， し A， [J， iA， 味 也 ii, ii, 1 聲， i 备 ， も 分， 分，2 蚤，2 皆， d 普，2 聲, 2|, and 3 inch. ANGLE IRON- 2 x \ to .y in. 2 各 x 為 to さ. in. 2 穿 . & 3 X 晷 ね 普 in. 3- 各 X | to 普 in. and 4 x 蚤 to 聲 — 20 — Sections & Sizes of Rolled Iron Manufactured by the Shelton Bar Iron Company, Stoke on Trent, Staffordshire and 122, Cannon Se- London E.C. CHANNELS. Depth in Inches. Width of flange in inches. Thickness of Web in inches. Weight per foot in lbs. Min. Max. Min. Max. Min. Max. 、4 2 幼 6.75 10.08 4 2 4 11.50 14.00 5 ij if 1 普 9.10 13.15 5 Ä 10.50 13.48 5 3 ä f 12.00 18.00 6 ゆ Ä 1 12.75 18.00 7 ハ 4 A 士 14.00 18.00 7i A 14.00 18.00 7i 消 dH Ä & 16.00 24.00 7i 3Ä t & 18.00 23.00 H ■Ä i 14.50 20.75 m 3fr A Ä 17.00 21.00 9rV 蛣 f 5 ao.oo 26.50 ' 3ft t 21.50 26.00 \ 34 3Ü t 為 22.00 30.0c IO 3Ä 3f 1 a 4.00 28.00 12 3Ä 3U も 37.50 47.00 — 2i — ANGLES. Thickness in inches. Weight per foot in lbs. Min. Max. Min. Max. r 各 2.38 5.20 3-<3 5.85 為 2.70 7.38 a.92 5.42 普 2.70 5.16 普 3.96 9.11 1 4.38 10.16 i 3.96 7.50 聲 4.38 11.88 去 1 4.77 13.15 f i 7.03 15.15 i I 9.17 19.10 i 5，ai 14.58 t 蚤 6.25 9.90 4.79 12.17 A 聲 6.45 14.38 i 5.63 17.86 i 4.79 13 •” A 6.45 10.00 i 5.63 15.6; 1 i 8.91 21.67 i 6.46 20.78 f i 8.91 16.88 Weight per foot in lbs. Min. Max, 9.53 18.13 10.78 23.70 9.53 20.78 10.16 19.38 10.78 20.63 11.41 21.88 15.83 3〇'.〇〇 [2.49 20.63 8.53 a2.-24 10.78 20.61 11.41 28.35 12.03 36.00 ”•50 35.33 19.17 36.67 13.95 26.61 14.67 28.07 15.28 29.5 3 16.13 50.99 16.86 パ. 45 20.00 38.33 17.59 33-91 21,67 36.82 Size. 2X2 i} Hx H 2ixi* 2jx 2 ai Hx 2 聲 3 x 2 3X2! 3X3 3X3 3 X 5 3ix d Six if o.\ 3ix 3 3ix 3^ 4 X a 4 X 2 备 4X5 4 X 3i 4X4 4ix 3 Size. 4iX lh 4iX 4* 5 X 3 5x3* 5x4 5 X 5 X 5 5iX 3i 6 x 6 X 3 6xd 6x4 6x5 6x6 7 X 3 7 X 3 皆 8 x 3 8 x 3* 8x4 8 X 4^ 9 X 10X 35 Tmckness in inches. Min. Max. * f Ä i — 22 — JOISTS. I 2 4» lbs. per foot. 3 X 3 X § and up ioj to I4 5i X 2 X Ä »» 9 it IS 6 X 3 X 1 »» 15 »， I9 6i X X 1 * i7i »» 20 8i X 3 X to * from 171 8i X 3 X »t "To >» 20j 9i X 3f X § and up to 28 9i X 3各 X 1 » 21 25 9i X X Ä » ” J ft 28 9 X 5 X Ä »> 34 >» 40 IO X 5 X J 38 » 48 IO X 6 X i »> 48 »> 52 ioj X 4i X » 34 » 40 12 X 5 X \ ft 42 a 56 PLATES. Maximum Length 40’ o，r ，， Width 6 8 a Thickness . . . . i 各 ! FLATS. I to 5 inches wide ； also Sh Sh Sh Sl, 6, 6J, 6*, 7, : 7h 7 备， 8， 8J, 8i, 9， 9h 9h 10, ioj. 叫， II， nh 12， i^i, 13, aud ェ4， inches wide. ROUNDS. From n // . J to 1 rising by み n 普，， 4 ，， »> み » 4 ，， 6 士 ，， >» 4 and 7 inches. SQUARES. From V ¥ J to 音 rising by ■h »> 旮 ，， 4 ，， » iV ： » 4 ，， 6 ，， » i aud 6¢ inches. Sections of Iron rolled at the Earl of Dudley's Bound Oak Iron Works. • F.LATS. 2^, 2^, 3^, 3|^, ^ ^ ^ ^ ^ ^ ^ 6i，， 幼' 7 へ 7*，， 7| ク， 8へ デ， im, ii ク and ia" wide. ROUNDS. Up to diameter. Up to si* square. 5f wide from to thick. i! 2m wide and thick. SQUAEES. PLATES. — 23 — TEES. HEAD. STEM. Width. Thickness. Width. Thickness. 6 ， r & **• 6 ， Y to -ft» 丨 6 r i'p, s% & r 3 "* g，„ 1， 5 ， 4- & 6 ^ n 5 ， i- & 5 夕 i- ,» a* 5 ， g-,4 つ 4 ^ r ,， ！， 5 ダ lY n 5 ， 3 ^ n 5 ^ r & v aj. 経、 y 5 v ^■Y r ,, 1， 化 r & ダ 4P n 4-^ § 夕 & ビ 斗夕 n aY 4 ク r » i" 4 ク -Y & ^ 5 グ n 4 ， 4 デ 1^ „ V 4 ^ r & r 4 ^ r ,, 1， 4 ^ 1， &i- 4 ^ r ，， r 4 ^ 1- &i- 3 ^ n 4 ^ ^ &V ず r ,, ? 4 ^ ^ & ぐ 2 ^ n 3F V 3 ^ r lY §，， Ä，， p Ä f 3V 1， to が W r & ^ 3 ^ 1， ，， y \ lY 比 n j 3 _ r & v 5 夕 r >, ^ 3 # g， & p & 沪 4 ^ 音 へ， r 5 y r & V 3 ド r ,, y 3 ^ 1* & i- 3 打 g へ， y 3 ^ r» v & r ” r ,, r 3 ， ぐ & A， 3 ^ ir ,, A- 1，， r & v n 3 ^ a% r & v 2 ダ A4* >» ^ 2 4 ■ ANGLES LEGS. THICKNESSES. 7 X I •• い. X 6 " 6 " X 3 " 5 " X 5 " 5 〃 X 4 " 5 ^ X i\" 5 " X 3i" 5 " x 3 /; 4l/; x 4i/; a¥ X 4泰" •>< 3 " 4 " X 4 " 4 " 4" IV 3r l¥ 3i" IV 34" i\n ず X l\u X ず x ir X 5 " x ず x ir X 1%" x 3 " X 2|" X 2 " X ず x ir i " to f " i " to I!" t " to 聲 " Ä" to l\n t " to }f/ 音" to 聲" 普" to V f to %n t " to i " i " to r， I " to v I" to v f " to i〃 I w to i" 在" to f " I /7 to i " 赤" to 聲 " Ä" to I" I " to if/ •A " to Ä" ■A" to I " to I " i " to i" to r， I " to 蚤" i " to r i " to if/ — 25 — ェ BEAMS. Depth. Width of Flanges. Thickness of Web. i ゾ to 6^ to icj^ 5t" i* 6 _ ド 中 »» ず »» r 5" »» sv ft 化 74. 5i" it 5が ぐ t» i. 4^ ，, 4i" V t» 4" r »» Y >» Sections of Iron rolled by the Societe Cockerill at Seraing, Belfrium. ANGLES. Legs. Thickness. Weight per ft. Legs. Thickness. Weight per ft. si- X Si* 22.85* 31" X 小 A， 6.87* 5P X 4i# V 17. 5* 3i" X 31" 6. 7* 5i" X 3 沪 r 13. 5# X 才 5.74* SV X V 22.85* X r 7. 4* 5i# X 少 V 15.15. X 6.07* 5P X 3i" 12. 8» X 中 A" 6. 70 4 化 X 5i" 8_ 10. l* 出， X 中 3.88* 4” X 4 轳 H. 5* 才 X 中 r 5.07** 4A" X r 11. i* 中 X 5.07* ぐ X 3# iV 8.07* 中 X r 4.5W X 1 _ 10.77* 才 X Il-r 3.77* 31" X 10. l* 才 X 6.07* 3!， X 3iV 9.43* ず X 十 r 4.72» X ザ， 8.07* 中 X 中 r 3.57* 3Ä， X 7_ 4. X r 3.54* 3i" X 妒 7. 4* •NJ5. — rhe mmimum thiokaesses are given : they can be increased by nearly fifty per cent. -1 — 26 — * : L BEAMS. Depth. wiatii. Tliiclaiess. Weight per foot. .1 が.. .. fir 6。 •又* P ク • 5 姑-. .备ゲ 5 7 ぐ 4ぼ * $zv 39.“ .91 " , i ぃ h¥ 30.25 .n ク ， n ^ 20.15** s9i 41 、 3:” ^ u す , n " 22.15 ,tt .一 巧， . 上ヶ . n*. . 1 い .a. ♦- 26.9 # 1 い 3l " .H ¥ 26.S5* » 2ä%^ . . ^ \ し，”” M7 … ll'M !<* 20.15 tt 7 い 7iV .あ1 ノ - . 3金 f: 17 •” • 12.4 XÖT 你 ?i r .七 'r 10.7 : 5” aj ¥ 1 u，43tt 5-” . ' 2 * ： P 8.7 な 5 ^ ..W 11.43 # 4 が ' 2 ク 8.0 » N. B. The wiatlis and thicknesses are given at their minima, and can be • I - • » r ...... increased by a quarter of an inch or less. 一. 27 — . TEES: レ : Hea^ Stem. Tln^kneßS. Weight .per loot. .7!/' v W .fi 〇 ，、- # . 24-9 ft | 6} ^ 4 ド 20.8 n ” 62、 " m" ' h" '17.5 n ^ 6^ 4Ä" ぃ j " 23.5 tt ^ 6 ° 、4* " ä" V 18.8 v5i-r 、 *" ノん 5 tt ,5 妒 n ° ダ 14.0 n 5*" 3 •• IO.-2 * 5 A" r， 12.1 tt "54' " w メ 音'， 12.1 ，4 把 ず ,14.5 » .A\V' w .皆,’ 8.07 tt . 4 長,， 3.” ダ ,17.85* 4*" 3 击" を' 15.82** 4Ä" 、枝" も,， 10.4 * 一 31^ • す' を0 T0.7” 3äw 2聲 " 7.74、 _. %-h" 2} " ” ■fs" : 5.7” ，， N. B. Hie dimensions of the tees are invariable. — 28 CHANNELS. Depth. Width of Flanges. Thickness of Web* Weight per foot. iiH" 23.5» ic} " W 21.1* : 9i ° */# 26.0* 9i 〃 3*〃 ”•5* 9i ° 3” A" ai.a* 分，， 3*" 21.5* 7i ° 26.4* 7l " 3 長" 18.8» W 各，， 13.1* 5Ü" ず 10.8*» 4” 4，， 17.1* H 0 ■h” 6.9« N. B. The widths and thicknesses are given at their minima, and can be increased by a quarter of an inch or less. 一 29 — Sections of Iron Rolled by .De Leeuw and Phillipsen, Antwerp, Belgium. X BEAMS. Depth. Width. Thicks. Wt. per ft. Depth. Width. Thicks. Wt. per ft. nr, r 111.5.+ 9i° 440 5 tr ^ to It 19® to 27.5* 響 7° M 91-5 •+ 9° 4" to 4^^ r to w ず to 29.5* 6r Wf 77*+ sr 6 去" to 6 鉍" üv to w 39* to 45* 1 6!" 6*w 7〇#+ 8J" to 4#/ rto r 12. 5* to 29.5* 1 6" 6^ to 6 A" A -to y 57* to 67* 6" to6i" rto r 35* to 57* i5r' 6" to 6 為" 矗 "to $7* to 6 广 8" 5" to 5 }" r to i" W to 37.5«* 151" ii" to SW ä”。 r 57* to 68.5» 7i° 5" to W r tor 26* to 34.5* i5" 5i"t0 5g" ^ to 61* to 67* 8" 4" t<>4Ä" rto r 28.5* to 33.5** 5wto5|" n r 50.5 * to 67* 8" 4'， to 4*- r to af ai.5* to 33.5« V 6" to 6J" aVtoiT 57* to 67* 7iff 4" to4J" rto r 20.3 • to 27* 14" 6" to 6*" h " to W 53.8a to 64» 7i" to 3 お" A"to r 15.8* to 2^9 ； H" 5i,#to Ä^toü« 53.8* to 65.8** 7 表,, 4" to 4J" rto r 20.3* tO 27* 5*" to 5 お" 玆 "to 姑" 55.8» to 65* 7° to r A" to ^ i8.” to 24.3* i ず H" to b-A" 60.5* to 63.8** 广 to 3 聲" ☆" to 17.3* to 2i，S9 夏 ず 5i" to r to 祎" 53.5» to 59.8« er r to r 19.5* to 24.2** Si"tos^" g"to 1" 50.8* to 65* 6|" to 為" to A" 14.3* to 17.8* 叫" 5*^05^« ■ha to a " 43.5”〇 48.5«* 6h° Si v to 3 聲" Ä"t0 r i6* to 21* 12° 7j" to 7i" 1" to I" 70* to 80.5* 6i^ 3i り to 3*， A" to r 15.5* to 24, 12° 6" to 6|， 5 1* to 67* 6° 5" to 5!" rto r 25.3* to 31« 12° 6" to 6 が to H" 47* to 55* 6° 5^ to i\° 各,, い 'Y 14. to 19* I 2° 5 な to 5!，/ A" to 40.3* to 57* e,p 35^ to i\in ^ to r aa.5# to 25.3* 11° 5" to 5I" A" to 褚" 56.3* to 49.8* SH° 3*" to 3 鉍" to r 13.3* to 17.3** io° 6" io6 み，* r# to h° 54.5. to 57* si" 3 A"». 3«- Ä"to r 21.3* to 24.5* IO々 S°io 5i/; A" to 衧" 34» to 47» 5iv 5" to 3*々 r to a" 12.3* to 16.5* 1。， A\° to 他 Awto V 30.3« to 43* 中 to 3 i"to r 12.3. to 16.3* 10" 4" to 4 丑" 28.5* to 59* Si° to 3 ド 如” to 'V 13.5* to 18.3* 10" 4^ to 4 各" 為" to 矽 aa.5® to 27.5* 5" 4i" to 4 李'， rto r 21. S9 to 279 9 い 4暑" to 4}|" to 班" 34-3* to 39.5» ぐ i" to 3Ä* isf, to A" 11.8* to 15.5** 9i'， +i"to4{i" 8" to 教" 27* to 39* S,9 3i" to 3i» i" to H" 17.5. to が 9i° 才， to 4 ふ" if, to to 33.5* 4r to 3 A，' *##to r 12.3. to 皆 M"to 茲’ 21，ln tO 28.5* 4!" lv to 3j#, A" to U" 1 0.8 • to 16.5* 9if, iir, to 4 み《 i" to to 33.5* 4r 4" to 、ふ.1 r to 好” 9.8* to 13.5*» 9i° 3i"to4" 音" to 21* to 29.5* 4" 5" to 3 合" r to ^ 11.5* to 13.5® 9i" 3 為" to ぐ 蚤" to 枝" 21.5* to 33.5* 4/# 2 昼’, tO 2 聲” rto r 8* to io* N. B. Beams can bo rolled to any thicknesses and weights between tlie mini， mum and maximum sizes. — 30 — ■* ： v?-t-；v.t ^ ? ^ fp ^ rr •* パ.‘ 丨. - * ノ:. •''•ベ.？ ベ CHANNELS. Deptli. Width. Thickness. Wt. per ft. Depth. -- Wi 識. Thickuess. ■ .! •.■一 Wfc. pßi' ft. 14" r ■ ノ r 、 4” 3i" V • i8.3tt 3«， 1，1 3!.5* 5i\ 免"’' 12.8« • 12°> - r 音"、 n-sn ■ sV 、 十 •Ä4 ICY1 w 丑々 22.3* - 5*" - 中 、 .3.// ia..5 典 IO ガ 音'， ' 5[ .、 a" 、、 、 r 1!， 吹 3Ä" 、を"' 26.3* sv - V 啬 " ， 8 … 9i" * .H// a 5Ä" . 祝, 14,8 ‘ ' . 8^ 中 X» 18.8» i J" ' r 11.，5* ' 8p 3o5'// ^5* 5r ' i 聲" ，'ä" 7 ••卜 8*" . 3H" 上‘. -23* 5' . i" . 4” 8". 5Ä" ぐ V ダ aW 2 聲" 為" 12 ぶ 8々- . a" ' 4i々 ず 知 •' 15** 7i° 3 耖 21.3* 4 聲々 Ij" 9.8* 7i° 3レ 18.8* 4f，' ’ 'ャ ,t>/ lV 3iV 27.3* 4ド . ■r u.5tt 7+" 十 が 12.8， を, 14" rr x>t '16.19 4P ゲ， か 7， ' 6|'» 中 -h° 12.8» な V JL々 12.5* ゆ ず ■is" 12.5* • 4Ä" . 2° . 1。 ぶ*. 2 皆々 ■&" 12.3** ■■ 4i" 如’ 10午 ' .も V. f" 14.3** 4*〃 1 才〆 Ä" 9.3* 6" • ' * h .r. i/； i 十 3 费 4r . o--h" . iW . 7.5^ 6V 2}° r I5tt 4° ' -h" 、■ IQ-5* .6、 中 10.5* 4" v • ，5 ゲ 6，， —I 音'/ fi* r If，’ .み" 9-5* Si" ず 15.8* 斗".. iyj ' Ä" . . 7-5 # ^•B. 一 Owing to a mistake of the binder’s eight channel sections of depths from 9|" to Qiff were omitted from the catalogue from wliicla this tabid was pi*e-: pared. The thicknesses of the webs and tlie weights can be increased. 31 — ANGLES. T Legs. Thickness. Weight per foot. Legs. Thickness, Weight per toot. 1° 26.$n ダ X3" : 2r 9* : X4^ M° 20*» 4ド X ず Trr 6.9* 8"， X5;i" H° 28.5** 4 ド X2*" iV 6-4* 8»* .X4" S' メ パ. 3*» 4"- X4" n\ IOtt 7i，f xiYr 4" 、人 IY， ir 9 ゲ 7 b， x か ä" • 18.3* 4" x3r が 8* 6 録办 X3P •r' ず 4" 晴 & か 10.8* xs1^ ä" 2l9 4V X3" u° 8* - 6 か 父4か I9tt 4" X 喊" ■h“ 6.9* サ x6p 19.5» 4" X2j" M" 8» 6" x6" ao.8* 3l り X2|" t," 6tt 6，/ ><4J- 11 n 18.31 3ä" X2^ も： 6« 丨 い X4" aV 1 7.3 ね Hf/ X3i" SSW I7.5tt b" x-W 弱" 14.3* W1 w 8.3 林 6" X3i" 1 // s 15.3* w* w W1 7-5tt ； 5^ Xsh'f w 18.8« 3 各" Xif" iV 7.5* 5i" X4" ir 22.8** lVl X 十 6tt ^ 5 ジ X4" ii° 14.3* xaj^ 5.1* 5 ぐ X3p * Ä" 12* l\u X2U が 4 ゲ 5i* xsi" i" 16.8» 3f/y X3l" ii" va 7-5° 5h" X4" ir, i8.3tt X2^f/ Wl 7n 5 去" X.3j" 、者 r ntt 3 暑" X2^° Wk 6.9* X3V • v 12.5* ii" x か 合" 6,4* \ Sh° X 3/y 9n 3*" X2f" ぎ, 5-4* i 5" Xs° if 3*" X2W ， & r 6* 4iT'X4ip X H 15 ゲ JiVxsA" が 6.3* ] Wf i2.8tt 3" X5" が 6n 4轉"><5 吾" • w. 9 ゲ 3" x 2!" ir 6.7* w x4r M" 14.5* 3" X2^' ir 1， 4 聲ッ X4" U° 14.5* ダ/ w が 5 •な • ；. 4t/y X3i" M" 12.8» 中 X2 聲" ぎ 4.9* , x iY1 -h° 8tt 4" X2iVy 5* - Ah° X/\h° ' 12.8** 2 聲" X2!" 3.9* : 4*" X.3" U° 9-3* 2 聲" X2fi r 3ゲ 4l" X4|" n°. ii* 4.6 • ? 4i" xwf 105® xH* i" 6.4* ’ 4 ザ X2ä" • a" - 广 ir& そ ö" 5 ゲ . 4f/# X2yf n° 8.8* ず w* 3n Mi-" X2f/ …啬っ 5.8* 2 發" X a|/y iu 3.7* ; 44" -X 4" 10.5* i\n X2 去" V 3-4n : 4i" X 3 P 10 .3’ 3 // 10 2.7* 4 浐 X が ']r 11.8 作 2a, X2,J が 2.5 * 32 — • TEES. Head- stem - Wh per ft. Head. Stem. Wt.perft. » » » » »9 ß 9 0 o 0 m o * «« 99 a t» «« « »»« « 4» _ « *> • a 58 — 38 n R 8 58 8 38 5555* I I 55* 58 38 58 5«» 8 58 3 3 38 5 3 » 58 35«» 8 5# 555» I 5 9 t ン 5 o 8 5 3bo 1 O 56 5 -2. 0 o 9$ o. o 18 422 I 086 0. 2 I 92 Ivo 08 9757 76 9 5 2 5 5 98 5 98 7 5 76 メ 11 IIIOAII1IIII 1111 11111 III II I I xxxxxxx x xxxxxxx x x x xxxxxxx x x x x x x x x x x x xxxx x x x x x x x xxxx x x x x x x x 丄 lo y" ；• " A, li A i, ^ 0 3不 ^ " ^ %. * -^ 1& ^ ^ '^ ^ ^ 為 * |" |" ^ ^ ^" * ^ 為*|;5;;^" 5 〃 " 3 3 0» 2 0* 3433533332 3334-5 36 54332 2 0*332 ^—o* 253 3 2 2 2 I 2 21 30« 1 2 2 2 3332 2 2 2 x xx x xxx x x x x x x xx x x x x xxx x x x x x x x x xxxxx x x xxx x xxxx x x xx x x xxxx x x x 555544 4*4444 4 44 4 4 44444333333333333333333553 33? 3353333355333 n « 8 3 5 fl 3* * B B n 355555 3» 58 8 38 8 58 553* 3*8fc 3 58 3 3 5 58 3 J5 # 58 5 3» 8# 8 3838 3» 8 2J 9 5 2 8 15 1 36 9 7 5 3 9 5 28886 5416 45341 2 759916 I 470 70-6 o 5 9 58 I 2760 432 1 9 I 2 2 3 2222221122110 «211 111311111112211212221110 ^2II22I1J 211111 C* MiMr ärr^ärr ßßäpffßA^fff x x x x x xxxxx x x x x x xxx x xxx x x x x xx x x x xx x xxxx x x xxxx x xxx x xxx x xx x xx x |, *, 1 ^> 1 Tlr ^. 長 Ä ^, H H, 「CJX i, ^ ®K®^ l- 4 A, y" H, iJH-" " 為 丄 süoc Ä vf" M ff -r u lö " 1 , am" " ^r A, < i/ Äy" l, a" V" " 邊； ■ 4 4 5 344443333 4 5 33 4 3443395333 3 3 2 li 334333433326 3 36 4 4 2 0* 36 3433326 a#.Mrrä^^rr^rfi^^^err^rÄrr*rr*Mr^f r^rÄrrirÄHIMrsMrrrrrM^^ x x x x xxxxx x x x xxxxxxx x x x xxx x xx x xx x x x x x xx x x x x x x x x xx x xxxxx x x xxx 8 8 8 8 7 76 66666666666666666666666 55555555555555555555555 •- — 33 — UN KV EN LEGS. 6 x 6."..“. 4备 x 4 备 斗 -V 斗“ ♦••••， t ズ 5 « • ••• •• X ホ… 2 ^ X 2 J 2^ X 1} 2 X 2 •…. I 空 XI}.. »X 1^.. I|x 1].. IXI 1x2 ••… 1x1 •…. ☆金 a I i 64. 3 71. I 77. ^«4. 4 47.55^.357.261.9 i i ä ^ H 57.5 41 .8 46. 1 50.5 52. 5 36. 2 ^.843.4 f Ä i 21. 1 24.4-27. 5 n * m 20. 7 2*2. 2 25. 6 n I } n 9I14. 7 16.0,17.3 *8.6 i I #i i\ ' Ü } 10. 6|ii. 913. 1 14. 5 15. 5 9. 4 10. 4|ii. 5 ia. 6;i 6 Ä 1 ä i A A 6. 21 7. 18：«. 1319.05 9. 96 5. 27 6. 09,6. 881 7. 64 8. 40 Ä I h $0.657.5 57.5 4 5 i I Ä ^8. 6155. i 24. 8"28. 7 i ! A 14. 4 17.7 ☆ ! } l6. 2 10. Q 54.4 30. 6 l 75. 0 70. 0 i6. 8 A 66 丨 4. 34 2. 34j2. 88 3. 40 -2.03 2. 48:2.93 72 丨 2. ooh. 46 A ! Ä .9713- ¢>6 . 3412.88 h 4.99 5.9】 5.65 4.38 91.0 97. ll ii 76 .6, 56. I ^ • 3 卜 7. II I i 21. 2 22. * I 17. 8 f x4" …… , $r w”., 3" X 多" 2U X 2f， 5" x iV 3" X2° ボ X ず…. 2" X i" 長" 55*» lbs. 長" 28.7 “ Ä". 長' A".. ,.14.7 lbs. •9.4 tf ,.30.9 .14.6 “ • 7.4 “ . 6.5 “ Ä;;： .•37.5 "52.5 ..27.5 ..17.3 ,•11.5 ••55.0 ..17.5 lbs. Flats, all Sizes. Hounds, up to h" er yard of tlie Trenton sections are given instead of the weights per foot, this being tlie method employed by the company. 呈 《5 w •S V： II S Ä D bo _ •3.S •■4-( ^ 0 b/ 6 § 35 1§ 砂 W BEAMS. •200 5f 5 .6 り み 150 h 叫 叫 170 5i .6 125 4.79 •47 ici *35 5 .47 i loi ro5 4i ,ci 90 4i A 9 【25 4i 4 .57 } 9 35 9 8 70 80 3i •3 f 8 65 4 •5 7 6 55 51 •5 120 5 + 金 6 90 5 h i 6 6 50 •5 40 3 k 5 40 5 •Ä 士 5 30 4 37 5 A 4 P 4 4 18 2 w _ CHANNELS. »5 190 4 令 15 1对 120 4 I I40 4 3 叫 «5 j7 1 lci 60 旖 9 70 3i '4 •h 9 50 8 8 45 .26 33 2.2 .*20 7 2¢ \ 7 6 6 25¢ 2.0 •20 45 33 ^2 2} .40 .28 6 *22 .i • 18 5 4# 19 ii .20 •*20 5 15 u .ao Sections of Iron Iv oiled by the New Jersey Steel »and Iron Co, Trenton, New Jersey. U. S. A, 聲 9 8 6 5 4 7 1 TÄ 3 JL 1 (1 7 , 斗 r* ii 64 3- 5 8 c c A8 9 1_9 5 0 6 I • • • a.^0 • • • SS8 9 5 PT6 J 瀛 2 4M. 7 5 4 4 5 2 1 js • • • • s.i • . WT 3 4 9 X3 2 1H 0 4 5 415 丨 2J. 2 I 147. 140- - * 28. A.® 9. *is 2. 8 3 9 f^u • • • r.i I 5 0 ?> »5 5 7 Aß 4 1^« 7 X4 I 0. 6. ^ O. A Ö. Ä O. 5 0-211 i.. X X la 6 5 4. — 34 — Size 一 | Thickness — Inches, j Inches. v\ t . Der Ft,, in Jbs. f to I ito i 善 8 to i | 1 j tO 1 4 I J to l \ 2 to 4 to 6 4 to 7 4 a to ic 6 to 12 7 名 to i 5 [O to 1 と 15 to 2C IQ to 3C N. B. Tlie author lias heard that tlic Passaic Holling Mill Co. lias increased tlie number of its shapes, but lie lias not yet seen a copy of its new album. T1】g weights per yard arc given here also. ilxi^ 2 x 2^-Xl J 2^X2 4 X3 4 4aXJ 5 X3 5 X3i 3 - 16 to 5-16 3 - 16 to 5-16 ito| i to I 舞‘ to 脅 f to I t to f I to f i to 聲 ii to 1 4 2 to 4 3 to 6 4jto 7 2 to 9 to i? 9 to i{ 10 to iJ 11 to 2 く Uiiequal Siaes. AXGI.ES. Kqmil Sides. Sections of Iron Uollecl by the I^assaic Rolling Mill Co. Patterson， New Jersey. Ü. S. A. TEE IRON. Kqisal. Size — Inches. Thiele ness — Inches. Wt. per Ft., in lbs. I XI 舍 i 3— 16 i 各 I Jx U 3-16 & \ i J to a l!{ X I? 3-16 & | a to 3 2 XI + & 5-i6 ^ to 5 llx -2^ 5 — 16 ふ 貪 q to 6 3 X3 ^—3. /—1 6 & .j- 7 to IC 3 ^ X >2 7-16 & 9 to 1 J 4 X4 7-16 & } 11 to 13 Uiie<|«sal. 2+X 1* 3 3 X2 a s 6 4 X2 a 7h 5 X2j 1 to J 9 to 13 5 X3 t to 1 JO to 1*2 6 X4 各 to 金 16 to 1C 3 X4 ri CHANNEL BARS. Depth Inches. Flange Inches. Wt. per yd. in lbs. 6 - 8 - 9 一 12去一 2 to Q-ä- 2 to 2 逢 H to 5i 3 to 4 4 to 22-i to 56 30 to 5c 45 to 7c 85 to 14c 150 to 20c j Rounds and 1 Square r to 4r j Fiats V to 8 " wide I BEAMS. Height in Inches. 1 - 九 11 字 「一 .* 三0 e 窆… s Width of Flange in Inches. Thickness of Web in Inches. 200 5】 .6 iS 3.16 15〇 5 l 12 5-16 、7。 5! .6 IC 士 125 4.7? •48 JC 各 り 5 5 •47 IC-各 J05 4 8 ici 9ö 4 .35 9 85 4 •ゾ 9 7〇 •3 8 8〇 4> •37 8 65 斗 •3 7 6〇 3 a 3 6 5〇 3¢ •3 6 4〇 3 5 4〇 3 5-16 5 3〇 i 4 37 5 5-16 4 3〇 2! . i 4 18 5 - 32 • 6 6- 6 6 卜 3 - } 5 - 5 - 3.8 1 2 1.2 A4 0«4 3¥ OJ. to to to to to to to to to to to to to to Iff A8 13 6 6 6 1¢ A4 XT 1^4 6 38 1 2 1 2 T T -I T «5 2^ Vi~> 28 1^4 va- 0^ X4 l u 12 11112 2 2 3 •+ cy 6 x x x x x x xxxxxxxx 34 .r. 8 -i4 i IT 12 11112 2 0* 2J. 4 CJ» 6 — 35 — Section« of Iron Rolled by Carnegie Bros. & Co. , Union Iron Mills Pitteburgli. Pa. U. S. A. I BEAMS. CHANNEL BAUS. g 4 0 feD iSx； 1 lil 8 § ä? ö i|l Designation. «2 «M ei s «M '•§ «4H cd S "0 O S OO^ o 名 Designation. ① Ph ■+J To 0) の SM -p fco c3 S M *3=S.S i a 0 A OJ 0 in 口 u < 方 H 与 H 障 . — Lh«. Sq. In. In. In. Tn. Lbs. Sq. In. In. In. In. ；5： Light, 5〇. 15.0 •47 5.03 .02 I5" Light, 40. HOC •525 3.53 .0200 1 5 Heavy, 65. J9.5 •77 5.33 15" Heavy, 60. 18.ee .925 5.95 67. Bo. 20.1 24.O •67 •95 5.55 5.81 .Od ! i ゲ’ One Weight 70. 6.0C .318 3.01 ；;：； ゆ 1 2 Heavy, 12" Light, 22. S 6.75 .324 3.01 .0250 4 交. 1*2.6 •51 .96 4.64 .025 : [2" Heavy, 5c. 9.oc • 512 3.20 6o. 18.0 5.09 12" Light., $o. 9，cc •457 2 71 .C25O Ici Light, fo 士 "Heavy, 31.5 45. 9-5 !3.5 ■41 •79 4.54 4.92 .029 I2,f Heavy, 1。" One Weight 5。* 16. 15.0 c 4.8c .957 .329 3.21 a.52 f0 Light, rc,// Heavy, 9" Light ぐ 30. 9.0 • 52 4.32 1。" Light, *7-5 5J5 •300 2.45 .O3OÖ 45. 13.5 •77 4.77 1。〃 Huavy, 30. 9.0c •675 2.80 23.5 7.0 .26 4.01 .〇33 1。" Light, 10. 6.0c • $05 2.56 .0300 9 Heavy, 33- 9.9 .58 4-33 1。" Heavy, 55. 10.5c •755 3.01 9： 歡， 45 - 13.5 •75 4.94 •〇33 9" One Weight 9" Light, 14.5 4.55 .316 2.5c So. 15.0 .91 5.10 ,038 18. 54C • 305 2.43 •-333 •22. 6.6 •31 5.81 9" Heavy, 50. 9.0c •7。5 2.83 35. 10.5 •79 4-29 8" Light, 叫 3.75 .264 2.01 •。375 し, 卜 产 18. 5.4 3.61 •。43 8" Heavy, 15.5 4.65 *376 2.13 / Jleavy, 6" Light, 6" Heavy, 25. 7.5 •53 3.91 8" Light, i6. 4.8c .5〇3 2.30 .0375 *3-5 18. 4.1 54 •24 •46 3.24 3.46 •〇5 8" Heavy, a8. 8.4-: •755 2.75 •0429 5:: 砂 U, 5 Heavy, 4" Light, .〇6 7" : Light, 10.5 M5 •247 1.00 10. 5.0 •225 2.73 7" Heavy, 4.5 4.05 •575 2.15 M. 3.9 .405 2.91 2.48 1" 丁« 14 - 4.-2C .2()6 2.30 .0429 8. 2.4 •。75 ln Heavy, 20. 6.0c .554 .2.55 4 Heavy, 10. 5.0 .38 2.63 1.76 6" Light, 7.5 2.25 .196 .0500 _ 6" Heavy, 9.5 2.85 .296 r.86 6〃 Light, 10. 3.0c .127 1.98 .0500 6" Heavy, i6. 4.8c •5ス7 -2.28 5" Light, 6.5 1.95 .119 r.66 .0600 5" Heavy, 8.? 2.55 •539 r.73 .0600 5" Light, 9 - 2.7c •245 1.93 5" Heavy, 14. 4,2c •545 2.25 4" Light, 6. 1. 8c .246 1.62 .0750 斗" Heavy, 7. 2.IC .^i 1.70 4" Light, 7- 2,10 •244 1.74 •0750 4" Heavy, 9 - 2.7C •394 1.89 — 36 — ANGLE IKONS. T IRONS. Weights per Foot corresponding to thicknesses varying by み". I One cubic foot weighing 480 lbs. Size. Inches. r r V Ä" r Ä" r A" r Uf, r ii" 16 r Equal Logs. 6 x6 • • •• ... 19.7 21.7 24.2 •26.7 29.2 31.7 34 •つ 4 X4 .. 9.5 11.2 12.9 r4-5 16.2 17.9 19.5 •• 8.3 9.7 11.2 12.7 14.1 15.6 17.0 3i •• 7.7 9,0 10.4 [1.7 ゆ】 14.4 15.8 5 X3 5-9 7.2 8.4 9.7 10.9 12.2 • ■ 2 聲 X2j 5-4 6.5 7.7 8.F 2¢ X-2\ 4-9 5-9 7.0 8.c . , H X2\ 3.5 4-5 5.4 6.4 7.3 •• 2 X2 3.1 4.。 4.8 5.6 . . lj X l} 2.1 2.8 3.5 4.5 5.0 . • la XI! 1.8 2.4 5.0 3.6 • • . . ii Xi]- I.C 1.5 2.0 .. • • . . ij Xij 0.9 1.4 1.8 • # • • I X I 0.8 I.*2 1.6 . . • • • • i x 4 0.6 0.9 •• •• • • • • •• Unequal Legs. 6 X4 • . 15.9 i6.c 18.1 •20.2 •22.3 24.4 •26.4 5 X4 10.8 12.7 14.5 16.4 18.3 •20.2 22.0 5 X3i 10.2 11.9 13.7 J5.5 17.2 I9.O 20.8 5 X3 9.5 11.2 1 2.9 H-5 16.2 17.9 19.5 4 X3i 8.9 10.5 1 2.0 13.6 15.2 16.7 18.3 4 X3 8.3 9-7 11.2 12.7 14.] 15.6 17.0 3i X3 7.7 9.0 10.4 11.7 13.1 14.4 15.8 4.2 5.3 6.4 7-4 8.5 • • •• .. • • 3 4.4 5.5 6.7 7.8 9.0 . • • • • • 3 xa 4.。 5.0 6.0 7-1 8.1 . . . , . , . . 3-5 4.5 5-4 6 ベ 7.3 . . 馨 • . . 2 X l} _• Size, Flange by Stem. 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O f-"> Q ^ ^ OO \〇 ur> rr\ »- OOOvO Lr»r^>-« 〇 OC'O ^r\ rr\ *-. 〇0〇>0 «■r»rr\-»Ö0C'O げ \"*' — 。〇〇'〇 • • • • • • • • «■♦着 • • • • *••••••• ? • • • ►■< C« rA 寸 tr* げ|>〇 C^-OC O' 〇 〇_ヴへ、 寸 *J~i «^vO 卜- 〇〇 O' 〇 〇 ^ ^ ^ w 00 vO 寸 rr\ _ ON »n r ハ NH 0»00 VO 汁 C 丨〇 OC •〇サ •'f' H-Osl ヽ W\ ff>— i^OO 'ö "1* ^ 〇 1、 め O'VO 寸 C< 〇〇〇…， ハ^- O' •卜 w-, OÖOC'O ff\ O 00 vO U . ; ci ふ rA 4 vAvd 1^. 1^.00 CT* d d —* rA *4- ^ vA so t^CO O' O 2 ^ w 〇\ rf -o O' tr>0O O -N-v VO O' r< t-r> CC «-* づ *t、 〇 rrs W>00 f •寸 へ 〇 r^NO 0 r< ^05 2 ^ ONvO vr\C»Ot、 寸" OnsO *4- — 00 VA »V> O 1-^. ” CT'nO -1* t-J OC vO ^ * m cl rA vA vA >d l^-OC? 00 O' 0 d c< -f »AsC »O OÖ OC O' 0 •-； « 2 ^ w に m — awo 叶 c« 0 000 •OM — O'^C 汁 O n 、 ハ 〇 〇〇 00 〇 〇 wn 1A00 Q rr\ t^oo 〇 r-n \r\0C Q ，へ ir\00 〇 »•ハ moo 〇 >0 C< OO tr* hl、r/>Q *0 C« OO ^ 〇 \〇 C< OO »-J c^. O •>© c« 00 ^ rC • •二“ d rr\ r^. r}- «A tAsO sd OO OO O' Ö Ö ^ ^ C* rr» rA Lr,vO vO 1、 OO CO O' O M ^ ^ — 味— ^ ^ N4 ^ ^ ^ ►H C' t^w> "Of ••寸 >-* 〇»\〇 rr> tr> M OO サ、 〇 >•/> 11 1、 f ハ 00 rf 〇 u~> m t>- 00 〇、 二 1、 O' rj- O v^*tc^' へ •' •““cl c< rn rj- «4- »A vAvd vd r4co 00 O' cr> 0 O •-• c« c< r>A rj- ^ vA^d no ^ c^oo U C» 寸 \〇 00 〇 rr *.r\ O' ^ rn vr\ O' ^ ^ w>00 〇 c< 寸 vO 00 O P* 寸 vO Ö0 〇 『 ハ vr» 卜* u~> 〇 t-r* 〇 so \C — so c* 卜 " t~«» d 〇〇 rrs 〇〇 •»や 才 Ö* 才^' で 〇 vr» 〇 vr> ^ '〇 ^ ^ .;(4d ciA ベ 分寸* ~A lt»'0 nCC'»1、00 000'OsO 〇 m M i'rvr'j ■»寸 十 Wv'。 vO " >-1 M M M — *~-« vO 。1へ〇^'\(7'寸〇'»^00产ハ1'>»" ir» 〇 VT\ 〇 . .一 •》■! c< cl r-AfA «j-^-iA»AvOsd t^OC OO O' CT> 〇 O "-J «-1 c< C**^ rA*4''i-»A »«w L vr» 1、 00 O C« »-A め t>.CO 0 c« »'A tr* l^. 00 〇 O r-r\ «y% 卜〇〇 O c< 〇 寸 OO C« %〇 Ow~\Ow ハ ト》—!« ■ハ 〇 寸 OO C« >〇 〇 »-r\CTx»r> t^»i— vr>0 寸〇〇 C< >〇 〇 で で で • • c^cici^A fT^rt-Tt-vn vnso vO C'«. t*-00 00 O' ¢7» 0 OOMh C< C* C* «ijt SO ^ Ovsß c< O'V^C» OO «J^i-iOO サ〇卜 》«AOsO へ"' O'vOC^Q'^'vhOO ォ C> •才 Ot— ♦'Alx-O 寸〇 SO 〇 rA 1-. サ 00 o «j% Ox C< VO 〇 rr. t^» 1- 寸 OO C« W> O' *^>vO . •二》 4 h4 c< C< rt-iA»/\Lr\'0'd'0l>» t^.OO 〇〇 OO O' O' O' Ö 〇 〇 " ^ vooo O'O r/NrJ-t-T*vOOO O'O *-i «vr\Tj*t/>NOOO O'O »h rA'^-vA'OOO rr>vO ov c« xnoo «-• w» OO *-< -^- t^. 〇 r^,\0 〇 »m^'O O' rj vr>oq h< vr> 〇〇 « ^ l>» 〇 ^'〇 〇 * * * « »4 hJ C< c< c< rArArrv rj-«4-r}*»A «A^A vAvÖ vO vd f^OO 〇〇 〇〇 O' O' O' O 〇 ^ vO C< 〇〇 寸 〇 vO (S 〇〇 寸〇 \〇 rrs O' u~i i-< r ハ o> vr> «-< 卜 f\A O' u~i h O' ^ rlj C< U> |>. 0 (V> VT»00 O r ハ VO 〇〇 •— rAvO 〇 tn 寸\〇 O' fS 寸 t>-0'C» LO O c< ur»0O Ü 'v • * * t-I バ；；〆 d ^}-^-^}-xA w^ir\ vAvO vO \〇 tA t>* f*»00 OO 5h O •-> r« »■ ハ 叶 i^so 〇〇 〇〇 0 O m r» r>A ^ vr\«o t^oo O' Q ^ c« C< tj-so 〇〇 〇 C« 寸 VO 000c*t^> t^avi-.rA LT>t^O>»-. rr» U-» 0 C» 寸 S S Q. TS • • . • “バ c« c< rr»rA tr\ rr\ ^r\ *}■ vr\ir»vr\Lrv\0>0'0v0 I Thickness 1 in Inches. ^H*ccls-hf ^ •#8J olqn o Jaa •s Ä o gt bD .s II bß Jadi §JJ •SJ み e? T 0.¢ •!!_ T SPTJ slf £ ) r ll P15 •UJ« O 物 J® L tuo. c sas « 01151.1 Jtf h . lw ciJ ■ILOOii rrv H -NEIT: HiEd-N： 〇 K I a H J T: 〇 « LL Ön 〇 c» rfs© 〇〇 〇 >-<* rn t^. C^ c< *4-\〇 oö «»•iM C< C< ci r.r* rr\ r/»! rr> r ハ寸寸 rj* 寸寸寸 vr> vr» lt» lt\ vr» > 00 rj- «-i 〇〇 ir, «r* O l^. 叶 — C» 〇\〇 rr> 〇 〇〇 iT\ 0^\〇 〇 rf- >-« 〇〇 «ハ f'nOf% l->. w-\ r/N 〇 OO 'O ^ •-'OO'O c*OOCi-n r^i-öN^c h へ、 u~v t、 〇〇 〇 口 4 vr> 卜 ふ 《 r •ハ t^-*o 〇〇 cJ バふ 1 ハ rC.OO 〇 C« ■ef'vO rC. O' "j-vd — t-itf )-i M I-M c< C« C< C< C* IV> め rr\ »V> fVi «V\ 寸 rj- «r^- 寸寸寸 VTi W"\ vr\ w\ VJ 1.72 3.44 5.j6 6.88 8.59 10.51 12.03 J3-75 : 15.47 17.19 13.91 20.63 ^2.54 24.06 25.78 27.50 29.22 30.94 32.66 34-38 36.09 37.81 39*53 41.25 42.97 44.69 46.41 48.13 49.84 51.56 53.“ 55-co 00 ギ ミ q；S^rp 8£-ä8 与 M rrtvnvO 〇〇 〇 1-1 rr, »v\sOOC 〇 ►-. mvAvO 〇〇 〇 r-> rr\ «^sCOOO •-• rA \^\〇 〇〇 〇 •-< rA hhh M « 1-. "C*C«C« C«» ■ハ fv>"'»r/'iry>« ■ハ 寸寸七 .4 •オ寸 vrvvr*t_r\ is; 今 s i：^-% & 5-2.S， S.S' す SS S' =S M ^ 寸^1 00 O' - n ャ 〇 l ヽ ふ 〇’ d 4 O* cA t^OO* O* rA ^ 〇6 6 - <_ ri r- >H t< C-l t« C» C« C« r^rrv rr^ rr\ r^, rr\ -rf- ^ -rf- 5 «O rr. 〇> <-r, 〇〇 寸 〇 \〇 •'A O' tr\ dOO 寸〇 <〇 rn On ►-« 〇〇 寸 〇 no rr> O' u% m CO r*- 〇 tr» *-i NO C< OO 〇% vn 〇 vq *-< C>* ^OC ^ O vr> m \〇 c< CC »-A 〇 v/S 〇 \〇 — i-^. ivaqo 寸〇 M rA rj-vO t>. O' d r« nj- ur\ t^.OO ö ^ rT\ tr» <3 〇〇 O' C< *^-tArC cf'O T« r^K lAsOOOÖ ctM — 一” 一 cl Cl C* C 〇 一 寸 vrvvo t>. OO ON 0 M "r/N 叶 "LAvO t>.CO 〇*> 〇 一 C» P ハ 〇 O w^r-vOMso—'Or- NO»-i^«S h c< 1、 C< 1、 （S t、 c.i 00 rnoo rr\ 广ハ マ' cJ t'«. cj' ö C« «VN urwo 00 O' -• cj *4* lA tAoo 〇 v-1* rA rj-»c* 〇' 〇 C« rri vr»^0 OC M-I ►-<«»-.— — ■CHCIO r« O ^ r-r\ rr\ rr\ t'iy rrv m rh rf- 'rj- 'O OC rr\ O >-/> — !■、 W00 寸 〇 sOC<0O»'AO'， ハ h|>^ r» CC 寸 ◦ vO び CO へへ 才 9 «'aoo ci t^. rj so *- q vr\ O' *i*oo で h c« 1、 h \o o. u~v q 寸 O' .00 ö 1-* rA rj-vO f^- OC Ö >-> r-r» V^-CT' Ö C< ^r>vr»«，C) tA^c5 rAi vA^O 卜 》一 m •-< >-( i-i c< C< C< C< ' C< C< C< … … げ' rr» rr\ r-ri 寸 寸 寸寸寸 « «s rvA rn 寸寸 、r»\OvO t^-OO 00 O' O' 〇 M>-« rtf'r! rATt-^v^sOvO t、00 CO O' O' 〇 マ CJ VO 〇 ^〇〇 C< »O 〇 ^〇〇 CS so Ü *-r> ハ ト》 叫 W^ci^ml、 M v/^On で 1、ch 1^ 0 •-< c< 寸 wx t>»od Cf' »- rl »|-Lr»<0 〇〇 CT'-' Ö r^s lA'O CT» 〇 C< rA vA 1-1 m n c< c< d c< d «sw»*N"\»>A»v\mfV'»~*i 寸 才寸寸 % «1« S $ SL 1、 ^92. ^ O' -+ 0 '-n 0 VO h-1 «OC rr^oo 寸〇 >め〇 vA m >〇 r> f>* rAOO rA T ^ °. *t t て 才 S m O' P« 'O CT« r^vo Q ••ハ 1、 〇 寸卜 w 〇〇 C< m 7 r« vO O' rA •-■ c< ^h»-r\Nooooso c« r^\ 寸 so t^-oo 〇 •— r ハオ i-»» co on i-I cl »v> unso cr> 0 ^ >-< m 1-^ ei *-i h — ¢4" C4 C4 dc^mmr>/>rnfv'«r4'Tt_^h «0 ?r5a.q 孑;? 艺す Hi C* ， ハい VO N O' 0 »i r へ寸 vr> < 〇〇 〇 0 n rn 叶 J ぺ〇〇. ふ； m rA vAvO ベ C?» 〇 •; M — - ^.-t^ C-IdClCS C< C« cs rr, rr>rr,r^7r, $ai?§ ^at?8 i?&K：8 ?9,S8 ¥&；cg S^ICS . c^^so^o >0^000 ss；r---»o W O 0 0 0 O' O' O' 00 00 00 00 CO Nt'»Nr's'0'OsO»OvOw'*u'kv/*Vvr*l_r» 才寸 CJ 寸 で 17 9 1 でで 9 h ■で tr, Cr> i-H r,? ^ l-7 二で1 ^ t O' •- rr> vo ^ rv> M c« OA tj- 1X\ t>«.OC O' 〇 1-. rA -4- »^>vd cf* c5 »-< CS rr\ xAvd t>-eÖ cfs M c< W -4 - vA l>-od 卜 >_|M— (H C< C< C< H C» n C» C< «S-« rn r/' rrv fNTt rn ry> % H« W ? 〇 7 二 令名^ ^g'S'rs^Rs.'g s >-( r>A LT»vO 〇〇 0> 〇 »-(# c-« f'ry ^J-vO r^OO C> 〇 M d wavC 1^. OO O' 〇 C< »nÄ rt- lA'O hC4CtC4 C« C» C< C« (S d rA rA r/\ m r^, rn j.cg 2.19 3.28 4.38 547 6.56 7.66 8.75 ! 9.84 10.94 ia.03 13.13 14.22 15.51 16.41 17.50 18.59 19.69 20.78 21.83 22.97 24.06 25.16 26.25 27.34 28.44 29*53 30.63 31.7.2 32.81 33.91 35,00 1.04 2.08 3-13 4.17 5.21 6.15 7,29 8.33 9.38 10.42 11.46 12.50 13-54 14.58 15.63 16.67 17.71 13.75 19*79 20.83 21.88 22.92 23.96 25.00 26.04 27.08 28.13 巧 .17 30.21 31.25 32.29 35.33 I Thickness 1 in Inches. 七 H»— S+ #«!* 屯， ％ 啦 辦 H^2 -|2 H«ccI®Hk 味 rt|* 屯吻 游咖 鹏 咖笨 M MMh， M Hi M >H hHHMV~l r-i M M ( .aanKIXKS ) EH o o lil Tiv H Nn ■a w d 艺 〇ぱ I a H TI 〇 UIiVT： 恥 恥 o tß ILH-DIHM — 39 — 5 «l-f VO vw t>»r^OO •rf-O'vrt i-ivO c»O0 r^ON 寸 OvC>k«il、rAOO 寸 dvu~\w->oc«00 r/'\0"' 叶 〇 so r ハ 0、\C. ct O '-r» ri 0> げ、 C1» OO u~» ►- 〇〇 .で »- OO rh •-• O 〇 〇 'O Ö ¢4 Cr> Ö rr> \r,ZC •— rrwC^ O' — « rj-L"» 0s C* »i~» l'» C> «*r\ Vr,cc i-* >-n \C O' -h h O r< m —1 卜 t h »— C« CH C"t »V» * ■ハ广 へ》 •ハ 寸寸寸 U*» '■Ti W» v_r、>0 >〇 vo SO C>* t'» l->. 1、〇0 〇〇 5 -« 一 O t_ M d 寸サ 1 ハ《 ■T\W\'>OvOl''*l、 0000 CO O' O' O o O t-1 t-1 c< « »sr> rr\ OdOO 寸〇* OC_ 100 才 OvOdOO 寸 〇心 a 00 寸 Ö'0~0S' ハ •■■•卜 r ハ 0NLr>- t^r ハ ■ ■ ♦ • * • ■ a ■■•華 » * • • • • « • 9 % • • • • •••• CJ w\ 1、 〇 rv\ u%0O o mvO 〇〇 y-i r ハ sO O'« — 寸 sO O' (S 寸 r>- O' h c* eic^Cff^wr^rr» 寸 -寸寸 《■r* »れ 《_rv \〇 *0 1、 1»» t、 t>*00 CO ^*H N H 2.55 5.10 7.66 10.21 12.76 15.51 17.86 20.42 m.97 ! 25.52 ^8.07 50.63 33.18 35.7; 38.28 40.85 斗； .59 45.94 48.49 51.04 53.59 56.15 58.70 61.25 65.80 66.35 68.91 7146 74.01 76.56 79.11 I 81.67 TH 0 0 0 0 0 0 0 0 O Q O 0 0000 0000 0000 0000 0000 vr» 〇 »-a 〇 vr» 〇 i-A 〇 u-iO ir>0 - w\C >-^0 C) iA 〇 ir» 〇 vr> 〇 vr> 〇 t.r\ 〇 vrw 〇 vn 〇 c< tA o cs »A t^. o r^. ö c« »A i4. 0 c< vA t^. d d »A i>. ö r: »，- 1 1、 〇 « … t、 o —1 1-1 c« c< C< C« rr\ r^-\ rr\ rf-rj-rj-vrx mw» vr»sO vo vC nO f»» t>» l>» l>*00 5 «H- \r> 〇 寸 O' 〇> 寸 00 f ハ OC rr\ 20 1-.ur»0ir»0>^>O'rl- Ovri-O'rr» 守 CJN.f'n 1、 >0 •-■ >-rv 〇 O' r ハ CO " 1、 一< *〇 〇 vr% rJ-〇〇 ぐ ハ r>^ v© 〇 vr> O' 寸〇 O rr\ »•■■ • • « • ■•■参 •••響 ♦■»« • • • • ••••••• • C'» rj- iv. 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H 寸 〇〇 C« vO 〇 寸 〇〇 0» vO 〇 叶 〇〇 »1 tr% »sa t>» m u> O' *- *.r\ O' rr\ C^. CI 寸 1、 O' c» 寸 NO 〇 « 寸"0 CO H IV> tr» 〇〇 0 rr\ 〇 > a>r» 寸卜 O' *-• 寸 \〇 d ^j-sO oö M lA t>. O ci 斗' 〇 M rrs tr» OC 0 CH *+■ t ヽ cJ'mA «j^CO O *4" *-< m M >-< >-< c« C< d ri c«rr>r/'i»sr»rA^l ■寸 ■寸寸 め め vr» w\nO vO vO >0 *0 卜 © 〇>〇〇 vo vrv 寸 r ハ m 〇 0^00 vO 寸 f,， *- 〇 O'SO sO vr> *4* «»r* m 〇 0^00 <0 vr» Q rv% urv VO CO 〇 c* す'^ 〇〇 〇 H«»vso-vr^ cr*«^u^voooqc< ^f'O 〇〇 O ri «4-vo 〇〇 〇 r>r. tA c> ^ r}-\d cö d c» »A t>. O' >-< 1A00 d c< -4-so o ■- m » ■ハ i ヽ〇 t-iM — M c< c* c* c< め 《vn げ' »v» 寸 才寸寸 v/% vr> v/S め tr>vO \〇 \〇 s© を ” H 寸 N 一 寸 00 vr»00 c^urvCT'CI'OO^t^ 〇寸 寸 CO M ur\ O' M vO O' *^nO O t-< 00 O'O t>. O' 〇 *-t r，n vr» OO CT« ~ CJ r-n u^vO 1^. C> O CJ »V' ci *4*\〇 〇〇 d cJ tA. 0^ ^ f-r^ xr\ rl c< -i- vo 00 d c{ O' *- ^ vr> O' •-* ^»w\w"\w»'0'0v0'0 o rt 2.08 4.17 6.25 8.33 10.42 12.50 14.58 16.67 18.75 20.83 22.92 25.00 27.08 29.17 31.25 33-33 35.42 - 57.50 35-58 41.67 43.75 45.83 47.92 50.00 52.08 54.17 56.25 58.53 60.42 62.^0 64.58 66.67 Jj «4- OJ rrwo ONfvAvO 〇> r< vtnoo ti 寸 〇〇 ^ 寸卜〇 ^*0 ^ vO O' J+£0 — ^ ^ S 000 m hhdr« 十寸寸 v^vrvur» w>vO vO *〇 > 1、 1^00 〇〇 〇〇 O' O' O c； 4^« 〇 2 <2 § 3 ? ^ -丨， 1 00 so -?h cs 000 vr\^ k-i a*r>.»r\ o>t^ vr»r^>ooo vo O og»o 〇 〇〇 w~\ O' O' O'«» CO 00 CO t>» t^so vo <5 <5 '〇 ^ t^'V0*C'UC' T す T オ オで で1^\ M rA»Al く O' rrv iA r>. O' W rA\ »A t>. ^ fv>w\ い 。 でで卜 や*""1 ^ ^ = T C*"C«»'A»VNW>«V>/V> 寸寸 寸寸寸 W\ *^SO vO Cs «v\ LT»eo m 寸 vo 〇\ 寸 1、 〇 *v» vr»eo •-< *v> 〇 O' v-< ^ O Ci vr\ 〇〇 〇 »v^vO c» m す^^ 0^00 l'v VO UTV *4- m C» c« >-i 〇 O' O' 00 1->.\〇 \〇 ur> 寸す r ぐ cj •-• *-jO CT'OOOO m rr> iA t^. 〇\ >4 rA »A t^. ^ r^s lA»0 〇〇 Ö ■^•'O'OO Ö r< 寸 vO CO O rt rA w> I、 = w »h >-4 tS c< C< rn rf\ r^\ rr\ r}*»r*rr^t* 'T vr> w% vr\ u^vo C5 OO tr\ rrv 〇 〇〇 w> rr* 〇 〇〇めめ〇 CO ^ *v\ 〇 〇〇 vr> ^r> 〇 〇〇 vr» »y^ Q 〇〇 vr\ C 00 ^ 5 00 r^.vO rrt c< ►-! ö 00 r^vo rr. t-j q CO t^.vo urv rr\ cj Ö SO t^vO tn rC ^ ^ . ; vA !>. O' hh rr\ iA VO 〇〇 (5 d *|-vO OO Ö M rÄvr»t>. rr>vr»' 000 〇 C« *4*'〇 °® 〇 H»«h hh"C< め》' 'ハ… 寸寸 寸寸寸 め' ■r'w''vnw'''° I Thickness | 1 in Inches. ^-ice«l®H^ 母《丨*» お-:« a|®ie(«^es!f •ZjtrH «ま r-]^-|ce«i2 -*H- 杉-：« ボ ♦コ J^Ha5^2 M HCHMH) HHHH- M M »H Mh-MC» ( . 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O O v 〇+ ur\ 。 ％〇 -• »O t» t、 C< 〇〇 r ハ； 》 汁い 寸〇 * ■"< M ci cl r,\ rö «4* "4* »A vr»vO \〇 l A «4.00 cf» 〇 〇 h — cl“ 》vir ハ M — »■«►■一《 — h 一《 M 1-4 M OD vO M »v> «.r»\0 CO O' W rf-«0 O' O " Q0 ^ tJ- \r> U"»xO 1、 l、O0 OO O' C> 〇 O •-• — d ct-1 — h — 00 0 0 0 0 0 0 0 0 0 0 0 0 OOOQ 0 0 0 0 0 0 0 0 O Q o Q o Q o Q 〇 O ^0*^0 vr> 〇 cr\ o w% O vr» o vr» 〇 vr» 〇 v/> 〇 tr\ 〇 vr» 〇 〇 m 〇 u-> 〇 m c< C*rv>rr> 寸寸 》A wvcj >0 C^OO OO 0s Ö c5“》-^ci tAvO >-t を 寸 O' OO'O u%*f- d t-1 0^20 NO Ooo t^»T\ rAO 〇 Os t^.vO 000 SO U~\ *vn " 〇 . , «tj- 0s 寸 CS オ Qn *v\oü rAOo rr^oo rr» c^. «S C* c< vO •— sO ” \〇 — u*> 〇 〇 %r\ 〇 vr» • • • ■ • • • • t •參 • •••• • • « « • • • • • • • • ••«• i-> M C< Ci fVA rr\ 寸寸 W'jk^TvsCsO l、t、OOCO O' O' 〇 〇 — 卜 < c«CH*'Arr> サ寸 va«^1 一 — «Mh 云 O'OO vO «m>00 »v>r^.M j^. u, s£> |-H w-i 〇 wr> 〇 • •*•• • • • • • • • • • • _ • • • • • • • • • • • • • H h C* C« «V、 《v> rj •寸 '■ハ ぱ\ O vC !•、 1 ヽ い、 〇〇 〇〇 0s O' 〇 〇 -« h rr» 寸寸 Lr\ l-t HH »-t H4 fl 1— • t-< >-1 «-r\ 〇 vO h-t 1、〇<1、^0〇め3〇 才 O'*i*0^s>0'OHvO . r« 00 f^sOO fr\ O' 寸 On lt» 〇 寸 CT« r.、30 M 1、 >~i 〇 〇 W\ 3n ri- OO f^>00 r* *-< '〇 O O' 寸 OO rr> t、 ぐ《» O <-i 〇 vr\ • ••■ • • • • ♦■•■ ••♦■ • • • • • • • • • • • • • ■ • • <~I 一 n " »s、 m »i* 寸ネ Wv tr\>o NO 1、 rs.ao CO (7» a\ O' 〇 〇 一 卜 rr. rn rl- •-■ 一 t— 1 t— i »-i »-< V-( t— 1 V- 1 u OO u% •VN i ヽ H tr» O' rr>\0 〇 才 OC *-i vrv O' »'ハ' 〇 〇 寸 _"X3 *-« u~» O' mvO 〇 寸 OO t-> ^Tx r ■ハ》 〇 〇 寸 〇〇 IV» 1 ヽ ト >0 。 W\ 〇> r ハ 30 C* VO —1 WT\ 〇 rJ-〇〇 «v> t>- *-H \〇 〇 u-> 〇> moo c< »O >-< vr, 〇 «»•礫 • ■ • * « • • • • • • • ■•参 ■ •■_> ■ • • • -1 *-< C< <■* rr\ rr\ r/-N «J- rj- vr> LnvO \〇1、 い、 い、 3000 O'* 〇 〇 〇 t- •-< M C* rv% rf Hhi M M »1 ^ M »H i c< サ a 十 p«-OH*ir ハ u-,'30 〇 .0>c^ ^t*vOcO Q m ur»c^»0>M ensO 〇〇 〇 サ OC cs O >-( ir\u>r»->O0 C-< cic«C«"'v<'A'4 ■寸 め、 ハ ば'»' C'O l ヽ C>»00 〇〇 〇〇 〇> 〇 〇 〇 >-( to-, r» C» rA » *-« o~» 〇> r/-. t-. 〇 h ” cJ d cliv» 寸 v/> u~»0 \〇 \Ot'«*V'>*CO 〇〇 OO O' 〇 〇 〇 **-■ t-i c< 6 ふ M M M M — c 一 O'SC l>*sO rr^ rr\ c< O O'OO t>.\0»-r> h-t 〇 O'OO CO 1、\〇1_/>サめヴ《〇 rv» 1、 — 》 »J'k 。、 m 1、 一 la O' rc\ \〇 〇 寸 〇〇 cl \〇 〇 寸 〇〇 " O' >— »v> 1、 一 u~» m « i-i c» c« rr\ rr\ rr\ vr»ur» vr>*o so 000000 O^os。。。 一 Mt*r« ' —4 M M 一 h >"H c Kht »-n 〇 OO u-> rn Q OO «Y^ rr» 〇 OO u-\ r>-» Q OO rn O OO u-\ 〇 OO w> ivn 〇 〇〇 vr» r^. 〇 . rr»l、e*1_rv00c<'OÖ «•ハ l、~u •、〇 Or^NCÖ u-»CC C^VO 〇 -* »-1 MCrA 寸寸寸 tA WTvsO <〇 C^* l、CO OO O' O' 〇 〇 Ö 一*-1 ベ O' 〇 •ハ《" too 寸 〇\〇け《3〇 rr\ \r\ f-t f^rr%0>«^ i-^ l^rAC% ur»i-< t^»*r\CO ^OvC c>00 寸〇 f で 1、 〇 tJ- 〇〇 ft t ハ 30 rs LT» CT'' fVN so 〇 >-■ 寸 OO M c> C< vO O' f ハ 1、 〇 叶 1、 ►- , ハ ' W ri »1 CH C« C» rr\"ArA^- '4-u-»vAv/,vd'0*0t'^ t>>00 〇〇 OO O' Ö 〇 Ö — — >■* HH I" M m マ 〇〇 寸 no »VNOO C* vO 一 w» ひ 寸 so 卜* ■» \〇 〇 寸 ry>cO c* \〇 nh lt> CT» 寸 30 rr\ 1、 — >0 O で'^ Q ， ハ 1、 〇 才 1、 〇 4 1、 一 寸 oc — 〇〇 hh \.r\so r* >o O' 〇 m — xiC4C<“ rnrvr»rA*t* Tj-r}-tA»A vr>\0 sO ^ t>» t>. 1 く OO OCOOC'O'O'OO*^ iO OO « 〇才 C* げ\0〇 _ 才 t、 〇 ltnOO m 寸 O' r« OO >-> #V»sO O' C» WV30 〇 rrs»0 〇> ヴ 寸 t>» 〇 r •ご' 〇 O' rr> sc O' rr» OCvO r* wr\0^c< vr\ C« vr> CC C< ij%OC u%CO t— u^OO ㈣ •1 “； C»“ cI*^^ArA ^ \AvO "〇 \〇 CSO 〇〇 OC O' O' O' 〇" O « め w\00 h"fv\i_r»voooox。 一 rr% す tA'OOOC'O *-• f'Art-vrvvooo 〇>〇 *-< rviH-vr»>000 O'O W>c n u-\ 50 〇〇 — 斗 1、 O r^\0 〇 »vssO CT» c< «j%oo « u> OO •- ■寸 1、 Ö «>'0 0 • ■•• •••« •••« •••• • • ■ • •••• • • h i-h —1 c< CH 〇 m rr» rr\ u~»vr\ u~>vO VO vO 1、 【、 l、00 00 00 0s O' O I Thickness I in Iuches. ?S1SH®32 七 ベ 2— »担'1!« CH M •-> » PI 卜《* ■—卜 HM 一 C< 1 (awü ^ J H Ä oo} • Izl o tf I a H TIO tf EH ^I fo Fq o — 42 — *> 9f 一 O' O' O' O OQ OC OO CO 卜 C^NO vO »-Tv w~i 寸寸叶 rrirwrAfsn N O C< h v-i -< 〇 〇 1、 で で 二 ^ ウ でで 1 卜 で/' ハー》 Qn 1、 vy\ rv'« *-1 〇\ 1、 … fV\ >-< 〇 1、 w» r •ハ »-4 〇> »-r\ m C* 广 ハ*'*'' 寸 v/"\vo C>» 1 ヽ 〇〇 O' 〇 m ►-! rr\ ur* u~i vo l>.00 O' O' 〇 >— i c* rr\ rv> tJ* vr\ HiVtMH hhhHH HMMCH M C< C* C* C« C« C« C« OO VO 汁 ^ H O' VA -1 〇\〇〇 \〇 寸 《 〇 ウでで 1 ©''〇 寸〇 Ooou^m MO>t^.vr\ c< OOOSO 寸 《ONl ヽ vr>rrsOOOvo-^*ciO ; " rr» rr\ 4 vr»>o |>»〇〇 〇\ 〇 〇 m c< -4- vr* \〇 C>. t^oo c* **a 04 一 hM 一 M — H MW 一》-« C< C* C< C* C< W C* »• -1， H .766 1.55 2.30 3.06 3』3 4.59 5.36 6.13 6.89 7.66 8.42 9.19 9.95 10.72 11.48 12.25 13.02 13.73 455 15.51 16.08 16.84 17.61 18.38 19J4 19.91 20.67 aT.44 22.20 22.97 ^3.73 24-50 »■ « 0 0 0 y7' O 0 0 vr» Q u> 〇 ir> 〇 vr* 〇 Q vr* 〇 vr\ Q vrv 〇 u> O . ^ ^ ^ 17 cj q t>. vr\ c< 0 t>* »T» c< 0 t>. vr» c< q i->. w% c< q r^. c< o M C< … 寺 *-r\vO »0 t^»00 O « C< ci rr* rj- iA vr*vO t>»0O 00 O ^ — Clrr »寸 KtMM hMM — M --1 »-1 «-< M M c* C< c* C* C< C* — •734 1.47 2.20 2.94 3.67 4.41 5.14 5.88 6.61 7.34 8.08 8.81 9.55 10.28 11.02 11.75 12.48 13.22 13.95 14.69 15.44 16.16 16.89 17.63 18.56 19.09 19.8; 20.56 21.30 22.03 22,77 23.50 ^"iei _ •7 了 9 1.44 2.16 а. 88 3.59 1 4.31 5.03 5.75 б. 47 7.19 7.91 8.63 9-34 10.06 10.78 11.50 12.12 12.94 13.60 H.58 15.09 15.81 16.55 17.25 17.97 18.69 19.41 ao.13 20.84 21.56 22.25 23.00 _ «VN Q M «M >-« c4r«c4rrkP/\"> サ寸 《4-Lrt め i/iv© \〇 \〇 h 1、 r^.OO OO OO OO Cv O' 0> 〇 〇 ^ 〇〇 で ^ 〇 !>• ^- OO lt\ f< CJ'vO で O 1、 寸 hoo ir\ d Qvso rr>i 〇 OO lt» •-•Cici »v« 夺寸 tAsoi、 l~^00 O' O' O *-« *-T c« "tj- vriso \〇 r^OO 00 9>- 0 c< 二 .688 1.38 2.06 2.75 5-44 : 4.*3 4.81 5.5〇 6.19 6.88 7.56 8.25 8.94 9.63 10.31 11.00 11460 12.38 13.06 15.75 14.44 J5.I3 15.81 16.50 17.19 17.88 18.56 I9.M 19.94 20.65 21.51 22.00 ム H c< l> ••: J* C* O' »o r ハ 0 00 ir» C» O'VO #vi 一 CC ，- ハ d O' 1、 才 ►- OO m ka 〇 1、 叶 _ ©〇 < f/> 〇 で で O *0 〇 卜 产ハ 〇 r>. ^ r» 〇 1、 寸 Ö 1、 寸 〇 1、 + _ 1、 ♦ CC 叶 h 0¢ 寸 *■» 〇〇 v/> m 寸寸 vnvOvC t、00 00 0> 〇 0 ►■•cicirr» 寸 オ ir>»o »〇 1、〇〇 〇〇 O' 〇 〇 一 t— mm •-«>—>—<•-* M M M Mk» 一 to« HC'iCIC'l % H vo vy~> ■— 卜、 r ハ cc 叶 ひ ►— VO CO rr\0、 十。 \〇 «-t'f'ACC 计 >-1 \〇 «S 00 fw*%Os サ Q vO «V\ CJvvO て、 c* O' wr» cs <50 u~v — 00» ハ*- 〇〇 寸 w t、 ォ 〇1、 サ 〇1、》^\〇>0め〇 m H C« rv\ r>rs 寸 … tj^\Q 1、 lA CO O' C^> (5 二 h c< rr, lt» t,r\ vO l、ö^ 0> 〇 _ <-> —一 hh_ •- •-» m >-* — 1 r* サ H 寸 00 C« so 〇 外 00 »■n — a'fs-Nt's.H-i «-r, 〇\ rv»0O C-l'OO'+OOMsOO nC C< 〇> vr* C< OO ^ ~ 卜 叶 0^0 产 六 O^'C r* 〇〇 »ハ >— OC 寸〇 1、 》 ■ハ 〇 \〇 rv\ ，ハ 〇* 〇〇 w~> h h c< m m >-r\ *jwO 1、 ！>• CC OO O' 。 〇 一 C* " rrs オサ vr， \〇 vC 1 ヽ 1、 〇〇 O' O'* 〇 «• H xr\ C< wriOO 〇 rr\ w%00 〇 rr\ u~»O0 〇 … »-r»00 O rr, u~»00 〇 m w\0C 〇 rrs ur>CO 〇 m vr 〇 xc c* oc •»« C '〇 ^ ^C* ~ rr ^ C| 00 fs. ^ 〇 * m m c« r0 sd l>. 00 00 O' O Om — ch *«/1~、す|^ぃ1〇\〇|^〇〇〇〇ひ〇. — ^ W ^ ^ im N4 — • «Sf Ci O' 〇 rl rr «寸 u~v\0 0.00 〇〇 〇> O •— trv \〇 1、 OC 〇*— c< 广ハ r- ハ 叶 1ハ \〇 l、CO O' 〇 '〇び〇〇 寸 0>0r«ac 寸 〇1、》 ■ハ O'w* — l、rv\ONtr> — 〇〇 才 〇%〇 c«0C 叶 OvOC^OOtr» ►h 一 cJ K~> ^}- «4* '-^»no >o 1 二 t>-oö er» 0s ö 〇 c* w\v^ t、 t、oc oc 0^ \ Ci 汁 O' O^oc cc l、\OvCLTt 寸叶 一》- <0 c» CT'OC OO 1、nCnO ば' 今* +* ■ハ"'' "一*'~<〇 げ '二1〉 で 〇'…— い' r/NO'U'>— »>.»■/> O' LT> ü 'C1 C OC 寸 Ovc c* oc «4- 〇 SO C< oc 寸 5 C< fv% -4" rj- »r> ^\〇 1、1>*0〇〇〇^»(5(5“ 一 cl rr\ rr> «4- nf- <-^\〇 1、 卜 〇〇ふ i" 00 卜' ハ— OOONC rj- C« r^, rnt OC \〇 «1* r< O OC irs/VN — l^rf-c* 0 vr>-- t^^OC *4*q^O c^t^.r-ncr' °C — げ.0〇 寸〇 vO — 、、 rr. a 一一 c< c< »t* «r\ ur\*0 \〇 t^OO 〇〇 O' O' (5 Ö >-• ♦'ス 广 »AvO vC l 之べ 06 た O rr* vO rrt Oh vr> *- CC 寸。 nO O' vr» »- 00 寸〇 »O «v> O' vr, — 〇〇 寸〇 \〇 *v\ O' u~» 一 〇〇 叶 〇 w>i~«sO 〇 〇〇 "'>0>wf\ 〇 "-C — O- r^OO す Ö w» \〇 c* 〇〇 « •ハ un () 〇 — 1、 rrvoo Q 一-hC« c< rr\ f\-v vr> vr^vO \〇 Cn»1 ヽ aoO'O'O。《 d ci rn «i-'+tA»Avd'd 1^.00 i Thickness 1 in Inches. • H し!》 十'—' 取 咖 S!^H*^|2 帝《!» 丨长 H« ajs n VO O' Q O'VO Ml>»0 •- O' 0 〇， c» 〇 »ハ 00 〇 OO vr» O 〇 i-t 〇〇 寸 〇 •« 〇〇 *〇 オオ寸 O' c< '〇 ^ '〇 〇 vO vO ^ ^ T 〇 〇 ts 1 ハ r、 〇 fvAvo O' n wi oc r< 10 O' fs \Ci 〇 •-« vr> 〇> 广ハ OO c* »〇 ” 1 ハ 0 '-r' U ^ 寸才 + 寸 vr*u-1w\w、>C'0'0t'^N 卜 00 00 O' O' O' 〇 〇。 一《"« •叶寸 Weight of 〇 Bar I One Ft. Ion 劣. r/s vr»Q t^xrsvo 0^*+i-< 〇 ►- ^•O'vO vr>f^O 卜" >〇〇 *1 〇〇 vr\ I^/^•«^QO^OO t>. vO ir> tr* «■/ >\〇 \〇 t'*»00 CT» 〇 OO 〇 ^ va _• • • • • • » • ••♦参 • • • • «•參 • • • • • • _y 鲁 _• Oh — Cl — 寸 v^tvo t>*C50 00 O' O — " r/> rf- t_nvC t^OO O' 〇 C« W'+'-O'O00 OQ — 1 ■«叫 h 卜 《mmm C« c* c* r* c* c* #^r>nr^*^A rr\ m rr\ ^ Weight of □ Bar One Ft. long.; J3.33 14.18 15.05 !5.95 16.88 17.83 18.80 19.80 20.83 21.89 22.97 24.08 2$.2l 二 6.37 27.55 28.76 30.00 31.26 ル 55 53.87 55.21 56.58 37.97 59.39 40.85 4M。 45.80 45-35 46.88 48.45 5〇.〇5 51.68 If Thickness or Diameter 丨 | in Inches. w n Area of 〇 Bar in sq. inches.! *-• ^vO ►- rr» ir»oo c» OO \r\ fr\ rrs サ nO 〇 ir> 〇 O' 〇 O' u> J ^ ^ m C« 卜 〇>\〇 00 nCOCvO*-* — OO 〇 …"〇 寸 t'» 1、 ，へ 七 rrv 1、 …》〇 W\ 。 一 OO O C< 峰 1、*— u~ »か 叶 〇|>»オ》-〇〇' 00 000 '〇 r< vr»oo C* •— r-*rr> 〇 OO vO OOO OO — h «"rAP/Nrj" vrwO »〇 ('■»OO O- — C< l'*0'0" 寸 vrxt^O- h •ニニ-: _ •ニー • d C： パ cJ Ci Area of □ Bar in sq. inches. .0039 .0156 •0552 .0625 •0977 • 1406 バ 914 .*2500 .3164 •;9〇6 •4727 •5625 •6602 •7656 •8789 1.0000 1.1289 1.1656 1.4102 1.5625 1.7227 1.8906 2.0664 2.2500 2.4414 2.6406 2.8477 5.0625 5.285 a 5.5156 5-75^9 Weight of 〇 Bar One Ft. lonq：. O *- c» rf-vo CO — 叶 CO rr. 00 叶 >— OO rr\ r» *-< 0 〇 〇 O C» rr\ tr\ C>0 ■-< 才 00 ズ叶 CT» \〇 »J~. vO 〇 ir-, r» o) »v> t、 〇 〇 〇 — , —< 〇\ On vt~> •— 〇 •-> 〇 O ^ OOO で rj- q *n^ \q 〇> fsnsO O «r\ O' rt- OO で^' す 〇 '〇 ^ 〇〇 一*>< m m d C< C* fi r^\ rr\ vO f». OO 00 O' O' Weight of □ Bar One Ft. Ion*?. ^ d 00 \〇 On 〇〇 vr* C< nO w. c» 〇 rry rr\ 〇\ t-i 〇〇 cl MOO O OO ^ ^ Oc*sO»v>eAvr»Ot^. rr%sO — O Ö 寸 〇〇〇 〇 〇 〇 〇 *-< CJ 寸\〇 〇〇〇 m vr, OO dvoON rr\c>.C t'*. c« t>. r^OO w»i»jOO す fj CT» ^ • • c< C< C< rn »4- nt* iA iAvO vO l>.00 OO O' 〇 O ^ Thickness or Diameter in Inches. H2h«HS ^«|Srt]*K^ H«a|2 •和； •屯 ♦皱中：3： ® *x rc • » £ 1 0 at ^ b«l sfq tc f (> > i* .4OOJ v lflsa ^ flo •Jsro M I EH II-0.ao « AV fe o sar^ m CLN： 110 PH a.N: d c^OO ir% ct^oc 令.《 ika rr. 1-^vOvOsO 000 > r+-oc CH t^cl oou-xd 〇 OOt^t^t^OO O'« •+ t>. « \〇 i-i NfAOOC CJOO ^ « oo 寸 f"00w'\c<0'>l、 寸 — O'nO 寸 《hOnI-、4 〇〇〇〇〇^〇 o r ハ m 寸 ，ハ lt»\o rA. eo <> 〇 *4 ►-* c? r-A *4- *4 - t^.oo o c< CS c« rr\ m rn m rr> rr\ rr\ m rr\ rr\ rr\ m r/\ 寸寸寸 + 斗寸 寸寸 寸寸 寸づ Area ot □ Bar in sq. inches. 36.000 36.754 37.516 38.285 39.063 39.848 40.64 1 41 .441 42.250 43.066 43 •名 91 44.725 45.563 46.410 47*266 48.129 件〇〇〇 49』79 50.766 51.660 52.563 53.473 54 •州 55.316 56.250 57.191 58.I41 59.098 60.06 3 61.035 62.016 fti.cns VVeigiit of O Bar One Ft. 10112 f. W* げ け ^ rAvnt>*。 «S-INC5 O' C> \〇 〇 r^-〇〇 rv> 卜 C» IS C> OO ^ O' OO Q rf-vo 00 〇 d 士 C?» f-nvo OC Ö C* ^ t>. 〇 ri ^ C< rj- l て ふ“— O' 0s* 0> 〇 0000 Hi « »h «- c* C< c* rrs «v> *vn r>r\ 寸寸皆 寸寸 \_r» ，_r> ，，、 vr*vO sC W ei ざ lit of □ Bar One Ft. long. 120.0 122.5 125.1 127.6 130.2 132.8 135.5 138.1 140.8 145.6 146.3 149.1 151.9 154.7 _ 157.6 160.4 163.3 166.3 169.2 172.2 175.2 178.2 181.3 184.4 187.5 190.6 195-8 197.0 200.1 203.5 206.7 *2 10.0 Tmcknerfs or Diameter in Inches. O i* 3|i O 念 Ö C» -rf* C< vO »m~sO »f-OO C>» *-< 〇 t-r\t^. u~»0'0'vr<00\0 ►-< »-( 00 M 〇\〇 •ハ ^OC vONOvOf^OCO «'ハ' O O •^Ou~> C»G^vO r-n C* c* rn C>c« ^0^0 'O^'OOO u~v CT' r.~! 卜 •-« VO O rt* O' *v>CO — \〇^-\〇1-( •0**^V0C^ I'J- *sr>00 •+ CT* »-T» ^ 'C ri cs rrv »A ム tAvd \〇 t^.OO OO O' O' O Ö ^ •— C* C» ^ VT\sO — 卜《 »hm — m *-* d c< c< r< c< c* d c-^-〇> vr,-* C't>»sO>OvC t-^ C)r«\CM\OMC?'vO 、ハ 十寸十 \〇©0»1，广. O <-ri 〇 v.-% 〇 m — vO 000 で O' vr> t-j. rrs 〇 vo r' O' OO »-n C* r^v 〇 ^ ^ 'O'Ot^-t^.COOOO'CT' 00*^»-< c< r<-trA*4 - lA'^i'O'O r^.OCOOCT' 〇 O ^ r 产 r/* •斗 LT 一*" « hh m •-! c* c« c< M c< C» c« c< c< c< c< d c> c< m rrs rr\ rr\ rr> rr\ rr< ■BaoH 0110 〇 JO HT^TO \\ 〇% M iri >— 一《 vr\*~»OOr« t^. »T> c> vr»OvO vr^vo O^r^O O' 〇 *VN O' \〇 vr»\C O' S ' て， で vO >-^ t-r\ O «r, 〇 w-^ 〇 \〇 c» CO 令— 1、 寸 OC vO 寸 •-< 〇 〇〇 vO vr, r}- rr. c* + 二 い、0^ 〇 — rrv 斗' O 1、 CT' 〇 c< »-A C^-OO 〇 ri r-rs -A O' k-I CH r}- 'C 〇〇 〇 c» す寸 す 十寸 ，ハ ，-ハ Vi~\ t-r» vrv vr>«0 \〇 \〇 \〇\〇\〇 1、 1、 1ヽ 【、 1、 卜* 000000 0000 〇 O' Weight ot □ Bar One Ft. long：. ^ 'Si ^ 2^ 〇 才〇 〇〇 叶*- OcivO rnf^vAO 〇〇〇〇 〇 u> « " . ^ c! ^ でで m け e> ひ " r< r>nrj-^i^oo 〇 f^u^oo m u^oo c« vo h ty*> 益ぶ' ii'ii. 8 S'S'S- 2 d Tnicku«s6 or Diameter in inches. ^ 七 十嘴 +喵 叶》» 相 ォ 叫 ル 相:^ 咖辦 -I« 筇 ホ is + 喵—喵 咖$吻： ^ ( p w p KI H § o 」 .2u d s_ sunl 6r. tA\ JOCJ assa 210 ■JSEO M I &H H o noyrM 闳〇 s w Y fp 0 : N!Il :o PH GiIy s PH vxlös ^ o s olts either built; into tlie masonry, in wiiicli case there aro washer — 55 — plates at thoir lower end»«?, or driven into holes drilled therein. In tho latter case the ends of tlie bolts aro split, wedges inserted in tliG slits, tliG bolts driven down lull’d so as to sproad the ends; then molten sulphur poured into the holes. Expansion is provided for at tlio other peolostal in short spans by a tonguo on tlie under side of the slioo pkto fitting into a groove in the upper sulo of the bed plate or by such an arrangement as that shown oil PI. II, Fig. 15. In other spans tlie shoe plate rests upon a nest of turnod rollers, held in a light framo and rosting on a planed roller plate, wliicli has angle iron rivet ted around its edges so a*s to form a shallow box : this box is arranged so as not to hold wn-tcr. Tho bottom of tlio shoo plat-o is so planed down as to leave along its centre line parallel to tho length of tlie bridge a projecting rib about two inches "wide and from an eighth to a quarter of an inch deep, which fits loosely into notches turned on tlie rollers. A similar pro- jecting rib on the upper face of the roller plate also fifca tightly into tlio notolies on the rollors, effectually preventing lateral motion of any magnitude. Tlie reason wliy tlio projecting portion of the shoe plate does not fit tightly into the notches in the rollers is because, if ifc did so and if the roller plates were not laid more accurately than can generally be done in practice, tho end lower lateral strut might prove to be too long to enter tlie space assigned to it, or not long enough to fill it completely. Vertical motion is prevented by turning over tlie top of tlie outer angle of tlio roller plate so as to almost touch the top outer edge of the slioo plate* These pedestal details are all illustrated on PI. II Fig. 12, and on PI. IX, Fig. 18. Shoes are sometimes made hinged so as to make certain of there always being an even bearing upon tlio rollers, but most of tlie best bridge designers do not recognize the necessity for tliis refinement of con- struction : its uso would cause an increase iu tlie section required for the batter brace. Iu double intersection bridges tlie long diagonals are halved and connected by pins， passing through tlie middle of tho posts, the channels of which are reinforced by plates at tlie pin holes to compensate for tlie metal cut away. Tlieso 1101 es sliould be slotted in tlio direction of tho main diagonals, in order that tho extension of tlio latter may cause no deflection of tlie post at the midillo, but still permit of figuring 山0 post as of half length with both ends 11111 ged. Tlio extension of the counters is not so important therefore the pin holes need not be slotted in tlio direction of their length. Centre posts, wliicli are crossed by counters only, nearly always have a superabundance of strength, so their centre pin holes require no slotting. Filling plates are usod for top chords wliore there aro abutting channels with Webs of unequal thickness, in floor beams and track stringers to fill tlie spaces bet- weeu stiffeners and webs, at pedestals to fill between tlio outer chord bar heads anti the webs of- tlie batter brace channels, and at first panel points of through bridges below the chord heads so as to make the floor beams at these places on the same level as that of the others. Lateral struts are connected to chord pins botli in tlie upper anti lower systems 】)y jaws as shown on PI. YTTT Figs. 1, 2 and 4. Wliere bent eyes are employed for the lateral rods there are two nuts of different diameters used for attaching the strut to tlio chord pin. The larger serves to hold the jaw against the cliord, tlie smaller to resist the pull of the lateral rods : of course tho pin has to be shouldered down, and it is evident tliafc it should be inserted from tlie outside of the bridge. Jaw plates are either single or double ； the former wliere a special vertical pin is used for tlie lateral rod attachment, the latter wliere the rods are connected to the chord pins by benfc eyes. Tlieso bent eyes aro not used on rods exceeding one and three quarter inches in diameter. The function of tlie inner jaw plate is to reduce the pressure of the bent eyes upon the mit on the end of tho chord pin, and to avoid tlie oblique action of the same. This oblique action is not so objectionablo in the case of light rods pulling against well proportioned bolts and nuts, as in tho case of some vibra- tion rod attachments. Portal braces are connected to tlio batter braces bty large sliort bolts through tlio medium of single jaw plates as shown on PI. VIII Figs. 3 and. G. When tliere are vibration rods at the portal the portal stmt channels are placed closely together with their webs parallel to the piano of tlio batter braces, in which case one bolt through each jaw is sufficient ; but, when there are no vibration rods, the portal strut chan- nels are spread far apart with tlieir jianges parallel to tlie piano of the batter braces, in wlncli case two bolts through eacli jaw will be required. Portal vibration rods aro attached to the struts by pins as shown on PI. VIII, Fig. 8. Ena upper lateral rods, if small, may be attached to tlio liip pins by bent eyes, provided that the nuts for said pins be well proportioned ; but, when they exceed one and three quarter inches in diameter, they are coupled by split eyes to special verti- cal pins passing through the flattened ends of the hip pins as shown on PL VIII Fig. 5. Intermediate vibration rods are attached to upper portal and intermediate struts by bolts or pins as on PI. VIII Figs. 2 or 4. Intermediate struts for single track bridges are connected to tlie posts by two bent plates at each end as shown on PI. VIII Figs 2 and 4 ; those for double track bridges l>y jaws. Knee braces or brackets are used to connect upper lateral, portal or intermediate struts to posts or batter braces. Where no vertical sway bracing is used these knee braces are very important portions of the structure, and have to be proportioned to resist calculated stress, but where isway bracing is employed tlieir uso is principally ornamental. They can be in ado of either angle, channel or tco iron ; preferably tho former : they are not to be bolted but rivetted to the parts wliicli they connect. Side braces are to be connected to tlie top chords and floor beams as shown on PL IX Figs. Iß and 17. There are two different floor systems, to be described presently : in tlie first of tliese the lower lateral rods pass through the wooden sliims ; and tlio lower lateral struts between tlie ends of tlie track stringers ; bufc in tlie second both rods and struts pass through holes in the webs of tlie strmgers. The first system is shown on PI. Ill tlio second on PI. IV. Floor beam>s are liung from bottom chord pins by beam liangers, formed of square iron with enlarged ends, which is bent into tlie shape of tlie letter U. The ends of the hangers pass through holes in a plate, called a beam hanger plate, which acts as a sort of stirrup for tlie floor beam、 Nuts on the ends of the hangers are — 57 — turned so as to press the floor beam against the bottom of tlie post (or the filling piece at the first panel point) and are prevented from getting loose by lock nuts. ■Hds attachment is illustrated on PI. II, Fig. 10. Floor beams in deck bridges should resfc upon tlio top chords, directly over tlie posts : their lower flange 日 should bö rivetted to the chord, plate, and brackets of angle or channel iron should be used to prevent injury from the rackiug effect of passing trains. This detixil is sliown 011 P】. IX, Fig. 15. It is not legitimate to use such floor beams as upper lateral struts, although they undoubteclly aid the upper lateral system. The two floor systems referred to n； few lines back avo for these two cases viz., where there arc wooden sliims resting oil the track stringers and where there arc not. The former is employed wlicn the stress in the eud lateral rod is not sufficient to necessitate the use of double rods, and tlie latter in all other cases, tlie reason being that four rods passing througli a sliim ■would cut it up too much, besides taking it inconvenient to get the rods and sliims into place. Iu tlie first case the track stringers rest on shelves of angle iron supported by short stifiening angles^ tincl aro also attached by bent plates rivetted to tlie webs of both beams and stringers. To obtain greater stiffness, plates of tlie full width of the top flanges may bo run through the lateral struts and rivetted to the flanges of adjacent stringers, but these are not absolutely necessary and may be omitted, ü so desired. This style of floor system is shown on PI. III. . Iu the second case tho stringers pass over ilio floor beams, wliicli are a few mclies lower than in tlie other case, and are made continuous from end to end. of span by means of splice plates on both wobs aucl flanges. Heavy stiffeners are placed beneath tlie points of support of the stringers to avoid all tendency to buckle tlie wob of tlie beam. Additional support and rigidity are given to the connection by rackets extending from the bottom of tlie bo am to the bottom of the stringers. This metho(Us illustrated on PI. IY. All built track stringers Lave stiffening frames lying in planes transverse to tlieir length jiikI spaced from seven to ten feet apart. None fire required cit tlie ends, ^vlieu the stringers abut against the floor beams, but tliere is one near each end when tlao stringers rest thereon. Extra stiff frames aro required at the ends of stringers which rest upon tlie piers or abutments. Bed plates witli grooves or some similar arrangomont aro to be used for tho stringers where they bear upon masonry, aüd are anchored to same in a manner similar to that described for the case oi pedestal bed plates. Similar bed plates aro used at ono end of plato girder spans. Lock nuts are used on all adjustable members : auy style tliat will act efficiently may be employed, but those illustrated ou PI. II Figs. 5, 6 and 10 are quite simple and effective. • Ornamental work can be placed at the brackets on tlie portals, at the intersec- tion of the portal vibration rods, above the upper portal struts, and even on inter- mediate brackets. A small amount of ornmental work will go a long way in an iron bridge. In floor beams, track stringers and plate girders it is hotter to concentrate as much of the sectional area of tlie flanges iuto the angles aud to use plates sparingly» 一— ö 合 —— in spite (H an apparent economy iu employing tlie latter ; for the iron acts more efficiently wlien tlio stresses iliereon are not irausmitted to too many parts. Angle stifleners for these members are preferable to tees or channels : they should bo made flush witli tlie vertical legs of the flange angles by filling plates» instead of being bent around the flanges, and at tlie same place there should always bo one on each sido of the web. In making turn bucklos, a littlo expense can be saved by having only one adjust- ing-end ; the other haying a hole, through which passes one end of the rod, which is enlarged into a head. One advantage of this style is, that tlio turn buckle can never bo lost from tlio rod. Such a turn buckle blioukl always be used on portal vibration rods, for a reason that will be given iu Chapter XXII. CHAPTER V. 孔〇 Oß SYSTEM PEOPEß, RE-EilLLHG & DITCHING APPARATUS. . Tlie floor system proper, or the arrangemeut of ties and guard rails, liei’e ^ocommemlecl is not tlie one in common uso in America, bat is a modification of that proposed by W. Howard White, Esq. C.E., in tlic Transactions of the American Societu of Civil Engineer^ Nov^ f88, the changes being tlie substitution of angle iion for tho wooden guard rails, tlio sliorteniug of tlie ties, tlio diminution of the spacea betwoen them, aud the providing of a place of safety for auyeme wlio nmy ヤ upon the bridge wlien a truiu is passing. Tlio usual American floor system is much heavier than tho one proposed by Mr. White, and consequently is not only move costly iu itself, but by increasiug tlie dead load of tlie bridge necessitates tlio use of デ〇1〇 iron for the trusses. For short spans tliis might be considered advantageous, 111 that it tends to lessen vibration, but for long spans it is decidedly tho conti aiy. Tlle employment of long tics and outside guard rails necessitates tlio use of two extra stringers to sustain a portion of the live load in case of clerailmeiifc, because tho guard rails being higher than the rails must bo placed at such a distance outsiilo 0“he latter, in order to permit of tlio passage of snow-plouglis, that tho unaiclec ties would not be strong enough to uphold a derailed locomotive. • Because of tlie flanges on tlio wheels an inuor guard rail of tlie same liciglit n,s tlie rail is fully as efficient as an outer guard rail two in dies Iiiglier, aiul li^-s the advautago that it may bo placed closo to tho rail, tlius preventing excessive lateral movement of a derailed carriago or locomotive. Tlie floor system recommended by the author is illustrated on Plates I [I 娜 IV* Most of tho ties are of T x 8;, x G; oak, laid on tlicir flats, and spaced not more で lian twelve inches centre to centre, tlius leaving an opening of no more than four inches, "whicli will not causo excessive jolting of derailed wlicels. Every sixth or seventh tie in single track bridges is twelve foot long, so as to support at each end a 3 x 12 r pino planlf, extending ffom end to end of bridge, in order to nilou-1 a yUc し of refuge from passing trains. Each foot plank is to bo spikod to eacli long tie y two 7" cut spikes. • エ11 double track bridges the long ties arc to be twenty- two feet in length, extend ing clear across tlio bridge, and supporting a run of plank at each end fl»ncl another at tlie middle. The latter serves merely as a stepping place to pass from one tiack to tliG other, the outer runs only being intended for places of safety. — ßO — When wooden slums arc used, as m Plato ill, tlio tics at the panel points aro made of 7" X 14” x 6’ timber so as to span the opening left between tlie ends of tlio stringers for tlie passage of tlie lower lateral struts. The ties are dapped about an incli onto the shims, whioli are generally of 7,f x 8’’ oak， and are connected thereto by drift bolts of three quarter inch square iron driven into three quarter inch round holes, bored obliquely tlirougli both ties and slums. Tlio bolts are provided witli square heads, so that they may bo withdrawn by a claw bar, when tlie timber is to bo replaced. The wooden slums are useful in affording an easy means of attaching tlie ties to the stringers, besides adding somewhat to tlie strength and stiffness of the latter, — enougli in any case to componsato for tlie loss of strength caused by the holes for the attaching bolts. Tlie latter should bo staggered and spaced about two feet apart, but there should bo no bolt placed nearer than two feet to the middle of tlie panel, whore the bending moment on tlie stringer is at a maximum. These bolts are to be J" in diameter, and the holes tlirougli wliicli they pass U" iu iron find 1" in wood. Tlie guard rails are of 5" 乂 4" x 士〃 angle iron, eacli weighing 14^** per lineal foot, the five inch log being vertical, and tlie four inch leg perforated for tlio passage of tlie 每" bolts which attach it to alternate ties. The distance between the inner face of the head of the rail and the outer face of the guard rail is six inches. To avoid splitting the wood a small hole should be bored whenever a track spike is to be driven. When shims aro not used, tlie ties are attached directly to the stringers by bolts. By glancing over the bills of iron and lumber in Chapter XVIII and choosing those weights which belong to tlie floor system proper, tlie weight of iron per lineal foot of span in tills portion of the bridge will bo found to bo 87 pounds and tlio weight of lumber per lineal foot 195 pounds. When sliims are not used the weight of iron is almost unchanged, but tlio weight of lumber is reduced about 40 pounds per lineal foot. Plate V illustrates a re-railing device to bo placed at each end of a bridge. By its use any car or locomotive which is off the track, at a distance not greater than half the gauge， will bo returned thereto before coming upon tlie bridge. This ingenious device is the design of E. McClure, C. E. Esq. use larger letter, Cliie f Engineer of tlie Chicago, Burlington and Quincy E. E. system, to w liosc kinduess tlie autlior is indebted for tlie drawings from winch Plato Y was prepared. The autlior lias been obliged to introduce several unimportant modifications to adapt it; to the change of gauge and to the peculiar guard rail employed. It consists essentially of an ordinary frog point placed nndway between tlio rails at a short distance from tlie end of the bridge, from which point diverge two ordinary rails produced until their centre lines approach the centre lines of tlio track rails within about a foot. The ends of the former rails rest on an extra wide tic, and between each of them and tlio nearest trade rail is a ^r, plate resting on two ties and having the end benfc down. This plafco joins onto a 4：" x G" angle iron with the four inch leg vertical, and cut and bent as shown on tlie drawing, tlie outer 一 61 — vertical face being made continuous with the outer face of tlio rail head. The angle iron and a portion of the plate rest upon and aro attached to a 5" x 9" on-k timber laid on its flat, dapped and well spiked to the ties, and having the end bevelled off so as to mako the plate and angle iron form an inclined plane. The other end is also bevelled off, but 1110 re suddenly. The vertical legs of tlie angle irons are so trimmed as to liavo tlieir upper edges horizontal, and the other legs so that they will not approach too closely to tlio track rails. The outer facos of the vertical legs approach the inner faces of the track rail heads till the distance between thorn is two and a half inches, then run parallel thereto for a sliort distance aud again diverge. The greatest elevation of the upper face of the six inch leg of tlie angle iron is three quarters of an inch loss than that of tlio track rails. On tlio outside of each track rail and close up to its lower flange is a 吾" plate resting upon an oak timber 4 i" deep ancl of varyiug width : tho width of tlio plate also varies. The timber is bevelled off at ouo end so as to form an inclined plane leading up to a level surface of the same height as that of the rails. The outer plate begins a few feet further from tlio bridge that does the inner one, and its rise ls greatoi. and more rapid, thus giving tlio derailed carriage or locomotive a cant towards tlie track, which with its momentum helps to throw it back on the rails. The modus operandi is as follows : a derailed, car, for instance, approaches the bridge, and tlie wheels which are between tho rails strike either tlie frog point or one of the diverging rails. These direct the wheels unto tlie inclined planes up wliicli they mount and upon which they are conducted by the vertical legs of the angle towards tlie track, approaching it so closely that the outer portion of their peripheries will rest upon the rails as soon as the angle iron begins to descend. The space between the outer plate and the liead of the rail is so small that tlie flange of the wheel lias no cliance to enter it, so that the car cannot but regain its Place upon the rails. Mi’. McClure lias experimented upon this apparatus with perfect success, but as not yet adopted it on his roads ; because it infringes upon a safety switch device already patented. But as Americtan patent laws do not extend as far as Japan, there seems to b。 no objection to tho use of tlie apparatus on Japanese roads. • It is possible though not probable that a car may jump tlie track when on the bridge, to provide for -which case tlie author has adapted tlie apparatus so as to 1 e-rail sucli a car ： this portion of tlio design may, liowover, be omitted without in- curring any possibility of injury to tlio bridge. There is still one case in which a derailed locomotive might injure a bridgo with this appliance in use ; that is, wlien the wheels are more than half tlio of the gauge out of line. There is nothing to be done in such a case except to ditch the train at tlie nearest comparatively safe place to the bridge. This can )e done very easily by the apparatus shown on Plate YI, a design of the author s, ^liich is probably also an infringement oil one or more American patents. Its action is very simple : one of a pair of diverging angle irons, beginning at a distance frora tlie track rails equal to half tlie gauge, catches tlie wheel flanges on one side 一 （52 — of the derailed vehicle and throws it clear of tho track. The inclined planes on the inside of the track enable the other wheels to jump the rails. Stiffening angles, with the vertical legs turnod clown so as to offer no obstruction to passing wheels, aro used where there exists the greatest tendency to tear up the deflecting angles. They are to be well spiked to the ties. Plates V and VI are not intended to be complete drawings in respect to detail， for the spikes, fish plates &c. are omitted. These details are, however, not essential to a thorough understanding of the devices illustrated. From the ditching to tho re-railing apparatus there should bo a rail midway between the track rails to prevent any derailod vehicle, which passes the ditching apparatus, from diverging more than half tlie width of tlie gauge before reaching the frog point of tho re-railing apparatus. By the use of this combination perfect safety from derailment is insured to a Drulge. CHAPTER VI. Moving Load. GENERAL SPECIFICATIONS. The moving load for eacli track is to consist of two engines, whose weights and distribution of same are given in the accompany- ing diagram followed by a train of cars whose weights per lineal foot of track are to be taken from the following table Span Live Load per lineal foot. Under 15c/ 1200 pounds. From 150’ to 200， 1150 ,， ，, 20 0， to a51 2V „ 221 4000 ” 3/ ，， 3 か 3200 ” 23， ，， 24， 3900 ,, 39% 4〇, and 4V 1 100 ” s6r 3800 ，， 4A 4 ダ，， 44， 3000 f> 37°° ，， 45', 46' ,， 47f 2900 ,» 29’ ” 30， 3600 ，， 48', 49， ，， 5〇， a 800 ，， ii 35°° ，， 5 1， to 60’ 2700 n — 64 一 Dead Loatl. Wind Pressure. The live load stresses in floor beams and track stringers and in all plate girders not exceeding twenty- five (25) feet m length are to be iucreasecl by twenty-five (25) per cent., in order to provide for shock. For the same reason the stresses in plate girders of and ex- ceeding twenty-five (25) feet in length are to be increased by the percentages given in the following table Span. Percentage. Span. Percentage. 2$' and 26' 24 yf and 38' 18 27’ ，， 28， 23 39’， 40’ and 41' 16 29’ ，， 3。’ 4 ゲ ，43' ，， 44’ H 3 ヅ 3 ゲ ai 45’， 46’ ，， 47’ 12 ll' » 20 4 か， 4ゲ ，， 5〇' 10 3ダ ，， 36， T9 5ir to 6of 8 The dead load is to include tlic weight of all tlie iron and wood in the structure, excepting those portions resting directly on the abutments, and whoso weights do not affoct the stresses in the trusses. Oak lumber is assumed to weigh four and a third (4|) and pine two and a half (2|) pounds per foot board measure. Should, in any bridge of or below two hundred (200) feet span, tlie calculated dead load differ more tlian seven (7) per cent., or in any bridge above two hundred (200) feet span more than four (4) per cent, from that assumed, tlie calculations of stresses &c. are to be made over with a new assumed dead load. Tlie -wind pressure is to bo divided into two parts, one a moving load of two hundred and forty (240) pounds per lineal foot and tlie other a fixed load of thirty (80) pounds per square foot of exposed bridge surface. Tlie latter is to be determined by adding together tliG area of tlie cloyatton of the floor system, figured by multiplying tlie vertical distance from the top of the rail to tlie bottom of the track stringer by the length of the span, and twice the area of the vertical projection of one truss. Trusses of less than two hundred (200) feet span are also to be proportioned for a pressure of fifty (50) pounds per square foot wlien unloaded, those of from two hundred (200) to two hundred and fifty (250) feet for forty-five (45) pounds per square foot, and "― ()*5 • Stresses due to Curv- ature. Clear Boaslwav. those of two hundred and fifty (250) to three Inin cl reel (300) feet for lorty (40) pounds por square foot. Tho area subjected to wind pressure is to be llgiu-ocl as just described； and tho greater stress 】)y oitber method of computation is to be used in determining the sectional area of the bracing. In through briilgcs aud pony trusses the wind pressure on the tram is to be assumed as taken up by the lower lateral system, and m deck bridges by tlie upper lateral systen"). Tlic wind pressure on tlio l)i*i(lgo itself is to bo divided botwoen tlie upper and lower systems according to tlio proportion of total area above and below the niidtllo horizontal plane of the structure. When a structnro is upon a curve the stresses in chords and lateral sj’stcms and in tlio one! transverse sway bracing of deck bridges due to tho centiifngal force of the heaviest assumed train moving at a velocity of sixty (00) miles per hour are to be pvoviiled for. These stresses arc to be coii.sidci.od (if iis importance as any o 山 ei. stress iu tlic membors aftectod Uioruby. In all tlirough bridges ami pouy trusses the clear distance between nearest 11101 labors of trusses «hall l»e at least twelve (12) focr six (0) i nc lies for single track 1) ridges and twenty- two (22) feet ior donblo track bridges* LenßUi of Span. LanRths of ?,fau Different Hear Roadways. 、\ lien such a structure is upon a curve, these minimnm widths are to be increased b}r the product of tlic radius and tlie versed sine oj one half tlie arc of the curve which is Hubtemled by the span, plus seven (7) times llio .super* elevation of tlie outer rail above tlic centre line of the track. The longtli of span is to be understood as the distance between centre of cml pins for trusses and between centres of bearing plaU'H foi. aU rolled beam ami plate ginler spans. The greatest lengths of span for the different clear road vv fly s are to be taken from tlie following table • CWi， Hoadway. Greatest Lon^fh of 8pan. 12.5， 75， 13.0’ 120* > J3.5’ り。， 14 .o’ lg。， 1 14.5， 210’ f 15.0’ 240， _ 15.5， 27O’ 30 o' ! Clear ITcadway. — 66 — Styles of Bridge for Different Span*-, Limitiiif： Depths of Pony Trustic.s. Limiting Slope fm’ Batter liraces of Pony TruBH^s. Limiting LungHi of Span for Dimlilf In- tersection Biitljfes. Side Braces, Limiting Sizes of Sec- tions. Limiting Widtlis of riates. Limiting Sizes of Up- per Lateral Rods. Expansion. Anchorage. Tlie clear headway or vortical distance between tlio upper sur- face of the rails and the lowest part of the overliead bracing shall be at least twelve (12) feet six (6) inches. Spans below fifteen feefc are to consist of rolled beams ; spans between fifteen (15) and sixty (GO) feefc of rivofcted plate girders ; spans between sixty (60) and seventy (70) or eighty (80) feet of pony trusses or deck bridges, and spans above seventy (70) or eighty (80) feet of through or clock truss bridges. Tlie groatost allowable dq)tli, measured from centre to centre of chords, for pony trusses is uino (0) foot. The least allowable slope for batter braces of pony trusses is to bo two (2) horizontal to ono (1) vortical. The least allowable lengths of span for double intersection trusses arc one luuulrcd ami seventy (170) feet fov single track bridges and one hundred and fifty (150) feet for doable track bridges. Tlie least allowable batter for side braces in pony trusses is five (5) inches to tlio foot ; and all side braces are to be made to resist both tension and compression. In no case is a side brace to have loss streiigth than tlmt of a 3" x 3" — 7* angle iron. All pony trusses arc to be provided with side braces. No vouncl rods less than oue (1) inch in diameter nor square ones less than seven eigfchs (5) of an inch on a sido are to be used : 110 bars less than five eigfchs (J) of an inch thick for diagonals, no large plates less than five sixteenths (T5ff) of an inch thick, nor, except for filling plates, any iron less tliaii a quarter of tin inch in thickness anywhere in a bridge. The least allowable depths for channels aro four (4) inches for lateral systems, five (5) inches for posts in pony trusses aiul six (0) inches for posts in trusses of through anil deck bridges. Tlie unsupported width of any plate subjected to compression must never exceed thirty (30) times its thickness. The least allowable sizes of upper lateral rods are tlioso given in Table XIII. All spans shall bo proviiled with some means of expanding and contracting longitiulinally witli a variation in temperature of one hundred anti fifty (150) degrees Falir. as must also the track stringers wliore they rest upon tlio piers or abutments. Spans of over sovonfcy-fivo (75) feet in length are to have at one ciul two nests of turned wrought iron motion rollers running between planed surfaces. One eml of every span must be firmly anchored to the masonry, and the other end must be so attached thereto as to prevent vertical and lateral and permit 01 longitudinal motion. — 67 — At each bearing tliere are to be four anchor bolts firmly at- tached to the masonry, the diameters being not less than seven eights ⑴ of inch for plate girders, ono (1) inch for pony trusses tiud one and a quartei* (1 iuclios for ihrougli and deck bridges. Except iu the case of swing bridges consecutive spans are not to be made continuous over the points of support. The cambres for bridges of the different spans are to bo taken from the following table. The cambrcs of the rails may bo reduced to two thirds of these amounts by varying the deptlis of tlie daps in tlic ties. Span in feet. Cambre in inches. 5〇 一 7〇 1.0 7〇 — 100 1.5 ! loo — r?o _ "2.0 130 i6o 2.5 l60 — JQO 3.0 19° — 220 — 3.5 ； 220 一 dÖO 4.0 200 — -300 4-5 In all deck bridges and in all through bridges, where tlie deptli 10r^ to centre of chords is twenty-four (24) feet or over, vertical sway bracing is to be used. It is to be proportioned to resist the stresses produced by the wind pressure ; and, in double also thoso produced by the greatest inequality of panel mo* In deck bridges where tlie track is on a cuito, tlie ver- 1Cal sway braciug is to be proportioned to resist the stresses clue to centrifugal force. Portal and lateral struts subjected to bending must first be P^opoitionod for direct stresses clue to both wind pressure and the initial tensions on the rods meeting at the end of tlie strut, and leu to tli oir sections must be added sufficient area to resist tlie Uciuo» the intensity of working bending stress being taken equal to six (6) ton«,. Tlie effect of wind pressure on posts and batter braces of double lack bridges need not be considered ； nor need it be considered in single track bridges, unless the section which it calls for exceed fifty Couiiuuoub Spans. Cumbie. Vertical Sway Brac- ing. Portal ami Lateral Struts Subjected to Bending. Effect of Wind on PostB nud Batter Brace«. —— 68 — Effeit of Wind Pres- sure on Chord StresHes. Initial Tcnsioiu. (50) per cent of that needed to resist tlie live and dead load stresses; the intensity of working bending stress being taken as five (5) tons, and that for the transferred load stress as given in Table VIII. In case the area required to resist tlie wind stresses exceed fifty (50) per cent of that required to resist tlio live and dead load stresses, the total section is to be obtained by adding to the former area one half ( J-) the latter area. The effect of wind pressure on bottom chord tension in double track bridges need not be considered, but in single tract through bridges tlie bottom chords are to bo proportioned first for the sum of the live ami dead load stresses with au intensity of live (5) tons, then for the sum of tlie livo load, dead load transfered load and wind stresses with an intensity of seven and a half (7 i) tons. If there bo stresses duo to centrifugal force the areas found as just described are to be increased by amounts sufficient to resist tlie last named stresses using an intensity of working stress of five (5) tons. In case of single track deck bridges the upper chords are to be proportioned to resist the whole of tlio live and dead load stresses, or six tenths (T^) of same plus tlie wind stresses minus the trans- feree! load stresses whichever of these two quantities be tlie greater. If there bo stresses due to centrifugal force, they are to bo ad tied to the greater of tlie two quantities already found. The intensity to be used is given in Table "VIII. Wind pressure on top chords of t] 11.011 gli bridges need never bo considered. It is only tlie outer bottom chords of through and pony truss bridges and tlio iimor top chords of deck bridges, in respect to tlie curve, that need to have tlieir areas increased to resist the stresses produced by centrifugal force. To allow for the stresses caused iu adjustable main members by tlie screwing up of tlio turn buckles or sleeve mits, tlio stress in each such member is to be increased by tlio amount given in the following table i〃 Q — i.oo tons. 1 穿" O — 2.50 tons. O — I*<25 tt iF O — 2.75 „ 卜 V’ O — 1.50 ，， O — 3.。。 ，； O — J.75 ” ず O — 3.25 ,， ii"0— :2.00 ，， ボ 〇 — 3.5〇 ，， け" © — 2.25 ” ^ 0-3-75 « 2 各" 〇 — 4.0。 ” — (59 — Square or flat bars are to receive the (allowance for round rods of equal sectional area. Lateral struts are always to be attached to the chord pius. comuction for Lit- T “ t eral Systems. Lateral rods arc also to bo attaclied to tlie oliortl pms by bent eyes when tlie larger rod at the connectiou does not exceed one and tlu’ee quarter (If) inches in diameter« In other cases they are to be connected to special vertical pius passing through jaws on the lateral struts. Floor beams arc not to be used in any case as lateral struts. In figuring the stress in a lower lateral strut at tlie roller end stresses i» e», 4.00 „ 5.00 ，， 4.00 & 5.00 4.0。 „ 3.00 »» 5-00 4.00 jf 7.5〇 3.00 ” The intensities for intermediate main diagonals are to be inter- polated according to position. intemitiea of work- For struts composed of two channels with plates or latticing or btre^. 111 lacing, or of two channels 'vith an intermediate I beam, or struts built of plates aucl angles in a shape resembling that of the cliannel strut, the following formulae arc to be used m finding intensities of working compressive Btrcss. 1st. For lateral and intermediate struts. v = -で 3+ w and 2nd, for all oilier struts. + 导 where p is tlie intensity of working compressive stress, U tho length of strut divided by least diamotcr of same, (19.25 for two fixed ends / == J 19.25 for one fixed end and one hinged end ( 18.90 for two hinged ends 15,820 for two fixed ends and C= J 3,000 for one fixed end and one hinged end (l,900 for two hinged ends The working loads for I beam struts arc to be taken from Table X. — 71 一 For the flanges of rolled beams the intensity is to be taken equal to five (5) tons, and for those of built beams four (4) tons on the gross section. Tlio intensity of working bending stress for pins and rivets belonging wholly to tlio lateral systems or sway bracing is to be taken equal to eleven and a quarter (11+) tons, and for all otlier pins and rivets seven and a half (7J) tons. Where steel pins of good quality are employed, the intensity may be assumed at twelve (12) tons for trusses and eighteen (18) tons for lateral systems. Tlio intensity of ■worldng bearing stress for pins and rivets belonging wholly to the lateral systems or sway bracing is to be nine (9) tons, and for all other pins and rivets six (6) tons. Hip verticiUs in pony trusses, having lass tlian five (5) iDauels, ai’c to bo stiiYonecl so as to resist compression duo to initial tension °n counters. If the section employed consist of two cliaunels, tlie het section of the webs alone is to bo relied upon to resist tension， aU(l ü* trussed bars be employed the intensity of working tensile stress on tlio net section is to be reduced to tliroo (3) tons. Middle panel diagonals, counters, lateral rods, vibration rods 如 d all other adjuBtablo roils are to liave their ends enlarged for the SCI，®W threads according to tlio dimensions given in Chapter XIX, and aro to be provide tl with check nuts. All threadö except tlioso on the ends of pins must bo of a ^mfonn standard. Trussing is to be employed only for stiffened bottom chords 乳 nd hip verticals. The least allowable section for trussing bars is a quarter (全） of an inch by three (8) inches. The least dimensions for the upper plates in top chords and batter braces aro to be taken from tlio following table. . With eliannols greater than seven (7) inches in depth, should lie width of plate eraployed exceed that given iu tlio table by from Jorty (40) to sixty (60) per cent., tlie thickness must bo increased ド ope sixteenth (7^) of an inch: if it exceod by from sixty (GO) ? eighty (80) per cent., tlio thickness must be increased by one 哪她 ⑷ of a ム uch. Depth of Chord. Least Tnickness. Least Width, 6f, V 8" r r 9" 87/ 9" i" 10" 11^ IO" 12" 各" r 1 2 辜" 15" : 】5" r jSV 1 8" r 2 ず 20" 22° 27" ] 24" r W ； Intensities of Work- ing Beinling Stress. Intensities of Work- ing Bearing Stro 33 • Hip Verticals in rony Trusses. Up?et Roils. Tlircfttls. Trussing. Least Dimensions for Chord aiul Batter Brace Plates. Stay riatcs. — 72 — Lattice anti Lacing Bara. Diameters of Rivets for Different Chan- nels. Built Channels. Splice Plates. Sizes of stay plates are to be taken from Table XXII or XXIII. Stay plates on latticed or lacod compression members are to bo placed as near the pin holes or ends of strut as possible. Latticing or lacing must never be used without stay plates at the ends. Sizes of lattice and lacing bars are to be taken from Tables XX and XXI. Lattice bars shall make with each othor, as nearly as circumstances will permit, angles of ninety (90) degrees, and lacing bars angles of sixty (60) degrees. Tlie ends ot lattice bars and single rivetted lacing bars arc to be semi- circular, tlie centre being taken a little outside of the outer edge of tlie rivet hole. Foi. attaching plates and lattice or lacing bars to the flanges of channels tlie least diameters of the rivets to be used are to be taken from tlie following table ; and the greatest diameters must not exceed those there given by more than one eighth (^) of an incli. Depth of Channels. 4" 5" 6" 7" 8" r I。" じ〃 15" Dia. of Rivets. r r i" 10 r w ■w r Channels built of plates and angles are not to be less than eighteen (18) inches in depth, nor have webs less than one half (去) inch thick, nor flanges less than three (8) inch by four (4) inch angles weighing tlnrtoen (18) pounds per lineal foot, the shorter logs to be rivetted to the web. For all built channels there are to be employed, instead of tlie ordinary latticing or lacing bars, pieces of angle iron having dimensions not less than two (2) inches by tlirec and a quarter (8J) inches by a quarter (J) of an iuch or weighing four and two ton tbs (4-^) pounds per lineal foot, used as lacing bars and attached to tlie flanges of the built cliaimels by two-staggered rivets at each ernl. Tho length of a splice plate is to be determined by the number of rivets necessary to transfer the stress from one main member to tlio other : the sum of tho working bearing resistances of all tho rivets on either side of tho joint must not be less than tlie stress in the main member upon that side. The rivets must also bo figured for bending. When practicable, a splice plate must be placed on each side of every member where a joint occurs. The transmission of compressive stresses shall be considered as entirely through tlie medium of the rivets anil connection plates, ami these must be proportioned accordingly； so that the area of tlie — 73 — section of the two splice plates connecting two channel bars must e at least equal to that of the larger channel. Simple reinforcing plates or plates rivet ted to webs at piu loles in order to compensate for strength lost there, or to pi-ovitle additional bearing for the pius must have as many rivets to attach iem to tlio webs af5 will give bearing and bending resistancor, for ^ame e^nivaleut to afc least the greatest stresses that can come upon the 1，emforciDg plates* Cover plates for top chords or batter braces are to have the section as the chord or batter brace plate, tlie joints in which y cover, ami enough rivets on each side of every joint to take up 16 öieatost stress that could ever come upon the cover plato. • Extension plates on tlie end of a strut, for the purpose of liing- 卜 tlie latter, are to have from the pin holes to tlio nearest edges le s^ay plates at least twice tlie sectional area of the strut, ami ?e thickness must be sufficient to give proper bearing upon the う1:; The length of the extension plates is to be such as to allow xe Use of enough rivets to provide tlie proper bearing and bcml- resistances. ^ The thicknesses of shoe plates autl roller plates for batter 1 a?° c^anuela of tlio various depths are to be taken from the fol- l0^ng table Depth of Channel. Less than デ 9/y and io° 12〃 ず Built Channel.-;. Thickness of Plate. r r \" >r ず gr , et^ Plates afc pedestals must be of such dimensions that tlio (200、 Pressure on tlio masonry shall not exceed two hundred as . j P°nU(^s per square inch, and the thickness is to be the samo of tlie shoe plate resting tlioreon. incl f】'am ^a,1^Gr plates aro 'never to be made less than one (l) * ' ilc、 and their avec^s are to be such that the lianger nuts will Wa【s Uave a full bearing thereon. fön tlVe ド わ1 top chord aiul batter brace plates shall bo spaced り 1 ) (】iaiuetei.s apart for a distance on each siile of evci y joint i to one ami a Jialf (H) times the width of tlio pln-te, and no Qoi*e than five (Ö) inches elsewhere. l.i 6 Llistance between the edge of any plate and tlio centre of n. dia i0】C mUSt uever be less than one and a half (1J) times tlie 1 な】010 ぐ 山6 ホ“， Preferably twice the diameter. e diaiuetei* of the hole shall never exceed that of tlie rivet y 11101 e °ne sixteentli (y6) of an incli, lleiufoiring Matesi. Cover riatci. Extension Plates. Shoo TM 丨 ite% Roller riates, nn so it lias been adopted in this treatise ; because bridges slioukl be 1 1 opoi tioned for tho greatest loads that can ever come upon them. Iu regard to car loads the iu formation obtained shows that the freight cars W ien 1〇11如(1 briiig the greatest loads upon the track, and that a loiulecl car weighs 110 laoie ^ian eight tons twelve liuiulred weight or 19,204 pounds. The length of ^dl flom Sutler to buffer is eighteen feet, making the greatest loatl per linoal foot 1〇7〇 pounds. Now as cars arc sometimes overloaded, although it is very bail for the springs against the rules of tlio railroad, the author lias thought it best to assume a car a( of 1 200 pouiuls per lineal foot for spans under one liuutlred aiul fifty feet in enotli, aiul to reduce it gradually to 1050 pounds for spans of three hundred feet. 乃16 reasou 'v】、y öueh a re luction is permissible is because the chance of a long ‘ pan e'ei. being covered from end to end by tlie maximum loatl is very small, while — 82 — Span. 5^ and and 37f and 39、 40， and 42，， 43， and 45f, 46f and 48，， 49， and 5i; to Uuif. load. 4080 pounds. 5927 •• 5776 " 3596 " 3420 •• 3H8 •• 3080 •• 2916 •， Unif. load. 5150 pounds. 5125 •， 5000 " 4875 •• 4712 " 4551 45.92 " 4255 " for short spans it is not at all improbable. Another reason is that as the length of span increases tlie ratio of (lead load to total load increases ami consequently the injurious effect of impact relatively (lecieases. I’liis reiluction, of course, does not a fleet tlie stresses on the floor system and liip vertical?, which are proportioned for the assumed engine loads. The table of equivalent uniformly distributed live loads given in the last chapter will be found to save much labour : aliliougli not perfectly accurate it is correct enough for nil practicul purposes. The table which follows it gives the percentages by which these equivalent loads are to be increased to resist the shock of rapidly passing engines. The percentages agree 11111. 】y well with the results of experiments upon the vibrations of bridges under passing loads. 'The two tables can be combiucd into the following, which is the one to be used iu calculating stresses. The engine excess for one truss of a single track bridge is found by subtracting from the total weight of engine tlie product of the length of engine by the assumed car load per lineal foot and dividing the remainder by two - making tlie various engine excesses to be used as given in the following table. Car Load. i aoo* per ft. 115。* per ft. 1 ioc* per ft. 1050* per ft. Engine Excess. 10.35 tons. 10.7 tons 11.05 tons. 11.4 tons. For double track bridges the engine excesses are, of course, twice as great as the above. Wlien the panel length is eighteen feet or over Ü10 engine excesses of the two coupletl locomotives are assumed to bo concentrateil upon consecutive panel points, 1 川 t fhr sliorter panels there is supposed to lie between them a panel point without engine excess. Of course this envision does not represent the actual distribution of the loading, nevertheless it is convenient and gives a small error oa the side of safety. I11 double intersection trusses greater web stresses are found by assuming a car to be placed between the two engines, thus bringing both excesses upon tlie same system of posts ami ilijigoimls, so this arrangemeut was adopted when calculating the web stresses for Table IV. Accurate values for the dead loads of single track bridges are given in Table I. The column for dead load is obtained by adding togetlier the 'veiglits of iron per 468 1 470 c 3 3 5 4 4 4 5 6 sp : to 3 0 2 46 00 0 2 1 2 222 2 33 d d d d Pd d -n -n Ln 瓜 Ln Ln ,n — 83 — lhieal foot in the trusses, floor system and lateral systems, the weight of lumber per liueal foot and that of tlie rails, and subtracting from the sum 32 pounds to allow for the weights of those portions which rest upon the masonry, and which do not affect tli o stresses in tho trusses. This allowance lias been checked for several spans of various lengths, and has been found to bo almost constant for all lengths of span. , • By doubling the dead loads of Table I can be found approximate values for the dead loads of double track bridges. Although this method would be a ratlier rough aPl)roxiiuatioii in calculating the weight of iron for a double track bridge from that a single track bridge, still it will be found so accurate, as far as dead load is concerned, as not to necessitate a re-calculaiion of stresses. This is as one might anticipate ； for the truss weights are almost directly proportional to the total loads, except when tlie change is so slight as to cause no alteration in the depth of tlic top cli?rd and batter brace channels ; tho weights of the lateral systems, iliough not wice as great, are considerably greater in double Ilian in single track bridges； for, although the total areas opposed to wind pressure arc only slightly greater in tlic former than in the latter, yet all the members are longer, and those subjected to compression are consequently of larger sectional area ; and the weights of the floor system are more than doubled ； for those of all the members except the floor beams arc doubled, while those of the latter are increased both by reason of their length and h tlic doubled loads thereon. The author lias tested an actual case, and lias found that both the weight of iron and the dead load are almost exactly twice as great in a double as in a single track bridge of the same span and live load per track. From actual measurements of a number of cars tho average area per lineal foot of train exposed to wind pressure lias been found to be about eight squaro feet. Tho assumed wind pressure of lliirty pounds per square foot on the train agrees with that the best American practice : moreover it is as high as economical reasons will allow， for it would probably overturn any ordinary train, as the following calculations 、vill show. Let P — pressure per lineal foot of train h =： height of centre of pressure above rails d = distance between centre lines of rails and W = weight of car per foot which will jubt resist the over turiiing moment then Ph = iWdmi W= Tl】e value of h is about seven feet, that of d exactly 8.7 foot tuid that of p two hundred and forty pounds. Consequently W = -x2^x7 ^ ： 908 potuuls. 0.7 Äs the greatest allowable car load per foot is only 1070 pounds, it is highly improbable that the average load would reach nine hundred pounds, so that a pres- sure of thirty pounds per square foot iu upsettiug a train ou a bridge would destroy — 84 — tlie structure in any case, for bridges are not proportioned to resist the blows of derailed trains. It is true that higher pressures than thirty pounds are sometimes recorded, but they extend over very limited areas : on this account the empty bridges are propor- tioned to resist from fifty to forty pounds per square foot according to the length of span. C. ölialer Smith Esq. C. E., one of the highest American authorities upon bridge building, proportions all his bridges under two hundred feet span to resist a pressure of fifty pounds per square foot, and considers that thirty pounds upon tbo loaded bridge will be large enough for all greater spans. But as tlie upper lateral systems of through bridges and the lower lateral sys- tems of deck bridges are not affected by the wind pressure upon the train, the author considers that empty spans from 200 to 250 feet iu length should be proportioned for forty-five poniuls per square foot, and all greater spans for forty pounds. In reality these figures have not been exactly adhered to in making tlie designs for Uiis treatise, because tlie author lias considered it better to reduce the intensities of wind pressure gradually than to change them suddenly by decrements of üve pounds per square foot. Theodore Cooper Esq. C. E” the author of the best American bridge specifica- tions, provides for a wind pressm.o of 150 pounds per lineal foot for upper lateral bracing in through bridges and lower lateral bracing in deck bridges. This is a rather small allowance for a country visited annually by typhoons. In preparing Table XIII tlie author used 150 pounds for spans of 100 feet and under, from that to 200 pounds for spans between 100 find 200 feet and from 200 to 240 pounds for spans from 200 to 800 feet as tlie pressures per lineal foot for upjier lateral bracing. The pressures per lineal foot ou trusses only for tlie lower lateral systems were calcu- lated to be from 2Ü0 pounds for spans of 100 feet to 320 pounds for those of 800 feet for empty bridges ; and from 170 pounds for spans of 100 feet to 240 pounds for those of 800 feet for bridges covered by the moving load. The pressures per lineal foot upon tlie upper lateral systems with an intensity of thirty pounds are about 00 pounds for spans of 100 feet and under, from W to 180 pounds for spans between 100 and 200 feet, and from 130 to 180 pounds for spans between 200 and 300 feet. The method of calculating these pressures was fully explained in the last chapter. A portion of tlie leeward truss is protected by the train, but no deduction should be made oil tliis account, because the surfaces of tlio cliannclsi being coucavo towards tlio wind, tcml to increase tlie intensity of pressure : indeed it is well in figuring areas to allow an inch or two of extra width to compensate for this concavity. In this particular system of bridges the effect of wind pressure on bottom chord tension need not be considered in spans under ono hundred and thirty feet in length. Wind loads upon empty bridges are treated as moving, for it is possible for one part of a bridge to be protected while the remainder is exposed ; besides the centre of a whirlwind lias a motion of translation which would cause the pressure to really act as a moving load. This method of treatment affects principally the lateral rods aucl 一 85 — struts near tho middle of the span. The pressure upon the train is undoubtedly a woving load, but the coexisting pressure upon the trusses must be treated as static ; for it would be highly improbable that a maximum wind and a train could advance together and with the game velocity upon a bridge. CHAPTER VIII. STRESSES IN TRUSSES. . Tlie causes of stresses in trusses are the following ; 1* uniform live load 2* dead load 8® engine excess 4° wind pressure directly 5° wind pressure indirectly 6* curvature of track The uniform 】ive load and engine excess produce tension in the bottom chords, main diagonals and counters, and compression in the top chords posts and batter braces. The dead load affects similarly the chords, posts and main diagonals, but does not affect tlie counters, or rather it tends te diminish the stresses on the counters. The direct stresses due to wind pressure are compression on upper and lower wind- ward chords, and tension on upper and lower leeward chords. The indirect stresses duo to wind prossure are equivalent to those produced by increasing the dead load on the leeward truss : they will be called “ transferred load stresses/1 Tlie wind also relieves the (lead load on the windward truss : the stresses due to the difference between the dead load on this truss and the reduction will be called “ reduced dead load stresses/* The curvature of the track produces a centrifugal force which acts only on either the lower or upper chords, according to whether the bridge be through or deck : it affects also the corresponding lateral system, and the vertical sway bracing of deck bridges. The combination of all these stresses is a little complicated, especially as the direct and indirect stresses due to wiud pressure may bo subdivided into tlie two cases, first when the bridge is empty, and second wlien it is partially or wholly covered by tlio moving load. Tho following table will facilitate the comprehension of the effects of the various loads upon the different members, T standing for tension and C for compression. — 87 — — 8R — To properly apply this table one must distinguish between a probable or ordi- nary combination and an improbable or extraordinary combination of stresses ; anti must recognize which stresses matj and which stresses must exist together. There are two distinct conditions, first when the bridge is empty, and second when it is wholly or partially covered by the moving load. Distinction must be made between the stresses in certain members of deck bridges and tlxose in the corrcspouding members of through or pony truss bridges. Again any particular member may receive its greatest stress when it belongs to the windward or to the leeward truss. Keeping these facts in view let us analyze the table. First when the bridge is empty we are concerned with the horizontal lines numbered 2, 4, C, 8, aud 12； and, when it is loaded, with the lines 1, 2, 8, 5, 7, 9, 10 or 11 and 12. Commencing with the top chord, first when the bridge is empty, wc have 2 •’ 4,* 6* and 8° acting but the latter is a combination of 2* and G° so need not be considered. We see that for both windward and leeward chords there are both C and T or — C acting simultaneously, for 4° and 6* cannot act independently. On this account and because the effect of 1° and 8* is so great we conclude that the top chord stresses when the undge is empty need not be considered. When the bridge is loaded 2°, 8#, 5*, 7° and 9° act in through or pony truss bridges and for deck bridges 11。 may also act. In deck bridges 5* has a much greater effect than iu through or pony truss bridges, for it then includes the wind pressure upon the train. As before 9* may be omitted as it is a combination of 2° and 7*: this leaves for through and pony truss bridges 1°, 2* and 8* as the ordinary loading and 1°, 2°, B#, 5* and 7° as the extraordinary loading. In tlie latter it will be noticed that for both windwtii tl äud lööwtird cliords W6 liave botli C uud T or— C acting situiiltdiiöously j for 5* and V must act together. On this account and because of the great effect of 1° and 8° compared with 5°, it is evident that lc, 2° and 8° are the loading to be considered. In general as will have been noticed in reading chapter YI, extraordinarv loads need not be considered unless their effects exceed those of ordinary loads by about fifty per cent. In deck bridges it may be possible, though it is not probable, that the combined effect of l°f 2e, 8®, ö° and V may be bo much greater than that of 1°, 2° and 8° that the method of proportioning given in chapter YI will Lave to be adopted. If there be curvature in the track 11° will always exist with both 1°, 2° and 8°, and with 1°, 2*, 8°, 5° ami 7°. Its effect may bo considered as an increment of that of 1° aucl 8° in proportioning by the method of cliapt. VI, but it is to be noticed that it need increase the sectional area of the chord on the concave side of the track only. In 11。 ifc is seen that the effect may be either C or T, but C must be taken, as the wind may act in either direction and consequently both with and against the centrifugal force. — 89 — Although the centrifugal forco really reduces the stress on one chord, it should not be assumed so to do ; for the trains do not necessarily pass over the bridge at tlieir maximum velocity. Passing to the bottom chord we may conclude at once both from the table and from our general knowledge of bridges, that in through and pony truss bridges the stresses will be greatest wlieu the bridge is loaded. When, however, tho bridge is empty wo liavo acting upon the windw ard chord 2°, 4° and G°, or wliat is the same tiling 4C and 8°, tlie former producing C and the latter T ; and as in most cases for the bridges dealt with in this treatise the former exceeds tlie latter, tlie bottom chords should be proportioned to resist a compression of C4 — Ts, the subscripts denoting the horizontal line to \vliicb the utresses belong. When tbe bridge is loaded, 1°, 2°, 3° and perliaps 10。 act together as an oi.ili- llary load while 1°, 2°, 3°, 5°, 7° and perhaps 10° act together as an extraordinary load. Where the latter exceeds tbe former by more than fifty per cent, tlie chords should be proportioned to resist tbe stresses produced by the second loading using an intensity of working stress of 7. 5 tous, but otherwise the stresses clue to tho first loading are to be taken, using an intensity of working stress of 5 tons. It must be noticed that TJ0 affects the sizes of the chord sections on tlie con- vex side of tlie track only, and that., although given as either C or T, T must be taken, as tlie wind acts iu either direction. In deck bridges 11° cannot act, and as tlie effect of 5。 is small compared with that of 1° and 8°, the loading to be considered is that of lc, 2° and 3°. For the empty pony truss Passing to the posts we may conclude immediately that tliey tako tlieir greatest stresses when the bridge is partially loaded, in which case 1°, 2°, 8° give tlie or. iuary 1 , 2°, 8°, 7C and 12° tbe extraordinary loadings. Except iu tlie case of very ight posts the latter loading need not be considered ; but when it is, the post must be proportioned as directed in Chapter VI. Passing to the main diagonals we Lave 1°, 2° and 8° as the ordinary loading, aud 1 , 2°, 8° and 7° as the extraordinary loading. It is self evident that the latter not be considered. Tlie same remark applies to the counters and bip verticals. Finally passing to the batter braces we may immediately conclude tliafc tlie stresses existing wlieu tlie bridge is empty need not be considered, hence tlie ordin- aiy loading will be for through bridges, pony truss bridges and deck bridges witli straight track 1°, 2° and 8®, and the extraordinary loading 1°, 2°, 3°, 7° aud 12% It !s Mghly improbable that the latter loading need ever bo considered. For deck li (n1 一 1) + 2/i 2 This was obtained under the supposition that the load W on top of the post passes down the post before being separated into the portions which go to the right and left, but the author has come to the conclusion that the portion, which passes to tho farther end of the span, goes down the main diagonals as compression or in reality as a reduction of tension. The error in the last for- mula is upon the side of safety and varies between zero and moreover its greatest effect is upon the posts at and near the middle of the span, which posts in many cases have necessarily greater sections than the stresses call for. Besides the load comes more quickly upon the posts of deck bridges than upon those of through bridges, so some engineers might prefer to use the less correct formula. — 95 — to each pier. Then (lie stress in any main diiigoiml of the left-hand half of tlio “tlge ia to be found by commencing at the rigtt-liand end, and adding the numbers at the panel points until the loot of the diagonal consklcred is reached, multiplying 山6 si™ by 1 W sec 0, and to tlie product adding the number of panel dead loads between the central plane and the panel point at the foot of the diagonal considered (including the one at this point) multiplied by Wi soc 0, For instance, in a ten- pan cl bridge, tlie stress in tlie end main diagonal, tlio number at its foot being eight, will be (1+2 + 3 + etc. . . . + 8)-W~~- +{i + l + l + l)Wlsec 0. The stress iu a counter on the right- hand half of the bridge will be found by adding tlio numbers at the panel points until the foot of the counter considorod is leached, multiplying the sum by TF sec Q, and from tlie product subtracting tlio ^ead-load stress of the main diagonal which crosses tlie counter. Thus, in tlio ten- pauel bridge, tlie stress in the second counter from tbe centre iu tlie riglit-liand half of the spans, or tlie one at the foot of tlie third panel point, is (1 + 2 + 3)-^^ g- (Hl)^isec e. The greatest stress in any post of a through or pony truss bridge is found by adding I ド, to tbe vertical component of the greatest stress in the main diagonal attached to Us upper end, or ^ W + Wf in caso of a deck bridge, thus in the as- sumed bridge, which may bo taken as a through ouo, the stress in tlie 1 他 tlie left-hand cud, or tlio one at tlio eighth panel point, is (1 + 2 + 3+ etc + 7斤 + (* + 1 + 1) Wt+ W/ For tlie case of a middle post, the stress in one of the counters at tlie upper end must be substituted for that of the main diagonal ; thus, in the same bridge, t le stress in tlie middle post is (14-2 + 3 + 4)-^- i W1+W，. The stresses in tlie chords are to be found by the following method : 一 Pass a plane through tlio foot of the post at or nearest to the middle of tlio iiiss, aiul take tlio centre of moments at this foot. From tlie moment of tlio re- action at the nearest end of the bridge subtract tlie sum of tlie moments of tlie loads (TP') lying between the centre of moments and this end, and divide tbe 1 lienee by the depth of the truss. Tlio result will be tlie stress in the panel of tlie 0P c]101d nearest the centre of the bridge : it will be some multiple of Wff tan 0* 奶1(3 stress in the panel of the bottom chord immediately below will be equal to o one found, loss tlie horizontal component of tlie main diagonal of tLo panel, when — 96 — the billige is covered by the moving loaa. This horizontal component will be zero for a truss with an odd number of panels, and ^ W 1 tan 0 for a truss with an even number of panels. The stress in the next panel of the bottom chord towards the nearest end of the bridge is found by subtracting from the one already determined the horizontal component of the stress in the main diagonal at the panel point between tbo two p «au el a considered ; the bridge, as before, being fully loaded. This component is a multiple of Wn tan 0. In this way can bo found all the stresses in tbo panels of the bottom chord, the correctness of the work being checked by seeing if the stress in the end panel be equal to the re- action multipliod by tan Q. If so, the remaining upper-chord stresses may bo at once written by inspection ; for tlio stress iu tlio nth panel of the top chord, counting from the nearest pier or abutment, and supplying the missing pauel at tlio end, is numerically equal to that in the (n + l)th panel of the bottom chord. Next let us consider the double-intersection truss. The formulas for this case are so complicated that it is better not to employ tlicm. The simplest method is to draw a skeleton diagram, and number tlio panel points, as in the single- intersection truss. The double -intersection truss really con- sists of two trusses, as may bo seen in the accompanying diagram. Sucli a division is necessary in order to calculate the chord stresses when the ti.uss contains an odd number of panels. This is accomplished by finding by the method of momonts already explained, the chord stresses in each of the trusses shown in Figs. 2 and 8, and then combining them. Thus the stress in panel 9-10 of the lower chord in Fig. 1 is equal to tliat in panel 9-11 of Fig. 2, plus that of panel 8 - 10 of Fig. 8. Tlio live-load stress in any diagonal sloping upward from right to left is found by noting whether the number at its foot be odd or even, then taking tlio sum of tlio odd or oven numbers, from one or two up to tlio number at tlio foot of the diagonal, and multiplying the sum by ^ sec a, or sec ßf as the case may be. The stress due to the dead load is found by taking the sum of tho same numb- ers, and from it subtracting tlio sum of the odd or even numbers from one or two up to (n 一 nf — 2), wliere n is the number of panels in the span, and nf is the number at the foot of the diagonal considered. Whether tho odd or even numbers should be — - 97 — taken can bo ascertained by following out towards tlie left the system to 1 ゞ diagonal belongs : if the system contain the short diagonal at that end, then い even numbers aro to be taken, otherwise the odd ones. Tho difference thus found, multiplied by ^ ■ s^— > or — — - — , as the case bo, will give the cload-load stress in tlio diagonal. Thus, in the diagiani, tlie dead- load stress in the main diagonal at the panel point 10 is * • [(2 + 4+ etc. + 10 ) - (1 + :]) ] ^~jh As in the case of the single intersection, tlie stress in a main diagonal is cqvul to tlie smn of tlie live and dead load stresses ; that in a counter, to tho diftVicnce between its live-load stress nncl the dead- load stress of tlie main diagonn-1 cu)s、iiig it tlie mitldlo of its length ； that iu a post of a tlirougli oi* pony truss bridge, l>> tlio sum of Ip/ au(| tho vertical component of tlie greatest stress iu tlie main 八 i (0r， if there be none, that in tho principal counter) attached to its upper end. 心 batter braces belong to both systems of triangulation, tlieir stresses are tlie .’um the stresses found by each s3Tstem, or by tlie formula : [1 + 2 + 3 + etc. • • • + ( れ (Tf+TFi) see a If tlie number of panels be even, tho calculation foi* tlie deacl-loail sti esses maj ho much simplified l)y coiuiting the number of panel points on tlio system coiisivloi oi •】>ing between the central piano and tlie panel point at tlie foot of ^，1,1^<>11A * ^ichuliug tlie latter, remembering that the load at the middle panel ia liahcnl, aiu Multiplying tlie result by W\ sec a, or W\ sec ß, . The finding of tlie chord stresses is also simplified when there is an even mini ei panels ; f oi’ they can then be calculated by tlie method explained lot* the siur,le intersection truss. To find the stress iu a post of a douLle-infcersectioa deck-bridge ad«l to^< tlitr If f and the vertical component of tlio greatest stress in tUo principal s less than eighteen feet, by tlie equation T=z 2 ("/— 1 ) (^n — nr)^ tan 0 一- 99 — where nt ( greater than | ) is the number at that end of the panel considered lying next to the lietircr end of tlie spjin \ ioi* tlic bottom chord in these cv this formula of the stress in tlie miiltlle panel of every truss having an odd mimber of panels ； but such a calculation is unnecessary, for tlie greatest eugine ex- ces 3 stress in the midillo panel is equal to that in the next consecutive panel. From Uüs formula it is apparent that all tlie panels of tlie bottom cliord, excepting the first and second from tlie ends, take their greatest stresses when the engine excesses ai，e separated by a panel point. It was seen that such is rarely the case ^vitli tlie top chortl panels. Tlie engine excess stress in fl-ny main diagonal oi* counter of a single intciseo tion truss, iu which the panel length is not less tlian eighteen feet, is given by tlie equation T = (2 rJ- 1 ) ^ sec 6 ； aud, if the panel length bo less than eighteen feet, it is given by the equation r = 2 1 ) ― sec 0 For double intersection trusses tlie corresponcling formula is j? T = 2 1 ) ^ec a, (or sec ß ) For single intersection through or pony truss bridges where the panel length is not less than eighteen feet, tlie engine excess stress on any post is given by the fonnula O— (2 n'- -6) - ; aucl» where the panels are less than eighteen feet, it is given by tho formula C = 2 いし 2) 会 一 100 — l?or double intersection trusses the formula is 0 = 2 {nf~ 3) ^ Foi. deck bridges the coiTespomliiig formulie me respectively (2 が— 1) 会 C =2 (nf- 1) J and C/ = 2 ( が 一 1 ) ム It seems almost needless to say that tlio engine excess, being merely a conventional load, ölioulil not be used iu finding stresses in hip verticals ; but that the method previously given takes into account the panel engine load though not the engine excess. The use of all the previous formultc may always be avoided Ly employing • Tables III and IV, which give tlie greatest stresses clue to tlio uniform live load, the dead load and the engine excesses on the various members of trusses for all practical cases. The wind stress oil any windward panel of either top or bottom chord when the span is empty iö given by the equation 0= ^ tf„tanö/ and tliat on any leeward panel by the equation T= — ” W.2 tan 6 ' where n' (not less than 登) is the number at that end of the panel considered which lies nearest the centre of the span. The corresponding wind stresses when the span is covered by tlio moving load can be found by substituting Trr8 for in the last two equations. It is obvious that these equations apply to thron gli, pony truss and deck bridges. Thoir use may be avoided by employing Table V, which gives the wind and ciu'Viiture stresses foi* nil practical cases. To asccrtaiu tlie amount of tlie transferred load when the bridge is empty. Let h — vertical distance between horizontal plane of shoe plates and the centre of gravity of the vertical projection of the trusses and p = total wind pressure per lineal foot of bridge on both trusses. Then the overturning moment will be p //, Avliicli is a couple formed by a pres- sure p and an equal horizontal reaction ^ » where P is the total horizontal reaction of the tlie four shoes and S the length of span. This must be resisted by another couple of e(iual but opposite moment. The forces of this couple can only be a — 101 — ^leased weight iv4 upon the windward truss aiul an increased weight of the same amount upon the leeward truss, which will give the equation 2) Ji = w4 b or n\ = ~ An approximate value for the overturning moment can be found by calling p1 the piessure per lineal foot of span concentrated upon the upper lateral systeiu, then J)f d =r ?r4 b and ir4 =~y ■fhe latter value of is not so exact as. the former, but is much more easily calculated. The transferred panel load ib^of course equal to tr4 /, and the reduced panel oad Tr6 = TF! — 了 F4 = % - «.4 /• The following table gives approximate values for tc4 for tlie single track through biulgcs of this treatise Span W\ Span «.4 Span W4 7 び 160 16c/ 290 220f 440 8〇， 180 i7cf S. I. 300 230， 460 gcf 210 170, D. I. 340 240， 480 ioof <230 18c/ S. T 520 2$Cf 500 IIO' 240 1 8c' D.I. 560 26of 520 I20f 250 19。， S. I. 340 TJC， 540 1 3 ヴ 260 19c， D.I. 580 2 さ。' 560 】4。， 270 200^ 400 29。， 580 i go， a8o 210' 420 . 30 o' 600 Tlie value of tr5 , the transferred load per lineal foot of span, may be calculated as follows. • Tlie wind pressure of 240 pounds per lineal foot acts with a leverage of about feet, producing an overturniug moment of 9 x 210 = 1920 foot pounds. If in the equation U，4 pfd ぐ 'e substitute ir5 for w4 and (tlio pressure per lineal foot of spau upon the upper a eral syßtem, when tlie wind pressure is thirty pounds per square foot) for 〆， and acW 1920 foot pounds to the moment, we will have n'6 : p"d + 1920 From this equation lias been prepared the following table. —— 102 — Span Span w5 70r 240 160' 300 Sor 250 1 70f S. I. 3.0 9ヴ 260 170 ' D. I. 350 ioof 270 180^ S. I. 3-20 IIC^ 275 180» D. I. 340 !2Cf *280 1 90^ S. I. 330 リヴ 285 19^ B. I. 350 I4C/ 290 370 I50， 295 2ICf 390 It limy bo noticed that these values of do not agree exactly iu all cases with those used in preparing the diagrams of stresses which accompany this treatise. Both values are merely approximate, but those in the table are preferable. Tlie teason for the disagreement is that the area per lineal foot of span opposed to tlic wind lind fiisfc to bo n/ssiuiiotl (inti fiftor weirds cliGckcd. As tliG clisftgi'CGiiiciit varies from zero to only seven per cent of the transferred load, aiid as the latter is but it small poi tioii of tlie to till lon.fl, it is not \\^>rtli wliilc to correct the dingrcims of stresses. Tlie formulae for the stresses due to 1V5 and Wß are identical with those for Jl’!： they can either bo obtained from the previous part of this chapter, or from one of Tables III and IV. To calculate the values of ]V1 and let v = maximum velocity of train iu feet per second g = acceleration of gravity r = radius of tlie curve W W=1 1 , W7 and ?r7= 了: : live load per foot of span centrifugal force per lineal foot due to car load then u、 w ?,2 ff’ r For sixty miles per hour v iv (88)2 マ t，7 : 3 2. 2 r 88 ; and 〇 = 32.2, therefore 240 ~ . from wliicli it is evident that, in order to make tlie centrifugal force Lave the same effect as the live load, the radius of tlie curve must be 210 feet. Generally it is not much less tliaii 1 ，〇 00 feet, consequently the ceiitrifugal force seldom produces stres- se& one fourth as great as those clue to the live load. In ci similar maimer we cau establish the equation = 240 — The formulae for the stresses due to JV7 are identical with those clue to Wn and TF3. . The formula for the concave side chord stresses due to Ev w)icn tlic panel length is not less than eighteen feet is 5 000005050 w 14780 I?) 46 4 4 4 4 5 5 5 5 5 SI CCOOGOOC — 2 2J 4 56 700 9 c 220* 2 22 2 23 — 103 — 0 = {2 n’— 1 ) [n — nf)— tan O' ''liei’o (not less than is the number at that end of the panel considered nearest the middle of the span. When the panel length is less than eighteen feet the formula is C = 2 (?〆 一 1) tan 0f When there is an odd number of panels the stress in tlic middle panel is the same as that in tlie next consecutive panel. • The formula for the convex side chord stress clue to Fm when the panel length ^ not less than eighteen feet is (2 m'-1) (h-m，) 会 tan 6' where n' (greater tliau is tlie number at that end of tlie panel conaidoved furthest fl-01a the middle of the ’ span. For a midillo panel, when the number of panels is 0 山 1， tlie stress is tlie’same as for tlie next consecutive panel. If tlie panel length be less than eighteen feet, tlie formula is T = 2 (n'-l) 1 tan 6'' This being inapplicable to the case of a middle panel, when tlic number of panels 1S 0(飞(1， the following formula is to be there used T =( (" 2”- 1 ) IT tan e， As before stated these stresses clue to curvature can be found for all practical Cascs l)y consulting Table V. i'Gcapitulate : the following are the steps to bo taken in calculating tlie sti esses in tlie trusses by means of the tables. 1 • Make table of data. 2 • Find live ami dead load stresses. ° * 上、 iu(l curvature stresses upon one cliord, if any. 4P. Find wiml stresses on windward bottom chord with empty bridge. り。. Find reduced dead load and the corresponding lower cliord stresses, when hi ■巧 ge is empty. 6。. Detevmiuo whethei* the bottom cliord will require to be stiffened ； and, if so, wllafc «Besses it will have to resist. 7 • Find wind stresses on windward top chord of deck bridge, or on leeward 0 10 m chord of through bridge, when the span is covered by the moving load. 8 • Fiud diminution of stresses on windward top chord of deck bridge, or in ere - nient of stresses on leeward bottom chord of through bridge due to load transferred a wind pressure bf thirty pounds per square foot on trusses and train. 9 • Combine the stresses found by 2° and 3°. • Coinbino the stresses found by 2°, 8°, 7° and 8°. CHAPTER IX. STRESSES IN LATERAL SYSTEMS AND SAVAY BRACING. Without making any material error the wind pressure, for the purpose of sim- plifying calculation, may be considered as equally distributed between the two sides of the bridge, although the windward side does receive the larger share. When the bridge is empty, the stress in any lateral rod can bo found by the formula 卜# ±i). Ti^. [Eq. i] , anti that in any strut except those at the ends of tho lower lateral system by the formula where W is the sum of the pressures at a windwartl anti leeward panel 130 iut, ?/ the number of panels in the wind bracing counting in the two lacking at the ends of the upper lateral bracing in through bridges, ( not less than f ) the number at the leeward end of the rod or at either end of the strut, the panel points being marked as directed m the last chapter, and 〇 tho angle that tlie rods make with the struts. When the moving load is upon the bridge the stress in any lower lateral rod of a through or pony truss span or in any upper lateral rod of a deck span can be found by the formula T ?パ("'+ 1) W sec 〇 2 n + n1- it — sec 0. [Eq. 3] ami that in any corresponding lateral strut, except those at the ends of the lower lateral system and any strut at tlie middle of the spau, by the formula n’ （"’ 一 1)+", 2 n . W+ (»〆一 [Eq. 4] * This formula is not exact, and, on account of the ambiguity iu the division of wind load between windward and leeward panel points, it would be difficult to make it so. It gives iu every case a stress greater than that which could ever come upon the strut. Tlie error is never very large, is greatest for the light struts near the caatre of tlie span, and roduces to uearW zero for the heavier struts near the end of the span. The same remark applies to Eq. 4 of this clmpter. 一 105 — a middle strut in a span with an even number of panels tho formula is G =^4^ W + \ [Eq.^A.] where W is tlio pressure on the train which is concentratel at one panel point or 40 times the panel length in feet divided by 2000, W\ is the panel pressure upon °wer half of the trusses and the floor system, calculated for a wind pressure of Ul y pounds per square foot, autl tlio other quantities have the same values as before. When the span is empty tlie stress in the lower lateral strut at the free end of a sPau わ given by the following formula 2 n — 1 cn パ TVa wb - ^ (G-2Ö0. [Eq. 5] ^lieie Tfa and Wb are the panel wind loads (both windward and leeward) for tlie Wer and uPpör systems respectively, l is tho length of span, G the cloud load per üeal foot 0f bridge and G[ the released load p*er lineal foot u actor tlio assumed Maximum wind pressure. . the span is covered by tlio moving load the stress in tlie same member is Gj: 2 n 一一 1 JVa WV- 占 (Gf-2 G.'MEq. 6] 4 a 1 4 『heie TPa i8 tlie total panel load (both windward and leeward) for the lower system e. tlio sum of the fixed and moving panel loads, IF* the panel load (both wind- and leeward) for tlie upper system at thirty pounds pressure per square foot, le of span, Gr tho sum of tlio assumed live and dead loads por lineal f jot a e en°llie excess is not considered) and (7/ the released load per lineal foot under Pressure of thirty pounds per square foot ou trusses and train, • he stresses in Eqs. 1 aucl 8 are to be increased for initial tension as tlircdel laP^i* VI, or, what amounts to the same tiling, those stresses arc to bo used gUt sizes of tlie rods determined by Table YI : and tlie stresses in Eqs. 2, 4, 5 and 公 こ re ^ he increasoil by tlio sum of the components in tlie direction of tlio strut of of t ふ111 teilsi0üs iu all tlie lateral and vibration rods meeting at tlie windward end If the track upon tlie bridge be curved, the stresses upon that lateral system, c resists the centrifugal force, are to be found by adding to tlio value of W in Is. 3. and 4. tho value of Wi from the last oliaptor, and by combining these ^ ressos tlioso due to the centrifugal force of the engine excess as calculated y the following formulae T = 2 (w， 一 1) 0=2 (が一 1) and On = 2 (n — 2) 色* . Ei — 106 or r = (2 1) ~ sec ¢7= (2^-1) * and Cn = (2 ?i— 3) ~ wliere nr (not less than -2~j is tlio number at the leeward end of tlio member con- sidered, and E\ has tho same value as in the last chapter. The first group of equations is to bo used when the panel length is less than eighteen feet, and the second group for all other cases. As before Cn represents tho stress in tlie lower lateral strut at tlia free cml of tlio span. These stresses for all practical cases are given in Tublc V. The method of calculating the stresses in the vertical sway bracing is as fol- lows : the part relating to siiiglo track bridges' is essen Ü* 1113 r the same as given by Prof. Wm II. Burr in his treatise on “ Stresses in Bridge and 110 of Trusses” Tlio loads assumotl, uuless otherwise stated, are those obtained tincler a maximum wind pressure upon the empty bridge. In Fig. 1 let r be the pressure concentrated at the upper panel point on one side of the bridge : it is tliat which comes upon a panel length of top chord, one half tlie area of tlie diagonals meeting at the panel point wlien the truss is single intersection or one fourtli of said area when tlie truss is double intersection, and tlie portion of tho post above tlio piano A B. Let P’ be tlie pressure conceuti-ated at ono end of tlio intennediiito strut J K : it is that wliicli comes upon oue half of tlie post or the portion between tlie planes A B and C D, the latter being half way between J K and E F ; also, in double intersection bridge«, that which comes upon one half tlie area of tlie main diagonals and counters coupled at K, wliicli point would then be midway bet- ween H and F. Tlie pressures concentrated at the feet tlie posts tlo not affect tUo vertical sway bra- cing, so arc not considered. Let df /, b and Q reprksent the measure* ments indicated in Eig. 1 The total pressure 2 (P +P')=H is assu- med to be equally resisted by tlio feet of the posts : this assumption is probably as correct as any other that can be made. Taking the centre of niomonts at E, the moment of the pressure is 2 P d + 2 Pf (d—f) * These stresses are figured as if the loads JEi were concentrated on the chord nearest the coucave side of the track. This assumption was made so as to provide for the worst possible dis- tribution, because the exact method of divxsiou is unknown. 一 107 — V sec 〇 sec 0 ^lucli can bo resisted only by tlio moment of a released weight V upon tlie foot F, thus 2 P d + 2 Pf (d— /) = F み and 2rf( P + Pf) — 2 Pff b This released weiglit must pass up the vibration rod KG, causing a tension therein, represented by 2 d( P + Pf) — 2 Pff b ^ — wliicli stress must be increased for initial tension. To find the stress on the strut JK pass a plane through the bracing cutting GH, GK and JK (HJ not being strained), take the centre of moments at G, and consider the forces acting on the leeward side of the truss, tlieu the moment of tlie stress in will balance the moments of and ^ H, thus {JK) = ±lld~p,f P+F)- P， to which must be added the horizontal component of tlie initial tension in JH. (JK) represents tlie stress in JK. Tho stress iu GH is found by considering it a part of the upper lateral system aud not to belong to the vertical sway bracing. But if it be supposed to belong to 山6 ^tter, its stress may bo found by passing a plane as before, taking tlie centre of foments at K, autl considering only tlie forces acting at the leeward side of the |luss, so that the moment of the stress iu GH will balance the moments of the orizoutal reaction at E and tlie pressure at G, tlie moment of the increase of weight at E balancing the moment of the increase of vertical reaction at that point ; thus い G 7/ = 」 " いヒ (1 f 二 + ( 十 1)， 卜 F 0r equal to tlie stress in JK. The bending moment on tlie post, if tlie lower end bo considered free, would bo i 孖 w —/) = (p + 尸 j -: n as the foot of tlie post is rigidly attached to tlie floor beam, it may be considered as 丘 xet し Comparing these two conditions of the portion of the post between tlio foot and the iutermediatG strut, we see that they are similar to those of one hall* of a eam loaded at tlie middle, first with tlie ends supported and second with the cutis xe • It is well known that the bending moment in the latter case is only one half ブ tlhit iu the former, so we may conclude that the bending moment to be provUetl for is HP+ p，） （d —/) m bo tlio distance between centres of gravity of post channels, tlio stress on one C iailne】 produced by the bending will be 一 2 m — 108 — \ The reloasoil weight V on the windward post passes down tlio leeward post, nroducing a stress equal to f on each channel and making the total wind stress on one channel It is only for light posts that this stress need be considered, because when it is to be combined with the live and dead load stresses both C and V must be calculated for a pressure of only thirty pounds per square foot. The method of providing for this ■wind stress is clearly indicated in Chapter VI. All the formulae for vertical sway bracing, except that for the stress in GH, may be made applicable to tlio portal bracing by putting for d the length of tlio batter brace, for / the perpendicular distance between coutre lines of upper and lower portal struts, for JJ/ the pressure on one lialf of the batter brace and for P one fourth of the sum of all the pressures concentrated nt windward and leeward panel points of the upper lateral system. If Pe be tlio pressure concentrated at the leeward hip, the stress on the upper portal strut will be given by the formula C = j{P + F) — F+ P - Pe It must not be forgotten that the stresses on all portal vibration rods must be increased for initial tension or the rods bo proportioned by using Table VI, and that the stress on each portal strut is to be increased by the sum of the components in the direction of the length of the strut of the initial tensions in all -the rods meeting at one of its ends. In the case of a deck bridge with a curved track thereon, the centrifugal force of the greatest panel load will affect the vertical sway bracing in the same manner as does tlio wind pressure; so for P must be put P 屮 i (T ド 7 + 穴 i ), the last two quantities having the same signification as in Chapter YIII. Tlio portal bracing will also be affected by tlie centrifugal force of the whole train, so for P must bo put one half of the greatest reaction at one end of the span, clue to the combined wind pressure affecting the upper lateral system, and the cen- trifugal force of the whole train, or ギ un+w) +-^-3£1, and for Pe one half of a panel loading ot wmd pressure, centrifugal force of car load and centrifugal force of engine excess or i (TF3 + W7 -f Ex ) When there is no verticul sway- bracing, stiffness is obtained by the use of knee braces or brackets AB, CD, Fig 2, making angles of forty-five degrees with the vertical. Let tlie notation be as shown in Fig. 2., F being as before the relief of weight at F. P in this case is the sum of the pressures at H and G. Taking the centre of moments at E gives. — 109 Vb == I\l and V Pd Again taking the centre of moments A givos the value of the bending mo- inent Mon the strut at that point, thus Mz ド ひ-*) ~^Pd = ~b ( b-2 Let み =3 the distance between centres ofgiavity of tlio two ehaunels of which 幻10 upper lateral strut is composed, then the beuding stress will be O M T -JP »v—、 The intensity of the working bending stress being six tons, tlio number of square ⑽ ies to be added to the area of each channel in order to vesist the bendiug "will be A C Pd 0 s The stress in A B is found by takiug the eentro of moments at G, aud making 10 moment of its stress R equal to tlie moment of the horizontal reaction at E, thus li 8 V\ =5 ^ Pd and 2? = ^5 Vi = 0.707 — Ä S • Tlie bending momeufc to be provided for in the post, considering it fixed at its • *4 and tlie correspondiug stress on one channel will be given by the equation C = P(d-s\ 4 m ^ lere w lias th© same value as iu the last case. As before to make tlieso formulae applicable to a portal, make d equal to the eng 1 of the batter brace and P equal to one half of the sum of tlio pressures con， centiated at all the panel points of the upper lateral system. only one track of a double track bridge is covered by the moving load, Recording to the law of the lever, one truss receives more load than the other. Now tlie two trusses could act independently tins distribution would hold while the load coveied the track ; but if the two trusses were connected by perfectly inelastic ver- !Ca SWay bracing they would have to deflect equally, which could only occur when f e loads ou each truss were equal, so that a portion* of the load equal to the dif* ,Glenco between the greater division by the law of the lever and one half of the whole would have to be transferred by the vertical sway bracing. In reality neither these conditions will exist, the true condition lying between tlie two ; for the trus- sos do not act independently as if there were no vertical sway braoiug, anti the latter 18 ai from being perfectly inelastic. — 110 — What the actual transferred load is it is impossible to say, but it will be mak- ing an error on the side of safety if it be assumed that the load is equally divided between tho trusses ； any extra iron that may be thereby used in the vertical sway bracing will be well employed, iov it will be in a good place to resist vibration. Under this assumption let us investigate the stresses in the bracing. Let the nota- tion be as in Fig. 8, II and B! being the reac- tions due to tho weight W, distributed ac- cording to the law of the lever, so that R = W 2 a + b Let G be the weight transferred by the brac- ing, then The stress in the vibration rod is therefore Fia .s. j i T= G&ec 0 = TV a sec q 2 (a + b) The stress in J K is found by passing a piano to cut G IT, J K and J H, sup- posing that the only weight acting is ^äTb] E, and taking tho centre of moments at H. This gives f r Tn J ^ 2(a + b) _ JVa - 取 W ~T~ — 了 Again taking the centre of moments at J and using the same cutting plane wo find tho stress in G II to be zero； for the moment of the increase of weight at F is balanced by tho moment of tho increase of reaction at that point, making the resul- tant moment of the external forces zero, and the stresses in J II and J Kt having no lover arms, tlieu. moments are zero, consequently the moment of the stress in G H is zero and the stress itself zero. To find the bending effect upon tlio post at K let us pass a plane cutting K F and J E, and take the centre of moments at K, then M=2^)l2(a+b)]=Wa If h be the distance between centres of gravity of post channels and an intensity of four tons be employed the ffl*ea of one channel necessary to resist this bending will be A M Wa ， — 4 ん一 4/7 But as this effect does not exist at the same time as the maximara load stress upon the post H F, it need be consiclered only when the post.is very lights — 111 — To ascertain whether it needs consideration, find the stress on the post with one train only upon tho bridge, reaching from the most remote end of the span to the foot of the post considered, and under the supposition of an equal distribution of tho チ rain load between the trusses ; tlieu proportion the post to resist this stress accord- lng to tlie method to be explained iu Chapter XI, and to oue half the section thus f°und add the value of A in the last equaiion. If the sum exceed the area of oue of the post channels required to resist the maximum live and dead load stresses when both tracks are partially covered by the assumed moving loads, then the post section is to bö increased accordingly. The vibration rods should be proportioned to resist the transferred load stress Us 出 g an intensity of five tons, or to resist the sum of the transferred load stress and the wind stress under thirty pounds pressure, using an intensity of seven and a lialf tons. If the formei* give the greater section, then tlie strut should be proportioned ド resist the transferred load stress using the intensity given in Table YIII, bufc, if not, ^ should be proportioned to resist tlie sum of the transferred load stress and the wind stress uuder thirty pounds pressure using tho intensity given in Table IX. It 姐 ust not be forgotton that the effect of initial tension is to be allowed for in propor- tioning both vibration rods and intermediate struts. In double track bridges without vertical sway bracing the trusses will j>robably act nearly independently, but of this oue cannot bo certain, bo it may be well to calculate tlie formula for the bending effect on tlie upper lateral struts duo to the transferred load under tho assumption of equal distribution between trusses, and aPl% it to a practical case. * Let the notation bo tho shihg as in Fig. 3., but let s have fclio samo signifioa- tiou as in Fig. 2., then the bending moment upon the strut will be 亚=“[2 ㈣ _s] f tlie distance between centres of gravity of strut channels bo h and tlie intensity of working compressive stress be six tons, the area required for one channel to resist bending will be ^ M Wa [2{a + b) — s] z — 顶一 m o+ り， Let us take the case of a 20, panel and assume a 十み = 12, / 各 = 1, and s == 7, we will then have the following data 、 • W = 21.2 a = 4.8 b t= 7.2 h = 1.0 and s = 7.0 which substituted above gives A 21.2 x 4.8 x 17 . 1 . A = ザ =12 square inches, 一 112 — corresponding to a 40 pound channel, which is far greater than would ever bo used in practice. Hence we may conclude that it will be necessary to assume that the trusses deflect independently in all cases where their depth is not great enough to permit of the use of vertical sway bracing. It might be well however to increase the sectional area of the upper lateral struts in order to resist the racking effect which the vibration of passing loads pro- duces in these members. It is difficult to say what the amount of increase should be, but the author considers that if six inch channels weighing eight or ten pounds per lineal foot and spaced ten or twelve inches apart be employed, the struts will bo strong enough. It is obvious that no unequal distribution of moving load can affect the portal bracing, for tlio loads at the feet of tlio batter braces rest directly upon the foantla- tions, and those at tlio first panel points produce an inconsiderable shortening of the batter braces. CHAPTER X. RIYETTING. The subject of rivetting is 0110 wliicli seldom, if ever, receives its duo amount of attention from britlgo designers. Many structures otherwise very strong are extremely weak in detail, owing to the insufficient number of rivets employed in tlie connections, and to their improper arrangement. The principal rules for rivetting have been given ia Chapter YL • Rivets should be proportioned for bending and bearing pressure, i. e. for any connection the number of rivets necessary to resist properly each of tlieso 8 leases should bo determined, and tlio greater number chosen. Table XVII gives the working bonding moinents and bearing pressures for rivets ln trusses and floor systems. It can be used for lateral systems also by making a pro- Per rethiction in tlie calculated stress : this will be exemplified in Chapter XVIII. In tliia table the first two liodzonbal lines coutaining vulgar fractious and decimals give the widths of bearings, and the other horizontal lines in the portion Jßlciting to bearing give tlio working bearing stresses for rivets of different diameters, he rest of tlio table needs no explanation. The diameters for rivots ia railroad bridges vary from half an inch to an inch, 1 far the larger number aro from three quarters to seven eighths. When two plates aro rivettod together, the rivets, being driven when hotf contract or tend to contract in length when cooled, thus drawing tlie plates together ail(l Pr°Jucing a friction which it is necessary to overcome before shear can como Upon tlie rivets. Whether this friction will dontinue indefinitely is doubtful, for Rivets .occasionally become loosened wLcn tlie structure is subjected to oft repeated 0ads ; so it« is not legitimate to depend upon the friction in order to reduce tlie う11111 her of rivets. Perhaps it is on account of tlxis factor that rivets are. seldom, 1 evei， Proportioned to resist tlie bending moments that come upon tliem , notwith- standing the fact that it is this last consideration which in most cases should L eteunaie tlio uumber to be employed. It will probably have been noticed by tlio reader that shear iug stress upon rivets las been entirely omitted from consideration. The author would hesitate before faking the broad assertion that rivets cannot shear, altlioagli it is probable^that lu u】g is tlie stress which ruptures rivets that arc generally considered sdeareli: — 114 — this mucli tliongli he will stale as the result of botli theoretical investigation anil many practical cases of designing, that when rivets are proiiortioncd for bending they u'ill have wore than sufficient strength to remt shear. Sharp edges on rivet holes will certainly cut tlio l.ivet.s， but this is not shear proper ; and it may be possible that tlierc is a certain kind (f fixedness about a well drivon rivet, which will make tlio bending moment less than its calculated value, but this fixedness is obtained by a high initial tension, which increases the stress on tlie tension side of the rivet subjected to bonding. As tins lmtial tension crtimot be measured or calculntecl, it is safer to assume no reduction of bending moment ou account of its existence. Comitersinking is a term useJ to clonotc the sinking of rivet heads into the plate so as to make tliem flusli witli its surface. Tlio least allowable depth for the countersiuking is a quarter of «"in incli, ami the least thickness of plate used for this purpose should be three eighths of an inch : for rivets over three quarters of an inch in diameter these dimensions should l)e increased by an eighth of an inch. liivets may be counter sunk at oue or both ends. Making parallel rows of rivets staggoretl avoids unnecessary weakening of tlic parts rivetted togelher. There lias been much discussion as to wlietlicv punched or drilled holes aro preferable, the general conclusion being that drilled 1101 es weaken the plates less, and, when slightly countersunk do not iuevease the shear upon the rivets ; but that punched holes tu.e so much more economical as regards shop work that, when properly made, they aro pi.efei.able to drilled ones. Tlio improvements made of late years ia ri vetting machines have increased the efficiency of work with punched rivet holes. Should for any reason it ever be necessary in bridge designiug to put a rivet through a plate whose thickness is greater than the diameter of the rivet, the rivet liole should bo drilled. Machiuo rivettiug is preferable to hand rivettiug, but there are cases when tlie latter lias to be employed. Field rivettiug is always inferior to shop rivettiug, so should l)e avoided as much as possible in making designs. "Wlien a stress is transmitted from one plate through one or more plates to another plate, the number of rivets must be increased. The rule given by Dr. Weyrauch is that “for every single shear connection the indirect force transferred ce requires for m intermediate plates m +1 times as many rivets as for direct transferrence f,. Keeping this in view tlio designer ’will avoid using more than one flange plate in floor beams or more than on。 plate for covering the channels of top chords. • CHAPTER XL proportioning of main members of trusses, lateral systems, and sway bracing. TT . tli 】aVU】g fouu(l 心 tlie stresses in the main members of the truss ami in those of a eral systems and sway bracing, and haying written them alongside the res- 幻扣1' ぶ. members iu tlie diagrams, the next step is to calculate the sections required. laol，a^s for the lateral systems and sway bracing may bo roughly drawn in 。 二1 ’ foi they need not be preserved, as the sizes cf the members are to be written 0U the truss diagram. ^ Foi the ten 81011 members cf tho trusses, tlie sections required can be found by lc the stresses on Ihc diagram by the proper intensities of working-stress, as ^ fU 111 ^iaptor VI, remembering that the intensities for main diagonals are to 11 eipolated. When found, the required areas for the sections should bo written } e diagram， after the stresses, prefixing them with the letters S. E. ( section そ U:ed)， as sliown on plate XV. It must not bo forgotten that the sections i e- わ1 山6 ^°^om ehords must be calculated for live and dead load a tresses s い aU :uten8ity of five tons aud for combined live load, dead load rm (し wind tablSSGS, au iu tensity of seven and a lialf tons. Then, by using the proper . es 111 Clmpfcei’ II， there Cfiu be found the sizes of tension members which will ive at leaM the section required. e. 8 lesses in tlie counters are to bo increased for initial tension by the amounts ^ GU. m Chapter YI， oi. wliat amounts to the same thing, the size require 1 can be Sti；:L f10lu fahle VI. by looking dowii the column heatlotl 4< Iuteusifcy of Working jss — i tons ’’ until a stress is readied which is equal to or greater than one-lialf e 、vl10】e of tlie stress on the diagram, according to wliotlier double or siiiglo ^uuteis be employed； then, by following the horizontal line which contains this ess ’ either to right or left, will be found the size of the counters or counter required. fhe sizes of lap verticals can be fouucl without calculation from Table YII. . 11 P0ny trusses having less than five panels it is necessary to make them stiffened, ^sing either trussed bars or two channels laced or latticed. . stated iu Chapter YI, if the former be employed tlio intensity of working stress . be l educed to three tons, and, if the latter, tlie effective area of the webs alone ls o be relied upon to resist tension. — 116 — The sizes of the lateral and vibration rods can bo found from the last mentioned table by looking in the column headed u Intensity of Working Stress = 7.5 tons ” in tlie same maimer as explained for counters. If the panel length correspond with the one given in Table I, or if it do not differ gre- flifcly tlioröfroui, tliGro need l)o no Ctilculutioiis lnfidö for stresses in tlio laterril systems and sway bracing ; because the dimensions of all the struts and rods for these systems are given in Table XIII, In that table the dimensions in the columa marked Pan. 1 M are the sections respectively of the portal vibration rods (if any), the lower portal struts ( if any ), the end lower lateral rods, and the lower lateral strut at the free 'end. Those in the second column are the sections respectively of the upper portal struts, tlie upper lateral rods, the lower lateral rods of the second panel, and the lower lateral strut at the first panel point. Those in the other columns are res- pectively the sections of the upper lateral strut, the upper lateral rods, the vibration rods ( if any ), the intermediate strut ( if any) the lower lateral rods and and tlie lower lateral strut. Thus the portal rods, lower portal struts, end lower lateral rods, and end lower lateral strut are assumed to belong to the first panel ； the upper portal struf, end upper lateral rods, second paucl lower lateral rods and tlie lower lateral strut at the first panel point to belong to the second panel ; the end tipper lateral strut, the vibration rods and intermediate strut attached to the first pair of posts, the lower lateral rods of the third panel and the lower lateral strut at tlie second panel point to belong to the third panel etc. etc. Spans abovo one hundred and fifty feet in length have vertical sway bracing. If the counter stresses be largo, it is preferable to use double counters : sometimes botli single and double counters are employed in tlie same truss. Where there is an odd number of panels, the centre diagonals should be made double and adjustable. Tho number of main diagonals per panel is generally two ; but, if the sections bccoAe so great as to necessitate excessively large chord pins, it is bettor to employ four ; placing two inside, and two outside, of the top chord and posts. Tho widths of tlie main diagonals should, for tlie sake of appearance, increase from the centre of tlie bridge to the ends. For the same reason, it is well to have all the chord bars of tlie same, oi neaily the same, depth ; the correct area of section being obtained foi. each paucl by varying the thickness and the number per panel. In large bridges it is peimissiblo to reduce the depth of the chord bars towards tlie ends of the span in or(kr to economize on the pins. It is also permissible, when there are several chord bars in tlie samo panel, to employ depths varying bv a quarter of an inch, provided that the bars of smaller depth be placed on the inside. If tlie bottom chord contain a channel strut, it will be necessary to proportion this member before deterniiiimg the 11111 aber and sizes of tho bars, which is accom- plished by subtracting from the total section required the effetive area of tho trebs of the channels, and using the remainder as the section required for tlie bars. In order that tlie strut may never be subjected to more than the stress assigned to it, each pin liole should be elongated towards the nearer end of tlie span a cer- tain amount which can be determined by tlie following method. Let A = the effective area of the strut webs in the middle panel, or panel — 117 — nearest the centre of the span. B = the total area of the chord bars in the same panel. C = the gross sectional area of the chord strut. T == the intensity of working tensile stress for the chord bars, and 2V ts the intensity of tensile stress upou the gross section of the strut when the bars are subjected to T, and when the strut is pulling tlio . proper amount, then AT —GT ox Tr =~ E be the coefficient of elasticity of the irou tlie stretch of each chord bar will be S- II/ kliere l is the panel length The stretch of the strut due to the stress A T will be Sf Ttl ATI 丸— CE ' Now, if the number of panels in the span be even, the elongation of the pin hole at the (昝 + 1 ) 也 panel point will be s~s， =ir if the number of panels be odd the elongation of each pin liole nearest the centre of tlie span would be “S-S’) = ^(2 -+) he stretch of tbe chord bars in tlie next parcel towards tlie end of the span will レ as before Tl S： an(l that of tlie strut I S” Tl 了: Af Tl unr it, as should generally be the case, tbo strut has tho same sectional area gom end to end of span, A == A， ， C = C , and therefore = S ’ or convenience of demonstration let it be assumed that the number of panels in le sPan is even, then tbe total stretch of the chord bars in the two panels lying 0 one side of the middle of the span will be 2 and tlio stretch of tlie strut in tlie same two panels will be 2 S, ; therefore tlio elongation of tlie second pin hole from 1 10 mWdle should be 2 ( 5 — 夕） 2 Tl = ■丨、 ” Similarly that of the next pin hole would be Pi „ . E V2-- C ) ally， if h and nf have the usual signification the elongation of the pin 1101 g at ◊- 告） 一 118 — the r n ; ) fc.!1 panel point should be The following important fact should never be forgotten iu designing this member 一 “if the pins pass through the holes in tlie struts and lie as nearly as possible to the centre of tlie span, the distances between tlieir centres should be I plus the allow- able play of tlie pin in the hole of an eyo-bar or l + ^ n .n Let us anticipate a little and consider the case of the bottom chord strut designed in chapter XVIII : its gross sectional area is 5. 7 square inches and its effective area 2.8 square inches, so that ^ may be take equal to \ . Let us assnme l = 22 feet, ancl E = 28,000 ,000 pounds or 14,000 tons. Then tlie elongation at the [ nr panel point is レ n —2 — 5x22 ザ X 0.0471 — I} 14,000 With an evon number of panels the elongations for tlie various pin holes, begin- ning at tlie one next to but not at the miciale of tlie span would be 0.047 ff , 0.094" , 0.141 ff , 0.18 8 " , 0.235 ^ , 0.282" &c. And with an odd number of panels they would be 0.024 ", 0.071 ^ , 0.118 " ， 0.105 0.212^, 0.259, 0.306 ^ &c. But in connection with this investigation there is another point which must bo considered ； viz. that when the bridge is empty the dead load should generally be great enough to put tlie chord strut in tension near tlie ends of tlie span, in order to prevent botli vibration and undue stresses on the chord bars at these places. Whether this condition exist can be determined by finding tlie dead load stress at the middle of the span, dividing it by five and comparing the ratio, which this quantity boars to the actual sections of the chord bars at this place, with the ratio ^ . If tlie former be the greater the strut will be in tension, and all will be right. Otherwise it may be necessary to reduce the amount of tlie elongation of those two or three pin holes nearest the ends of the span ； because, supposing that the strut were not in tension when the bridge is empty, as soon as an engine covers one or two panels at the end of the span, the chord bars in these panels will bo subjected to a greater intensity of stress than will those in tlie other panels, and if there be any play in the strut eyes which is not already taken up by the dead load, these chord burs may be stretched more than the allowable amount p , even before the strut comes into action as a tension member ; but, if the play be taken up by the dead load, and the chord pauols near one end of tlio span be strained more than tlie others, the strut will immediately begin to do its share of tlie work as 8001 a as the live load is applied, and none of tlie chord bars will be overstrainod. Tlie danger of overstraining the chord bars of tlie end panels necessarily increases with the ratio n or that of ~h • These ratios increase with the length of span, but fortunately the ratio of dead load to total load also increases, causing the danger of overstraining to diminish. For example in the 30CK span on plate XLII the clead load stress at the middle panel of the bottom chord is about 141 tons, which, ctividecl by five gives 28. 2 square — 119 — niches. The ratio of the latter to tlie total section of the chord bars 13 = 0,54 Tlie ratio of ^ is ^ = 0.50， showing that if tlie elongations of the strut eyes be ma(le according to tii e preceding theory, there will be a little play nofc taken up by 尤 ho dead load, so it will bo necessary to make tlie elougfttions at say tho shoes and first panel points equal to that at the second panel points. Again in tlie 21 )0’ span on Plate XXXII the dead load stress at the middle is about 58 tons making the section for same 11.6 square inches and tlio ratio = H Tlie ratio of ^ is — = 0.50, or greater than that last founcl, showing that in this case also tlie elongations of tlie pin lioles at tlie shoes and first panel points musfc he reduced from the theoretical amounts. Finally iu tlie 120， span on Plate XXII the dead load stress at tlie middle is =out 23.23 tons, and the ratio of sections -q= 0.414; while tlie ratio of 合 is 口 = 0,55, This great difference is not of muclx importance for the ratio of ^ in tlio Glu^ Panels is so small that the chord bars alone are about sufficient to take up tho stresses caused by an engine load or engine loads near one end of the bridge, consequently if the pins do lie loosely in the strut eyes when tlio bridge is empty, no urm will be clouo ； for vibration may be avoided by carelul cliord packing. Henco wo may conclude that the preceding theory of strut eye elongation may be adopted in all cases at all the panel points except one or two at each end of long sP^-us, at wliicli places they may be made equal to that at the next panel point towards tlie middlo of tlie span. “ Chord packing M is a term applied to the arrangement of the chord bars, chord strut, diagonals, posts, and beam hangers upon tlio bottom chord pins. It is a matter of great importance, but is very often neglected. The three principal consi- ^eiations to be kept in mind while arranging the packing are, that tlie bending- ^oments on the pius are to be made as small as possible, that the packing is to be as close as circumstances will permit, and that there be sufficient clearance to avoid all clianco of finding the space between tlie post channels too narrow wlieu the bridge is being erected. . The wicltli of the packing is tlepeudenfc, not only upon the number and thickness 0 tlie bars, but also upon the width of the top chord plate. The latter is often, in 1 8 ^lu, dependent; upon the chord packing. The best arrangement is to pack tlie main diagonals, counters, chord strut aud beam hangers inside of tlie posts, and the chord bars outside ; bringing the ei * ho'vevGi.， within the batter braces at the shoes, unless the end panel contain bars per truss, wlien two should go outside, and two inside. It is nofc abso- / ely necessary that the chord bars pull in tlie exact line of tlie trusses ; an incli or of deilectioii in twenty feet being scarcely noticeable and making no appreciable 1 eience in tlio length of the bar ; nevertheless it is bettor to mako tlie bars as neaily aa possiblo parallel to the planes of the trusses. The main diagonals should e P aceu next tlie post, then the beam hangers, and inside of all tlio counter or coimters an(i chord strut, if there be one, any vacant space thus left being adjusted 1 The arrangement of tlie chord bars will be treated further on. — 120 — The width of the top chord or batter brace plate is dependent upon the depth of tho channels, as the transverse distance between the centre lines of rivets, which attach the channels to tlio plate, should never be less than the depth of tlie channels : the chord packing often demands tho use of wider plate. The least widths and thick- nesses are given in Chapter YI In pony trusses tho channels are spread apart and the width of plate increased to give lateral stiffness to tlio truss. To proportion tho top chord or batter brace for a given stress, assume the depth of the channels and divide the length of panel or batter brace by it, both dimensions being expressed in the same unit. Referring to Table VIII， look down tlio column marked “Ratio of L to D’’， until the ratio jusfc found is reached, tlio number to the right, in the first of tlie three columns, is the intensity of working- stress to be used. The three columns are for the three cases, — both ends fixed, one end fixed and one end hinged, and both ends hinged, marked 隨 面, 恩®, and ©㉘ respectively. Then, to find tlie area of the top chord or batter brace, divide tho stress given on tho diagram by the intonsity of working- stress taken from the table ; from tlio quotient subtract the area of tho top plate, and divide the remainder by two : tho final quotient will be the area of each channel. This calculation should bo made with both the stress in the panel nearest the middle of the span and that in the end one, or, in long spans, that in tlie ono next to the end. If, then, with the depth of channel assumed, it be found that there is, in the table of channel sections employed, a light channel that will not bo much too heavy for the end, and a heavier one suitable for the middle of the chord, all right: if not, another trial must be made, with a channel of a different depth. The greater tlie depth of channel, the less the ratio of length of strut to diameter, and consequently tho greater the intensity of working-stress, and tho less the sec- tional area required: so, generally speaking, it is well to use tlie lightest and deepest channels possible, unless the saving|in section be small, when it will be more econo- mical, for other reasons, to use tlio next smaller depth. These reasons will be given in Chapter XYL The dimensions of the channels and plate should be written on the diagram of stresses as shown on Plate XV. The sizes of the post channels are to be found in a similar manner to the one just described, with these two exceptions, — that the column for two hinged ends is to be used, and that there is no plate. After all tho posts are proportioned, the light ones should be tested according the method explained m Chapter IX to see if they are strong enough to resist tho combined effects of loads and wind pressure. If not the aections slioultl be increased so as to make them strong enough. In high double intersection bridges where tlie diagonals are halved, and con- nected by pins passing through the middle of the post channels, as shown in Plate I, tho posts may be proportioned for half-length with both ends hinged ; but in this case tlie counters must extend to tlio ends of tho span, although there bo no stress in some of them, for the purpose of preventiug the posts from moving laterally at tlie middle. All lateral and portal struts, also tho intermediate struts in double track bridges, 一 121 — are to be proportioned by using Table IX for one fixed and one liingod end, and adding, if necessary, to the section thus found enough area to resist bending as determined in Chapter IX. Those struts do not really liave one enil fixed and the oilier liingecl, but the strength of a strut connected by abutting jaws is intermediate between that of a strut of tlio same size with both ends fixed and that of another strut of the same size witli both ends liingocl. This is because tlie inaccuracies of shop work may cause a slight deviation from axial bearing. It is not positively necessary to use a lateral strut between pedestals at tlie nxea end of all spans, but it is much better to do so, not only to distribute tlio horizontal reactions, but to keep the chords in line ; for there is necessarily a little play in the anchor bolt holes. There is generally no objection to making theso struts lighter than those at tlio れ ee en Os_>、l 00 00 •— 、1 vO 一 、1 00000000 …… 5 g Sr ll' and 34' げ， ， 3 か IV « 39% 40， and 4 ぴ 4八 4” ，， 44' 45，， 46' ，， 47’ 48', 4V ,, 5 ぴ 5 ド to 6c/ 2 370 pounds 2300 ” 221〇 ,， 2160 ，, 2090 m 2020 ,i I95O ” ' 1 83o ，， 1 Tlie value of the greatest bending moment for a floor beam for a single track udge may be dotevmiucd as follows. — 124 — Jjet W = tlie load applied at tlie bearing of iwo a butt in f? track stringers : it includes one half of the greatest combined engine anti car loads that can be concentrated at a panel point, the allowance for shock, one half the constant track load per lineal foot multipliod by the panel length, and the total weight of one stringer. 祕 = tlie weight of floor beam per lineal foot 心 = the perpendicular distance between central planes of trusses. x = the distance from the central plane of the nearer truss to tho point of the beam considered ； then for any point between the stringers fclio moment is given almost exactly by the equation M =W ( 1.8 5 ^ J w Is and for any exterior point by the equation M= Wx + [b — x) For a floor beam of a double track bridge tho moment at any point between tlie inner track rails is given approximately by the equation M=W { ^ — 9.8 8 ) + itc h2 Untier the outer rails it will be given approximately by the eo nation Af= JF ( i - 1 8.5 8 ) + ^wb^) and for any exterior point exactly by tlie equation M=2W x + The area of a flange for a floor beam is determined by substituting the value of M ill one of the equations A M A M A A = YIorA1 = +A" which were given for girders. The economic depth for floor beams of single track bridges will vary from for short panels to for long ones : for double track bridges the corresponding ratios will probably be found to be and 1^. Tlie values of IF for tlie different panel lengths are given approximately in the following table. Pan. Length. w Pan. Leugtli. w 1C， 13. 84 toils 18， 19* 79 tons II， 14. 85 ,, 19， 20.43 ，， 121 】5-79 2Cf 21.20 „ げ 16. 67 ,, w.95 ，， 17.36 » 22.62 „ 15， 18. 06 „ 23， 23.26 ,， i6r 18.73 „ 2" 24. 00 „ 11， 19.28 „ 24.64 ，， — 125 — For the floor beams of single track bridges tho value of IF may be taken from 0.06 ton for short panels to 0.08 ton for long panels ; and the corresponding values for floor beams of double track bridges at 0.12 ton and 0.15 ton. The method of determining the rivet spacing in the flanges of plate girders, track stringers and floor beams was indicated in Chapter VI : it will bo further illus- trated by an example. To find the mimbcr of rivets necessary to connect a track stringer to a floor beam where the former abuts against the latter. let W = as before the total reaction upon the floor beam caused by the total loads on two abutting stringers, including allowance for shock. t = thickness of web of floor beam tf = tliiclmess of web of stringer 1" = thickness of a connecting bent plate j) = the intensity of working boariug pressure rn = tlie working bending moment for ouo of the rivets used in tlie connection and cl = diameter of same rivet. then tho reaction at one end of a stringer is and the working bearing pressure for °Ue rivet passing through the web of tlie stringer is ノ） "パ； consequently the total dumber of rivets through the stringer web necessary to resist tho bearing pressure Wll be given by tlie equation JV n = 2pt，d Tlie stress ^ is equally divided between the two connecting plates, making the stress upon each equal to — and its moment equal to ^ X -十〆’， therefore the number of uvets through the stringer web necessary to resist bending will be given by the equation 8 m て he greater of the two numbers n and nf is to be taken as tlie proper number of U vets to use. Additional strength is gained for this connection by the supporting • shelf, but it is well not to depend tlieroon, as the bearing on the slielf may be impel* - fect， and this rivet ted coimoction is more affected by impact than any other rivetted connection in tlie bridge. The number of rivets required to attach each bent connecting plate to tlie floor earn as iar as bendiug is concerned will be given by tlie equation But for bearing upon the floor beam web, the total pressure being W , tho number of rivets for connecting each beut plate will be given by the equation n”， = __W 2p t d s before the greater of tlie two numbers nn and nf,f is to be used. — 126 — In general t = V コ t" = p = G tons, and if three quarter inch rivets be employed, cl = 0.75", and m = 0.311 inch ton (vide Table XVIII). Substituting gives n= n’’’= and が = れ" = —池一 nearly and as W varies from 13.84 tons to 24.64 tons the number of rivets passing through each leg of each bent connecting plate will vary from five to eight, which numbers it would be well to increase to seven and eleven. In plate girder designing care must be taken to so stagger the rows of rivet holes passing through the flanges that tlie latter will be weakeued as little as possible. If there be but one plate a single row of rivets on each side spaced about five inches will be sufficient ; if there bo two plates, a single row spaced three and a half inches will answer ; but if there be three plates, they must be wide enough to contain two rows of rivets on a side, with a spacing of five inches. It is bettor to use l,r rivets to pass through three tliiclmossos of plate and tlie leg of a flange angle, or even to pass through two thicknesses and the leg, if tho plates bo as thick as half an inch. Beam hangers may be proportioned by tlie equation where A is the area of the section of one leg of a hanger, and Wt tho total weight of a floor beam and its load not including any allowance for shock, the latter being provided for by the low intensity of working stress. Let us take, to illustrate tlie desgniug of a girder, the case of a track stringer for a 21’ panel. Tlie uniformly distributed live and dead load including shock is given in the first table of this chapter as 2750 pounds = 1.375 tous per lineal foot. The moment at tlie centre is 7 5.8 foot tons. Let us assume the economic depth of web to be 29" and take tlie thickness as 普", making d about 26.5" = 2.21 feet, therefore ^ = tx 221 = 8.5 8 square inches From tlie well known fact that a bar of wrought iron one square inch in section and three feet long weighs almost exactly ten pounds, we can determine the weight per foot of each flange angle by multiplying A by ten and dividing by six. This gives the weight per foot to be 14.8 pounds. Consulting Carnegie's table of angle irons given in Chapter II, we find that tho nearest size is a 3" x x U” angle, weighing 14.4 pounds per foot, which section we will adopt. The area of the section of the bottom flange is 8.58 十」"， where An is equal to tlie diameter of a rivet hole multiplied by twice the thickness of the leg of one of the lower flange angles. The thickness of the upper augle legs being Ur\ we can assume tliat of tlie lower legs as 蚤"， for there is to be a bottom plate. Let us use 栽" rivets for both flanges, because of the rather large thickness of the upper flange — 127 — angles, ami let us use a bottom plate 岳" x 8' By a careful arrangement of the tlii’eo rows of rivet holes through the legs of the angles, wo can have no section weakened by more than one rivet liolo, nevertheless it will be better to add say four tenths of a square inch to Au as thus found, because the holes of the rows in t lie vertical and horizontal legs come pretty closely together. A" m.ay therefore be taken equal to 2 x 蚤 x 5 + 0.4 = 1.28 square inches, making the area of the bottom flange 8.58 + 1.28 = 9.80 square inches. Subtracting therefrom the area of the plato or ^ x 8 = 8.5 square inches, leaves G.B6 square inches as tlio area of the two angles, which multiplied by ten sixths gives 10.6 pounds as tlio weight per foot of each angle. The most suitable section given in tlio table last used is Bin x i.r, x anil weighs 10.5 pounds per lineal foot, which is near enough for all practical purpo- ses* The assumed thickness of half an iucli uaod in determining kff gives a slight eu*or on tho side of safety. Laying out the sections of the flanges to scale, the distance between their centres of gravity is found to be a little over 27〃， so that in assuming d s 2(5.5" a slight error on the side of safety was committed. The difference is so small as not to necessitate a re- calculation. We can either let the bottom plate extend over a little more than tlie middle half of the stringer or calculate its theoretically correct length as follows. If in tlio equation M - 尤） We Su^stitute for iv and l their values and for M the greatest allowable bending foment ou the beam at tlie end of tlie bottom plate, wo can solve for x and thus find the length of plate by the equation V = l — 2 x Ihe effective area of tlio lower flange at tlie end of tlie plate ia about 6 x 1 0.5 10 0.7 7 = 5.5 3 ^Wch multiplied by 4 gives 22.12 tons as tlie permissible stress on the bottom ai】ge, and this multiplied by tlio effective depth 27" = 2.25’ gives 49.77 as the peiimssible bending moment. Substituting this gives 49.97 1»37 5 /fx 1 0 \ — 2—(21* — a：3) or x2 —21 x 9 9.5 4 1.0 7 5 7 2.4 nearly therefore x 21 土 V — 7 2.4 • on8equently the length of the plate V is ^crease it to 14 feet. 71IV 4.2 3 21 いノ 8.7 = 12.8 feet : but it is better to • 0 Bud tlie rivet spacing for the upper flange angles let us divide the beam eiigtlig of two feet commencing at both ends and moving towards the middle, Ü et us transform the equation — 128 — M — ^-( l- x) = ATd to AT=S = IV X (l 一 X ) 2 cl and substitute for ivf l and d their values, and for xt 2, 4, ß, 8 and 10, S being the actual flange stress at the point considered. Making tlie substitutions gives for the various values of S, 11.6, 20.8, 27.5, 81.8 and 33.6 tons. Subtracting each from the one following gives 11.0, 9.2, 6.7, J.3 and 1.8 tons as the horizontal stresses to be taken up by tlie rivets in the different two feet lengths. In addition to these horizontal stresses there is in each length a vertical stress caused by the two ties pressing on the angle irons. What the amount of tliis vertical stress is it would be hard to say, for the stiffness of tlie rails tends to distribute the pressure of the wheels over several ties, but if wc assume that two thirds of the weight on one wheel or 4,17 tons is supported by the inner angle in a two feet length, we will provide for a sufficiently unfavourable case. From Table XVIII we find that the working bearing pressure for a rivet on a 蚤" plate is 1.829 tons, and that tlie working bending moment for a rivet of that diameter is 0.395 inch ton. The total bearing pressure on tlie rivets in the first length is l/(11.6)a-j-(6.26)2= 18.2 tons nearly, which divided by 1.829 gives 8 as tlie number of rivets required for bearing. Tlie stress on the inner flange is [/*(5.8)2 十 (4.17)2 = 7.15 tons, and the lever arm is i (fi x J) — 好"， making the bending moment 7.15 x M = 3.8 inch tons, which divided by 0.395 gives 10 as tLe number of rivets required to resist bend- ing: this corresponds to a rivet spacing of 2.4", or about three diameters. At tli o fifth division tlie stress oil tho inner angle is ，/ ^O.ÜJ2 十 （4.17)2 = 4.3 tons, and the corresponding bendiug moment 4.3 x fS = 2.28 inch tons, which divided by 0.895 gives G as the number of rivets required, corresponding to a rivet spacing of 4." A larger spacing would do for the lower flange, but it is scarcely worth while to make any difference between the spacings of the upper and lower flanges. The change in the spacing from the end of the stringer to tlie centre should be made abrupty between stiffeners and not gradually : this is to facilitate tlie punching by machinery. Generally speaking it is unnecessary except in the caso of very shallow girders to calculate the rivet spacing for the flanges, because tlie designer may rely upon bis previous experience, but, if he be in doubt, he will break no rule of good design- ing by putting in a few extra rivets. The stiffeners may be made of 2 士, ’ x 3" x angle irons, and there should bo eight or nine pairs of them. The filling plates will have to be x 2 皆 •び In a similar manner may be designed auy plate girder or floor beam. CHAPTER XIII. THEORY AND PRACTICE OF PIN PROPORTIONING. The subject of li bridge pins ’’ is one deserving of more consideration than lias been accorded it by engineers, and authors of teclmical works. Until 1878, when Hr. Charles Bender, C.E., presented his paper on ^Proportions of Pins used in fridges ” t0 the American Society of Civil Engineers, very little was known concern- luo it； the usual custom among eugineers when proportioning pins having been to allow one square inch of pin area for every eight or ton thousand pounds of shear in 也〇 section most subject to shearing- stress. As Mr. Bender states generally, and as ”11 be shown farther on to be true for iron bridges, it is not tlie shear, but the bend- lrig- moment, wliicli oausos tlio greatest tendency to rupture ; so that in tiny iron structuro it will Lo sufficient, in finding tlie sizes of pins, to calculate the greatest foment induced in them by tlio various members coupled tliereon, and to proportion ，〇 rdingly, due regard being paid to tlia stresses in the eye -bar heads. Before mak- lug any investigations, it will be well to review and summarize the most important results of the investigations of others iu this subject. . Tho principal conclusions arrived at by Mr. Bender are, that, for a well-fitting of large diamoter, a pressure on the bearing- surface of six tons per square iucli not too large ； that for simplicity it is well to assume that this pressure is uni- ブラ 1ァ distributed over the diameter of the pin ； that wrought- iron, after millions 0 impacts, may break on the side where the stress is tensile, but never on the こ1 e where ifc is compressive, the ultimate resistance to crushing being about thirty on s per square inch; that tlie shearing- stress afc the centre of ft pin is one and uee-eightli3 times the average shear on the whole section ; that in iron and 8 eel the ratio between the greatest allowable tensile and the greatest allowable S eö,r^g-sfci*esses should be as 5 fco 4, which would make the uniformly distributed ear 2.91 tons per square inch, to correspond with a tensile stress of 5 tons per square inch; and that, owing to various considerations, iron in pins may be strained mUc^ more than similar iron in tension members. 一一 130 — Mr. B. Baker, C.E., in tl Beams, Columns, and Arches,” treats of pins merely incidentally. He finds, that, for iron in solid circular beams, tlie average value of 0 is /, where / is the ultimate resistance per square inch to rupture by ten- sion, and 0 the difference between the apparent ultimate resistance per square inch to rupture by bending anti /, according to the equation F =/ 4 - 0, F being the apparent ultimate resistance per squaro inch of tlia extreme fibre which first gives way ; and, that for steel, tho value of 0 varies between 1.7/ and 1.9/» Professor Burr devotes five pages of his work on li Stresses iu Bridge and 110 of Trusses n to the subject, of pius, ami illustrates tlie particular case of a suspension- bridge cablo pin, and a goneral case for ordinary truss-bridge pins. Professor Du Bois, in ** Strains in Framed Structures,” also gives a mathema- tical discussion of how to find tlie maximum bending-momeiifc. Table XIV. gives the working bendiug-moiueuts on all tlie iron and steel pins, and tlie working-sliear on all the steel pins, which will ever be required. Having calculated tlie beiuliug-moment, the requisite diameter for the pin can be found by looking down the proper column until a bentling-moment at least equal to the one found is reached. The diameter will bo found at either end of tho horizontal row thus located. The use of the column for shear will be made apparent presently. Tlie upper anti lower horizontal lines iu tlie table of bearings (Table XV) give tlie diameters of the pins ; the extreme vertical lines, tlie necessary widths of bearing- surface afc each end of the pins, iucliuling both cliauuel and re-enforcing plates ; and the other vertical lines, the permissible pressure, on the bearings. Tlie method of using these tables is tlie following. The pressure which the pin is to carry is to be taken from tho diagram of stresses. A trial diameter is then assumed. The ver- tical column, headed by this diameter, is to be followed down, until a number nearest the pressure to be carried is found. At either end of tlie horizontal row thus located 、vill be found the proper witltli of bearing. Knowing the width of bear- ing, diameter aiul pressure, tlie moment to which the pin is subjected may be at once calculated. Tun], then, to Table XIV, and see if this moment agree with the working-moment coiTespoudiiig to the trial diameter. If it does, all right: if not, another trial is to bo made, with a new assumed diameter. After a little experience, tlie first trial will be sufficient. A consideration of other details, such as wkltlis and depths of eye bars, etc., will frequently aid very much in these trials. Tablo XV can be used for bearings in members of lateral systems, portal brac- ing an cl vertical sway bracing by multiplying the calculated stresses by t'vo thirds. To find the least value of tho ratio of tlie diameter of pin to depth of eye bar in an iron bridge, by considering the tension in the bar, and tlie pressure between tlie pin anil bar, —— Let w = width of bar, di = depth of bar, d = diameter or pm, C = intensity of working compressive stress, T == intensity of working tensile stress ; then — 131 — and wd\T = tension in bar, tv dG = compression on pin and eye. ^lieso, of course, are equal ; and, as (7 = G tons when T = 5 tons, there results tlle equation, • d = = 0.838 rfi, 'vhicli shows that the diameter of the pin should never be less than eighty- three per cent of the depth of the bar. It is possible, though, that good iron of twenty-five tons tensile strength will resist more than thirty tons per square inch in compression : consequently d may be taken at 0.8rfi as a matter of convenience. lo find the proportion between width and depth of bars for the smallest allow- able PiQ in an iron bridge,— Let the notation be as before, and first let us suppose that there be but one pair ブ bars acting at each end of the pin, and that the total tension be a fixed quantity. ” stress in one bar is ivdiT, and its moment is u2di T. This must be equal to the lesi8ting- moment of the pin, w-liicli is given by the well-known equation. M Here R ^ ^ ^ j RI 万 • 著 7H*4, and = r = 菩, substituting wliich gives M = AttW3. •^luating the two values of the moments gives i^iTx = ^7rJ(/3, • or w2 37T ds 64 d\ Now, to make the diameter of tho pin as small as possible, the moment of the Ss be made as small as possible ; and, as the stress is constant, the lever - ^ must be made as small as possible. But tlie product of w and di is a con- 11 • so when w is smallest, must bo greatest. But the greatest value of d\ is が； su^stituting which gives wJ and w が ： 0.7 5 4 rf,s , W : 0.2 7 4^, 01' abI°ut °»e-fourth of the depth of the bars. 於.1 ere わ0 two pairs of similar bars acting at each end of tlie pin, instead of one 1 1 lr, the equation of moments will be or 2 iv2 di 為 7T Td3f to2 ; 87T (P 128 . di — 132 — As before, to make d a minimum, w must be made a minimum, or di a maximum ; therefore d = | the actual moment is represented by tlie diagonal of a rectangle whose to 8 lePlesent the vertical and horizontal moments. It is usually more convenient of th laie ^lG com^ouei1^ moments, add tlie results, and extract the square root sum, than to make out a diagram. 10 of the stresses can be easily recorded by drawing two curved lines, as Bhown in the accompanying diagram, representing tlie directions in Tvhicli the stresses tend to bend the pin, and writ- ing each moment as calculated under one or other of them, according to whether it would produce positive or negative rotation. Tlxo difference between tlie sums of each column ^ ， will give the actual horizontal or vertical moment as the case be. — 134 — As a rule single beam hangers and large single counters are to be avoiaed on account of the great bending moments wliich they produce upon the pins. The size of the pin for the liip joint depends greatly upon the arrangement of the bars which it couples. In a double intersection bridge where tliero are two liip verticals, two long main diagonals and two short ones meeting at the hip, the best arrangement is to put one pair of diagonals on the outside of the chord and the other pair inside, close to the bearing, the verticals coming next and being kept apart by a filler. If the moment on a liip pin be very great, the use of a steel pin will prove advantageous in reducing the size of tlio eye-bar heads. Except when the cliord pins are small it is not necessary to consider the effect upon them of the stresses in the lateral rods, but whenever possible the latter should be so arranged that the effect of tlie stress in the outer ono will be to diminisli the horizontal component of tlie moment on the pin caused by the stresses in tlie truss members, i. e. if tlie tondency of tlie cliord and web stresses is to bend the pin convex to the middle of the span, tlio outer rod, wlien bent eyes are employed, should point towards tlie middle ; but, if it bo to bencl the pin concave to the micldlo of tlie span, the outer lateral rod should point towards the nearer pier or abutment. The ends of pins have to be reduced in diameter, so that the nuts and pin pilots may be screwed thereon. Care must therefore be taken in proportioning small pins to see that sufficient area be left under the root of the thread to resist the tension on that section caused by tlio greatest transverse components of the stresses in tlie lateral rods. The principal objection to tlie use of large pins is not always tlie undue weight of the pins theruselves, but tlie increased size of tlio chord and tie-bar Leads, and the room that they take up. On the other Land, it is not always desirable to use the smallest possible piu, as the width of the bearing is an inverse function of the diameter of the pin : so if, owing to the necessity of a large number of rivets, the re* enforcing plates be long, it might be economical to increase the diameter so as to reduce the width. Thicken- ing the heads of eye bars lias an mjurious effect on the pins, although a beneficial one upon the heads, for the lever arms of tlie stresses are thereby increased. Bridges with weak pins will not necessarily fail by the rupture of the pins. Tlie reason for this is thus stated by Professor Bim •:“ Tlie distortion of tlie pin beyond tlie clastic limit will relieve the outside eye bars of a large portion (in some cases, perhaps all) of the stress in them. This result will produce a redistribution of stress in the eye bars, by which some will be under strained, and the others cor- respondingly overstrained. Thus, although the pin may not wholly fail, tlio safety of the joint will be sacrificed by the overstrained metal in the eye-bars. n The preceding portion of this chapter may be termed tlie theory of pin propor- tion and the subsequent part the practice. The ordinary method of pin proportioning is to figure the diameters of a few principal pins, and to make tlie others of tlie same sizes. Tims, by inspection, can be found which pin near the middle of the bottom chord is subjected to the greatest bending- moment. If there be an even number of panels in the span, it will be the middle pin; but, if there be an odd number, it may be the first, or second pin from — 135 — the middle, according to the number and arrangement of tlio cliord bars. The ver- tical component of the bending- moment on any one of these pius is so small in com- parison with the horizontal component, that it may be neglected. For bridges with mi even number of panels, — Let T = tension in middle panels of lower chord , • anil w = the average thickness of chord bars in these panels ; then, approximately, ^ = bending- moment on middle pin. * his formula may be applied, but perhaps with less accuracy, to a bridge having an 0 ⑽ number of panels ； and, it* the chord be properly packed, the error will be upon the side of safety. With the exception of the chord pins at the shoes and at the first panel points ^10m the ends of the span, all the lower chord pins may have a diameter corres- ponding to this maximum bending-moment, unless the bridge be a long or very heavy one, when some of the intermediate pins may have their sizes determined Gitiiei* by calculation or by interpolating ; taking care in the latter case that they be liberally proportioned ; for tlie strength of a pin reduces rapidly with the diameter. To find the sisse of the lower chord pin at the first panel point, use the formula, for the horizontal component of the moment, and the formula T- t J ( d + d’ ) . V ~ 4 ぐ?1 山6 vertical component； t being the intensity of working- stress for the liip ver- 1Cak, a their area (S. E.), to be taken from Table YII, d the diameter or thickness of a hip vertical, and cV that of a beam hanger. Tlie moment giyen by the formula M = \/>I2+ F2 ^Pplied to Table XIV will determine tlie diameter required. This diameter 111 ay e used also for the pin at the shoe. Where a bottom chord is composed of a continuous strut and eye-bars, the 8 less on the former cannot affect the pin, for it lias no lever arm, consequently in Pjopoifcio^jng any bottom chord pin except that at the shoe for such a case tlie value ° T is to be found by multiplying tlie sum of the areas of all tlie chord bars in tbe COnsitlered by tlie intensity of working stress for those bars. To fiud the size of a liip pin, lay off the stresses in one liip vertical and one whioVi Very lon 叾 span double track bridges this formula will give an excessive diai^ete 卜 in foments868 arranSement of the chord packing must be relied on to reduce the bending — 106 — • end main diagonal to any conveniem; scale, and nnd the value of their resultant bv tlio parallelogram of forces. This resultant will determine tlie thickness of the bear- ing, a trial diameter beiug first assumed. Ifc is possiblo that tliis bearing will have to be increased, so that there will be enough iron to transfer tlie stresses from the batter brace, liip verticals, and diagonals, to the chord, as will be explained in the next chapter. An approximate test of the sufficiency of the bearing in this respect maybe obtained as follows : — Let d = tlie area of the section of the end panel of the top chord, d = depth of chord channels, t = thickness of web of an end chord channel ; then the bearing should not be less than that given by tlie formula B =4d +t Next find tlie distance l between the centre of the bearing of tlio chord and that of tbo diagonal, also tlio distance V between the former and that of tlie liip vertical, the latter being on the inside. Calling the stress iu tlie liip vertical F, and that in tlie diagonal S, tlie vertical moment will be FI’， and tlie inclined one SL Next lay out these components to any convenient scale in tlieir proper directions, and find their resultant by the parallelogram of moments. This resultant will determine the diameter of tlio pin. If the diameter found agrees with the one assumed, or if it does not agree, pro- vided that the bearing was not determiued by the trial diameter, all right ; but if the bearing were so determined, and the two diameters do not agree, another trial must be made. Where there are more than two main diagonals coupled at tlie hip, as is tlie case in double-intersection and in heavy single-intersection bridges, ouo pair is coupled on the outside of the bearing, and the other on the inside ; so that theor- etically the greatest bending-moment is equal to the stress in tlie outer bar multi， plied by the distance between tlie centre of the bar and tlie centre of the bearing. But practically tlie moment may be greater, for the distribution of stresses among tlie diagonals may not bo as assumed : so it is well to determine tlie moment by imagining the outer bar not to exist, and proceeding as explained above for the case of only two main diagonals at the liip, excepting, of course, that tlie thickness of tlie bearing must be ascertained by finding the resultant of tlie stresses in the two diag- onals and tlie liip vertical. To calculate tlie size of an intermediate upper chord piD, tlie widths of chord and post boarings are to be determined as shown in the next chapter. The former is given approximately by the last formula, where A is the section of the panel of the chord on the side of the pin towards tlie middle of the bridge, and t the thickness of tlie corresponding cliannel. The other is given by tlie formula B= T3 —— 137 — ^heve .jj iy the area of the section of the post, and k the depth of one of its cliannela. Next resolve one-half of the diagonal stress vertically and horizontally into 1 aud Z)’ respectively. Let l represent the distance between the centre of the diag- °ua^ aud that of the extension plate, and lf the distance between the former and that d Ü10 cUord- bearing ; then 1* FI, h = vn\ aud M— K üie bridge be a small one, it will he necessary to calculate only the size ot the at the top of vertical post from tlie end of the bridge, aud to make all “e ^texiuediafce top chord pins of the same size. But, if the bridge be a large 0 加， it will be bettei* to calculate the diameter of the pin on the post midway between tlle vertical post ami the uiitMlc of fclie span, and to make all the pins between tllese Peaces of tliis diameter, and all the others of the same diameter as that at tlie eMof the first vertical post. After the diameters of the top chord pins are cletev- miued， the posfc au l chord bearings should be tested by applying Table XV, al- 1 10ugh in most cases they will be found ample. In double-intersection bridges, \vhcre the diagouals are lnilved, and coupled on losing tlirough the middle of the posts, the size of any one of these pins may be foui1^ from the moment ^töie S is the stress on the diagonals as given on the diagram of stresses, and ir the width of oUe 0f tlie main diagonals. In all pin proportioning it must be kept in mind that the diameter of the pm is never to be less than eight- tenths of tlie depth of the deepest bar coupled thereon. Tlie moment on any pin belonging wholly to a lateral system or sway bracing Cau always be found by tho formula ü/= PL |vheie iJ iy ^]ie reaction at one beariug and l tlie distance iroin the centre of this Jeaiiug to tlie centre line of the force wbicli produces l\ It must not be forgotten la onb" one set of diagonals of a lateral system can be in tension at once, and that le 也 ess on any diagonal (where single diagonals are used) should be divided ly between the bearings, making P equal to half the greatest working stress on le cliao°nal including initial tension. The value of l and consequently that of M can be reduced by making the eye 文 square iron and welding it to the rod. The author wishes to call attention to the superiority (in bis opinion) of the lln^e Method given for proportioning lower chord pins by formula over the apparently 111016 ac(iui，ate one previously explained. the former method, when the proper proportion of width to depth of bar» is — 138 — Lidliüi.edto, the diameter of the pms will be almost eight- tenth« of the depth of tlie bars, and will be great enough to resist the bending- moments produced by any legitimate method of packing. Moreover, after the diameters of the pins have been deter- mined, the chord can be packed, if it be advisable, so as to reduce the bending- moments. This superabimtlance of strength in the pins is obtained at tlie expense of a slight increase in the weight of iron ; and the increased sizes of heads for diag- onals can do no harm, because they clo not enter any limited space, as do the heads at tlieir other ends. But if, by a skilful arrangement of the packing, we can so reduce the bending- moments on the pins, that the diameters may be made small, and the proportion of width to depth of bars larger tlian ihat ibiincl in tlie last chapter, the pins may not bo as strong as 、ve imagine them ; lor we cannot be sure that all the bars are going to pull as avc Lave asbiimed that they 'vili. It may be tliat one of the outer bars iii a trifle long, mid 、\ill not pnli at all until the others are well stretclied : what, theu, becomes of our calculated bencliiig-moments ? Any one of them may be ,mc> greatly exceeded, that the pin will be strained beyond the elastic limit, and will bend perceptibly, so clianging the distribution of stress in the panel that one or more of the bars also may be strained beyond the elastic limit. But if the pin be large enough, or more than large enough, it cannot bend per- ceptibly : consoqucntly the distribution of stress will be much more uniform, even it. the bars be of slightly uncciual lengths. CHAPTER XIV. PROPORTIONING OF OTHER DETAILS. • The sizes of stay plates used at the ends of systems of latticing or Rouble -riveted ^a°ing are given in Table XXfL and the sizes of those used afc the ends of systems 0f single-riveted laciug, in Table XXIII. The headings of these tables fully explain their use. Stay plates are to be employed at the middle of posts (see PI. IX, Fig. 8) the (Vuigoruils are halved, and connocfcetl by pins passing through the posts ; their sizes being taken from the before- mentioned tables. Stay plates, it* they can be 8 ぐ called, are also to be used on the lower porfcal struts, for the purpose of attaching the knee braces. Kn bearings are sometimes figarecl, conn ting in both ro- enforcing plates cind 'Ve】〕 ； but tlio latter is often omitted. This would be necessary when the holes in the web are boi’ed independently of those iu the re-enforcing plates, for then it is very im- P lob able that the different holes will coincide ; but, wlieu the re- on forcing plates are ^veted to the web before boring, such a precaution is not only unnecessary, but is ft 卿 ste of material. ヤ consulting Table XVI. can be found afc a glance, accurately enough for all Practical purposes, the thickness of web of any Union Iron- Mills channel bar, when le Weight is given, or I'ice versa. here ro- enforcing plates act also as splice plates, tliero bIiouUI bo when pi’ac- e one on each side of the web in order fco insure a good, substantial joint. , The length of a simple re-enforcing pLiie depends upon tlio number of rivets ^^uired, and is thus determined. Find, by dividing the stress given on the diagram ^ Miesses between the various thiclcnesses of iron which constitute the bearings, the ^nioiint 0f stress which the plate considered is to carry. It is well, though, to make 1 レ61，】 al】owance， say twenty per cent, for the possibility tliafc the stress may not 1 :'1 e(l Proportionately to the thicknesses. Next multipl3r the stress so oLtaineil ’ le PerPenilicular distance between the central plane of the re-enforcing plate and — 140 — that of the plate or web re-entorced ; the product will be the moment of the stress upon the re-enforcing plate. Divide this moment by the working bending-moment, taken from Table XVIII, for a rivet of the diameter to be employed for the connection : the quotient will be the number of rivets required to resist bending. Next find, from tbo same table, the working bearing-stress for one of the rivets upon a plate of the thickness of the re-enforced plate or web, and divide it into tlie stress which the latter carries : tlie quotient will be the number of rivets required to afford sufficient bearing. The greater of the two numbers thus obtained is tlie one to be employed. Next make to scale a drawing of the rc- enforcing plate, laying out the rivets, if it be possible, symmetrically, and thus determine the length of the re-enforcing plate. In case of a re-enforced pin 1101 e, if the diameter of the hole exceed one-lialf the width of the plate, it will be necessary to put more rivets in front of the pin hole than behind it ; the ratio of the number in front to the whole number being equal to that of the diameter of the hole to the width of the plate. The method of proportioning splice plates or connecting plates is somewhat similar. For instance, let us take tho plates at a joint in the top chord ; which joint, for reasons stated in Chapter IV, is always to bo placed a few inches to that side of the pin 11010 farthest from the middle of the span. The stress on tho por- tion of tho plates to this side of the joint is that due to the stress in tho panel where tlie joint occurs ； while that on tlie other portion of the plates is due to the stress in the next panel towards the middle of span. The number of rivets on each side of the joint will be dependent upon tlio stresses carried by the channel bars of the two adjacent panels, which stresses are most readily determined by multiplying the area of the cliannols by the intensity of working stress given in Table VIII, and by which they were proportioned. The stress on each channel is to be divided equally or otherwise between tlie two connecting plates, and the number of rivets on each side of the joint is to bo determined in the same manner as for rc-enforcing plates. To determine tho length of tho cover plate, find in the same manner the number of rivets upon each side of the joint, which will take up the stress carried by the chord plate, which stress is to be found by multiplying the area of the section of the top plate by the same intensity as in the last case. At tlie liip .1 0111 1 tli g section ot the connecting plates must answei* two re^iiire- rueiits; fiisf, theii iiio’x (neglecting， on account of its being bent, tlio effect of tliG covgi* plate) must be sufficient to transfer to the chord a stress equal to that in the first panel ; and second, that the pin bearing be sufficient for the resultant of the tensions in the diagonals and verticals meeting at the hip. The length of the cover plate at the hip cannot be calculated, for it carries no stress, simply adding to the rigidity of tlie joint, and keeping the rain therefrom. The area of the greatest section of the connecting plate at one side of the shoe made by a plane perpendicular to the direction .of the batter brace should be equal to tliG circfi of ohg bfiltcv brtico clitiniicl, or greater if tlie slioo pin require grcfitcr bearing than this would afford； and there should be enough rivets to transfer the stress from the Latter brace channel to the connecting channel or plate. Should the batter-bracc channels bear against the shoe plates, as they ought to do, there —— 1 4 1 will be more rivets than necessary ； but such a bearing should not bo counted upon. Tlie rules for proportioning shoe, roller and bed plates are givon in Chapter VI. At the iutennodiate stmt connection, there should be enough rivets used in respect to bending and bearing to transfer the calculated stress upon the strut to tlle connecting plates. The method of determining the dimensions and number of rivets for extension plates on the npnor ends of posts is similar to that explained lor splice or connect- ing plates. The thiclvness of tlie re- enforcing plates at the lower end of a post is determined by tlie Leaving required; and tlieir length in the manner already clesoribed. The reason for cutting away the bottoms of the post channels is merely to p ick the chord more closely, and thus reduce the bending moments on the pins. But, if tho method of Pm Proportioning recommended be adopted, tlie necessity for cutting away the chan- nels， to any extent, vanishes ; for at the middle of tho span the web stresses are so sma】l， 认妣 their moments aro neglected, and the pins at the feet of the other posts have aa excess of strength. When, because of their large diameter, the lateral rods cannot be attached to the clioixl pins, but must be connected by vertical pins passing through the lateral ^ nit jaws, they must be made to pull on the middle point of each of the latter pins y using a double eye on one of tho rods, with a space between large enough to a^mit tlie eye of the other rod. This is to avoid all tendency to rotate the lateral stnU about its axis. The rods can be retained in place by fillers above and below. With this detail, there is a tendency to break the jaw through the pin holes, because of the moment of the longitudinal component of the lateral rod stress : 二 e jaw plate must therefore be made wide enough to properly resist this moment. f easiest way to proportion the plate is to assume its dimensions, and to fmd its ^Gsistancc to bending, neglecting the area lost by the pin holes (which area is" close 0 ヲ ie neuti-al surface), and making up for the omission by providing a little extra resistance. To illustrate the method, let us take a two-inch lateral rod, making an angle of 01 ^7*^ve Negroes with the planes of tlie trusses, and let the distance between cen- /es of pin bearings be six inches. The stress on such a rod is 8.14 x 7.5 — 23.55 0ns, ami the bemliag-momenfc on tlie pin is ^ x 23.55 x B = 85.3 inch tons, coi •- iespon(JiUg (vide Table XIV) to a diameter of three inches and a fourth. The dis- fuace from tlie axis of the pin to the centre of tlie jaw bearing will bo about « •+ 2" + i” + 吾" = め The longitudinal component of the stress on the lateral .° 18 23.55 x 0.7 = 10.5 tons, making the moment on the jaw about 5 x 16.5 = 82.5 C 1 tons. The thickness of the jaw plate should be and let us assume the width The resisfcing-niomenfc is given by the well-known formula, to be 7" M= where II gives m : て’ 11.25 tons, I = ^b(P = T\ x x (7)n, and dx Substituting, — 142 — ^ 11.25 X ^ 3^ X 49 X 7 X 2 w , ili = ij = 1 h) inch tons, nearly. The difference between 115 and 82.5, oi. 32.5 inch tons, is greater than tlic re^istiug- moment of tlie material lost by the pin liolo: so the dimensions assumed aro ample. A similar calculation is necessary at the portal rod connection to portal struts. It. is evident tliafc tlie pin holes just treated should be placed as near tho ends of t-ho strut as circumstances will permii, iji order to reduce the bending moments on the jaws. It is not customary to calculate tlie thickness of a beam liangev plate, but to make it from an inch to an inch and an eighth: it can, though, untlev certain as- sumptions be calculated. If the load on a plate be considered uniformly distributed over the portion between the beam-liangei* holes, and if the flange oi tlie beam bo supposed to take up no bending- stress, the plate may be considered as a beam sup- ported at tlie ends, and uniformly loaded. For instance tako the case of a twentv- foot panel of a single track bridge ； the reaction at each end of the beam is about. 18.5 tons. Suppose the centres of the beam hunger holes to be situated on the comers of 几 4J" x 6" rectangle, the latter dimension being transverse to the bridge, and tliafc the sides of the plate are 8" and 9"， tlion the bending moment is M = 1 - W/. = i x 18.5 x 4.5 - 10.4 inch tons. The resisting moment is where R = 4 tons, I - moment of inertia = i l){^ - 3 d3 and dt = Equating the moments, substituting and solving, gives d =： l.H inches. • Bat as the flanges do assist m resisting the bending, and as some of the weight comes upon the plate outside of the beam hangers, it is safe enough to take the thickness as low as an inch and an eiglitli. Lacing, or, as it is often improperly termed, single latticing, is about tlie most common detail foi* keeping pairs of channel bars in line: nevertheless, it must he inferior to latticing, especial^ when the lattice bars are riveted together at their intersection. By inspecting Tables XXII. and XXIII. it will be seen that a system of lacing-bars with one rivet at each end of a bar requires much larger stay plates at the ends than does a corresponding system oFlatticiug or double-riveted lacing. Tlie actual sizes of lattice or laciug bars for any strut can be detenuined only by experiment: it is thought that those given in Tables XX. ami XXI. are so strong, that the struts on which they aro employed would break in the channels rather than in the bars, aud yet not so heavy as to cause much ud necessary wsa of material. It will be seen also in these tables, that the requisite dimensions of latticing aud lacing bars depend not only upon the sizes of the channels winch they connect, but also upon the distance apart of these channels : this ia due to tlie fact that the bars are subject to compression as well as to tension. The lengths and weights of latticing and lacing bars can be found from Table XIX. It must not be forgotten that these lengths are to be used for estimate onhj ； as they were obtainocl from a diagram, and not checked by calculation. — 143 — Ilie smallest trussing- bars used should be no less tlniu a quarter of au inch by tlu.ee inches, and the bend for attachment should be no less than three inches long， 'so as to permit of the use of two staggered rivets. The heavier the trussed bars, and the greater the distance between them, the greater should be tlie section of the nissing- bars. At the ends of a system of trussing, the bars should be turned and Cached, as shown on PI. IX, Fig. 10. • The lightest bracket used should bo no weaker than a 2}/f x 4.9- angle uou, which section is to be employed only to attach intermediate struts to posts. Where there is uo vertical sway hracing, the stresses on the brackets are to be calculated as shown in Chapter IX., and tlie sections are to be proportioned Ly using the following table of approximate intensities of working-stress. Length of Strut, in feet. Intensities of Working-Stress. ずし. 广 X3" し ih"Xih"L- 〇" し 4 ,0 3.5 4.o 4.5 6 4.5 3-0 3.5 4,o 8 2.0 2.5 3.0 3-5 The number of rivets that connect the bracket to the lateral strut and post must e efficient to transfer all the stress in the bracket to each of these members. CHAPTER XV. DÜÜ13LE TRACK BRIDGES. For reasons given in Chapter I, special attention has hitherto been given to single track bridges, Inifc ns the Japanese engineer may sometimo be called upon to design a double track bridge, there will be given in this chapter, although they may have been previously mentioned, the principal differences between bridges foi- sin- gle track and those for double track roads. In the first place, of course, double track bridges are wider and their live loads twice as great as for corresponding single track bridges. This causes the weight of the track stringers and floor system proper to bo doubled, and a largo increase on the size and weight of the floor beams. Tfee live and dead load stresses on the trusses arc about doubled, thus necessitating in many cases the abandonment of rolled channels for the top chords and batter braces. The total wind pressure per lineal foot is increased because the area of the ver- tical projection of one truss is greater, fincl as the trusses are farther apart the lengths of all the members of the lateral systems and sway bracing are increased, consequently the weights of these portions of the structure are doubly augmented. For reasons given in Chapter IX, the stresses in the vertical sway bracing are greatly iucreasecl. The wind pressure ueetl not be considered to affect the stresses in the chords or posts, for in the first place ceteris paribus tlie wind stresses both direct and iudirect are reduced by the increase of width of bridge, and in the second place they are relatively less important by reason of the doubling of the live and dead load stresses. For the >samo reason stiffened bottom chords are not required in double track bridges. In these low particulars only does the designing of double tvack bridges clitfer li-om that of single track bridges, and the author is confident that anyone who has thoroughly studied the latter and perfected himself therein will have no trouble whatsoever mill the former. CHAPTER XVI. ROONOMY. TIig first point to be considered, when deciding upon the stylo of bridge for a certaiu stream crossing, is the number of spans. It is, in reality, a consideration of economy which determines this; for the best bridge to build, provided that the water-way be not too much contracted, is the one for which the sum of the cost of superstructure and the cost of foundations is a minimum. If the water-way be to° mucli interrupted, the design would not be an economical one, even if its first， cost were tlie least, because of the risk of washout to which the bridge would always l)e subject. In most cases there is not much choice concerning the number of spans, local considerations often determining it ; but there is occasionally a choice between two 0v even three numbers. The only way, then, to decide is to make a rough es- of the cost of the superstructure and the foundations for each number ; tlien， tlle choice fall about equally between two numbers, it is better nearly always to a^°pt the longer spans, because the actual expense for the foundations usually ex- ceeds the amount of the preliminary estimate. Tlie spans iu this country at river crossings are in the author s opinion al- ogetlier too short considering the sudden rises and the immense volumes of water ln 山6 mountain torrents. Tlie recent washouts in the neiglibourhood of Kioto will give force to this statement. The next economic consideration is that of depth of truss. Upon this subject ^ucli has been written, and many investigations have been made ; the general con- C Us'otl being, that the depth should be from one- seventh to one- tenth of the span : oniG English writers say from one- tenth to one- fourteenth of the span ; "while only 了11^’ as fai. as the author knows, — Benjamin Baker, Esq. C. 1^., in his treatise on earasf Columns, and Arches, n — makes it from one-fifth to one- seventh of the span. —— 146 - Such investigations bomg purely matlicmatical, and involving the use of the differential calculus, are of little practical value, as they camiot take into account the numerous variables that ought to be considered. Not only do the stresses in a truss vary with the depth, but also the intensities of working- stress in the com- pression members. These, ngaiu, vary witli tbc uumber of panels ; ami this variation is according to a law or laws altoge tlier too complicated to be handled by the calculus. Again : the iutensity of working- stress varies, or should vary, accord- ing to tho position and importance of the member. In view of the complexity of the question, and wishing to determine the most economic depths for Pratt ami Whipple trusses, the author, a year or two ago, under- took to solve the problem in a practical manner by figuring out a number of dia- grams of stresses, and bills of materials. At first lie considered that it would be necessary to calculate the total actual cost for every case, but upon further inves- tigation found that it would be sufticient to figure out tho sections and weights per lineal foot of. tho different members of ono truss, multiply these by their respective lea jfchs, ami sum up tlio products, neglecting all consideration of details, because the differences in the weights of the latter balance each other. Thus, if the depth of a truss bo increased by 0110 foot, thefo would be a little increase in the weights of the lattice bars aud rivets and a decrease in that of the pins and eye-bar heads. These may bo taken as balancing each other, without making any appreciable error. Tho most economic length of panel was at the same time invostigatetl, and was determined, without preparing complete bills of materials, by considering only those portions of the structure which arc affected by the variation in the number of panels. Economy in pony trasses is an element which ought seldom to influence the design, for a good bridge of this kind will generally require more iron than the or- dinary calculations demand. Instead of trying to avoid a little expense, regard should be paid to obtaining a good distribution of plenty of material, in order to partly compensate for the lack of rigidity which is characteristic of the pony truss. In very wide pony-truss bridges, especially when the length of span approaches its superior economic ifc might be well to make a few calculations concerning tho economic depth ； bufc tJie number of panels should bo regulated by the slope of the batter braces, which should never bo less than two horizontal to one vertical. The superior economic limit of tho pony truss is not a fixed quantity, but decreases as the width of the bridge and the load increase. After making oufe diagrams of stresses, and bills of materials, for over one lumdred spans, tho author came to the following conclusions : 一 That if the economic depth be calculated for any span, where the panel length is iu the neighbourhood of twenty feofc, and if the economic depth for the same span, bufc with ono panel les.^, be calculated, the latter mil exceed the former by one or two feet. The principal objections to the use of the double intersection for short spans are, that, as the rods are long and slender, they will vibrate more than the shorter and larger 0110s of the single intersection. Auy Haw in a small rod will have a propor- tionately greater injurious effect than the same sized flaw in a larger rod. Long % — 147 — - aud slender rods are dilticult to transport, and arc liable to become twisted and bent ; though this objection can be partially removed by halving them ; and, as the posts arc light， they will spring more under the shock of rapidly moving loads. tlie width of roadway and the live load increase, the inferior limit of the double intersection may be lowered. The common idea that a double- intersection bridge should, for economy’s sake, have more panels than a single-intersection bridge of the same span and loading, is incorrect. The economic depth for a double- in ter section truss is about three feet greater than that for a single-in torsection truss of the same span, and number of panels. These investigations were made for highway bridges, but as the loads did not (liffev very greatly from tlio loads used in this treatise most of tlio conclusions arrived a' will hold good here also. In regard to economic panel length and limiting length ot sPau for single intersection trusses the author has derived tlie following results 咖 le taking the calculations for tlio trusses, whose diagrams are given on Plates 幻 "V 〜 XLII. First that for spaus above one liundrod feet iu length the longer tlle Panel up to the limit of twenty four feet, or perhaps more, the more economic design . But as one lias to be guiJocl somewhat by appeai.ances， H is better to ave five panels in all spans uiidei. 0110 hundred feet, and not to exceed a panel eugtli of twenty-four feet in any case. Web diagonals having a slope much flatter than toi'ty-five degrees do not have a graceful appearance. The panel lengths that the author would recommend are given ia Table I. And second that in railroad bridges the economic limit of single intersection musses is higher than iu liigh^vay bridges. This is because of tlic engine excesses, ^hich are made, by placing a panel point between them, to simultaneously affect e 'Veb members of the same system of triaugulation in double intersection trusseb. 奶16 economic limit for single intersection trusses in the system of bridges lieve よ eated is ( vido Table I ) one hundred and eighty feet for single track bridges, but eie would not be much waste of iron if this limit were raised to two hundred feet. , 'e authoi’ has not made similar investigations for double track bridges, but would = ge that the economic limit would bo from ten to twenty feet less tlian for single l'ac^ bridges. The limits given in Chapter VI are merely to prevent tlie designing rUsses Wtlx too light diagonals and posts. addition to what precedes, the following general economic considerations 吣 0uld always receive attention. Field riveting should be avoided as much as possible, and designs should be e so that all the parts will come together readily during erection. ド' し slioulcl be spaced with regularity, so as to facilitate the puncliiug of tlie by 出— gmachi 臟. out Senerally better, in tlirougli bridges, to pack all but tlie end chord bars e of the posts, and reduce the width of top chord plate to a minimum* It j ch 13 always better to employ the apparently most economical depth of ä, ^or instance, if there be a choice of using ten or twelve inch channels for the top chords and batter braces, and it the sections alone would indicate a saving of say tlii.ee lmndred pouuds of iron by the use of the twelve- inch cliannels, tlie others would bo more economical; for the twelve-inch channels require larger stay plates, lattice bars, and re-euforcing plates, besides a wider top chord plate, which would increase tlie weights of the cover plates, chord pins, post latticing, posfc stay plates, shoe plates, etc,, and even add a little to the lengths of the floor beam«. CHAPTER XVII. BILLS OP MATERIALS, AND ESTIMATE OF COST. hi ^^kiiig out bills of materials, tlio list of members given iu Chapter III. will J: °.ve of great assistance. By its use, one can avoid an umlerestimate due to an fission of any of the parts of the structure. A 'で ieet， for the heads, upset ouds, and sleeve nufs or turn buckles. Should t0 a ?iC.cura*cy bo required for the weight of an adjustable rod, it will be necessary the mfltaiU lougtli will be needed at each end for the Iieads, and how much for P ⑽ t ends and titljusting-nuts by the following table of equivalent lengths of rods for upset ends, nuts, sleeve nuts, and turn buckles. r —l" 1 upsot end and x nut feet of rod は"一- if i upset end and i nnt i upset end and i nut ig feet of rod 1 4} feet of rod 中 一 i upset end and i nut 、毛 feet of red 2 upset ends and i sleeve nut 2| feet of rod XA' 一 2 {” - upset ends and i turn buckle 3 feet of rod —— löU — These equivalent leugths do not include the lengths of the upset ends themsel- ves : they represent simply the extra lengths to be added to the bar to equalize tlio weight of the nuts, sleeve nuts, or turn buckles, and the extra iron for enlarging the ends, which are six or eight inches long. It is not necessary in a preliminary estimate to ünd the exact quantities of materials, so approximations to actual dimensions can be made. This will be fully illustratetl in the next chapter. The following table, taken from Carnegie's u Pocket Compauiou,，， will be Ibuml useful iu preparing bills of iron, as will also many of the tables given in Chapter II. WEIGHT OF KIVETS, and KOÜND HEADED BOLTS WITHOUT NUTS, PER 100. Length irom under head. One cubic foot weighing 480 lbs. Length. r fV* r r 1° け" Inches. liia. Bia. Dia* Dia. Dia. I)ia. Dia. Bia. U. 54 12.6 21.5 c8.7 4 口 65.3 91.5 123. itf 4 6.-2 13-9 23.7 31.8 47.3 70.7 98.4 り 3. 6.9 15.5 15.8 54-9 51.4 76.2 105. 142. 2 7-7 16.6 27.9 37.9 55.6 81.6 112. 】5〇. 8.5 18.0 50.0 41.0 59.8 87.1 II9. 159. 9.2 19.4 44.1 63.0 92.5 J2Ö. 167. 2$ 10.0 20.7 34.3 47.1 68.1 98.0 I53. 176. 3 10.8 22.1 36.4 50.2 72.5 103. I40. 184. Si ir.5 q.5 38.6 53.3 76.5 109. I47. 19〕. 3i 12.3 24.8 40.7 56.4 80.7 114. 1 54 - 201. 3 冬 13.1 26.-2 42.8 59.4 8^.8 lao. i6i. 210. 4 13.8 27.5 45.0 62.5 89.0 I2S. 167. 218. 4 + 14.6 28.9 47.1 65.6 93.2 ip. 174. 227. 154 30.3 49.2 68.6 97.4 136. i3i. 236. 4 16.2 31.6 51.4 71.7 102. 14.2. 188. 244. 5 16.9 33.。 53.5 74.8 io6. 147. 195. 253. 5 七 17.7 344 55.6 77.8 no. 153. 202. 5| 18.4 35.7 57.7 80.9 114. 158- 209. 270. 5? 19.2 37.1 59.9 84.0 118. 16^. 216. 278. 6 20.0 3&5 62.0 87.0 122， 169. 223. 287. 6i 21.5 41.2 66.3 95.2 I3I. 180. 236. 3〇4« 7l g 24.6 45.9 46.6 70.5 74.8 99.3 106. i39. 147. 191. ao2. 250. 264. 3!r. 338. 49.4 79.0 112. 156. 213. 278. 355. u 9 9i IO 17.6 29.2 30.7 $2.*2 52.1 54.8 57.6 60.5 83.3 87.6 91.8 96.1 Il8. 124. ISO. I36. 164. 173. 181. 189. 223. 234. 245. 256. 292. 306. 319* 333. 372. 389. 406. 423. 10 蚤 II 3 3 ぶ 35-5 65.0 65.7 ior. 105. 14a. I48. 198. 206. 267. 278. 547. 361. 440. 457. 1 i i ?6.8 68.5 109. 155. 214. ^89. 575. 474- 12 38.4 71.2 113. l6l. 500. 388. 491. Heads. 1.8 5*7 10.9 13.4 22.2 38.0 57.0 82.0 Before considering a bill of material as finished, it is well to look it over to see that no mistake has been made in the number of the pieces. It is not an un- common error to pufc clown only half the correct number. As soon as tho bills of iron anti lumber arc made out and checked, the dead oa ヴ 州 foot should bo calculated, to soe if it agree with tho one assnrned within the luait specified in Chapter VI. Estimates of cost should bo liberal ； foi*, as a rule, tho actual profits on bridges こ 11 short of the amounts estimated. They can be made very readily by using a 〕 ank «i^ilar to the following : — ^»thnatcon Jhldftc across Lenfjth 巧) a", 'ft. Height .ft. Clear Boadway Static Load per lineal ft” 1bf(. Motvinff ノ む， Ih?. Weight of engine Ihs on,. -Vo. of Panels Length of Panels ... ,oad p ... @ ... @ loads @ 押 ^ TönghtAron, lbs Cau-iron, Jbs dumber, ft ... .. PiIcst ft Jfaulinff> ,,, , FreWht Fra— ■FaUcioork 五 軸’ ⑽ Painting ^acksmitMng Coal •* • •參 # . . . • • • ••• •• FreifJht on tools Travelling expenses Men'8 travelling ^gineering expenses 1 eam^9 during construction ... • Incidentals Total cost of biid/je Cost per lineal foot On fair country roads a day's work for one man may be averaged at 500 pounds awn ») i’i， that for a horse 1600 pounds drawn 5 ri and that for a bullock 8800 1 ounds drawn 4 ri : this allows for the time lost in returning with tho empty carts::: The aesigniug of falsework will be treated in Chapter XXII. Its cost will c u e that of the piles iu place, if any be required, and that of the lumber, to which i, °U ( >e atWed about two yen per thousand for framing and raising, and a yen per ousand for taking down. Falsework timber can generally be sold for something 11 ie bridge is completed : so a reduction may be made iu its cost when the Ornate is to bo a close one. lineal wheels ft. These data have been obtained through the courtesy of Ta^unobu Kono, Esq. M. E. Assistant Enpneer*Tokio-TakaSaW E-y. ■ 1 ö 发 *— — * The cost of ejection can be found approximately for ordinavy conditions from the following table. It must not be forgotten that there is a great variation in the cost of erection ; for it depends upon the locality, weather, skill of laborers, efficiency of foreman , etc. Those who feel inclined to question the correctness of this table should mako some allowanac for tho difficulty which tlie author lias experienced in getting any data whatsoever upon the subject. 一 Span. Yen. Span. Yen. Span. Yen. 6。’ 6o 150， 330 2 4 ぴ 1010 7。, 70 i6o, 420 w 1100 8or no 170， 480 、 26of 1*200 90， 130 x8of 550 27c/ I30O 10 o' 150 iqof 610 28of 1410 110， . 170 200， 690 •29c/ 1520 J20r 200 770 300' 1650 24O 221 3， 85〇 14ぴ a80 230 f 930 In the following table will be found approximately what it ought to cost to givo three good coats of paint to bridges of the different spans. Spjin. Yen. Span. Yen. 60, 8c/ 40 70 200, 220f 300 350 10 o' 100 24 O' 410 120f 125 26cy 470 14^ 160 280' 550 160^ 200 3〇0^ 600 1 8c/ 250 • The data, from which this table was made, were taken from the actual cost of painting two Tokio bridges. The contractor’s figures were ‘20 sen per tsubo (86 square feet) for tlie first coat, the object, of wliieli is to prevent rust, 12 sen per tsubo, for the second coat, and 24 sen per tsubo for the third or finishing coat, mak- ing in all 5G sen per tsubo. To the author’s American ideas the figures of cost given in the table seem exor* bitanfc. At the time when the Tokio bridges referred to were painted labour was more expensive than it is now, and kinsatsu were cheaper, so it is more than probable that, if present prices were used, the figures in the table would he materially reduced. But as both labour and kinsatsu are always varying, this table will be as good as any other ; for l>y divitliug by 56 the cost there given for any particular case and multiplying the quotient by the proper cliargo per tsubo will bo found the probable cost of painting for nny number and quality of coats of paint. In the following table the author has endeavoured to give what he considers ought to bo tlie total actual cost for the single track bridgrs of this treatise. He lias assumed the cost of finished wrought iron at the nearest railway station or seaport to be six sen per pound, that of oast iron four sen per pound, lumber twelve yen per — 153 — ousaud, falsework two yen per lineal foot of bridge, hauling one yen per tou, flection and painting as per tables, blacksmitliing and coal fifteen sen per lineal 1 spau, travelling expenses thirty sen per lineal foot, engineering expenses 】 011 e to two yen per lineal foot, teaming during construction fifteen sen per a toot， common labonrer's wages twenty five sen per day, and incidentals ten Per cent. If there be two spans in the bridge, tho estimated cost of the two may be uced by five per cent., if there be three, the total cost may be reduced by six per Ceut, And, if there be more than tliree, by seven per cent. Span. Yen. Span. Yen. Span. Yen. 6。， 3,500 】5 び 12,710 240， 3 l,CCO 70f 4，170 16 c/ 14,540 25。， 3 5,450 8。， 4,950 1 7 び 1 6,^90 i6or 36,150 S。， 5,6 i8or 17^5° 27c/ 39>45〇 iocy 6,650 19〇# 19,850 280^ 4 ろ 5co 110， 7,440 2COf 21 ,800 290' •46 パ co 120， 8,580 2lCf 24,130 w 49,5 こ。 IJC， 10,110 ■220* 26,100 1 4 ヴ l し 300 23O, 28,060 One paper yen lias been taken equal to ninety-five cents In Mexican oi. Japanese u v , and 01le dollar or yen of the latter equal to ninety cents gold. The prices alw( 。ど ^ 0n aro American. The prices in the tabic are in paper yen : they 0110 uld Vays be changed to suit tlie varying values of paper and silver money in compari- 8011 witl1 goW as a standard. c y\ 03118 い10 1 be forgotten that the estimated costs in the table are for aceraye 1^°ns, sucli as fairly good roads and weather, absence of freshets, a single tier ^ raiIle^ falsework on piles not exceeding twenty feet in length, a favourable looa- lal)U ^ 仙6 す01 s^01^nS materials, erecting tents &c., no probability of a scarcity ot foi.0l^leiS 01 【heir heiug attacked by disease, workmen to provide food and shelter timb lerüse^ves> 110 special tools required, and no extraordinary loss of tools oi. Before niakiug an estimate on a bridge, one should endeavour to obtain as aüy as possible of the following. DaTA FOR DESIGNING IRON RAILROAD-BRIDGE SUPERSTRUCTURES, AND ESTIMATING THEIR COST. Length of span or spans. distance of bridge site from nearest railway -station or seaport. Quality and condition of the roads between these places, ature of bed of river, and velocity of stream, eight of lower chord above bed of river. l0ss 8ectiou of stream at crossing, showing borings, if any liavo been made, which the direction of bridge makes with axes of piers or abutments. — 1 〇*4 - Nature of tlie country at the site. Any special difficulty that may be anticipated for the raising. Kind of falsework it would be advisable to use. Cost of piles at various places in the neighborhood， if any be required. Cost of transport of same to site. Cost of timber per thousand for falsework. Probable value of f also work timber after bridge is finished. Cost of withdrawing piles, if necessary. Numbei. of lineal feet of piles required, dumber of feet of lumber for falsework. Cost of spikes, bolts, and nails for falsework. Cost of driving piles. Cost of transporting pile- driver to and from site. Common laborer's wages. Skilled laborer's wages. Foreman's wages. Wages for team and teamster. Cost of supenutemlence by engineer or engiuoers. Number of days' teaming ou work. Date when bridge must be finished. Probable length of time it will take to raise and complete bridge. Chances of fair or foul weather dining this time. Chances of lmviug falsework carried away by a sudden rise or au ice -gorge. Chances of a scarcity of laborers. Chances or sickness among laborers. Expenses attendant on same. » Cost of tents or oilier housing for laborers, if any. Cost ot iron at mill or foundry. Cost of trau sport of same to nearest railway-ytation or seaport. Cost of lumber per thousand at mill or market. Cost of transport of same to nearest railway- station or seaport. Probable expenses for blacksmitliiiig and coal. Cost of tools, if it be necessary to buy special ones. Wear a-iicl tear of plant, ami loss of tools. Loss of bolts and timber^ Actual cost of raising similar structures umler similar circumstances. Travelling expenses of employees to and from site. Engineering expenses. Office expenses in preparing plans, etc. Advisable allowance for contingencies. CHAPTER XVIIL COMPLETE DESIGN FOR A BRIDGE. 卜％】 的 山6 bridge to l>e designed be ft through bridge of one span for a single straight ^an(l le“he leilgth of span be 108 feet from centre to centre of end chord pins. Co Chapter VI. we find the live load to be 1150 pounds per lineal foot. 2 . ing Table I. we see that there should be eight panels, making the panel length uia 6 ド’ that 山6 depth of truss should be 25 feot, and that the probable dead load ^ 6 ^S8umed as 1480 pounds per lineal foot.* toils U VII. we find tlie engine excess for one panel of one truss to be 1().7 Chapter \丄 gives the clear roadway about 13.7 feet, aiul by consulting the be 2QamS 0U ^a^es XXVI. and XXVII. we find the probable wicUli of choril plate to 15 4 f1UChes or 】.7 feet, making the width of bridge between central planes of trusses e^Df^10111 VII. we fiatl the wind pressures per lineal foot when the bridge is the ° a】)out 180 pounds for tlie upper lateral system and say 310 pounds foi* low 0『ei hteral system ; also 240 -J- 200 = 440 pounds per lineal foot for the an“ay 120poumls for the upper lateral system when the f10n：l Chapter VIII. we find Uie approximate valae of to be 300 pounds, and 认 at of '810 pountis The ta«gent of the inclination rpi 一 tlia j- 001 responding secant (vide Table II) is about 1.80 6, making tlie length ^«gonal 25 x 1.300 = 82.05 feet. p ie tanReut ^0l* the lateral systems is — = 1.3G1. 1X1 山6 preceding data we can fill out the following list. of a diagonal to the vertical is 0.84. of ：8_ 21 w . n ' ^ sec 6 : 0.7548 0.9858 reasou for n ^ ，ftVe hy the letter C to denote that tlie stress is compressive. — 157 — hus the stress in the second panel is 0 W2 tan ゲ •= G x 4.440 = 26.640. The next step is to find the reduced dead load stresses when the bridge is em* 1%: they will he multiples of }V6 tanQ, aucl the coefficients are given in the Col_n for Ir, in Table III. They are to be written on the same diagram under tlio other stresses, and are to l)e followed by T to denote that they are tensile. Thus in the second panel the stl，ess is JV6 tan 0 = 3 x 3.661 + 1.830 = 12.81 3. へ The next step is to subtract the values of T from the corresponding values of ’ m order to find the greatest actual compressive stresses that can ever come upon le chore subtracted from the total sections required, when finding the necessary areas for the chord bars. The next step is to find the wind stresses in tlie leeward bottom chord when the Ul(ge is covered by tlie train : they will be multiples of Tr：* tanQ^ and the cooffici- Gnts are given in Table V. Thus in the third panel tlie stress is ^ tan 6 x 6.302 = 37.81 2. he sti esses thus determined are to be written on the principal diagram beneath 6 live and dead load stresses already found. The next step is to find the stresses in the leeward bottom chord due to the ^ansfeired load, when the bridge is covered by tlie train : they will be multiples of ° 没， and tlie coefficients are given in Table III. under the heading hus in the third panel tho stress is ö W^taii 0 =6 x 2.734 = 16.404. or こ St1GSSeS t】Uls detemiued are to be written under those last found, and tlie two placeTb S^lesses ^or each lower chord panel are to be added together, the sum being mi e 〒ext step is to find the sections required for the tension members. ⑽ d tl 6 仏6 aml load stresses of tlie bottom chord are to be divided by five, ins 10 stresses by seven and a half, and tlie greater result taken. By tio ^le ^aoram it will bo seen that tlio combined stresses determine the sec- US 111 evei’y case but that of the end panels. The intensities for the main dia* aie 5, 4 普 and 4i tons, which divided iuto the proper stresses give the ßonals s©ctiong ieqiui’ecl as marked on the diagram. 0r lnoportion the counters we must first decide whether they are e, then consult Table VI. With channel struts iu the bottom c to be single the bottom chords, single — 158 — counters are preferable, although they necessitate rather large pins for the ' tipper chord. Looking clown the column for square sections headed“ Intensity of Work- ing Stress = 4 tons ” in tlio table we come to a stress of 0.81, the next groater yalue to 9.746, and following oufc the horizontal line containing this stress wg see that a square bar will be required. Although theory does not call for one, 've will put a single V round counter in the third panel, to aid in adjusting the bridge and to assist in taking up shock. By referring to Table VII. we see that two l\n X 2^ bars will be required for tlie hip verticals. Next let us proportion tho bottom chord strut. The greatest stress was found to be 13.827 tons. It will be necessary to use six inch chamiels, for the webs of smaller ones would bo too much cub up by the pin boles. The ends of each panel length of strut may be considered fixed, and tlie number of diameters is - 12 = 42. Consulting Table VIII. we find for these data a working intensity of 2.422 tons, which divided into 18.827 gives 5.7 square inches, correspondmg to t、vo (i" — channels. As this member acts as a strut only for wind stresses, it might appear better to employ Table IX., but because it acts also and generally as a tension member, it is better to employ a small intensity of work- ing compressive stress ； besides, as said before, any extra material put in the Avebs of the channels is not wasted, for it will assist in resisting tension. Referring to Table XVI. we see that the thickness of web of a 6" — 9,5* Union Iron Mills’ channel is 0.3 inch. If we usg g" rivets for attaching tlie connecting plates at the joints, the area lost from each channel will be 2 x 0.3 x = 0.41 口", and from the two channels 0,82 口" leaving 2 x 0.3 X G — 0.82 = 2.78 say 2.8 □” as the effective area of the webs, which area must be subtracted from S. R. in pro- portioning the bottom chord bars. By referring to Carnegie’s sections of flat bars in Chapter II. we can propor- tion the main diagonals ami chord bars as mauked on the diaguam. The pro- portion of width to depth of chord bars should be noticed : ife is made as nearly in accordance with the theory of Chapter XIII. as cii.cumsfcauces will premit. For appearance tlio widths of the main diagonals decrease towards the middle of the span. Next let us proportion the top cliord. From Plates XXVI. and XXVII. we find that 12" channels must be employed, which makes the ratio of length to least diameter equal to 21. Referring to Table VIII. we find the intensity of working stress for two fixed onds to be 3.543 tons, which divided into oaclx of the stresses gives tlie sections re- quired as marked on the diagram. The width of top plato was assumed as ?.0 パ (we will check it presently to see if it be sufficient), and its thickness 811011 U be 蚤" (vide Chapter VI.), making the area 3 ノ X 20" = 7.5 öubfcractiug this from each of the sections requived aihI multiplying each remamaer by ten sixths will give the weight of one channel bar for each panel as marked on the diagram. Next let us proportion the batter braces, for which the ratio of length to least 一 159 — diametei. is 32.6 5, and the corresponding intensity from Table VIII for two fixed euds is 2.889 tons. Dividing this into 84.628 gives 29.29 square inches as the section required. • Subtracting from this 7.5 square inches and multiplying the remainder by ten 81x^ls gives 86.82 pounds as the weight per foot of each clmimel. Next let us proportion the posts. Assuming 12" channels for the end ones, makes the ratio of length to least ^lameter 25, for which Tabic YIII. gives for two hinged ends an intensity of 2.71 tons, us divided into 87.122 gives 13.7 as the sectional area of the two cluimiels. ultiplyiug by ten anti clividing by six gives 22.83 pounds per foot as tlie weight eacli channel. Consulting Carnegie's cliaunel sections in Chapter II., we find that hls sectio» is obtainable. k) ^SSUm*uo ten inch chaunels for the next post makes tlie ratio 80, the intensity T the section vequirecl 9.93 □’’， corresponding to two 16.55 pound channels. 'vill be necessary, however, to use 17.5 pound channels, for the Union lion Mills nothing between this and 1G pound channels. Let us assume six inch channels 7 le post, making the ratio 50, tlie intensity 1.256 and the section required s 口,， corre8pondiiig to two 18.22 pound channels. Tliis is not an economical • 10n, 80 let us try seven inch cliamiels, making the ratio 42.86, the intensity 1.565 the section required 0.87 □パ, corresponding to two 10.62 pound channels, wliicli ud from Chapter II. are obtainable. to P し now time to look to the chord packing and see that tlie assumed width of tht V°1^ Plate わ sufficient, yet not too great. Referring to Tablo VII. we find that ^ e Slze of the beam hangers is 1A" square. From Table XVI. we find the width of prod 6 f°r & W 一45 •* channel is about 3.1" doubling which and subtracting the Kh IT む0111 20" leaves 13.8 ノ Tlie area of bhe top chord inner connecting plate 1〇 ず. （ e a little more than half tlie area of one chanuel say 7 口", which divided by this ;フ8 ftbout 0*6 say I" or 0.68" as tlie necessary tliicknoss. Subtracting twice 12 ^2^ 1U 13.8 and allowing a clearance of ir/ for the post inside tlie chord will leave thick 邮 如 distaüce between pinner faces of post cliaunels. Allowing for tlie 8l)ace 郎8 。ざ [I】6 plate は the foot of the post will leave 11.42 ^ as the clear packing the cl 1以〇 must go four main diagonals each 1,( thick, two beam hangers and 6.68" 肌6 sum of the thicknesses of tlie diagomik and beam hangers is 4.29" f0 adding そ" for clearance and subtracting the sum fi.om 11.42 leaves plates 的 山〇 咖此 As the latter should be about square, and as the connecting "will b 〇 二1/ 山 6 outside should be half an iiioli thick, the space required by tlie strut ; ’’ showing clearly that this arrangement will not suit. ^idcl] 1Gle U0 reason why wg should not pack tlie main diagonals outside of the next 6 1)〇8も’ ^^i*efore we will do so, and obtnin if, more room. At the foot of tlie side of こ 】ere わ .lns^ room enougli, for two main diagonals go inside and two out- Sam,、 16 り0“， aud the counter passes between the chord strut channels. Tlie the u lemai】、s aPP^y to the feet of the end posts, and as there is abundant room at l^ght ^ ^ei l〕auel Points and at tlie shoe, we see that the assumed width of 20" is ju&t — • lbO — For the lower lateral system we have the moving panel wind» load equal to =>.52 tons, and the static panel wind load = - = 2.10 tons. The secant will not differ essentially from that found for the upper lateral system. We can therefore fill out the following table of data, the notation cor- responding with that of Chapter IX. This completes the proportioning of the main members of the trusses. The sizes and weights of the track stringers and floor beams we will take directly from Tables XI. and XII. , for the method of proportioning these members was sufficiently exemplified in Chapter XII. We can either interpolate the sizes of the lateral, portal and intermediate atrutsj and of the lateral and vibration rods from Table XIII. or determine them more exactly by calculation. For the purpose of exemplification we will adopt the latter method. Let us begin with the upper lateral system. Tlie panel wind load is 180 x 21 1 QA A —2000 = 1-89 tons， ttiid the iucliuation of the rods to the struts is about equal to the arc whoso tangent is the panel leugtli divided by the clear roadway or tan -1 = tail-1 1.533 or (vide Table II.) 56*53 へ Tlie corresponding secant is about 1.83 making tlie length of the diagonal 18.7 x 1.88 = 25 feet. The following is, therefore, table of data n = = ö W - = 1.89 W n = 0.2363 and — sec 6 - = 0.4324 Using the formulte at the beginning of Chapter IX. or employing Table Y., we ciui calculate tlie stresses in the lateral struts and rods and record them as in the ac- companying diagram, # ° 公11 d the stress on the strut between pe*lest ils we mu.^t employ Equations 5 11 び Chapter IX., ancl a.lopt the greater of the two stresses tlms found. Poi 5, we have 310x21 Wn G 2UU0 TR0x21 •ZvJUU 3.255 tons, .89 tour, 1480 ^Üüü "•4 = 0.715 800 2U)Ü 0.15 ton. g gives Cn — ~-x 3 255 + x 1.89- 10« — iü ( 0.71 厂)— 0.，) 00 厂 1 1 . 1 5C) tons. For %• 6 we l ave jyf __ 4>U) x 21 2(), 0 120x21 2000 (p — 1 1 50 _j_ 1 4 30 2()00 and G> 810 200() U2 tonr, 1 .2 > tonp; = l.*29 tons, 0.155 ton — 161 n - = 8 W 二 = 2.52 WV = 2.10 w _ = 0；315 n W — sec 6 ~ n = 0.5764 WtHec 6 = = 3.843 Using the formulas of Chapter IX. or employing Table V. we can calculate the esses on the lower lateral rods and all the lower lateral struts except; those between le Pe(^st：ils, ami enter thorn upon t-ie following diagram •J/f CD —、 寸—が Substituting gives G,!=. — x 4.62 + -I x 1.20 - ^(1.29 — 0.31) = 9.24 tons, allowing that when the britlgo is empty the stress on the ond lower lateral strut is greater than wlicu the span is covered by the moving load. The reader must not conclude that such is the case for all spans, as it is probable that the reverse would be true for spans exceeding two hundred and thirty or two hundred and forty feet. Next let us ascertain the stresses in the vertical sway bracing. Using the notation of Chapter IX. we can obtain the following data P' = I x 25 x 1 x 50 x -rj— = 0.313 ton 2 2000 F = な』1 -- ~ = 0.945 - 0.156 = 0.789 ton b = 15.4 = 25 / = 10 sec^ = -iiAM£±Wli = = li83G The stress in the vibration rod is therefore V sec 6 2x25 (0.789 + 0.818) — 2x0.313x10 15.4 x 1.836 5.824 The stress in the intermediate strut is (7 = ~ (0.789 + 0.31 3) 一 0.313 = 2.442 tons. For the portal bracing F'= i x 32.6 x 1 x 50 x — = 0.408 ton 2 2000 P = 31 x ■9^.r2.1 -1^- = 3.308 - 0.204 = 3.104 tons 2 200U 2 90x21 201 )1) 0.945 b — 15.4 d = 32.6 / = 13 sec 6 == [0” + (l2 が 13 17.7 18 = 1.30 氺 The stress in one pair of vibration rods is therefore _ 2 x 32.6 (8.104 + 0.40S) ― 2 x 0.408 x 1 8 丄— 一 151 x 1.36 It is evident that this method of obtaining sec is approximate. — 1G3 — = 19.280 町扣 stress in the lower portal strut is C = (3.104 + 0.408) - 0.408 = 8.399 tons ud that in the upper portal strut is C， ~ G + p pe== 8.399 + 3.104 — 0.945 = 10.558 tons. rpi , ie portal stresses have been entered on tlie diagram for the upper lateral 8 fm. Nexh by referring to Table YI. ami using the column for round sections 1 e( ‘ Intensity of Working Stress — 7.5 tons,” we can proportion all the lateral tlie portal vibration rods as marked on the diagrams, also tlie intermediate ra^0u ro(^s> which we find will have to be 1 J7 diameter. To proportion the intermediate strut we must add to tlie stress found tlie 12 on tal component of the initial tension in one vibration rod, which Table YI. 8h0W8 ^ be 1.25 tons. lior The cosine of the inclination to tlie horizontal is 功 1836 — 0.84, making tlie bori- component 1.25 x 0.84 = 1.05 tons and the total stress on tlie intermediate ^■ut 2.442 + 1.050 ^ 3.492 tons. 011sulting Table X. we see tliafc a if, I-beam 14f long will have sufficient Htt?!'： be well to use a ö" — 11 pound beam, as a 4f/beam allows very loom foi* the connecting plates to fit between the flanges. ac|(| A x 118 pioportion the portal and lateral struts. Before doing so we must in 11 1 s^ress already fouiid, tlie longitudinal components of the initial tensions ^ 10 rod8 meeting at one end of tho strut. 8tres examl)】e let us take the second lower lateral strut on which the calculated ^ Ls Hi 75 tons. The cosine of the angle wliicli the rods make with strut is j.1^ ~ 〇以6. Table VI. gives the initial tensions on a 2y square and a 2 み" round 8.960 GS^eC^Ve^ aS 4.128 and 8.125 tons, the sum of which multiplied by 0.546 is )en . も 011 s’ which added to 14.175 makes 18.135 tons for the total stress. The assutJ °| S)rut may be taken as 18.7 ieet, and the depth of tlie channels may be evid t aS ^ inches, even though larger ones might be more economical, for it is ticabi。 fr°m Plate HL that the width of tlie strut should be kept as small as prac- . ,e* These dimensions make the ratio of length to least diameter about 33, for Work) 0ue ^xe<^ and oue hinged end, Table IX. gives 8.445 as the intensity of re 8tress. Dividing this into 18.180 gives 5.27 square inches as the section in p!lG( 5 corre8Poucling to two 8.78 pound clianuels. Consulting Carnegie's sections Din, er ^'r we that no such channel is rolled, so it will be necessary to em P °y9 P°«nd channels. 8ec は011 s 0f aU tlie other lateral and the portal struts are found in a similar diagr:r ’ ai】d are written both on the diagram of this clmpter and on the principal Sectio^ XIII.), as are also the sections of the portal and lateral rods. The s the intermediate struts and vibration rods are marked on the principa- ani uP°n the end vertical post. —— 1G4 — Comparing the sections of tlie members given in Table XIII. with those found in this chapteL* we do not in all cases find an exact agreement. This is because tlie t.iblo w.i-s m tde l>e *OL*e the exact wind pressures per lineal loot were determinea, nevertheless with ono exception the agreement is sufficiently close. The exception is in tlie sizes oi* tlie ujjpor lateral rods, whicli tlio t ible gives ns greater than those found in this clia[>t«r. This was done advisedly in preparing the table, in order to insure sufficient lateral stiffness to tlie bridges ami thus prevent undue vibration under passing loads. It is only lor sp ms under '2UÜ feet that this allowance is necessary. It is now a convenient time to test the size of tlie middle post to see it it be strong enongli to resist the bemling ami trail Hferrecl load stresses clue to a wind pres- sure ot* thirty pounds per square foot, in addition to tlie live and dead load stresses. Chapter IX. gives the stress produced by bending as (/，+/•') (ゴ ー/) = c 2 //A Hei.e /， and / 7 have values equal to of those used when calculating the stresses in tlie vertical sway bracing, while tlie values of d and / are the same as be- foi.e. The value of m is nearly 1.1 feet. Tlie following is then the table of data P + Pf = 0.735 d = 25 / = 10 m = 1.1 a 0.735 x 15 _ , , 】 ヽ There；ore C = 2 x 1.1 = 5 toi】s (^eavly). Using an intensity of five tons makes tlie section required lor one channel, to resist bending, 1.00 square inch. The simplest way to find the value of the transferred panel load V is to multiply the panel length by tlie wind pressure per lineal loot, multiply the product by tlie deptli of truss ami divide by tlie perpendicular distance between centres of trusses, reducing the result to tons. Thus V = 21 X 320 x 25 15.4 X 2UÜU = about 2 tons. Using the intensity for which the post was proportioned viz. 1.565 tons, and remembering tliat V must be equally divided between the two channels, we find the additional area of each channe], necessary to resist the stress considered, to be O.u* square inches, making the total area of one chamiel, needed to resist the effect of wind pressure, 1.00 + 0.64 = 1.64 square inches. This is slightly greater than one halt* tlie area ot* one channel, or 1.59 square inches, as previously determinea, but the tlilierence is so small that we will conclude that the post is strong enough. Next let ns proportion the pins, bogi lining witli the middle one of the bottom cliofd. The value ol* T in the formula M = ^ of Chapter XIII. is most easily obtained — 165 — by multiplying tlie sectional area of tlio bars by the intensity of working stress, so that T^z 21.96 x 5 M-- 109.8 say 110 tons, therefore 110x 13 2x 10 44.7 inch tons. . Consultiug Table XIV. we see a 4,7 pin will be required. We will use this size for the pins at the next panel points. For the pin at the first panel point we may take T = 8.70 x 5 ■= 43.8 say 44 tons, making the horizon tul momeufc II 44 x 5 18.8 inch tons. ascertain the value of T, Table YII. gives A = 4.74, and t is equal to 4 tons, ^ 1-25,/ and dt = 1 為" = 1.31", therefore 12.1 inch tons. Consequently M =： 1/* て 1J3.8 )2+ ( 12.1 )2 = 18.4 inch tons rresponc]iUg to a diameter of 8". t may be well to increase this to 3士" so as lo correspond witli tlie diameter of s ioe pin, which we must assume of this dimension, so as to allow for the un* ain PuU on each channel of the strut acting with a lever arm of three inches. も Of course there will be an intermediate bearing used for this pin. W e can in- polute the size of tl:e other bottom chortl pins as diameter. 1 °'v let us pass to the liip pin. Tlie bearing must be at least equal to that given by the equation B 26.25 i = 1.6" the ^ x 12 - 6 V^lue °； 1 being obtained from Table XVI. . 1 this value will make the lever arm l for the diagonal stress ßay 2 ナ 0.8) = 1.2" and that for the liip vertical stress i (1.6 -|- 1.25) + 0.8=»2.28 16 tons, and (F), that in a The stress (S) in one diagonal is approximately hip ^'tical, 1x^74 = 9i5 tons； maklUg tlle inclined moment, 16 x 1.2 = 19.2 iucli tons, and the vertical moment, 9.5 x f 二 21.4 inch tons. tons 町)11® these off to scale we find the resultant moment to be about 44.5 inch 仙8 ’ C0lle8P°nding nearly to a 3g" pin, tlie smaller diameter being chosen, because ^ethod gives an excess of strength. ail(j g パ11 g may now be checked by finding by scale the resultant of twice 16 tons ° UP0ri 山6 diagonal and kip vertical respectively. It proves to be about 40 XV： we find that for this stress and a pin 8|7/ diameter, a 0 of 1 8’’ will be required, showing that the assumed lever arms are ample. —— 166 — Next lefe us calculate the size of the pin at the top of the end vertical post. The chord bearing is given by the equation B = ^ + 0.75 = 2.1"Say2 会〃 and the post beariug by the equation B = - 1.14 " sa" U〃 These quantities make the lever anus I = i ( 1* + H M " say 1 " to allow for play, and Z / = ^ ( + Ü) +H= " say 2ド to allow for play. We must again suppose tlie outer bars with tlieir stresses not to exist, therefore the vertical and horizontal components of - = 11.3 tons, determined graphically to be respectively 8.6 and 7.3 tons, are the stresses to be considered as producing the bending. The vertical and horizontal component moments are therefore respectively V = 8.6 x 1 = B.C inch tons and H = 7.8 x =： 19.2 inch tons, making tlie resultant moment M = V ( 19.2)2 + (8.6)3 = 21 inch tons, corresponding to a diameter of 3 長’’. As there are but two diagonals in the. next panel, the stress on one will be 18.5 tons; and as the lever arms are but slightly greater in this case than in the last, we can obtain the resultant moment approximately by multiplying the preceding value by 器 or 1.2, making the required value 25.2 or say 29 inch tons to allow for the slight increase in the lever arms. This corresponds to a 3i^#pin, which dimen- 8ion will not only be adopted for this panel point, but for convenience also at the end of the outer vertical post. The same diameter may be adopted for the middle pin, or its proper size may be determined in a similar manner. The total stress on the counter is 9.746 tons plii3 the initial tension of 8.83i tons, as given in Table YI., or 13.080 tons. Tlie half of this stress, 6.5 tons, passes to each side of the post and to each side of the chord, or would do so if a double eye were used on one counter. The vertical and horizontal components of this stress determined approximately by scale are 5 tons and 4.2 tons. The corresponding lever arms may be roughly taken as 5 inches and six inches respectively, making the component moments 7 = 5 x 5 = 25 inch tons and H = 6 x 4.2 = 25.2 inch toii3 — 167 — The io sultan t moment is about K = 25 \/2i = 35.0 inch tons c°Uespoadiug to a pin. As the horizontal components of tlie initial tensions may be taken aa balancing each other, the calculated value of H is too high, so we ay conclude that a pin will be strong enough. Had the counter stress been larger， it would have been necessary to use double counters close together at lr eefc and spread apart at their upper ends, so as to reduce the size of tlie middle u j C t} ^n, because it is bad practice to let tlie single counters pull eccentrically The portal pins may be proportioned by assuming tlie lever arm of tlie stress a P°l，tal rod to be 1*"， and tlie stress (vide Table VI.) 10.298 + 1.875 = 12.173 y making the moment approximately ^ x 12.17 = 18.7 inch tons, correspond- no to a 2|” piu, foi* tlie column for lateral pins is to be used in this case. The stress at eacli bearing of the vibration rod connection to the upper lateral is (vide Table VI.) ^ (6.205 + 1.250) = 8.78 tons ; and tlie lever arm may . 6 assumed as 2+"， making the moment 2} x 8.73 = 8.39 inch tons, correspond- lng to a 2^ pin. • . diameter of the bolt for coimectiug tlie vibration rod to tlie intermediate UU may be calculated ； but, if it be assumed to be 1 it will have abundant ^ Provided that the round iron of the eye be properly flattened so as to c l^ce the bending moment. 如 Ve“ical pins will be required for tlie lateral rod connections at tlie ends of tlie g.le^ lower lateral struts nearest each eud of the span. As tlie lateral rods are & 8 e， they must be attached to the middle of tlie pins. To reduce tlie bending je ^ie centres of bearings must be brought as closely together as possible. The the f> ^°SS^^e is six iuches, raakirig the beruliug moment SPt where 2P is Yj olea^e^ worJcing stress on the rod. The several values' of 2P as founcl from Table 87. le 83.867, 25.058 and 14.881 tons, making the corresponding moments 50.8, 21.57 inch tons and the corresponding diameteirs 8 备 ", 3 士 " and 2 聲" • ftp . ? aie 110w ready to proceed with tlie ** Bill ol* Iron,” in making which, close ^ximatioag of lengths are allowable. tlie 1. は US l)rePare the blauk form recommended in Chapter XVII., then turn to g0 ^ given iu Chapter III., aiul till out the form, proportioning as we 0f thl ( °^a^S w^i08e sizes have not been previously determined. The filling-out little ，抑“ denomimited “ Main Portions is a very simple matter, and needs but diacr0 X^aila^01i« It is to be noticed tliat the lengths of tlie chord bars and main ai]f t/1 S 】mVe ^een increased by three feet to allow for the weights of the heads, Ur»«“ ）SG 〇1 a 11 atliustal)lo ro.ls by five feet to allow for the woiglit of tlie eyes, s， aua adjusting-nuts. It iu *" ol°nping of members having some similar dimensious is to bo observed, hi 卿 C0nsi(lerable economy of labor if one li is to estimate ou many bridges. “•〇11 ⑴。 0l】t the last verticiil column, tlio tables of weights of flat, round and square Ueai* the eiui of Chapter II. will be found of great assistance. —— 168 — Let us employ latticing for tlie top chords, batter braces, posts, and portal struts, and single-riveted lacing for the upper lateral struts, and bottom chord struts. Referring to Tables XXII. and XXIII., we find the size of stay plates for the top chords and batter Lraces to be x 8^ , d being a little greater than D ; that foi* the middle posts \，r x d being nearly equal to 2 1); tliafc for the next lai’gei posts ^ x 8^, d Mugless than 1.5 D but greatei* tluin 1.25 /); that for tlie largest posts x 8jf,, cl being a little greater than D ; that for the upper lateral struts i" x 7Y，， d being a little greater than 1.5 D; that for the channel lower lateral struts Yr x 7,;, d being a little less than 1.5 D ; that for the 5f, channel lower lateral struts i" x d being a littlo less tlmn 1.25 D, that for the portal struts \,f x 5*"， cl being a littlo less than 1.25 D ; and tliat foi* the bottom chord struts {r, x 9,f, d being equal to D. To find the thickness of the connecting or reinforcing plates at the hip we niuht divide the area of the section of tlie first panel length of top chortl by twice tlie suni of the depths of the outer and inner plates, i. e. 26.25 一 2(12 + 9) = o.g-25 = r To find the length of each plate beyond tlie centre of the pin hole, let us assume as an approximation that the total stress on the chord is equally divided between the four plates, making that on eacli one about 23 tons. The lever arm for this stress is 士 (g + 吾） = ふ" making the moment Ä x 23 = 12.94 inch tons. Let us use rivets, the working bending moment for one of wliich (vide Table XVIII.) レ 0.494 inch ton, wliicli dividetl into 12.01 gives 27 as the number of rivets required to resist bending. The total pressure on tbe bearings is about 46.5 tons, and as tbß web (vide Table XYI.) is nearly thick tlie working bearing pressure for one rivet is (vide Table XVIII.) 2.G25, making the number of rivets reiiuivetl for bearing 46.5 2.025 or 18 showing that for tlie coimectiug plates of tlie top chords the rivets neetl be pi.opo い tioned for bending only. By making a rough sketch of the connection it is readily seen that we may use four horizontal rows of rivets two inches apart, and a pitch of 3" without bringing the centres of rivet boles more closely together than good prac- tice allows. This arrangement will bring the end of the plate about 28" from the centre of the pin hole. We could make a similar calculation for the plates attache^ to the batter brace, but we can see that tlie same number of l.ivets will suffice, f^1' although tlie stress carried by each plate is less, the lever arm is greater on account of the greater thickness of the clianuel web. In order to allow for tlie bolt 1101 e 〇丈 the portal strut connection we must add two or three inches to tlie length of the plate, so if we say that tbe total length of plate measured along the centre lines of chord and batter brace is 5r, we will be pretty near the mark. To find tlie thickness of the connecting plates at the first joint in the top chord we must divide the area of one channel of the third panel by the sum of the widths of an inner and an outer plate. It will therefore be = 0.G : if, however, — 169 — 比 ft g the inner plate ir, thick and the outer one 為’', tlie total area of section will be just right ami the plates of procurable sizes. Although one plate lias a considerably gieatex area than the other, we must still consider that one half the stress on the uel is carried by each plate, for such is tlic probable division. It is impossible ermine tlie exact method of division, but this one will cause no undue stress ^ eitliev plate, because the actual intensity of working stress for tlie plates may be east one fourth greater than that for the strut itself. 8^gss on each plate on tlie side of the joint nearest tho middle of the span jg eie^°i*e, about G.3 x 8.548 = 22.3 tons, which multiplied by i (1 + 3) gives • 3 iuch tong as the bending moment, upon tlie rivets. Dividing tliis by 0.494, the lug bending moment for a l,r rivet, gives 32 as the number of rivets required 011 he centre side of the joint. the inimLer required for the other side, we ascertain the stress by 沿11 jplyiug % を by 8.548, making 16.(5 tons, multiplying this by i (I + i) and 1 the product by 0.494, which gives 19. y making a sketch of tlie connection and using the same arrangement for the a' the liip, a plate about four feet long will be required. shnilai’ calculation for tlie next joint shows that tlie inner plate should be J", of tli め °U^ei* 01ie ^f， thick ami that tbe length should be about The thicknesses jeil j for the middle joint will be tlie same as those last determined, but the 1 Aould be a little greater, say 5.5'. All these dimensions of plates are to be Proreriy entered on the bill of iron. 111 江 ke tli MW16 c^meils^ons a coüiiectiug plate for tlie bottom chord strut, let us cjla e area of tlie section of same through the pin hole equal to the area of oi】e 似ぬ116 ’ 饥 s which divided by 1.46, the approximate working bearing pressure for a i" rivet on a plate 0.32 5" thick, gives 10 as the number of rivets required for bearing. It will be bettor to uso a greater nuiuboL, of rivets than the calculations call for, because tlie roi a forcing plates should extend a few inches higher tliau the lower edges of the stay plates so as to stiffen the otherwise unsupported projecting ends of the post channels. A drawing to scale would show the height required to bo about 2’ mak- ing the total length of tlio inside plate 5' and that ol the outer say 2.4’. These tli mentions are applicable to fclie other post reinforcing plates, tlie widths for which should be equal to the depths of the cliannels to which they are attached, provided that; sucli depths be not less than 8". These dimensions are entered on the “ Bill of Iron.” Next come the plates for connecting tlie intermediate struts to the posts. It is not worth while to make any calculations for this counecfcioii, because the stress on the strut is eo small. We will use two bent plates each 象" 4" x 2.5, A simple calculation shows that the cliamefcer of tlio pin for attaching tlio vibration rocl should be 1J7, 'vliicli would leave 1 lf, of iron outside of tlio pin hole, which is sufficient. Next come tho plates for counecting tlio lower portal struts to the brackets, the dimensions of which we will assume to be x 0r, x 15". Next come those for connecting upper portal struts to name plates, tlie size for which we will assume to bo ゐ" x 9" x 2\ Next come tlie connecting plates for track stringers over floor beams, the dimen- sions for wliicli may be taken as ^,r x Sr, x Next come the cover plates. The length of tliose at the hip may be taken ⑽ 2', feu. they carry no stress that can be calculated. Tlie stress carried by any intormeduite cover plate is f x 20 X3.543 = 26.57 tons, which multiplied by f gives 9.96 inch tons as tlie moment on the rivet's. Using ln rivets we have 9.96 — ■ 173 — — 20 for the number . 0.494 requu*ea on each side of the joint. W we use five rows and a pitch of 8^, tlio plates will have to be about 2’ long. Next come tho filling plates, the dimensions of which for the top cliovd we may averageat^ x 12^ x Next come the jaw plates for the upper lateral struts. The greatest working stiess that could ever como upon one channel, under the supposition that it belongs to t，le triiiiSi is 1.8 x 2.013 = 3.G2 tons, the intensity being found from Table YIII. diameters and one eiul fixed. The thickness of jaw plate should be i", and the width, where the chord pin Passes tlu’ough, least 6" : it may be reduced to 4 :,, where it is attached to the c 1 ‘飞 miels. Tjie level* arm for tlie moment upon the rivets is 4(1 + i)= -h'\ mak- InS the moment Ä x 8.62 = 1.58 incli tons, which divided by 0.311, the resisting eudmg moment for a i，r rivet, gives 6 as the number of rivets required. Of the 【了 ets passing through both inner ancl outer jaw plates but one half the uumber should counted upon as acting, thus if three pass through but one jftw plate and six through J’ the effective number will be six. Uis method of proportiouiug is, of course, not exact. Lotting the distance be- tween drawi】 叫 innei. faces of lateral struts channels be Tf, we can determiue by making a 8Calö the length of the outer jaw plate to bo about three feet, and that of or Ulüei one 江 bout two feet. The thickness of the latter need be only -V1 and it« Ratest width at the hole, where the chord pin passes tlirougb, bfr. We can average ° で th of the outer plate at 5" and tlie inner oue at iif\ m ext c°mo the jaw plates on the lower lateral struts. Those on the i,r clianuel3 be assumed without essential error to be of the same dimensions as those last eriained. Those for the 5,r channel struts may be proportioned by taking the ^elo 6S^ S^l，ess that can come on tlio heaviest channel, under the supposition that it TfihfS t0 t1ie "■»Wz. 2.63 x 2,5 = 6.58 tons, the intensity being found from ぞ01’ 33 diameters and one end fixed. み e lever arm is i (舍 + i) = 長", leaking the moment upon the rivets .58 =5 2.88 inch tons, which divided by 0.311 determines tlio number to be 10. n ルレ case there is no inner jaw plate foi* the lateral rods are attached to ver- ^Ye oiust test the assumed thickness for bearing. The greatest pull that _ — «*+4( tical ping# 0^ee^er c°me on the end lateral rod is (vide Table VI.) 29.789 + 4.128 = 83.867 the .af 0f this, or about 17 tons is supported at each bearing. Tlxe diameter of ,WaS Prev^ous^y determined to bo Eeducing the 17 tons to 11.3 Ly As tf by 普， and consulting Table XV., we find the necessary beai’iug to be 金". thick 6 bears against both the channel web and the jaw plate, tlio assumed t*he t htter will be ample. Making a drawing to scale we can determine tlie な) length of jaw plate to be about 4’. The width required at tho holes for rj „ 8〇1^° 一18 can be determined as explained in Cliaptei. XIV. It will be about ふ '0 e ave^age width may be assumed as 6.t7/* We can make the jaws for all the lanuel lateral struts of the same size. — 174 — The jaw plates of the portal struts act also as reinforcing plates, so their thick- ness may have to be proportioned for this condition. The pressure on the bearing is equal to the greatest working stress on a 1Ä rod, which for an intensity of 5 tom Table VI. gives as 6.240 + 1.875=8.115 tons. The diameter of the pin was determined to be 2^.,f Consulting Table XV. we find the nocessary width of bearing to be J", subtracting from wliicli the web thickness leaves ^,r for the thickness of the plate. As tho latter will have to resist bending, it will be woll to make the thickness +"• The width should vary from 8" to 5", making the average say 7^. This width strictly speaking should be calculated, 1311 1 H is liartlly necessary ; for, judging by a similar calculation in Chapter XIV., we can conclade that if the pin hole be placed as closely as possible to the end of the strut, and if the jaw plates be made 8" wide at the pin holes, there will be sufficient material to resist the bending produced by the transverse component of the greatest working stress on the portal rods. The greatest stress on one channel supposing it to belong to the truss would bo 2.1 x 2.488 = 5.12 tons, the intensity being taken from Table YIII. for 3^ diameters and one end fixed. The lever arm is 皆 (i + i) oi* i,r, making tlie mo- ment on tho rivets g x 5.12 = 1.92 inch tons, which divided by 0,311 gives 7 as tlie number of rivets required. A calculation for bearing would give a smaller num- ber. Laying out tho detail to scalo, we find that the required length of the jaw plate is about 3’. Next come the extension plates. Let us first proportion those for the largest post. The thickness for one extension is found by dividing tlie total sectional area of the post by the doptli of the channels, or 2M = 1.14 say li，r9 which Table XV. shows to bo more than su 伍 cient for bearing. This extension plate can bo made tip of two plates each ä " thick, the inner one extending two or three inches below the upper edge of the stay plate, and the outer one as low as requisite. The stress carried by tlio rivets is ^ x 87.122 = 18.0 tons and the lever arm is i (办 + 0.88) = 0.45", making the moment 18.6 x 0.45 = 8.87 inch tons. Using J" rivets we divide by 0.494 and find the number required to be 17. Only one half of those rivets which pass through both thicknesses of plate and the channel web are to be counted in making up the 17; and the countersunk rivets passing through only the two thicknesses of* plate are not to bo counted at all. By laying out the connection to scale we see that the inner plate should extend about 10" below the ends of tlie channels, and that we can use five rows of rivets with a 8" pitch, permitting of tlie passage of 18 rivets, lialf of which being deducted from 17 leaves 10 or 11 rivets to pass through the outer plate anti the web alone, making tho former extend 18" below the top of the post channels. The total length of the outer plate is, therefore, 28", and that of the inner plate 20." Similar calcu- lations for the extension plates of the other posts will give tho dimensions recorded in the u Bill of Iron.” Tlie thickness of the shoe plate is given in Chapter VI. as V, and its other di- mensions have been determined to be 25" x 30". The thickness of tlie roller plate is also 1", its width about 25 + 2 x 3 = 31、 and its length 80-j-2x3-f2 = 38". — 175 — The area of the shoo plate is 25" x 30" less about 80 square inches for the bolt holes, or 720 square inches which multiplied by 200 and divided by ’ gives 72 tons as the greatest permissible pressure upon the shoe plate, if it r°8 S C^rßctly on the masonry. 虹 e 8reatesfc actual pressure was ascertained to be 78 tons, therefore we must er Use bed plates at the fixed end of the span or increase the area of oach shoe 七。 マ ⑹ + ⑽ = 810 square inches. If we make tlie width 26^ and the length , we will have 882 square inches of area, and there will be no undue projection p = beyond the pedestal, therefore this method will be adopted, plate ふ ^or track stringers may be made J7 x 147 x 14", and tlie anchor 0£ , beam hanger plates may be made 14" thick. The distance between centres Ch G?m l)anger8 may he averaged at 9." A 1A" square bar upsets (vide table in 1 , , . 1 ん） to for which the greatest diameter of a hexagonal nut is (vide Sv 6 W Sarüe chapter) 4,04”, making the necessary length of plate 13". Tlie neces- Y width will be 4;, ^ - 1Ä" + 4〃 say 1)ゲ’. The weight [of each of tlie two name e^inay be ftssumed to bo 50 pounds. 1 -X eX^ come the latticing and lacing bars. Tlie spread oftlioso foi. the top chords .a^or braces is about 17", aud tlie stretch should be about the same. The ^i'ac 1 ^ sPace latticed on each chord panel is about 18f 67f and that on each batter 26 ba: ，明 ’ 6 '， which distances divided by ll,r and multiplied by 2, show that 1Yln レ rs be required for each panel length of chord and 40 for each batter brace, makmg the total number 472. ip._ a^e XX. makes the size of the bars 普" x 2i,f9 and Table XIX. makes tlie i\ *008 .+ 0,281 = 2i， nearfy, aud 1 U *a 8^m^av manner are determined tlie number and climoiibions of all the lattice 、vill aCmg bars recorded iu the u Bill of Iron For simplicity in shop work we the i) Se May 1〕1心8 instead of lacing for tlie lower lateral struts : these will permit of age of the stringer connecting plates through the struts. atl(j a eil?^s of the pins on the ft Bill of Iron n include an allowance for tlie liufcs, iu Cli lCf( Uc^on ^or diminished diameters. The diameter of tho anchor bolts is found \V ミ eiH to be lj/f, and their length may be assumed to be 6,. lasted allow 100* for temporary bolts used in erection : these need not be Au all， Let 1 fo て they can bo saved for erecting another bridge. owanoe of 150* for ornamental work will be sufficient. foot of ^j?S a'era8e the length of filler for each piu at 4", ami the weight per lineal P°unds el% 以 12 pounds or the weight of each filler or pair of fillers on a pin 8 the middle16 仙⑽ over en 2\f 19,87; 8 12° 45.i”[ ) 8 12" 36.$”[ 34， 9,879 4 ず. ro.6a*[ I 8 IO" I7.5*C 卜 5.5， 9,3H 8 22.83 •[ ) IO 4" 6 •[: 】4， 840 6 4" 6 •[: 15， 468 4 S，. 7 •し r 9*[ 切 ! 864 4 5^ M-5r 4 5,# 7*[ Hf 392 8 5" 7»[ 14.2' 795 4 6，， 9-5 *L 169， 6,422 5 5" H.[ 14 •ゲ 787 j 7 @ 3400» each 2 3,800 8 pairs @ 5100 11 each 40,800 5"X4" M-5Ä[ 17V 4,988 2 r 20° 12 つ， [9,8， 4 1'/ 2。" 35; / B il 5+" 16 l\u } 35-65， 1 3，M 16 ir 斗" ) 8 が 2Sf 1,867 24 4}° ) 24 r 4r 16 B'/ 3i" • ) 24' 17,883 8 I 為" sr 1 ToP Gl>ord Channels Batter Brace Channals Poet Channels Lat. Strut Channels W_ Pwtal Strut Cl'anneis … ^ Chd. Strut Channels ^tcrmediate Struts … Ploor Beams * Stringers + Quard Eans T«P Chord Upper PUe... Batter Brace Upper Plate Main Diagonal HlP Verticals Chord Bars Including j + Tri , all details for same. A^lucUng all details for same and the bracing frames. — 178 — Counters 4 i" 0 [ 37.65 f 2,044 ，， … A i IT □ ) Up. Lat. Rods 4 0 ” >> ，， 4 ず 0 • a » ” 4 i*r/ 0 IiOW» )} ，， ••• ••• ••• ••• 声 •• 4 0 y 3 ソ 5,762 ，， ，， ，， * 4 W 0 }y ff ，， ••• ••• … ••• ••• 4 0 ，， ，， ，， … … 4 ず， □ Port. Vib. Rods 8 iiV 0 22.7， 982 Int. \ib. Hods io ず 0 23， 76-2 Total Weight of Main Portions. … … … ... 172,110 Stay Plates on top chords 24 r 20° 1 535 ,, „ „ batter braces 8 r 8r iq' ,, ,, postiS ••• ••• ••• 8 y . 7 ゲ， 18" 73 ff ，， ” *i i6 224 ff ” ，i >> … 16 3，， 20" 29-2 ” ，， np. lat. struts ... 20 r ' 7iff r 94 t> )» low. ” j» ••• 6o y 1° 204 ，， >i ，， ，， ，， ，， ••• 120 H'1 in 496 n ,， „ port, struts 16 9" 53 „ ” ，， bot. chd. struts ... 64 r ず 6” 240 Hip Con. Plates, Inside 8 r I*2/y 5, [1,75。 ” ” > Outside 8 i 9" 5, Int. Con. Plates, Inside 8 V 12° 4; ) ,， »» >t ，， ••• ••• ••• 8 r' J2° 5r l M50 ” »» ，， »» 4 r 12" 5.5， ) —170 — Int. Con. Plates, Outside 8 iV 9° 4， 5 斗 0 ，， ，， 8 9° r 5； 825 ’， ，， ，， ，， 4 vr 9f, 5.5， 454 Con - P1ates, Bot, CM. Struts 12 1 >> 4， 6 So Eein- - ，，” ... i6 7 / 435- ，， ，， ，， ，， ... 8 lY， nf 150 C°n- Plates at Shoes , 4 V H" 3。 … ” ” ( 8 V 2r" 54?> ^ein. PI. at Feet of Posts, Inside ... 4 I2々 1 ” •• •• ，* ,， ，， „ ... 4 5// 10 グ 5, 650 M ” 》衫《 〇 „ ... 2 8" ! ” ，，” ”， Outside... 8 r 9n j ’’ ’，，，，，，， ，， „ ... 8 r 7 V， 卜 2.4， 456 ! ’’ ，，，， ，り， ，， „ ... 4 r 5，， j C0U. P1. Int. Struts to Posts 20 •5." -4' 2.5， 250 ’ ’’ Port. Struts to Brackets ... 4 h" 9" 15" 47 ” ’’ ” ，， w Name PI. ... 1 が 9" 38 ” ** Tr. Str. over PI. Bins. ]4 2。" V 420 C°Ver Plates - Top Chords ... . 14 V* • -2。" 2, 700. P 〜 Hates", 24 r . J2° *240 PI. , Up. Lat. Su. ， 0ufcei •… IO r' 5' • V 3*3 ； ’’ ’’ ，， ，， ， Inner ... IO r 4r • 150 ' ，* - W. Lat. Sti-., Outer … 6 r 5". . ゲ 188 ” ” ，， 幻， Inner ... 6 r 4r 2f 9。. ’’ M ，， ，》 ， Outer ... 12 r' 6Yf Af 650 ! Struts ... g 1 •! 280 Extension P1>> 0uter 8 hU 12" [ ti ( 770 ” ，， 8 IO/# 28" »f ’’ ，， 4 ブ 心" 109 • 1 RO • Extension PI. , Inner … 8 i ザ 2。" ( 550 ，, ” f> ••• ••• ••• 8 iV I。" 20° ； ” >> ” "•’ ••• ... 4 か r 2。" 68 Shoe Plates ... 2 l" ず 3。"- 4*7 >i •• • ••• ••• •• • ••• 2 r# 公6" 3 ぐ， 462 Roller Plates 2 i.. 31" 3" 654 Tr. Stringer Bed Plates 4 3'/ 14" H" 163 ,, ，， Anchor „ 8 6" V 、 53 . Bemn Hanger Plates i 斗 ir 9 V i3/； 54。 Namo Plates 2 @ 50* each ICO Lattice Bars, Chds. and B. Br. ... 472 A" ず 处 3,319 Lacing Bars, Bofc. Chd. Str 1280 r 2n 0.6， 1,280 Lattice Bars, Posts 普,， 1,306 H ft » ••• . ••• ••• <272 っ r し 355 ft ft ff ••• ••• ••• ••• 136 為" ヤ 2 去， 565 Lacing Bai'3, Up. Lat. Str 300 r ir o.8 5 f 399 Lattice Bars, Port. Str. 2^8 i.” 3*4 Pins, Top Chords 4 sr O 2' 315 t* !» »> 脅》» ••• ••• ••• 10 3r O 2.5， 8o2 ft IjOtl* fy •• • •• • •• • ••• 8 3r O 2f 44。 ft ，， )f ••• ••• ••• ••• 4 3i" O 2.8， 385 yi ft ft «参《 ••• • • • • • • 6 4" G グ 754 ,, Low. Lat 4 W* O \ » » f> 4 5^ 0 446 y* tf »> 4 ず 0 ff 1. M • ••• • ( « ••• 8 O ) ，， Yib. Rod Con. to Lat. Str. ... IO O o.6' 63 Bolts, Name Plate 4 @ 1* each 4 „ , Vib. Rod Con. to Int. Str. … IO ir O 92 ,, , Portal Strut« to B. Rr. ... 8 ャ O 158 — 181 — Anchor Hofe 16 ir o 6' 593 ” ••• ••• ••• … ... 16 r 0 4， 128 0lts， Shiuis to Tr. Stringers … 160 r G 15" 295 Brift Bolts, Ties to Shims 162 r □ 15" 380 Bolts, Gnard Eails to T，es 162 i° O ず m Tempos Bolts for Erection ... 100 Brackets H arx2i，y 4.9*1 - V 4<3q Ornamental Work 150 i Beam Hangers 22 □ 12, 1,926 ; Expansion Rollers 16 o nt 524 ^lhv Barnes, Sides 4 2.Q.1 21 ” ，， t Rods 咖- ::: lee Iron Fillers oyer End FI. Bms. 6 r 0 Q.1 24 6.2 @ 3K each j86 4 Alnx6,1 2I*T *•5， 126 ； Sh0e Pin Supporting Pieces 斗 12° 60*1 $60 人峨 s for RoUer Plates 2 9.7”- ゲ 78 Anchor Pieces for Boiler Plates ... a r 9° 3; 90 Spikes*F°ot Planks to Ties dashers 96 @ each 48 Nuts ... 532 ® each 532 ••• ••• Pilot Nuts ... no @ each 55 Weight of Details ... V. 二 50 3W WeigM of Main Portions … … … … 172,210 209,337 抝 仲 t Heads 3 〇/〇 6,280 T°tal Weight of iron 215,617 1 — lo^1 BILL OF LUMBER- Shims ( Oak ) 16 1" 8" 2V 1568 lOS yf •■餐 ••• •《春 ••畢 • 0 • 138 r 8r/ 6, 3864 y} • • ••• • • * • • • * 9 r C> 378 it ff ••• ••• •• * •寧》 2 斗 r 8,; i a， 1344 Foot Planks ( Pine ) i6 3 ひ 12" iV ioo8 Total Number of feet b. m._ ... … … … … 8162 The total weight of iron, less ü small amount belonging to the floor system pro- per projecting beyond the end pins, divided by 168 gives 1282 pounds as the weight per foot for the ironwork, agreeing very well with the amount found by interpolation from Table I. T】ie total weight of lumbor i.s 7154 x + 1008 x 2^- = 38,521 pounds, "which divided by 172 feet, the distance over which tlio lumber extends, gives 195 pounds as the weight per foot of the lumber. Tlio total weight per foot will therefore be 1282 十 195 + 45 = 1522. From this must be subtracted something to allow for the weight of iron that rests directly upon the masonry, such as tlio heavy pedestals, ena lower lateral struts, bed plates, rollers, anchor bolts &c. , in all about 5800 pouuds weight or 32 pounds per lineal foot, making tlio proper dead load per lineal foot 1522 — 82 = 1490 pounds. The assumed dead load was 1430 pounds, making tlio difference 60 pounds per lineal foot, or just four per cent., which is within the allowable limit of error specified in Chapter YI. It will, therefore be unnecessary to make the calculations anew. It may appear to the ro«ader who has carefully followed out all the calculations in tliis chapter, that the designing of iron bridges, and estimating weights thereof» involve a great deal of work, and demand considerable time : but such is not neces- sarily tlie case ； for an expert could have made tins design in from three to four hours, because liis experience would have told him tlio sizes of many of tlie details and the mimber ot rivets to employ. In this chapter everything lias been figured out carefully enough for making working-drawings, instead of merely an estimate of weight ; for the author considers that it is better to teach the beginner exact metlio^6 iu the first place, and leave him to develop approximate ones as his practical experi- ence increases. CHAPTER XIX. WORKING-DRAWINGS. le fii'st points to be determined before commencing a working-drawing ara one . 及 6 aU(^ ^le size of tlie paper. The least scale wliicli it is convenient to use is coedlnC 1 *^° ^16 f00t， and the greatest scale for a whole drawing should seldom ex- d ffi aU 一】1 aiid a half to the foot. Jf a smaller scale than one inch be used, y will be experienced in writing the rivet spacing between the rivet holes, five ^l° l)aPer 8l10Ukl be from three and a half to four and a half, or even 山， ,.GG. * aut^> for the length, it is better to use roll- paper, and not to cut it until ^ , 1 s the drawing be determined ; for it is a great convenience to be able to ^ he working- drawings for a bridge upon a single sheet, me" こ， foUoWug ミ8 a cli'augbtsman'a equipment for making working- drawings in a to 1Cal 加は exPe(litious mnniier : a table from four to five feet wide, from six ris 0 ^ eGt long， about three feet higli ; a pair of steps each four or five inches co a- ル1’00 feet long ; a bevelled steel straight- edge, at least three feet long ; a beam 吻 广' ^auoeu^ screw afctacliinoufc ; a couple of small triauglos ( rubber ones duod 把. 的 り； Somo and six-H pencils ; a little tracing-paper ; a finely divided a 〇00 ぶ' 出ぬ hoxwood scale (tlie subdivisions being quarters, eighths, and sixteenths); a ふ tlic)0X ば ^US^rnmeu^s, including a protractor and a pair of hairspring dividers ; offices «^SUal of rubbers, tiles, pens, etc., that one finds in draughtsmen’s 姐 akh o ■s iu which case it will be necessary either to make separate drawings In F ai1 ail<^ elcvatioi], or to place one alongside of the other on the same sheet. so tracings of the working-drawing, the traciug-cloth can be shifted about :)s to group similar parts and so as to avoid too much intersection of different Potions. Provided that any piece be symmekical about a plane cutting it at tlie middle the S. en 抑 ailtl at i'ight angles thereto, it will be sufficient to show only oue-lialf of cent! 初6 ’ aU(】 仏6 measuremeu も be referred to the end of the member, to tlie it is no/) aUe’ 0r も0 hotli. Where the same detail is used in more places than one, k a necessary to show it more than once, provided that it be exaclhj the same m every respect. bril aU illUs【ration of liow to make a working. drawing, take the case of tlie four ぶ ea ed in the last chapter, and assume that the paper and table are each G]eva^ a 卜 l】f feet wide. Using the scale of an inch to tlie foot, the depth of the five i °|U about two feofc two inches, and the width of tlio plan about one foot elevati 的 Allowing five inches above the elevation, and as much more between of tlie U aU(i l)lan, bring tlie lower side of the plan within an inch of the edge with t/ 沖61 ’ 咖牙 arrangement will do very well. The first step is to draw a line parallel S^ra^1^"e(^®e, as near^y as possible, without taking too much trouble, below tl わ 】ength of tlie paper, and at a distanco of two feet five inches be ma、le 叩㈣’ e^^e# This line should be very fine and perfectly straight. It can War^s 1 so by prolonging it half tbe length of the straiglit-edge at a time, mil after- ^ left ^ ln° ^ 8everftl places. On this line take a point a foot or move from alon„ aiRl eiul of the paper, as tbe centre of the end lower chord pin. Lay off 0f the dme W“l“]ie greatest possible accuracy the panel length, until tlie cenlie At the -,11 reached: in this case twenty one feet must bo laid off four times. penjjcujaUe P0ints erect short perpendiculars with tlie triangles, anti on t.lie per- Cliapter マ/1 も — ceu^l，e ^ay the camber, which in this case is three inches ( vide been ne • . 打 ^ the bridge contained an odd number of panels, it would have each eU(^SSf1^. draw tliG middle panel, and lay off tlie camber of tlu.ee inches at the fa]} f0 18 Paue】. Tlieu, assuming the curve of the chord to be a parabola., 也1* Uiplie ぶ0 f 讼10 cen 也1. e to any panel point is equal to the camber at the centre from .? -^ie 8(luare of tlie ratio of the distanco of tlie panel point considered ThuJ^1 也 び 出6 sPan to the balf-lengtli of span. Will ]^e S m case considered, tbe falls at the first, second, and third panel points of these 1 eSpCC^ve^ 8( そ)2, 3(i)2, and 3 ⑴ 2, or 科"， ami ず making tlie heights 各”、 0X f 二 ts above the horizontal lino respectively 3"— 料", 3" — 普"， and 8" — Oculars ’ 2 】 and 2Ü"; which distances are to be laid out upon tbe perpen- Panels as 〇十 aS 七0 ^oca^e centres of tlie lower chord pins. Tlie length of tlie happrecilbl U1S determined differ from those of their horizontal projections by an e y moving the panel points of the lower half of the n^alf a l)auel length to the right. t レ a e 又. was prepared by the above method, but was afterwards traced from than ma^ into a more compact form. The scale of 香" = 1/ used is smaller Cause ;ou ^ be employed in practice. This is both for economy of spaoo ami be- chapter 0 c|raw^nS8 were prepared for a model of tlie bridge designed in the last It 对邮1 パ 1 U 山6 latter reason there are no details drawn on an enlarged scale. 贫 oi.ki author’s intention to illustrate on this and succeeding plates all the dojnfy ^ Evings ior the model of the bridge, but lie lias been prevented from so も ie unU8Ua^y large estimate for printing this memoir. The complete of Can ゎ6 seen at any time in the rooms of the Civil Engineering Department な oluo Daigaku. Which ^ で1 dimensions, e<)0 ， upon a working- drawing, it is immaterial from any Uv ° 1〇^ waiting be read ; that is, it may be read sidewise, upside down, or Matter Uec^on most convenient to tlie draughtsman. In making tracings, this tiu.ei. I an 1，ectifiecl if it be thought advisablo. Full directions for the mauufac- 列: 二 “ e on tlie drawing. ]10t ろ tliG list of members, ami go carefully over tlie drawing with it ; llients * °U^T “加 eacli piece is represented, but that there are sufficient measure- レ ?lave ^ manufactured. 炊011 1) of •ヲ l0Wlllg additional directions and hints may be found useful. Refer each ^vets to some local line, which is itself referred to the end of tlie piece, or — 190 — some other m'omment part. Show a section of each member, and write tlie dimen- sions of all channels, angles, I-beams, etc., near the section. Write along eaclx piece its extreme length or lengths, its length from centre to centre of eyes, and of wliat ic is composed, Tlie ends of the two pieces of an adjustable rod should be separated by at least three or four inches in the turn buckle or sleovo nut. Mark what rivets are countersunk, and at which end. It* the scale of the drawing be large enough, the rivetting can bo thus represented — draw full parallel lines across the rivet for countersinking on the upper side, dotted parallel lines for countersinking on the lower side, two sets of parallel lines crossing each other at right angles for countersinking on both sides, and solid black circles for rivet holes to be left open. Be careful to always note how many pieces are to be made as shown and liow many opposite hand, when there are both rights and lefts. Lay out all bevelled ends on an enlarged scale say from half to full size, anti mark their dimensions along the edges, referring all measurements to a transverse line through some well defined point as the centre ot* the pin liolo. These measure- ments should be checked by calculation. The slight bevels at the joints of the top chord sliould bo treated with as much accuracy as the bevels at the liip joints ; but» as the bevel is very slight, it will be legitimate to put it all on one of the abutting ends making the other a square cut. The centre lines for lacing bars on the under side of a strut should be dotted* In laying out a long row of rivets, for instance kttice rivets or those for the top plate of a chord or batfcor brace, calculate the distances of some of the intermediate rivet holes from one end of the strut, then interpolate the other holes ； because, the spacing be laid out continuously from one end with the dividers, any error iw the span of the dividers will be multiplied by the number of times that the distance is laid off. After laying out a complete system ot rivets for any member, check by seeing that the sum of the distances between rivet holes plus the distance of each end rivet from the end of tlie member is equal to the total length of the member. Make duplicates of as many parts of the bridge as possible even at tlie expense of a small amount of iron, not only to save time in draughting but also in the shop and to facilitate tlie work in erection. Arrange to have as few loose pieces ior shipment as possible, and mark on the drawing of each connecting piece to what ib is to be atta- died or whether it is to be left loose. Thus the hip connecting platos should bß attached to the chords and braces and tliose for the top chord to that portion tl ば0 • ugh which the pin hole is bored. If there bo any reason to fear rougli liaudliug tJie iron in transit, it may bo necessary to send some of the connecting plates sep^* rately, but the more loose pieces the more field rivetting, and the more field rivettinf?» tlie greater the erecting expenses and the longor the time and the greater tho in raising tho bridge. Rivet spacing should bo as regular as circumstances will permit, and all cliun* ges in spacing should be made suddenly instead of gradually so as to facilitate thc punching of the holes by machine. All measurements should be in feet, inches and the following vulgar fi.ncti ⑽ 13 — 191 — 0【 inches viz., halves?, quarters, eighths, sixteenths, thirty seconds and sixty fourths : ^°ikmen do not seem to understancl decimals, so ifc is better not to use them. マ id also the use of the development method, as it is beyond the comprehension of oulinavy workmen. The lengths of all main members should be measured on the awing then checked by calculation. 'Vlien nuts are placed in a confined position, for instance pin nuts in jaws, care ould be taken that thero be ample room for them to turn iu, as it is very awkward aud sometimes impossible to screw up a nut, wliicli is stationary, by turning tlie P111 ; nuts in confined positions may be turned by hammering them eccentrically. 仏 careful to design no connection in such a maimer tliat tliero will be rivets ⑽ cannot be driven without iucouveaience. This remark is especially applicable o field rivetting. It must be borne in mind that, no matter liow carefully the bill of iron was Plepaied, there will be many minor changes founcl necessary in making the working • rawi«gs; but, as a rule, such changes do' not materially affect the total weight of lr 如 m tlie bridge. The following tables taken from Carnegie's u Pocket Companion 5 5 will be found very useful in making working drawings, as well as in preparing bills of iron. UPSET SCREW ENDS FOE ROUND & SQUARE BABS. Standanl Proportions of tho Keystone Bridge Company. Dia. of Round or Side of Square Bar. IncheB. ROUND BARS. SQUARE BARS. Pia. of Upsefc Screw End. Inches. D：a. of Screw at Boot of Thread, laches. Thread« Per Inch. No. ExcesH of Effective Area of Screw Eud over Bar. Per Cent. D ft. of Upset Screw End. Inches. Dia. of Screw nt Root of Thread. Inches. Threads Per Inch. No. Excess of Efftctive Area of Screw End over Bar. Per Cent. 古 聲 .620 10 5 斗 聲 .620 IO 21 h .620 10 21 I .731 9 33 i •731 9 37 I •837 8 41 Ü I •837 8 4^ I •857 8 17 ? 1 •837 8 25 ii .940 7 23 U •940 7 34 1.065 7 35 备 1.065 7 48 I« 1.160 6 33 if け 1.065 7 29 】l i 160 6 20 | I 1.160 6 35 1.284 6 29 | 1 is 1.160 6 19 If 1.389 5i 34 1Ä 了 皆 1.284 6 . 30 け 1.389 20 I 舍 1.284 6 17 If 1.490 5 24 1} if 1.589 5i 23 ll 1.615 5 31 if 1.490 5 29 If 1.615 5 19 if 1.490 5 18 0 J.712 4i. 22 l-h il 1.615 5 26 1.837 4 a- 28 1 士 2 1.712 4 圣 30 2 暑 1.837 4 a* 18 2 1.712 4 士 20 2! 1.962 4i 24 if 1.837 28 2ff 2.087 4i 30 Hi 1.837 4i 18 2| 2.087 Ai 20 】l 1.962 26 2.175 4 21 1.96a 4-s 17 2.300 4 26 2.087 4 各 24 H 2.300 4 l8 2.175 4 a6 4 2.425 4 1 2.175 4 18 2.550 斗 28 2f 2.300 4 2 斗 2.550 4 20 2.300 4 17 3 2.629 20 2 聲 2.425 • 4 . 23 2.754 24 2.550 4 28 3i 2.754 3i l8 2.55。 4 22 3i 2.879 3 卷 21 3 2.629 Ih 23 3l 3.004 3l 26 3i 2.754 28 3.004 19 3i 2.754 ii 3.100 21 3i 2.879 26 5 普 3-215 3+ 24 2.879 20 3l 3 •な 25 T9 3l 3.004 25 3 聲 3.317 20 3l 3.004 19 3l . 3.442 3 23 l\ 3.100 3i 22 3i 5.442 3 l8 3i 3.225 26 4 3-567 3 ai 3i 3.225 2J 4i 3.692 3 24 3 3 聲 3.317 3 22 4i 3.692 3 J9 3i 3i 3.442 3 21 4} 3.9W 2!- 24 H- 4 3.567 3 20 4i 4.028 21 3l 4i 3.692 5 20 4! 4.153 2? 19 .4-} 3.798 分 l8 3t 4 含 4.028 23 4 普 4J53 23 4 4¢ 4.255 21 ItEMARKS. — A« upsetting reduces the strength of iron, bars having the same diameter at root of thread as that of the bar, invariably break in the screw end, when tested to destruction, without developing the full strength of the bar. It is therefore necessary to make np for this loss In strength by an excess of metal in the upset screw ends over that in tlie bar. The above table Ls tlie result of numei*oiH tests on flnisheil btira made ftt tlie Keystone Bridge Conii«uiy4 Works in rittsburgli, mid gives proportions that will cfuwe the bar to break in the botly In preferunce to tlie upset end. The screw threads in above table are tlie FrauUin Institute standard. To make one upset end for 5" length of thread allow 6〃 length of rod additional. Threads per Inch. No. 20 18 16 H 13 12 II 10 9 8 7 5 士 5 5 4 备 4备 4 4 3i Si 3 Dia. at Boot of Thread. Inches. .185 .•240 •294 •344 490 •454 •507 •620 •731 •837 .940 1.065 1.160 1.284 1.389 1.490 1.615 1.712 1.962 2.175 2.425 2.629 2.879 3.100 3.317 3.567 3.798 4.028 4.255 4.480 4.750 5.053 5.203 5ギ3 SCREW THREADS. Angle of Thread 60°. Flat at Top and Uottom= I of pitch Nut* and Bolt Heads are determined by the following rules, which apply to Square and Hexagon Nuts both : Short diameter of rough nut =l^xdia. of bolt +Jin. Short diameter of finished nut =l jxdia. of bolt+1-10 in. Thickness of rough nut. = diameter of bolt. Thickness of finished nut = diameter of bolt — 1-16 iu. Short diameter of rough head =]^xdia. of bolt+i in. Short dia. of finished head =1 辜 X dia. of bolt+1-16 in. Thickness of rough head short dia. of head. Thickness of finished head =dia. of bolt — 1-16 in. The long diameter of a hexagon nut may be obtained by multiplying the short diameter by 1.15 5, and the long diameter of a square nut by multiply- ing the short diameter by 1.414. The above standards for screw threads, nuts and bolt heads, were recom- mended by the Franklin Institute in Dec. 18G4, The standard for screw threads has been very generally adopt- ed in the United States, but propor- tions recommended for nuts and bolt heads have not found general accept- ance because of the odd sizes of bar 一 not usually rolled by the mills — requir- ed to make the nut. WEOUGHT SPIKES. Number to a keo： of ISO lbs. Length. ^ in. No. Ä in. No. t in. No. ■Length. In. + in. No, A in. No. i in. No. み in. No. i in. No. 3 3 1-2 4 4 r-2 5 6 22$0 1890 1650 I464 1380 I292 1208 H35 1064 950 868 742 570 7 8 9 TO 11 12 1161 662 655 573 482 455 424 391 445 384 300 270 249 256 306 256 240 222 203 1 80 — 193 — STANDARD SCREW THEEADS, NUTS AND BOLT HEADS. Recommended by the Franklin Institute. i 83 x-ss- 1«-A2?¥3¥1_4 - 0* 2 2 2 2 222 of w. es L ch Di sc IU .-fTrl 香 x. JQ l 'a- ^ usi* 聲 .7. 30 -wl v ldoe l tf 普 3H- 备 n 聲 -41^1 5 聲 1111 1111 2 2 2 2 3333 444 斗 555 5 /; —— 194 — SIZES AND WEIGHTS OP HOT PRESSED SQUARE NUTS. The sizes are the usual manufacturers’， not the Franklin Institute Standard. Both weights and sizes are for the unfinished Nut. The weights are calculated one cubic foot weighing 480 lbs. Size of Bolt. Weight of 100 Nuts. Rough Hole. Thickness of Nut. Side of Square. Diagonal. No. of Nuts in 100 lbs. i 1.5 & i i .71 6800 A 2.9 ず ä i •88 3480 § 4.9 V3 t 聲 1.06 2050 7.7 n i ir i.H 1190 l 8.6 ■h 1.24 1170 h 11.8 i i 1.41 850 各 16.7 為 14， 1.59 600 17.7 ie 1 1 1.59 570 22.8 & 普 i i 1.77 440 拿 3 ム 3 §k 聲 1.94 310 39.8 H a. 2.1-2 251 i 53- U I 1 1 2.30 190 i 63. il i if 2.47 159 i 68. l i 1 聲 2.47 146 i 94. i i1 i： ■2 2.83 106 1 1 io“ Vi 2 2.83 97 i h 137. 铑 i 蚤. 3.18 73 U 145- Ii1ir i 1 3.18 69 ii 186. JfV i i 3.54 54 if 247. 】 蟲 2 塗 3.89 41 1 l 3【9* 1 A i i 4.24 3M it 4co. i 脅 3 1 4.60 24.8 i 穿 5〇〇， 1 義 1 it 3 i 4.95 19.9 ii 620. 1 ü 】1 y'i 5-3〇 16.2 . 2 750. iU 2 4 5.66 13.4 2 i 780. ii 2 h 4 5.66 12.8 930. 2 4i 6.01 10.7 960. 2 -2 - 4} 6.01 10.4 1 1 50. 2! 2 h 4h 6.36 8.9 2 ま： 1570. 4f 6.72 7.3 l 5-i 1610. 3 5 7.07 6.2 2110. 5i 7.78 4.7 2750.. 3 i 3 h 6 8.49 3.6 ; — 195 — Weight of Rough Thickness Short Long No. of Nuts in 100 Nats. Hole. of Nut. Diameter. Diameter. 100 lbs. 1.3 3Z } •58 8000 2.4 A •72 4170 4.1 M s. f •87 2410 6.8 ☆ i 1.01 T 460 7-r 1 1.01 1410 9.8 t7s i 1.T5 1020 14.0 a 1.30 710 14.7 為 1.50 680 I9.T 56 f i ^ M4 520 2a. 9 i i 】.44 44。 27.2 聲 it 1.59 370 39. Hi 1- i 或 1.75 256 44- §-1 i 1.88 226 50. iS I it j.88 198 57. i I if 2.0*2 176 64. l I Ä i f 2.02 156 96. 好 1 + a.3i 104 IH. 1 TiST I * 2 蚤， 2.60 75 180. 】 A 1 士 2.89 56 255. I-TÖ It 2 聲 3.18 42 300. 1 み I * - 3 5.46 554 370. I-h 3 + 3.75 26.7 IU a U 4.c 斗 cn.5 450. ifü- , 1 3 i 4.C4 2-2.4 560. U- 1 n 1 .. U 4-35 4.35 18.0 17.7 680. 810. 980. ^ w ^10 ^ 1 、 2 合 2 幸 斗 4.61 4.9! 5.20 H-7 12.5 1 0.-2 1150. 1340. 1580. 3 3 + 3 i 4ä - 5.48 5.77 6.〇6 8.7 .7.5 . 6.3 SIZES AND WEIGHTS OF HOT PRESSED HEXAGON NUTS. The sizes are the usual manufacturers', not the Fraukliu Institute Standard. Both weights and sizes are for the unfinished Nut. The weights are calculated, one cubic foot weighing 480 lbs. of L e ol IB arß^-T^HT^O i RffsTl III III III iH IV 9^8 Iw- $. It It — 196 — DECIMALS OF AN INCH FOR EACH, み th. -3TjCls, Atlis. Decimal. Fraction み ds. ^ths. Decimal. Fraction r •015625 33 .515625 I 1 •03125 17 34 , •53^5 3 •c 46875 35 •546875 1 4 •0625 卜 16 18 36 •5625 9-16 : 5 .078125 37 •578125 3 6 •09575 19 38 •59375 7 •109375 39 .609375 4 8 .125 i-3 20 4。 .625 5-3 9 .140625 4【 .640625 5 TO .[5625 21 42 .65625 I I .171875 43 •671875 6 12 • 1875 3-i6 12 44 .6875 1 1 一 1 6 13 .205125 45 .703125 7 *4 •21875 23 46 •71875 15 •M4375 47 •734375 3 j6 卜 4 24 48 •75 3-4 17 .265625 49 .765625 9 18 .•28125 25 50 .78125 19 •■296875 5-1 .796875 IO IO •3125 5_i6 26 5^ .8125 13-16 21 .328125 53 •828125 li 22 •34575 V 5 斗 •84375 23 •359375 55 •859375 12 24 •375 3-8 28 56 .875 7-8 25 •390625 57 .890625 1 13 26 .40625 29 5« •90625 27 .421875 59 •921875 14 28 .4375 7-16 3° 6o •9375 15-16 29 .453125 61 •953125 15 SO •46875 パ 62 •96875 パ •484575 63 •984375 16 32 •5 1-2 3-2 64 r. i The following extract on Workshop Drawings n from the American Engineer of Nov. 7fch the and 21st 1884, though perhaps not in exact accordance with the previ- ous p：ivfc of this chapter, contains so many useful hints tliafc ifc has been considered advisable to insert ifc. “ The following article is by Alfred D. Ottewell, who can speak with authority from a life long experience in the best shops of Europe and America : While eacli draughtsman has his own method, and each firm its own rules, ifc lS believed that the following process of preparing working drawings, having given tli0 general design and dimensions of the article to be manufactured, may contain poii^9 worthy of the consideration and adoption of both ; being the result of an extensive practice and detailed observation. — 197 — PROCESS. L Draw large scale details of general connections — し c” where the separate eCe5 aie J01ued together. These details are made chiefly fou office use, though (飞 = s ot them may be traced for the shops. Th.eir principal use is to enable the l 1 ド111 ⑽ to draw out each part separately for the shops. These details need niked in or traced, except for purposes stated in 11 1, as the subsequent draw- ge complete in themselves for workshop use or reference, t】、 • Draw eacli member separately in pencil by the previous details made. If du . ^Sman traees his own drawing the dimension need not bo put ou this pon- 1)1 f n ‘ lnS’ excel)t guiding dimensions for reference. It is easier and saves time to than C lmeU.S^°ns 出1. ec% on tlie ink tracing, since the tracing is more roadublo sio 6 Peneil c】l’awing ; whilst it also saves the time necessary to trace the climen- detail^* Trace pencil drawing spoken of in II on tracing clotli. If any parts of the gj S 111 Rawing mentioned in I are necessary to explain any part of the members ^ ü 011 が“ drawing it is traced in juxtaposition with those members. By this thei.eb a も i0 details of one member are shown together； if possible, on one drawing; e y preventing confusion of workmen, inspectors, draughtsmen, and everyone C0^ected with the work. ‘ fhe process adopted by tlie author of making this tracing is as follows : Tracing in circles or parts of circles. ” ” lines showing straight parts of members. ” ” freehand curves of members. ” ” centre lines. Putting in dimension lines. Marking off dimension points or arrow heads. Writing dimensions. Sectioning parts shown in section, i'iug a separate mark to eacli piece, utfcing on bill of material shown on drawing, u i，g title, including name of job and order number, nteiiug drawing in Drawing Book n and putting number on drawing, j Signatm.e of draughtsman and date, is to ti. 1CCeec^ since it is easier to trace two straight lines to touch a circle than it iii QCe a cir?le to touch two straight lines. iv i8Ueeeeds i and ii for a similar reason. tracing 111 • 仏0 position shown to adjust for any inequalities in tracing ; such as cilc】e slightly out; of centre on drawing. Will best：eCeed8 VU since じ facilitates dispatch, a.s the questions “ What dimensions actuaij r SU^ requirements of the workman ? M and “What size those dimensions viii< g aiC， are cousiclered separately instead of alternately, as is generally tlie case, the sanae ceec^s as it often happens that sectioning and dimensions should cover oi ground， in which case the former can be left out, thereby making the much more readable. ii. iii. iv. v. vi. vii. viii. ix. x. xi. xii. — 198 — The bill of material x, gives tlie number and size to order, of articles required to be furnished to satisfy that drawing, and is made as follows, for example : MATERIAL FOR TWO CEANES. No. DESCRIPTION. LENGTH. MARK. 2 Forgings A A 6 Angles 3" x $" x 6f ir AB. 4 Plates i2/J x fv 7f H" AC. 12 Bolts. .H. H. and N 6 ダ AD. 16 V Tap Bolts. H. H ir AE. ヰ V Bolts. CK. II. SQ. N AF. Thö marks A A, AB, etc., are shown on the details to which they refer. ix is adopted to givo each piece a mark to distinguish it readily from other articles, and also to assist the formation of x, as the bill x is a better arrangement than the old plan of marking off on each piece tlie number required, as it slio'vs tlie workman readily all that is on tlie drawing for him to make, and enables him to see at once wlien lie is tlirougli with the work shown on the drawing. Tlie title, xi, should be in the same relative position on all drawings ; preferably the bottom right hand corner facing tlie drawing, as this is the most convenient ^or reference when filed away in drawers or rolls. Wlietlier the tittle should or should not give tlie name of the firm or work for wliich it is for is an open question. Thß advocates for tlie affirmative say it is easier to remember a name, because move interesting, tliau an order number ; whilst the advocates for the negative say such information makes tlie work too public in many cases. xii, The signature, preferably initials, of the draughtsman should be given 〇11 tlie drawing to facilitate reference to liim sliould. any question arise. After tlie tracing lias been signed by the draughtsman let it be, IV. Examined or chocked by another draughtsman. In this examination every dimension and note on the tracing is to bo examined ; and all the necessary dimensions and information for tlie workman shown to be on the tracing ; and the fact ascertained that no two parts of the work will foul with each other. AVhen the examiner lias satisfied liimself on these points, his signature on the tracing is lequii’ed to attest tlie fact, which signature is a guarantee to the foreman that the tracing is ready to work to. Sometimes the tracing is made and examined by one and the same draught8* man. lliis is a quicker plan than tlie former, as the draughtsman is more with tlie woik on liis own drawing, blit it is not as safe, as the draughtsman is liaW® to make tlio same mistake twice over. After tlio tracing has been signed by tJie examiner let a V. Blue print bo taken 11011 1 tlie tracing and sent into the shops to tlio for 61118 engaged on the work, or to the “work’s manager, as tlie case niay require. The 199 narne of blue print should be entered in a book with the name of foreman sent to, üc elate on wliicli it is sent. These particulars are useful to refer to, in case of investigation being made into any delay in the proceeduro of the work. the blue print is taken directly from tlio drawing made on thin, semi-trans- 1 clrawiiig paper for tho purpose, the reader will readily see the slight modifica- tions to be made to the preceediug remarks 1 Tlie foregoing process may appear at lirst sight a lengthy one, but as it lias ouxied witli the primary objects of secTiring great acciu.ftcy and dispatch in thi acture， ifc is believetl that sliglifc excess, if any, in cost of drawings made by (心 ^an ^ doubly repaid by the saving in cost of mainifacturo. Ir' however, two l^ings giying the same iuformatioix and of equal efficiency are produced, ono £ ア tlao above process and one made by any other process, it is believed the 〔ご1 he made in less time, aud with less labor, than tlie latter. The principle luo °ne thing at a time is adopted throughout, and tlie practice sometimes of finishing and tracing one part of a drawing before anothei* part is coin- gQ ls, ln this liglifc, obviously Avrong, unless there are especial reasons for doing II. —RULES TO BE OBSERVED IN THEIR PREPARATION. ne Put as little as possible on drawings, to prevent confusion, but everything iy for tlio construction of the articles represented, etc • nnecessaiT details, fall or dotted lines, circles, shading, dimensions, notes, jra 0 ve a waste of time for both draught man and workman, besides making tlie a c| con fusing or more unreadable. Everything on the drawing should liavo ^acüit*it^ 叫 れ〇 わ0 tliere, so that if dimensionse tc., are repeated, it should be to Ujj l,e ^le workman iu uuderstamliug the drawing or in avoiding a liability to ^ し Oftnn rl vivil rrli 1 1 1 -PiTwn wnnf +1 imifrltf. nv IS SaToPleasaQt Often draughtsmen, either from want of tliouglit or because it is occupation, draw in detail, rivets, bolts, etc., where centre lines stood l) e(lually as well. It* the drawings were to be pictures intended to be uiitlei.- case • グ マ10 uu^ra^uec^ mind, such details would be necessary, but sucli is not the l，eprcseut Ung drawings are made up of a series of symbols which are understood to sfcaiKj a CGlta^u articles, materials or methods, and a workman will often under- W0llj(| , °e^le ^ne» with given dimensions, to represent a rivet or bolt where details II eU\ make the drawing confusing. yollr 〇 1 ave dimensions to suit tlie workman’s requirements iu preference to cess of iri ilaU^^Smau sh0uU， to carry out this rule, mentally go through the pi.o- make it ぐ叫 the article represented on tlie drawing just as the workman will wastes a workman's time to require him to add aud subtract a number 25 It is nu^^61 GaU obtained from Charles Schleicher and Sohüll, Düren, Rhenish Prussia. r<_Cl /8〇, aild OOltlPS in vr^lla trflc lnno* tn AT\ wirlA Pri Tlftr rol By its use 5, and comes in rolls 33 yds. long, by 38 to 40 inches wide. Price per roll considerable time will be saved in making blue prints. J. A. L. W. — 200 — of unnecessary dimensions to find an essential one, besides malang lmn liable to err. The draughtsman can more easily find such a dimension himself, and when once written on the drawing it is there for all tlie workmen requiring it. III. Make as few notes as possible on a drawing ; put dimensions or symbols instead. Such notes are easily missed and are seldom read. They belong more to speci- fications than to drawings, and where instruction lias to be given on drawings i\> can generally be given in a more readable form by symbols that catch the eye tlian by writing. By ‘• symbols n in this caao ia meant the usual marks adopted by different firms to indicate drilled holes, tapped holes, countersunk holes, holes left open, parts machined, steel, brass, etc. Such symbols are seen at a glance whilst a note re- quires moro or less study, is more verbose and is more easily missed by the workman. IV. Put all details and information required to make each article on^ne and tlie same drawing. To give one detail of an article on one drawing, another on another, and so on> requires the workman making that article to monopolize those drawings and pre- vents other workmen from using them for other parts of the work. The article itself is made under greater difficulties, as it confuses the workman if lie is required to pick out the details from several drawings and from among other details. V. Put all dimensions for each article as near together as convenient. Ifc wastes a workman's time to require him to hunt for the dimensions of tbe piece lie is making in the different parts of the same drawing. Thus if a web plate of a girder, say, be shown on tlie drawing the size may be given 8’ 6" x 普" x 7’ 3" say， instead of showing the width in one place, thickness in another, and length in another. VI. Make thick lines and thick plain block figures. These are more easily seen and read by the workman in the shops. The blue prints from such tracings are more uniform and distinct. Such line 3 and figures are not so soon obliterated or soiled by the dirt of the shops. The figures should be plain； the object being to make them easily readable, more useful than ornamental. Ornamental figures and lettering should be reserved for designs, estimates, etc. VII. Give inspector’s dimensions. These are generally main dimensions. In examining the work, and in the work when in place, the intermediate dimensions are not of much importance. For ex- ample, the dimensions used by an inspector examining the columns for a building are, say, distance from underside of bearing plate to bearing surface for shoe rafter or principal ； distance from underside of bearing plate to centre lino of hoi 掷 for connecting floor beams to columns. The former dimension, being a main dimen- sion, would generally be given as required, but the latter is often to be obtained only by additions and subtractions, trying to the patience of inspectors or examiners i11 inclement weather. VIII. Instead of the term “ right hand，’’ use “ as shown, n and instead of “ 砂 liautV’ use “opposite hancV’ —— 201 —— 1 left haul n aro ambiguous, since tliev do not say WhiclTlle teimS <y use. Of peily. le Pa^erns with voundecl corners for rough odd castings may be too ex- Ull|ess ^le above advantages are more impoitiint than Üie cost. ⑺ • 1 ut no scale on the drawings. but sli G ^0l^man ^ in no case to scale the drawing, except certain full size details, も. 'V0l.k to tlimonsioii3 given. Scaling a drawing is obviously wrong. If tlio case 'i Smau 】ias ^^cle the drawing to scale throughout, which is not always tlio fereui， 10 maker, fitter and smith will often on scaling dimensions give (lif- lf a ^ lesu】t’s’ thus maliing it difficult to fit the different parts of the work togeilier. ■^uttiurr 011 ^lmens^0u is not given the drauglitsman should be requested to give it. Woi.km。！ & SCa e 011 a drawing is therefore worse than useless, since it tcui, ts tlio to use it where dimensions have been accidentally omitted, rji . * ^ccurac.Y ami completeness in execution are more valuable than dispatch. 对 出 ha 1S 1IUgM ahnost be considered an axiom, but if based upon definite reasons it becottlese a ^rmer hold upon the mind of the drauglitsman. An error on a di.awing iiig ex m°le costly to make the longer the correction is delayed. Take the follow- 边 etei. i8 • * 加 the drawing of a cast-iron steam engine cylinder the inside (lia- ■fiW the ölyeim"， but on tlie drawing of the piston the diameter is given IB7, 'vhicli nomiS^a^° occurrec^ apart from tlie argumeut, since mistakes do occur for it -will o11]leaS°n CftU veil. If tlio draughtsman sees the mistake as 80011 as made h wiU r- ^ cost a fe'v moments of liis time to correct it. If tlio examiner detect it, W， • cost へ4 ore c somew^at more. If tlie workman or foreman should happen to detect it take • and な111 灿叫 the piston a little more expense is incurred in correcting tlie mis- ted , Tvh •卜 f • 的 Pi“011 aud rings are cast, on detection much more expense is in cur- ia incurred ^ 咖 chined complete, ready for fitting, much more expense Care， aij 山 C01rec^on, The argument is that the clrauglifcsman should woik with duty t0 n n°^ that he should go over tlie same ground twice, as it is tlie examiners Us clleek tlie drawiug ； for it is obviously a waste of time for the examiner —— 202 — to examine work that lias been previously examined. XIII. Make as few variations as possible. In repetition there is economy. If two castings can be made from one new pattern they will cost less than if they require a new pattern made for each of them. Again, if the two castings are slightly different from one another, the pattern can probably be made to suit both with a slight alteration, in which case the two castings will cost less than if they are designed so that they will require two whole new patterns» A* saving is effected if tlie two castings can bo designed alike witliout inconvenience, instead of opposite hand to each other, as, even if each does not require a separate pattern, the time taken by tlio moulder in taking the pattern for alteration to the pattern maker, and the time taken by the pattern maker in altering the pattern is entirely lost. Very often castings can bo designed by the careful draughtsman to be cast from one pattern slightly modified to suit each case, and by this means unnecessary expense saved. . Rivets of equal pitch cost less to mark off on template than if of unequal pitch， since the layer-off lias to set bis dividers once in the former case, and a number of times in tlie latter. Adopting tlie same sized rivet or bolt throughout a structure is often elieapor than varying tLe size to suit theoretical requirements, as tlie additional labor in changing punches, drills, cores, etc., tlie additional handling and liability to err, in the latter case are more costly than tlie waste of material in the former. This principle of tlie economy in repetition is of tlie greatest importance and cannot be too widely studied.’’ CHAPTER XX. 幻1 PROXIMATE METHOD OF DESIGNING A SINGLE TRACK BRIDGE. i. • or S0lne time the author has debated the expediency of writing this chapter, tliat it is poor policy to encourage the use of rule of thumb methods, but has ^ ア concluded that its advantages will exceed its disadvantages ; for not only will gj^.na^^e an ordinary draughtsman, who lias not studied tlie theory of bridge de- ajj Qg’ 七0 design any single track iron railroad bridge with sufficient exactness for practical purposes, but it will also serve as a check in many ways upon designs = by the more accurate method which this treatise explains. ber le aPProximate method is briefly as follows ； — to proportion the main mem- ^ trusses hy using the diagrams on Plates XIV. to XLII. inclusive, those of 111 し ⑻ Sptems by Table XIII. those of the floor system by Tables XI. and XII. in T 1 1 e^ai^s the rules and tables for same which are given in this chapter or ^ = VIL and XX. to XXIII. inclusive. bers 6 of span be exactly divisible by ten, the sizes of all the main mem- “not ”; わ' obtained exactly or very nearly exactly from tlie plates and tables ; but, direct! 81zes of the main members of trusses anil lateral systems may be either taken Panel】 r°m ^le greater span or may be interpolated from the plates : if the sy8temen°t l m 110^ a whole number, tlie sizes of the members of the floor tables ツ糾 be taken equal to those for tlie next greater panel length given in the of pane| aie ^ust be exercised in interpolating sizes especially wlien tlie numbers upon the m ^W° SPans nearest tlie one considered are different. After deciding havinff UUm^er panels, tlie bridge should be designed using as a guide tlie span ,10 satQe niltnber of panels. The following points should be borne in mind Actions 巧0 — increasing the panel length tends to increase the sizes of the and in 0ぞ the top chords, main diagonals counters, batter braces and lateral rods, chord 8 eas>Ulo ^ie depth of truss tends to diminish tlie sections of the top and bottom these ふ11^111.^10^0113^8 ant^ couutörs, but to increase those of the posts ; 一 decreasing As produces, of course, the contrary effect. detail8， let us take Chapter III. anil follow down tlie list there given u. es for the approximate proportioning of each member therein named, and the S1Zes 01^ s^ay plates for all cases are given in Tables XX [I. and XXIII” method of using these tables is fully explained therein. — 204 — Tlio next group includes the connecting plates at the laps and intermediate panel points. The widths of the inner plates are, of course, equal to tlie depths of the cliannels wliicli they connect, and those of tlie outer ones as great as will peruaifc of tlieir lying between tlie heads of the rivets which pass through the flanges: in case of necessity some of these heads might be countersunk so as to permit of a greater depth of outer connecting plate. Tlie limiting thicknesses and lengths of these plates are given in tlie following table, which has been prepared under the assumption that Carnegie’s sections are employed and that the rivets are spacoa a3 closely as good practice will permit. When applied to the hip connection, tlie lengths of these plates are equal to the sum of the distance from the centre of the pin hole to the end of the plate on the chord， and that from the same point to the end of the plate on the batter brace. It must be understood that very heavy shallow channels are not used, but that the most economic size for tlie whole truss is in every case employed. Deptli of 匚 Weight of 匸 Thickness of Plate Total Length of Plate 8" to 17 典 3 2° to 44" ゲ， 14.5， to 21* s" to 32" to 46〃 iow i6ft to i6M to ^ 32" to 48" 12° 20s* to 45** i" to 36〃 to 66" 15" 40** to 6o4 ä" to r 4*2’* to 7。" The next on tlie list are the reinforcing and connecting plates at the pin 1101 es in bottom chord struts. Tlie former may always be made 蚤〃 thick and three or four inches deeper at tlio middle than the strut channels. Tiicu* length should be about three feet. Where a joint occurs in tlio bottom chord strut, the thickness of each connecting plate should be Yrf and the depth at tlie middle from four to six inches greater than that of the channel, tlie increase being directly proportional to the depth of the channel. A length of four feet will be generally about right. Next on tlie list come the reinforcing or connecting plates at the shoes. The thickness for these may be taken as -h* for eight aucl nine inch clnin- neh, i,; for ten aiul twelve inches cliannels, and i,f for fifteen inch channels. The height of each vertical portion may be taken equal to twice the depth of the batter brace cliannels, and the length of the horizontal portion about the samo or little more. Next come tlie reinforciug plates at the feet of the posts. If tlie channels be light, not greater in depth tlian twelve inches, and with flanges untrimmeil, a thickness of will bo sufficient for each inner and outer plate. For heavy sections of n.ny depth, for all fifteen inch cliannels, and for clianuela with their flanges trimuie^ away ifc will be well to increase the thickness to half an inch. The width of tbe outer plate sliould be inado as groat as will fit into tlie cliannels, and for small clifti1" n els it is well to make the horizontal portions of these plates wider than tlio vertief portions, so as to give room for attaching to the floor beam. The width of the inner plates should be at least as great as the depth of the post channels. If the latter b0 一 205 — mad ’ 仏0 l.i0rizontal part of the aw formed by the inner reinforcing plates may be sh 1 ^ 、Vide as the upper flange of the floor beam. Both putor and inner plates ふ ）e long enough to extend u early to the upper edges of the stayplates. fei ，/ GX^ come the reinforcing plates at the middle of posts. These are placed pre- Rl〕eci ^ 仙 出6 inSl(!e 0f 【he posts, but may be put on the outside if there be any tlut 1 fleasou f°r 80 doing. When on the inside tlie thickness should be equal to tn fi、 〇 1 ル0 Web 。で the cliaimel, but neve i. less than %r\ The width should be equal Reptil of the post channel. allow f Placetl uP0u Üie outaide of the post, tlie thickness should be increased to (^epth of necessai.ily diminished width. The length should be about twice tlie inoi . ie channels， but should in all cases bo great enough to extend two or three ぶ：11111 m tlie stay plates. l)e 如 acj C01，G the bent connecting plates for intermediate struts to posts. These may 孤6 0 I X 4" iron about thirty inches long, to in COnnecUiig plates for brackets to lower portal struts, and for name plates X\lii .e\i ^)01 8truts may be made of tlie length and thickness used in Chapter strnfo 1 10 贫丄她， of course, will depend upon the distance apart of tlie portal Manuels. braces t ^|mens^ons the plates on the side braces and for connecting tlie side scale of 〇 $ ie 打001’ ^eams may either be scaled from Plate IX., wliicli is drawn to a Phfce at ^üe or may be left to tlie judgement of the clrauglitsman. The bent The end ば the side brace should be at least J7 thick, the form 10 、lless が a connecting plate for track stringers over a floor beam, when ness a 加 aoa^st the latter, need be no greater tlian f", and the same thick- plates b ;eUe か1’ 'lle connecting plates for stringers to floor beams. Octagonal 8honld b sh’ingers ami beams, used when the former rest upon the latter, Ca^ c^mensi01is for connecting members between stringers and beams c: ed fromtlie P]ates. ^icli the ^ a^GS 此01 侃 liave a thickness equal to that of tlie plates, the joints of Tlip f. C°Vei/ aU(^ they should be a few inches longer than their width. Tlr 1Üfllslons filling plates need no comment, channel to j10Ua\ a:.ea of an extension plate should be twice as great as that of the It is coixip0 二'1 し attached, and its width 811011 Id be equal to that of the channel, three or ム が. two e bat slioulcl be boxed before shipment. Oi.r»nw S も。 わ6 marked P. or I. (portal or interraecliate), also R. or L. namental Aktobe marked R. or L. — 22C — Guai.tl raus require no marks. Beam Jian.^ers to be mmihered so as to correspond to the panel points to which tliey belong. Rollers need ho marks. Fillers to be marked the same as the pins to which they belong. Turn buckles and sleeve nuts, being attached fco the rods before shipment, in- quire no marks. Bracing frames for stringers and girders to l>e numbered so as to correspond with the panel points and tlie upper sides to be marked U p. The frames may be considered as dividing plate girder spans into panels. Diagonal bracing angles for plato girder spans to be marked U or L (upper oi* lower) and to be numbered to correspond witli the panels into which they may supposed to divide the span. Washers need no marks : tliey slioukl be boxed, or strung on bolts, befoi*c shipment. Rivets need no marks, but should be boxed. Pilot nuts need no marks, as there are so few of them required. Lock nuts should be markoil Dv D2, &c., Ui, U2, &c., V.,, V.2, &c., L. 1, L* 2 II. 1， II. 2, &c. aud P, D coiTesponcliug to web diagonal, U to upper lateral l od, V I to Tibrfttiou rod, L, to lower lfiteral rod, IT. to befim hanger and P 切 portal rod . エ li addition to these marks, there should be others for those members which 糾〇 to be riveted together in the field, and which are assembled iu the shop when the l-ivet holes previously punebod are reamed. These marks should be punched tlie iron with a steel point, and should consist of one, two, three, or four dots up。11， each of tlie pieces so aHRombled, in orilev that no piece during erection will be pnt iiito the wrong plac^. CHAPTER XXII. ERECTION AND MAINTENANCE. 如 The immbev of men required to erect an iron railroad bridge will vary from a to a hundred and fifty or even more according to the length of span, location 1 11 the time to be occupied in erection. any one bridge, there is a certain number of men which will be more econ- t 11 广 ^ lan any other number ； and it is only experience which will enable one to 6 e|，°i,ehaiicl what this number is. ^ r 1 tliei’e are too few liands, the work will lag, and difficulty will be experienced iKUing heavy pieces : on the other hand, if there are too many men, they will lu ea°h other’s way, and the total aräounfc of effective work done by each man ^ day Will j10t bo a maximum. If, for any reason, there be need of haste, it will economical to have a large force of men, notwithstanding the last mentioned consideration. g 如 1 〇が叫 to certain well known peculiarties of Japanese workmen ifc is very dif- h 1 to say how many men will be needed in any particular case : this matter will も0 be left almost entirely to tlie judgement of the engineer. To such as have foil 丨 'o exPerience in bridge erection, the author offers with much diffidence the 0wh]g tables as a mere guide. FOR RAISING SINGLE TRACK BRIDGES SPAN No. OF MEN EEQUIRED Plate Girders From 12 to 18 Pony Trusses ” 20 25 T^ro. Spans under 10 O' >* »， 30 ioof to ia5’ ，， 30 ，， 35 >y 150' ，， 35 ,, 4。 ゆ，， ， 175, ，， 40 ，， 45 175’ •,， loo. ，， 45 >» 5° 20 O, „ 22s' ，， 50 ，， 60 叫’《 25〇; ,, 60 „ 75 25〇’ ，， 275， ” 75 ，， 90 ^7 S' » ?。〇， ,, 90 110 — 222 — FOR RAISING DOUBLE TRACK BRIDGES SPAN No. OF MEN REQUIRED Plate Girders From 15 to 20 Pony Trusses ，ノ 25 5〇 Tliro. Spans under 10 (V ，， ’ 3〇 ” 4。 10 0， to 125， ,， 4〇 ，， 45 125， ，， 150, ，， 45 « 55 150’ ，， W ，， 55 ，• 6〇 175， ” 20 o' •• 〇〇 „ 7° 20 Of „ 225' ，， 7〇 ，. 8〇 225’ ，， 250， >» 2〇 yy Q5 250， ，， 275， ，， 95 115 275, ” ，， 115 ,， 135 If the bridge is to be erected rapidly the number given in the table can be pro- bably advantageously increased by from twenty-five to fifty per cent. The cost of raising a bridge depends more upon the foreman than upon thö men. The best men will fail to do their full quota of work it* tbo foreman be not energetic. Nor does it suffice to have simply a good worker for a foreman : he must know how to keep the gang busy, or they will stand by and look ou, while he does tlie work. Ho should also have their good will, or the progress of the work will bß unsatisfactory. — 223 — The outfit fof a gang can be taken from the following table, in which the smaller numbers are for short spans, and the large numbers for long spans. IMPLEMENTS. NUMBEK : REQUIRED. Forges i or 1 Pairs of tongs 2 to 5 Button setts for each size of rivets •2 to 5 Drift pius of each necessary size 5 to 15 Reamers 4 to 10 Handle cold chisels 2 to 5 Handle drift pin« 2 to 4 Cape chisels J 5 to 30 Plain chisels 8 to 16 Bacliet drilla i to 3 Wrenches for 普’, nuts 5 to 10 Wrenches for %,r nuts 5 to 10 Wrenches for nuts 5 to 10 Wrenches for Vf nuts 3 to 6 Rivetting hammers 1 to 5 Light sledges I to 3 Heavy sledges i to 3 Hand lines dia 5 to 12 Guy lines 1" dia. by loOf long 5 to 12 Fall lines 1" dia. by 150’ long 2 to 5 Rope slings 10 to 20 Sets of 10" blocks 2 or 3 Öets of s,f blookH 2 to 5 Snateli blocks 1 to 5 Steel crow-bars 8 to 20 Cross-cut saws 3 to 7 Augers V dia 3 to 6 Angers ^ dia 3.to 6 Augers ^ dia .•け… 3 to 6 Angern l，f dia * 2 to 4 Axes 5 to 15 Aazes $ to 7 Timber trucks 10 to 25 Monkey wrenches 5 to 12 Chains ... … … 5 to 12 Cra も 8 2 to 5 Holding on bars 2 to 4 Jack screws 3 to 8 Large wrenches of different sizes for pius a to 6 — 224 — and it necessary a pile driver with its appurtenances. The ordinary weight of a pile driver liammoi" varies from sixteen hundred to two thousand pounds, and will pro- bably cost from two lmndrod to two hundred aud fifty or even three hundred yen. The height of the driver should bo about thirty feet. Plate XIi. illustrates nearly all the tools found in the list. The author wishes to apologize for the appearance of this plate and its very apparent want of scale ; for it was prepared from clippings taken from various advertising circulars. Some of the figures clo not represent exactly what they were originally intended for, but the agreemeufc is exact cuougli to give the reader a clear idea of the form of each too】. Besides the tools on tlie list, each carpenter should be provided with the usual special tools to be found in a carpenter's ldfc. In getting ready to erect a bridge the first step is to prepare the gi-ound in the neighbourhood of tlie site, so that there will be room to store the material and fov the men to work. When tlie iron is received at the site it should be checked ； and any pieces from which tlie marks have been obliterated should bo remarked. The iron should be piled «ystemuticiilly, similar parts being grouped, and no iron should be allowed to lio upon tlie gvouiul. It should be piled so that there will be no trouble in getting at any piece which may be required. The portions to be used first should be placed nearest tlie bridge site. Tlie piers aud abutments will be supposed to be erected, as this work does not aim to treat of foundations. The next step is to put the falsework in place. If the bed of the stream be dry or nearly so, tlie bottom hard, tlie distance from the Led to t]io lower chord be no greater than twenty feet, aud if there be no danger of a sudden rise of water with a swift current, vertical timbers resting on foot blocks with a cap and light diagonal bracing may be employed. If tlie ground be not perfectly firm, mud sills must be used instead of foot blocks, and, H at all soft, piles must be employed. Tlie size of a mucl sill sliould vary from 6" x 6” to 12" x 12” according to the hardness of the ground, the weight upon the sill and the height of the falsework. It is not necessary that the timbers be square : for ground not especially hard wide timbers laid on their flats are pre- feriible, as they distribute the press uro bettei*. b^uare timbers should be used where tlie ground is haul in some places and soft in others, so as to prevent unequal settle- meufc and a consequent distortion of the bent. It tlieie be but one tier per bent, two vertical posts will be sufficient for slio1*^ spans of single track bridges, but in all other cases a third vertical post midway be- tween the others will be required. The caps should be from 6” x 8” to 8” x 10" according to tlieir unsupported length and the magnitude of the weights which "vvill come upon them : they should project two feet beyond each truss. The upper ends of tlie posts should lie directly under the trusses, aud the caps slioukl be drift bolted thereto. Tlie bent should be braced by diagonal flat timbers, say from 2n x 6f, to 3" x 8"， according to their length, running in opposite directions, one on each side of the bent, and bolted or spiked to the posts and cap. • — 225 — If there be two tiers in a bent or one tier resting upon piles which project more n live feet above the surface of the ground, inclined posts having a batter of two 0 to the foot should be placed outside of the vertical posts under th« trusses. Each tier should be braced with diagonal timbers, as before. The greater the nger of high wind, the more effectively should each bent bo braced« Alternate secutive bents should also be braced diagonally on their outer laces, and all °usecutive bents should be connected by longitudinal horizontal planks well spiked 6 C.aPs. These planks will be useful, in fact often necessary, for tlic workmen 0- f acing from bent to bent. If there be more than two tiers per bent, tlie batter • e inclined posts should be three inches to tlie foot, A good height for each tier 8 Slxteen feet. j, Where tlie water is deep and rapid, piles will be required to rest the bents upon. a 6le 8houl(l be from two to five piles per bent, according to tlie width of the latter ; e eing placed below each vertical and inclined post. These piles should be that GC ^ direction of tlie stream by flat timbers bolted thereto. Any bracing 匕 may be given them transversely to the stream should be at such a distance above 0hjec_:ater level as to cause no obstruction to boats, trees, ice, or other floating ^ Ö the bottom be bare rock, incapable of holding piles, the mud- sills must again 如 .=01 ted to. They should be weighted so that they may be sunk into place, tlien 8ills 也61! to the rock. This can be done without tlie aid of a diver. Of course tlie =ust be firmly attached to the lower tier before being put down. ai,e ^1G t0P 8 of 认 U piles should be cut off to an exact level, so that, when the bents e 二 ected, tlie upper surfaces of tlie upper caps will lie in the same horizontal plane. ^ese caPs should be placed timber-beams stretching from one bent to the the ひぬ imaiediately under the trusses. It is generally customary to place が Gn^s Uüder tlie panel points ; but the author prefers to put them two ieet to one ^lse S° the floor beams may be swung into place without taking down tlie 0£ 仏浓。1]、’ This method may, and probably will, require an extra bent at one end 8Pau ； so, if fclie bents be expensive, it is better to put one under each panel l and remove the upper tiers before swinging the floor-beams. 和 he T 8Pans 'vhere tlie track stringers rest upon the floor beams, or for any spans of ^ e bents of falsework are directly under the panel points, the level of the top So : °ugitudinal beams should be at least twelve inches below tlie feet of the posts, angle P.ermit of the use of camber blocks, like those shown on Plate XI. The aü^je the contiguous faces make with the horizontal (less, of course, than the t]ifi 0 ° fiction of tlie wood) enables tlie under block to be easily knocked out wlien swung. t0 0llGU' で01’ the case of stringers abutting against floor beams, and falsework bents 心 t. び 山6 panel points blocks must be placed between tlie cambre blocks and lower f iG1 ^eaiüs» 80 that tlie track stringers may pass oyer the upper caps of tlie se^ with a couple of inches clearance. the siz 说 Ambers for the caps and posts of the falsework are generally square, and Zesfortlle latter are to be found from Table XXIV., after tliq stresses in — 22ß 一 • them have been ascertained as follows : 一 Let TF】 = weight per foot of the iron-work of the bridge, 下 ド 2= average weight per foot in height of one bent of falsework and the timbel，s whose weight it supports, = wind pressure per square loot, A = area per lineal foot which the two trusses present to the wind (it is genera レ ]y about live or six square foot), A* =： tlie average area subject to wind pressure per foot in height on one bei 山 and its share of longitudinal bracing, l = panel length, c：t Co, etc. = horizontal distance between centre lines of inclined posts 1 ⑽- sured along the caps, d = depth of truss, cllt d：9 etc- = lieiglits of the different tiers commencing at the top, h =» vertical distance between centre of chord and upper cap of bent, and 0 = the angle which the inclined posts make with the vertical ; then 2，Al = pressure on trusses at each panel point, 2^Afd\ = pressure on upper tier, pA’d‘2= pressure on second tier from top, ])A’da= pressure on third tier from top, and the stresses Fti F3, etc., in tlie inclined posts of tlie first, second, and third tiers respectively, will bo given by tlio equations, ^ =^[,<4 + /t + + 令] +(空+ 孕 )_， F2=^L(4 + /t + rfl + d\+£Siif^r\ + ■ [孕 +姊1+夺)卜 = ^-ÖT^(4 + h + di + d2+ rf3) + £I£L±ii±i2in + — ‘ “ か^^); P， F4 = &C. + &C. These formulae are obtained under the supposition that the inclined posts 似 not aided by the vortical ones, which supposition is necessary in order to avoi^ 8,111 bigaifcy : it would be correct, were the falsework on the verge of overturning. I“he tiaiber bo green, the error thus made upon the side of safety is advantageous ; if tlio timber be dry and of good quality, ifc is permissible to make a slight retlucfci011 ia the size given by Table XXIV. In applying the table, find the size of squal0 imber required for a stress Fi and length di sec 〇, that for a stress and length do sec 0, etc” then take the greatest of these sizes. — 227 — The \ ertical posts should be strong enough to withstand a working- stress given by Äe equation, ' 8： Wil 了 2 ( + t?2 + &C. + d n-i + 誓)， Verti，e U 11 啦 her of tlie tier considered, and S the stress ia the corresponding 他 ich” dhueiision of tlie vertical posts should be the same as the side of the square 贫他 tlT 山0 8ecti0n が the inclined posts; so that the diagonal braces may be flush Y ‘• le eutii’e faces of the bents, and be bolted to the verticals without the inter- VentlrOU ^fiUing-pieces. prop^e m°re elevated tlie bridge, the more important does it become to properly t0l ^tl0ü tlle falsework. The values of W2 and Af will have to be assumed, or shofü/l Calculafced, before applying the equations. Tlie ofcher quanitias are, or Ware い， ku°WU* The valueof V may be taken from ten to fifteen pounds per ta].e le ぞ00し unless the situation bo more than ordinarily exposed, when it may be tilß u ^ twenty pounds. One can afford to risk the chance of a hurricane striking Gbrid^ before it is swung. PostsTllVeCti°US °f tlie Cftps are SeueralIy ^ade tlie same as those of the inclined and .• . e caP3 should be dapped to receive both upper and lower ends of vertical b0jt ^ lued Posts. The vertical posts should be drift-bolted through the caps, tlie Posts Tg l0Ug enough fco project five or six inches into each post ； and tlie inclined pr -e h oul(1 be held in place by wooden splice pieces, one on each side of the bent, ^rou rllllg a')ove and ^elow the cap, and fastened at each end by a bolt passing Verti Y 心 tW0 81〕lice Pieces aud tlie post. This atfcacliinenf; may be used for tho Cal 抑也 instead of the drift bolts. splicf°r a(ldlfcl0nal security against slipping a third bolt may be put through the thp 4 l)leces and the cap, or cleats may be nailed to tho caps above and below at 6 0f eacli inclined post. fal 二 ひ ド holes in the timber should be accurately located and bored before the tevu 13 erected. On this account the bents should be all built after ouo pat- Uie va〆 ザ 山6 Par^s may I>o iiiterchangeble. If the bents be of different heights, 8Pikes f “ 的0 咖ア be effected in the lowest tiers. Bolts are always preferable to aiij re conüectmg timbers, especially wlieu tlie falsework lias to be taken down erected for another span. Care should be taken to avoid any unnecessary .le in order that it may not be sold at too great a loss after the 技13 finished. tru8Ses should be two plank walks on top of tlio lower falsework, exterior to the for 如 a runway midway between formed of several wooden joists set on edge, Purpose of bringing out the material thereon upon timber- trucks. ff ow|ug table taken from Carnegie’s ‘‘ Pocket Companion n gives tlie safe loa^s c ^ . istributed loads in pounds for these joists. Tlio safe concentrated central n e found by dividing those given in the table by two. — 228 — — WOODEN BEAMS. Safe Load, Uniformly Distributed, for Rectangular White or Yellow Pine Beams one inch thick, allowing 1200 lbs. per square inch fiber strain. To obtain the safe load for any thickness, multiply tlie safe load given in table, by the thickness of beam. To obtain the required thickness for any load, divide by tlie safe load for one inch, given in taole. Span in Feet. DEPTH OF BEAM. 6" r 9" 10" 11" 12r ず 14" i5" 16" Feet. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs 5 960 1310 1710 2160 2670 3230 3840 4510 5230 6coo 6830 6 800 1090 14*20 1800 2220 2690 3200 3760 4360 5000 5690 7 690 950 1*220 1540 1900 2}CO 274。 32*20 3730 4290 4880 8 600 8-20 1070 リ5〇 1670 1010 1400 2S20 3270 3750 4270 9 530 730 95O 1200 1 4 さ 0 1790 2130 2500 2900 3330 3790 JO 480 650 85O 1080 1330 1610 19-20 2250 2610 5000 3410 ii 440 59。 780 980 1210 1470 1750 2050 2380 2750 3 100 12 400 540 7IO 900 1110 1340 1600 1880 2180 a 500 2840 13 370 500 660 830 1030 1240 1480 1730 2010 •2310 2630 H 34。 470 610 770 95〇 1150 1370 1610 1870 2140 2440 15 320 440 570 720 890 1080 1280 1500 1740 2000 2280 16 300 410 530 680 830 1010 1200 1410 1630 1880 2130 17 280 380 500 640 7 含。 950 1130 リ 30 1540 1760 2010 18 270 360 470 600 74〇 900 1070 1250 1450 1670 1900 19 •250 340 450 57。 7〇〇 850 1010 1190 1380 15^0 1800 20 240 Wo 450 540 6ア〇 810 960 1130 1310 1500 1710 2T 230 310 410 510 630 770 910 1070 1240 1430 1630 22 220 300 390 490 6io 730 870 1020 1190 1360 1550 210 280 370 470 580 700 850 980 1140 1300 1480 24 200 270 360 450 560 670 800 94。 1090 1250 1420 25 I90 260 •今 40 450 530 650 770 900 1050 1200 1370 26 180- 250 33〇 420 510 620 740 870 1010 1150 1310 27 180 240 10.0 400 500 600 710 8jo 970 1110 1260 28 170 23c 300 390 480 580 690 800 939 1070 mo 29 170 230 ^9〇 370 460 560 660 780 900 1030 1180 Tlie posts for the upper falsework should rest on the caps of the lower falsewo1^ a few inches inside of tlie trusses : they should bo attached by splice timbers cleats. The height of the upper falsework should be such that tlie upper surface tlie cap will be at least six inches below tlie under sides of tlie top chord section 日， 玲0 as to permit of the use of cambre blocks between. The author would recommend that the encl bents of upper falsework be made till*00 or four feet higher than the others», and the use of four posts there instead of two, one ⑽ tlie inside and one on the outside of each truss, in order to aid in raising and retaini11® in place tlie heavy batter braces. After the latter are put in position a lioi.izoü ⑽ 1 timber may be firmly bolfced to tlie bent at the level of the other bent caps for 山 ö temporary flooring to rest upon. Stout beams stretching from bent to bent will — 229 — to acfc as fulcra for tlio levers by which the chord sections are lifted aud eW in place while being connected. The cap of the upper falsework should be deeper than it is broad, because it 0 act as a beam, and may be subjected to considerable shock, when the chord sections are being put in placo. The method of bracing sliowa on Plate XI. is spe- y advantageous in respect to this consideration. Tlie upper falsework should be braced longitudinally as well as transversely. The sizes of tlie posts will vary from G〃 x 6" to 8" x 8" according to tlieir no 1 and the weight which they have to support. . In both the upper and lower falsework the diagonal bracing in planes parallel e longitudinal axis of the bridge should for economy’s sake be placed between ^ lUa^e pairs of bents ; that is， every other space between bents will be braced : e end spaces should, however, be braced in any case. ^ Plate XI. gives an illustration of liow the working drawings for falsework should made. For economy of space the scale lias been taken at one quarter of an inch 16 foot ; bufc it should, if intended for an actual case of framing, be twice as Sreat. a. drawing of this kind should be accompanied by bills of lumber and iron in a similar manner to that explained in Chapter XVII. Measurements jj ls^auces between bolt holes should be both scaled and calculated : those on a e XI. were simply scaled, as the plate is intended for illustration only, j Ple foreman of the work should be furnished with a blue print of the working £=^叫8 fQr the bridge, unless the type of structure be one with wliicli lie is per- M y laimliar. He must also be provided with a raising bill, which should consist a skeleton diagram of one truss with the following information written thereon. Size of each truss stmt and tie and raark for same ; also number of pieces of ame ln a Panel of one truss. ^iaruefcors aud lengths s. to s. of pins with tlieir marks. Diameters, lengths and marks of fillers for same. • lz6s and marks of all separate plates belonging to tlie trusses, each in its pro- ^ ^agram for the lower lateral system giving the following information ; Sizes and marks of rods Positions of same showing which eyes are to go next the trusses. Sections, lengths and marks of lateral struts. Diameters and lengths of lateral pins, if any. , Diameters and lengths of fillers for same. • lagvara for the upper lateral system and portal bracing giving the following Sizes and marks of rods. Positions of same showing which eyes are to go next the trusses. Sections and marks of lateral and portal struts, diameter and length of mortal pins. Diameters and length of fillers for same. Diameter and length under head of portal strut attaching bolts. ― 230 — He should be also provided with a plan of the bottom chord packing, the trans- verse dimensions being exaggerated so that the size of each piece may be written thereon ; a bill of bolts giving the number and position of each kind, and a clear statement of the system of marking the iron. Before starting to erect the bridge the foreman should study carefully all tlio plans so that lie will have a clear picture of the bridge in liis mind’s eye, and will not have to be continually referring to tho drawings daring the erection. On a work of any magnitude there should be kept on hand a few standard nuts of each size ordinarily used, so that the loss of a nut or two will, cause no delay : for the same reason there should be a few extra bolts of each size. The material as a general rule is all piled on one side of the stream, the raising should therefore be commenced at tlie other side so that the passage of the material will not interfere with tlie work. If there be no objection, the far end of tlio bridg6 should be the fixed one, so as to start from something permanent, but this is not absolutely necessary. ' To illustrate the method of raising take for example the bridge treated iß Chapter XVIII. , and assume that tlio foundations with their anchor bolts and false- work, are in place. Tlie first tiling to bo done is to lay out the centre line of tlie bridge upon the falsework caps, marking it with a small-lieaded tack on each cap» then the centre lines for the trusses in tlie same way. This can be done either witli a transit, or with a carpenter's chalk-line ; care being taken to make the transverse measurements to the outer lines exactly perpendicular to the central lino. A test the accuracy of the perpendiculars can be made by the three, four, and five method using a tape-line. Next, mark tlie exact positions of the panel points upon tho longitudinal beams under the trusses, and place tlie camber blocks, levelling over them so as to make tlie lines joining the central points of their upper surfaces parallel to the curve of tlio chords. It is better to have the blocks a trifle high, say, 任 quarter of an inch near the centre, and au eighth of an inch near the ends, or iuo1'®» it on account of tlie height of the falsework, a greater settlement be anticipated. It better to liavo tlio height too great than too little ； for, if on account of too much cambre the last chord connection cannot bo made, it is only a few minutes， wort to tap the blocks a little, so as to lower them tlie requisite amount. Foui* small nuils will 110 Id each pair of camber blocks from slipping during tliß work, and they can be left so as to be easily extracted before swinging tlie brid^0. Next transfer the centre lines of the trusses to the tops of the camber blocks, ^ mark accurately the first panel points from the fixed end, then, starting there, pack the chord bars of both chords. It might bö convenient to have a few hard- wood pins to fit tlie 110 les pretty tightly, so as to aid in getting the bars properly placed longitudinally. After tlie chord packing has made some progress, run out the two baiter braces» and hoist them into place by means of pulleys attached to the cap of the first bent of falsework, which bent should have been previously guyed and braced so that it cannot possibly be disturbed by the effect of the pulleys. As soon as each battel* — 231 — - 51 ace is raised, and the anchor bolts pass through the holes in tho shoe plate, the Ul^s s^ou^l bo tightly screwed clown in order to aid in holding the batter brace in Position. It will not however, to rely solely on these, for the tlireada of the encl bolts 七 be stripped : consequently a bard-wood supporting block must be strongly 0 ted to the two adjoining posts of the bent of the upper falsework. This block 1 1 c ^ave a bevelled edge, tho angle of bevel being equal to the slopo of the batter bar で 的 t】iat the iron-work will not rest on a sharp edge of wood. * If the lattice a S. luterfere with the buaring, as they aro liable to do, rough notches can be cut in inute oa the bevelled face so as to bring the bearing upon the channels, the eaüWhilG the end lower lateral strut, the end lengths of the lower choril struts, •th l)0rtal struts ancl the portal and end lower lateral rods, having been run out, ミ く aie to be put into place, the portal struts being retained there by their connect- tb° i° S， aU<^ lateral stvut by the end chord pins, which should also pass through 6 C l0l，c^ bai’s, chord struts and the fillers. be 八.8 the portal rods are adjusted by turn buckles with single tap ends, they may °^itted until after the portal struts are in place, to ,e . rUü ouk and hoist upon the falsework, by means of pulleys attached there- pj luioers used as leters, tlie end sections of tho top chords, working them into 如0 y the levers, and attaching them by the hip pins, which should also pass ck .プ]1 the end main diagonals, hip verticals and fillers. Tlie other ends of the r sec^01ls rest on the cambi.e blocks. end v . lUn 。加， an(i hoist into place, the first vertical posts, letting tlie upper le la the open ends of tho chord sections, and the lower ends pass around the l0^ chord struts. Pagc^eXt hing out the second sections of tlie top chords and the second set of lev \ S， 丑 心80 tlie chord sections into place, as before, with pulleys and beam the ’ 01 山 叫 them there until temporary bolts aro put into a few boles through 如〇的で咐㈣咖⑽， 础叩 plates and channel webs, and until the pins are run f tlie posts, diagonals, and fillers. be b 1 8QiallJpovtious of the structure as pins, fillers, and beam hangers, should not ovovi °11^^ ou^ upon the falsework until required for use, for fear of their being lost ti:0bard.. Nothb】 Oh ノ _ U ^ wi】l be assumed that they will be at hand when wanted. It should be ti0llg 〇 ぐ r' Nothing more will be said about running out these and other small por- ⑽ Uu(])U ^ assumec^ that they will be at hand when wanted. It should be Portioif び1001 thing between the foreman aud the men, that any one who drops any arranry1 ^le bridge into the water forfeits a certain amount of liis wages. Such an general ぐ ent ma^e green hands a little more careful than they are apt to be as ；{； p 二8 も い r^ve^ gang at work at the portal and let them follow up the work on the t でノ; m 0” am! into place, as before, the second pair of posts ; then bring CoUnter Uc sec^0ns of the chords, the third set of main diagonals, the first set of before で 〔1 心 nex^ ^engths of tlie bottom chord struts, putting all into place as n so on until the end of the bridge is reached. — • 232 — ■ Just before the riveters complete the riveting of the portal, the first of the upper lateral and intermediate struts should be run out, and put into place ; but the upper lateral and vibration rods should be omitted, as they would bo in the way of tlie riveters, and can be readily inserted afterwards. As the chord bars will be in the way of tho rivetters when connecting tlie lower chord struts, tlie latter can be temporarily removed by withdrawing the pin む〇瓜 tlios0 oil one side of the strut at the panel point where the connection is to be made and hoisting the bars out of tlie way until the connecting plate on that side is atta. ched, then putting them into place again, and repeating the same operation on the other side of the strut At these panel points it might be well to use wooden p^s until the strut connection is mado. About tlie time that one-half the span is erected, commence running out lower lateral struts and rods, putting thorn into place, inserting tho liip verticals and fillers, and coupling the lower chords into tlieir final position, leaving the beam hangers lying horizontally, so that, when tlie longitudinal supporting-timbers removed, they will drop into tlieir proper places. A little before the riveters reach the end of tho span, the upper lateral and vibration rods should be put into place, and screwed up about tlie right amount. When the end of the bridge is reached by the riveters, *the last couplings of the bottom chords can be made at tho pedestals. The shoes rest upon the rollers, which should Lave been put in exactly trans- verse to the direction of the bridge, and blocked so that they cannot move. Tlie last connection for each truss can be easily made by raising the liip either ■with levers or by jack-screws, and either pressing against the shoe with jack-screws abutting against blocks cliained to the roller plate, or by attaching a pair of blocks to the pedestal and first panel point lower chord pin. After the final coupling lias been made, and tlie riveting is finished， knock tlie upper chord camber blocks, so as to bring all tlio weight of the upper part tlie bridge upon tlie posts ; then take down tlie upper falsework. Next knock out the camber blocks of the lower chords, lowering them together gradually so as to bring no shock upon the bridge, and remove tlie beams that sup- ported the trusses. The arrangement of the cambro blocks will generally have left sufficient lio^a" way between the lower lateral struts and the runway to allow the floor beams and track stringers upon timber trucks to pass between ； but if not it will be very 妙 印 to construct a new runway by blocking up tlie middle of each lower lateral strut from the old runway and laying a line of planks from strut to strut : should the plaok® spring too much, they can be blocked up at their middle points. Next run out the end track stringers with their bed plates and bracing fra 位 and leave them on the pier, then bring on the end floor beam, and take up as of the runway as is necessary to get it into place. It should be lowered beneath th0 ends of the hangers then raised into place, after which the filling plates should be placed on top, the hanger plates below and the nuts screwed up tightly and locked Now gefc the end stringers into place, removing the runway and inserting the braci^ — 233 — 土. 1 .e°* stringers can rest upon the supporting brackets until it is convenient ^ lve them to the beam. Next run out the second pair of stringers putting them ce at the far end and supporting them from the lower strut temporarily. as .. . len bring out tlie next floor beam, swiug it into place removiug the runway 1 ftei’fei’es with the work, and so on until the end of the bridge is reached. jj .. 8 80011 as the second floor beam is in place the rivetters cau commence cou- n、. ハ 1 •气 ie sfcl_ingei.s to tlie beams, and follow up the work as fast as these members aieWia place. - ei ^10 track stringers rest upon the floor beams, quite anoilier method of are ^0ü mils 也 bo pursued. The stringers must be brought out at the same time as lateral struts and rods, both of which pass through holes in tlioii* webs, tiou 10 08 mu8t be large enough to give considerable play, both to allow for cleflec- Unc^ei Posing loads, and to facilitate the passage of the lateral system. The fels ^ei S ル011】(1 be supported temporarily upon blocks from the caps of the lower Sf)|- W°l^> au1IAKES OX BOTTOM CHORDS. Afier roaming tliis treatise tlms f?ir some Japanese engineer may still liavo n,n iileii that some portions of the brulgos designed are too light, more especially i^10 bottom chords. This is due to preconceived notions caused by the stiff lower clioi'^8 ot the Japanese brklgGR. The chords here designed were proportioned for the combined eftects of tJit* maximum live load and the wind pressure : they can only too liglifc thevetoro, in resisting tho sliock of pas.siug loads. Let us investigate tliis point. The most destructive effect of a train would be when it is allowed to coiuo upon Uie bridge Avitli all the brakes set. To be on the side of safefcy let us assume n train ol engines, and take the coefficient of friction between wheels and rails to ^10 0.8. Michael Keynokls C.E. in his treatise on u Continuons Bailways Brakes M p» 207 makes the actual maximum value of this coefficient 0.25, although two pages tlier on he assumes it as wo have done to be 0.3. With tho train covering the Rpan the combined live and dead load tensions in the lower chords would bo so gi.ßM that the thrust of the braked wheels would most assuredly bo insufficient to overcome ifc, when tlie first pair of wheels conics u])on the bridge, the thrust which they pioduce will also be too small to counteract tlio dead load tension. Between thos0 two extremes there is one position of the loading which will be more effective tlift11 tiny otJier position in causing thrust upon the chords. Tlic train should be brought on at the expanding end af the span, iu which case the part upon which the thrust will act with greatest effect will be the end panels of the lower chord at the fixed cn^# Lefc tlie dead load stress in the end panel of the bottom chord of one truss bo denoted by T, Let the variable reaction of the live load on one truss at the fixed end be repre- sented by /7, then the corresponding end panel bottom chord stress will be 7? tan 〇 wliere Q is the inclination of tho batter brace to the vertical. Let w =5 the uniformly distributed live load per lineal foot on one truss 1 = tlie coefficient of friction between wheels and rails I = lengtli of span. and x = length covered by the moving load, the origin of coordinates taken at the expanding end of the span. The reaction 2S7 n 肋 <1 t]ie UW2 ~w， corresponding end panel chord stress 2L tan 6 10 tlirusfc i neglecting the partially compensating rolling friction afc the expanding ot the span) is / ^ x. The compressive stress on tlic chord at t-ho fixed end, if 6 )e any> will consequently be given by the equation C = fwx~ ^ tan 0 - T ^Pientiatiug to find a maximum gives differ, dC 17 e^tiating again gives r ti'X J ハ f w j— U m 0 o and x = ~ fl Ian 0 w tang , in which X to the zero power, so that, when fl oc — - — - • tan 0 Sl^stitufced tlierciu, the second differential coefficient is negative, denoting a ^^stituting fl in tl . 1m 6 le equation giving the value of C, gives for a maximum value of the ComPressiou wf‘Jl T 2 tan 0 sale 'a^ue ^ cleduced from the Chapter on General Specifications J, is 0.07 ton -p[v ?，? t011 per h •職 1 鼠 19 11 lot us try the 100’ span where T = 10.9 tons and tan 0=1 0.7 x 0.3 x 0.3 x 100 sho^vj 2 10.9 = — 7.75 tons. before Oni in^ that the thrust cannot overcome the tension, Again taking the 140’ span, we have T = 16.97 and tan Q = 0.87, which S^ves X 0.8 x 0.8 X 140 ■16.97 11.9 tons. s^o\vii 2 x 0.87 j, AU^ that the tendency to buckle the chord decreases as the span increases, t しノ 糾 118 try a 70’ span through bridge, which is the one least fitted to resist eth_. Here T 6.G6 tons, and tan 〇 = 0.988, hence ^lLA_0-3 X 0.3 x 70 6 66 _..ilS 2 x 0.983 0,0b 4,0 238 — showing that even in this case there is amplo tension. Hence we may conclude that the bridges which we have designed are fu 取 capable of properly resisting any stress or combination of stresses to which they can ever be subjected. CHAPTER XXIV. RECAPITULATION. Before closing this treatise it may be advisable to give a resume of the various Ps to be taken by an engineer in designing and building a briclgo. They are as IOUows : 〜 し Ascertain as much as possible of the list of data in Chapter XVII., so as üo\v wliat kind of bridge is required, and what are tlie peculiarities of location lat may affect ita construction, • Determine the live load, dead load, number of panels, depth of truss, engine j ^ess, wind pressure 011 each panel point of top and bottom chords when bridge 8 botl: empty and loaded. Fill out the table of data given in Chapter YIII. 4 • Find stresses in trusses by method of Chapter YIII., recording them on a kelet^ diagram. ^ * Proportion main members of trusses recording dimensions on diagram, te 6 • Determine from the tables sizes of members of lateral systems, floor sys- ’ Portal bracing and vertical sway bracing, and write them upon diagram. マ • Proportion pins and write their diameters on diagram. 8 • Make out bills of materials, proportioniug the details as they come in order the list of members. ^ * Check dead load. 0。. Make estimate of cost. • Make working drawings. 1 • Make order and shipping bills and send to manufacturer together with ex* ^oo011 °f methods of marking iron. 打 • Check all materials when received at site and pile them up in a convenient ^ * Erect the bridge. • 240 — ADDENDA. Since the preceding pages were written the author lias seen in an otherwise very favourable review of liis keatiae 011 “ Tlie Designing of Ordinary Iron Highway Bridges.' 5 by tlie American Engineer a serious objection to the usual attachment of a floor beam by four hangers. I11 tlie words of the review “ tlie inner loop will take nearly, if nofe quite, all tbc load at the panel point ; when the bridge is first adjusted ; and this not only become 只 constrained itse]t. but also overstrains the inner tension brace. -：: The number of inner hangers wliicli arc constantly working loose, presumably by stretching» railroad bridges in which this detail is usecl, demonstrates its iui8atisfiicfcoO, character. 5, Tlie author has long recoguizecl the inequality of diatribukion of floor beam between tho inner and outer liaugers, but considered that the low intensity working stress on tlieso members would compensate for the objectionable iueqi 以 1办* buch has been also in all probability the opinion of most American eugiucers ; beams, when not rivetted to the posts, are nearly always suspended by four liangel，s， 丄 lie fact of the inner hangers working loose can have been only lately discovered ： ^ shows, however, that this detail needs improvement ; and as the aim of this treatise is to design structures not only equal but in some respects superior to the best America11 bridges, it bocorues necessary, even at this late hour, to correct tlie newly discovered fault. Tlie simple method of using singlo beam hangers will no fc always work, 〇、咖轻 to the great bending moments which they produce upon tlie pius. For instanco tlie case of a double track bridge with panels twenty-four feet in length. The weigU supported by each single hanger would bo about forty tons, and the distance betwee，i centres of main diagonals would not be far from twelve inclies. Those data give Ä vertical bending moment upon the pin equal to one hundred and twenty inch to が’ whicli alone would require an iron pin five and a half inches iu diameter, or a one of four and three quarter inches ; but when combined with the horizontal mon1011^ would call for a pin much larger than any intelligent designer would think f01' a moment of using. Tlie double hangers iu such a case are a necessity, but tlie connection must be such as to distribute the load equally upon them. Such a distribution can be assured by using the following detail. On tlie under side ol the beam at ^eacli end is attached by four rivets a が ポ about five eighths of an inch thick, six inches long and as wide as or a life tic wi み1 than tho beam flange. This plate is placed symmetrically to the plane of tlio ti’u# and the middle of the under side is grooved so as to receive one sixth of tlie of a pin about two inches in diameter, which rests in a similar groove on the top the beam hanger plate. The lateral dimensions of tliis plate will be slightly gi*e^ter than usual, but the thickness need not exceed one inch. To prevent the plate む 〇 似 ^ Main diagonal. — 241 — rilPture by bending there are aitxclied to the underside by countersunk rivets two ang】e irons or plates bent into th) form o.' angle irons, the vertical legs being con- necteJ by countersunk rivets, wliich in the neighbourhood of the pin pass as nearly as may be through the neutral surface of the T beam, and elsewhere near tlie lower etlges of the angles. As tlie axis of the pin is parallel to the lengtli of the bridge, they ertical legs 也 Ust be transverse thereto. This detail will be readily understood from tlie accompanying diagram. To illustrate how to find the sizes of the stiffening plates, number of rivets re- &c, it will be well to design a beam hanger plate for a 24f panel of a single track bridge. The total weight on the four hangers is about; forty tons, and the centres of tlie arn hanger holes may be assumed to be situated on the corners of a six inch quaie. Uiig would make the bending moment on the plate thirty inch tons, which Mould be resisted by tlie T shaped section of the two bent plates combined with the portion of tlie beam hanger plate below the pin. Assuming the latter tliick- i ， and the plate stiffeners to be of Gff x Gr, x angle iron would make the T 0 ut 12" 父 6 务" x 1", tlie centre of gravity of which is about 5" above tlie bottom. The moment oi' inertia is thereibre ^ x 12 + 12 x (1.Ö)2 + ^ (5.5)3 + 5.5 x (2.25)2 =： 54 + 丄 he resisting moment is given by the equation M: hi so taking E = 4 tons 4x54 M ■ 5 ：43.2 As the bending moment was 30 inch tons, the sizes assumed are ample. 你 、 be well to use three quarter inch 031111 tersauk rivets (tlie largest pos- e?’ so a[to make tho ditferent portions oi* the T head act together. (|e _ is a tendency to bend the plate iu a direction at angles to tlie one consi- res. ’ ’ 出3 moinent for wliicli is fifteen inch tons on oach side o：' the pin. This will be . e a couple whose forces acb as compression ou the top plate of tlie T and te at the lon on fclie riveks near the bottom of tlie angles. T ikiug the centre of moments of the top plate ami the distance therefrom to tlie horizontal centre ton ^1G rivet holes as 4 g inches, will make the tension on tho rivets = 3 42 tli マ如玆 au intensity of only two and a half tans, bscause of the initial tension Uvefc、 will make the section required 1.37 square inches ; consequently two ，1V^fcs will be sufficient. tL,ac、 仏 size of stiffened beam hanger plate may be adopted for all panels of single 、 bridges， or tlie fchickaess of the angles may be retlueed to three eigliths of ani^ for short p,nel, 'つ difftii’eiice in tlie total weight of iron per lineal foot caused by the use of* —— 242 — this detail will be from six to eight pounds for single track bridges, and from ten to iifteen pounds for double track bridges, the smaller numbers being for short spans and the larger for long ones. It will bo noticed in the diagram that the floor beam stiffeners at the support are placed close together so as to take up the vertical reaction of the hangers trans- ferred by the auxiliary pin. The sectional area of these stiffeners should be about equal to that of the hangers. Since this treatise was written, the author lias prepared for the Institution Civil Engineers, Loudon, a paper entitled An Analysis of the Weights of Iron Dead Loads for Iron Pratt and Whipple Truss Railroad Bridges ”, the following deductions from which will be iound use fill to Japanese engineers. For loiiir single intersection deck trusses the economic depths are about one less than those for the corresponding through trusses : for short double intersection1 trusses they are about three feet less, and for long double intersection trusses abo^t one foot less. The ratios of the total weights of iron per lineal foot for single track deck ⑽ ユ through bridges, excluding the weight of the iron bents over the piers and abutments, a1，e [riven in the following table. Span. * Ratio. Span. Ratio. 6of 0.88 i8of S.I 1.01 8o, 0.94 1 8c/ B.I 1.08 1。。， 1.00 l<)Of 0.1 1.01 150' 1.05 200r D.I 1.07 160^ 1.04 250， 1.05 170， 1.02 30 o' 1.05 Tlio ratio o.' total weights of iron per lineal foot for double and single trftc^ through bridges are as given in the following table. Span. Ratio. Span. Ratio. 6c/ 2.00 18。， 1).1 I.Q-2 Sc/ 2.00 20 C, 1.87 I00r 1.94 24 O' 1.25 15c/ 1.91 280^ 1.83 1 8c' S.I 1.90 50V 1.82 The ratio of total weights of iron per lineal foot for double and single trac、 (lech bridges, when the weights of the iron bents over the piers and abutments a/ß ^ considered are as given in the following table. Span. I Ratio. Span. Ratio. 60’ 1.99 180^ D.I 1. 7 斗 80' 1.92 20 Or 1.74 I。。' 1.83 24c/ 1.74 J40, I 1.76 280^ 1.74 180* S.I 1.76 300' 1.73 Imj ironed Beam Hanger Plate . o of 0 o 〇 〇 o o 〔 > 〇 O 〇 o 〇 〇 〇 o o 0 〇 〇 〇 〇 〇 〇 〇 〇 〇 〇 〇 〇 〇 〇 〇 〇 〇 〇 〇 〇 〇 GLOSSARY OF TERMS. ^djmtabie Member.. 一 A member of a bridge the lcu^tii of which can be increased or di- ^Hedatwill. Adze. — x tool for cutting timber. ( Plate XII., Fig. 8.) Anchor Plate or Anchor Piece. 一 A bent plate for holding* down the expanding pedestal ； Ute II, Fig. 12. AnSie iron. — Iron rolled into the shape show n in section on Plate II., Fig. 3. — The intersetition of a brace with a chord or flange ； called also a panel point. a , of Synunetry. 一 A line dividing ail area into two parts equal and similar to each other, simUarly disposed to the line. Bap. — A piece of iron flat or square iu section. 0f — Slope, or iucliuation, to tliQ vertical j usually measured by tbo tangent of the angle, 60 many inches to the foot. ® 技 tt©r Bruce. 一 The inclined end post of a bridge. (Plate 1.) Beam. — A member intended to resist bending. Hanger. 一 A rod oi* square bar supporting a floor beam from a chord pin. (Plate I* M P]ate II., Fig. 10<) a? •Bea，^*,lan*er w«t*. 一 Nut4« on the ends of beam hangers, serving to press the floor beam ^st the feot of the posts or against the chord heads. (Plate II., Fig. 10.) »»•Uiuiger Plate. — A plate placed beneath tlic end of a floor beam for the beam-hanger 10.) Bea t0 rest against. (Plate II., Fig* Bean Bear,nS-Pi>«#u re . — The pressure on a bearin«：. Bed »,1 ^ late* 一 A plate to distribute pressure upon masonry. (Plate IX, Fig. 11.) pj. en«tngof0)nentt 一 The moment of a force or forces which bend or tend to bend a B«Hcling,StreM 一 The stress produced in a piece by bending. «nt. — x frame of timber or iron, usually the former, as a bent of false-work. Ä - Au eye on the end of a bar, the plane of which makes an angle with the CUon of the length of the bar. (Plate II, Fig. 11.) — The slope on the end of a piece. 0ther °f Ä,aterlttl* — A. list of various portions of material giving dimensions and weights, or quantitative measurements. 边 ult. i — A system of one or more pulleys or sheaves, so arranged in a frame or shell as to 2 ^ ^ P0wer 0f the rope passing around them, or to change its direction. (Plate XII. fioara 1Qch ÄIoa*«re. 一 The measure of timber, the unit being a piece one foot square and one b. m C • Timber is sold at so much per thousand feet board measure, usually written, per M. Öolt. ■ 00 on ' An iron rod with a square head at one end, and a thread and nut at the other. am* 'The English name for chord, ce. 一 Generally a strut， but sometimes the term is applied to a tie. (Plain =cket .〜 A knee or knee brace to connect a post or barter brace to an overhead strut 1 - 0r P1ate II., Fig. 11.) Pigs ^ClnK Frame. - g * 1(5 and 14.) ÄuwJÖeam* ~~ A. beam uiade up of plates and angles riveted together. (Plato IT., Fig. 10.) cH«，unei, 一 An assemblage of plate and angles in the form of a channel. {Plato - A frame to brace or stiffen parallel stringers or girders. (Plate I [り •— 244 —— IX., Figs. 3 and 6.) Burr. 一 A rough edge cr ;.idge left by a tool in cutting metal. The term is sometimes used for a nut. BuUon Sett. — A tool for fornüng the heads of rivets. (Plato XII., Fig. 5.) Camber. — The upward curvature of a truss. It is measured by the height of tbo middle point of the centre line of the lower chord above tlie line joining the contres of end pins. Camber Blocks. — Blocks of wood used in erection, so placed as to be easily removed. (Plate XI.) Cape Chisel. — A tool for cutting iron. It consists of a rounded edge on the end of a short rod. The edge is very obtuse, so as not to break easily. Centre of Gravity. — That point of a body about which the weights of all the different portions balance. Channel, or ciuinnel Bar. — Iton rolled into the shape shown in section on Plate II” Fig. 1. Ciieclc Nut, «r Lock Nut. 一 A contrivance to prevent a nnfc from turning* when subjcctea to shock. ciiord. 一- The upper or lower part of a truss, usually horizontal, resisting- compression or tension. (Plate I.) Cl&ora Bar. — - A member of the chord which is subjected to tension. (Plate I.) Chord Ilea«!. — The enlarged end of a chord bar, through which the pin passes. Chord Pncicing. — The arrangement of the bottom chord of a truss. Clear Headway. — The vertical distance from tlie upper surface of the rails to tbe lowest part of the overlieiid bracing. It is a measure of tlio height of the highest car that could pass through the bridge. Clear Roadway. 一 The horizontal distance, 7iieasnred perpendicularly to tlie planes tho trusses, between the inner edges of the batter braces. It is a measure of the width of the widest car that could pass through the bridgo. Cleat. — A narrow strip of wood nailed to something for the purpose of keeping a piece J work in its proper place. Co-eiilcient of Friction. 一 A numerical quantify, which, multiplied into the normal pres- sure， gives the frictional resistance. It is equal to the natural tangent of the angle of repose* • C’oltl Cliisel. — A tool for cutting iron. (Plate XII., Fig. 12.) Column. 一 A pillar or strut; a 1011 ^ member which resists compression. Component. — Ono of the parts into which a stress may be resolved or divided. €ompres«ioii. — A stress which tends to she r ton tlie member which is subjected to it. Concentrated Load. — A load which is, or may ho considered, collected atone or more poi0^* Connecting-Plat«». 一 A plate used for connecting two pieces. Continuous ^paiis. — Consecutive spans connected over the points of support. Counter. — An adjustable diagonal which is not subjected to stress by a uniformly disti’ レ buted load covering the bridge. (Plate I.) Countersunk Rivets. — Rivets, the heads of which are let into one or both of the plateS which they connect, so as to leave a flxish surface or surfaces. Couple. — Two equal and parallel forces not acting in the same line. Cover Plate. — A plate used to cover a joint, or to connect two pieces of tlie toi) chord 切. (Plate II., Fig. 11.) Crab. — A slow-motion machine, worked by a crank for the purpose of winding a rope a drum, thereby raising a heavy weight. (Plate XII., Fig. 1.) Crow Bar. — An iron lever. (Plate XII., Fig. 17.) Curvature Stre*s(，a • — Stresses produced by the centrifugal force of passing trains, ^e1X the bridge is on a curve. Dap. 一 To notch timber onto its bearing. I>ead Load. — The weight of all the^parts of the bridge itself, and any thing that ^ —— 245 — eÜla^n llPon it for any length of time. Deck BrWge. 一 A bridge in which the passing loads come upon the upper chords or the ll^enflS0fthep0sts> öeiiectioM. — Motion laterally, or at. right angles to the length, of the piece. It is also used e atQo«nt of motion, ;tnd i：i generally expressed in inches. Depth of Truss. — The vertical distance between the centre lines of upper and lower chords . DiaS«nal. — A member running obliquely across a panel. In this work till the diagonals P the batter braces are tension members. • /^^a»rani of Stresses. - 016 diflertint, (Plate XIIL) - A skeleton drawing of a truss, upon which are written the stresses ffervmt members. (Plate XIH.) /tj Ajiparatii«. 一 A contrivance for tlirowin^ a derailed vehicle clear of the track Wate VI 、 VI.) « Doill>Ie Intersection. — The style of truss where the diagonals cross the posts at the middle e!r as in the bridge shown on Plate I. Doi,fele-rivetejl Lacing. — Lacing in which each bar is connected by two rivets at each. ent1- (Plato II., 10.} Doul*le T«>e. 一 Another name for I-beam. örjft Bolt, — A round or square piece of iron, usually from one to tliree feet long, without. °r nut used to connect timbers. Drift Pin. 一 A. slijrhtly tapering rod of bard steel, used for making rivet Boles coincide. Use is more convenient than advisab]o. (Plate XII” Fig. 14.) ßffectiv© Area. — The gross area of a section, Ie3s that lost by rivet or pin holes ； the net 似执. ^ Limit. — That intensity of stress at which the ratio of stress oyer strain commences 0w a cided change. For wroüght-iron it is from twelve to fifteen tons. ecti,1s-Biii. — A bill of material for a bridge, so arranged as to facilitate tlie finding and ClDg of members during erection.' ®xpansion Joint. 一 The connection of pedestal to bed -plate, shown on. (Plate II. Fig. 15.) ^pansion üoiier«. — A set of half a dozen or more turned rods of exactly the same ir G er, Placed under the shoe plate at one end of a truss to permit of expansion and con- ■ミ011. (Plate II., Fig. 16.) it x，3xt°nsloM **la<«* 一. A plate riveted to the end of a strut channel, and projecting beyond ° ^ermit of tbe passage of a pin. (Plato II., Fig. 9.) Eye. 〜 人 holo in the end of a member to permit of the passage of a pin. も e Ear. 一 A bar with an eye at each or one end. W 0|* factor of Safety. 一 The ratio of ultimate load to greatest allowable working- Th .^S ^ rm ^ getting out of favor among engineers, as its use has been somewhat abused. Clsuchth 峋 as a factor of safety for a well-proportioned bridge, for each member should . lntensity of working -stress proportionate to the character and amount of work which it perform. •—人 rope used in erection for raising and lowering weights, e^vork. 一 Temporary timber work to support a bridge during erection. ^»veting. — Kiveting done in tlie field, or during erection. It is the poorest and 取 こ!) endive kind of riveting. h the け 一 ' -^n end of a strut so firmly connected as to prevent all motion of the strut 扔 lUn; UeighlDorhood of the end. S-Plate. — A plate the function of which is to make flush two surfaces. (Plate II.j no the T** 〜 A s^nal] ring of iron or piece of pipe placed on a pin in order to keep in position 加 ）ers coupled thereon. (Plate II., .Fig. 11.) a 8tr IXetl レ》 ad. — a : Ctureor Portion of a structure. load remaining permanently, or for a considerable length of time, upon •■衊 ^ Flange. 一 Tho upper or lower chord of a beam. It is the principal part for resisting citbe* compression or tension. Flexure. 一 Bending. Floor Sy«tem. 一 That part of the bridge whicli directly receives the travel. Floor Heam, 一 A beam to support a portion of the floor aud its load. (Plate I. and Plate II., Fig. 10.) F. o. B. — Free on board ship, a term used in speaking of freight. Foot Plank. 一 A plank for walking upon. (Plates I. and III.). Forge. — An app.aratus for heating iron. (Plater XII., Fig. II.) Framing, 一 The carpenter work on timber. Girder. — Any structure to cross a chasm or opening. The term is generally applied to short structures for places wbere it is not advisable to uso trusses； for instance, a plat« girded or a rolled girder. Guard Rati. 一 A rail to prevent a derailed train from running off a bridge. (Plate I し Fig. 14.) Guy*, or Guy TAnea, 一 Lines for bracing the top of a pole, derrick, or any similar apparatus. Ciyxntioii, — Seo radius of ffyration. Hammered Head. — a head formed on the end of a bar by hammering. Hand Liiios. — Small ropes used in erection. Headway. — See clear headway. Hinged Bnd. 一 An end of a strut connected only by a piu. i«p. — The place at which the top chord meets the batter brace. IIII, Joint. "— The joint of tho top chord and batter brace. Hip Vertical. 一 A rod hung from tlio pin at tho hip for tho purpose of suspending the fl°°r beam. (Plate I.) Holding on Bar. — A lever to hold against one end of a rivet while the head at the other end is being formed with a button sett. (Plate XII., Fig. 16.) I-Beam. — A piece of rolled iron of the section shown on (Plate II., Fig. 2.) initial T«n«ion, 一 The tension caused in any adjustable member by screwing up the justing apparatus. intensity. 一 The intensity of a stress is the amount of stress upon a square inch of section* Intermediate strut. — An overhead strut in high bridges, attached to the posts of opposite trusses, and lying between the upper lateral strut and the floor. In deck bridges, if used at it would lie between the upper and lower lateral struts. (Plate I.) Jack Screw. 一 A machine for raising heavy weights. (Plate XII., Fig. 】0.) Jaw. — A connection on the end of a strut similar to that shown on Plate II., Fig. 11 り Plate VIII., Figs. 7—10. •Joint, — A place where two abutting or lapping pieces are connected. Joist. — A beam. Knee or Knee Dracv. 一 See bracket. • Lacing. — A system of bars, not intersecting each other at the middle, used to connect tb0 two channels of a strut in order to make them act as one member. (Plate II., Fig. 11.) liacing-nar. — A bar belonging to a system of lacing. Lateral Rod. 一 A tension diagonal of a lateral system. (Plato I.) Ijateral Strut. — A compression member of a lateral system. (Plate I.) Lateral System. — A system of tension and compression members forming the web of 级 horizontal truss connecting the opposite chords of a bridge. Its purposes are to transmit pressure to the piers or abutments, and to prevent undue vibration from passing loads. Latticing. — A_ system of bars crossing each other at the middle of their lengths, used to connect the two channels of a strut in order to make them act as one member. (Plate エ し Fig. 9.) Lattice Bar. 一 A bar belonging to a system of latticing. 247 —— Pratt busts •〜 One of the two portions of an angle iron separated from each other by the bend, ^ever Arm. — The perpendicular from the centre of moments to the line of action of a Ce, The lever arm of a couple is the perpendicular distance between the lines of action of the 贫0 eflUa^ and parallel forces. 1401 id. — The moving* or passing load upon a structure. Mnviiio Tru** (also called ' Double Quadrangular/* “Whipple.” and a Double System truss). 一 A. truss with vertical posts and diagonal ties spanning two panels. It is the ^presented on Plate I. hock Nut. — See check nut. r 40011 Kye. 一 An eye on the end of a rod or square bar, elongated into the form of a loop, S shown ⑽ Plate II,, Figs. 4 and 8. howor Pal»« work. — The falsework below the level of the lower chords, th n,»«ono l. — A tension member of a truss, sloping upward towards the nearer end of span. Main diagonals in iron bridges are not adjustable, foment. 一 The product of a force by its lever arm. 加1* meut «f inertia. — Represented by the equation, 1 -- Ap = 2 r2dA, where A is the the section considered, p the radiu? of gyration, and r the distance of any point from au 0f ecl 】ine lying either in the surface or outside of it : in other words, the moment of inertia surface about, any axis is the product of the area by the square of the radius of gyration : or e summation of the products of each differontial of the area by the square of its distance in . • 6 aX^S, 灯 the axis lie in the surface, the moment of inertia is called a surface moment of a > while, if the axis be perpendicular to the surface, the moment of inertia is called a polar 〜ntof inertia.. donkey Wr«»ncii. 一 A wrench capable of being adjusted so as to fit nuts of different (Plate XU., Fig. 9.) 句 zes. W. Moving Loa) Wer Bui. — a form of bill used in ordering material from the manufacturers. e»pn, na，n«'ntai work. — Fancy work at the portals of a bridge to give it architectural . (Plates I. and IX.) UsUall ea<, BracI«»S» 一 The upper lateral or sway bracing in through bridges. The term is aPp]ied to the vertical sway bracing, if there be any j if not, to the upper lateral bracing. ^a«king. 一 gee chord packing. CaUed a^el* That portion of a truss between adjacent posts or struts in Pratt truss bridges ； pttnel t4en8*h. — The distance between two adjacent panel points of the same chord. — gee apex ^e«le*tal. — The foot of a batter brace or end post. (Plate II., Fig. 12.) to s^res??m，lÄent Set- — The alteration in length of a piece of material which has been subjected ’ remaining after the stress has been removed. — See column. ，〇 r Pin Pilot. 一 A nut, one end of which, is a truncated cone, used to protect the — 248 — thread on the end of a pm when the latter is being driven into place. (Plate II., mg. 8 •ノ Pin. 一 A cylindrical piece of iron used to connect bridge members. ( Plate II., Fig. B.) : Pitch. — The distance between centres of consecutive rivets of the same row. Plane of Symmetry. 一 A plane dividing a body into two equal and symmetrical Pal^s similarly disposed in ret'eronco to tlio plane. Plant. — Tools and apparatus used in construction. Plat©, — A piece of flat iron wider than a bar. The common distinction between the is that a plate is attached to something else, and acts with it, while a bar is an independent member. Plate Girder. 一 A beam, built of plates and angles, used to span a small opening, general less than sixty feet. Pony Truss. 一 A truss so shallow as not to permit the use of overhead bracing. Portal. — The space between the batter braces at one end of a bridge. Sometimes the tei，rö is applied to the portal bracing, though incorrectly. Portal Bracing. 一 The combination of struts and ties in the plane of the batter braces at a portal, which transfers the wind pressure from the upper lateral system to the abutment or l^er, Portal Strut. 一 A strut belonging to tho portal bracing. (Plato I.) Positive Rotation. — Rotation in the direciion of the hands of a watch. Po»t. — A vertical strut. (Plate I.) Pi.att Truss, (called also the “ Murphy- Whipple,” or (< Quadrangular truss). — A sing】e intersection trass with vertical struts and diagonal ties. Quadrangulär Trugs. — See Pratt truss. Racliet Drill. 一 A hand machine for drilling rivet holes. (Plate XII. t Fig. 4.) RarUus of Gyration, 一 The radius of gyration of any surface in reference to an axis is 作 し distance from the axis to that point of the surface in which, if tlie whole area were concentrat0 * the moment of inertia in reference to the axis would be uncliangecl. It is therefore equal to square root of the ratio of the moment of inertia over the area. Ream. 一 To enlarge a rivet hole, Reamer. 一 A tool for enlarging rivet holes. (Plate XII., "Fig. 13.) Re-enforcin|； Plat©. 一 A plate used for tho purpose of providing additional pin beariD^# strength to compensate for material cut away. (Plate II., Fig. 10.) Re-railing Apparatus. — A contrivance for returning to the track a derailed vehic ら (Plate Y.) Resolve. 一 To amde a force into its component parts. 一 k Japanese mile equal to about 2 | Euglish miles. Rivet. — A short piece of round iron tightly connecting two or more thicknesses of and having, when in place, a head at each end. Roadway. 一 Tlie passage-way of a bridge for vehicles ； usually means dear roadway, (Z* v, 11 oa masonry (Plate II., Fig. 12.) Rope Sling. 一 See sling. liun. 一 A line, or string ； as, a run of joists. Set. 一 The extension or compression of a piece of material under stress. ^ Sliear, or Sfioaring-Strea». — The resistance which a body offers to the passage^ 01* tendency to passage, of one section along the next consecutive section. … Siiim. — A filling piece. Here applied to a timber between the track-stingers and 1 (Plate I and Plate II., Fig. 14.) — 249 — S^ipi»ing-Biii. 一 A list of portions of a bridge, arranged in a manner to facilitate counting checking when the material is received after shipment. Stioe. — Another term for pedestal, q. v. Shoe Pin Supporting Piece. — Iatermodiate bearing for a shoo pin. (Plate II., Fig. 12.) s，4°° piate. — 1'ho plute on the under side of the shoe, resting on the rollers, bed-plate, or Masonry. (Plate n., Fig. 12.) Side Bracing, 一 A. bracing for pony trusses to attueli the panels of the top chord to the floor eanis Prolonged, in order to fix the panel points of the ^op cliord. (Plate IX” Fig3. 16 and 17.) . s*ngie intersection. — The style of truss in which the diagonals do not cross the posts. It 13 Resented in skeleton on Plate XIII. Sk«leton Drawing. — A drawing which shows only the centre lines of members, such as a agram of stresses. (Plate XIII.) of BrWge •一 A bridge in which the horizontal lines joining corresponding panel points e opposite trusses are oblique to the planes of the trusses. Sleoa t ov siu»if. — A shelf of bent plate or angle iron rivetted to a floor beam for • 私 ア0的 of helping to support a track stringer. s . 〜 入 member which resists compression. rea^jj I>UucliiuS* — The launching of rivot holes which have to be afterwards enlarged by — Bracing transverse to the planes of the trusses. Its objects are to resist r*. め Ure ’ and to prevent undue vibration from passing loads. (Plate I.) Te, 文 e: of Data* — A list of the known circumstances that affect the designing of a structure. ^ 人 screw for cutting a thread in a nut. r T il0il* "— A. piece of rolled iron of the section shown on Plate II., Fig. 4. °w * — & stress tending to elongate a body. — 250 — Thermal Stresa. — A stress causyl by variation m temperature. Thread. — The spiral part of a screw or nu+. T：aroi«gU Bridge. —— A bridge with overliead bracing. Tie. — A tension member ； generally refers to a main truss. A sleeper. Timber Truclc, — A small, strong wooden frame» with an iron roller set entirely below the upper surface. It is used in l)ridge erection for moving large timbers and heavy weights along" runway. (Plate XII., Fig. 7.) Tonga. — Part of a riveting outfit； used for holding and carrying heated rivets. (Plate XU Fig. 18.) Truck； Stringer. — See stringer. Track Tie. — A sleeper. Transverse Ctm&poiieiit. — A component in a transverse direction ； generally intended a component perpendicular to the planes of the trusses. Truss. — An assemblage of tension and compression members so arranged as to transit loads from intermediate points to the ends. Trussing« 一 A poor substitute for lacing or latticing. (Plate II., Fi^. 13.) Turn Buckle, — Similar to a sleeve nut, and for the same purpose. The sides are opeI1» s° that a crowbar may be inserted for tlie purpose of screwing up. Turn buckles are used for larger bars or rods thn.n are sleeve nuts. (Plato II., Fig. 5.) Ultimate streiigtu. 一 The greatest load that a, portion of material can bear. Uniform lioad. — A 10.1 cl so distributed over an entire structure, tliat equal lengths where receive equal portions. ir-init. 一 A piece of iron, in the shape of the letter it, througli which passes the threaded e11'^ of a rod, and which affords a bearing for the nut, with room to screw up tKe latter. Its use not permissible in first-class bridge construction. Upper liaise work. — The falsework that lies above the level erf tlie lower chords. Upset 1211 cl. 一 An end of a rod or bar enlixr^od far tlie cutting thereon af a screw-thread* Verbatim, — Word for word. Vibration Rod. •一 A tension member for vertical or portal sway bracing. (Plate I.) Washer. 一 A piece of cast or wrought iron to distribute the pressure of a bolt-head or ntr 七 over timber. (Plate II., Fig. 7.) Web. — The portion of a truss or beam between tlie flanges. Its office is. principally 切 resist shear. (Plate II., Fig. 15.) Welded Headit. — Heads first worked into ^lapc, then welded on the bars. Wlilpjil© Truss. 一 See Linville truss. Wind sitakea. — Cracks in timber caused by the wind while the, tree was living-. Woikiug-Ora wing*. — Drawings containing all the measurements necessary for ㈨形 一 truction. Working-Stresa. — The stress, usually the greatest stress, to which a. piece of material 运 ゴ sliould bö subjected. Sometimes incorrectly 6131 ployed, for intöusity of working-stress* Wrench. — A tool for screwing up nuts. . (Plate XII., Fig. 15.) Yen. — A Japanese paper dollar of fluctuating value INDEX.* Add|VSSeS °f bl.Wge し11 iWers, 10. 1 esses of mauufacturors of shape iron, 13, ;4» 16, j7, ，8, ゆ <2。， '22, 2$, 29, 35, 34, 55_ °w.tnco for waste, 176, 209. ご 咖 an bridges. 2. A^eriCan floor system, 59. 人11 a ysis of stresses in trusses, 86. a ytical table of stresses in trusses, 87. ^^orage, 54, 66. ^C^0r plates or pieces, 54, 175, 208. ，ge ll，onsi 18, 19, 2J, 24, 25, 31, 33, 34, 36. ^P^oximate method of designing single track . nages, 205. opposed to wind pressure, 64, 84. 油 gement of working drawings, 184. ^air. biGSt pr°1X)rtions for^ Sb x3i. 也 , raCes, Kdting slope for, 66. race Plates, min. dimensions of, 71. 妇 at: :)mces, P^l^tioning of, 120, 159. CeSGCtions ，认 69 Beain fanSer Plat 的,56,7 い42,24 a angers, 56. 77, 2o8. Table VII. S—n，227. 8 - 54. 7i, !3o, ,04. s r75, 206. of,, . 0 °^ect of wind on portal and lateral ^Ud* 6?， *°9, bra， e®ect ot. wind on posts and batter BeMineS， l7, 107 f I09- st，lesses, intensities of, 71, 109. Place to buy bridges, 9. BeveIs!? 90 tl0nS f°r WS， Sh I?jU SS: 卜91 し。. Mw of iumber — 0 refereuces Bill of rivets, 176. Bills, erecting, 229. Bills, order, 209, 210. Bills, shipping, 215. Bolts, 193, 230. Bottom chords, 52, 68, 69, 89, 95, 115, 117, 119, ⑴， 157- Bottom chords, effect of brakes on, -236, Bottom chord struts, 52, 116, 158, 189. Braces, side, 6, 5 3, 66. Braces, batter, 52, 66, 69, 71, 120, 159. Brackets, 56, 77, 109, 143, 208. Bracing for falsework, 22^, 229. Bracing frames for track stringers and plato girders, 51, 75, 123, 208. Brakes, effect of on bottom chords, 236. Bridge builders, addresses of, 10, Bridge designing a specialty, 2, 3, 7. Bridge inspection, 234. Bridges, cost of, 153. Bridges, stylos of, 5 1, 66. Built floor bey ms, 56, 74, 124. Table XII. Uuilt track stringers, 57, 74, 12?. Tabic XI. Butterlee Co., 14. Buying bridges, 9. Cainbre, 67, 185. Cambre blocks, 228, 230. Car loads, 63, 81. Carnegie Bros, & Co. , 9, 35. Carpenter's tools, 224. Cast iron, 77. Causes of stresses in trusses, 86. Centrifugal force of trains, 86, 8g, 102. Channel bottom chords, 52, 1 16, 1 58, 189. Channel connecting plates, sizes of, 204. Channels, properties of. Table XVI. Channel sections and weights, 15, 16, 17, 19, 20, 成 30, 33, 54, 35* Table XVI. are here made to the Glossary or List of Member. — 252 — Checking, methods of> 151, 189, 190, 19 只， Check nuts, 57, 71. Chord bars, 52, 53, 115, 119, 【31. Chord heads, 187. Chord jiacking, 76, 119, ‘133, 135, 138, 159, 1^9. Chord plates, 7 し 12 o, 158. Chord proportioning, J15, 116, 120, 121, 157, 158* Chord sections, 52, 69. Clear headway, 66. Clear roadway, 65. Cock er ill, Socictc*, 25. Columns, formulae for, 70. Coinpari 8011 between American and English bridges, 2, 4, 5, 8. Complete design for a bridge, 155. Compressive stresses, 70. Tables VIIT & IX. Connecting plates, 54, 72, 73, 140, 168, 169, 1 7c, 204. Connecting plates for cliannols, sizes of, 204. Connection for lateral systems, 55. Construction of chord heads, 187. Continuous floor system, 52, 57. Continuous spans, 67. Cost, estimates of, 151. Cost of blacksmithing, 1:2. Cost of bridges, 153. Cost of erection, 152. Cost of falsework, j 5 r, 153, Cost of framing, 151. Cost of hauling, 151. Cost of iron, 9, 151. Cost of lumber, 152. Cost of painting, 152. Coit of pile driving, 154. Counters, 53, 93, u6. Countersunk rivets, 114, 190. Coyer plates, 53, 73, 14c, 172, 205. Criticism of present Japanese bridges, 5. Curvature stresses in lateral systems, 65, 105. Curvature stresses in portal bracing, 108. Curvature stresses in trusses, 86, 88, 89, 102. Curvature stresses in vertical sway bracing, 108 • Cutting off flanges of channels, 53, 77, 141. Dapping, 60. Data, table or list of, 91， J53, J55. Day’s work for men and animals, 151. Dead load, 64, 82, 83. Table I. Dead load stresses, 93. Deck bridges, 8, $7, 57. 89, 94.- Decimals of an inch fur each 在を1 .l 1 96. De Lccuw and Phillipsen, 29. Depths of beams, economic, 122, 124 Depths of trusses, economic, >45. Table I. Derailment, 7, 60. Design for a bridge, 155. Design for a track stringer, 126. Details, proportioning of, 1 39, 167, 203. Diagonal bracing for plate girder spans, 5 7^* Diagonals, lengths of, 1 86. Biiigrams of stresses, 92, 156, 160, 161. Plates XCII — XLII. Diameters of rivets, 72, 74, 113. Different kinds of floor system, 56, 57. Different styles of bridges troatea, 51. Dimensions, marking of, 189, 197, 200. Direct wind pressure stresses , 86, 100. Disposition of material in flanges and chords, S3- Ditching apparatus, 6 r. Doable intersection bridges, 5 2, 66, 91, 96, 147* Plate I. Double nut connection for lateral struts, 55* Double track bridges, 144, •24-2. Double track bridges, weights of, 83, 242. Draughtsman’s equipment, 182. Draughtsmen, hints to, 189. Drawings, working, 18-2. Dunk eric ley & Co., 16. Earl of Dudley’s Round Oak Ironworks, 21» Economic depths, 122, 124, 145. Table I* Economy, 145* Economy of Pratt and Whipple trusses, 8， Effect of brakes on bottom chords, 236. Effect of wind pressure on members, 64, 67, 69, 84, 86, 88. Elongation of -pin holes in bottom chord struts’ 116. End lower lateral struts^ 69, 105, 161. Engines, Japanese, 8r. Engine, standard, 63.81. Equipment, draughtsman’s, 182. Equipment for raising gang, 223. Equivalent lengths for heads, nuts &c. , 149* Equivalent uniformly distributed loads, 63, 名2. Erecting bills, 229. Erecting bridges, method of, 221, 23c. Erecting gang, 221. Erection, 22 r. Estimates of cost, 151. Excess, engine, 82, 86, 98. Expansion, 55, 66. — - 253 — ®xPansion joint, 55. Mansion rollers, 55, 66, 76, i?r, 208. pension plates, 54, 73, 141, i74, 2〇5. ^-bar heads, 75, !87. 軋 yes， 75. falsework, 224. Rework pillars, sizes of. Table XXIV. ‘•“呢出叩， 5, 77, 114, 147. Plates, S5> 74. p：Ue^ 76, I75. ^al order bill, 21I. 卜3, 57, 74, 75, 【“• :l ラ ges, function of, 74, m *l % sections of, ig, 19, 22, 40. ^weights of, 37. り beam connection to stringers, 57, 75, 125. 卜 W:4. earns in deck bridges， 57. J1 beams in double track bridges, 124. j,)001" beams details for, 74> 於 こ w beams limiting depths for, 75. j,, Jrsystem, i2Ij PoT Ttem proper, 59" j, tplanks. 59- 卿 m 叫 ねい 巧. ^«laf01.C0lurnn3> 7a f°1' flanSea of floor beams, 1 24. IV 〜 ラ ‘“01’ 忍⑽ぱ辟 of stringers or , 122. ，叫. ^lln ,?U °f rivette(1 plates, rij. 0ns of webs and flanges, 74, 122. I Beams, 16, 17, 19, 22, 25, 26, *29, 53, 34, 35. Imperfections of lattice girders, 7. Inclinations of lattice and lacing bars, 7 2. Inclined end posts for deck bridges, 52. Inclined stiffening angles for plate girders, 51. Increment of panel length in top chord?, 186. Indirect transference of stress by rivets, 114. Indirect wina pressure stresses, 86, ico, lor, 107. Induced stresses, 77. Initial tension, 68, 107, 10 8, 111, 115. Table VI. Inspection of bridgos, 234. Inspector’s dimensions, 200. Intensity of bearing stress, 71, 129. Intensity of bending stress, 71, 109. Intensity of compressive stress, 70. Intensity of tensile stress, 70, 71. Intermediate strut connection, 56, 141., 172. Intermediate struts, 5*2, 107. Iron, bills of, 149, 177. 11.0 n, cast, 77. Iron, cost of, 9, 15-2. Iron joists, 16, 17, 19, 22, 25, 26, <29, 33, 34, 35. Iron weights of, 83, 241. Table I. Japanese bridges, criticism of present, 5. Japanese bridges, weights of present, 7. Japanese engines, 8r. Jaws, 55, 56, 77, i + r, 173, l74, 205, ^°6- Joints in bottom chord struts, 54, 169, 204. Joint., sliding expansion, 55. Joints, top chord, 53, 140， 168, 204. Joists, 16, J 7, 19, 22, 25, 26, 29, 33, 34, 55, 227> > Of track, 9. ^aldescril)tion5i_ QiriT jPe°|ficaUons> 6>' 二. Wg diagonals, 55< I20. d?Üedl.iVer ，叫 甘: 4:r 〜 5,办 C?toUllllUtS，taWe0f* '95' l89. Hip n ，on* 53, 140. 168, ao+. Hip vertiTaT^11011 10 lateral rod, 5… 55, 70, 7i,3„89, 9〇, ,, 228. Knees or Knee braces, 56, 77, 109, 143, *208. Labour in erecting, 2-21. Labour in framing, 151. Lacing bars, 72, 142, 175. Table XXI. Lateral pins, sizes of, 206, 207. Lateral rod connection, 56, 141. Lateral rods, 53, 56, 69, 116, [60, 161. Table XIII. Lateral strut connection, 55, 69, 173, *205. Lateral strut も 51, 69， 16 0, 161. Table XIH. Lateral systems, 52, 69, 104, 1 16, 160, 16 し Table XIII. Lattice bara, 72, 142, 175. Lattice girders, imperfections of, 7. Least diameters for pins, 76, 130, 206, *207* Lengths, limiting, 45. 65, 66. Lengths of diagonals, 180. 一 254 — Lengths of lattice and lacing bars. Table XIX. Lengths of span, 65. Limitations, nmuufacturing, 78. Limiting depths of floor beams, 75. Limiting depths of girders, 75. Limiting depths of pony trusses, 66. Limiting lengths of iron, 45. Limiting lengths of span. 65, 66. Limiting sizes of sections, 66. Limiting slope ot’ batter braces, 66. Limiting thickne3s of webs, 66. Limiting widths of plates, 7 1, 75. ljiinit of clear headway, 66. List of data, 91, 153, 155. ijist of members, 46. Live loads, 6$, 81, 82. Loads, dead, 64, 82, 83. Table I. Loads for wooden beams, 227. Loads, live, 65, 81, 82. Loads on floor beams, 64, 124, 125. Lock nuts, 57, 7 し Locomotives, Japanese, 8r. Loop eyes, 75. Lower end of post reinforcing, 54, 141, 172, -204. Tjumber, bill of, 182. Lumber, list of members, 50. Main member«, 46, 51, 115, 155, 203. Maintenance of bridges, 233. Manufacturers of iron, addresses of, 13, 14, 16, 17, 18, 19, 20, 22, 25, 29, 33, 34, 35, Manufacturing limitations, 78. Marking iron, system of, 218. Marking of dimensions, 189, 197, 200. Material in struts, distribution of, 53, Materials, bills of, 149, 176, 177, 182. Materials, tests of, 79. Measurements, method of recording, 189, 197, aoo. Measures, Bros & Co リリ. Members, list of, 46. Method of erecting a bridge, 221, 230. Method of finding lengths of diagonals, 186. Method of record iu^ measurements, 189, 197, •200. Methods of checking, 15 1, 189, 190, 198. Middle of post connection, 55, 205. Minimum dimensions of chord ami b. br. plates, 71- Name plates, 【75. New Jersey Steel and Iron Co., 33. Nomenclature for loads on trusses, 90. Notches in rollers, 55. Number of men for bridge erention, 121. Nuts, 55, 76, 193, 194. 195. Oak lumber, weight of. 64. Order bill, final, 21 t. Order bill, preliminary, 209. Ornamental work, 57, 175. Ottowell’s notes on workshop drawings, 196. Outfit for drau glitsman, 18-2. Outfit for erecting gang, 223. Overturniug of car^, resistance to, 83. Packing, chord, 76, 119, 133, 135, 138, 159, Painting, 78, 235, 234. Panel length, economic, 146. Panel length of top chord, exact, 186. Passaic Rolling1 Mill Co., 34. Patent Shaft and Axletreo Co. , 19. Percentages or increase for shock, 64. Philip Williams & Sons, 18. Pile driver, 224. Pilot nuts, 78. Pine lumber, 64. Pin bearing, 54, 71, 130, 204. Pin holes, 75, 78. Pin holes in bottom chord struts, eloncf^00 of, 116. Pia pilots, 78. Pins, proportioning of, 129, 164, ao6. Table XIV. Pins, steel, 129, 132, 206. Table • Pins, working bending moments Ac. for, XIV. Plant, 223. Plate girderä, 51, 74, 75, 111. Plate girders, bracing for, 51, 75, 123, 208. Pony trusses, 6, 5 1, 66. Portal pins, sizes of, 207. Portal strut connection, 56, 14 2, 174, 206. Portal 8ti*uts, 52, 69, 16 2. Posts, 5a, 67, 69, 120, 159, 164. Post sections, 5-2, 69, 120, 159. Practical method of pin proportioning, 134* Pratt truss, 8, 52. Preliminary order bill, 209. Proportion for bars, best, 53, 131. Proportioning of batter braces, 120, 158. Proportioning of beam hanger plates, I42, Proportioning of beam hangers, 126. — 255 二 ^l，oportioning of bottom chords, 115,121,157, J58. ^oportioning Qf bottom chord struts, 121, 15?. roporticming of brackets, 143, 208. ^portioning of chord bars, 115, 157. ^portioning of count,ers, 115, 157. ^portioning of details, 139. loportioning of expansion rollers, 171. /oportioning of falsework, 225. r°portioniug of floor beam connection to stringers, 125. ^portioning of floor beams, 124. ^oportioning of floor system, 122. ^portioning of hip connection, 140, 168, 204. roportiouing of intermediate strut connection, !4し 172, 2〇5, ^oportioninn, 0f intermediate struts, 121, J63. ^portioning of knee braces or knees, 143, ぐ！ ^rtionin ぱ of lateral rods, 116, 163. ^portioning of lateral strut connection, 141, ベ0!) ortioning of lateral struts, 120, 163. ^oportionmsts, 141, 172, メ 04. • ^roportionjng i0W0r ]a(erai struts, 120, 163. ^^oportioning of main truss members, 115, 155. t» P0rt^>ning of middle of post connection, 205 . oport:oning of pins' [巧， 心， 心. Pro^°r^!°n^n^ Plate girders, i22_ P°rtioning of portal strut connection, 14a, p 】74, 206. P«^°l^0nin^ portal struts, 120, 163. ^ Portioning of posts# I20f ,59, ^ °Portioning of rolled beams, 122. POl，Uon|n? of rollers, i7r, ao8. ?ro!!nl!-0rilUg °f shoes, MO, 丨 70, 204. Pro °n!n°0f side facing, 205. 0f stringer connection to floor Pro ?* I25* Pro^°mng Gf_y bracing， 116, 163. 2〇斗 lonin^ of top chord connection, 140, 168, ho ミコぐ01111^0 f ㈣ chords, 加, 158. Prop0rt!°n!Ug of track stringers, 126. 10ninS of upper end of post connection, . j- . ^on^nf? of upper lateral strut connec. _ IXW 二;:“0 upPer lateral struts, 120, 10nin? vibration rods, 116, 163. Quadrangular truss, 8, 52. Quality of workmanship, 78. Eailsj 60, 83, 182. Raising gang, 221. Katio of width to depth of bars, 53, 13 r. Recapitulation, 103, ^39. Recording of measurements, 189, 197, 200. Reduction of ends of pins, 56, 134. Regularity of rivet spacing, 74, 128, 147, 190. Reinforcing plates, 54, 73, 1 39, 168, 170, 204, 205. Ec-railing apparatus, 60, 77. Resistance of cars to overturning, 83. Rivet heads, 49, 78. Table XIX. Rivets, bill of, 215,218. Rivets, countersunk, 114, 190. Rivets, diameters of, 72, 74, 113. Rivets in flaugeä of beams, 74, 127. Rivets, bending moiAents <&c. for. Table XVIII. Rivet spacing, 74, 128, 147, 190. Rivetting, field, 5, 77, 114, 147. Ri vetting, rules for, 73, 113. Roadway, clear, 65. Rods, equivalent lengths for upset ends Ac. , 149. Roller plates, 54, 73, 141» 174, 206. Rollers, 55, 66, 76, 171, 208. Round Oak Iron Works, 22. Rounds, sections of, 18, 19, 22, 44. Rounds, weights of, 44. Rules for ri vetting, 73, 113. Scales, 182. Screw threads, 71, 193. Sections, limiting sizes of, 66. Sections of angle irons, 14, 18, 19, 21, 24,15, 31, 33, 34, $6. Sections of channels, 15, 16, 17, 19, 20,28,30, 33, 34, 35* Table XVI. Sections of flats, 18, 19, 22, 40. Sections of I beams, 16, 17, 19, 2, 2,2 5, 26, 29, 3% 54» 35- Sections of members, 5a, 53, 69. Sections of rounds, 18, 19, 22, 44. Sections of square bars, 18, 19, 22, 44. Sections of tees, 19, 23, 27, 32, 53, 34* 3^* Semi-transparent drawing paper, 199. Shape iron, addresses of manufacturers of, 13» 14, 16, 17, 18, 19, ao, 22, 25,29, H， 54, 35. Shearing stress， こ 74, ill, 122, 129, 132， 153. — 256 — Shelton Bar Iron Co. , 20. Shipping bill, 215. Shims, 56, 57, 59, 60, 77. Shoe connection, 54, 55, 140, 170, 206. Shoe plates, 54, 73, 141, 171, 206. Shock, percentages of increase for, 64. Side bracing, 6, 53, 66. Sizes of connecting plates, 204. Sizes of floor beams. Sizes of liip verticals. Sizes of lacing bars. Sizes of lateral rods. Sizes of lateral struts. Sizes of lattice bars, Sizes of pillars for falsework. Sizes of pins, 206, 207. Sizes of portal rods. Sizes of portal struts, Sizes of rollers, Sizes of sections, limiting, 66. Sizes of stay plates, & XXIII. Sizes of track stringers. Sizes of vibration rods. Skew bridges, 9. Sleeve-nuts, 76. Sliding expansion joint, 55. Sliding of pedestal, 55. Snow plough, 5q. Soci^t^ Cockerill, 25. Spacing, rivet, 74, ia8, 147, 190. Spacing, stiffeners, 74. Specifications, 63. Spikes, 59, 193. Splices in webs and flanges, 57, 75. Splice plates, 54, 72, 140, 168, 169, 170, 204. Square bars, sections of, 18, 19, 22, 44. Square bars, weights of, 44. Square nuts, table of, 1 94. Standard engine, 63, 81. Stay plates, 72, 139, 168, 203. Tables XXII & XXIII. Steel pins, 129, 132, 206. Stiffened bottom chords, 52, 116, 158, 189. Stiffened hip verticals, 71. Stiffening frames, 51, 75, 123, ao8. Stresses in batter braces, 89, 90, 93, 97, 108, 109. Tables III Panel length of, 186. P chords, 52, 55> 6()j I20> ,58> Ti^k> gauge of, 9. Tract StlIngers， 56, 57, 74, ⑴， 126 Tran P8tnngers, bracing for, 51, 75, 123, 文^ erre<^ loads, 100, ioi, 102. sVei*sc bracing for plate girders &c. , ^Si l23, 208. '5leTn0miC dePth 吡 ⑴， "4, 145 な：1 7 f 公51，66 • ：J^:WkieV7；.143' ^ng in of channel flanges, 53. • 208 ^ironMil: 灯 如 厂从 り11 mills, 35. 心 こ11 Y1Vebad stresses, 93, 96. g2 m ^ distributed loads, equivalent, end of post connection, 54, 75, 141, Rework, 22g. r ateral rods, 53, 56,69,116, 160. Upper lateral strut coimectiun, 55*69, 173, 205. Upper lateral struts, 52, 69, 160. Upset rods, 71, 192. Use of glossary, 5 r. Vertical sway bracing, 56, 67, 106, 1 10. Vibration rods, 56, 107, 110, 1 16, 162, 163. Washers, 77. Waste, allowance for, 176, 209. Web, function of, 74, 122. Webs, limiting thickness of, 66. Web stiffening, 74. Web thickness of, 66. TV eights of angle irons, 14, i3, 19, -21, 24, 25, 51, 33, 34, 36. Weights of channel bars, 15, 16, 17, 19, 20, 28, 50, 53, 34, 35. Weights of deck and double track bridges, 83, 242. Weights of flats, 37. Weights of I beams, 16, 17, 19, 22, 25, 26, 29, 35, 34, 35. Weights of iron, total in bridges, 8 3, 241, Table I. Weights of joists, 16, 17, 19, <22, 25, 26, 29， 33, 34* 35. Weights of lumber per lineal foot, 60, 83, 182. Weights of materials, 64, 126. Weights of present Japanese bridges, 7. Weights of rivet heads. Table XIX. Weights of rounds, 44. Weights of square bars, 44. Weights of tees, 19, 23, 27, 32, 33, 34, 36. Whipple trass, 8, 52. Widths of flanges of cLannels, Table XVI. Williams (Philip) & Sons, 18. Wind pressure, amount of, 64, 83, 84. Wind pressure, area opposed to, 64, 84. Wind pressure, effects of, 64, 67, 68, 69, 84, 86, 88. Wind pressure on cars, 83. Wind stresses in lateral systems, 104. Table V . Wind stresses in portal bracing, 106, 109. Wind stresses in trusses, 100, 156. Wind stresses in vertical sway bracing, 106, no, 162. Wooden beams, working loads for, 227. Working bearing stresses, intensities of, yi> 129. — 258 — Working bending stresses, intensities of, 71, 109. Working compressive stresses, intensities of, 70. Working drawings, 182. Working loads for wooden beams, 227. Working shearing* stresses, intensities of, 74, 123, 129, 132. Working tensile stresses, intensities of, 1。， V. Workshop drawings, 182, 196. Wrought iron, weight of, 126. Wrought s^jikos, table of, 193. 明治 十八 年 三月 廿 三日 出版 版權届 同 年 六月 廿七 日出 版 不販賣 11^— P1 i MEMOIRS OF THE Tokio d aigaku (UNIVERSITY OF TOKIO) No. 11. A SYSTEM OF IRON RAILROAD BRIDGES FOR JAPAN BY J. A. L. WADDELL, C.E., B.A.Sc., Ma.E., ' OU 0F CIVIL ENGINEERING IN THK UNIVERSITY OF TOKIO, JAPAN : CONSULTING KNOINKKR FOR tHE FIRM OP RAYMOND AND CAMPBELL, BBIDOE-BDILDRE8 OF COUNCIL BLUFFS, IOWA : MKMBEB OF THE AMERICAN SOCIETY OF CIVIL ENOINKEKK, BKN86ELAER SOCIETY OP ENOINEHR8, ENarNEERS’ CLUB OF PHILADELPHIA, AND WESTERN SOCIETY OF ENQINRERS； ASSOCIATE MEMBER OF THE INSTITUTION OF CIVIL K 闕 INKERS, LONDON : AUTHOR OF THE DE8IGNINO OF ORDINARY I EON HIGHWAY BRIDOK8. (2 alles and Plates) 今 PUBLISHED BY TOKIO DAIGAKU TOKIO： 2545 (jAPANEgE 1885 A. D. MEMOIRS OF THE Tokio ^daigaku (UNIVERSITY OF TOKIO) No. 11. A SYSTEM OF IRON RAILROAD BRIDGES FOR JAPAN J. A. L. WADDELL, C.E., B.A.Sc., Ma.E., R0i，ES8OR OP CIVIL ENGINEERING IN THE UNIYEBSITY OP TOKIO, JAPAN : CONSULTING ENGINEER **OR THE FIRM OF RAYMOND AND CAMPBKLL, BRIDGE-BUILDERS OP COUNCIL BLUFFS, IOWA : MEMBER OF THE AMERICAN SOCIETY OF ClVIIi ENGINEERS, RENSSELAER SOCIETY OF ENGINEERS, ENGINEERS' CLUB OF PHILADELPHIA, AND WESTERN SOCIETY OF ENGINEERS; ASSOCIATE MEMBER OF THE INSTITUTION OF CIVIL ENGINEERS, LONDON： AUTHOR OP THE DESIGNING OP ORDINARY IRON HIGHWAY BRIDGES. . (fables and ^Plates ) PUBLISHED BY TOKIO DAIGAKU TOKIO： 2545 (Japanese Era) 1885 A. D. Printed by 65' a » ft ••• ,,, ### XVI. » ” 70, n » tr ••• ,,, XVII. » » ” 1(y ” > through. XVIII. »> ff >t 80, a > »> •參. »»镰 ••• XIX. ” ” ” 90^ ft > ... ... XX. »> » 100/ ” f ” ••春 ••癱 ••鲁 XXL it n ，》 110 产 ” f ** »•奉 »• ••• XXII. a ，， 120, ” f tt ... ... XXIII. M 1» 130, ” 9 y* XXIV. ft 3> ” 140/ ” f ，， XXV. » » ，i 150, ” > a ••着 •», ... XXVI. >» 9* ” 肅 »> i y> ... ... XXVII. tf ” 9> 170, » i ” ... ••• ... XXVIII. ” ft ” 180, »> t ” Single Int. XXIX. ” 蕭 ” t n Doub. Int. XXX. i» »> ” 190' » > » Single Int. XXXI. » ” ” 游 f i% Doub. Int. XXXII. » »> 200 ” y >» »y XXXIII. f» »» a 210' a > ，， t» XXXIV. ” ” 220, rt t it ft ” XXXV. »> it a 230, »» f ” » >y XXXVI. >» ft 24(V i» i »» » y% XXXVII. » » 250' »f > » f% ” XXXVIII. ” ft ft 260^ ” f ” ，》 >> XXXIX. ff ” ” 270, ” f ” ” 3» XL. »» » 280, » »» » » XLI. »} 9> 290^ f a »y ” XLII. » » » 300, » > » » » 11.826 12.251 1 1.868 12.291 12.706 J 5.197 13.727 12.745 13.235 13.763 14.301 14.924 15.605 14.556 14.958 15.637 16.350 17.169 18.075 16.380 17. 198 18.103 19.081 *20.206 21.470 19.107 20.2 30 21.494 22.904 24.542 26.432 22.926 a 4.562 26.451 28.636 3 1.242 34.368 a 8.654 31.258 34.332 38.188 42.964 49.104 58.202 42.976 49.IJ4 57.290 68.750 85.940 57.299 68.757 85.946 14.589 71.885 43-774 - 114.5 171.888 ⑷ -775 TABLE I. WEIGHTS OF IRON AND DEAD LOADS FOR Plate, 切 .ww .UUVJW '•4M - i90 3-77ÖO , , IO .0901 •09« .0058 1.4183 3.9061 IO .9964 11.826 11.86« 20 .0929 .09 .0117 1.4225 ^.8208 5.9495 20 衫7 12.251 12. 2Q! 3〇 •0958 .〇9(.〇176 1.4267 3.8667 3.9939 3〇 •9969 I *2.7〇6 12.745 4〇 •0987 .og .0235 1.4310 ^■9i36 4.0394 4〇 •9971 B.I97 1い35 5〇 .ioi6 .io*,0295 1.435 ^ 3-96J7 4.0859 5〇 •9974 13.727 13.763 0 〇〇 •1045 • 10.0555 1.4596 56 4.0108 4.1356 86 00 .9976 14.501 I4-356 IO • 1074 .10' .04] 6 1.4459 4.06 1 1 4.1824 10 •9978 H-9M 14.958 20 .1103 •n .0477 1.4483 斗. 11 26 4.2324 20 .9980 15.605 15.637 3〇 • 1132 .11.0538 1.4527 4.1653 4.2837 3〇 16.350 16.380 4〇 .ti6i .11'. 0599 1.4572 4-^193 4-^6?. 4〇 _99«5 17.169 17.192 5〇 .1190 • I 1 .0661 1.4617 4.2747 4.3901 5〇 •99«5 18.075 18.103 7 〇〇 .1219 •12 .0724 1.4663 57 4-5515 4.4454 8T 〇〇 •99^6 19.081 19.107 IO .1 24H • 12 .c.786 1.4709 牛. 097 4.50*22 10 .9988 20.206 20.13 〇 20 .1276 .1^.0850 14755 斗. 4494 4.5604 20 •9989 21.470 21.494 5〇 • 1305 .13 .〇9*3 1.4802 キ .5107 4.6202 3〇 •999〇 a 2.904 22.926 4〇 ' •I334 •13 .0977 1.4849 4.5736 4.6817 4〇 •州 2 24.542 24.562 5〇 .1363 • 13 .1041 1.4897 务 .6 582 4.7448 5〇 •9995 26.432 26.45 1 8 〇〇 .1392 • 106 1.4945 58 4.7046 4.8097 88 〇〇 •9994 a 8.636 28.654 1〇 • 1421 • 14 .1171 1.4993 +•7729 4.8765 IO •9995 31.242 31.258 *20 • 1449 1.5042 斗. 8430 4.9452 20 •9996 34.568 34.3 か- 1〇 •1478 •T4.i303 1 5092 斗 .9152 5.0159 5〇 •9997 38.188 38.202 4〇 • 1507 •*5 .1369 1.5141 4*9894 5.0886 4〇 .9997 42.964 42.976 5〇 .1536 •»5.1436 1.5192 5.0658 5.1636 5〇 •9998 49.104 49.1 M 9 〇〇 • 1564 •15.1504 M ユ 45 59 5.1446 5.2408 89 00 •9998 57.^9° 57.299 •1595 .16 .1571 1.5294 j.27C,2 5.5205 10 •9999 68.75° 68.757 20 .1622 .16.. 1640 i -5 3.45 5.3093 5.40:6 20 •9999 85.94。 85.946 3〇 .1650 .16 .1708 1.5392 5.3955 5.4874 1.0000 HA.58Q 114.5 4〇 .1679 •17 丨 .1778 1.5450 5.4845 5-5749 4〇 1.0000 171.885 171.883 5〇 .1708 • 17.1847 1.5504 5.5764 5.6653 5〇 1.0000 343-774 ?4 3.775 TABLE II. TABLE OF NATURAL SINES, TANGENTS AND SECANTS, Advancing by 10 min. FROM CARNEGIE，S POCKET COMPANION. I)e g. Min. Sine. Tangent. Secant. Deg. Min Sine. Tangent. Secaut. Deg. Min. Sine. Tauge 11t. Secant. J)eg. ilhu Sine. Tau geilt. Secant. Deg. Min. Siue. Tangent. Secant. Deg. Min. Sine. Tangent. Secant. Deg. Min. Sine. Tangent. Secant. Deg. Min. Sine. Tangent. Secant. Dug. Min. Siue. Taugent. Secant. 0 OC .0000 .0000 1 .COCO 10 OO • 1756 .1763 1.0154 30 OO • 5420 •3640 (.0642 30 OO •50CO •5774 J.I547 40 OO .6428 •8391 1.3054 50 OO .7660 r.1918 1-5557 GO 00 .8660 1.7321 2.00CO 70 OO •9397 2.7475 •2.9238 80 00 .9848 5.6713 5.75% IO .0029 •0029 1.00 CO IO “765 •1793 1.0160 IO • 3448 .5673 1 •つ 653 IO .5025 .5812 1.1566 IO .6450 .8441 i ぺ 086 lo .7679 1.1988 1.561 1 10 .8675 »*7437 -2.0I0I IO •9407 2.7725 2.9474 IO .9853 5.7694 5.8554 20 .0058 .0058 1.0000 20 •1794 .1823 1.0165 *20 •3475 .3706 1.0665 20 .5。5。 •5851 1.1586 20 .6472 .8491 1.3118 20 .7698 1.2059 1.5666 20 .8689 1.7556 a. 0204 20 •94*7 2.7980 2.9713 20 .9858 5.8708 5.9554 3〇 .0087 .0087 1 .0000 50 .1822 • 185; 1.0170 30 •3502 •37 仂 1.0676 30 •5075 *589。 1.1606 SO 如 94 .8541 MI51 SO .7716 1.2151 t.57n BO .8704 1.7675 2.0308 SO .9426 2.8239 2.9957 SO .9863 5.9758 6.0589 40 •0116 .01 16 I.OCOI 40 .1851 AÜSi 1.0176 4。 • 3772 1.0688 40 .5 roo .5950 1.1626 40 .6517 .8591 1.5184 40 .77^5 1.2203 1.5777 40 .87 J?) 1.7796 2.041 5 40 .9436 ■2.8502 3.0206 40 .9868 6.0844 6.1661 5〇 •0145 .0145 1.0001 50 ,1880 .1914 1.0x81 So •3557 •38。5 1.0700 SO •5125 •5969 1.1646 SO •6539 .8642 1.3217 SO •7753 1.2276 1.5833 SO メ 732 1.79 け 2.0519 SO •9446 2.8770 3.0458 SO .9872 6.1970 6.2772 1 oo •0175 .0175 1.0002 11 00 .1908 .1944 1.0187 41 CO •3584 •}8$9 1.0711 31 OO .5150 .6009 1.1666 41 OO .6561 別 93 1.3250 51 OO ■7771 叫 49 1.5890 01 OO .8746 1.8040 2.06*27 71 OO •9455 2.904 2 3.0716 81 OO ■9877 6.3138 6.3925 10 .0204 .0204 1.0002 【0 パ 957 »1974 1,0193 IO .3611 .5872 1.072 ^ JO •5 リ 5 .6048 1.1687 IO .6585 •8744 1.3284 IO •7790 1.2423 1.5948 IO .8760 1.8165 2.0736 IO •9465 2.9519 3.0977 IO .9881 6.4348 6.51-21 20 .0253 •叫 3 1.0003 20 • 1965 .2004 1.0199 20 •3638 .3906 1.0736 •20 •5200 .6088 1.1707 20 .6604 •8796 1.3318 *20 .7808 1.2497 1.6005 20 •8774 1.8291 2.0846 ao •9474 2.9600 3.1244 20 .9886 6.5606 6.6363 3〇 •0262 .0262 1,0003 30 • 】994 •州 5 1.0*205 SO • 3665 •5939 1.0748 30 •5叫 .6ia8 1.1728 30 .6626 別 47 1-335^ 30 .7826 1.2577 1.6064 50 .8788 1.8418 2.0957 30 •9483 2.9887 3.1515 SO .9890 6.6912 6.7655 40 •0291 .029! 1.0004 40 .2022 •2065 1.021 I 40 •3692 ♦3973 1.0760 40 •5250 .6168 J.I749 40 .6648 .8899 1.3386 4。 .7844 1.264 / 1.6123 40 .88oa 1.8546 -2.1070 40 •9492 3.0178 3. *79^ 40 .邙94 6.8269 6.8998 5〇 •0520 .0320 1.0005 SO .2051 •ao% 1.0217 SO .3719 .4006 1.0773 SO .5275 .6208 1.1770 50 .6670 .8952 1.3421 50 .7862 1.-2723 1.6183 SO .8816 1.8676 2.1185 50 .9502 3.0475 3.2074 SO •9899 6.9682 7.0396 3 00 .0349 •0349 1.0006 ia OO .ao79 ,2126 1.0223 OO ,3746 .4040 1.0785 33 OO •5299 .6249 1.1792 4« OO .6691 •9〇〇4 1.5456 sa 00 .7880 1.^799 1.6-243 62 00 .88-29 1.8807 2.1 301 72 00 •9511 3.0777 3.2561 83 OO .9905 7.1154 7.1853 10 •OJ78 •0378 1.0007 IO .2108 • 2156 1.02 50 IO • 3773 .4074 1.0798 IO •5524 .6289 1.1813 IO .6713 •9〇57 1.5492 10 .7898 1.2876 1.6503 IO .8843 1.8940 ■2.1418 IO .9520 3.1084 $•2655 IO .9907 7.2687 7-537^ 20 .0407 .0407 1.0008 ao •2136 .2186 1.0236 20 •3800 .4108 1.0811 IQ •5348 •6330 1.1835 20 •6734 .9110 1.3527 20 •7916 J.2954 1.6365 20 •8857 1.9074 ^•1537 20 •9528 3]$97 3.2951 20 .9911 7.4287 7.4957 3〇 .0436 •〇4 37 1.0010 30 •2164 .2217 1.0-243 30 •3827 •4142 r.0824 BO •5373 •6371 1.1857 JO •6756 .916; 1.3563 丨 50 .7934 1.3〇32 1.6427 SO •8870 1.9210 2.1657 30 •95 そ 7 3.1716 3.3255 30 •99『4 7.595 只 7.6613 40 .0465 .0466 1.0011 40 •2193 .2247 1.0-249 40 • 3854 •4176 1.0837 40 •5 398 .6412 1.1879 40 .6777 .9217 1.5600 40 •7951 1.31" 1.6489 40 .8884 1.9347 2.1786 40 .9546 3.204» 5.3565 40 •9918 7.7704 7.8544 5〇 •0494 •0495 1.001 a 50 .mi .2278 1.0-256 SO .3881 .4210 r.0850 SO •54:2 ■6455 1 _ 1 90 1 SO .6799 •9”i 1.3636 50 .7969 1.J190 1.6553 SO .8897 1.9436 2.1902 50 •9555 3.2371 3.3881 SO .992-2 7.9530 8.C156 3 oo •0523 •0524 1.0014 13 00 •2250 •”〇9 1.0263 23 00 • 3907 •4245 r, 0864 33 OO •5446 .6494 1.19-24 43 OO .6820 •93^5 T.3675 53 OO •7986 1.3770 ».6616 03 OO .8910 1.96-26 12027 73 00 •9563 3.1709 3.4 叫 83 OO •99*25 8.1445 8.2055 IO •0552 .0555 1.0015 10 .•2278 •2339 1.0270 IO •3954 .4279 1.0877 IO •5471 •65 36 1.1946 JO .6841 .9380 i.$7H IO .8004 1.3351 1.6681 IO •89^3 1.9768 2.2153 IO •9572 3*305*2 5.450 IO .99^9 8.545。 84047 20 .0581 .0582 1.0017 20 .2206 .2370 1.0277 20 •3961 •4314 1.0891 70 •5495 .6577 1.1969 20 .6862 •9455 13748 ao .8021 1.6746 20 .89^6 I.9912 2.22S2 •20 •9580 3.3402 34867 20 •9932 »•5555 8.6138 3〇 .0610 .0012 r.coi9 50 •W54 .2401 1.0284 SO • 59” •45 48 1.0904 30 •5519 .6619 1.1992 50 .6884 •949〇 1.3786 50 •8059 1.5514 1.6812 30 .8949 2.0057 2.2412 30 .9588 ?-3759 5.5209 SO •9936 8.7769 0537 40 .0640 •0641 i .0021 40 .2452 1.02 Ql 40 •4014 .4583 1.0918 40 •5544 .6661 1.2015 40 .6905 •9545 M824 40 •8056 1.3597 1.6878 40 .8962 2.0204 2.2545 40 •9596 ?-4^4 3-5559 40 .9959 9.0098 9.0652 50 .0669 •0670 1.0022 50 .2391 •2462 1.0299 50 •4041 •4417 1.0932 50 .5568 .6703 1.2039 50 .6926 .9601 1.3863 50 •8073 1.3680 1.6945 SO •8975 2.0353 2.2677 50 .9605 3-4495 3.5915 SO •9942 9'^553 90092 4： 00 .0698 .0699 1.0024 14 00 •MI9 •2493 1.0306 24： OO .4067 •4452 1.0946 34 OO •55W •6745 1.2062 44 OO .6947 .9657 1.3902 54： 00 .8090 r.3764 1.7〇了3 64 OO .8988 ^.〇5〇5 2.2812 74. 00 •96t3 34874 3.6280 84 OO •9945 9.5144 9.5668 10 .0727 .0729 1.00-27 10 •2447 •25 M 1.0314 10 .409 斗 4487 1.0961 IO .5616 ■6787 1.7086 IO .6967 •97 ^ 1.3941 10 .8107 1.3848 1.7081 10 .9001 2.065 $ 2.2949 IO .96-21 3.526 i ^.66^2 IO .9948 9.788-2 9.8391 ao •0756 •0758 1.0029 ao .2476 •2555 1.0321 20 •4120 •45% i-°975 20 •5640 .6830 1.2110 ao .6988 •977〇 1.3980 20 .8124 1-3934 1.715 ^ 20 .90 リ •2.o8c9 2.3088 20 .9628 5,5656 3.7032 20 •9951 10.0780 10.1275 •0785 •0787 1.0031 30 •25。 斗 1.0329 30 •4147 •4557 1.0989 30 •5664 •6875 1.2154 30 .7009 •9827 1 .4020 SO ■8141 1.4019 1.7221 30 .9026 2.0965 2.3228 SO •9636 多 .605 9 30 •9954 10.3854 I0.4B4 40 •0814 .0816 1.0053 40 ♦253*2 •2617 1.0337 40 •4173 •4592 1.1004 40 .5688 .6916 1.2158 40 ■7〇3〇 •9884 i .406 1 40 .8158 1.4106 1.7291 40 .9038 •2.1 123 2.3371 40 •9644 3.6470 3.7817 40 •0957 10.7119 10.7585 50 .0843 •0846 1.0036 50 .2560 .2648 1.0345 50 .4200 .4628 1.1019 SO •5712 •6959 1.2133 50 •7050 •9942 1.4101 SO .8175 1.4193 1.7362 50 •9051 2.1283 2.35” SO .9652 3.6891 3.8222 50 ,9959 ii.c 594 1 1.1045 5 00 .0872 .0875 1.0058 15 00 ,2^SS .2679 1.035 3 25 00 •4226 •4663 1.1034 35 00 •57$6 .7002 1,-2208 45 00 .7071 1.0000 1.4T42 55 00 .8192 1.4-281 1-7454 65 CO •9063 2.1445 2.3662 75 OO .9659 3.7 川 3.8637 85 00 .9962 11.450 11.474 10 .0901 .0904 1.0041 10 .2616 •2711 1.0361 ro •4699 1.1049 10 •5760 .7046 I •叫； TO .7092 1.0058 1.4183 IO .8208 1.4370 1.7507 10 •9〇75 2.1609 2.381 1 IO •9667 3.7760 5.9061 IO •9964 11.826 11.86« 20 .0929 •0934 1.0043 ao •2644 •2742 1.0369 20 •4279 •4754 1.1064 20 •57” .7089 1.2258 20 .7112 1.0117 1.4225 20 .8225 1 .4460 1.7581 20 .9088 2.1775 2.3961 ao •9674 3.8208 3.9495 •20 •9967 12.251 12.291 jo •0958 .0963 1.0046 3C .2672 .2773 1.0377 30 .4305 4770 1.1079 30 •5807 Jin 1.2283 SO 1.0176 1.4-267 JO .8241 1.4550 1.7655 30 •9100 2.1945 ■2.41 14 30 .9681 3.8667 5.9939 SO .9969 12.706 12.745 40 •0987 .0^92 1.0049 40 .2700 .2805 1.0386 40 •43 51 .4806 1.1095 40 •5831 .7177 1.2 309 40 •7*53 1 •叫 5 1.4310 40 •8258 2.4641 1.7730 40 • 9112 2.211? 2.4269 40 .9689 3.9136 4.0394 40 .9971 リ.197 13.255 50 .1016 .1022 1.005 a 50 .-2728 .2836 1.0394 50 •4358 .4841 1.1110 SO •5854 .7221 1.2335 50 •7173 1.0295 1.4352 SO 細 4 M733 1.7806 SO .9124 2.2286 a.4426 50 .9696 3.9617 4.0859 SO •9974 13.727 15.763 0 00 •1045 • IO5I 1.0055 16 00 .”56 .1867 1.0403 26 00 •4384 •4877 1.1 126 36 OO .5878 •7265 1.2361 46 OO •7*95 1.0355 1.4596 56 00 .8290 i .4826 1.7883 66 OO •9135 2.2460 2.4586 76 00 .9705 4.0108 4.1336 86 OO •9976 14.301 14.356 10 • 1074 .!08o 1.0058 10 •2784 .2899 1.0412 10 •441。 •4913 1.114-2 10 •5901 .7310 1.2387 IO .7214 1.0416 M459 IO .8307 1.4919 1.7960 IO •9 »47 2.2657 2.4748 10 .9710 4.〇6 1 1 4.1824 IO •9978 14.924 14.958 20 .1103 • 1110 1.0061 ao .•2812 .巧” 1 .04-21 •20 .4456 •4950 1.1158 20 •5925 .7355 1.2415 20 •7^34 1.0477 T.4483 •20 .8 ⑴ 1.5013 1.8039 20 •9】59 •2.2817 *2.4912 20 •9717 4.1126 4.2324 ao .9980 15.605 15.637 30 .1132 .1139 1.0065 30 .1840 •2962 1.0429 SO .4462 •4986 1.1174 SO .5948 .7400 い 44。 SO •7254 1.05 38 1.4527 3D .8539 1.5 108 t,8i 18 30 •9!7】 2.199^ 2.5078 SO •9724 4.165; 4.2857 30 •9981 16.35。 16.580 40 .ri6i .II69 i .0068 40 .2868 •な 994 1.0459 40 .4488 .50-27 1.1190 40 •5972 ♦7445 1.2467 40 .7275 1.0599 1.4572 40 々55 1.5204 1.8198 40 .9182 2.3183 2.5247 40 .9730 4.2195 4-^6?. 40 •998; 17.169 17.1# 50 .1190 • II98 1.0072 50 .*2896 .3026 1.0448 SO .4514 •5059 1.1207 SO •5995 •7490 1.2494 50 .7294 1.0661 1.4617 50 .8371 1.5301 1.8279 50 •9194 2.3369 2.S419 SO •9737 4*2747 4.3901 50 •9985 18.075 18.103 7 00 •1219 .122^ 1.0075 IT 00 •2924 •3〇57 1.0457 27 OO •4540 •5095 1.1-2 2^ 37 OO .6c J 8 •7536 1.25*21 4T OO •75M 1.0724 r.4663 57 OO •8387 1.5399 1.8361 or OO •9^05 2.3559 2.5593 77 OO •9744 4*5 315 4.4454 8T 00 .9986 19.081 19.107 IO .1248 .1^57 1.0079 10 •2952 .3089 1.0466 IO .4566 .5132 1.1240 IO •6041 •7581 ぃ 549 IO •7533 i.c7^6 1.4709 10 .8403 L5497 i メ 443 IO M750 2.5770 IO •9750 4.5897 4.5022 10 •9988 20.206 *20.230 20 .1276 .1287 1.0082 20 •2979 • 31*21 1.0476 10 •45外 .5169 1.1257 •20 .6065 .7627 »•2577 20 .7353 1.0850 1.4755 20 .8418 1.5597 1.8527 20 .9228 2.3945 2.5949 20 •9757 4.4494 4.5604 20 •9989 21.470 21.494 BO • 1305 • 1317 F.0086 30 •3007 .3153 1.0485 30 .4617 •5106 1.1274 30 .6088 •7675 1.2605 30 •7171 1.09 »5 1.4802 JO •8454 1.5697 1.861 a SO 州 9 24141 2.6151 30 .9763 4,5107 4.6202 30 •9990 2*2.904 22.926 4° •M54 • 1346 1.0C90 40 .3035 •5^5 1.0495 40 •4045 •5243 1.1291 40 .6111 •7720 1.2633 40 .7592 1.0977 1.4849 40 .8450 1.579^ 1.8699 40 州〇 2.4342 2.6316 40 .9769 4.5736 4.6817 40 •yyw 24.542 24.562 50 .1363 • 1376 1.0094 50 .3062 •3217 1.0505 50 .4669 .5280 1.1308 50 •6134 •7766 1.2661 50 •7412 1.1041 1.4897 SO •84 も 5 1.5900 1.8783 SO .9261 2-4545 ■2.6504 SO .9775 4.6532 4.7448 50 *9993 26.432 •26.45 1 8 00 • 1392 • 1405 1.0098 18 00 • 5090 .シ 249 1.0515 2S 00 .4695 .5317 1.1516 38 OO .6157 .7815 1.7690 4：8 00 .7431 1.1106 1，4945 58 OO •8480 1.6003 1.8871 68 00 •9^72 2.475' •2.6695 78 OO •9781 斗 .7046 4.8097 88 00 •9994 *28.636 28.654 10 • 1421 •1455 [.0102 10 .3118 .^8i 1.0525 IO A720 •5 354 J-I345 IO .6180 .7860 1.2719 JO •7451 1.1171 1.4993 IO .8496 1.6107 1.8959 IO .9283 2.4960 2.6888 IO •9787 4.7729 4.8765 10 •9995 11 ”•258 20 • 1449 • 1465 1.0107 20 •3145 •33H 1.0535 20 •4746 •5392 1.136 j 20 .6202 .7907 1.2748 20 .747〇 1.1237 1.5042 20 .8511 1.6213 1.9048 ■20 •9^93 2.5172 2.7085 20 •9793 4,8430 4.9452 20 •9996 34.568 34.332 30 • 1478 •1495 1.01 11 30 •5*73 •3346 1.0545 30 •4772 • 5430 1.1579 SO .6225 •7954 1.777 S 30 .749〇 1.»3〇3 i 5097 5O .85-26 1.6319 1.9139 30 •93〇4 ■2.5386 2.7285 SO •9799 4.9152 5.0159 30 •9997 38.188 38.202 40 .1507 • 1524 1.01 16 40 .3201 1.0555 40 •4797 •5467 1.1597 40 .6248 .800-2 1.2808 40 .75〇9 1.1369 1.5141 40 •8542 1.6426 1.9230 40 •9315 2.5605 2.7488 40 •9805 4*9^94 5.0886 40 •9997 42.964 42.976 50 • 1536 .1554 1.0120 50 .5228 •3411 j.0566 SO .4823 .5505 1.1415 50 .6271 •8050 1.2837 50 •75“ 1.1436 1.5192 50 .8557 1.6534 1.9323 50 •9325 2.5826 2.7695 50 •9811 5.0658 5,1636 50 •9998 49.104 49.1 J4 9 OO • 1564 • 1584 1.0125 19 OC •叫 6 •3445 1.0576 29 OO .4848 •5543 1.1454 39 00 •6293 .8098 1.2868 49 00 •7547 M504 1.5245 59 OO .8572 1.6643 1.9416 «9 OO .9336 2.6051 2.7904 79 OO .9816 5-*446 5.2408 89 00 .9998 57.290 57-^99 IO .1595 •1614 1.01 29 IO •3 吨 •3476 r.0587 IO 4^74 .558i 1.145-2 10 •6316 .8146 1/2898 IO •7566 1.1571 1,5294 IO •8587 1.675; し95" IO •9346 a.6279 2.8117 IO •9822 5.2252 5.3205 10 •9999 68.750 68.757 ao .1622 • 1644 1.0134 20 •Hu •3508 1.0598 20 •4g99 •5619 1.1471 20 .6338 .8195 1.2929 -20 •75h 1.1640 し 53,45 •20 .86oi 1.6864 1.9606 20 •9356 *2.6511 2.8334 20 .9827 5-3^3 5.40^6 20 .9999 85.940 85.946 30 •1650 • 1673 1.0139 SO •r>^ .3541 1.0608 50 .4924 .5658 1.1490 30 •6361 .8243 1.2960 30 •7604 I.i7c8 1.5 398 SO .86i6 1.6977 1.9703 30 •9367 2.6746 2.8555 SO •9叫 5.3955 5.4874 30 1.0000 114.58 q 114.595 40 • 1679 • 1703 1:0144 40 •3565 .5574 1.0619 40 •4950 .5696 1.1509 40 •6385 .S7()2 1.1991 40 •7623 1.1772 1.5450 40 •8651 1.7090 1.9801 40 •9377 2.6985 2.8779 40 .98 ミ 8 54845 5.5749 40 1.0000 171.885 1 71.888 50 .1708 .1753 \ 1.0149 50 •5395 .3607 1.0631 50 .4975 •5735 1.1528 SO .6406 •細 1.502-2 SO .7642 1.1847 1.5504 50 .8646 1.7205 1.9900 SO .9奶 9.72-2^ u.9006 SO ■9843 5.5764 5.6655 50 1.0000 343.774 H3-775 Member. Top Chord. ” ” 4 Bot. Chord. i Batter Brace. Diagonal. Post (Thro. B.) Post (Deck B.) TABLE III. STBESSES IN SINGLE INTERSECTION TRUSSES. Member. 5 Panel. 6 Panel. 7 Panel. 8 Panel. 9 Panel. Multiply W Wi E W Wi E W Wi E • W Wi E W Wi E by Top Chord. I 3 3 ¥orl 4 4 V 5 5 ¥ 6 6 ¥ 7 7 f ，， ” 2 3 3 ¥or! 4i ¥ 6 6 や 7i n 2,7. 9 9 ，， >» 3 6 6 や 8 8 IO IO ” t> 4 10 IO や jtan. 0 Bot. Chord. I 2 2 2 备 9. 3 3 ¥ 3 音 ¥ 4 4 ¥ ，， >y な 2 2 号 〇岭 パ 3. 3 3 ¥ 3i ¥ 4 4 - ¥ , >， 3 3 3 4 4 Ü 5 5 爷 6 6 ザ 7 7 ” 4 6 6 2,l_ 7i 7i 9 9 i* »» 5 IO IO Batter Brace. 10 T 2 ¥ 3_ ¥ 3 V 等 ¥ ¥ 4 Diagonal. i 6 J fort- 号 ¥ 2 导 f ¥ ¥ 3 ¥ » 2 i O iorf i \ 'S ザ 1 i ¥ 1¢ I 2 )Sec. 0 ハ 3 -I 1 -i f 令 O f ¥ i ¥ I 普 »* 4 f -I f 5. -i f ザ O を ，， 5 t t 6. -I | Post (Thro. B.) i >1 o i°r| fl 普 ダ I 子 ¥ a 号 2 a \ >» ” ^ 署 I' f o f V h i I £. •» »* 3 G. ィ 普 O To the stress on each post must be added Post (Deck B.) i i o for-i .誓 ¥ I ¥ a 1.1 » it 2 i 暑 ¥ o 子 ザ i li. ，， ，， 3 . 铲 1 ¥ o f > SSES. 12 Panel. 13 Panel. Multiply by w, E w w, E 一 12 48 IT 172 IF 172 IT 54 73 'Tan. a. ノ 59 15 59 IT 318 13 218 ~T3 U6 73 55 17 67 U 250 "TF 250 13 76 ir ” 18 71 12* 270 17 270 IF 8*2 IT ?? r 18 71 H 276 73 276 84 IT 276 13 276 ~U 84 13~ p,< 21 IT 78 TT 78 IF 23 IF ” H 21 IT 78 13* 78 IT 23 Is ，， 8 3H IT 114 TT 114 IT 40 *13* ，， 12 48 12 17*2 TF 172 IF 54 ~I3 I ” 15 56 ~12 218 ~fT 218 TT 64 TF ” ” 17 60 Tf 250 TT 250 13* 70 IF 264 IT 264 Ts- 70 13 H 21 IT 78 TT 1 23 13 1 fto/» rr TABLE IV. STRESS IN DOUBLE INTERSECTION TRUSSES. Member. 8 Panel. 9 ranel. 10 Panel. 11 Panel. 12 Panel. 13 Panel. Multiply by w w, E w W 1 E W w, E w w 1 E w w, E w W l E Top chord 1 7 7 27 了 74 ~T 74 ~F 32 *9~ ()1 t；2 *2 37 lö 118 TT 118 ~TT 42 12 12 48 IT 172 1F 172 1F 54 13 Tan. / ,， ，’ 2 8 8 31 "8~ 8R ~Y S8 "IT 3H 11 务 ui 45 7Ö 146 ir 146 ir 5*2 TT 15 15 59 IT 318 lä 218 ~I3 (i6 "18 ，， ，， 3 8 8 SI ~ 92 T 92 了 40 ~9~ 1 马 吗 49 I 162 TT 1C*J TT 58 ir 17 17 67 U 260 ~n 260 13 76 ir ，， ，， 4 92 ~Y 92 ‘10 吗 49 lö 1Ü8 11 168 ir G0 TT 18 18 71 12* 270 1F 270 ly 8-J ir „ „ 5 l(i8 n~ 168 60 "TT 18 18 71 12 276 13* 276 T3 84 "iT ，’ ，， 6 276 13 276 Ts- 84 可 Bot. chord 1 H H n す 36 ~9~ 36 15 IT 4 务 17 lö 65 TT 55 iä TT H 21 TT 78 TiT 78 l3~ 23 IF ■， ，’ 2 H 了 36 ~9~ J»6 ~9" 15 料 H 65 TT 55 rr 19 TT H 21 T2* 78 13* 78 TF 23 13 ，， ，， 5 5 20 "T 52 IT 5J 下 24 T 6 务 •2S lö 80 IT 80 3*J TT 8 8 sn IT 114 l3~ 114 73 — 40 A ，， ，， 了 7 7 24 IT 7-1 74 T 30 9 务 9 を 3U "To 118 11 118 IT 42 ir 12 12 48 12 17-3 TT 172 TF 54 ~13 5 ，， ，， ° 84 ~9 - 84 ~9~ 30 IT 1H 40 uT I4fi ~rr 146 TT 48 TT 15 15 66 12 218 TT 218 IT 64 iT ，， ，， 6 156 TT 156 48 TT 17 17 60 rl - 250 nr 250 If 70 百 ，， ” 7 264 13 - 264 Iä- 70 13 Batter 】))race. 28 了 H 13 ~8~ 36 Y 36 ~ 15 45 1Ö 4 务 17 lö" 55 rr 55 TT 19 TT 66 17 H 21 IT 78 TT 78 1z 23 1s • Sec. a. Diagonal. 1 '~8~ H 10 T 16 了 16 *~ir 12 *9 - ?0 "TcT 2 14 lö 25 25 TT 30 TT n 18 U 36 13 36 ir SO n Diagonal 2 - 1 8 ~8~ 12 it 9 10 了 16 Tö H 12 20 TF J9 14 TT 25 IT 2 16 12 30 百 29 13 18 丨 Sec. ß. / „ 3 6 ~~8~ i 6 丁 9 下 8 丁 12 *10 1 10 hT IG TT 14 TT 12 TT 20 IT ] 2 14 TI 25 TIT 23 13~ 16 百 ，， 4 4 0 4 T 6 丁 2 ■~9" 6 丁 i 8 ÜT TT 8 TT 10 "TT 16 JI 1 12 77 20 U 17 1? ]4 IT | ，， 5 2 ' 2 2 ~8~ 丄 o iT 4 9 6 ~]〇 0 iir 9 H 3 TT 8 12 U i 10 TT lß TT 10 TF 12 T3 ，， 0 2 _ _ 7_ 2 ~9~ 士 ] 1F 6 TT 3 TT 6 TT 9 IT 0 8 12 12 •I iT 10 TT ，， 7 17) -1 士 4 8 4 6 Tä 1 ' 2 •t 17 去 3 ~ 8 *13 ，， 8 4 TT -1 4 "TT 去 10 "TT 6 TT 9 ，， J 4 IT 16 ' 13 Post (Thr‘>. R) 1 6 1 ß 9 ~V 7 9 8_ y~ 12 1 10 ITT 16 n" 14 TT 12 20 IT 14 ?5 IT ?3 TF 16 \ rlo the stress on each : post must be added W\ \ | ，， ，， ム 4 丁 0 4 6 丁 2 9 _ 6 ~ 9 ~ÜT i 8 TcT 12 *TT 8 TT 10 IT 16 1? 1 12 ~iT 20 78 17 TT 14 ，， ，， 3 2 丁 ■h 4 4 9 2 ~9~ 4 丁 6 Tö" 0 0 3 R ~TT 12 1 2 10 IT 16 13 10 n i? TT ，， ，， 4 4 ~nr -i 6 3 - -jy 6 ^TT 0 8 "TF 12 TT 去 10 ir ，， ，， ° 6 12* 6 ir 9 TT 3 ■ IT 8 TT Post (Deck. B) 1 12 * 8 _ i 10 ~ Hi ~r 12 丁 20 ~W 1 14 lö- 25 TT 14 ir 16 TT 30 Tä 18 IT 36 1F 23 IT ：o TT ，， ，， 2 0 ~~S~ 0 8 ~ 12 ~ 2 10 16 ~W 12 可 20 ll" 8 H 25 12 - 1 16 'u 30 TT 17 IT 18 nT ，， ” 3 6 丁 ■i 6 丁 9 ~9" 2 ' 丁 8 12 ~W 0 10 lu 16 "TT 3 ^TT 12 TT 20 *TT 2 14 T2~ 25 IT 10 13 16 TT ，，” ^ 9 IT 8 ~IÖ" 12 __ 3 TT 10 TT . 16 12~ 12 TT 0 12 yr 20 ir 3 TT 14 IT ，， ，， ^ -i 10 IT 16 1F 3 _ 18' 1*2 1F E Y. UEE STRESSES ：*ERAL SYSTEMS Pauel. 10 13 Panel. Multiply w, E 1 WorW 7 WorW 7 w< E 1 Wind 4 15 H 6 6 23 n 、 ； ( tan •ダ. 7 56 ~9~ 8 11 11 42 13 9 33 IT 10i 15 15 57 T3 10 36 丁 12 18 18 68 13 10 36 丁 12i 20 20 75 *13 21 21 78 13 21 21 78 T3 Leew；0 0 〇 0 0 0 4 15 一《 6 6 23 IT 7 26 *9~ 8 11 11 42 13 9 33 m 15 15 C7 13 10 36 12 18 18 68 13 20 20 75 13 21 21 78 13 Later4 15 45 To 78 IT 6 23 IT > sec. 0. ノ 3 13 36 66 "13 5 21 13 2 11 丁 28 To 55 IT 4 19 IT 1 9 丁 21 1Ö 4 & 13 3 17 13 0 7 15 IF 36 13" 2 1« 13 28 13 1 13 IF 21 13- 〇 11 IT Lateril 15 丁 41 1Ö 145 ■26" U3 '2 13 丁 33 lo — 、 123 16 马 21 IF i 11 ~ 26 TÖ 103 ~26" n 19 IF 1 I 9 了 20 lo 85 2 全 17 nr 15 1Ö 69 W n 15 TF 55 26 13 13 TABLE Y. WIND AND CUBVATUBE STRESSES IN CHOBDS AND LATERAL SYSTEMS. Member. o Panel. 6 Panel. 7 Panel. 8 Panel. 9 Panel. 10 Panel. 11 Panel. 12 Panel. 13 Panel. Multiply ty WorW 7 w, E l WorW7 w, E l WorW_ w, E 1 WofW 7 - w, E】 WorW7 _ w,. E l WorW 7 w， E ] WorW 7 w, WorW 7 w, E l WorW_ w】 E 1 Windward Chord. 1 2 2 T ( ，r T 2 全 H 9 ~ 3 3 4 3 务 H 21 4 4 15 T 好 骑 17 kT 5 5 19 5i- 21 TT 6 6 23 TT } tan •ダ. ，， 2 3 3 « 10 T orT 4 4 14 5 5 18 T* 6 6 22 T* 7 7 •?ß ~9~ 8 8 30 "To" 9 9 34 IT 10 10 38 U' 11 11 42 H ’’ 3 3 3 T 44 15 6 6 21 T u 27 T" 9 9 33 丁 10 务 10^ as •kT 12 12 45 lT 131 13 务 61 12 15 15 57 13 ，， 4 6 6 21 8 8 28 10 10 36 丁 12 12 44 W 14 14 ß2 TT 16 16 60 12 18 18 68 T3 ” 5 10 10 36 ~v 12 务 45 1Ö 15 15 55 TT 17务 65 12 20 20 75 TT ，， 6 15 15 55 18 18 66 H 21 21 78 13 ，， 7 • 21 21 78 13 Leeward Chord. 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 o 0 ，， 2 2 2 H H 9 丁 3 3 11 ~ 32 32 13 4 4 15 ~ 马 17 5 5 19 n" 5 金 21 *12 6 6 23 TT ，， 3 3 3 -for^ 4 4 14 ~ß~ 5 5 18 ~ 6 6 22 T 7 7 26 丁 8 8 39 To 9 9 34 IT 10 10 38 IT li 11 42 13 ,， 4 6 6 21 H 27 9 9 33 I0i 39 IF 12 12 45 13| m 51 TI 15 15 67 Is ，， 5 10 10 36 12 12 44 IT 14 14 52 n 16 16 60 IF 18 18 68 n ” 6 15 15 55 TT in in 65 T2 20 20 75 73 ” 7 21 21 78 13 Lateral Rods. 1 10_ 2 T orT 15 H 9 T 21 3 11 了 28 "T H 13 36 ~9" 4 15 下 45 IW 马 17 To 55 TT 5 19 IT 66 12 h 21 IF 78 百 6 23 TT 1 sec. 0. ，’ 2 6 T 1 7 10 下 H 7 了 15 ~ 2 9 T 21 丁 H 11 ~8~ 28 ~9~ 3 13 B6 nr si 15 lö* 45 4 17 *iT 56 W 4} 19 IT 66 13 5 21 *13 ，， 3 3 0 T or f 6 ^6* 2 5 T 10 T~ 1 7 了 15 了 H 9 * T" 21 2 11 丁 28 lö 2 蚤 13 1Ö" 36 If 3 15 TT 45 12 H 17 12 55 13 4 19 IT ” 4 6 ~ 0 5 了 10 ~ i 7 T 】5 1 9 丁 21 lö 11 lö- 28 IT 2 13 IT 36 2k ]5 45 IT o 17 13 ，， 5 10 0 7 15 ~W h 9 IT 21 IT 1 li IT 28 12 13 36 13 2 Iß IF ” 6 15 17 0 9 TT 21 IT 2" 11 ’ 12 28 13 1 13 IF ” 7 21 TT 0 1] IT Lateral Strut. 2 17 W ]2 T or 4 13 2 9 T 37 14 H 11 'T 25 3 13 ~T 65 V 16 丁 41 lö" 4 • 17 lö" . 】01 ~22 分 19 61 IT 5 21 -IT 145 ~2ß • 5J3 IT ” 3 11 1Ö i 4 or4 1 7 1 T 27 TT H 9 了 id 了 2 li T 61 W 13 了 33 lö o o 15 lo 83 "2? 3 务 17 51 ~12 4 19 12 123 16 4 务 21 IT ，， 4 - i 5 19 "14 i 7 ~ 14 "T 1 9 ~ 39 TT 】4 11 9' 26 2 13 lö 67 ■22* n 15 ~rr 42 ir 3 17 IF 103 26 - H 19 IT ，， 5 10 了 h 7 29 ir i 9 ~ 20 lo 1 11 To 63 22 H 13 TT 34 IT 2 15 IT 85 17 Tb ，， 6 15 lö i 9 lö" 41 IT 2 n 27 li- 1 13 ~ 12 69 瓦 n 15 IF ，， 7 n 21 IF 11 IT 55 26 13 1¥ TABLE YI. WORKING TENSILE STRESSES AND INITIAL TENSIONS roa Adjustable Round and Square Bars. Dia. intensity of Working »tress = 4 tons. Intensity of Woikmg stress = 7.5 tons Initial Tensions. Dia. m u & 圈 % 聲** 1.268 J.517 2.815 3.574 0.500 0.635 聲夕 1.451 1.846 3.261 4.157 0.625 0.794 1.650 2.111 3.760 4-789 0.750 〇*955 1.885 2.405 4*3〇5 5.481 0.875 1.111 i 〆 a. 1 40 2.7?〇 4.890 6.2 30 1.000 1.270 j ク irV 2*423 3.087 5.525 7.。; 8 1.125 1.429 ぼ ip a.726 3.476 6.205 7.904 1.250 1.588 3.057 3.894 6.931 8.830 *•375 1.746 】 か i ォ， 3.408 4-347 7.704 9.814 1.500 1-9。5 中 3-787 4.828 8.5 a; 10.856 1.625 2.064 i A" 中 4.190 5:34i 9.387 11.956 1.750 2.22} if" 4*617 5.883 10.298 15.117 1.875 2.381 iä， I レ 5.068 6.460 11.253 J4.335 2.000 2.540 “メ 5.547 7.065 12.256 15.611 2.125 2.699 1 か i 音'， 6.046 7.706 13.304 16.947 2.250 2.858 ip 6.573 8.576 14.399 18.342 2.375 3.016 中 7.120 9.077 15.540 19-794 a. 500 3.175 中 7.695 9.810 16.726 21.305 2.625 3.534 十 8.294 10.571 17.959 22.874 2.750 3.495 中 8.917 11.365 19.257 24.503 2.875 3.651 2 * 9.568 11.190 20.562 26.190 3.000 3.810 2 * ^tV 10.239 13,047 21.933 ^7-935 $•125 3.969 小 10.938 13.936 W.349 29.739 3.250 4.128 中 命 11.657 14.854 24.812 31.603 3.375 4.286 2 か 12.404 15.807 ■26.321 33.524 3.500 4*445 中 命 13.175 16.788 27.875 35.504 3.625 4.604 命 2 ! 夕 13.970 17.801 29.476 37.541 3.750 4.763 小 命 H.793 18.843 31.1a; 39.64。 3.875 4.921 •ク 2 ^ 15.636 19.920 32.815 41.795 4.000 5.080 * TABLE VII. Sizes of Hip Verticals and Beam Hangers For Single Track Bridges. Panel Length. Hip Verticals. Beam Hanger. S. R. Size. Size. 10’ 2.96CT 2 — iJ^Ü I '□ up. i if 3.I8CT 2 — im WO up. it! 3.38er 2— ず 口 口 up. 3.56CT a — ず 口 ira up. 3.70C1" a— ira ず 口 up. 丨 15， 3.86CT 口 1*" 口 up. 16， 4.00 □" 卜ず 口 itk，#D up. 17， 4.14〇" 2-1 *"□ 1為々口 up. 18， 4.26 □" 2—iro 1*" 口 up. 19， 4.4。 □" a—ii" 口 Ii" 口 up. io1 4.58 口" 2— ii，#xa#/ ず 口 up. 2Ir 4.74CT 2— ii"xa" iä-,g up. 22f 4.9° 口" 2 — ii〃x， !*"□ up. 23， 5.〇4〇" 2 —ず x 2 去" iA" 口 up. 24， 5.20 □" 2 — ず 口 up. TABLE VIII. INTENSITIES OF WOEKING COMPRESSIVE STRESS FOR Channel Struts in Trusses. Uati( fjtol) □ □ □ O 00 ll-atl it LoD □ □ □ 〇 00 Rati« LtoD □ □ a 〇 OO Ratio LtoD □ □ 口 e> OO IO 4.205 4.140 3.990 28 3.14-2 2.826 2.477 46 2.241 1-79^ 1419 64 1.569 1.130 0.80 1C* 4-175 4.103 3-947 峋 3.114 2.792 2-44* 464 2.219 1.769 M98 64j 1.553 1.1 16 0.820 I I 4.145 4.066 3.904 29 3.086 2.759 2.404 47 •2.198 . t-746 >•377 65 1，50 1.10 *2 0.809 •I 基 4.114 4.029 3.862 294 名. 05 9 2.725 2.368 47i 2.176 1.723 1.356 65i 1.52; 1.088 0.797 12 4.085 3-99? 5.819 多〇 5-0?i *2.691 2.332 48 2.155 1.701 1.535 66 1.508 1.075 0.786 12* 4.053 5-956 ミ .775 パ 3.005 2.659 a.^97 4H 2.M4 1.679 1.315 664 i-49? 1.062 0.775 り 4.02 3 3-9*9 3,70 Bi 2.976 2.627 2.26a 49 1.1 1 1 1.658 1.296 67 了 .479 i.o 斗 9 0.765 3.995 3.882 5.688 31 士 2.95〇 ^•595 2.227 49i 2.09-2 1.636 1.276 67! 1.464 ，•〇 36 0.754 14 5.962 3.845 3.645 3ユ 2 州 2.56; 2.193 50 2.071 1.615 1.256 68 MS。 1.0-24 0.744 Ji4i 3.9^ 3.807 3.601 Pi 2.897 2.551 •2.160 5。！ •2.05 1 >•594 1.238 68i 】.455 1.01 I 0.754 I 15 5*901 3.770 3.557 S3 2.870 2.KOO 2.127 Si 2.031 M74 r.219 69 1.421 0.999 0.724 3.872 3.7P 3-5H 33! 2.844 •2.469 1.094 5ii 2.011 1.554 1.100 69i し4。7 0.987 0.714 r6 3.8 斗 i 3.695 5-47〇 H 2.818 2.40 2.061 51 r.99I 1-534 1.181 70 1.393 o-975 0.704 16 各 3.81 1 5.657 5.424 54 备 •2.79! •2.4〇^< 1.050 5^i r.971 1.514 1.165 7。 查 1.379 0.963 0.694 17 3.721 3.620 5-382 35 2.766 ^•37« 1.999 53 1.952 1.495 1.148 7i 1.366 0.951 0.685 り圣 5-751 3-583 3.341 55i 2.740 2 ィ 4 只 1.968 53i r-933 1.476 1.130 7i* M5? 0.939 0.676 i8 3.721 3-546 P95 36 2.715 2.318 1-937 54 1.91 斗 J.457 i.i 13 7! 1.340 0.9-28 0.667 iPJ 卜 692 5.508 W2 56i 2.689 2.189 1.908 54i 1.895 1.458 1.097 7^ 1.327 0-9*7 0.658 19 3.662 ?-47i 3.209 M 2.664 2.260 | 1.878 55 1.876 1.420 1.081 73 i.m 0.906 0.649 19* 3.434 ^.166 M\ 1.231 1.849 55i 【•857 1.402 1.064 1.301 0.895 0.640 20 3.602 3-397 3-123 38 2.614 2.20^ 1.870 56 1.839 1.384 1.048 74 1.288 0.885 0.612 20^ 3-573 3-?6o 3.08 つ 例 2.589 2.175 W 561 i.8u 1.366 r •叩 74 各 1.275 0.874 0.624 21 5.545 3-〇?8 39 2.565 2. [47 1.765 57 1.803 M49 1.018 75 1.-26^ 0.864 0.616 5.514 5.286 2.996 391 2.540 2.1 F9 1.758 57i 1.785 1.352 1.003 75i 1.251 0.854 0.608 22 5.485 3.250 2.95 3 40 2.516 2.092 T.710 58 1.768 1.315 0.988 76 1.-238 0.844 0.600 •2H 5.456 3.214 7.912 4°i 2.492 2.065 1.6 只 4 5 Si 1.751 1.298 0.974 761 1.226 0.834 0.592 M26 3.178 -2.871 41 2.469 叫 9 1.658 59 1-734 1.282 0.960 77 1.214 0.824 0.584 3.597 5.142 2.830 2.4 斗 5 2.015 i.6y 59i 1.717 1.266 0.946 77i 1.202 0.814 0.576 叫 H69 5.106 2.790 杉 1，422 1.987 1.607 60 1.700 1.250 °-933 78 1.191 0.805 0.569 3.340 5.070 2.750 4 つ 4 <2.599 1.962 1.583 6ci 1.683 1.235 0.910 78J 1.179 0.795 0.562 25 5.311 叫 5 2.710 43 q75 1.937 1.558 61 1.666 I.-2I9 〇.9〇7 79 1.168 0.786 0.555 25-s 3.282 2.999 2.676 43i 2.552 i.9ia 1.5” 6ii 1.649 1.205 0.894 79i r.i57 0.777 0.54 お 26 3.254 ■2.964 2.630 44 *2 1.887 1.509 62 1.652 1.188 0.881 80 1.146 0.768 0.541 '26* 5.-2 -26 2.9-29 2.591 44 i •2.507 1.865 1.486 62* 1.616 M75 0.868 8ci 1.135 0.759 0.554 27 3.198 2.895 2.553 45 2.185 1.839 1.464 63 1.600 L159 0.856 81 i.i«4 0.750 0.527 •27* 5.170 •2.86o 2.515 45 i 2.263 1.813 1.442 63* 1.584 1.145 0.844 81^ 1.114 0.74 r 0.502 — •- * ' * TABLE IX. 111 tensities of Working Compressive Stress for Channel Struts in Lateral Systems, Portal Bracing and Vertical Sway Bracing. し‘ oD □ □ □ 0 OO Katin LtoD □ □ n O OO l.iatio LtoD □ □ □ 0 OO Ratio LtoD □ □ □G OO IO 5.677 5.588 5.386 28 4.3【3 5.880 3.401 46 •2.49O 1.972 64 •2.200 1.585 1.166 IO-J 5.6+c 5-54-2 530 4.”6 沐 5 3.352 46i 5.084 2.458 1.9 4; 64 表 2.179 1.566 1.15c II 5.601 5.496 5.177 29 4.240 3.790 5.302 47 5.C55 2.427 1.913 65 2.158 1.547丨 1.1^4 ii! 5-565 5.448 5.1*22 29! 4.194 3.746 3.254 47-i 5.0261 2397 1.885 65 喜 2.1 58 1.5281 1.1 1 c 12 5.525 5.402 5.167 30 4.167 3-701 5.206 48 2.998 *2.366 1.856 66 2.117 1.5091 1.103 I 2 各 5.486 5.354 5.111 50! 4.1p 3.658 3.159 4“ 2.9691 2.357 1.829 66^ 2.096 1.4911 1.089 13 5.448 5.307 5.055 パ 4.096 卜 6i4 S.in 49 2.941 2.307 1.801 67 2.076 *-473| 1.C7J 13« 5.41c 5.260 4.999 4.06c 5.571 3.065 49* 2-9*3 *2.278 1.775 67* a.056 1.4551 し 〇5(, »4 5.372 5.212 4.945 3^ 4.025 3.529 3.019 50 2.8851 2.150 1.748 68 2.036 1.458 1.045 '4 a 5.553 5-^4 4.885 Y*-\ 3.990 3.486 5c| 2.858 mi 1.725 68* 2.017 1.42 1「 1.051 15 5.295 5.116 4.828 33 5.955 5-444 5* 2.830 2.195 1.697 69 1.997 1.403 「 1.017 1 5 或 5.15: 5.068 4-77» 33i 5.92c ?-4°3 2.886 51! 2.803 2.166 1.67-2 69 為 1.978 1.3871 1.003 i6 5.218 5.019 4-7 1 3 34 3.885 5.561 2.84 2 52 2.776 2.10 1.647 7〇 1.959 1.570 •W i6\ 5.180 4.971 4.656 341 5.851 5.521 2.80( 5^ 2.750 2.II-2 r.6” 7。 蚤 1.94c 1.5541 •97; 17 5.HI 4.922 4.599 35 ?.8i6 3.180 2.757 53 2.723 2.085 1.599 V 1.9-22 1.5381 •964 »7¢ 5.10; 4.874 4.5 0 多 .782 3.240 2.716 53i 2.697 2.059 1.576 74 1.905 r$ — •95' 18 5.065 4.826 4.485 36 5.748 3.200 2.675 54 2.671 2.035 1.553 72 1.885 1.506 .958 5.027 4-777 4 .斗 28 辦 $•715 3.161 2.635 54! 2.646 2.008 i-5 3 1 7^ 1.867 1.2911 .926 19 4.988 4.7-29 4-371 37 3.681 5.122 2.594 55 2.620 1.983 1.50^ 11 1.849 1.2761 •914 19! 4.95。 4.68c 4.314 5.648 3.084 2.555 554 2.590 1.95 お 1.487 75i 1.832 1.261 .90: 20 4.912 4.6 p 4.258 38 3.614 5*〇45 2.516 56 2.57。 I-9S3 1.465 74 1.814 1.246 .89c lOj 4.874 4.584 4.202 柯 3.581 5.008 2.479 56 或 2.545 i.9ic 1.444 74i 1.797 1.2311 .879 21 4.8561 4-535 4.145 39 3.549 2.970 2.441 57 2.5-21 1.886 1 .叫 75 r.779 1.217 •867 21士 4.798 4.487 4.09c 卜 516 2.933 2.404 57 士 2.497 1.862 1.403 75i 1.763 I •叫 | .856 72 4.760 4.459 4-〇54 40 3.484 2.897 2.367 58 2.472 1.839 1.382 76 1.746 1“89丨 •845 22 毛 4.722 4-39^ 5-97? 4c| 5-452 2.861 2.332 sH 2.449 1.816 1.363 7H 1.729 M75| .834 4.684 4-344 5.924 41 3.410 2.8-25 2.296 59 2.425 f.794 1.343 77 1.715 1.161 .8-23 4.647 4.297 3.87c 4 卜 J 3.588 2.79。 2i76l 59 委 2.40 *2 1.772 1.324 ll\ 1.696 1.1481 .815 H 4.609 4.149 3.816 斗 2 5.357 2.755 2.127 6〇 2.378 1.75。 1.505 78 1.680 .803 4-571 4.202 3.763 44 3.526 2.72c 2.194 6c* 2.355 r .㈣ 1.287 7H 1.664 1.122 •793 4.534 4.155 3.71。 43 P95 2.686 2.160 61 2.50 1.707 1.269 79 1.648 1.1091 •783 叫 4-497 4.109 3.657 43i 5.264 2.652 2.128 -2.310 1.686 1.251 79i 1.633 1.096 •773 26 4.460 4.062 5.605 4 斗 2.619 2.095 62 2.788 1.665 r.235 80 1.617 1.0841 .765 26* 4.4W 4.016 3.553 44i 3.203 *2.586 a. 06 4 62^ 2.266 1.645 1.216 8oi 1.602 1.0711 •754 27 4.586 5.97。 3.502 45 2.55; 2.03? 63 2.244 1.624 1.199 81 1.587 1.0591 .744 咐 4349 3-9^5 3.45】 45i 3.143 2.522 2.002 2.222 1.605 1.183 81* 1.572 1.0471 •735 APPEOX： INI Length of Strut in feet. 7"— 20* □ □ □〇 〇〇 Side- ways. Ec wa i 26.7 T 2 1-5 i 26.4 2 丨 4 3 2 25.0 2 6 4.5 3 23.0 1 8 6 4 20.5 2 IO 7^ 5 18.-2 2 12 9 6 15.7 2 14 10.5 7 13.7 2 l6 1*2 8 12.0 2 l8 13.5 9 10.5 2 20 15 10 9.0 Q 22 16.5 11 8.0 5 24 i8 12 7.0 ク 26 19-5 り 6.2 つ 28 21 14 5.5 BO 22.5 り 5.0 C 32 24 i6 4.5 J 34 25.5 17 4.0 36 27 18 3.5 38 28.5 19 B.d 40 30. 10 1 3.0 TABLE X. APPROXIMATE WORKING LOADS FOE I BEAMS USED AS STRUTS IN LATERAL SYSTEMS OR VERTICAL SWAY BRACING. Length of Strut in feet. 7"— 20» I ; 7" — IS， I 6" — IG* I 6"— 13.5* I 5" — 12* I 5" 一 10* I 4" 一. 10» I 4"— 8 3 I Length uf Strut in feet. □ □ □〇 〇〇 Side- ways. Edge- ways. {Side- ways. Edge- ways. Side- ways. Edge- ways. Side- ways. Edge- ways. Side- ways . Edge- ways. Side- ways. Edge- ways. Side- ways. Edge- ways. Side- ways. Edge-1 ways. □ □ 口〇 〇〇 i 26.7 •27.0 1 24.2 24.5 21.5 ar.7 18.2 18.2 ^6.0 16.0 1 3.8 13.8 13.5 13.5 10.8 10.8 I 2 i-5 i 26.4 26.9 24.0 H-4 21.2 21.6 17.7 18.1 15.5 15.9 J 3.0 13.0 12.7 10.2 10.6 2 1.5 1 4 3 2 25.0 26.7 21.7 24.3 ao.o ル 5 16.5 18.0 *3.7 15.7 11.1 12.8 11.2 13.0 9.0 10.4 4 3 2 6 ヰ. 5 3 23.0 26. s 21.0 24.2 18.0 2i.a 15.0 17.9 11.7 15-5 9.7 12.6 9.2 12.7 7.4 10.2 6 4-5 5 8 6 4 20.5 26.2 18.7 24.0 15.8 a 1.0 ip J7.7 9.7 15.2 8.1 12.4 7.4 ia.5 5-9 10.0 8 6 4 IO 7^ 5 18.2 26.0 16.5 23.7 1弘7 20.7 11.5 17.5 8.0 14.9 6.7 12.2 6.0 12.2 4.8 9.8 10 7.5 $ \i 9 6 15.7 25.7 14.5 •23.5 11.7 cio.a 10.4 17.1 6.5 14.5 5.4 12.0 5.0 1 1.6 4.0 9.3 ii 9 6 i 斗 10.5 7 i?-7 25.2 12.5 25.1 10.0 19.7 9.2 16.7 5-4 14.0 4.5 11.7 4.0 11.0 3.2 8.8 14 10.5 7 x6 ia 8 12.0 24.7 u.a 12.7 8.7 19.1 8.0 16.1 4-4 *3-5 3-7 11.3 10.5 a.5 8.4 16 12 8 18 13.5 9 10.5 24.2 9.7 ^2-2.2 7.5 18.7 6.7 15.7 3-6 1;.。 3.0 10.8 2-5 10.0 2.0 8.0 18 G.5 9 20 15 IO 9.0 8.5 21，7 6.5 18.1 5.5 15.2 3.0 M.5 2.5 10.4 d.*2 9.5 1.8 7-5 20 15 io 1 22 16.5 ri 8.0 23.0 7.5 21.2 5.7 17.5 5.0 14.7 2.6 ia.o 2.1 10.0 2.0 8.8 1.6 7.0 22 16.5 ii I 24 18 12 7.0 22.3 6.5 20.7 5-0 17.0 4.5 14.1 2.3 H.5 2.0 9.6 1.7 8.a 1.4 6.6 H i8 12 1 16 19.5 13 6.2 21.7 5.7 20.a 4.2 16.2 4.0 ”•7 2.0 11.0 1.8 9.2 1.5 7.7 1.2 6.2 26 19.5 1 28 21 14 5.5 *21.1 5.0 19.5 3-7 ”•5 3.5 1.8 10.4 1.6 8.7 7.1 1.0 5.8 28 •21 14 30 22.5 5.0 2O.5 4.5 18.7 3.5 15.0 3.1 12.7 1.6 9.7 1.5 8.1 r.i 6.7 。.9 5-3 30 •2-2.5 T5 16 4.5 19.8 4.0 18.0 3-0 14.5 2.7 12.2 i •斗 9.0 1.3 7.5 0.9 M 0.8 5.0 32 24 16 3 斗 25.5 17 4.0 I9.-2 3.5 I7#5 2.7 14.0 2.5 IT.7 r.a 8.2 i.i 6.8 0.8 6.0 0.7 4.8 3 斗 W.5 17 1 36 27 18 3.5 18.6 3.2 17.0 2.5 13.5 2.2 11.2 i.i 7.5 1.0 6,2 0.8 5.6 0.6 4-5 36 27 18 58 28.5 19 3.2 I8.O 3.0 16.5 *2.*2 13.0 2.0 10.7 r.o 6.8 0.9 5.7 0.7 5.2 0.6 小 2 38 28.5 19 1 4〇 3〇. 20 3.0 】7 •斗 2.7 16.0 a;o 12.5 1.7 io.a 0.9 6.1 0.8 5.1 0.6 5.0 0.5 4.o 4〇 3〇 *20 ' TABLE XI. DIMENSIONS AND WEIGHTS OP Track Stringers. Panel Length. Track Stringers. . Web Up. FI. L. FI. Weight of two Stringers and their Bracing. 10， 15" 50 • I 1100 11， 15" 50 • I 1200 ii* 15" 5c • I 1300 15" 67 * I 1842 14， 67 • I 1976 15， 15^ 80 - I 1500 16^ S’ x 24， a — 3. X3i" — 1〇ずし 2— rxsi'-ij-i'L 3400 17， 2— 3/7 X 3 io.4*L 2— 3"X 9.o*L i-rx7r~pi. 3570 18， 1^X26" 2— ， — ii.7*L 2 —广 x ;V’一 io.4*L i-r><7 "pi. 3860 i ゲ 87/ x 27* ^—3^ x iv — I2.7，L 2 —化 X5V-9.7*L 1- WPP1. 4240 2<31"—14.丨*し 2-3rx?r-9^L y X7 姜 "i，i. 4650 4750 2lf 1" x 29" 卜 3"X*— 14ず1_ 2 —3f'X4"—io.5*L i-^x^Ph * 5100 . 5*220 22r r'xw 2— •— j5.2*L 2—1V X4/7— io.5*L i-rx^n. 5490* 1 5610 げ 2-3 "xsi"— I5.6*L 1 — 3* X4" — L 1— r xB^-Pl. 6040 24 卜 X32" 2 — 4" X 4" — 1 6.， L 1 一 ず X4 へレ2轉し i— i"xS"Pl. 65-20 ; ホ The upper line to be used when wooden shims are employed, and the under line when not. TABLE XII. Dimensions and Weights of Floor Beams for Single Track Bridges. Panel Length. Floor Beams. Wob. Up. FI. L. FI. Weight. 10， |"X24" 2 — ぐ X 4’ 一 i6.7n L 2— 3"X5, 一 17.9* L 2350 1ぴ 2— 4^x5^ — x6,4#L 2-3~X5，,-i7-9L° 2400 ； 12， x 26" 2 — 3" x 4, 一 17.* L <2— 4" X5" — i8.3*L 2450 13， 2— 3 名， x 5，一 17.2* L 2WX5" 一 i9.*L 2520 H' i" x 28， 卜 3 る， x 5, 一 17.2* L 1-3*" X 5"— 19- L 2580 15' r x 30， 2— 35^ X5^— I7^*L 2-54、5"—19*し 2600 16， X3 ブ 2 — 4"X5, 一 16.4* L 2— 5" X 5，一 17.9* L 2620 17， 2— 3^x4^— 16.7* L 2 — 4〃X5" — 18.3. し 2720 18' 1， x 34" 1 -5 去， X4" — i6.7**L 2 — 4" x 5" — 18.3* L 2.770 2— ?rx5-— i^l 2— 3-i X5 し I パ* L 3000 19， rx35，y 2 一 3, X4, 一 I7*L 2— X5. — I デ L 2850 卜 3**X5，一 I9.5.L 3.i"X5，一H. パ L 5130 2(y r'x36. 1 一 4.X 5’一 18.3 •し 2_3f x5-_,3.7.l I— X 10° PI. 2950 or 3200 2— ぐ X 5’ 一 20.-2* L 2 -3rx5"—M.3.L T-g'XTO^Pl. 3280 or 3530 21， X 36， 13-7*L I — X 10 士 ’1*1. 2— 4" X5"— i6.4«»L I 一*" xio"P1. 3400 or 3650 22' l"X36^ 2— X5，一 I5.5**L I — 吾4* X Il^Pl. 2—4* x 5, 一 18.3* L i—^n x ic^P], 5750 or 4000 rx36 - 卜ず X5" 一 15.5.L i 一 Y x roiPl. a— ぐ X5"— 1— 务 "xio"Pl. 4050 科' 香. X36， *2— か x 5" — 17. 1— 長,, x rc^Pl. «— 4^x5^— rg.^L 】 一 rn4' X 1C， PI. 4100. N. B. Thes^ weights do not include those of tlio portions of pony truss floor beams projecting outside of the trapses. Where two floor beams are given, the 】ight one is fur spans below two hundred feet in length and the heavy one for spans aboyo the same ； and where two wei^lits are given for the same beam the smaller is for the case of abutting stringers and the larger for stringers resting on floor beams. AND VERTICAL SWAY BRACING IIDGES. TABLE XIII. DIMENSIONS OF MEMBERS OF LjATEEAL SYSTEMS, PORTAL BRACING AND VERTICAL SWAY BRACING- FOR SINGLE TRACK THROUGH AND PONY TRUSS BEIDGES. Span Pan. 1. Pan. 2, Pan. 5. Pan. 4. Pan 5. Span. Pan. i . Pan. 2. Pan. 3* Pan. 4 - Pan. 5* Pan. 6. Pan. 7. Pony Trusess if'O i¥'Q 1#/〇 aocy. 2—5"— 9尊[ 2 ー ヰ ゲ ー 6* [ 2— 斗 办 一 6*[ 2 — 4" — 6*[ 2 — 4" — 6* [ 2— 4"— 6W[ 2一4" 一 6轉[ ず〇 1 各" (D wo 70 ノ 2 一 5#/ 一 7*[ 2 — 4" — 6轉[ 卜 I|"G) i*"o I 為， 〇 i"Q 1#/〇 2 一 5"— ”[ 1—5 ク ー11.1 I — 5 #'— 11*1 I — • 5" — ii**I 2—1『〇 i-WG) I 一， 〇 1-ず〇 1 一 iro ii"CD 1"〇 2— 6"— 8ゲ[ 2 — 6" — 11**[ 2 一 6"— 8.5 •[ ト ヴ，ー パ[ 1 一 4"--6*[ 2 — 4"— 6マ 2— 4，一 6轉[ 2 — 斗"一 ”[ 210。 a-_6/y-8.5»[ 2 — 5"— 7*[ 2 — 斗" 一 6*[ 2— 4"— 6 マ 2 — 4* — - 6"[ 8o\ 2 一 5" — 7*[ 2 ー ヰ" 一 6*[ iHf/Q I 蟲 "〇 iro す, 〇 1"〇 1"〇 2-iro 1 ぎ 0 1*,;〇 i&"0 i^ö WO 1,7〇 2— 5" — 8*[ 1 — 5" — 11.1 2 — 4" — 6**r 2 — 4" 一 6* [ 2 — 4" — 6*[ 2—1^0 i 一ず 口 I -ポ〇 i-iro i-iro 90，. 2 — 5" — 8*[ 2 — 4 つ 一 6* [ 2— 6"— 8.5* [ 2 一 ず’ 一 10.5 *[ 2_6"— 8ゲ[ な 一 5" — ”[ 2_5"_7.[ 2 一 4" — 6*[ 1^0 1'/〇 22Cy. a — 6"— 9.5* [ 父 一 5" — 7*»[ 2— 4" — 6*[ 2 — 4"— 6*»[ if^O 中 〇 ”〇 1^0 ず〇 1**0 】ro 2-1 iro 中 〇 iJ^O Ji"0 2 一 4" — 6* 「 2 — 斗" 一 6*[ 4" — 6*[ 2— 6 " — 8.5*[ I 一 5^— 11*1 1 一 5" — 11轉1 i — 5. — unl i — s" — i i^I io*y. 2 一 6" — 9*[ 1 — 4#/ — 6*[ 2 —ゲ '〇 2—1^0 1 — 2 各" 〇 1 一 I 始 "〇 1-1^0 li'O 1"〇 2—6°—9^[ 2 — 7" — 11*[ 2 一 6* — 8.5*[ 2 一 6"— 8.5 •[: •2— 5"— 7*[ 2 — 4" 一 6* [ 中 〇 广〇 23 1 — 7 " — 10.5* [ 2 一 5" — 7*[ 2 一 5" — 7*[ 2_一4" 一 6*[ a— 斗" 一 6*[ 2 — 4"— 6*[ 2 — 斗" — 6* [ 2 — 4"— 6轉[ m°Q 中 〇 碭"〇 I I O~ 2 - -6° — 11*[ a— 4" — 2— 4" — 6*»[ 2 一 1^0 I! で） WO 中 G) 卜 6"— 8.5, [ I 一 5"— 1”1 I— 5"— i”I I— 5"— i— 5" — ii -I 1，'〇 卜 wo a-iro I 一ず 〇 I 一 ず〇 1-1^0 to ず 〇 wo 2 — 6. — 10 *[ a 一 7" — iin[. 2 — 6" — ro*r 2— 6, 一 8ゲ[ 2_5»_7.[ 2 — 4" 一 6" [ 2 — 斗" 一 6*[ 2— 4"— 6.[ a — 4" — 6*[ 2 一 4#, 一 6*[ 24〇 へ 2 — 7, 一 10,5* [ 2 — 5" .— 7*[ 2 一 5, 一 7*厂 2— 4"— 6«[ 2 — 4" 一 6尊[ 12Cf. 2 — 6" — ij*[ 2 — 斗" 一 6’ [ 2— 4"— 6尊[ デ メ〇 iWQ ir'o i|/yO ず 〇 1"〇 2 — 2みク〇 iro ず〇 iro ず〇 I— 5"— ”*1 1^0 IÄ々0 !i，'Q 2 一 6* 一 8,5*[ I 一 S* — ii*I 1 一 5" — 1 1” 1— 5"— 2 一 5" — 7*[ 2 — 5"— 7*[ 2 一斗"— 6«(； 2— 4"— 6*「 2ーォ0 a— ず 〇 2— I 碧" 〇 I 一 i-iro 1 ― 1〇7//〇 , I JO へ i 14〇 へ i5cy. 160，. 170，. 2— 6" — I 斗《 [ 2— 4"— 6.5* [ 1 一 4" — 6*「 a— 7，/— io*54[ 1 一 7" — 12*[ 2 — 7" — 10.5 *[ 2— 6" 一 8.5* [ a — 5"— 7.5*[ な 一 5 ゥー 7*[ 14"0 1#/〇 I" 〇 25〇,. 1 — 7" — 11* 匸 2 — 5"— 7.5 •[ 2 — 5" — 7*[ 2 — 4"— 6**[ 1 .一 4" 一 6*[ iWO WO ir;o li'O ゲ/〇 1 普" 〇 iA/yO 1#/〇 2—2^0 i^O li^O ii"Q jro 1 一 5" — 7*[ 2 — 5" — 广[ 2— 4" — 6*[ 2 — 4" 一 6鱗[ a 一 6’ 一 8,5*[ I — 5" — ii*I i—5#— I 一 5" — H*I i— 5"— n*I 2 一 6" — 15"*(] •2— 5"— 7.5* [ 5"— 7#[ 2 —中 〇 HH て） 3一了 暴" 0 I 一* 2赤"〇 I— I^,y0 1 一 tä"G) 】が〇 1"〇 〇. .一 7"— 10.5* 匸 2 — 8" — 12.5. [ 2 一 1¥ 一 10.5*[ 2 — 7" — 1。-5*[ 卜 6"— 8.5«» [ 2 — 5" — 广[ 才 〇 iro 中 〇 . 1.0 26c/. 2 — 7" — 11*[ 2— 5 "— 8*[ 卜 -5，' 一 7*[ a — 5"— 7*[ 7 一 4リ ー 6,,[ 2 — 5"— 7*[ 2— 5"— 7*[ 2— 4/y— 6*[ 2— 4"— 6.[ 2,0 1备"0 il^O WO 2—6°—i6n[ 2 一 5"- 8.5* [ 2— 5 ぁ一 7.5*[ 2—2^0 作', Q I 為" G) iA で） ^°〇 中 〇 1"〇 2 — 6"— 8.5"» [ 1一5 ，，一 11 *1 1—5"— 1*1 i— 5" — ii*I r 一 5"— ii*I ポ〇 iro iro ず〇 2 —靖" 〇 a — ゾ〇 iro I 一ず 〇 了一 '一' h.’Q a— 5" — 7*[ ,_5»_8«[ 2 — 5" — 7*[ 2 一 4 "一 6«[ 2 一 7" — 1〇.5*[ 2 — 8" — 12,5*[ 2 — 7 ダ ー ii**[ 2一7" 一 io.S^C a—ö^— 8.5»[ 2 — 5" — 7韓[ ユー 5〃 一 7#[ a— 4，一 6*[ 2 一 4" — 6**[ 2—4"— 6難[ 27 A"Q IlVO i か, G) jtV'G) Q — 5" — 7*[ 1 — 5" — n*I 1 一 5"— 11*1 i— 5"— ii*I 1 一 6#/ 一 8.5 *[ I 一 5" — i”I a み" 口 iro 中 〇 2 — 边"〇 H み" 0 卜 KD 1 一分" 〇 i-iro ]— 中 〇 2 一 5" — 7*[ 2— 5，' 一 9.5* [ *2 — 5" — 7Ä[ W— 7.[ *2— 4" — 6*[ 〇. — 7" 一 ii-S^C 2— 8"— 12.5* [ 2 — 7" — ii.5*[ 2 一 T — 10,5** [ 2 — 6" — 8.5 •[ 2 — 5" — 7 •匸 •2— 4"— 6«[ 2 — 5 w — 7.5* [ W 一 !一4" 一 6*[ 2— 4"— 6*[ 280。 1 — 7" — 12_[ 2— 5，一 8.5*[ 2— 5’ 一 7*[ 2— 5"— 7#[ 2— 4"- <2 — 4, 一 6*[ 中 〇 中 〇 1/70 ォ 〇 中 〇 wo 4"〇 WO 2—1^〇 iro iro ii"ö 卜ず 〇 iro iro iro iro iro 卜 5 W[ I 一 5办 一 II»»I T— 5'メニ11*1 1— 5"— i”I 2 — 6" — 9*[ 1 一 5，一 11*1 i 一 5"— i”i i — 5, 一 i i*I トー 5 "—11* i i 一 5"— iin 口 I 封" 0 1!"0 2 —2 A"Q 。一 4"0 1一2か〇 I-I^O i— ず 0 卜 .5" 一 8*[ 2 一 5" — 10*[ 2— 5"— 7.5.[ 2 — 5" — 7*「 a— 4/7— 6*»[ 2 — 7" — 12.5. 「 2— 8"— ず「 2 — 7" — 12*[ 2 — 7, 一 1〇.5*1 2— 6" — 8ゲ [ 2 — 5" [ 卜^'— 7*» [ 2— 5"— 8*»[ Q. — 4#/ 一 6*[ 2— 4" — 6*[ a— 斗" 一 6*[ 2—7" — 12.5轉[ 2 — 6. — 8,5#[ 卜 5，一 7*[ 2 一 5 ダ ー . 7**[ a— 斗"一 6« 「 2 —ぐ 一 6*[ ず〇 iro 1^0 2gof. ル， Q 喵"〇 中 0 ir.o 吩〇 I^T^O i8cy. 2-1^0 叱 〇 中 0 中 〇 す〇 iro iro iro iS#0 2-5 "— 7*[ I— 5" — n**I I 一 5#/ — I i*I I— 5"— i”I 2 — 6" — 1。*[ 1—5"— ii*I 1 — 5, 一 i—5" — r”I 1 — s*~ — 中口 旧で） 中 〇 卜 地,, Q な一 40 文 一 iW"G) I 一中 〇 I 一 •命 O 1 — i*H’0 1— '**0 a 一 5"— 8»[ 2 — 5" — 11*[ 1 — 5"— 8*[ 2 — 5 •.— 7尊[ a— 4"— 6* 「 2 — 8" — 12.5* [ 2 — 9" 一 14* [ a 一 8" — J2.5*[ 1 — 7, 一 1〇-5*[ 2 — 6#— 8,5*[ 2— 5" — 7.5 •[ 2 一 5 "一 7.7«[ 190，. 2— ぐ— 8.，[ 1 — 4’ 一 6*C 2 一 斗" 一 6*r 2— 4"一 6#[ 30CA 2 — 8" — 12.5*[ 2 一 6" — 8.5 *[ a— 5, 一 7.5* [ 2— 5#— 7*[ 2— 5" — 7叮 2—4，,—69 [ 1 i&"Q WO i^O 】i"Q 地" 0 2"〇 liTO iro ii/yO け" 〇 2—1 聲二〇 中 0 ii"0 中 〇 2 — ホ〇 iro IVO »ro iro i-ro 2 一- 5#/ — 7tt[ I 一 5" — 11*1 i 一 sr/ — u*I I 一 5" — ji**I 1 一 7" — 10.5* [ 1— 5 "— ii"i 分， 口 中 〇 ず 0 2 — 斗" — 6**[ 2 一 2 金' メ〇 ュ ー 2iVO i—^O 2 一 l|^0 1— ず〇 i — if 〇 1— iiwO a — 5" 一 8.5* 「 2 — 5" — 11**[ 9*[ 2 一 5" — 7Ä[ ず〇 2 — 8" — 12.5** [ 2 一 9" 一 14*[ 2 — 8" — ia，5*[ 2 — 7" — 10.5* [ 2 — 6* 一 9*[ 2—5'，一 8轉[ 2 一 5"— ”[ ckness web inches. D.250 七. 2 7 5 ).^00 5.325 ^5〇 »•375 ，4〇〇 丨ギ 5 •45〇 *475 •5〇〇 5^5 ；55〇 575 600 525 55〇 \is ，5〇 75 ^5 :5〇、 75 DO 25 5〇 TABLE XIV. BENDING MOMENTS &c. FOR Iron and Steel Pins. Dia. Eesistmg Moments for Bending. EesistingShear- ing Stress. Dia. Resisting Moments for Bending. ResistingShear- ing Stress. Iron. Steel. Steel. Iron. Steel. Steel. Trusses. Iiat. Syst. Trusses. Lat. Syst. Trusses Trusses. Lat. Syst. Trusses. Lat. Syst. Trusses. 1.1 4 i " 56.5 84.7 90.4 135.6 54.8 i 2.9 4 f " 61.7 92.5 98.7 148.1 58.1 X i ^ 3.7 4 音" 67.1 100.6 107.4 161.1 61.5 if" 4.8 4 I w 72.8 116.5 65.0 J f " 5.9 4 f " 78.9 126.2 68.5 I i " 7.2 4 1 " 85.3 156.5 72.1 2 〃 5.9 8.8 9-4 14.1 12.1 5 " 92.0 147.2 75.8 “,， 7.1 10.6 11.4 17“ 13.7 5 i " 99.1 158.6 79.7 8.4 12.6 13.4 20.1 15.4 5 706.5 170.4 83.7 2 音" 9.9 14.8 15.8 23.7 】7.i 5 1 " 182.9 87.8 11.5 17.2 18.4 27.6 18.9 5 i " 122.5 196.0 91.9 2 普,， 13.5 19.9 21.3 32.0 20.8 5 蚤" X3I.O 209.6 96.1 “,， 15.3 *22.9 24.5 36.8 22.9 5 ” 140.0 224.0 100.4 17.5 26.2 28.0 42.0 25.1 51" 149.3 238.9 1 04.8 3 " 19-9 29.8 31.8 斗 7.7 27.3 6 " 159.0 丨 54.4 109.3 3 i ° 22.5 11.7 36.0 54.0 29.6 6 i 7/ 169.^ 270.7 113.4 3 士 " 25.3 37.9 40.5 6o.8 1 2.0 6 1 ' 179.8 287.7 118.4 3 f " 28.3 42.4 45.3 68.0 34.5 6 { " 190.8 305.3 121.2 3 ド 31.6 47 •斗 50.6 75.9 37.1 W 202.2 323.5 128.0 3 蚤" 35.1 52.6 56.2 84.3 39.8 6 f " 214.1 342.6 133.0 • 3 聲〃 38.8 58.2 62.1 91 ュ 42.7 6 聲 " 226.5 362.4 138.0 3 i° 42.8 64.2 68.5 10-2.8 45.6 6 1 " 239.3 38cz.9 H3.3 斗" 47.1 70.6 75.4 115.1 48.6 7 〃 25*2.6 4。4.5 148.5 4 i 7, 51.7 77.5 82.7 J^4-i ( 5r*7 i“r 名， 小 I ]v 5-i6.o$ 1 r 5*I7-8i IT 6.19.59 r 6.21.3?. ホ 7外 16 7.24 .94 化 8,26.72 , i" i ! 9/28.5。 丨 W 9^0.28 ir 1032.06 i か* 1053.84 屮 1135-6? 丨 i 舟, 1157.41 ir 1259.19 牛。. 97 iV f2-75 i| マ 牛 6.31 中 4-Q.88 Sickness of wtb i inches. 0.250 0.275 0.500 O. 325 P. 550 0.375 0.400 0.425 0.450 o-475 0.500 0.525 0.550 0.575 0.600 0.625 D.650 5.675 X700 >•725 >•750 ••775 .800 -825 ,850, ^?T 900 925 TABLE XY. WORKING BEARING STRESSES FOE PINS. iV 中 *r 2° 味, ず ず 中 ず ■ 5" a" 3i" 3r sr 3聲" ! ii" 4" 4r 4" 4r 4i" 4r 4r 4r 5" sr 5r sr 5¥ 5§" sr SV 6" 6-r 6务" 6r 6f" r V 4.50 4.88 5.巧 5.63 6.00 6.38 6.75 7.13 7.5。 7.88 8.2 5 8.63 9.00 9: 9.75 10.1 3 10.50 10.88 1 1.251 I2.0C 12.38 12.75 13.13 15.5。 1 3.8 卜 5.06 5.48 5.91 6.35 6.75 7.17 7-59 8.0-2 8.44 8.86 9, 心 9.71 10.12 J0.55 10.97 11.40 11.81 m3 12.66 13.08 13.50 ”•92 14.34 14.77 !5.i9 15.61 16.05 r 5.63 6.09 6.57 7.03 7.50 7.97 8.44 8.9» 9-?7 9.84 10.31 10.78 I f.25 11.72 12.1() 12.66 13.13 13.59 14.061 14.53 15.00 15.47 15.94 16.4] 16.88 J7-S4 17.81 18.28 • r 化 6.19 6.7 っ 7.22 7.73 8.25 8.77 9.28 9.80 10.3 1 fa” 11.34 11.86 12.38 12.89 H.4I 13.92 M.44 14.95 15.47 15.98 i6.5o 17.02 17.53 18,05 J8.56 19.08 19-59 20.1 1 20.63 ir r 6.75 7.5】 7.88 8.44 9.00 9.56 10.1 $ 10.69 11.25 1 1.81 12.58 12.94 13.5。 14.06 14.65 15.19 15.75 16.31 16.88 17.44 18.00 18.56 rg_i3 19.99 20.25 20.80 21.3 尸 21.94 22.50 2 3.06 23.63 r n- 7.31 7-9^ 8.53 9.14 9.75 10.36 10.97 i i.sS 12.18 リ .8c J3_4i 14.0: 14.65 15.23 15.84 16.45 17.06 17.67 18.28 18.89 19.5c 20.11 20.77 21.53 21.44 22.54 •25.16 23.76 24.58 24.98 25-59 26.2c r 7.83 8.5; 9.19 9.84 10.50 11.16 11.81 "•47 【3.1.2 ルフ8 14.44 15.09 15.75 16.41 17.06 17.72 18.38 19.03 19.69 2。 34 21.00 21.66 22.11 22.97 23.6; 24.27 24.94 25.59 26.25 26.91 27.56 23.-22 28.88 29.55 r か 8.44 9.14 9.84 10.55 11.25 11.95 1 2.66 13.56 14.06 H-77 1547 16.17 16.88 17,58 18.28 18.98 19.69 叫 9 21.09 -21.80 22.50 23.20 25.91 24.61 25.31 26.01 26.72 27.42 •28.15 28.8 ^ 29-53 30.23 30.94 31.64 叫 4 iT I" 9.00 9.75 10.50 1 r.25 I2.0C 1，275 13.5c 14.25 14-99 15.75 16.50 17.25 18.00 18.75 19.50 20.25 •21.00 21.75 22.50 25.25 24.00 24-75 25.5。 •26.25 27.00 27.74 28.50 29,25 50.00 30.75 31.50 32.25 3 3.oc 33.75 34.5。 $5-^5 56,00 a" 9.56 10.36 1 1.16 ri.95 J2.75 13.55 14.34 15.14 15.93 16.73 17.55 18.33 19.13 19.9 ビ 20.72 21.52 22.51 2 3.1 •• 23.91 24.70 25.5。 •z6.3。 27.09 27.89 •28.69 29.47 30.-28 31.08 jr.88 32.67 33.47 34.27 35.01 55.86 36.66 37.45 38.25 39.05 59.84 w a ク 10.13 10.97 i f.81 11.66 1 5.5c H-54 15.19 16.03 16.87 17.72 18.56 19-41 20.25 21.09 21.94 22.78 23.6; 24.47 25. 3i 26.16 a 7.00 27.84 28:69 29.5 3 50.58 51.21 32.06 32.9c .53.75 34.5V 35.44 36.28 17. ii 37.97 38.81 39.66 40.50 4*^4 42.18 43.03 45.88 ir IlV* 10.69 11.58 12.47 13.56 14.25 15.14 16.03 16.92 17.8c 18.70 19.57 20.48 21.38 22.27 25.16 24.05 24.94 25.85 26.72 27.61 28.50 29*39 $0.28 51.17 32.06 0.94 llM S4-73 35.63 ミ 6.5*2 37.41 38.5c 39- iv 40.08 4°-97 41.86 斗 2.75 43.65 44-54 454? 46.32 47.21 48.ro 中 11. 25 12.1() 13.13 14.06 15.0c 15.94 1 6 及 17-81. 18.74 19.69 20.63 21.56 2-2.50 23.44 24.38 25.31 26.25 27.19 28.1 3 29.06 30.00 30.94 31.88 32.81 33.75 54-68 35.6; 36.56 37.50 58.44 39-38| 40.31 41.25 4^19 45.13 44.06 45.0。 45-94 46.88 47.82 48.76 49.6(； 50.62 51.56 52.50 ず 1 1.81 12.80 13.78 14.77 15.75 *6.75 17.72 18.70 19.67 20.67 21.66 22.64 23.63 24.61 25.59 26.58 27.56 28.55 29.53 50.52 31.50 $2.48 33.47 34.45 35.94 36.41 57.41 38.59 59-38 4M4 42.3 3 43.31 44.3 c 45.2? 46.27 47.25 48.24 49-m 50.2c 51，18 5U7 53.16 54.14 55.12 iÄ，y ir ia. ^8 ”.4! 14.44 15.47 16.50 17.55 18.56 19.59 10.61 21.66 22.60 2 ミ .72 24.75 25.78 26.81 27.84 28.88 29.91 3°-94 31.97 33.00 34.03 35.06 36.09 37.13 38.15 $9.H 40.21 41.25 42.28 45.31 44.54 45.38 46.41 47.44 4847 49.5。 5〇-53 5 し 56 5^5c 53.62 54-65 55.68 56.72 57.76 ir 命 14.0a 15.09 16.17 17.25 18.33 1941 20.48 21.55 22.64 25.72 24.80 25.88 26.95 ■28.05 29.11 30.19 3i.<27 P.3 斗 3 3.42 34.5。 35.58 36.66 37,73 38.81 39.88 4。.97 42.04 43-13 44. 2C 45.28 4636 47.44 48.52 49-5^ 50.67 51-75 52.83 53.90 54.98 56.06 57.14 58.2*2 59.50 60.38 w 16.88 18.00 19.13 20.2 c, 21.58 22.4h 23.63 24.75 25.88 27.0c 23.13 寧 5 30.38 31.50 32.63 53.75 34.88 36.00 37.13 38.25 39 .ゾ 40.5c 41.62 42.75 43.87 45.0c 46.15 47.25 48.38 49.5C 50.63 5 し 75 52.88 54-oc 55-M 56.26 57.3^ 58.5c 59.63 60.76 61.88 63.00 !r ii .ク 20.52 21.94 ■23.16 24.36 25.59 26.81 28.0 3 29.25 3〇-47 31.69 32.91 34.13 35-34 36.56 37-78 39.0。 40.12 4144 42.66 43.88 45.08 46.31 47*5 ^ 43.75 49-97 51.19 5M】 53.65 54.84 56.06 57.58 58.5。 59.72 60.94 62.16 63 .び 64.60 65.82 67.04 68.26 中 23.63 24.94 26.23 27.56 28.88 30.19 31.50 32.81 54.13 35*44 36.75 38.06 39.38 40.69 42.0c 43.31 44.63 45.94 47-25 48.55 49.88 51. if- 52.50 53.81 55.13 56.44 57.75 59.06 60.38 61.69 63.00 64.51 65.6-2 66.94 68.26 69.57 70.88 77‘.i9 73.50 中 26.72 •28.1c 29.53 30.94 3^.34 33-7S 35.16 36.56 37.97 39.38 40.78 42.19 斗 3.59 45-oc 46.41 47.81 49.22 50.65 57.02 53-44 54 .む 56.25 57.66 59.06 60.47 61M 63.28 64.69 66.09 67.5。 68.91 7〇.3 ^ 71.72 73.12 74.53 75-94 77-55 78.76 2 ク 29.97 31.5。 53.0。 34.50 36.00 37.50 39-。。 40.50 42.00 43.5C 45.00 46.51 斗 8.00 49.5。 51.00 52.5: 54.00 55-49 57.oc 5 8.4v 60.00 61.50 63.00 64.5c 66. oc. 67.5。 69.0c 70.50 72.GC- 73.5。 75-oc 76.50 78.0 c 79.5。 81.00 82.50 84.00 ゴ’ 才 35.06 ^.65 38.25 39.84 4(.44 43.03 44*63 46.22 47.31 49.42 51.00 5^-59 54-19 5 5 .7 と 57.58 58.96 60.56 62.15 6?.75 65.54 66.94 68.55 70.M 7J-72 75-31 74.91 76.50 73.09 79.68 81.28 82.8F 84.47 86.06 87.661 89.26 58.8】 40.50 4 公. 19 43 .肋 45.56 47.25 48.94 50.63 52小 5 斗 .oo 55.69 57.38 59.06 60.75 62.43 64.13 65.81 67.50 69.19 7).88 72.56 74.25 75.94 77-6^ 79-31 81.00 82.69 84.38 86.07 87.76 89.4 4 91.1a 92.81 94.5。 ボ 命 44.53 46.32 48.09 49.88 51.66 53.44 55.23 57.0c 58.78 60.56 62.54 64.15 65.9c 67.69 69.46 71.25 7 3-C3 74.81 76,5 S 78.58 80.16 81.94 も .72 ?5.5〇 87.28 89.06 90.85 92.64 94.41 96.18 97.97 99-76 才 48.76 50.63 52.50 54.0 56.25 58.14 60.00 61.86 63.75 65.63 67.50 69.37 71.25 73.1, 75.。。 76.88 78.75 80.63 8-2.50 8438 86.25 88.1 3 qo.oo 91.83 93.75 95.64 97.52 99 59 101.26 103.13 105.00 55.13 57.09 59.06 61.04 6$.oc 64.97 66.94 68.91 70.88 72.83 74.81 76.77 78.75 80.72 82.69 84.66 86.63 88.59 90.56 92.53 94.5c 96.47 98.44 100.41 102.38 104.35 106.32 108.29 110.26 ず 61.88 63.95 66.00 68.06 70.13 72.^9 74.2 5 76.50 78.38 80.4? 8*2.50 84.56 86.63 88.69 90.75 9*2.81 94.87 96.94 99.00 10(.07 103.13 105 j 9 107.25 109.32 11 1.58 115.44 115.5。 ず 中 69.00 71.16 73.31 75-47 77.65 79-77 81.94 84.0?, 86.25 88.41 90.56 92.72 94.88 97.03 99.19 101.34 103.50 105.66 107.81 109.97 1 12.13 1 14.29 1 16.44 1 18.60 120.75 ず r 74.25 76.50 73.75 81.00 8叫 85.5c 87.74 90.00 92.25 94.5。 96.75 99.0c 101.25 105.50 105.75 108.00 110.-25 112.50 U4.75 1 17.CX： T 19/15 121.50 125.75 i *26.0。 3 ど 8*2.0 多 84.32 86.71 89.06 9 し 4c 95.75 96.09 98.44 100.7 ^ 103.13 105.47 107.81 i io.i 6 r 12.5c 114.85 H7.i9 119.54 121.8? I 24.22 126.56 128.911 1 31.25 sr 少 90.18 92.6; 95.。5 97.5c 99.94 102.38 104.81 107.25 109.69 1 12,12 114.56 1 1 7.0c i r 9.44 1*21.88 124.32 126.75 129.19 151.63 1 34.07 136.5。 3i" 38" 98.71 101.15 103.78 106.51 108.84 11 1.38 iiS-91 116,44 118.97 121.5c /•24.05 1*26.56 1-29. IC … .63 r 34.16 136.69 139.22 J 41.75 -f — 107.64 1 10.25 1 12.88 115.5c 1 18.1 3 120.75 I パ.; 8 126.00 128/)5 156.5 ヒ 159.15 H^75 t 44.581 147.00 n" 3f" J 16.91 119.63 125.06 127.78 1 30.5c … .22 135.94 1 38.66 141.38 144 .ic 146.81 149.53 152.25 3r 5^ 叫 .75 (26.56 119.57 132.19 I35.C。 137.82 140.63 145.44 146.25 149.07 15 1.88 >54-69| 157.5° 3f" ぼ 135.69 156.59 139.5。 1 42.4 f 145.51 148.22 151. H 154.04 i 56.94 159.85 162.75 sr r 144.00 147.00 150.00 153.00 156.00 15 9.00 162.0c 165.00 168.00 4" 一 i54-69 157.79 160.88 163.97 167.06 170.16 173.25 4r A-}*1 1 165,75 168.94 i 72.13 175.32 178.50 4r 4ä" 177.19 180.47 183.73 4r 4 V 1 1 189.00 4r ABLE XYI. SIONS OF UNION l OF SECTION IN TCHES. 8"[. B. 9"[_ J i，[. B. i^[. C. iS，[. A. Thickness of web in inches. W A F W A Y A F w A F W A F 0.250 0.275 1 6 .00 4.8c •2.30 0.500 p i6.59 4.98 2.52 14.50 4-3i.54 6.76 3.01 0.325 ro 17-25 5.18 2.35 1.54 7.06 3.04 p.350 b i7-92 5.38 2.57 f-54 7.?6 3.06 o-575 18.59 5.58 d.40 ;.54 7.66 3.09 0.400 J9.25 5.78 2.42 し 54 7.96 3.11 0.42 5 19.92 5.98 2.45 ’•5 斗 8.26 5.14 30.00 9.00 2.71 0.450 20.89 6.18 2.47 .54 8.56 3.16 30.72 9.22 2.7; 0.475 21.25 6.58 2.50 .54 8.86 3.19 31.72 9.52 2.75 0.500 21.92 6.58 2.52 3^-7^ 9.82 2.7P 40.00 12.00 3.53 0.525 22.59 6.78 2.55 53.7。 10.1 a.8c 41.25 12.38 3.56 0.550 ' 23*26 6.9? H-7^2 1 0.4 ■: 2.83 42.50 12.75 3*58 0.575 23.92 7.18 2.60 35.72 lO.jQ 2.85 45-75 13.13 ^.61 0.600 24.59 7.58 2.6գ 36.72 1 1 .02 a.88 45*0。 13.50 3.63 0.625 25/25 7.58 2.65 57.7 ゥ I I.31 2.9c 46.2 5 1 3.88 3.66 0.650 25.92 7.78 2.67 38.72 11.62 2.93 47.5C 14.25 0.675 26.59 7,9 只 2.70 39-72 11.9*2 2.95 4 え 75 14.63 ?-7f 0.700 27.25 8.18 2.72 40.72 12.22 a.98 50.00 15.00 3.73 0.725 27.92 8.38 2.75 4r.72 Ta.52 3.00 . 5U5 15.58 5.76 0.750 斗 2.72 12.82 3.03 52.50 ，5.75 3.7? 0.775 43-7^ I?.I2 3-05 53.75 16.13 3.81 0.800 44-72 15.42 5.08 55.0。 16.5c 5.83 0.825 45-72 13.72 3.1c 56.25 16.8? 3.86 0.850- 1 46.72 14.02 57.50 17.25 3 別 0.875 47.72 14.32 3J5 58.75 17.65 ?-9i 0.900 斗 8.7 2 14.62 3.18 60.0c 1 8.0c 3.9? 。•州 49-72 14.92 5.2c I 0.950 TABLE XYI. . TABLE FOE FINDING- THE DIMENSIONS OF UNION IBON MILL'S CHANNEL BAUS. W EEPEESENTS THE WEIGHT PEB FOOT IN POUNDS ; A THE ARK A OF SECTION IN SQUARE INCHES AND F THE WIDTH OF FLANGE IN INCHES. Thickness of web in inches. 4W[. A. 4"[. B. 5"[. A. 5"[. B. 6"[. Ä. 6"[. B. ri a. 7"[. B. 8"[. A. 8"[. B. 9"l- A. rC. b. io，[. A io.[. B 10, [• C. 12^[. A. i ブ [• B. 1 2* [. C. 1S_[. A. Tliiclaiess of wtb in inches. W A F W A F W A F W A F W A F W A F W A F W A F W A F W A F W A F w A A W A F W A F w A F W A F W A F w A F W A F 0.150 6.05 1.8*2 1.62 7.0P 2. 【5 1.75 7.0*2 2.11 1.69 9.08 2.73 1.94 8.58 2.57 j.8) 10.46 3.H 2.0c 10.57 M7 1.0c 0.-250 0.275 1.9*2 1.65 7.41 2.-25 1.77 7.44 2.24 1.77 9.5C 2.85 1.96 9.08 7.72 1.84 10.96 3.29 7.03 11.15 3.55 2.05 12.79 レ 84 2.07 ■ 0.275 c. 300 6.71 1.02 1.67 7.74 1.80 7.^5 2.36 1.74 9.91 2.98 1.99 9.50 2.85 J.86 11.46 3.44 2.05 ri.74 3.52 2.05 14.09 4.23 2.30 13.46 4-°4 2.04 16.00 4.8c •2.30 1 8.0c 54。 24; 17.50 5.25 2.45 70.00 6.00 2.56 * 0.500 0.05 7.00 <2.10 1.7c 8.0P 24; I.R? 8.27 2.49 1.77 io.W 5.10 2.01 11.96 3.59 2.08 12.32 3.70 n.oP> 14.681 4.40 2.33 i 斗 .13 4.24 2.07 16.59 4.98 2.5-2 1 14.50 4.35 2.50 1 8.6c 5.58 2.45 16.00 4.80 2.52 18.33 5.5。 2.46 10.67 6.2c 2.58 20.00 6.00 3.01 2154 6.76 3.01 0.325 0.350 8-4i 2.5? 1.85 10.75 •2.04 12.46 3.74 2.IC 12.90 3.87 2.10 15.-26 4-5^ 2.35 14.79 4.44 2.10 17.25 5.18 2.35 19.35 5.81 2.48 19.17 5,75 2.48 21.50 6.45 2.61 2 ヨ .54 7.06 3.04 P*35o 1 o.m 8.74 2.63 1.^7 11.17 3.35 2.06 12.96 3.89 2.13 13-49 4.05 2.15 15.84 4.75 2.^8 15.46 4.64 2.12 17.92 5.38 2.37 20.10 6.03 2.50 20.00 6.00 2.51 22.33 6.7c 2.6^ H-54 736 3.06 0.375 0.400 9.00 2.70 i メ 9 1 1.58 3.48 2.09 13.46 4.04 2.15 16.43 4-93 2.40 18.59 5.58 2.40 •20.85 6.26 2.55 20.83 6,2s 2.53 23.17 6.95 2.66 25.54 7.66 3.09 0.400 0.425 1-2.00 3.60 1A I 13.96 4.19 2.18 17.01 5‘ic 2.45 J9.25 5.78 2.42 21.60 6.48 2.55 21.67 6.50 2.56 24.00 7.20 2.68 26.54 7.96 3.11 0.42 5 0.4*50 1?ギ 3.73 2.14 14.46 4.34 2.20 17.59 5.28 2.45 19.92 5.98 2.45 22.35 6.71 2.58 22.50 6.75 2.58 24.83 7.45 2.71 27.54 8.26 5.14 30.00 9.00 2.7 j 0.450 0.47 5 1-2.8^ 5.85 2.16 14.96 4.49 2.2 ^ 18.17 5.45 2.48 20.89 6.18 2.47 23.10 6.95 2.60 29.33 7.00 n.61 25.67 7.70 2.73 28.54 8.56 3.16 30.72 9.2c 2.7$ 0.475 0.500 I3』5 3.98 2.10 15.46 4.64 2.25 18.76 5.63 2.50 21.25 6.58 2.50 23.85 7.16 •2.65 24.17 7.25 2.65 26.50 7.95 a.76 29.54 8.86 3-19 31.72 9.52 2.75 0.500 0.525 13.68 4.1c 2.21 15.96 4.79 2.2? 19.54 5.80 2.53 21.92 6.58 2.52 24.60 7.38 2.65 25.00 7.50 2.66 27.33 8.2c 2.78 32.72 9.82 2.7P 40.00 12.00 3-53 0.525 0.550 14.00 4.20 2.23 • 19.92 5.98 2.55 22.59 6.78 2.55 25.35 7.61 2.68 25.8^ 7.75 2.68 28.17 8.45 2.81 55.72 10.1*2 2.8c 41.25 12.38 3.56 0.550 0.575 23*26 6.92 2.57 26.10 7.83 2.70 *26.67 8.00 2.71 29.00 8.70 a.83 H-7^ 1 0.4 ■: 2.83 42.50 12.75 5.58 0.575 : 0.600 23.92 7.18 2.60 26.85 8.06 2.73 27.5° 8.25 2.73 29.83 8.95 2.86 35.72 TO,7? 2.85 4^-75 13.13 5.6] 0.600 0.625 24.59 7.58 1.62 27.60 8.28 2.75 28.33 8.50 2.76 30.67 9.20 2.88 36.72 ! 1.02 2.88 45.00 13.50 5.63 0.625 0.650 25.25 7.58 2.65 28.35 8.51 a. 78 29.17 8.75 2.78 51.50 9.45 2.91 37.72 11.32 2.9c 46,25 13.88 3.66 0.650 0.675 25.92 7.78 2.67 29.10 8.73 2.80 30.0c 9.00 2.81 32.53 9.7。 2.9$ 38.72 11.62 2.93 47.5C 14.25 5.6? 0.675 0.700 26.59 7 •邙 2.7c 29.85 8.96 2.83 ”•[7 9-95 2.96 39.72 r 1,9*2 2.95 4^.75 14.63 ?.7r 0.700 0.725 27.25 8.18 2.72 34.0° 10.20 2.98 40.72 12.22 a. 98 50.00 15.00 J-73 0.725 0.750 27.92 8.38 2.75 34.83 10.45 3.01 4^7*2 12.52 3.00 • 51.25 15.58 3.76 0.750 0.775 42.72 12,82 5.03 52.50 15.75 0.775 0.800 —■ _ 43.72 15.12 3.05 53.75 16.13 3.81 0.800 0.825 44.72 1 3 ギ 3.08 55.00 16.5c 多 .83 0.82 5 0.850 45.72 13-72 3.1c 56.25 16.SP 3.86 0.850、 0.875 46.72 14.02 3-U 57.5。 17.25 lM 0.875 0.900 47.72 14.32 3J5 58.75 17.63 L91 0.900 0.925 48.72 14.62 5.18 60.00 1 8.0c 0.925 0.950 49.72 14.92 3.2C 0.950 •SJ OJ 1 91 u rf IrT ^ F ^ r l 5-r 一 I' l s ^ 1 1 ^ TT llr a pl nd Dia. IC ir \ i-i \ ザ 2 — ： 才 1 ホ i 才 1 r 3^ 3 ゲ ▲ 1\¥ 3^ - 3妒 3 聲， - IV 1 4 ク 1 Dia. 1( TABLE XVII. Permissible Pressures on Rollers. Formula p = 0.25 Vd , where p is the pressure in tons per lineal inch of roller, and cl the diameter of roller in inches. The first and last vertical lines give the diameters, and the upper and lower lines the lengths of rollers. The intermediate spaces contain the permissible pressures on the rollers. Dia. 1。， W* 1"2, 14" 15， 16" 17， i8. 19， 20r 2J. 22r 23， 24， 25 一 26 デ a 广 28" 29， 5 ブ Dia. *r 3.31 3.64 3-97 4.5。 • 4.63 4.96 5.29 5.62 5.95 6.28 6.61 6.94 7.28 7.61 7.94 8.27 8.6。 8.93 9.26 9.59 9.92 中 3.42 3-77 4.11 4-45 4.79 5.13 5.48 5.8。 6.1 6 6.50 6.85 7. 1 9 7.53 7.87 8.22 8.56 8,9。 9.24 9.58 9.93 10.17 中 で 3.54 3.89 4.24 4.60 4-95 5.30 5.66 6.oj 6.36 6.72 7.〇7 7.45 7.80 8.13 8.49 8.84 9.19 9-55 9.9〇 10.2 5 10.61 3.64 4-01 4.57 4.74 5.10 5.47 5.83 6.19 6.60 6.92 7,29 7.65 8.02 8.58 8.75 9.1 1 9ギ 9』4 10.20 10.57 10.93 中 3.75 4.13 4.5。 4.88 5.25 5.63 6.0c 6.38 6.75 7.U 7.50 7.88 8.25 8.63 9.0c 9.38 9-75 10.13 io.5c 10.88 11.25 中 3.85 4.24 4.62 5.01 5.39 5.78 6.16 6.55 6.94 7.32 7.71 8.09 8.48 8.86 9-^5 9.6 s 10.02 10.40 10.79 1 1.17 11.56 ず 才 3.95 4-?5 4.74 5.14 5-5 5 5.93 6.35 6.72 7.12 7.51 7.91 8.^0 8.70 9.。？ 9.49 9.88 10.28 10.67 11.07 1 1.46 1 1.86 才 4.〇5 4.46 4.86 5.27 5.67 6.08 6.48 6.89 7.29 7.7。 8.10 8.51 8.9】 9.52 9.72 10.15 10.53 10.94 11.54 11.75 12.15 才 2 聲夕 4]5 4.56 4.如 539 5.80 6.22 6.63 7.〇5 7.46 7.88 8.29 8.71 9.12 9.54 9.95 10.37 10.78 11.19 ii.6j 12.02 12.44 中 ず 4.24 4.66 5_。9 5.51 5.95 6.36 6.78 7.21 7.63 8.05 8.48 8.90 9.33 9.75 10.17 10.60 11.02 11.45 1 1.87 12.29 12.72 ず r 4-35 4.76 5.-2C 5.63 6.06 6.50 6.9 ミ 7.36 7.79 8.25 8.66 9.09 9.53 9.96 10.59 10.83 11.26 1 1.69 12.12 12.56 12.99 V 3 卜 4.42 4.86 5.3。 5.74 6.19 6.65 7.〇7 7.51 7.95 8.4c 8.84 9.28 9.72 10.16 10.61 11.05 ii.5c 11.92 12.57 12.82 13.26 5 矿 3 耙 4.51 4.96 5.41 5.86 6.31 6.76 7.2 1 7.66 8.11 8.56 9.01 9.46 9.92 1037 10.82 1 1.27 11.72 12.17 ia.62 13.07 13.52 少 3 蚤， 4,59 5.〇5 5.51 5.97 6.43 6.89 7.55 7.8i 8.27 8.7 ミ 9.19 9.65 10.10 10.56 11.02 1 1.48 11.94 1*2.40 12.86 n.32 15.78 3-P IV 4.68 5.14 5.6t 6.08 6.55 7.02 7.48 7.95 8.42 8.89 9-35 9.82 10.29 1076 11.22 11.69 12.16 12.63 13. IC 13.56 14.0$ 3， 5妒 4.76 5.24 5.71 6.19 6.66 7.14 7.6-2 8.09 8.57 9.〇4 9が 10.00 10.47 10.95 11.42 11.90 12.3? 12.S5 13-33 1 3.80 14.28 3 聲， 4.84 5.33 5.81 6.29 6.78 7.26 7.75 8.25 8.71 9.20 9.68 10.17 10.65 11.13 1 1.62 12. JO 12.59 13.07 13.55 14.04 14.5。 ホ 比 停 5.41 5.91 6.40 6.89 7.38 7.87 8.57 8.86 9.35 9.84 10.3 5 10.83 11.52 11.81 12.3c 12.79 13.29 13.78 14.27 14.76 4" 5.00 5-5〇 6.00 6.50 7.00 7.50 8.00 8.5。 9.00 9.5〇 10.00 10.50 11.00 11.50 12.00 12.5c 1 J.OO 13.5。 14.00 14.50 15.00 4" Dia. IO， n〃 12^ 14" 15〆 i6 一 17〆 18， ず 20^ 21" 0.1* ず 24， 25， 20r ず 28 ク 2 デ W Dia. FOB RIVETS. Diameters. Bending Moments I in inch-tons.s . Diameters. ¥ iT ir 1" 成, 礆" ず 鳩" I み,， 碭" ir 0.25。" .938" 0.96 9" i .000" 1.。3 1" 1.063" 1094." 1.125" M56" i.【88" 1.219" 1.25。" V 0.092 0.750 i〃 r 0.131 0.844 */r r 0.180 0.938 r IT 0.239 1.032 w r 0.311 1.125 r H/f o-395 1.219 w r 0.494 1.312 4-922 5，c86 5.250 ノ 1 1 . 1 r Wf 0.607 1.406 5.274 5.¢。 5.625 ■ 0.736 1.500 5 -625 5.613 6.000 6.1881 6.3751 6-563 6.7501 1〃 w 0.883 1.5945 -977 6.176 6.375 6.575 6.774! 6'975 7.i7a •tV ir 1.049 1.687 6 .3^8 6.559 6.750 6.961 7.172 7-383 7.5941 7.805 8.0161 8.2271 8.438 ir TABLE XVIII. WOBKING BENDING MOMENTS AND BEARING PRESSURES FOR RIVETS. Diameters. Bending Moments I in inch-tons.s BEARING STRESSES IN TONS. , Diameters. r A", uff ira r を" 殺" r 5" r r §i" a" %" W r IT r UL" 16 ir i" 1 み" ぼ ず は" iA" Jä" Ii" 0.25。" 0.28 0.313" 0.344" 0.57 5" 0.40 6" 0.438" 0.46 9" 0.500” 0.531" 0.56 3" 0.594" 0.62 5" 0.65 6" 0.68 8" 0.719" 0.750" 0.781" 0.813" 0.844" 0.875" 〇.9〇6" 0.93 8" 0.969" i .000" 1.031 ^ 1.063" 1094." 1.125" i.I56" 1.188" 1.219" 1.25。" r 0.09-2 0.7 5。 0.844 0.958 1.032 1.125 1.219 1.315 1.407 1.500 1.594 1.688 1.782 1.875 一 r 0.131 0.844 0.950 1.055 1.161 1.266 1.372 1-477 1.583 1.688 r.794 1.899 2.005 2. IIC 1 ■h" r 0.180 0.958 1.055 1.172 1.289 1.406 1.524 1.641 1.758 1.875 1.993 2.110 2.227 2.344 2.461 2.5781 2.696 2.813 r 0.239 1.03*2 1,161 . 1.-290 1.419 1.547 1.677 1.805 1.934 2.063 2.192 2.321 2.45。 ム 579 2.708 2.8361 2.966 5.094 w r 0.311 1.1^5 1.266 1.407 1.548 1.688 1.829 1.969 a. no 2.250 2.391 2.50 2.673 2.813 2.954 3.0941 3.W5 3.375 5.516 3.656 3-797 3.938 r o-395 1.219 i •仍 1.524 1.677 1.829 1.981 2.133 2.286 2.438 2.59。 2.742 2.895 5.047 5.200 3.3521 3-5〇5 3.657 3.8091 3.961 4.114 4.266 \r r 0.494 1.11գ 1.477 1.641 1.805 1.969 2.133 2.297 2.461 2.615 2.789 2.952 3.117 3.281 3.445 3.6091 3.774 5.932 4.102 4.266 4.430 4-594 4.758 4.922 5.086 5 .な 5。 | 1" wr 0.607 1.406 1.58: 1.758 1.954 2.110 2.286 2.461 2.637 2.813 2.989 3.164 3.540 5.516 3.692 3.867! 4.044 4 •叫 4-595! 4*571 4-747 4.922 5.。9? 5.274 5ィ5。 5.625 務" 0.736 1.500 1.687 1,875 2.063 2.250 2.438 2.625 3.813 3.000 5.188 3.376 3-563 3.75。 3-938 4.125 4.313 4.500 4.6881 4.875 5.063 5.2501 5.458 5.625 5.813 6.00 G 6.188 6.375 6.565 6.75。 l" ぼ, 0.883 1 1.594 1.793 1-993 2.192 2.391 2.59。 2.789 2.989 3.188 3.3871 3.587 3.786 3.985 4.184 4-383| 4*583 4.782 4.9811 5.1801 5.380 5.578 5.778 5.977 6,176 6.375 6.5751 6.7741 6.973 7.172 -xV ir 1.049 I 1.687 1.898 2.110 2.321 2.531 2.742 2.953 3.164 5.375 3.5861 3.797 4.008 4.119 4.43。 4.641 4.852 5 均 5.274 5.435 5.696 5.906 6.117 6.3281 6.539 6.750 6.961 7.172 7-383 7.594 7.805 8.016 8.227 8.438 ir IO" O44 1.000 ioi" 667 1.704 1.7： 11^ 689 1.725 1.7! ur 7I4 1-749 1.7： 738 1.771 1.8( 762 1.795 1.8 1.821 1.8 ず 786 I3f 8ll 1.841 1.8 i4" 835 1.869 1.9 Hi" 863 1.895 1.9 15" 892 1.925 1.9 W 92I 1.951 1.9 16" 95。 1.980 d.O i6!" 977 2.009 2.C 17" ,008 2.036 2.C •037 2.067 2.C 【7r •068 2.098 2.1 18" i8r »IOC 2.119 a.i ず 2.I5S a.] 19V .161 2.18^ 2 •く 20" • 19' 2.221 1. ioY1 叫 ; a. 21° 15 2.7Si 本 a. 2lT ..28 2.31 9 a. TI" j .32 キ ^-34 9 2. 4"7" i?r li XIX. TABLE LENGTHS OF LATTICE OR LACING BABS. Weight per foot of same, and weight of rivet heads. Approximate Lengths, in Feet between Centres of Rivets, Width in inches. Weight per foot, in pounds. End allow- auce for ono bar. Eivet- Heads. 4； 5" 5i" 6U 6广 r 7hn 8^ 9" 9r 10， IOi" i ず ia" J2i0 I〆' ⑴,, i4" 14V I〆’ !5i/; i6f/ ley 17" I7V： 18" 科" i9" 19V 20" aof ii" 21士" aa" r 1.25 A" r Diame- ter, in inches. Weight of two heads, hi pound 4" 0.468 0.500 0.534 0.563 0.599 0.636 0.669 0.706 0.741 < 4V 0.500 0.55。 0.560 0.591 0.6*27 0.660 0.695 0.730 0.766 0.802 0.845 丨 5" 0.5 34 0.560 0.59』 0.621 0.652 0.684 0.719 0.75 J 0.787 0.824 0.861 0.897 ミ 0.934 5" 0.145 0.08 sr 0.563 0.591 0.621 0.650 0.679 0.711 0.745 0.776 0.809 0.84 斗 0.880 0.916 0.952 0.990 j.027 5V 6" 0.599 0.627 0.65-2 0.679 0.709 0.737 0.770 0.801 0.835 0.868 0.904 0.936 0.974 1.009 1.045 1.081 J.H9 1 (/• if 1.36 » 0.153 0.12 6r 0.636 0.660 0.684 0.711 0.737 0.768 0.797 0.829 0.860 0.890 0.929 0.960 0.996 1.03 j 1.065 1.104 1.138 1.175 1.214 « 6 叫 if 1.46 0.161 i • 0.16 V 0.669 0.695 0.719 0.745 0.770 0.797 0.827 0.857 0.886 0.920 0.951 0.985 1.019 1.05*2 1.086 1.122 1.157 1.195 1.230 r.269 1.307 7# i\n 0.706 0.750 0.751 0.776 0.801 0.829 0.857 0.884 0.916 0.945 0.979 1.012 1.043 1.074 1.1 10 1.145 1.180 1.218 1.250 1.28g 1.327 1.364 M99 7V 1.57 1.95 0.180 0.20 8" 0.741 0.766 0.787 0.Ä09 0.835 0.860 0.886 0.916 0.94? 0.972 1.004 1.038 1.067 1.102 1.135 1.169 1.204 1.238 1.274 1.309 M47 1.383 1.420 1.456 1.494 8^ 2 1.67 a.08 0.188 f O.25 8*" 0.802 0.824 0.844 0.863 0.890 0.920 0.945 0.972 1.002 1.034 1.063 1.094 1.128 1.160 1.194 1.226 1.261 1.295 MP 1.367 1.402 1.440 J-475 1.514 1.548 1.587 sv 9" 0.843 c.86] 0.880 0.904 0.9-29 0.951 0.979 1.004 し。 34 1.061 1.090 1.123 1.155 1.187 1.219 1.252 1.284 1.320 1.553 1.388 1.416 1.458 1.495 1.531 1.567 1.602 1.640 1.678 r T.78 2.21 0.197 0.52 9V 0.897 0.916 0.936 0.960 0.985 1.012 1.0 38 1.063 1.090 1.121 1.150 1.181 1.213 1.246 1.275 1.312 1.344 1.377 1.414 1.447 1.478 1,517 1-553 1.588 1.625 1.661 1.700 1.739 1.774 IO" 0.954 0.952 0.974 0.996 1.019 1.043 1.067 1.094 1.123 1.150 1.180 1.210 1.24a 1.270 1.306 【•538 1.369 1.404 1-437 1.471 1.502 1.50 1.572 1.610 1.644 1.680 1.720 1*755 1.793 1.8^0 1.867 10， , H 1.88 2.34 0.215 1 0.40 叫" 0.990 1.009 t.031 1.052 1.074 1. 10a i.iaS 1.153 1.181 1.210 1.24。 1.268 1.300 1.362 1.395 1.428 1-459 1.494 1.527 *•559 1.596 1.630 . 1.667 1.704 1.759 1.776 1.814 1.850 1.886 1.925 1.959 ioV； ii^ 1.0-27 1.045 1*065 1.086 1.110 1.135 1.160 1.187 1，213 1.24*2 1.268 1.298 1.529 1.357 1.390 1.422 1.453 1.485 1.518 1.550 1.584 1.619 1.650 1,689 J-725 1-759 1.795 1.833 1.868 1.905 1.94。 1.977 2.016 1.051 ji° 2& 2.47 a.97 0,721 0.47 1.081 1.104 1.122 1.145 1.169 1.194 1.219 1.246 1.270 1.300 1.329 1.356 1.388 1.422 1.450 1.480 1.514 1.546 し 577 1.610 1.644 1.679 1.714 1.749 1.779 1.817 1.851 1.888 1.926 1.959 1.996 2.034 a.070 I ず a.6o 3.13 0.231 I 0.55 12" 1.119 1.138 1.157 1.180 1.204 1.126 1.252 1.275 1.306 1.331 1.357 1.388 1.419 1.448 1.477 1.509 1.54。 1.572 1.604 1.637 1.670 1.704 1.738 1.771 1.807 1.840 1.877 1.9 f 5 1.947 1.98$ a. 020 2.057 2.094 12° w 1.175 1.195 1.218 1.238 i.aöi 1.284 1.312 1.338 1.361 1.590 1.422 1.448 1.476 1.506 1.536 1.567 1.599 1.630 1.664 1.697 i.7?o 1.762 1.795 1.829 1.864 1.900 1.936 1.969 2.005 1.040 2.076 a.i 14 I ず 2.73 3 •巧 0.250 rr 1.214 1.2 30 r.250 1.274 1.195 1.310 M44 1.369 M95 i .斗 2 2 1.45。 1.477 1.506 1.535 1.565 1-595 1.627 1.657 1.689 r.723 1.75; 1.786 1.821 1.852 1.887 1.923 1.956 1.990 2.026 2.060 2.099 :〆 1.269 1.289 1.309 1.532 1.353 1-377 1.4〇4 1.428 1.453 1.480 1.509 1-536 1.565 1.59; 1.623 1.652 1.681 1.714 1.745 1.776 1.811 1.842 1.876 1.911 1.944 1.978 2.013 a. 048 2.083 2.120 a.i53 W 2.86 3.44 0.258 I4" 1.307 1.327 1.347 1.367 1.388 i ギ 4 1.437 1-459 1.485 1.514 1.540 1.567 1.595 1.623 1.650 1.680 1.710 1.742 1.771 1.805 1835 1.869 1.902 1.935 1.969 2.003 2.037 2.071 2.106 2.140 2.178 14" 5.00 3.6o 0.266 HV 1.364 1.40a 1.426 1.447 I •斗 7 1 1.494 1.518 1.546 1.572 1.599 1.627 1.652 1.680 1.709 1.740 1.769 1.801 1.851 1.863 1.895 1.928 1.960 1.994 2.028 2.061 2.095 a.119 a.164 2.200 W I5" 1-399 1.420 1440 1.458 1.478 1.501 1.527 1.550 1.577 1.604 1.630 1.657 1.681 1.710 1.740 1.770 1.800 1.830 1.861 1.892 1.925 1.956 1.988 2.022 2.053 2.089 2.122 a.i55 a.189 2.225 15" l 3.13 3.75 0.274 i5r 1.456 1.475 1-495 1.517 1.538 r-559 1.584 1.610 1.637 1.664 1.689 1.714 1.742 1.769 1.800 1.829 1.859 1.890 1.921 1.951 1.982 d.oi6 2.046 2.081 2.115 2.146 2.179 2.214 2.248 I5F 1 6" 1.494 I.5H 1.551 1.553 1,57 な 1.590 1.619 1.644 1.670 1.697 1.725 1.745 1.771 1.801 1.850 1.859 1.889 1.920 1.95。 1.980 1.013 a.041 2.077 2.109 2.140 a.I72 2.206 a. 240 1.273 16" 1.26 5.91 0.282 i6!" 1.548 1.567 1.588 1.610 1.630 1.650 1.679 1.704 1.730 1-755 1.776 1.805 1.851 1.861 1.890 1.970 1.948 1.977 a.009 2.038 2.070 •2.101 2-133 2.165 a.i99 2.22g 1.264 a.297 16^ 3.39 4.06 o.a9i 17" 1.587 1.602 1.6^5 1.644 1.667 1.689 1.714 1.758 1.76a 1.786 1.811 1.835 1.863 1.892 1.921 1.950 1.977 2.008 •2.036 2.068 2.100 2.131 2.161 2.19-2 2.2^4 2.257 7.-288 a •叫 17" i7r 1.640 1.661 1.680 1.704 I.7W 1.749 1.771 1.795 1.821 1.84a 1.869 1.895 1-9^5 1.951 1.980 a.009 2.037 2.067 2.098 <2.129 2.159 2.189 2.221 2.2s ^ 2.184 2.319 M49 3 吾 4.11 0.299 18" 1.678 1.700 1.7*20 1.759 1.759 1.779 1.807 1.829 1.851 1.876 1.^02 1.9-28 1.956 1.982 1.013 2.038 2.068 2.098 2.127 Ci.156 2.187 •2.219 2.24g 2.280 2.313 2.343 2.374 j8° i8V' 1.739 1.755 1.776 1.795 1.817 1.840 1.864 1.887 1.9/1 1.935 1.960 1.988 2.016 *2.042 a.070 2.100 2.119 2.156 1.186 2.216 2.244 1.176 *2.308 2.537 2.568 1.400 i8y 4.38 0.307 r.774 1.793 1.814 1.833 1.851 1.877 1.900 x.9^3 1-944 1.969 し 994 2.022 2.046 1.077 2.10-2 2.151 2.159 2.187 7,216 2.*244 ^7i 2.304 2.534 2.364 2.396 *2.428 i9" 3 音 4.54 0.515 WV 1.850 1.850 1.868 1.888 1.9 了 3 1.956 1.956 1,978 ■2.003 2.028 a.05; 2.081 2.109 2.133 2.161 2.189 2.219 a.-244 2.-273 2.303 2.33? 2.36; 2.39 ミ 2.425 2.445 I9r 20" 1.867 1.886 1.905 1.916 1.947 1.969 1.990 2.013 a.o?7 2.061 2.089 1.115 a. 1 40 1.165 2.19a 1.221 2.249 2.276 2.S04 2.553 2.362 2.392 2.423 2.452 ■2.482 ion 5 聲 4.69 0.323 - 1.925 1.94。 1.659 1.983 2.005 2.026 2.048 2.071 2.095 2.122 2.146 2.172 •2.199 2.22գ 2.253 a.28c 2.308 2.554 M63 2.392 2.422 2.45。 2.479 2.5 1C 20iM 21° 1-959 1.977 1.996 2.020 a. 040 2.060 a. 08 3 2.106 2.129 2.155 2.179 2.206 2.229 a.257 2.284 2.513 2-337 2.364 2.393 2.423 2.450 2.478 2.509 2.545 •21" 3i 4.85 0.532 2 I 2.016 *2.034 *2.057 2.076 2.099 2.120 2.140 2.164 2.189 2,214 1.140 2.264 a.^88 2.319 2.343 2.368 2396 2.425 2.452 2.479 夂.5。9 2.54/2 2.570 2 ず 斗 5.00 0.340 22’’ 2.051 2.070 2.094 i.t 14 2.134 2.153 2.178 2.100 2.225 2.248 2.297 2.324 2.549 2.374 2.400 2.4-28 2.455 •2.482 2.51c 2.543 2.57。 7.596 22° 4" 4P 5" 5^ 6々 广 IV 8'， 8i° 9" gr IO_ ioi， ii" ur 12" T2i° 15" T3F 14" ず 151 16" I7" i8，# i8V， 19， I9r 20" 20^ 71° 22° 4i 5.16 0.348 TABLE XX. Sizes of Lattice Bars for channels of various depths and spaced at various distances. D=z depth of channel and d = distance between inner faces of channels. If the value of d lie between the values given, the size of lattice bars is to be taken from the column containing the next largest value of d. t D Sizes of Lattice Bars. d=D. d=i.25 D. d=i.5 D. d=i_75 D. d=2 D. 4" ず rx ず r x ir ず 5" Vx ず r x ir rx ii' tx 中 Vx 6r ぐ X ir rx ir rx ir r x ir Vx a" r rx ず r x iF 去" X a" if 8^ ^ X 中 X で A"X 味, r か X 才 ■Ä"x Ä,;x ボ ず iTX ず 1。， が 'X 7\r- tTx 舟" X ず 11* l^x 才 rx r x 迹’ I5# rx rx 烀’ TABLE XXI. Sizes of Single Rivetted Lacing Bars for channels of various depths and spaced at various distances. D = depth of clianne1, and d = distance between inner faces of channels. If the value of d lie between the values given, the size of lacing bars is to be taken from the column containing the next la iff cat value of d. D Sizes of Lacing Bars. d—D. d=i.7^ D. d=\.$ D. d=i. 75 D. や D. 4" ヤ ギ rx ず r X ゲ， i"x 成, 5^ rx ir r X oT rx Ä-X %• A,yx ^ X oT f；x {V x 2" Wx ■h'x r ^ X ず ふ,, X 丑" X ず ず か iV X n ず r ホ ず Ä7,x A/7x rx ず io¥ 舟,, x ず r rx rx ダ， 11* r rx ir r x ?r 15^ rx sr rx ， TABLE XXII. Sizes of Stay Plates to be used in connection with latticing or double rivetted lacing. -^ = depth of channel, d = distance between inner faces of channels, t = thickness of stay plate, l = length of same and n = number of rivets on each side of stay plate. If the value of d lie between the values given, the size of stay plates is to be taken from the column containing the next largest value of d. B Sizes of Stay Plates. d=i.25D dz=i.^D d=i.yc)l>. d=-czD. t i n t i n t i n t i n t l n 4" r 4r 3 r 4r 3 t 3 V 5 r sr 3 5W r 5" 3 r sr 3 i" 5 V 3 i" sr 4 r 5" 4 6" V 5F 3 V 6" • 3 6 耙 3 r 6r 3 r 6J" r r 3 r 3 6 聲" 3 r r 3 r 1 ゼ丨 4 8" 3 祝. 6 聲" 3 ■h" r 3 iT 4 1U 7V 4 ず iV 3 7r l か 8" 3 ■h" w 3 菇" •8*" 4 I。" が 8" 3 8 去,， 3 Si，r 4 A" sr 4 A" デ 4 12" r 8 音" 4 t 8 聲〃 斗 9" 4 r 9^ 4 1 5" r I。" 4 r u,f 4 12" 5 TABLE XXIII. Sizes of Stay Plates to be used m connection with single rivet. ted lacing. D =. depth of channel, d = distance between inner faces of chamiels, t — thickness rf stay plate, l = length of same and n = u umber of rivets on each side of stay plate. If tlie value of d lie between the values given, tlie size of stay plates is to be taken from the column containing the next largest value of d. B Sizes of Stay Plates. d= 1.25Ü dz=i.c)T> d 二 1.75 1). ケ D. t i n t i n t i n t i n t i n 4" r 6" 4 V 4 r 5 r 7V 5 r 8" 5 5f# r 8;/ 5 r '«r 6 r 6 i" 9V 7 V I。" 7 6° V 9" 5 V 5 ior 5 r i ず 6 r n° 6 1" yf ioi" 6 r nv 6 ur 6 r 12" 7 r i ず 7 Zn ii" 6 -hn i ず 6 ■h" 1*2" 7 A" I ず 7 13" 7 デ 12 n 6 各" ，ダ’ 6 ■hv 6 ■hf, 14" 6 ■iVf mF 7 IO" W 6 長" 14" 6 が nr 7 各" 15" 7 7 12" r 16" 8 r 17" 8 18" 9 r ず 9 15" 20" 8 r 22" 9 r 24" 10 DOUBLE INTERSECTION WROUGHT IRON RAILROAD BRIDGE. 3 沒 1 斗 U.OO 41>^V| クリ. 吁* ” 山 レ w « * フフ り… , / t r — , - … U W Q 39.81 44-43 49-58 54.66 60.3 c 66.281 72.62 79-^ 86.5? 9$. わ 34^ S 38.97 43.5〇 48.56 53-56 59.1。 64.981 71.22 77.83 84.79 92.11 35， C 38.14 42.59 47.37 5^-48 57.95 63.7 叫 69.87 76.56 83.” 90 .4」 35V 8 37.54 斗 1,72 46.41 51-43 56.79 67.48 68.54 74.94 81.6c 88.8? .36， 7 36.56 40.85 45.47 50.41 55.68 6 し 29 67.24 7?-55 8C.-2C 87.22 财 8 55.8。 40.00 44.56 49.41 54.59 60.12 65.98 7-2.-21 78.74 85.6 フ 37， •2 35.07 59.21 43-67 4&44 53.54 58.97 64.74 70.85 77-32 84.1/ 17 V — 7 34.55 33.^8 4^.8〇 47.49 52.51 57.86 65.54 69.56 75*93 82 ふ： ル 4 55.63 37-66 | 斗 1.96 46.57 5し51 56.76 62.35 68.28 74.56 Bi.i: 财 — ル97 36.90 41*14 45.68 50.53 55-7〇 61.-21 66.98 75.25 79.76 59' 叫 I 36. 1^ 4°-^ 44.“ 49.0 54.67 60.0? 65.84 71.92 7ん3，） 39*， U.6/ 35-47 39-5ぞ 43*95 斗 8.6/： 53.66 丨 58.94 . 64.6c 1 70.65 77.cc 4〇, 31.〇 34.781 59-〇 W 47.7 ょ 52.6, イ 57.9' 63.541 69.4 1 75.“ TABLE XXIV. Table of Working Stresses in tons of 2000 — for Square Wooden Pillars calculated by the formula P = ,0.625 where P is equal to the Working Stress, A the area in □ inches, L the length in inches and D tlie length of side of square in inches. Length. 3" sr 4" 4V， 5" 5r 6" •:6 各" 1.. 7¥ 8" 8i" 9" 9F IO" 1。*" 11" n 蚤" 12" 12卷" 1广 il¥ 14" 15" 16" 16*" 17" n¥ 18" 18^ 19， 城 ao;/ か I. IC 1.91 3.02 448 6.51 8.5 j 11. u 14.10 J7-42 21.74 - 2538 29.90 34-79 40.05 45.66 51.64 57.96 64.64 71.65 79.01 86.71 94-74 105.10 111.81 j 20.83 130.18 159-^6 149.86 160.19 170.85 181.81 193.11 204.72 216.67 228.91 8 が 1.00 1.74 a.78 4.14 5.86 7.95 10.43 13.30 16.56 20.20 24.24 28.65 33.48 38.61 44.13 50.02 56.27 62.87 69.82 77.12 84.75 92.73 • 101.04 109.69 1 18.69 127.99 157*63 147.6。 157.87 168.52 179.45 190.71 202.28 214. 22 226.45 9f 0.91 1.59 2.55 $.83 5.44 7.45 9.80 12.55 15.69 19.22 23.13 27.44 52.12 37.18 42.62 48.42 54.59 61.10 67.97 75.20 82.78 90.69 98.95 107.54 1 16.48 125.74 155.54 145.26 【55.52 166.10 177,01 188.24 199.81 vii 1.68 叫 .89 9ri 0.83 1.46 M5 3.55 5.07 6.95 9.21 11.84 14.86 18.27 22.07 26.26 50.84 35.79 41.12 46.83 52.90 59.33 66.13 75.28 80.78 88.63 96.92 105.36 I I4.W 了”. 45 13 1.00 142.88 I53.C9 165.63 174.51 185.69 197.22 209.07 211,16 icy 0.76 1.54 2.17 3.29 4.73 6.51 8.65 11.17 14.07 17.37 21.05 25.15 29.59 3443 39.66 45 ■仂 51.24 57.58 64.28 71.35 78.77 86.55 94*67 103.15 111.96 121.12 130.61 140.45 150.61 161.10 171.94 185.09 194.58 206.40 218.53 ioJ^ 0.70 1.գ/. 2.01 3.06 4.41 6.10 8.14 10.55 13.34 16.51 20.08 叫〇; 28.38 33.n 38.25 43.72 49*59 55』4 62.45 69.44 76.77 84.48 92.52 100.9 2 109.69 118.76 128.20 137.97 148.09 158.54 169.51 180.43 191.87 203.65 215.76 IV 0.64 1.14 1.86 2.85 4.13 5.72 7.66 9.97 1*2.64 】 5.70 19.15 12.99 27.21 51.85 36.8; 42.22 47.99 54“ 3 60.64 67.54 74*78 82.39 90.36 98.69 1〇7-37 116.39 125.77 135.47 145.53 i 55.93 166.65 177.72 189.12 200.84 212.91 叫' 0.59 1.06 1.74 2.66 3.87 5.38 7.22 9.4: ji.99 14.93 18.26 21.98 26.04 50.59 55,48 40.75 46.42 52.45 58.86 65.65 72.82 80.3 3 SS.22 96.46 105.06 114.01 I2J.3I 132.97 142.96 153.28 163.95 174.98 186.28 197.99 ■210.01 I2r 0.55 0.99 1.6*2 a.48 3.62 5.05 6.81 8.9] 1 1.38 14.11 17.42 21.02 ^5.〇1 叫 59 34.16 39-52 44.87 50.80 57.11 63.79 70.58 78.28 86.06 9P4 102.75 111.62 120.84 150.43 140.32 150.62 161.2 2 1 72.19 183.48 195.10 ■207.07 1 2 が 0.51 0.92 1.51 3.59 4.75 6.43 8.4 斗 10.79 13.52 16.62 20.11 W.98 な8.25 52.89 37.94 43.37 49.19 55.0 61.97 68.92 76/25 83.95 92.02 100.44 109.23 118.35 127.88 137.73 147.97 158.49 169.37 180.60 192.17 204.08 0.48 0.85 1.41 a. iS ?.I9 4.48 6.08 7.99 10.26 12.87 15.86 19.24 22.99 27.1 斗 81.67 36.59 41-91 47.61 55-7〇 60.17 67.02 74.25 81.85 89.82 98.16 106.85 115.92 125.35 135-12 145.25 155.72 166.54 177.71 189.22 •201.07 W 0.44 o.3c 1.32 2.05 3.01 4 •■ょ 3 5-75 7.58 9.74 12.27 15.15 18.41 22,05 26.0 y 50.49 35.30 4〇.49 46.08 52.05 58.4】 65.16 72.27 79.75 87.64 95.89 104.5° i[3.47 122.81 132.50 142.55 152.94 163.69 174.79 186.23 198.05 H' 0.42 0.75 1.24 1.92 2.83 3-99 5.44 7.19 9.27 1 1.69 14.47 17.62 Ü.I5 25.06 29*36 34-^4 39.12 44-59 50.45 56.69 63.32 70,33 77.73 85.50 93.64 102. J 5 Xi i.öj 1 20.-29 129.89 139.84 150,19 160.86 171.88 ^3.25 194-97 1 4^ 039 0.70 1,17 1.81 2.67 3.78 5.16 6.83 8.82 11.15 13々 16.88 20.29 24.09 28.27 32.84 37.79 43.14 48.88 55.02 61.52 68.45 75.71 8;.;8 91 半 99.83 108.62 117.77 1 27.29 137.17 147.40 1 58.00 168.95 180.25 191.91 15， 0.57 0.66 1.10 r.7i 2.53 3.58 4.89 6.49 8.40 TO.Ö4 im 16.16 19.47 <23.16 27.22 31.68 36.52 斗 1,75 47.37 53-39 59.78 66.57 73.74 81.29 89.23 97.54 106.21 1 15.28 1 24.70 133.87 144.64 155.16 166.02 177.25 1 88.82 】5V 〇-?4 0.62 1.04 1.62 2.39 3.39 4.64 6.18 8.01 10.17 12.65 15.49 18.7。 22.27 *26.26 30.56 35^8 40.39 45.89 51.79 • 58.07 64.75 71.81 79.25 87.07 95 •な 8 103.86 I 1-2.81 122.14 131.84 141.89 152.32 J 63.13 174.25 185.75 16' 0.^2 0.59 0.98 1.55 2.-27 3.22 442 5.88 7.64 9.71 1-2. 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I ブ /X. - — — — — - — — — 0 J . J)^Jh Ck of Z マ i4 s S . - •••-• Zö ft 、 Ln/o io - - /ZOO A y^tr Ctrv. f,t . 及 必ン 厶么^ •、一 -• 一 • _ • • /0 サ〇 格，, ； ., 二 Mjr> 心 ビ で々". 、、一 一 - - 、 - •も I 幺 ü 〇 # 一 ぬ々 "ポ, /^.33/(r. Z/./tr. - /Z 0 0 ム^ -j/^. J f 4 Ö キ r， f •， 2Z,?oo ホ // 0 公 卜 Truss Diu^r“ 外 j 7% t*o ^3 户 (■ン y む rf. / がぶ. z -/！/ •一 Zo 守 [ : /2、。° 〇 I -3 4 れゞ W 尸し， r-^ ° 厂ジ么 ：“. ， H “ c Lr. 〇 f3 s. ^ //. ^7 n ジン. Az. o Ci 厶刀 口" p" irut,Sj t fit it> 广 !% 〇" fru^f<.t^ lo (k. 一 9 家 r\ 又し々 0 U , S、R, 二/之.？ ö ゴ 卜ぞ乂 H、/ み. バゴ, /i. 33/(r. : U .fö. /Zo o^ J»**' ム， J/^o 芽 〜 — 2Z,^oo 7t- P T/ •£ A f^ “ ミニ/ ^/3. D /t/x 3〇 t. ― }/- ^ シ乙 S 〜 -. Tah-4 ^ a^A Cf/ ^lytSS - -Liv^ ac^ ^ - 一 ^ 0 A aL. - — /Z of か、 ‘， 1 0 f た、 2//，. ./〆 ゾ ä/j* “I ir/L, n = /. / / a 7/ C^%yzAt x/?. 二 尺 『口 x 3^i ， ： Z2 d " Z[s =r ス J. 0 Jot. S^c. on / Tut^C S l2Jxa-^ /厂ゾど = 7-/^ a" 丁〇か J'ii. =. Zi-ii'o' ?■ /p- Z2.^i- n Vru^s JPra. / Of' a- -t__ , I "TTirt-c^ ， ん -e. .3? ふ. 4 ノ ,4/ ノノ.《. gA?u" 4 ZU% XR.-131 d ' S, “ゴ, , 2 Cs-. = ノ. 〆 7»^. Sie.. — ?, ^7 o /ff. Z-Cf S. M. = Z4-. oi' p' /Df. j/f 5. ぞ . =/4.ö 知’, ^-4V3|w- ",2 い.， ZCs. ，• J. 夕 .口" 75¢ . /t e^e-C-e-S^. - _ /3 a /^, 7- //. Z Z .ル JZ^> 弄/ >tr" /从〇 养 ，. U ふ产 A- 7Ya な X X / 1/ . ノん 〇/6. 2 〇 产 . 一 Z3 〆. ノ - ノ U 〇 年 户 か バ w . ,。， 一 / 3 〇 〇 『ハ " ，• 一 /Z か’ /々O' ん S-rctx!^^- ァ/决 な XX iiy JL-/Z 二： U 卜 奪'、/， % = 7. / 3 u" ~nt. S^c. = 2./. i'J a " ?J.i%/' S. ^2 /.i% o' 4-/2 "-30. n .c 二/ 2m '' ゞ / fFL = 7, ノ 《3 口 7~if i • J^c ^ ■«- か- 心 口 f2.2 アブ 5： 尤 ミロ" ^C./lZ 义 ，.ニグ. バゲ 7 ジア 从ノ， " n= テ, 43 ü ノ- 分!^: /. バロ" : Us す X n ゲ 石 ど .ム 《••二 乂 3 < ° アム 如 «T •，二 乃':; T ノ ö " "7、从 し n ,. 广ぞ， : /s.i い X^- */J. /> P ICs = 2,2 a，； m SUe- ^/ir, 3 o, Z-2-^7 / / ,, S •尺. r ノ/ •厶 /a 今- f 、 ネ豸； /厂 ブ I 口 2r>. ズク./ ジ ゲ' 丁 ott s-ec - =/尤/ ノ D • y — ラ、 tT £T <9^* e t. ザ r 枝 =フ， / 〇 " フ ctln( 〇^ jJa.(^u リ^^ ^ — _ ■ • 〇1 ゎ一 “ : 一 — re-ど Cf C^, c/ ^fufS - - 上 2rt/<. Zo Ck え 〜 一 _ 刀 fad~ Z 〇 a. cC - — 一 i 外 ダ f K 心 -C4C (T^ s / - 一 / ん 〇/6, 厂 之。 产, ハ〆， /Z パ ツ W ’ 一. ，じ， ノ 3 〇 〇 # '• " 〜 / ノ ，ア "ギ •-ク y -;>v,v> V 尸 ど》々 2277 身 - /ra 〆• - Z 23. -/Ar〆 户ハ / 3 各 c1 卜" / ムイ 6 . Bf “ 〇卜 - - 今 <2 ゴー ht-r (■ *»♦■ - J- t . 2^〇 ^ „ ，‘ V * 斤》々 ^2rr /'t'OL S S uD-r a. a^a. err- 6 . ^ c . 2^f. ア a " /Ö 5~Z3 . 5,/f. ^ 2^.y / T2. S. ぞ = /义 / a' /A // / XA ^/O./^ C7/# ム ，ン冷、 L 0 口., ノ/ ■>• = ス / 口 " / 办 t r=. / 〇 ^ ^ p >f 又7, S /r s 又 : 1% n プ /j ん 《?"' 义 ，.亡/ ス " p" 先 \ ff 〇 ゴ 2c^. =： 2. y ° Tot, Sn *v ス f C7 ‘ s ./f. 二 之ク •ク ei v ノ /ジ. S//, S. >f.^/ J/D ’ 2-/; 设、,、0〇 W 2-/沾々= スバ。" ICs. ^ i. fß a" TaH. =2/3^ a，r チ ö^^S" 冷 シ .•ん 石が ン "a. ■= フ,〆 a ’ 丁ん ム Z . ^ Ä***"^r — — - •> V». » ■» ■— -_ 八- イ 七艺 s — — — — — — / Cf /2t —一 — 一 一 一 - 刀シ^0 咏 〇ア jV . - _ _ _ , ム tu り loee dn_ - « 一一— 一 « - / む/ベ y / Z/ •々ボ ‘ 23. -/Ar〆 j0^o.(?u て 〇 久〇1 - •一 一 / 3 ^ 0 /T >rգcyL<^ < で ど 必 J* / - - _ 一 L 〇 OLOL- デ yt^ 1> 0 Ao~n ノ- — 一 一 を K “ 〇‘ ■—*• — ザ ふ-。 - 2?〇 ^ .. /^c . ^6 •パ' S 、r 、Qur K H V “ w r/ 4/ 之 K y、 =_7V 乂ヽ Ir n/y = w KI XI 7./N CJ Kk-N u-/ y ゾ p フン。#' / S'0^/3*r し-/^. ^ „ '■ '■ r/ ノ <■ Z IT ギ产 er じ- ’ 产 ^ , ü. J^SVL, I、 ン 〆 r し ül J^KTL. D t ec •卩 T oc ザ yi- ノ OY* 久 ノ ‘ 0 ä-v-w # / ArrocA.j ん 2 夕 4 >v^l，^Cg^ し/ 1 .し Z 23 产し〇 .心10“ ，_3々\i/rn、 ^ 7 a] 丁 ot 、 s^c . =- z^&. n 口 H-Zfi. s.mm" zH3Jlh2、” a” ュ クタ。 口" Tot. «f.e „二*»〆 a* /0^.7U. サロ" l- ti. "—ht-l.^C -2.^-, 77° /-%'^zoyL = 7-^ aA ァ。と s^. ^ 3J.z/ ^ "L /?S y. ぞ .= 3 2.2/ 口" ，'ン . r/. US Zfl - 2 ^ o g -/cf.3Z a' ；.^.s/0. 3S uf, 7%K /, 心 r/ ジ .r/P ーゼべぞ：川 Q>, i“. = ふ" p" ^e. — /C.i f o /r S 2. is% , z.^ - o,f /3y, i32. H = /^.t>? Ü“ 之-^^ みぐ： Z 今今00 之 Hw 气 2Cs. = 2.f 0^ 7ö しぐ ふ す/ f. D ⑴，” え、 S-^2ZiT3 〇 ノ -音シ 4 = / , //〇 v 令- V x 今 f 二/ 3. trz ゴ1 2^. _: 7 " 口 了“' 々ご. D，y t な. £/f、 ム c, = ス / 〇 7cct>l^ Oi _______ /Kf 〇^ • 厂 aT^\. — oJ l^ucS'T - Lt ul ^l. ~ — jÜ-e/t at. l0 a.oL - 一 - 一 _ — ■t-HgtnA £^ご之仏 一-—- _ ~}^ t*tal Ita trx ^>crtfe7rt e- ム トビ ，r«-*^'*y'rt.ji la6-eC - - - — - /心 A. か/ ム Z ‘舛' / / ム •/’. /4 “ザ * - ： ，厂 / ノ 41 ■之 有户 er ■し*.〆, •2 ヲ〇 ^ " " 丁 Tt^S S /0> ■I TUle ^JM：. / 7 U ’ S 产 , 77trotyt^A. Srt'oi ，み i-n-3o. " 卜％1'} cZc/丨 PL: スぬ0 r0c. St^t. —2^C.o8 p S.Z-2L08 <=> '' a a" 2.- /• ^~S [: 2-A. 今 ダ。 -Z — ノ 之 一斗 4 了？ C 二 2し 客/ /-^y^oVL = 7'^ 〇 ,r /-%W' 戶乙 ' = 7, 广0 、 'To&. = $J3.AS~a" Tiz^. Si.e . - 3^. $' / a // ん 冬 アグ. s.^.^32.Mb~p" /2/. Z3C, SA = 3A<3/ > mu 上 叫 (> 3.2 SO 5. ぞ.= /o.yya " 之 一 iyiV=7xo ゴ, z 匚 公' 二 3.3Z 口‘ 706. S<,c. —/〇. ^2. ü，/ S3, ,gi / ク. < ノ f 22. 斗： if か, /// s.K.-n.^So" 2-/V メ 3ゼニ8 •砵ゴ -? 〇, = 3. 奴 口’ 7ö〆. Jld- - //, y C a 92. 0 2.0 / ら. /“ JJ. け 4 ) b (a 、 又 ぞ .=/ グ .rr □ ’’ フ- = /. fS a 7/ 2 - 2CS - 3. 3z r'" Tc(. See.. = / 夕. < 今 ^7 7 2 〇 、 ノ g 3 外，“？ /?2. 73〇 义 /?. ニノん 3 7 ci ^ ぃ 耳 a ヶ I 二 2/. Z い,, 之“ ■= 3. 3 之 口’ ん 6 «Tcc, = Z“. 6 S 〇 ^ 一* 一 一 /Z 乙 /A^O^C i9/i t JV し = 又 3 之 C7" H 〇/ 刀 ▲. S ^9 CCy^i^. 一 — 一 - - — - - /V^?〆 尸 〇认 レし：—〜 ムし し （凡 卩 汰 一 一 JJc^hCh. a/ L /^lc CX JLtlZ-C louU. ^ - 一 』 シ Ä 〆 l 0 CL 丄- ，- 一-— 一 一 •一 [ ä メひ rt ^X>C^S S h 八ん IoclcL cryL. ö ’了 fcr\ 公表 e/fy* 名 レし C^a ^ - - J 7 〇 / そ、 z/. zr/t パ,. "6 -〆/^ し、/ か / 今/ バ ぬ： (>0 0 cAerr 义 4 4 〇 /yc^r- /^〇 • ノ^ f • y … か 3 /〇 © 、 A v> l ふ ^ 一"^ J.O/ .~l ly ~ rl 3 = . fv ‘ 7 c s 0 、 气 b h'o/ UJts/ zf olz b ? ベ、 ミ" » < oi ^fQ co N ‘p i/ !~ Eff、 レし st t 3 ^ 〇 0 ^7ui oj! ' 。户 脉 ■*<- ~- — — -w — I ^ 0 ^ 亡- hr 一 呼 ru^Us — 2 7^ yt~ft9tyt^ €^3CCC^S - ，一 一， 名 S) 6 0 0 ゃ 'T/l/ri yt-d, Iocl 3^ 0^ - i c~^CÖy^ Cy/\,o^ii. 4^ 3 ^ 卜 ~c^~ ^r-cu^s t / uct^- 一^ 3 n な み^. f n XJ、 4 忍々 XKZX, ノ-， ^ Cs 7c /fo /f, f. ノノ， r/r, 3o/t, / / パ \ / 0 " “ f/ 。チ 々 3 o た^！^ f わ' 亦 3 S~0' ✓/ " ひ 丁 r U.^S hi «:フ ret -‘ y oy^ 心， 尸〆《 冷 XKZX > m oi ( C " ■?/>, z=_4>.no" 厂ぬ 心 0 々 "“ C^Sf. 一 一一 一 - 〇〇 ^ ^ io rto24^ C Aöy 义一 一^' 名 6 キ 户もゲ 乙 、 ^ ■も、 ^ t 〇 U. 4^ ••，一'-"-〜 — 3^0 •• " メ’ み / fO s 严、 (ASS ßlCL£fy 久ァ ^ レ : f or ん 吃 -rouL^h, JD r^ c dj . 之-/ ゲー々 〇’ [二 1 各 ，0 0 w I -％ WK， 7 .パ。, T^s An ミ/. 丨 / 〇 ' / ノス％ 尺 LJ?.^g7AZo 2-/6- -4/. ZA /^vzm. 丁 fit、 S もし '.没0,:, i-n-'^y 『な p" i 2 ベ ！ 〇 .双 n レ Jf バ ，• 7 fit, S-eC /2B^77. s.^2^/o° U%3ok 卜 R、 二 3 谷 •み キ £：:2^.2^ビ パ〆 私. ノ令〇 ' ST0. /OiXLL- いべ 73' ." S.X. =： /(?. OZ D 2 Cr. = /i ど. JVc. =v ジノ 冬 p " J-汐, 23, / 么 o or 夕 irz. rf/ 7々. nr s.^^//.^fo ノ -Tv。 表 m-^v 2C^. = W // ^./^. o 1 アん /フ(> f/^ /^：2 9J ノ^, 3 ダ r ,, nt7 ね 口 み K 一 2.7““ 之 乙 s、 二 么 ダ/' 口' 7ot. s^e. 〇 / へ */ ^xkzt. 7 一 • —— ^ 2c 0 f 亡， f 一一… 、ZZ,U/6. / / o 〆 产次 ムレ，; f 亡、 - • — 一 一 0， " ” ’* g? •わ 0 象 py'aL - - ^ 3iT^ pC . 一 .-J/ クタ〆 ." " ルな ~XXKR\ Zao 's/» 2 — /C— Jf-t 口 /-泠"メが乃；=,2 デ0 丁 ，t. Uc. - 3J.2i~° ///.3i'0. sx-=2j. r/P a.； ■紡. zf い 巧- /7°"„ ^22. fL- ~o T,t. See. = 37.1 I c /Z?. C /4 . S-K.-27.// ^ /r レ tSS ^t(X.yrA / が 么 . 典 プん -3 t" t も， njo{ 3 バ ^■*77 , ノ r ぶ •> f.^o a， Tti.itc- -==/*. i ^ a i-3. r// xi. tn. 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DAS LEUKOSKOP. Es soll im Folgenden ein Instrument beschrieben werde», welches ich zuerst unter dem Namen 11 Leukoskop M (^€VIZOS—6 ICOTTO) in einer kleinen nur für einen beschränkten Leserkreis bestimmten, Schrift ャ bekannt gemacht bal>€. Das Instrument, wie ich es nach meinem eigenen Entwurf construiren Hess, ist in der Fig. 1. Tof. dargestelH, und zwar im Horizontaldurchsolmitte NjNjs sind zwei Nicols Prismen, Kt K2 bedeuten zwei in gleicher Lage befindliche Kalkspailirliomboeder ; G ist ein dünnes Glimmerblättclien, so dünn, dass es zwischen zwei gekreuzten Nicols eines Polarisations apparates augebraclit Interferenz- farben erster Ordnung zeigt, d. h., entweder bläulicli-weiss, oder gelblicli-weiss erscheint ; 6 eiu Spalt, dessen Breite durch eine geeignete Vorrichtung nach Belieben geändert werden kanu. Q ist eine senkrecht zur optischen Axe gesoli- liffeno Quarzplatte von gewisser Dicke, über die noch beliebig verfügt werden kann Q2 Q3 sind zwei ebeu falls seuktreclit zur optischen Axe geschnittene Quarzkeile, Q4 ist wieder eine Quarzplatto h 12 h U sind Linsen, ileren Brennweiten so regulirfc sind dass das beobachtende Auge von )4 aus ein scharfes vergrossertes Bild des Spaltes und zugleich ein scharfes Bild entfern tor Objecto sicht. T ist endlich ein in Graden getheiltcr Krei«, an welchem eiu mit dem Nicol N2 beweglicher Zeiger Z spielt. Das Ganze isfc in einem inwendig geschwärzten 1101 ir enthalten, um fremdes unwillkommenes Licht abzulialteu. 、Vio mau sieht, ist das Instrument Leukoskop eigentlich nichts anderes, als ein Polarißationsapparat und besieht im Wesentlichen aus drei besonderen Theileu, welche ich einzeln beschreiben will. Der erste Tlieii eutliält ein Nicolsches Prisma N1 und isfc mit leiser Reibung in dem Eohr des Instrumentes drehbar. In g. ist das Nicol- tragende liolir durch eino ebenfalls mit leiser Reibung drehbare Metallhülse verschlossen, woran ein so dümies ölimmerblättchen geklebt ist, dass es, wie bereits bemerkt, zwischen zwei gekreuzten Nicols Interferenz färben erster Ordnung zeigt. Wenn die Metallhülsc an welcher das Gliinmerblättchen geklebt ist, so gedreht wird dass eine der Hauptsclmittebenen des Glimmerblättchens den Winkel 45* mit der Polarisationsebene des Nicols N1 einscliliesst, so erscheint eine der Interferenz- farben im Maximum ihrer Intensität. Da dio Metallliiilse, welche das Glimmer- blüttcben tragt, auch in dem drehbaren nicoltrageudon Rohr gedreht werden kann, so ist man im Stande, den Winkel zwischen der Polarisationsebene des Nicols N1 und einer der Hauptschnittebenen des Glimmerblättchens und somit die Intensität der Interferenz färben nach Belieben zu ändern. Wir wollen diesen ersten Theil wegen der Bolle, welche er bekommt, “ CoinpeusaLioiisnicol ’’ nennen. * D Kitao Zur Farbenlehre, eine Inaugural-dissertation. Berlin 1887. — Ueber dio Entstehungsgeschichte dieses Instrumentes sieh die historische Notiz am Schluss der gegen- wärtigen Abhandlung. Der zweite Tlieil bestellt zunächst aus zwei Kalkspatlirliomboeder Kj und K«, welche hinter einem Sparte (ざ) so angebracht sind, dass die Richtung dev Linie, welche die spitzwinldigcn Karten des Eliomboeclers mit einander verbindet der Richtung des Spaltes parallel ist. Aendert man nun durch eine passeiule VorricLtung die Breito des Spaltes, so kann man bewirken, class die beiden durch das Kalkspatlirhomboetler erzeugten SpJiltonbilJer sicli so innig berühren, dass man also statt zweier Spaltenbilder eilt einziges Bild sielit. Die Combination zweier K al ksp a thvli omb oed e r hat keinen andern Zweck, als die Anwenclung eines Kalk- spath rhomboetlers von liinreicliend grosser Länge zuumgolien und zugleich möglichst grosse Spal tonbilder zu erlialteu, was belmfs der genauem Yergleichung der twaigen Färbungen der beiden Spaltenbilder notliweudig ist. Unmittelbar nach dem zweiten Kalkspatlirliomboeder K2 und der darauf folgenden Linso 12 ist oino viereckige Oefinung in dem Eolir des Instrumentes ange- braohf, wo] ehe mit einem an einem Cliarnier beweglichen Deckel vessclilossen ist, und dazu dient, eine Metallliülse aufznnelimen, in welche seukreclit zur optischen A^.e geschliffene Quarzplatteu verscliiedoner Dicke eingescliraubt werden können. Der dritte Tlieil bestellt endlich aus zwei Quarzkeilen, Q2, Q3, welche ihre Solmeiden in clio entgegengesetzte Kiclitung kehren und mittelst eines oben mit einem gezahnten Rtul versehenen Knopfs in entgegongesefezter Eiclituiig senk- recht zur Axe des Instrumentes bewegt werden könuen. Dieselben sind so gesch- nitten, dass die eine ICatlietcnfläche senkreclifc zur optischen Axe stellt, und drehen tlio Polarisätionsebene eines Liclits traliles in domselbeu Sinne, wie die Quarz- platte Qi. Unmittelbar hinter diesen Quarzlceilen ist eine ebenfalls senkrecht zur optischen Axo goschnittene Qaarzplatte unbeweglich eingekittet, welche aber die Polavisationsebene in enfcgcgengosefcztem Sinno dreht, wie die Quarzkeile Q2 Qs und ihre Dicke ist dabei so gewühlt, dass wenn die an der einen der beweg- lichen Keilo ftugebraclito Soala auf 0 zeigt, die Dicke der eingeschalteten Quarz- keilo gerade diejenige der Quarzplatte Q4 aufLebt. Es ist dies demnach genau die Vor rich fcung welche bei dem Soleil’sclien Saccharimeter Anwendung findet, um jede mögliche' Quarzdicke innerhalb gewisser Grenzen zu erzeugen. Die Scala an den Quarz keilen ist bei meinem Instrument so oingericlitet, dass man die Dicke der eingesclialtoten Quarz platte — d.li., den Uebeusclmss der Dicke der beiden Quarz- keilo über diejenige der Quarz])latte Q4 ganz bequem in eines Millimeters un- mittelbar ablesen kann. Hinter der Qaarzplatte Q4 folgt ein zweites Nicol’sches Prisma, welches wir fortan das Oculaniicol nennen wollen ; seine Polarisatiönsebene wird durch den gefclieilten Kreis T bestimmt, an welchem der mit dem Ocularnicol drelibare Zeiger spielt. , Ich bemerke biorbei, dass Herr Professor von Helmholtz, von dem die Idee daroli deren Verfolgung ich zu diesem neuen optischen Apparate geführt wurde, auch fiiL* sich ein Leukoskop consfcruiren Hess. Die Beschreibung dieses Instrumentes wurde von einem der Scliüler des Herrn Prof, von Helmholtz in verschiedenen Zeitschriften veröffensliclit, uiul aus derselben gellt liervor, dass Herr Prof. Helmholtz bei der Construction seines Instrumentes mit dem Leukoskop cine Ycrbesseruug vorgenommen hat." Es liegen nämlich in dem Helmholtz ’sehen Instrument die beiden Kalkspathrliomboeder Ki und K2 nicht hinter dem Spalt (5)， wie in meinem Instrumente ; sondern sie haben den Spalt (6) zwischen sicli und ilu’e Lage ist so beschaffen, dass der optische Hauptsclmifct der beiden Kalkspath- rliomboeder senkrecht zur Spaltenrichfcung zu stellen kommt, wobei die ELom- boeder selbst ihre spitzwinkligen Kanten gegen den Spalt kehren. Diese Anordnung der beiden Kalkspathrliomboeder hat nun den mileugbaren Voi.tlieil, dass man ein entferntes Object 011113 Unterbrechung an der Trermungsliaie des Doppelbildes des Spaltes sielifc ； dass man, wenn das Object auch in verschiedenen Tlieilen ungleich gefärbt sein sollte, den gleicli furbigen Tlxeil desselben ununter- brochen durch die Treiiiiiingslinie des Doppclbildes erblickt. Bei der Anwendung eines einzigen Rhomboeders ersclieinfc Jiingegon ein enfc'cniter Gegenstand an der Trenn ungslinie des Doppelbildes so verschoben, dass mau gleichzeitig einen und denselben Tlieil eines entfernten Objectes in den beiden Spaltenbildern sieht uml zwar so, dass die beiden Bilder desselben Ol>jecttlieils sich tlieihveise an der Troimngslinie des Doppelbikles übcnleckGii. Icli kann nicht umhin zu behaupten (lass, wenn es sich um die Beobachtung der etwaigen FarbenautlcruDg eines Objects- tlieils handelt, so ziemlich gleichgilfcig sein kann, ob man diesen Theil des Objectes contiuuirlicli durch die Treimmigslinic des Doppelbiltles sielit, oder einen und den- sclbeii Theil des Objectes, unmittelbar aneinantler, an der Trennungslinie des Doppelbildes gestellt sieht. Icli glaube daher clie Anordnung der Kalkspatlirliom- booder, beim Heltnlioltz 'scheu Instrumente iui* keine wesentliche Verbesserung halten zu müssen, so überaus scharfsinnig sie auch ei.daclit ist. # A König. Bericht der physik. Gesellschaft in Berlin 1882. Zeitschrift fiir Instrumentenkunde 1883. Wiedemann’s Annalen XVII” 1882. DIE MAXIMALBLAESSE. Die Efsolieinungen, welche mau in diesem so zusammengesetzten Leukoskope walirnimmt, sind folgende : "Wir denken uns vor der Hand den ersten Tlieil weg, welchen wir mit dem Namen n Compensatiousnicol M belegt haben. Ein Bündel Liclitstralilen, welches die mit dem Leukoskop betrachtete Lichtquelle aussendefc, geht durch den Spalt (6) und wird dann durch das erste Kalkspathrliomboeilei* auf ein zwei in ander senkrecht linear polarisirten Strahlen zerspalten wo sie beim Austritt aus dem Bhomboödor divergiron. Die Divergenz der beiden Strahlen wii'd durch das zweite Kalkspatlirliomboeder ver- grössort und jeder von diesen beiden Strahlen wird nun in der Quarzplatte Qi in je zwei Strahlen zerlegt, welche in entgegengesetzter Riclitung kreisförmig schwingen. Diese Strahlen setzen sich beim Austritt aus der Quarz platte wieder zu zwei linearsolan- sirten Strahlen zusammen, aber mit verschiedenen Schwingungsphasen, so dass sie in dem Oculai'nicol N2 zur Iuterferenz kommen. Man erblickt demnach tlie beiden Spaltenbikleu im Allgemeinen verschieden gefärbt, wenn die mit dem Leukoskop betrachtete Lichtquelle kein monochromatisches Liclit aussendet. Die Ffirbimgen der beiden Spaltenbilder siud aber auch abhängig von tier Diclco der eiugoschalteten Quartzplatte und man beobachtet im Allgemeinem Folgendes in Bezug auf die bei wachsenden Quarzdiclie in den beiden Spaltenbildern auf- tretenden Färben, wenn mau ein weisses Liclit wie das weisse Tageslicht amvendet. Zunächst nimmt man bei der Einschaltuug einer sehr dünneu Quarzplatto, deren Dicke einen kleinen BrucLtlieil Eines Millimeters betragt, sehr wenig Farbeuunterscliied in den beiden Spaltenbildern wahr. Dreht man das Ocularnicol so kann eins der Spaltenbilder so nahezu zum Verscliwinden gebracht werden, dass das andere Spaltenbild so weiss, und hell erscheint, wie das ursprüngliche Liclit. — Es giebt daher auch einen Winkel des Ocularuicols, bei welchem die beiden Spaltenbilder nahezu gleich hell und gleichfarbig d. i. weiss erscheint. Wir wollen diese durch kleine Quarzdicke und eine dazu gehörige Dreliuug des Ocular- nicols herstellbare Entfärbung der beiden Spaltenbilder kurz Maximalblässe bei verschwindender Quarzdicke ” nennen. Diese Maximalblässe ist nicht mehr herstellbar, sobald clie Dicke der ein- geschalteten QuarzplaUe 0,4 麵 übersteigt. Die beiden Spaltenbilder erhalten durch die Drehung des Ocularnicols abwechselnd nur dunkle Fiirbontone wie Braunviolett und hello Farben töne, wie Hellwasserblau und keines von den beiden Spaltenbildern kann mehr zum Verschwmaei], sie können folglich auch nicht zur Farbengleiclilieit gebracht werden. Wird lim) dio eingeschaltete Quarzplatto dicker, so treten immer brillantere Farbentüne auf und die Ungleichheit derselben in den beiden Spaltenbilder wird immer grösser. Die Drehung des Ocularnicols bringt immer neue prachtvolle Farbeutüiio von grosser Siittiguug hervor, ohne class es einen Winkel gilbe, bei welchem dio beiden Spaltenbilder gleichtaruig werden. Wächst die Quarzdicke bis zu 9wm* so treten immer noch klüftige Favbentoue auf ; allein alle Farben- iiüancen, welclie die Drelmug des Ocularnicols liervorbringt, zeigen das Lemerkens- wertlio Bestreben iu die beiden Farben töne Purpur (eine Mischung von Violett und Iloth) mul Grün, die Farbentone welche den Ueborgang yon diesem einen Far- benton zum anderen vermitteln, aber das Bestreben iu dio beuleu Farbentone Blau und Gelb aufzugelien. Uebersteigt die Dicke der Quarzplatte 10 so redaoiren sich nlle Farbentone, welche überhaupt durch die Drehung des Ocularnicols liervorgobraclit werden kann, auf die 4 unterschiedliche Farbentöne rötbliches Purpur und bläuliches Grün, Blau und Gelb. Die beiden ersten zeigen noch eine kräftige Sättigung ; allein die beiden letztem treten in so geringer Sättigung aut* dass sie als Bläulichweiss mul Gelblicliweiss bezeignefc werden können. Diese weisslichcn Farbentöne bilden die U ebergangsfarben zwischen dem rötlilichen Purpur und Grün ; der Uebergaug selbst gellt dabei so rasch vor sich, dass eine sehr kleine weitere Drehung des Ocularnicols sofort in dem einen der beiden Spalten- bilder eine rötliliclio Färbung auf treten lässt. Wenn die Dicke der Quarzplatte nocli weiter wächst;, so erscheinen bei der Drehung des Ocularnicols keine neuen Farbentone mehr, ausser denen, welche oben angegeben sind. Abwechselnd erscheinen nur diese 4 Farbentüne in den beulen Spaltenbildern, so viel man das Ocularnicol auch drehen oder dio Quarz- dicke waclisou lassen mag, das Wachsen der Quarzdicke bewirkt nur, dass die vier auftretenden Farbentone immer geringere Sättigung zeigen. Bei der Einschaltung einer 13 細1 dicken Quarzplatte wird die Sättigung des bläulicliweissen untl gelblich- weissen Farbentöus bereits so gering, dass die beiden Spaltenbilder nahezu als farblos betrachtet werden können, wobei jedoch die beiden andern Farbentöne Purpur und Grün noch eine namhafte Sättigung zeigen. Uebersteigt die Dicke der Quarzplatto 15mm, so verhält sich dio Sache wie vorhin ; es treten keine andern Farben- töue mehr auf, als Purpiu., und Grün Gelb und Blau und die gelblichen und bläulichen Farbentüno nähern sich immer mehr dem reinen AVeiss und gleichzeitig nimmt dio Sättigung der beiden andern Farbentüne immer mehr ab, bis bei der 27 mm 一 28m/« (licken Quarzplatte auch die letzte Spui， von Färbungen in den beiden Spalten- bildovn verschwindet. Die Erklärung der Erscheinung dass die beulen Spaltenbilder des Leukoskops lTnter der Einschaltung einer 10 ⑽ *一13 麵 • dicken Qnarzplatte uudbei einem gewissen Winkel des Ocularnicols nahezu gleichfarbig d. li. weiss erscheinen, geschieht ohne alle Schwierigkeit. Es lelirfc uns nämlich eine prismatische Zerlegung der beiden Spaltenbilder, dass in den Specfcris derselben im Allgemeinen drei dunkle InterferenzstTeifen bei der obenangegebenen Quarzilicke auffcreten, welche gleichsam gewisse Strahlen von bestimmter Wellenlänge, denen bestimmte Farben entsprechen, aus dem weissen Licht wegschneiden. - Es seien A und B in Fig. (2) Taf. die prismatischen Spectra der beiden Spaltenbilder mit den Interferenzstreifen (5i ö2 63 und ö4 ö5 (5o* Wie man sich leicht durch Versuch überzeugen kann, hat eine Anederuug der eingesclialteteu Quarzdiclco die Erscheinung zur Folge, dass die Anzahl der dunkleu Streifen in den Spectris der beiden Spaltenbilder sich im gleichen Sinne, wie die Aendcrung der Quarz dicke, ändert, wahrend eine Drehung des Ocularnicols eine blosse Verschiebung der Interferenzstreifen längs cler Spectra bewirkt. Es ist demnach klar dass es bei der oben angegebenen Dicke cler Quarzplatto durch eine gewisse Drehung des Ocularnicols leicht daliiu gebracht werden kann, dass der dunkle Interferenzstreifen か in das rotlie Ende des Spectrums A, 52 Uml ö3 aber in den gelben und blauen Theil desselben fallen, wiihrend die Streifen ß5 gß den rotben, grünen, und violetten Theil dos anderen Spaltenspectrums B be- decken ; also dass in dem einen Spaltenspectnim Both Grün und Violett im Maxi- mum, in dem anderen Spaltonspocfcrum aber Gelb und Blau im Maximum vorlianden sind. Da Eotli und Violett zusammongemisclit den Farben ton Purpur geben, dessen complementaire Farbe das Grün bildet, da ferner Gelb und Blau zusammeugemisclit bekanntlich Weiss geben, so sieht man ein, dass dio beiden Spaltenbilder unter diesen Umständen farblos, oder nahezu weiss erscheinen müssen. Wir wollen diosen ausgezeichneten Punkt der grössten Entfärbung der beiden Spaltenbilder, il die Maximalblässe bei grosser Quarzdicke ** nennen. Es ist klar, dass das Eintreten der Maximalblasss niclxfc notliwendig an dio obenangegebene Dicke cler Quarzplatte also an das Ersclieinen der drei Inter- ferenzstreifen gebunden ist. Die angegebene Quarzdicke ist vielmehr diejenige bei dor dio Maximalblasse anfaugt, zu erscheinen. Diese erscheint auch bei einer grösseren Quarz dicke und zwar um so vollkommener, je grosser die Quarzdicke d. i. die Anzahl der auftretenden Interferenzstreifen wird. Erst, wenn die Quarz dicke 丄 i. die Anzahl der Interferenzstreifen so gross geworden ist, dass fast jeder Tlieil (101: Spaltenspectra von denselben durchzogen wird, danu verschwinden die Fär- bungen der Spaltenbilder und diese ersclieinen weiss. Wie aber bereits geschilclerfc worden, ist die Entfärbuug cler beiden Spaltenbilder bei cler Einschaltung einer miissig dicken Qnarzplatte mir maximal, nicht absolut. Es ist; dies der Punkt wo die Uebergangsfarbon Bläulich weiss und Gelblich weiss in den beiden Spaltenbilder erscheinen. Bei eiuigermassen grossen Quarz dicken werden (leise Uebergangs- farbeu von aussorordentlich geringer Sättigung ； allein auch nur von geringer Safc- tigung und die Spuren von Uebergaugsfarben lassen sioli durch keinen "Winkel des Ocularnicols zum Verschwinden bringen. Diesel. Umstand wirkt indessen weniger störend auf die Einstellung des Leu- koskops in die Maximalblässe zurück, als man vermutlieu könnte ; denn dio Veränderung der U eb ergaugsfarb en gellt, wie bereits oben bemerkt, rasch vor sicli und eine sehr kleine weitere Drehung dos Ocularnicols, oder eine sehr kleine Aenderung der Quarzdiclco liat sofort die Zorstörung der Maximalblitsse zur Folge, so dass das eine Spaltenbild eine rötliliclie und das andere eine grünliclie Färbung zeigt. Besonders angestellte Versuche haben es ergeben dass die Grenzen innerhalb deren die Quarz dicke, oder der Winkel des Ocularnicols variiren kann, ohne dass die Zer- störung der Maximalblässe eintritt, ausserordentlich klein sind, und dass sie Fehler veranlassen, welche höchstens denjenigen gleich sind, welche man bei der Mossung der Drehung des monochromatischen Lichtes im Quarz begeht. Diese unvoljkoramene Entfärbung der beiden Spalteubilder kann deshalb auf die Resultate der Messung von relativ geringem Einfluss sein, sobald (las Lenkoskop nun zur quantitativen Untersuchung benutzt werden soll. Wenn aber das Lenkoskop auch ziu， qualitativen Untersuchung dienen soll, so ist diese unvollkommene Entfärbung der Spaltenbilder ein so lästiger Umstand, dass man sich nach einem Mittel Umsehen muss, um denselben zu beseitigen. DAS COMPENSATIÜNSNICOL. Die vollständigere Entfärbung kann indessen mittelst des Compensationsnicols erzwungen werden. Dieses besteht, wie bereits oben beschrieben worden, aus einem Nicol, und einem so dünnen Glimmerblattclien dass cs in einem Polarisations- apparate Farben erster Ordnung zeigt. Ersetzt man bei dissem Versuch den Analy- sator des Polarisationsapparates durch ein Kalkspatlirhomboeder so, erblickt man im Allgemeinen zwei Bilder, von denen das eine blaulichweissen und das andere gelblich weissen Ton zeigt. Es ist nun selbstredend dass man dtirch das Anbriugen des Compensationsnicols am Leukoskop gleichfalls zwei Spalfcenbilder von den angegebenen F iiibung selin wird, wenn alle Quarzplatken ausgeschaltet sind. Gerade solche Farbentöne besitzen nun die beiden Spaltenbilder im Punkt der Maximal- blasse und die Intensitäten der Farben der Spaltenbilder iu den beiden Fällen können cladurcli gleicb gemacht werdeu, dass man den Winkel, welchen der eine der Haupt- eclinitte des Glimmers mit der Polarisationsebene des Nicols (Ni Fig. 1. Taf.) scliliesst, durch eine Drehung der Metallliiilse, woran das Glimmer geklebt ist, gehörig ändert. Mau kann (lemimcli eine vollständigero Entfärbung des Doppel- bildes des Lcukoskops dadurch erzielen, dass man das Compensationsnicol so ein- 8 teilt, dass dasjenige bläulich gefärbte Spaltenbild， welches man ohne Einschaltung der Quarzplatte erblickt, mit dem blaugelben SpaUeuTbild zusammenfallfc, welches in der That ohne das Corapensationsnicol durch das Einsclialten der Quarzplatten entstellt, und so aucli mit dem anderen Spaltenbilde. Es decken sich also durch solche Einstellung des Compensationsnicols zwei complementiir zu einander stellende Farben in jedem Spaltenbilde ; die beiden Spaltenbilcler werden unter diesen Um- stünden farblos erscheinen. In der Timt geliugt es durch das Compensatiousnicol fiine solche vollständige Entfiirbuug der beiden Spaltenbilder im Leukoskop herbeizufüliren, dass sie gleich weiss ersclieinen. Allein das "Weiss, welches die beiden Spaltenbilcler zeigen, bat euiscliiedeu nicht dasselbe Aussehen, wie das Weiss des urspriingliohcn Liclitea ; die gemeinsame Farbe, welche die beiden Spaltcubilder dann besitzen, ist vielmehr immer ein blasses Gelb, so dass es hierbei strenge genommen mu* von einer Farbengleiclilieit des Doppelbikles die Eede sein kann, nicht von einer Entfarbimg desselben. Jedenfalls ist die Farbengleiclilieit des Doppelbiklers unter Anwendung des Compensationsnicols eine so vollkommene, dass nur eine angestrengte Aufmerksamkeit dazu gehört, die geringe Spur vom Niiancenunterscliiede in den beiden Spaltenbilder zu entdecken. Obgleich die Angabe der zur Construction des Compensationsnicols nöfcliigen Daten olmc allen Nutzen ist, weil dieselben von vorwiegend subjectiver Bedeutung sind, und weil sie ausserdem von der Natur der angewandten Lichtquelle und von der zur Auweuilung gekommenen Quarzdicke abliiiugen, gestatte ich mir die fiir mein rechtes Auge gütigen Daten anzageben, uud zwar für eleu Fall, wo die angewandte Lichtquelle eine vom Sonnenlicht erleuchtete Wolke war, mul die Herstellung der Maximalblässe durch die Eiusclialtuug einer 10,47 mni dicken Quarzplatte geschah bei einem Winkel des Ocularuicols 0° (der Nullpunki des getbeiltcu Kreises an meinem Instrument willkürlich, aber uahe zu der Punkt, wo eins der Simltenbilder verscliwiuden würde, 、ve】m alle Quarzplatten ausgesclialtet 'worden ). In diesem Fall war ein 0,00273 _ dickes G limmerbl iit tcl len liinreiclicnd, die vollständige Entfärbung der' beiden Spalteubililer zu bewirken, wenn einer der Hauptscbnitto des Glimmers mit demjenigen des Kalkspatlirhombotklei* nahezu tlou Winkel 45。 und gegen die Polarisafcionsobcnc des Nicols (Nj) genau den Winkel 45° einschloss. Ich werde von dem Compeusatiouswiukel keinen Gebraucli machen, wo es sich dämm handelt, mit dem Leukoskop gewisse quantitative Messung auszuf Uhren. Demi abgesehen von der durch das Nicol (Nj) (Fig. 1. Taf.) verursachten halb so grossen Helligkeit clor beiden Spalteubiltler werden die Grenzen, innerhalb deren die Quarzdickc, oder der Winkel des Ocul.^irnicols sich ändoren kann, oline dass die Maximalblässe dadurch zerstört wird, ziemlich erheblich, so dass der durch das Compensatiousjiicol bewirkte Vortlieil der vollkom melieren Entfürbung geradezu illusorisch wird. DIE SUBJECTIYITAET DES PUNKTES DER MAXIMALBLAESSE. Es ist wichtig zu bemerken, dass der Punkt der Maximalbliisse nicht so bestimmt ist, als sei für das Licht einer bestimmten Lichtquelle nur ein bestimmter "VVertli der Quarz licke mul des Winkels des Ocularnicols hinr eichend, um clie Maximal- blässe hei* vorzu rufen. Es giebt viel mehr unendlich viel coordinirfce Wertlio der beiden Variabeln, bei ileiieu dio Maximalbliisso fiir eine bestimmte Ijichtquelle ein- tritt, vorausgesetzt selbstverstiiacllicli, dass die Quarzplatte eine hinreichende Dicke habe. ]Cs scheint hiernach, dass, obwohl der Punkt der Maximalblässe durch den Werth der Quarzdicke mul des Winkels des Ocularnicols eindeutig bestimmt ist, diese beiden Grüasen nicht als unabhängige Variabcln betrachtet werden können, sonderen einer gewissen Function genügen müsse nt um die Maximalbli:isse liervorzu- rufen. Wemi wir nun die Ermittelung einer solchen Function in’s Auge fassen, so begegnen 'vir einer ausserordentliolien Schwierigkeit, welche durch den Umstand noch erheb lieh gesteigert; wird, dass wir hierbei in erster Linie mifc Farbenem- pfinduug zu tlnm haben, dass d&mnach ein subjectives Moment, nämlich die Sin- nestliatigkeit mit in 's Spiel kommt. In dei* Tliafc ist der Pimkt der Maximalbliisse, wie nähere Untersuchungen zeigen, uiclit allein von der Natur der angewandten Lichtquelle abhängig, sondern auch von der individuellen Beschaffenheit des Auges ; er ist nicht für alle Beobachter derselbe. Es genügt näiulicli eiue Quarzdicko, welche im Stande war, für mich die Maximalblässe licrzustelleu» nicht mehr für einen Zweiten ; die Maximalblässe er- schien fiir diesen zerstört, uncl ward erst wieder liergcstellt, wenn die Quarzdicke um eine kleine Grosse entweder yergrössert, oder verkleinert worden war. Ich habe Linsichtlicli diese Punktes melirere Individuen untersucht, indem ich sie auf- forder to, entweder durch dio Drclivmg des Ocularnicols, oder durch die Aenclerung der eingeschalteten Quarzdiclce die MaximnlLlasse d. h. dio grüsstmögliclie Aebnlicli- keit der Fiirbungen des Doppelbildes herzustellen. Manclie von den so Untersuchten waren mein* oder weniger mit pliyyikalischen Beobaclitungen vertraut mul dio Uiitersncliungen ergaben, dass auch keiner von ilnien eine vollstiincligo Entfiirbung der beiden Spaltenbilder zu erzielen wusste, uncl dass dio bei den Spaltenbilder welclio fiir mich sich im Punkt der Maximalbliisse befanden, fiir andere im Allgemeinen so ungleich gefärbt waren, dass die eine Hälfte des Doppelbildes rötlilioh erschien wahrem] die andere einen entscliicden grünlicben Ton besass. Es ergab sich zu- gleich auch dass eine entsprechende AentTerung der eingeschalteten Quarzdicke, oder eine entsprecliemle Drehung des OcuLirnicols jedesmal hinreichte, um die Maximalbliisse wieder lierzustellen. — 11 — Was nun die Ursache dieser Erscheinung anbelangfc, müssen wir dieselbe vor Allem im Bereich der subjectiven Sinnesempfindung suchen. Ich gestatte mir hier folgende Bemerkung. Die Perceptiousvergänge in der Netzhaut unseres Auges lassen sich in zwei im Wesentlichen verschiedene Momente zerlegen ; in qualitative und quantitative Perception. Dio qualitative Perception bedingt die Empfindung der Farbe, ilire Stärke lieisst il Sättigmig，’’ walirend die quantitative Perception die Empfindung des “Lichtes” licrvorruffc, deren Stärke Intensität M (im subjectiven Sinne) genannt werden kann. Wenn ich das von einer Lichtquelle ausgesaudte Licht aut* die Netzhaut meines Auges ein wirken lasse, so empfinde ich zunächst dass es ein Licht sei lind zwar ein Liclit von bestimmter Intensität. Die Starke der Empfindung il Liclifc n isfc abbiingig von der Summe der Strahlen aller Wellenlänge, welche iu meiner Netzhaut iiborlmupt die Empfinduug “ Lichfc” zn erregen im Stande sind. Die Stärke der Empfindung “ Farbe M hängt aber davon ab, in welchem Verhältnisse die einzelnen Strahlen yerscliietlener Wel- lenlänge, denen bestimmte Farbenompfiiulimgen entsprechen, in dein Liclit, welches die Liclitquelle anssendet, enthalten sind. Diese beiden Momente der Perception brauchen dabei nicht noth wendig im Verhaltniss des Causalnexus zustelien, sie künnen vielmehr von einander imabliängig sein ; denn die Summe derjenigen Strahlen, welclio die Empfindung Liclifc erregen, kann dieselbe sein, oliuo class tlio Yerliiiltnisso der Einzelstialilcn, denen bestimmto FarbenempfiiuluDgen entsprechen, gleichzeitig dieselben sind, und umgekehrt. Denken wir uns eins Liclifc einer Lichtquelle in ein Spectrum zerlegt, so dass Strahlen aller Gattungen noben einander zu liegen kommen. Wenn die Netzhaut meines Auges grössero Fähigkeit besitzt “Liclit” zu empfinden, als diejenige eines Zweiten, so werden zunäclist alle Strahlen, denea bestimmte Farbenem- pfiuduugen entspreclieu, für mein Auge relativ grössere Intensität besitzen als für dasjenig eiues Zweiten. Da die Empfindlichkeit meines Auges gegen den Eindruck des “ Lichtes n grösser isfc als bei dem Anderen, so müssen Strahlen welche ent- weder wegen der zu kleinen WellenliingG odor wogen ihrer zu grossen Wellenlänge von dem Anderen nicht mehr als “Liclit” empfunden werden, von mir noch ganz gut als “Liclit” empfunden werdeu können. Wenn demnacli dio Verscliieaenlieic der FiiliigKeit, t( Liclit n zu empfunclen, boi verschiedenen Individuen angenommen werden muss, so müssen die Grenzen der Strahlen im Spccfcrum, welche noch dio Empfindung “ Liclit ’’ in der Netzhaut unseres Auges zu erregen vermögen, bei ver- sclnedenon liulividuen inclit zusammemf allen d. li., es muss dio Breite des dem Auge überhaupt sichtbaren Spectrums für verschiedene ludivicluen versclneaen ausfallon ； als ob die Liclitemission der betreffenden Lichtquelle lileiiier, oder grösser geworden wäre. Nun zeigt das Leukoskop, wie icli weiter unten ausfülirlicli darauf zurück- kommen werde, eine Aemlcrung deu Liclitemission immer durcli eine Zerstörung der MaximLilblässG an. Um auf’s Neue zur Maximalblässc zu gclaugcn d. b., um das Leukoskop für eine andere Liclitemission in dio Maxim alblässo einzustellen, ist immer eino entsprechende Aendernng der Quarztlicko, oder eine entsprechende Drohung des Ocularnicols hinreiclientl, gerade, wie in dem Falle, wo das Licht- — 12 — perceptionsvermögen der Netzhaut oin anderes geworden war. Wenn hingegen mein Auge bei gleichem I jiclitp er cep tions vermögen grossere Fälligkeit liat, Farbe zu empfinden als dasjenige eines Anderen, so worden die Verhältnisse, unter denen die Lichtquelle Strahlen aller Farbongattungen aus senden, für mich andere Wer the besitzen, als für den Anderen. Das von der Lichtquelle ausgesandte Licht, das in mir eine bestirnte Farbeuempfindung wacliruft, wird bei dem Anderen Farbeu- empfindung erregen, welclie gleich der in mir erregten Farbenempfiudung sein würde, wenn die Lichtquelle um eine gewisse Menge Liclitstvalilen von bestimmter Farbe weniger, odor mehr als sie thatsächlicL thut, ausgesandt hätte. Es liegt mir nun ob, fostzus teilen, wie weit diese Verscliiedenlieifc des Percep- tionsvermögens des Auges die Subjectivititt der Punktes des Maximalbliisse bedingt. Wir müssen zu dem Endo das Verhalten cles Leukoskops gegen verscliieclene Licht- quellen vom Standpunkt der physiologischen Farbenlehre aus betrachten. DIE GRASSMANN'SCHEN REGELN ZUR BESTIMMUNG DER FARBENMISCHUNG UND IHRE ANWENDUNG AUF DIE FARBE DER LICHTQUELLE.* Wenn eine Lichtquelle Liclitstralilen aller Farbengattungen aussendet, so ist der Eindruck des Lichtes, welches die Lichtquelle aussendet, eine farbige Emp- findung welche man “ Weiss n nennt, aber das “ Weiss n verschiedener Lichtquellen ist verschieden. Die Sonne, dio glülieudo Kolile im electrischen Strom, und ein brennender Maguesiumdraht senden alle ein blendeud weisses Liclit aus, doch mit einander verglichen zeigen diese drei Lichtquellen wesentliche Vcrsclneaenheit in ilirera “ Weiss. Es müssen dann die Verhältnisse der Menge der Strahlen, denen gewisse Farbenempfinduug entsprechen, für ycrscliiedcno Lichtquellen verschieden sein. Es folgt hieraus, dass das Wciss vcrsclnecleuer Lichtquellen als zusammen- gesetzt aus verschiedenen Mengen der gesiittigen (spectraleu) Färber betrachtet werden müssen. Wenn uns im Folgenden mit dem “Weiss” verschiedener Lichtquellen bescliiiffcigeii, werden wir daher immer mit einer Farbenmischung zu tlimi haben. Nun bat Grassmann t als allgemeine Regeln zur Bestimmung der Empfindung, welche eine Mischung jeder beliebigen Anzahl Elementarfarben in unserer Netzhaut erregt, folgende Principien aufgestellt : (1) Jede beliebig zusammengesetzte Mischfarbe sieht aus, wie die Mischung einer bestimmten gesättigten (speclralen) Farbe (oder des niclifcspectralen aber gesättigten Farbentones ** Purpur n welches aus einer Mischung des spectralen Eotlics mit dem \ioiefct entstellt) mit Weiss. (2) Wenn von zwei zuyermisohenden Farben die eine sich stetig ändert, so ändert sich das Aussehen der Misclifarbo auch stetig. (8) Gleich aussehende Farben zasammeugemischt geben gleich ausseliende Mischungen. # Die Darstellung der neueren Farbenlehre, welche Helmholtz in seinem classischen Werke ft Handbuck der physiologischen Optik. Leipzig 1867’’ auf Gruncl seiner epochemnacliendeii U nter8cbungen gab, ist fiir die folgende Auseinandersetzung maassgebend gewesen. t Grassmann Poggendrof^ Annalen ß. LXXXIV p. 69. 1852. — 14 — Wenn wir diese unter Grassmann’s Namen belcannten Principien annehmen, können wir daraus folgende Folgerung zielm ; Es ist zunächst klar, dass das Weiss ’’ einer Lichtquelle als eine Mischfarbe * durch die drei "Variabein 1. die Menge Weiss. 2. die Menge einer gesättigten Farbe. 3. die Wellenlänge des Lichtstrahles, welchem diese letztere Farben- empfindung entspricht. vollkommen bestimmt ist. Was nun eine gesättigte Farbe sein soll, kann man festsetzen, dass sie die Empfindung bedeutet, welche ein spectrales Elementarliclit in unserer Netzhaut erregt. Was man aber unter der Menge einer solchen gesättigten Farbe verstehen soll, das kann nicht definirt werden, da die Menge des “Weiss” eben so wenig einer abstrakten Definition fällig ist wie das Weiss, denn das Weiss ist ein Begriff von durchaus conventioneller Natur und es giebfc darum kein Weiss an sicli. Will ich auf das Weiss des Sounenliclites als das Weiss an sieb, als das vollkommste Weiss, alle F arbenempfindungen bezielieu, so kann ich mir das gegen das Sonnenlicht röthliclie Liclit eines gl üb enden Platinadralitcs durch das Weiss des Sonnenliclites, von gewisser Menge und das spectralo Rotli von gewisser Menge entstanden denken. Aber auch das "Weiss des Sonnenliclites von der verlangten Quantität kann ich mir aus der Mischung zweier beliebigen jedoch comple- menter zueinander stellenden Farben e rnpfi n dn ngen i n entsprechendem ]\[cngimgs- verhältniss entstanden denken. Ich kann mir ("las Weiss des Sonnenliclites zu- sarumcnsetzei], ans dem spectralen Roth imd Grünblau so dass die so zusammen- gesetzte Farbe genau cLasselbe Aussehen liat, wie das ursprüngliche Sonnenlicht. Soll aber dieses durch Rotli und Grün zusammengesetzte Weiss, auch eben so hell erscheinen, wie das urspriinglieho Sonncnliclit, so muss dio Menge des Both, und Grünblau, welche beide Farben zur Miscliung benutzt werden, (jvüsser sein, als dio Menge der Farben liotli und Grün aus dem Spectrum der Soime. Es folgt aus diesen Ausoinaudorsclzmigen hieraus, (lass icli mir jede Farben- empfindungen (d) mithin auch die F arbenempfindung, welche das Liclit einer Licht- quelle erregt, ans der gesafctigt-en Fiirbe (a) von gewisser Menge, und aus zwei gesät- tigten Farben (b) mul (c) im gewissen VorLiültuiss dei* Mengung mit ((1) welche zus- ammengemisclit ein Wciss geben, in welches jene Empfindung (d) übergehen würde, wenn die Empfindung (a) andere Menge hätte, als sie tliatsäclilich besitzen muss, mit den Empfindungen b und c, die Empfind img (d) in meinem Auge hervorznrufen d.h., dass jede Fiirbeiiempfimlimg als Eesultat der Mischung dreier E lementarfarbenden — der so genannten Grundfarben, oder G ru nd emp fi n clungen wie sich Helmholtz treffen- der au sd rückt, 一 aufgofasst werden kann in gewissen relativen Mengen. Ich brauche hierbei woin kaura darauf aufmerksam zu machen dass cs mit der Keduction der Farbe einer Lichtquelle nur das gemeint ist, dass für mein Auge, auf das das Licht einer Lichtquelle einwirkf, dio dadurch licvorgcrufene F arbenempfindung durch gewisse Quantität der drei als Gi* und färben geltenden Einpfindungen ersetzt werden kann, nicht aber, dass jene Farbenempfindtmg durch tliatsiicliliclie Miscliung iener cu’ci Grundfarben erzeugt werden kann, wie deuiniberliaupfc eine E. eduction der Farben- empfindungen auf die drei Grundfarbeu nur eine subjective Bedeutung haben kann. DIE YOUNG-HELMHOLTZ'SCHE HYPOTHESE, UND DIE BEDINGUNG DER MAXIMAXBLAESSE. 1807 erschien Thomas Young’s “ Lectures on natural philosophy. M Es enthält eine eigentlninliche von all ihren Vorgängerinnen wesentlich abweichende Theorie der Farbenempfindang, welche indessen lange Zeit himlurcli ganz umbeaclitefc geblieben war, bis Helmholtz uml Maxwell die dieser Theorie liegenden Vorzüge erkannten, und auf dieselben aufmerlvSiim machten. Von dieser Youug'schen Theorie wollen wir nun ausgehen. Dio Grundliypothese der Young'sclien Farben- theorie lasst sich nach einer Modification von Helmholtz so ausspreclien.!：s (1) Es giebt in der Netzhaut drei Arten von Nervenfaser, welche drei G rundempfindtuigen leiten. Die G i* undempfinduDgen sind ßotli Grüu， und \ iolett so dass die Eeizung der ersten Faserart die Empfinilmig Eofch, die Beizung der zweiten die Empfindung Grün, und die die Eeizung der dritten die Empfindung Violett erregt. (2) Eia objectiv homogener Llclitatmlil erregt diese drei F ascr arten gleich- zeitig, abjr in yersoliiedener Starke je nach der Wellenlänge des Lichtstnilils. Hat der Liclitstralil grössere Wellenlänge, so wertlen durch ihn ilio rothempfiiulencleii Nervenfasßr am stiifksten erregt;, die grüuempfiuilenclcn scliwacli, am schwächsten die violetempfindenclen Nervenfixser. Hat die Wellenlängo des Lichtstrahles einen mittleren Wertli, so werden die griinempfimlenclen Fasern am stiiflcsten erregf, die rothemi)fiutleuden scwacli, und ebenso die violettempfiiulenden. Wenn die Wellen- länge des LiclitstraliU aber ldeineren Wertli hat, so werden die viovettempfimlemlen Nervenfaser am stiirksten, die grüiiempfindeiulen scliwacli, am scliwiiclisten aber die rotliempfinclenden Nervenfaser erregt. Die Erregungestärke der drei Faserarten isfc also eine Function der Wellen- länge. Denkt man sich die ErregnugsstärlvO als Ordinate eiaes rechtwinkligen Coordinatensystems die Wellenlänge (ス） als die entspreclietnle Abscisse Curven construirfc, anfangentl von der grössten Wellenlänge (Xu)* aer die Aetlier- schwingimg noch als “Liclit” ia unserer Netzliaufc empfunden werden kami, bis zu dem anderen Gi.eiizwei.th der Wellenlänge, (^,0) wo die Aetlierscliwingung wegen der Kleinheit ihrer Wellenlänge aufliürfc, für uns als ** Liclit n za exibfcireu, so erhalt man drei verschieden verlaufende Curven für drei Faserarten (Fig. B. Taf.)t welche wir * Helmholtz Physiologische Optik pag. 291. f Helmholtz e.d. — lß — fortan Empfindungscurvon nennen wollen. Ich werde mich liier nicht auf die Erörterung der rein physiologischen Fragen einlassen, ob die thatsäcliliche Existenz drei solcher Faserar ten in der Netzhaut sich nicht nachweisen lässt. Ich werde (lieso allerdings noch problematische Existenz einfach annelimen, mid zuselien, wdclio Consequeuzen aus der Anwendung dieser Annalime auf die Theorie des Leukoskops fliessen, indem wir diesen drei Arten Nervenfaser solche Eigenschaften beilegen, dass für sie Relation zwischen der Stärke der Erregung und der Wellenliinge des objectiv homogenen Lichtstrahls stattiindet, wie sie die Fmpfindungscurven darstellen. Es ist einleuchtend, dass die Gostalten dieser Curven in erster Linie von der lndivicluellen BcscbaÖenlieit des Auges abliängen müssen. Es muss ferner im All- gemeinen angenouimen werden, dass sie auch von der Natur der Lichtquelle, deren Licht auf die Netzliaut ein wirkt, abliiingen ; denn gesetzt es gäbe zwei Lichtquellen welche homogenes Liclifc ein-mul derselben Welleiilitngo auszusenden vermögen. Weim mm das Licht aus diesen beiden Lichtquellen objectiv verschiedene Inteusitiit lufc, (1. li., da die objectivo Intensität des Lichtes proportional iloi* lebendigen Kraft der Aetheroscillation ist, die eine Lichtquelle eine grössere Anzahl der Liclit- s trab len aussendet, wie die andere, so werden die der Wellenlänge dieses Licht- strahles entsprechenden Ordinaten der Erap fi nclungscur ven f ii r beide Lichtquellen verschiedene Wer the besitzen mässen, da die Grosso der EiTegungsstiirke der Nervenfaser, wenn aucli nicht direst proportional der objectiven Intensitiit des Licates, eine mit wadi sender objectiven Intensitiit zu einem Maximum wachsende Function isfc， Es folgt hieraus unmittelbar, dass die Empfindungscurven für verschiedene Lichtquellen, bei denen eine Verscliietlenlieit der Z ur sammen se tz ung der Liclit- stralilen \orausgesizt werden müssen, im Allgemeinen verschiedene mehr oder weniger von einander abweichende Gestalten haben werden. Was die Greuzwerthe der Wellenlänge (入) anbelangt, bei denen die Emp- findlings Curven die Abscissenaxe sclnieiden oder berühren, so mi'ißsen dieselben auch als verschieden für verschicdeiie Lichtquelle, wie für verscliietlede Iiulivitluen angeselien wenlen, da die Grenzen des Lichtspectrums bei verscliiedeneu Lichtquellen (loch vorscliieden siml. Ee seien .(ス ） 0ヴ（ 入） (ス） die Functionen, welche die Erregungstärke der drei Nervenfaser fiir irgend eine Lichtquelle in Ablningikeit von der Wellenlänge ( X) darstelleu. Es stellt dann die Grösse + M^) + die subjective Intensität des Lichtstrahls von der Wellenlänge \ dar und die Verhältnisse a. ) 0t ( A j / 1 \ AU) ^ ; * Die Berechtigung- zu dieser Behauptung liegt in der Thatsaclie dass jede Farben- empfindung das Bestreben haben, bei steigender objectives Intensität des Lichtes パ n die eine Empfindung ft Woiss >y uberzugehen. Sich Helmholtz physiol. Optik pag. 233. 一： 17 — aber, den Grad der Sättigung des Faibenempfiudung welche dei- bedachte Licht- strahl in der Netzhaut hervorruft. Sendet die Lichtquelle Strahlen verschiedener Wellenliinge aus, sodass sein Licht nicht eine vollkommen gesättigte Fai-bcnempfiiidung erregt, so geben die Flüchen, welche begrenzt sina vou der Abscissenaxe einerseits, unJ von Jeu E m pfi ucl ungscur ven andererseits, d. 1】，, die Integrale. f ル (九) ca, / das Maass fiir die Menge der drei Grunclempfindungen, welche die Farbe der Lichtquelle ersetzen, wenn die Integration über die ganze Breite des Spcctrums der betreffenden Lichtquelle ausgedehnt wirtl. Dann giebt das Integral / + M^) + (2) das Maass für die subjective Lichtintensität cler Lichtquelle und die Verhiiltnisso a = j 0,-(^ya f I 0»( \)d7^, f 0g[\)dX (3) bestimmen die Sättingiuig der Farbe, welche das Jjiclit der Lichtquelle besitzt d. li., die so beiden VerhiiltuisszaLlen a und b bestimmen die Qualität der von der Liclitquello ausgesandten Lichtes. Diese beiden für jede Lichtquelle und für ihren bestimmten E mi ssionsz us tau d charaktristisclien Cons tan ten a und b, welche aber von einem Individuum zum Aiidern variren können, werden wir dio öättigungscon stau ten nennen. Nun kehren wir zurück zu unserem Leukoskop und suchen die Bedingung auf, unter der die vollständige Eutiarbung der beiden Spaltenbililer bewerkstelligt werden kann. Ein objectiv liomogcucr Lieb ts trab 1 von cler Wellen lüngc (又） pflanzt sich durch die Kalkspatlirliomboe.ler (Iv2 Ki) Fig. 1. Taf. fort mul wird in zwei auf einander senkrecht polarisirtcn StraLleu verwandelt welche, durch die Quarzplatte (Qi) indem sie dieselbe durclisetzeu, eine cler Dicke cler Quarz platte proportionale Drehung ihrer Polarisatiousebone erleiden. Es sei A der absolute Werth der Schwingungsaiiipliluclo dieses Lichtstrahles, so ist die objectivo Inteiisitüt des Lichtstraliles proportional der Grosso A=, so dass wir als die objective Intensität cler beiden Spaltenbildcr erhalten wo u eine ohne alle Miilie ermittelbare Function von den drei Voriabclu ist: von der Dicke der Quarzplatte, welche wir fortan durch A bezeichnen wollen, von dem Winkel des Ocularnicols, welche jj heissen möge, und endlich von cler Wellenliinge des betreffenden Liclitstralilcs. Wenn cliose beiden Jjiclitötralileii mit diesen Iiitcu- sitäten zur Netzhaut des beobaclitenden Auges gelangen so werden die drei Arten Nervenfaser gleichzeitig erregt, aber in nngleicher Stärke. Von dem einen S p alten - bilde werden die Nervenfaser Erregungen erleiden, deren Stärke bezielmlicli durch 0r(^)(l - U) - U) 0/ス〇(] - u) 2 2 2 darstellt werden können ; wahrend die Nervenfaser von dem anderen Spaltenbilde Erregungen erfahren, deren Stärke beziehntlicn durch 0r( 入 ）（ 】 + 0.7( A) (1 + U) 0y( X) l J + U) 2 2 2 ausgedrückt sind. Es geben dann die 6. Integrale \ j 0 ベ 入 )（】 — u)d\, 2 j 0r( 九) 0 + u)d^j) 2 [ 0ク（久）（] — u)d^, a f 入 ）（ 】 + u)d 入， (ル U)(l -u)d\ f 0t；( 入 )(] + (4) iiitegi.ir t über die ganze Breite cles Liclitspectrums der Lichtquelle, welche wir mit dem Leulcoskop betrachten, die Mongon dor drei Gr un dem pfi nduugcn welche die Färbungen der beiden Spaltenbilder zu ersetzen im Stande siud. Die Wer the der G Iutegralo (4) liiingcn im Wesen fcliclien ab von dem Werth . der Quarzdicke A von dem Winkel cles Ocularnicols tj, und können daher clurcli passende Wahl der beiden Yariabeln A und 7), verscliietleno Grosso tumdimen， tl. li., wir können durch die AendeiHuig der beiden Variabein dem MeiigungH Verhältnisse der Grundempfimlungen in den beiden Spaltenbililern verscliiedene Wer the ertlieileu. Nun sollen die heilen Spaltenbilder genau dieselbe Farbe zeigen, wie das ui-sprüngliclie Licht der Lichtquelle. Diesem wird Genüge geleistet, wenn die beiden Yariabeln A und T) so gewählt sind, dass die Siittigungsconstanten der Färbungen in den beiden Si^altenbilder dieselben Wertlie haben, d. li., die Gleiclmugcn bestehen j* 0r( j ^6r{ A* J ( 1 一 j 0¢ {人 )（】 + ^ j" 0 ク （又) （1 一 f + u)d^ - u)dX / MW + u)d^ f MW - u)d^ woraus weiter mit Kücksiclit auf die Gleich migcn (1) folgt. ㈨ I (f)rU(l \ = CI f ^(JudX{b.) 一 19 — Diese Doppelgleicliung, ist die Bedingung, welcliei: △ und 7) genügen müssen wenn die beiden Spaltenbildor genau die Farbe des urspiingliclien Lichtes zeigen sollen. Aber jedes A 7}， welclies diese Doppelgleiclmng befriedigen würde, bedingt niclifc nofchwendig, dass diese Färbung der beiden Spaltenbilder auch dieselbe Helligkeit habe. Wenn auch dieses ein treten soll, müssen △ uncl 7) solche Wertlio liabei), dass die Lichtmenge, welche die Netzhaut in den beiden Spalteubildem empfinde f, genau dieselbe Grösse liafc. Die Bedingung hierfür ist / [ル (又） + も U) sM 入) P— ぬ =/ [於. (入） + ル UH ル U)](] +u)d?i. d. h., I [ル（ 入） 十 0 ダ （凡） + 0t， （入)] = O- woraus dann unmittelbar aus (5) folgt j = f = J fiv{ 7C)vd\ = o. (6) Dieses ist die Bedingungsgleicliung der Yollstiiiuligen Entfärbung der beiden Spaltenbildcr. Wie wir weiter unten sehen werden, giebt es keinen, wenigstens keinen end- lichen Werth von △， welcher streng diese Doppelgleichung erfüllt hätte. Nimmt man A sehr gross gegen die Welleuläuge des Lichtes, so können die drei Iutegrale j fi,.{X)udX I ^>0{X)udX I fiv{ 7011 d\ zwar durch einen wacliseiulen Werth von A *uif beliebig kleine Grösse herabgeclrückt werden ; sie können aber nie einander gleich werden, es sei denn, class A unendlich gross werden, wo die drei Integrale dann verscliwincien. Es folgt hieraus, dass die beiden Spaltonbilder bei der nicht unendlich grossen Dicke der Quarzplatte nie clio Farbe amiolimeu, welche das ursprüngliche Licht der Lichtquelle besitzt. Wir denken uns im vorliegendeu Falle flurcli das Allbringen des Compensa- tionsnicols eine solche Vertbeilung der Liclitstralilen in den beiden Spaltenbiidern herbeigefülirfc, dass die beiden Spaltenbilder keinen Farbenuuterscliied zeigen, und gleiche Helligkeit haben. Die G. Integrale in (4) sind dann zu ersetzen durch sin2 ク ~4~ cos2 汐 ( 彡/ 入 )(1 + の )(1 + — 〆 J* ん (入 )(】 "1 .う (1 +W) 似， [扎 (入) (]+«)" +M)，a. cos2ö — 20 — wo t). wieder eine leicht emiittelbare Function von den folgenden drei Variabel n ist : die Wellenlänge, die Dicke des Glimmerblättcliens, der Winkel, welchen ein Hanptsclmit des Glimmers mit dein Hauptsclinitt des kalkspaths homboeilers (Kt Ko) bildet und 〇 der Winkel welchen die Polarisationsebeno des Nicols (Nj) mit einem Hauptsclmitte des Glimmers einscliliesst. Die Becliiiguug, dass die beiden Spaltenbiuler genau gleiche Helligkeit besitzen, iöt dann sin2 ク /"[成 •(入） + がが （入） + ん （入)] (] 一 ^)(1 一 V )d\ = COB^O I C^,.( 入） + A (入） + ん（ 入)] ( ] + V X ] d. h., indem man sich der Formeln sin2/? = 音 （ 1 — cos2 夕） und cos2^ = i (1 十 cos20) erinnert cos2 沒 j ^{X){u+v)dX ( 0( 入) （1 +uv)cl\ ⑺ wo Pr(A) + p^(X) + 0t,( X) = 0( 入） gesetzt wurde Die Bedingung, dass die beiden Spaltenbilder dieselbe FäL*bung besitzen, wie das ursprüngliche Licht der Lichtquelle, ist : j* 1— «)(1 — f 木 u 、(]+«)(]+ 幻れ f 0,(^)(1+«X1+«)^ ノメ 。( 九) (1 + m)( 1 + 入 j ^(^)(1+«)(!+^^ woraus mit Rücksicht auf die Gleichungen (1) folgt. ( 0r{ X^uvdX : = a J ^v^\)uvdX Zur Erfüllung dieser Bedingungen (7) und (8) sind fünf Variabein vorliajiden, von denen zwei demnach ganz willkürlichen gewählt werden küimen. Mit den übrigen 8 Yariabeln können die drei Bediiigiuigsgleicliungen 7 und 8 eriullfc werden vorausgesetzt selbstvcrstiindlicli, dass die aufgestellten Gleichungen (8) wirklich bei gewissen Wertlien der in Rede stelionden Varitlbeln bestehen, was a priori nicht angenommen werden darf. Denn die Gleichungen (8) können etwas fordenif was durch keine Combination der Variabein beraerlistelligt werden kann ; sie küuncn also auf Consequenzen führen, welche mit den Voraussetzungen in Widerspruch stoben. Nun geleitet cIuvcJi die Erfahrung, class die beiden Spaltenbilder unter der An- wendung einer grossen Quarzdicke mul des Compensationsnicols miliozu vollständig entfärbt werden, aber das Weiss, wclclio die beiden Spaltcnbildei. daun zeigen, doch J ^v{ X)uvdX I ^g{X)uvdX (8) — 21 — entschieden einen anderen Ton haben, als das Weiss des ursprünglichen Lichtes, so glaube icli folgern zu müssen, dass die Gleichungen (8) nicht bestehen kimnen, dass also die Bedingung der Gleichfarbigkeifc der beiden Spaltenbildev unter Anwendung der Compcnsationsnicols anderes lauten, muss. Die Gleichungen (8) sprechen aus, dass die Mengen aller drei Grundem- pfimluiigon in genau gleichem Verhältnisse, wie in clem ursprünglichen Lichte, in den beiden Spnltonbildor vorlianden sind. Wenn mm aber die Menge jeder Gründ- ern pfindung unter der Anweiulung des Compensationsnicols in den beiden Spalten- bildern genau dieselbe geworden ist, dann müssen die beiden Spalteubilder gleiche Färbung zeigen, welche aber im Allgemeinen verschieden sein wird von der Farbe des nrsprünglicljon Lichtes der Lichtquelle. Die Bedingungen hierfür sind : sin2^ I 式 •（又) （1 一 w)( 1 — 入 = cos2^ j ^(^)(l + w)(l + v^A, sin2 夕 j — — = cos2 <9 ) 乡ズ 入： （ 1 + 沉)、 1 + siirö j 0 乂入 ）（ 1 — w、（l 一 v) 似 = cos20 I (f)v{ X) (1 + u) (1 + v )d\ (1. h., cos 2^? j 6r{X){u+v)clX j<^r{X){\+uv)dX j 似 入) (1 + uv)dX j ^>vW{u + v)d\ +uv)dX Da wir zwei von den 5 Variabein willkürlich wählen kömien, setzen wir fest, dass 0 den Werth — habe, dann kommt: ^r{X){u+v)dX = j X) {u -f v)dX = j 0v[X){u-\-v)clX, = 0. ⑼ wodurch zugleich die Bedingung der gleichen Helligkeit der beiden Spaltenbilder erfüllt ist. j ^(X){u + v)d\ o DIE BESTIMMUNG DER GRUKDEMPFINDÜNGEN. Diese Bedingungsleicliung der Gloicliheifc der Farbe in den beiden Spaltenbilder ist unabliäiigig von den Siittigungscoustanten der Lichtquelle a und b und bleibt also für jeden Zustand der Lichtemission und auch für joden Zustand dos Auges gütig. Wir lieliraen au, class die Gleiclifarbigkeit der beiden Spaltenbildor unter Anwendung der Corapeusationsnicols für eine bestimmte Lichtquelle, welche ein confciuuirliclies Spectrum besitzt, und fiir einen bestimmten als normal zu betrach- tenden Zustand meines Auges bewerkstelligt worden sei. Wemi mm mein Augo zeitweilig gegen eine oder zwei der Grundempfindungen im gewissen Glade blind werden könnte, so ist klar, dass die Bedingungsgleicliung (9), welche durch die- jenigen Wertho der Variabela, befriedigt ist wolclio für den als normal betrachteten Zustand meines Auges gelten, für diesen vom normalen abweiclienden Zustand meines Auges nicht mehr durch dieselben Wer the der V ariabeln befriedigt werden kann. Denn : gesetzt, ea werde mein Auge gegen das Eotli etwas farbenblind, so muss die Erregungsstärke, welcliG die rothempfiiideiule Faserart durch Licht- ßtrahlen von jeder Wellenlänge erfährt, geringer aus fallen, als in dem als normal betrachteten Zustand der Faserart, so dass die punctirte CunTe Fig. (3) Tat. die Empfiudungscurve der rotliempfinden Faserart in diesem Falle darstellen würde. Dio Functions wertho der Function 0y,( \ ) werden kleiner ausfallen als in dem Normalzustände des Auges ; es loigt hieraus, dass die Doppelgleiclmng (9) im Allgemeinen nicht für den vom normalen abwoiclienden Zustaml des Auges bestehen wird. Ob die larüengleiclilieit der bouleu Spaltenbilder trotzdem noch bestellen bleib fc, oder zerstört wird, ist davon ablniugig : (1) Ob die Netzhaut des Auges gegen eine der drei Grimdempfindungen weniger empfindlich geworden ist, als in ihrem normalen Zustande, oder (2) Ob die Netzhaut des Auges sieb gegen zwei oder drei Grmidempfindungen weniger empfindlich geworden ist, als in ihrem normalen Zustande. 23 In dem ersteren Falle müssen "wir als selbstredend betrachten, dass der Functions wertli einer der Empfindungsfunctionen (ス） 0ク（ 又） überall kleiner geworden ist, als in dem normalen Zustande des Auges, und dass auch der Werth eines der drei Integrale (9) kleiner ausfällt, als sonst. In dom letzteren Fall hingegen, wo das Auge gegen zwei der drei Grundempfimlungen geringere Em- pfindungsstiirke hat, als in seinem normalen Zustande, wird der Wertli zweier der Empfindungsfunctionen überall kleiner als sonst ; mithin auch der Werth zweier der drei Integrale, so class die Bedingungsgleicliung (9) durchaus nicht mehr besteht d. h., ist die Farbengleichheit in den beiden Spaltenbildern für einen als normal betrachteten Zustand des Auges liergestellt, so wird sie vollständig zerstört er- scheinen, wenn dasselbe Auge momentan gegen zwei der GrundempfiiHliingen im gewissen Grade blind geworden ist. In dem ersteren Fall aber, wo das Auge gegen eine der Grundempfinclungeu im gewissen G ratio blind ist, wird die einmal für den normalen Zustand des Auges hergestelltö Farbengleichheit der beiden Spatienbilder gar nicht zerstört sein : denn, wenn die Netzhaut des Auges z. B. zeitweilig mit einer Eothblindlieit vom gewissen Grade behaftet ist, so dass ist für diejenigen Wer the der Variabel«, welche die Gleicliungen (9) für den Normal- zustand des Auges befriocligen, so bestellt dennocli die Gleicnung cl. h., die einmal hergestellte Farbengleichheit wird nicht zerstört； das Doppelbild des Spalten wird unter diesem Umstand nun in einem Farben ton erscheinen, als fehlte eine gewisse Menge Rotli in dem Doppelbild, soclass es grünnlichweisse Färbung besitzt. Wie aus der Form der Bedingungsgleicliung für die Fiirbengleicliheit (9) unmittelbar licrvorgeht, bestellt sie noch unveräudert, wenn die Farbouperceptions- vermügen der drei Faserar ten gleichzeitig mul um dieselbe Grosso Aenderung erleidet, so hass die Empßndungsfunctioncu 0,.( 入） 0 が (入） (入） nm dieselbe Function vermehrt, oder vermindert ersclieinen cl. 1)., die Farbengleiclilieit in den beiden Spaltenbildern bleibt unzerstört, wenn alle drei Arten Nervenfaser gleichzeitig, gleiche Acnderung ihrer EmpfindlicLkeit gegen die drei GrunJempfindung erleiden. Wir sind glücklicherweise im Stande, Folgerungen aus der Bedingungsgleichgung (9) wio diese, am Leukoskop selbst experimentell zu prüfen, da es in unserer Macht liegt, das Farbenperceptionsvermögeu unseres Auges nach Belieben zeit- weilig abzuaudern. Bei jedem als normal zubetrachtendcn Auge kann namiicli der Zustand der Farbenblmalieit, wenn auch im geringen Grade und schnell vorübergehend hervor. — 24 — gerufen werden, in dem man Lichtstrahlen von gewisser Wellenlänge, für deren Farbe das Auge abgeblcndet werden soll, längere Zeit liindurcli auf die Netzhaut einwirken lässt und dieselbe in den sogenannten Ermüdungszustand versetzt. Dieser Zustand ist dadurch cbarakterisirt, dass die Netzhaut, nach dem die betreffen- den Lichtstrahlen aufgehört haben, einzuwirlien, für die Farbe, welche diesen Lichtstrahlen entspricht, geringere Empfindlichkeit zeigt, als in dem nicht ermüde- ten Zustand, geradezu so, als ob sich die Netzhaut gegen die JFai.br dieser Licht- strahlen im gewissen Grade blind verhalte, oder als ob in dem Licht der Lichtquelle, welche wir mit dem 80 abgeblendeteu Auge betrachten, eben dio Lichtstrahlen fehlten | welche eingewirkt hatten. Die Functionen 0；( X ) も（ 入）‘ （入) haben demnach gewisse Yermincloriuig ihrer Wer the erfahren, wenn das Auge in den Ermüdungszustand versetzt wird, mul zwar gleichzeitig aber um verschiedene Grösse. Wir (lenken uns zunächst : es werde die Netzhaut für einen objcctiv homogenen JLicIitstralil von grosserer Wellen- länge oder was dasselbe ist, für die Farbe, welche diesem Lichtstrahl entspricht, abgeblendet, so wird von den drei Faserarten die rothempfindend.cn Norvenfaser am stärksten abgebleudet sein, weil dio rotherapfiiulende Faserart am stärksten durch den Strahl, der eingewirkt liat, erregt worden sind. Die beiden anderen Faserarten werden auch gleichzeitig mit der rotliempfindenden Faserart erregt, und somit auch gleichzeitig abgebleudefc. Da aber die Erregung, welcbo diese beulen Faser- av ton durch Lichts fcralilen von grösserer Welleuliiage erleiden, sehr klein sma, wird auch die Abblendimg, welche diese beiden Faserarten unter diesem Umstand erfahren als verschwindeml gegen diejenige der rotliempfindenden Faserart betrachtet werden dürfen. Es folgt sonach dass man, wenn die Netzhaut, deren Farbenperceptious- yermügen sonst als ein Normales bezeichn ei werden mögn, durch die Einwirkung eines Lichtstrahles von grösserer Wellenlänge ermüdet isfc, dieselbe betrachten kann, als ob sie im gewissen Grade rothblma wäre. Ganz dem Analoges wird stattfinden， wenn die Netzhaut durch Einwirkung solcher Lichtstrahlen ermüdet wird, welche mittlere oder kleinere AVellenliiDge haben ; es werden in diesen Fällen die gr ii nempfi nd end e oder violettempmaaende Faser am stärksten erregt, und darum aucli am stärksten abgeblendefc für diejenige Farben, welche jenen Lichtstrahlen entsprechen. Mail kami demnach; je nach dem der eiuwirkonde Lichtstrahl die Empfindung Gr tin oder Violett wachruft, die so abgeblendete Netzhaut ansehen, als wäre sie mit der Grün- oder Yiolettblindheit vom gewissen Grado behaftet. Bind 111 m dio Folgerungen， welche aus der Bedingungsgleicliung für die Farben- g'leichlieit der beiden Spaltenbilder (9) gezogen werden, mit dem thatsächliclien Verhalten des Lm eine Constante ist und es während oiuer Eeilie der Beobachtungen bleibt, die aritlime tischen Mittel ihrer nach den beiden ßerecli- nungsweisen bestimmten Wertlic mit einander 11 aliez u übereiustimmen müssen, wenn man die AenderuDgen der Quarzdicke so voruiuimt, dass 一 ”2 ^3 etc. 61 = 62 = Ö3 = etc. Diese Bemerkungen sind in so fern, wichtig, als die beiden Bereclmungsweisen zu- sammen zur Controle dienen können, ob die Lichtemission der mit dem Leukoskop untersuchten Lichtquelle sich wahrend einer Eeilie der Beobaclituugen geändert liat, otler nicht. Denn weim die Lichtemission der Lichtquelle sich ändert, wahrend — 37 — nach mul nach dio Quarzdickeu etc. liinzngescbaltet werden, so nimmt auch andere Wertlie an, und die entsprechende Differenz der Compensations wink el ändert öicli um eine eutspreliendo Grüsse; es muss dann die zweite Berechnungsweise nahezu dm Werth liefercu welchen 0m wiilirend je zweier auf einamler folgenden Beobaclituugen besitzt. Gauz dem eutsprecliencl wird der nach der ersten Be- rechungsweise ermittelte Wertli von 0m einen zwischen der Aufangsbeobaclitung mul der betreffenden Beobachtung liegenden gewissen Mittehvertli repriisentireu, und es ist klar, dass die arithmetischen Mittel der beiden Wertlie, nur dann zusammen- fallen können, wenn die Liclitquelle, älirencl der ganzen Dauer der Beobachtungen constant geblieben ist. Ich erlaube mir im Folgcmlcn drei der Versuchsreihen mitzutlieile«, welche ich ausgofiilirt habe, um zu einem Urtbeil darüber zu gelangen, in wie weit der mittelst der Maximalblässe bei grosser Quarzdicke ermittelte Wert-li dor Drehung des Mit- tleren Strahles als eine nur von dem Emissionsverliiilfcniss der Lichtquelle abhängige Constant。 zu betrachten sei. Es möge hierbei noch bemerkt werden, dass die angegebenen Wei* the der Compensationswinkel [7)) aus je 4 beobachteten Wer then entnoiumen sind. ERSTE VERSUCHSREIHE. Lichtquelle : Tageslicht. Wetter : regnerisch. Eingeschaltete Quarzdicke A = 15.691 ö △匪 V imch der ersten Weise be- rechnet. nach der zwei- ten Weise berechnet. V berechnet. f mm. 0,0 1。。,〇7 io°, 24 + 。。パ 7 11°,72 16%5〇 i6°，5 12°,5〇 22°,6o 22° ,6 -f- 〇。,ア8 — o, ユ 15°,2〇 250,65 34°，8 I40,75 ゴ ,55 22°, 5 一 °。，45 一 〇,3 16。,72 22°, 1 6 15V ”°,oo ゴ ,5; 22u,5 + oV8 一。, 4 19〇 が 320,o 190»16 22°，3〇 21。, 6 一 c°，76 一 0,5 ゴ，75 230,36 i8°,3 23〇,02 »5。, 9 一 。〇,2斗 —o,6 24'4〇 V0,88 允0,5 230,76 が, 5 5 20。 バ •— 〇。，6斗 — 〇,7 26° ,6 2 斗 22° ,2 l6°,02 ゴ ,54 22°, 6 — 〇°,6〇 一 〇,8 2-/°,00 2l°,l6 3。, 8 28°,27 220,54 22°, S + i°^7 一 〇,9 3。。，52 55°^ 3。0,5】 M°,53 220,5 〇°,〇〇 — 1,0 3^65 ゴ ,58 21°,5 3^77 的53 22。, 5 十 0°.12 Im Mittel 22,63. 22,58 22,57 22,50 D/2=3,59. —— 38 — ZWEITE VEHSUCHSKEIHE. Lichtquelle: Gasflamme (frei brennend.) Eingeschaltete Quarzdicke △= 14, 77 職. <5a V 07,1 nach dor ersten Weise berechnet. nacli der zweit. Weise berechnet. V berechnet. 中 in /. mm — 0,0 —o,i 5。°,22 5i°»95 19。,;。 I70,5。 5〇°>4^ 5^37 1 8°，9〇 i8°，9 + 0°,2Ö 十 〇°，4^ ^—Ojl 5 ゆ i8°,oo 54〇,〇6 !70,9i i6°，9 十 oV4 —0,5 56°，55 2】。, 10 27°，5〇 55。, 85 17。,9〇 i8°,o 一 〇°,7〇 一 0,4 57。，85 19〜〇7 ij0,oo 57。, 65 17。,9】 I7°»9 一 o°,io 一 〇,5 590>35 19V26 ac°,oo 59〇,44 i80,34 I7°>9 一 。°， 41 一 o,6 61。, 5.2 i8°,83 6。,7〇 6i°,23 i90,9i I7°,9 一 〇°,29 ■ 〇,7 62。, 5 7 170,64 2〇°，5〇 6?,°,〇'2 り0, 8 + 。0,45 一 〇,8 64。, 6 2 i 含0,。 2 20。,5〇 64。,81 17,91 ”〇,9 + 〇。 パ 9 一 〇,9 66°，45 i80,oj i8°,5o 66°,6〇 I70,9r i70,o + 〇°,15 一 1，0 63°，4° iSV3 190,50 62°, 3 9 り。, 91 ”〇,9 — o°,oi Im Mittel i8°，54 i8°,i8 i8°,g5 I70,9 tf = 1〇»34 DRITTE VERSUCHSREIHE. Lichtquelle : Gasflamme (im ölascylinder.) Eingeschaltete Quarzdicke /^=lO,93Gmm' (5a V (pm nacii der ersten Weise berechnet. nach der zweit. Weise berechnet. V berechnet. JzS» 0« /■ mm 一 0,0 一 〇バ 一 0,2 一ら 3 — 〇,4 一 〇,5 — 〇,6 一 0,7 — 〇,8 —〇,9 —— 1,〇 Im 33°>53 35°,〇5 37M8 59〇,78 41。,7〇 45。，3〇 45°>3° 47°>43 49〇,48 5i°.45 5 が Mittel I5°»20 1845 2c°,83 20^41 19^54 I9°,62 19。メ5 19。, 9 5 I9°*9» 190 パ 5 15。 パ ^1°, 3 a6°, 0 19°, 2 160, 0 20°, O 210, 5 20。， 5 190, 7 130, 7 33°>55 35〇,5〇 37°,4Ö 3 9°, 杉 4i°>4° 43〇,36 45°,53 47。 パ 9 49°^6 510 パ 3 53V 9 i 9°,6o J9°，45 I90,63 i9°»67 I9°,66 19。,66 19〇,65 190,66 190,66 19。，64 I9°»7 190.6 190.6 I9°»8 ic，,6 19〇,7 19〇,6 り0, 7 !9。，7 19。, 6 o°,oo + 0〇,45: + 〇°,28 — o°，s6 一。0, 5 2 + 〇°,〇6 + °。,〇5 — 〇°,14 — 〇°,22 — 〇°,22 + 。0,41 り。… 19〇,64 19〇,7 ぴ=。。 為 — 39 — Die Con stanz der nach der ersten Bereclnulgsweise ausgerechneten Wer the von 0m ist wenig befriedigend. Zwischen den nach der zweiten Berechnngsweise gefundenen Wer then bestellt sogar gar keine Uebereinstimruung mehr, 97 22 ,0 一 o ,60 22 ,56 20 ,4 P ,15 2 し 97 21 ,9 一 0 ,45 1,0 “_，。8 22 ,32 14 ,8 34,37 2i ,98 21 ,0 + 〇 ,28 Im Mittel 21 ,695 21 ,56 21 ,91 21 ,97 ^/2==I ，99 Die liier unter “ 7} ” angegebenen Wer then sind die aritlimetischen Mittel aus je 8 beobachteten Wertlien. Es zeigen men liier wieder nicht unerlieMichc Abweicmmgen in den beobachteten Wcrthou vou 0m. In den Wei* then, welche nach der zweiten Woise bereclmefc worden sind, ist dio Nichtübereinstimmung fast eben gross, wio in den Wer then, welche nach derselben Weise für die Drehung des mittleren Strahls ermittelt worden. Indem ich die Beobaclitungsdateu der Methode der kleinsten Quardrato unterwarf, fand ich als Eelation zweisclien 7J und (5a 7j = 12,375 + 21,987 (?△ Die aus dieser Gleichung berechneten Wertlie von 7] sind unter 11 7} berechnet n so wie die Beobaclitnugsfeliler nnter zusammen gestellt. Die Zahlen, die unter 中;、、 und 0m stellen, sind dio Wertlie fiu* die Drehung des Natriumliclites, welche sich aus der oben stehenden Gleichung nach der ersten und zweiten Berecliungsweisc ergeben. 瘳 — 41 — Es scheint sonach ein etwaiger Fehler in der Construction cles Lcukoskop nicht daran Scliuld zu sein dass die beobacliteten Wer the von füi* das homogen o Natriumlicht nicht mit einander übereinstimmen, da ja etwaige Fehler in der Construction cles Instrumentes iVbweiclmngeu im einerlei Sinne verursaclien müssten} , was liier nicht der Fall ist. Denn : wie man sieht, ist die Vertheiluug der Beo- baclituugsfeliler dem absoluten Wertlio nach recht uure^elmässig und aucli dio Vertlieilung dem Yorzeiclien mich ziemlich regellos, so dass man 'volil amiebmen kann, dass die Bcobaclitungen selbst mit der bei der Bescliaffenlieit des Lcukoskops und bei der Natur des zu Beobacliteiulen überhaupt möglichen Genauigkeit geschehen ist. Berechnet man aus den Wer then der Beobachtungsfeliler den walirscliein- Heilsten Werth cles walirsclieinlicLen Feniers, so findet man 士 〇フ47 Indem man diese Zahl mit den einzelnen Wer then aes Beobachtungsfelilors 11 J、、 ver- gleicht, findet man in der That dass naliezu ß Beobachtungsfeliler unter dieser Zahl und G über dieser Zahl liegen. Unterwirft man die für die Drehung cles mittleren Strahls beobachteten Daten- geliclifalls der Methode der kleinsten Quadrate, so findet man die Relation zwischen 7) und ÖA れぱ (lie erste Yersuchsreilie T] = 10,24 4 + 22,5258 (5a für die zweite Versuchsreihe V = 50,581 + 17,91 (5A und für die dritte Yersuchsreilie 7) = 88,582 + 19,6599 ÖA Dio aus diesen Gleichungen berechneten Wcrtlie von jj sind ebenfalls unter ft 7} berechnet M mul dio aus diesen Wertlien von 7) nach der ersten und zweiten Weise betrechneten Werfclie von ¢„1 unter 0": und 0 怎 uud die Difforenzen zweischeu den beobacliteten und bereclmeten Wertlien 7/ sind endlich unter zusainmengcstellt. Für einen homogen gefärbten ljiclitstrabl ist die Möglichkeit vorhanden, das Leukoskop iu die gleiche Helligkeit der beiden SpaUenbilcler scharf einzastelleii ； dennoch war tier Beobaclituugsfehlor, der tlieils aus der Schwierigkeit, den Punkt gleicher Intensität der beiden Spalteubilder scharf walnztmclimcn, theila aus der luizuliingliclien Theiliuig des Kreises am Ocularnicol resultirt, aucli fiir diesen Fall nicht unei-lieblich. Man kann daher wohl enyarten, dass der Beobachtungsfeliler für den mittleren Strahl einer Lichtquelle viel grösser ausfallcu müsste ； weil liier zu den oben erwähnten beiden Fehlerquellen noch eine dritte hinzukommt, nämlich die Umnögncnkeit, die beiden Spaltenbilder gleichfarbig werden zu lassen. Berechnet man uen wahrscheiiilichsten Werth des wabrsclieinlichen Fehlers für die drei VorsucLisreiheii, so fiudot man für die erste Yersuchsreilie die Zahl r = x 0°,43 — 42 — für (lio zweite Versuchsreilio r = 十 0°,2G und für die dritte Versuchsreihe endlich r = ± 0C,20 Es gellt um aus don Wer then dieser Zahlen hervor, (lass man bei der Einstellung des Leulcoskops in die Maximalblässe im Allgemeinen keinen groösoron Fehler zu erwarten liat, als dcnj eiligen, Avclcbon man untoi4 gleicnen Umständen bei doi, Ein- stellung dos Lculioskpps in die gleiclic Helligkeit tier beiden Si^altenbilder für eine monocliromatisclic Lichiquollo begehen wi’u.de. Dass dio Zalil r fiti* die erste Yer- ßuchsreilie grösser ist, als diejenige für die beiden Folgonclen darf uns nicht Wunder nehmen; denn tiie fi'u* das Tageslicht durch das Einsclialten einer 1 511 im (licken Quarzplatfee herstellbare Maximalbliisse ist schlecliter, als die durcli dieselbe Quarz- dicke fi'ir eia Gaslicht hergestellte (wio denn überhaupt, um gleich gute Maximal- hliisse zu ei.lialtci], um so grössere Quarz dicke erforderlich ist, je grosser die Liclit- o mission einei* Liclilquelle ist) was oü'cnbav den Beobachtungsfeliler vergrüssern muss. Lm Yergleicu der obigen Wertlie fiu* den wabrsclieiiilicliou Felilor mit den Zahlen unter der Hub lick “•/•’’ in der entspuechciulen Beobficlitimg«rei]ie zeigt, dasR in der ersten Versuchsreihe ö F eliler über r und 6 Fehler unter yorkommen mul eLenso ia tier zweiten. In der dritten Yersuolisreilie eiullich sind von den Beo- bachtungsfelilern 5 linier r und 6 über r. Ich glaube hieraus scliliosseu zu iu iissen , dass auch alle Beobaclituugen iu deu oben 111 itgetlieilten drei VersucliBreilion mit der Genauigkeit gemilcht worden sintl, welche die Boschafienlieit des Leukoskops im cl die Natur dos zu Beobachtenden überhaupt gestattet, mul dass die einzelnen Abweiclnmgen in den Wcrfclien von (ßm eiuzig und allaiu den imvermiclliclien Beo- baclituugsfchlorn zuzusclireiben seien d. li., dass man zweisclien 7) und Ö/s oino lineare Beziehung annemen darf, in sofern ÖA sich innerhalb Eines Millimeters bewegt und dass, falls acnnocli eine Function der eingeschalteten Quarztliclco sein sollte, dio Aeadoruug, welche 小 m durch die Aenderung der Quarzdicko um 1 麵 erleidet, wohl nicht die erste Decimrlstellte ihres Werthes beeinflussen könne. Rathselliaft bleibt aber nocli das Yorherrsclien der nagativen Beobaclitungs- fehler nm die Mit fco dev beiden ersten Versuchsreihe. Iu der Mitte der dritten Yorsuclisreilio treten zwar positive Beobaclituiigsfobler auf, aber im Minimum. Auch in der Mit to der Versuchsreilio über die Drehung der Natriumlichtes kommen zwei positive Fehler yor und zwar im Maximum, Eine Aenderung der Liclitcmission der in Ecdc stehenden Lichtquellen kann es wohl nicht bewirkt liabon ; demi es wiire zu unwalirscliemlich anziuieliracn, dass drei Lichtquellen ^älivend dei* drei zeitlicli von einaudor getrennt angostellten BcobaclitiiDgareihen immer denselben Yerlatlf in der Aenderung ihrer Lichtemission zeigten. Weniger uiiwalirsdioiiilidi ist die Anualime, dass man hierbei mifc der Ermudmjg der Netzhaut zu tliuu hat. Am Anfang jeder Versucbsreilic als die Netzhaut nocli ihr volles Perceptionsvermögen besass, wurdeu gewoimlicli grössere Fehler bei der Bestimmung der Compensationswinkel begangen, als um die Mitte, weil das Auge am Anfang clo ——43 — BeobaclitungsreiliG noch nicht dieselbe Aufmerksamkeit bei der 1101 •Stellung der Maximalbliisse habon kann, wio in tier Mitte der ßeobachtungsreihe. Gegen das Ende derselben macht sich die durch die unausgesetzte Einwirkung des Lichtes verursachte Ermüdung tier Netzhaut gelteml, und die Precision bei der Einstellung des Leukoskops in die Maximal bliisse wird wieder germger, so dass am Ende jeder Beobaclitungsreihe wieder grössere Fehler auftreton müssen, als dioj eiligen lim die Mitto. Da aber (lio mittelst der Meiliodc clor Ideiasten QuarJrate gefundenen Relationen zwisclicn rj und öa voniussetzen, (lass alle dazu benutzten Beo- baclituugeu unter gleich giinst-igon UmstiÜKlcn, uml mit gleiclieu Pnecision gemacht \vordcii seien, so ist es leicht erkMrlicli, warum in der Mitto jeder Beobaclituugsreilie die BeobacbiuDgsfeliler mit einem und demselben Vorzeichen auftreteu mussten. Wir selien somit, dass cler Qualient nahezu einer Constaute gleich gesetzt worden kann, in sofern 6a iimerLalb der engon Grenzen Eines Millimeters sich bewegt, uml dass dieser Quotient die Drehung eines gewissen Mittleren Lichtstrahls giebt, dessen Wcllenliinge für verscliiodene ljiclitquello verschieden isfc, wie es schon die oben angegebenen Mittclwcrtlie von 0m fiir drei verschiedeue Lichtquellen auf's Deutlichste zeigen. Es liegt uns nun ob, zu imteisuclieii, ob diese Amialune einer linearen Beziehung zwischen ÖA uud 6 7) sticlihaltig bleibt, wenn (5a gross wird. Ich bomerke zuvörderst, dass die Maxitnalbliisse eine gewiss^ periodische Er- sclieinung in bezug auf tlio Y^riiiiderliche A ist ; denn : giebt man dem Winkel des Ocultiriiicols einen gewissen constanten Werth, so giebfc es immer mehrere beo- bachtbare Wertlie von A» bei denen die Maximalbliisso in den beiden Sp alten - bildern ein tritt. Hat nun die Bedingunggleicimng, der die beiden Variabein genügen müssen, witklicli eine lineare Form, so können die Wertlie von △, welclio bei einem bestimmten Wertbo von 7) die Maximablässe lierstellen von einander mir um eine bestimmte consfcaute Grösse differireu. Die Versuche lehren, dass dieses «allerdings anniilireiul cler Fall ist, wie es folgende Zahlen dartlnin mögen. LICHTQUELLE : PETEOLE UM LAMPE Der Winkel des Ocularnicols 7) = 06. △ Differenz. 11,671 1(3, 105 麵 4,484 20,795 露 4,090 24,075 4,180 - • 44 • V = 10° △ Differenz. 7,5(39 腦 i 11,551 麵 3,982 15,774 匪 4,828 19,854 4,080 V = : 20。 △ Differenz. • 7,289 麵 11,101 函 3,812 15,202 麵 4，101 19,G02 讎 4,400 24,295 w?» 4,G83 V = 45° A Differenz. 9,918 麵 13,784 3,961 18,049 麵 4,275 22,718 wm 4,664 Allein; da die zweite Decimalstelle in den angegebenen W erthen für die Quarzdicke noch sicher beobachtet werden kann, scheinen die obigen Zahlen dafür zu sprechen dass es streng genommen, von einer linearen Beziehung zwischen 7J und A nicht die Heile sein kann und dass dio Bedingungsgleichung der Maximalblässe, da △ keine — 45 — constante Periodicitiifc besitzt, eine audero Form als die lineare haben muss und zwar so dass für jeden Wertli von 7) die Differenzen der Wer the von △， welche die Maximalblässe L erstellen, nahezu constant bleiben. Es drüngt sich somit die Yer- mu tlmng auf, dass eine algebraische Beziehung zwischen 7) und A niclit besteht. Ich erlaube mir im Folgenden zwei Versuchsreihen mitzutlieilen, aus deren Zahlen man wolil auf die Form der Bediugungsgleichuug der Maxi m alb lasse scbliessen könnte. • LICHTQUELLE : PETROLEUMLAMPE. Eingeschaltete Quarzdicke A = 11,213 ww- (5a V beobachtet. V berechnet. i>m berechnet nach der zweiten Weise. 中， n berechnet nach der zweiten Weise. /• mm 2, 171 3, Ol 斗 34,〇4。 5^ iS 49, 75 2I,°o6 2i,°o6 + 2,° 2 6 + 40 3, 745 67, 4。 65, 06 21, 02 20, 90 + 3, 34 4, 585 84» 33 82,88 20, 74 20, 11 + し 45 5, 100 • 78 , 97. 85 21, 21 22, 90 + わ 95 6, 146 119, T3 55 21, 02 20, 79 + 3, 6o ly ISO 137, 07 157, 22 20, 49 17. 35 一 0, 15 7, 9°9 15 い 7 152, 50 2C, 71 22, 22 + 〇, 77 8, 75^ 168, -20 170, 19 198, 01 20, 33 17, 71 — i, 99 10, 080 195,65 20, 39 20, 67 一 2, 36 10, 9-3 212, 95 215, 70 w， 55 20, 52 一 2, 75 11, 65a 226, 50 23c, 99 20, 25 58 一 4, 49 12, 495 244, 75 248, 68 20, 38 21, 65 — 3, 95 Im Mittel 20, 68 21, 21 X f= 0f°8 LICHTQUELLE : VON WOLKEN EEFLECTIRTES TAGESLICHT. Eingeschaltete Quarzdicke A = 10,37 (5a V beobachtet. V berechnet. 07» berechnet nach der ersten AV eise. ¢1,1 berechnet nach der zweiten "Weise. /• mm 0,837 o° 17, 48 1，904 19, 99 20,。 名 8 io,688 - 1,〇9°4 - 2, 51 1,680 35,46 58, 21 21, IO 16, 6r 一 2, 75 3,108 70» 18 69, 08 22, 90 24, 01 - - I, 1〇 3,951 90, 86 86, 30 22, 99 23, 35 - * 4* 4,680 ]〇5, 11 105, 05 21, 90 22, 08 19» 55 - - 2, 〇6 5,523 121, 96 112, 17 19, 98 - - 〇, 79 6,240 】39, oi 136, 77 22, 28 23, 77 - - 2, 24 7,083 155,26 154,02 21, 92 19, 28 - _ I, 2 斗 3,017 I74> Sl 175, 18 21, 77 20, 63 - 〇, 65 8,746 187, 01 190, 92 21, 38 17, 12 - 3» 9^ Im Mittel ar, 92 20, 52 乂 f 二 0,266 — 4G ~ Wenn man diese Z ililoa dor Methode der klGinsten Quadrato unterwirft, so findet man für die erste Versuchsreihe die Gleiclning V = — 13,874 + 20,97 2 Öa und für die zweite Versuchsreihe V = 1,904 + 21,614 (5a. Diejenigen Wertlio von 7} welche aus diesen Gleichungen fl i essen, sind imtei. der Eublik <4 Tj bereclniet zusammenges teilt, lind ihre Abweiclimigen von den beo- bacliteteu W er then unter Ein Blick auf die obigen Tabellen lehrt uns sofort, dass eine lineare Beziehung zwischen 7J mul △ in der That nicht existiren kann ; denn die Abweicimngcn zwischen den beoba elite ten 1111 d berechn eten AVer then von 7J sind nicht allein zu gross als man sie hätte dem Beobaclitungsfelilem zu schreiben können, sondern sie zeigen auch in den beiden Versuchsreihen eine bemerken swertlie Eegelmitssigkcit m der Yert liei lang dos Vorzeichens. In der ersten Yersuchsreilie treten bis zur Mitte mu. positive Abweicliungen auf, und zwar so dass sie im Allgemeinen mit der wachsenden Quarzdicke wachsen. Von der Mitte an treten liingegen mir negative Abweichnugen auf, mul zwar so, (lass ihre absoluton Wortlie auch iiieu mifc wach- Bcnder Quarzdicko z mich men. In der zweiten Yersuclisreihe erscheinen zuerst nur negativ zuneLmende Abweichungen ； sie werden naher nur positiv, und verwandeln sicli scbliesslicli wieder in negativ ztinebmende Abweicliungew. Die minimalen Abwciclmugen treten da auf, wo die Abweichungen das Zeichen wechseln mul auch um die Mitte jeder Beobachtimgsreiho. Da aber das letztere ■wieder aus der Eriü üdung der Selmerven zu erklär en ist, bin ich wolil zu dem Schluss berechtigt, dass die wirklicliö Bocliugnugsgleicliimg der Maxima lblässo eiiio solche Form Laben müsse, (lass die aus derselben liervorfliessenden Wertlie für 7) bei wacliseuclem Wertlio von △ um diejenigen Wer the für TJf welche aus jenen mittelst der Methodo der kleinsten Quadrate ermittelten linearen Glciclinngen her- Vorgehen, hin mul her schwanken and dass diese letzteren AVcrtlie für 7) gewisse mittlere Wertlie für dieselbe Variabel, dars teilen welche aus der wirklichen Bcclingnngsgleichmig der Maxtmalbliisse her vorgehen, und zwar so dass diese Wertlie bei waclisemlor Quarz diele o, eben so oft über als unter jejicm Wertlio für 7) zu liegen kommei], und zwar aller W ahrsolieinliobkeifc nach um dieselben absoluten Grössen ； denn dio algebraischen Sumrno der Abweicliungen zeigt deutlich genug das Bestreben, bei grösserer Anzahl der Beobaclitungeii, mul boi der Yergrässevung der Grenzen, immerlialb deren (5 A varnrfc, immer kleiner zu werden ; sie betrügt fiii’ die erste Beobaolitimgsrcilie 0,08° für dio zweite Versudisrcilie aber 0,30® als ob zwischen 7/ m]d △ in der T]】at eine lineare Bezielxuug statt-gefuiiden liiittc. Ich glaube Hieraus schliessen zu müssen, dass man 7J als eine zweigliederige Function ■von △ anselien kann, im welcher das erste Glied der Variabel direct proportional, ist, während das zweite eine gewisse periodische Function von △ ciUltiilfc. Was 111111 die nacli den beiden Weisen bereclmeien Werllie für パ lie Drelmno* des mittleren Strahls anbelaiigt, zeigen die oben mittgetheiUen Zahlen dass auch sio um eiueu gewissen mittleren Wertlio hiu und lier scliwanken also —— 47 — aass man als Ausdruck fiii. (lio Drehung des mittleren Stralils auch eine zwei- gliedrige Function annelimcn kann, in der das erste Glied eine Coustanto, und das zweite Glied aber eine gewisse periodische F auction von △ ist. Es ist indessen bisher nicht möglich gewesen, gestützt ftuf dio exporimcntelleu Daten, wie die oben angegebenen, die Form der Function zu bestimmen, welcher 7} und △ gemiigen müssen, um die Maximalblässe liervorzimifen. Wir werden allerdings weiter unten durch theoretische }3etrachtungen zu einer transcendenten Beziehung zwischen 7) und △ geführt werden welche in der That die aus den beobachteten Wer then fiir 7) geschlossenen Eigenschaften hat. Allein ob die so theoretische Kelation in der That mit der AVrirldiclikeit übereinstimmt, das za präfeu ist mir bisher auch inimöijlich gewesen. Soll um das Leukoskop aber lediglich dazu dienen, zur Keim tin iss einer fiir jede Lichtquelle mul ihren Emissionszustaml charakteristisclien Constante zu gelangen, 80 ist die Kenntuiss der functionellen Yerbindung zwischen den beiden Yariabeln nicht gerade unumgiinglicli liotliwemlig ； ein man ja ein fiir alle Male eine Quarz - platte von bestimmter Dicke einzusch.alten und jedes Mtil um eine bestimmte Grosse die eiugcsclialteto Quarz die ko zu änderen branclit. Dann giebfc der Quotient ~ wenn ö 厶 imiei.halb Eines Millimeters liegt, immer anniilirend den Werth welchen die Drehung des mittleren Strahles unter der Einschaltung der betreffenden Quarzdicke Iiat, oder, wenn man ÖA gross nimmt, immer einen bestimmten mittleren A\rertli der Dreliuug des mittleren Strahls, welch。 ilen Quarzlickcn △ und △ + f ^ entsi) rechen würde. Ich erlaube mir im Folgenden dio llesultate einiger Messungen welche ich in (lioser Hinsicht ausgeführt habe, mitzutlieilen. Die Quarzplatte, welche in das Leukoskop eingeschaltet worden ist eine 13,37 _ dicke und dio Dicke, um welche diese Qnarztücke vermehrt wurde, betrug diuchgaugig 0，0 動“ Es möge noch bemerkt woivlen, dass die unten angegebenen Daten aus je 10 8 wenig von einander ab- weiclioiulen Beübaclitiuigen entnommen worden sind. SONNENLICHT. ( reflectirt von einem Carton.) (T fA 九’〃. 88,°25 80,27 21，90 0,000 587 wm SONNENLICHT. (reflect, von Wolken : Die Witterung : klar.) 0 <5a 88,°30 20°, -17 23°, OG 0,000 5G7wm SONNENLICHT. (refleci. von Wolken die Witterung trueb.) o <5a 8G°,98 208 21°, 20 0,000 597 SONNENLICHT, (reflect, von einer Gipsplatte.) 0 38°, 17 2G%21 28°, 92 - 0,000 5(54 襲 MAGNE SIUMLICHT. ( von einem Carton reüectirt.) 0* (f),n ao°,8C 41°, 00 2G°,28 0,000 53GWW EIjECTBISCHES KOHLiENLilCHT. ü し 0 m 入 m 40°, 86 i* 5i°,55 27°}38 0,000 52ümw* MAGNE SIUMLICHT. ( von einer Gypsplatte reflectirt. ) 0 (5a 4Ö°,«7 29°, Gl 2b*, 12 0,000 523wtm KALKLICHT. 0 (5a v d(/>{, d(ß v d X d X d X für drei verscliietlene Wertlic von 又 vei.schwiiiileu, und zwar so dass eine gewisse grössere, -gf fiir eine gewisse mittlere, und 机 dX ¢7¢,. dX für endlich für eine gewisse kleinere Wellonliinge verschwindet, wenn die Jjiclitquelle ein continuir- liclies Spectrum besitzt. Sendet aber die Lichtquelle nicht alle Strahlcngattung aus, ist ihr Spectrum ein (liscontinuirliclies, so worden die Differentialquotienten der drei Empfinclungsfinictionon für mehrere gewisse Wer the der Wellenlänge vcrscli- winden, da die Eiupfindvmgscurven dann für mehrere Wer the der Wellenlänge Maximalpunkt zeigen, und ausserdem iTu. mehrere gewisse Wellcnliingen uiieiullicli gross werden. 4. Was mm die Wertlio dieser ersten Dcfferentialquotienten für die Wellen- länge der Eudstralilen 久〇 mul Jinbelangt, so werden sie im Allgemeinen ver- schieden sein, je nach dem Wer the der Wollenliuigen Xo und 入/ 1 ; es ist aber klar, dass llmen gewisse Wer the zukommen, da die D i fferen tialq n o tien teil dgir diu di,, _ dX d\ dX die trigonomettfiscliG Tangenten der Winkel bedeuten, welche eine an den Em- pfinduiigscurven gelegte Tangente mit der Abscliissenaxe X einscliliesst. Nehmen wir an: Xo habe einen Werth, bei welchem ein LiclitstraLl auf höre die Enipfintlniig Violett zu erregen mul Xfi einen solchen, bei dem ein Lichtstrahl aber aufliore. die Empfiiuliing lioili zu erregeu, so Avinl so wohl 伯1. 入 = 又〇 als fiir \ = ス 2 als uiieiullicli klein angesehen werden cliitlcn da die Empfiuduiigsciu.ve für Grün sowohl für ab n eli m ende als fiu. wachsende Wellen länge sich der \ Axe nälirfc und zwar so dass die Curvenstücke für grössere oder kleinere Wellenlänge wohl als geradlienig betrachtet werden darf. Aus dem letzteren Umstande lainn wohl noch cZ 交 S festgesetzet werden class auch _c 汚?- sowohl für 入 = ん so als, für \ mi- endlicli klein werde. Ganz anderes werden sicli die Differentialquotientcn der beiden anderen Em- pfindungsfiinctioiicn verbal ten. Da die Curve 0〆 ス) gegen X ~ und die Curve 0r( X) gegen 又 = l hin (Fig. 8. Tai.) sich gleichsam asymptotisch der X Axe • ， , drf)¥ , dr6r , , dr6v n nähren, so 】iöimen 一''- und mr 凡 = ん otlcr 入 _ und -^乂2 - für X z=z XiL wobl als unemllicli klein angenommen werdeu . Welcher Werth aber 裳 f 又 mul 執 ~d\ fiu. 入： = 入 o beizulegen sei, dtiriiber lässt sich sclilecli- terdings nichts aussagcu, was hätte als feststehend angenommen werden können ; — r>] — da weder fin fig, fSVf nocli 又 0 rm(l 凡 bekannt sind. Es kann wohl sfcrcng genommen kaum von einem End strahl des l^ichtepectrums die Ilecle sein, wenigstens nach dem violettene Ende desselben liin; da die ultra- violetten Strahlen bekanntlicli auch dem blossen Auge sichtbar gemacht werden können* Allein, da die subjective Helligkeit der so sichtbar gemachten ultravioletten Strahlen ausserordentlich klein ist, so wird man sich mciit weit von der Walivlieifc entfernen, wenn man das Liclitspectmm da enden lasst, wo die Empfindung d 中 Violett aufliört. Es ist daun annehmbar, dass ■ fiir 久 = 入 nicht mi- endlicli klein ist, sondern einen bestimmten endlichen Wertli besitzt, der um so grösser ist, je steiler die Curve <^V{X) zum ualiliegenden Maximum steigt d. b., je mein* die betreffende Lichtquelle diejenigen Licntstrulilen aussendet, welche die violettempfmdondo Fuserart erregen. Hinsiclitlicli der Empfiiulungsfanction 0,.( 入), lässt sich auch dem Analoges nnnehmen dass ihr erstet* ])iffereniialquoiieiit einen endlichen Werth fiir 入 = 入" hat, dev um so grösser ausfullen wird, jo steiler die Km pti ndui) gsc ur vo von X = Xu aus aufsteigt d. 】i., je mehr die Lichtquelle Strahlen ausseutlet durch -welclie die rotlieinpfimlende Faserarfc starke EiTegung erleidet ; eine Aunalime, die in sofern als wahrscheinlich bez.eiclaiet werden dürfte, als (las Lichtspectrmn einer Lichtquelle viel scliiirfer mich dem Ulti.ai.otl】， als nach dem Ultravioletfc v.w begrenzt zu sein scheint, was daraus horvorgelit, dass, man mag die übrigen liellcren Hpectralfarbcn abblemlen, wie mau will, die (laduicli gewonnene Ausbeute an den sichtbaren ultriirotlien Btr； 1111011 mu. gering uleiut. Pies alles gilt jedoch nur fiir Lichtquellen, bei denen die spectrnlen Eadstralilen die ]*'mpfiiKlungen Ilotli mul Violett erregt. Ist dio Lichtquelle ab er so bcsclmffen, dass der eine der Eudstrahlen uicht die Kmptiuduug lioth, oder Violett liervorruft, claim worden wir uns vors teilen müssen, dass die Difterentialquotienten der drei Empfinfluugsfttnctioiien im Allgemeinen endliche Wertlie fin- X = und ^ = 入0 eflialten. Denn ； gesetzt ; dio Lichtquelle sende keine Strahlen kleinster Wellen- lünge aus, mul ihr Lichtspectrum reiche etwa bis zum Blau, soclass öinen Werili besitzt, bei dem ein Licbtstriilil massig stark die rotli- und violet tempfiiulende, stärker die griinempfindeude Fasorart erregt. Dio Empfiiuliiugscnrven werden dann etwa solche Gestalten buben, wie die punktiften Curven in der Fig. (8) Taf. sio darstellen. Vom Pnukt 又 = 入〇 uns steigt die Curveu (九) uml ¢„(70 massig steil, an steilsten steigt aber die Curve ル (入)， soclass mau aimehmen leano, dass die ersten Diöeuentialqaotieiiteu der E uptiiuluiig.sfanctiojien iu diesem Fall olme Ausualime für \ gewisse eudliche Wertlie besitzen. Wenn die Lichtquelle hingegen keine Strahlen grosser Wellenliinge 麵 sendet so dass eino 'Wellenlänge ist, bei der ein Jjiclitstralil miissig stark drei Faserarten erregt., so werden die Empfi ml ungscur ven etwa solche Gestalten, haben, wie die gestrichelten Curven in Fig. 8. Taf. zeigen und es kann daun wolil ebenfalls angenomiuen werden dass die ersten Difföreutialquotionteu der Eiüpfimlungsfunc- tionen auch in diesem Fall fiir 入： = 入 紅 Wertlie erhalten, die durchaus nicht loehr als vor sch windend angeselien werden kömieu. * Helmholtz Physiologische Optik, pa^?. 228, DIE BEDINGUNGSGLEICHUNGEN1 DER FAT ミ, TVEN- GLEICITHEIT. Ein objectiv homogener Liclitstrahl von der Wellenlänge X pflanze sich fort durch eine Quarzplatto von der Dicke /S, und seine Polarisation sebene erleide eine Drelmng ^ bei der Quarzdicke Eins. Ist A der absolute Werth der Schwingmigs- amplitude des Liclitstraliles, so geben A2cos2(A^ — 7})j A2sin2( △ % ） die objectiven Liclitiiitensitiiten der beiden Spalteubilder, Avenn 7] den 'Winkel bedeutet, welchen die Polariaationsebcue des aus der Quarzplatte her vor tretenden Strahles mit derjenigen des Ocularnicols bildet. Gelangen nun diese beiden Strahlen 7. ul* Netzhaut, so werden dt-ei Fitseraften erregt, gloiclizeitig aber in ungleicher Stiii.ke. Yon clem einen Spaltenbilde erfahren diese dfei Nervenfaser Erregungen jzif( ^,)coss( A ^ — V) jrf,(^}cos5(A^ — V) も (又) cos®( 厶 p — ”) von dem anderen Spaltenbilder aber 0/Sin2( 厶 ％ — ス) sin2〔 A 羚 一”) 0V{ 入) sin2( A % ” ） AVenn die lnchtquelle verscliiedene Strahlengattungen in gewisser Zusammen- setzung aussendet, so geben die drei Integrale j M 入) cos '’厶 P - V)d 入， j A(A.)cos2 (厶 ％ — ”)ぬ， I* 乡ズ 入) cos2(Ap — T})d\ ausgedehnt über das ganze sichtbare Spectrum der Lichtquelle die Farbeumengen, welche die Netzhaut in dem einen SpaJtenbiltl empfindet, während die Integral J 0,.( ^ )sin2( ^^-7] )dX, | ^^)sia2( \ が ズ 入) sin2 (厶 )d 入 (lie Farben men gen darstellen welche die Netzhaut in dem anderen S pal teilbild empfindet;. Dio gesammto Liclitmenge wclclio ilie Netzhaut in den beiden Spalten- bilder empfindet, wird durch die beiden Inetgrale j 0(A,)cos2( —n)dX, j 0(^)sin2( — ausgedriiekt, wo 0(. +' 0fJ + 0v = ^ gesetzt worden ist. — 63 — Es sollen die Bo.liiiguiigeii gesucht werden, unter denen die beiden Spulfccn- bilder gleiclie Färbung von gleicher Holligkeib zeigen. E.s sind hierbei zwei Moiluli- tiiteii iii’s Auge zu fassen : 1, Die beiden SpaUcnbilcler sollen gleiche FjiL-biiiig von gleicher Helligkeit und zwar genau dieselbe Farbe, -\vie die des ursprüngl eichen Lichtes, zeigen. 2. Sio sollen nur gleielie Färbung von gleicher Helligkeit zeigen. Die erste Motlalitür ist evfiillfc, wenn die in den beiden Spaltenbildern entlialteneu Mengen der GL-undfarben in genau demselben YerLaltnisse * stehen, wie in dem ursprünglichen Liclifc. Die B eclin giingsgleicli langen hierfür sind : ( ^)cos°(A^ — T})d\ I ^)cos2(A^ —v) 狀 ノ ¢r{ — T])dX J 0g{ ^)ccsr(A^ — 7j)dX wenn a uinl 1> die SiUtigungseonstauteu der Liclitquolle bedeuten. U nd die Be cl in gun gsgl e i cli u n g fiir die Gleichlieit der Helligkeit ist, f ん (、入 )sin2( 1\屮 一T\、d\ j ¢v{ 人) sin2、’ — T} )dX I p/、 ^)siir(A^ — T) )d\ f A)cos2(A^ — Tj)dX= I 乡 (又) sin2(Ap — T) )d\ d. li., * J 多 （凡) cos2 (△芦 一 T})dX = o woraus dann mit Eiicksicht aüf die Gleichungen (0) folgt (11) j 说 ,(；l)cos2(Z^ — ？?) d 入 =j^(A.)cos2( △羚 一 入) cos2( △今一々) cZ 入 =o. Die zweite Modalität ist, erfüllt wenn die in den beiden Spaltenbilclom eut- lial tenen Mengen jeder Gruncl färbe genau gleich sind; was einemt, wenn die Gleiclmngen stattfinclen : imd dazu d. li., I ^.( ^)cob2(A^ — T))d\ = | p5,.( ^；ßin-(Aj^ — •f 齡 。物-： 〇讥 = ):娜 柳， u j ^v( ^ )cos = T und A = cc 7j willkürlich ei.fiillt werden. Das Er stere ist ohne weiteres einleuchtend) aber nicht das Letztere. Nennt maii eins der drei Integrale in (11) IT, und setzt man W = | 0( A,)cos2( — Ti )dX 、vo 0 eine der Kmpfimlungsfunctionen bedeutet, und nimmt mit Ste(aij: und Broch | Hir ^ den Ausdruck で an, wo q und ß gewisse Constanten sind, die bekannt sintl, tlann kann das Integral in clie Form gebracht werden = oos2 rj j 0’( p )cos2 △か Zp + siu2ry indem man set/t ])i(j Integration ist dann zwischen ausziulelinen. Wenn wir m das erste Iutegi-iil statt 5^, ^ es sich in TT ein fiil iren, so ver- J 0^(^ — )sin2A^^J^ welches sich bei sehr grossem Werth von △ sich wenig imter scheitlet von * Stefan. SitzAingsbericht der Wiener Akad. Bd. L. f Broch. Dove's Kopertorium Bd. YIT. pa^. 115, Diese Bemerkung ergiebfc für sehr grossen Werth von A Es folgt hieraus für ill’s unendlich wachsende A oder }V X =(cos2” + sin2 7) ) lim j 0’（ 0)siu2 △か 7p welches bekaimÜich gegen = (cos2々+ siu2n)[o0’(o) — 〇0'(〇)] JL — 〇 eouvergirt, in sofern が {ifi) tfj zwischen den emlliclien Integrationsgrenzen nie imencllich wird. Diese beiden extremen Wortbe der Variabeln sind indessen die einzigen Wer the welche die Bedingungsgleichuiigeii (11) gleichzeitig erfülleu, denn : es ist •überhaupt ein Ding von Unmögliclikeif, jene drei, Integrale durch irgend einen Wer the von △ und einen jtassenden Werth von 7J gleiclizeitig zum Ycrsclnvinden zu bringen, was schon daraus liervorgclit, (lass uns iui Grossen und Ganzen um* zwei Viiriaheln zu Gebot stehen, wahrend die Zahl der Bedingungsgleichuiigeii, die erfüllt werden müssen, = 3 ist. Wir gelangen somit zu dem lieg.^tiven IlesuUute, dass weder die drei Integrale in (11) durcli einen emlliclien Werth von A 川 id einen dazu passenden Werth von 7j gleichzeitig zum Vorschwimlen gebracht werden können, das heisst, (lass die bei- den Spaltonbilder clarcli endlichen Werth von A nie vollstiimlig gleich farbig gemacht werden können. Dio Bedingungen der Miixiuiall)liisse der beiden Spaltenbilder müssen sonacli anderos lauten, als die Gleichungen (11). Wir setzen zur Abkurzung Wr = J 沐 0 s2( △殄一 n)dX \Vy = j X) cos2 (A^-jj)dX \V0 = j 0,(^>s2(A^ - T])dX Es sollen die Bedingungen ermittelt werden, unter (l.enen die grösste Aeliulichkeifc der Färbungen der beiden Spaltenbilder stattfindet. Wir setzen — ö(i — V a，r Lr, 0,.( A)cos2( A ^ - 7? )c/ A, j 0,.(Jl)cZA +1F,.' j + Wa j p',u>a + t ド „ \^{X)dX + wa I p,(x)ta - IV,. I 0a( A,)ccs?( A ^ — 7/ )d\ f 0,.( 又) cos?( L — r,)dX f 0,,( 入) CfS2( j* 0,(A,)siu:( L^> — 7])dX I も (ス) — ??)ca f 0v(Pi)siiv( l^u^ — n)dX f 0/^)sia2( /l.p-7/)cU (13) j 0/^)rA - Wa f 0,(X)6U-TF„ l'^dX-JV, Die Grossen a! U a 1 und b'r bedeuten die Verhiiliuisse, der in jedem Spaltenbilde entlialfcenen Mengen der drei Gruiidfarben. Es ist dann klar dass, wenn die Dif- ferenzen /； ir durch geeignete Wertlie von A und 77 möglichst klein gemacht und die Bedingung der gleichen Helligkeic j 0(X)cos2(A^ — ri)d\ = 0 (吼） zugleich erfüllt werden Icani), die Maximalbliisse tl. ]i., die grüsstmögliclie Fiirben- iilmliclikeifc in den beiden Spaltenbildeni statt iindet. Die Gleichung (iya) ist jeder- zeit clurcü gewisse Combination, der beiden Variabein erfüllbar. Was die erstcre IJedingUDg anbelangfc, so würde sie allenlings erfüllt sein, womi durch passende Wertlie von A und 77 die Integrale Wr Wv und Wt gleichzeitig zum Miuimum gemacht cl. 11., die GleilniDgen d]Vr -册〜 _ d]Vv d 匕 d/l clA 0) eine algebraische 2m ton Grades, und es giebfc im Allgemeinen zu jedem Wertlie von jj höchstcus 2iu AVer the von a welche die Gleichung (10a) befriedigen. Es ist ubor- hanpfc klar, dass, falls ¢0 zu 0^ in einem ganzzahligen Verhaltniss stehen, für irgend welclio# Wertlie von a die Gleichung (19fl) durch die Gleiclningen 2( 一 Tj) = (士/が 土 l)f. 2( a か 一 j?) = (4»’ 土 i)f. (190 befriedigt wird. Es besteht daun die Gleichung oder 2^( ^0 — ) = 2(V — 7Ur )TT = (2(nr — vif) + 1)7T. (心.） wenn n' und m! zwei mit dem absoluten Wertlie von A wachsende gauze Zahlen sind. Findet diese Gleiclmng statt, so muss i^L = -(fw； ± ^ d. h. = 上 (4m’ ± 1) 7T + 4^ m sein, woraus dann unmittelbar liervorgebfc, dass je einfacher das Vorhültniss ~~ d. h., je kleiner n urul m ist, bei desto kleinerem Wertlie von △ die Gloiclnmgeii (19ö) und mithin die Gleiclmng (19c) bestellen können. 1st hingegen das Ycrhaltniss complicirt, so kann die Gleichung nur für eine grosse Quarzdicke bestellen, die um so grösser sein muss, jo grosser die Zahlen n und m ausfalleu. Ist 11m das Verbiilfcniss irrationale, so kann die Glciclmg ( 19ö ) allerdings um so genauer bestehen je grösser der Wertlie von ^ ist, weil jede irrationale Zahl um so genauer durch einen Bruch dargestellt werden kann, je grössere ganze Zahlen zum Nenner und Zaliler genommen wird ; aber strenge genommen kaim sie nie bestehen. Es folgt hieraus, dass die Grösse 2 厶 〇〇 — nie einem Vielfachen von % gleich sein kann, falls das Verhaltniss irrational ist. Es lassen sieb aus den Gleichungen (18) Folgerungen ziehen welche mit der Erfahr uh g in kleinerlei Widerspruch stellen. Die Menguu g s v er li ältni sse der Grundfarben in den beiden Spalteiibildern af // a" lind b'\ nähren sich um os mehr den Mengungsverliiiltnissen a lind b d. li., die Maximalblässe ist um so voll- komraener, je kleiner bei dem Wertlie, welchen △ hat, die von ム少 abliiiiigigc Glcider ausfallen. AVeim ■wir uns an der Vorstellung festhalteil, dass dev Wertli von ( n — (衾 一 74 — im Allgemeinen mit tlou wachsenden Liclifccmission der Lichtquelle wacliseu, ,so folgt daraus, liothwendig dass die Maximulblässe um so scklccliter lier zu stellen sein wird, je grössere Mongo E mlstraljlen die mit Leukoskop betrachtete LichtqueJlo aus- senclet. Je kleiner also die Liclitemission auafällt, wird eine gute Maximalbliisse bei desto kleinerer Quarzdicke lierstellbar sein. ]^s darf aber dabei ^io Liclitemis- sion niclit unter eine gewisse Grenze herabsinkan, ohne dass die Maximalblasso wie- der sclilecliter ausfiillt. Daun die Gleichungen (18) und (19) sind unter der Voran s- setzung abgeleitet, das sowohl für 入 = ん） als füi .入 = ん für X = A-o und für ^ = Xß unondlicli klein werden, d. li., (lass die in Rede stehende Lichtquelle ein Lichtspoctrum besitzt, in welcliem keine der Spectral färbe fehlt. Wenn nun in einer Lichtquelle, wie ein rotligliilieuder PlatiuadraLit, noch die j eiligen Strahlen fehlen, welche dio Enipfindnng Violett her vorn fei), so dass 入 (j ii] diesem Falle die Wellenlänge eines Lichtstrahles bedeutet, welcliem etwa die Empfindung Blau entsprechen wurde, so 'verdci】， \~dx )> \~djrl wicht melir als unendlich klein betrachtet werden dürfen. Wenn die Lichtquelle Lin gegen solche 13eschaffenlieit Jiat, dass in ilircm Sped nun die Ljchtstralilen lelilcn , av<;1 ehern die Empgndimg Eotli ent spricht, sodas s Xu jetzt die Welleuliiuge eines Lichtstrahles bedeutet, welchem etwa die Emptinclimg Gelb entspreeden würde, so werden (普 X - HH schon bctracliLliclie AVertho haben müssen, so dass die mit; ihnen multiplizirten Glieder erst bein einem grösseren Wertlie von 厶， als sonst, als uiioncllicli klein vermichliissigt werden könuen. Die Bedingung JVr + WfJ + == 0 werden auch in diesen Fallen streng erfüllbar sein ; allein die Differenzen ar — a, b’ 一 b， a” 一 （I， b” 一 b werden auch noch so bcträclitlicli sein, dass bio erst, bei grosserem AVer the von 厶 einer und derselben unendlicb kleinen Grosso gleich werden, wenn die Bedingung Wr -f Wg 十 = 〇 erfüllt ist. Es folgt liioraus, dass dio Maximitlblässe, bei den Liclittjuellen von den obenbezeiclmeten Bcschaffonlieil, viel nnvolllvoinmoner ausfiillt mid dass sic erst bei einer grösseren Qaarz'licke, als sonst, vollkommeiiGr auftreten muss. Aelmlicli verhälfc sich das Leukoskop gegen das Liclifc einer Lichtquelle, welche nicJit ein continuirliclie.s Spectrum besitzt, d. li” fi'u* welclio die Einpfiiulimgsftmc- tionen für gewisse Wertlie von Wellenlänge, oder fiir eine Keilie von Welleuliingen verödnviaden, oclur unstetig werdeu , olme uneiidJicli gross zu AVer den. Eö werde # das Sl,ecfcnlm eiuer Lichtquelle fui- die Wolleulaugeu A 丨ん； l3 ••.•入" t dia (jontinuir- hclj, uucl W sei eins der drei Iuregralo lFr und Wv . Denkt man sich dieses Integral so zertheilfc, dass so kann jedes Integral in eine Keilie nach den Potenzen von - entwickelte werden Nlln enthalten alle Goefficienten dieser Reihen, ausgenommen das erste Glied, den ersten Dileventialquotienten der Empfiiiclungsfanctionen und werden im Allege- meinen an den Grenzen dor Infcegration so beträclitliche Wertlie annemen, dass Glieder höherer Orcbmig, als 去 uichfc mehr als xiuendlich klein angesehen wer- den liön nen, dass daher das Integral U erst bei einem ausserordentlicli grossen Werth von A verschwiiulend klein wird. Es folgt; hieraus, dass ob man° gleich a:icli im diesem Fall, wie sonst tlio Bedingung Wr + Tf^ + Wv = 〇 erfüllen kann, a — (t， b — b， a1 — a， uucl //' — み， noch bei grossem Wertlie you A unter Um- s tau a en noch eine beträclitliclic Grösse besitzen küimen, so das« es von einer Farben- almliclikeit der beiden Spaltenbilder jiiclit die Rede sein kam], wenn nicht die cijigesclmltete Q uarzdicke ausserordentlich gross isf, eine Folgerung, welche in der That durch die J^rfalmuig bestätigt wird. DIE DREHUNG DES MITTLEREN STRAHLS UNTER ANWENDUNG GROSSER QUARZDICKE. Wir 'vollen einen Ausdruck für die Drehung des mittleren Strahles abzuleiten «uclieii, unter der Voraussetzung, dass die Lichtquelle ein continuirliclies Spectrum habe. Wir setzeu, kß W = ^0 ( A,) cos 2 (Ap — D) 似 = O (20) 入 0 'vo 0 = 0,.(A») + -j- 0r (又) gegetzfc worden ist, und stellen uns vor, dass diese Gleichung erfüllt werde clm.cli 厶 und 7}. Wir denken uns dieses Integral in eine uneiidliche Keihe entwickelt mul dann nacli tj auf gelöst, so dass, 0 = coö 2tj(Uh sin 2 A 〜 + J7 パ cos 2 A 〜 一 [70 sin 2 A —厂〇 cos 2 A ) - sin2n(C^cos2A〜一rMsin2A〜-J70cos2 厶洳 +F0sin2A^o) (21) wo u ド w - w- 06 (A/l) . (2k)4 ひ u Vo 吸 - 似 入。) und (2/c)3 (2^cJ- *(2)07 (2fC)2 ¢3( 入^) (2/C)2 ( 又 P) 心 gesetzt wurde. 入2 m (2/c)- ß 0r»( D (2/C)4 札 (;u) (2k：)4 0s(^o) 7^C)r ' S^o ß Aus (21) folgt dann tag. 初 ひ パ in 2 A 0a* + F/j cos — U{] sin 2 A — V0 cos 2 A !^n の cos 2 A … 一 Fpsiu 2厶 心 一 U0qos2^^0 +Vo sin 2 A — 77 — Setzt wir zur Abkürzung den Nenner = .V und den Zähler = ^ sotlass mid bilden Es ist. 2d7J da aber ist,， folgt heraus Mithin isfc cos2(2r/) J、 = C1 +ta«.2(2")] 2 一 1-4.1) AT2 + ^2 A7*-' d7) l'lK f.T dZ ry dX N-d~K-ZäK ~(N2 + Z2) 7) + const. A d A ( lY^ + Z^~) ~ rfA (22). Bilden wir A’2 + Z2, so findet man dieses = U2ß + FV+ VI + V\ - 2(U0U„ + VoV^ ) cos 2ム〇0 — 〜 • + 2 ( ド〇 こ’” — U0V/i ) sin 2 △ ( 队 — 〜 ） und bilden wir ferner N dZ 5/4 sin 2 師 0 ) — 78 — + Uß Vo ^0(sin 2 A cos 2 △ 〜 一 sin 2 △心 cos 2 A p0) — Uß Vß (sin 2 A 〜 cos 2 — sinÄ ^\k cos 2厶〜） + V2ß ^/t(sia22A^/^ + cos2 2 厶 p 只) + U0 V /< (cos 2 厶 sin 2 A p / 乂一 sin 2 A J^o cos 2 厶 p " ) 一 Vo V ß (sin 2 A J^o sin 2 A m + cos 2 A }^o cos 2 A p " ) + UoV ii (cos 2 厶 〜 sin 2 A む 一 sin 2 A 5^o cos 2 厶}^ ) + Ul t/jQ (cos22Aj^o + sin2 2 厶 ル ） 一 Uo Vo j^o ( cos 2 A j^o sin 2 厶 — sin 2 A 0(, cos 2 △芦 〇 ) + Vo Uß ^ix (sin 2 Ago cos 2 厶 p バー sin 2 A m cos 2 A 5^〇 ) 一 V0 Vn (sin 2 A du 2 厶 ル + cos 2 A cos 2 A J^0 ) — V0 U0 f^o (sin 2 A % cos 2 厶}^ 一 sin 2 厶 cos 2 A p0) + V\ J^o (sin2 ( 2 A J^o ) + cos2 (2 厶 0。 ） 】 + iV/t — ZjT2 • (1. li., =(^ + P%)J^ + (W + ひ - cos2A(A -〜） O0+5^)(tW+F0Fr) + sin2 厶 （0O — b)(p0 + む） （UfiV0 — UQV(i) + Nfi — Zf29 was sich auch so schreiben lässt 〜 [ひゞ + 4- f^o — 2 cos 2 △( j^0— (U0Ufi + F0V/m) + sin 2 A ( J^o 一 ) ( U ßVo — Uo 灰’#)」 + [(T’2 + ひ 3 — cos2 A ( }^〇 — 卜） {UJJn + T’。。) + sin2 A (ii>0-^ß，)(U,iV0-U0Vß)~^ (和-和） + - Z/ Die Gleichung (22) verwandelt sich somit in V + const. = A + j --— ( 5<^〇 一 j (い、;’1 — ^2y ^ Ä (23) wo zur Ablvüvzuiig —1 — VI + VI- cos 2 厶 (队 一 〜） （叫 + F (み） j 卜 sin2 厶 (0() — ^ß) (UßVn — U(tVß) + 2sin2 A (}^〇 一 (U/aV0 一 ひ 0Tr/x) — 70 — gesetzt wurde. Es seien 7)r mul a' irgend ein anderes AVertlipaar der Viiviabela a un i TJ , welche die Gleichung (20), mithin (28) erfi'illen, so dass . { d ^ . \ . / d ^ ^ Ji — / ,2 ) ry + const. = 十 (0o 一 0从) + / — ist. Subtrahirt man dieses von (23), so entstellt durch Division mit (△—△’） ( (.、’/ 厂 私） 7) — ^ A— Af ル /』 免)〜— (△一 △，) (00 — 卜） + U， （ \-+^ ) (Ä— 一 △つ (乳） Die Grösse ， kann ein echter Bruch sein. Die Grösse u A 1 ( d 么 匕一し, ノ It stellt aber einen gewissen mittleren AVertli dar, welclion ― zwischen △ m]d liat. Bezeichnet man diesen durch e, so ist i^a7- = ル + s 卜- 和) + ä^ä7 ! (う ms、 A, (1. ll., V △ 一 △ Da die Grösse 7=*( 冗 Dm 一"^]) み/1 驚 △- ィ⑼ + £ LU— — wj dem reciproken Quadrate einer gewissen mittleren Wellenlänge gleich ist, wolclio zwischen und liegt, vorausgesetzt (lass ど ein positiver editor Bnicli ist, stellt (las Glied ®( 去 + e [如-^ d ) - 乃 also die Drehung eines Lichfcstrahls von gowissev mittlerer We!loitl；iii^o .l；i r, o'mo.s Strahles, welchen wir als den mittleren Sti.aldeii bezeiclmet lüiben. —— 80 — 、\rh. ersehon nun aus der Gleichung (24), class der Quotient イ ニ ”， nicht voll- △ 一 △ ständig die Drehung des mittleren Strahls ergiebt, so lange das Glied ih 一 ZfA cl 匕 △ — } (N2 + Z；1) 匕， nooli oiuoii ondliclion Worth bosifzt. Es wird aber unendlich klein, wenn wir A so gross ftimelimen, dass alle Glieder mit liühere】i Potenzen von ftls — als unendlich klein betrachtet worden dürfen. Denn es ist; Nfx — Zf2(l ヒ 已一 bJ J (iV2 十/2) A __ I __ f 仏 rr„ jKjl. —し Mjl + IT △ - a' ；(iv-+^)L 仏 十‘ dVo d/\ r 0 + si” 2 厶〇 0 — clVn (Z Al dV0 d 么 dl\ + cos2a(0o-~^m) ^Jr düß jr dV0 , Tr dVn + こ7 ❶昝 ） （的) 0 ] Wenn min A (1. li.， /c sehr gross ist, so ist U2 eine kleine Grösse von der Ordnung (な) ü > T2 e^ne solche von der Ordnung .( ■ムァ ， UV eine solche von der Ordnung (2^- von der Ordnung^, V^L von der Ordnung ^ von der Ordnung ， mid U endlich eine kleine Grösse von der Ordnung (2/c)c • Es folgfc hieraus (lass, wenn in (lei. Reihe V alle Glieder, «n-usgenommon (Ifis erste als unendlich klein gesetzt werden kann, die Grösse (25) unencllich klein wird. Unter diesem Umstande wird 1 一 VI 一 cos 2 A 〇0 — ^ß)(VnVß) T7iV + K - 2 cos 2 厶 〇0— 〜 ) ( F0 T， 心 oder da V, 命 (装 1 Vß==~(2ly-{l&), 1 __ 1 + // cos 2 A (^o — 1 + 2 u cos 2 A (^o-^n) + — (SI — gesetzt Avuitlen ist. Wir erhalten somit als Ausdruck füL* die Drehung Aca mittleren Strahls = a(w, + fi (H) ) - ^ (2Ö) wo ご— 1 /! + // cos2A ( 0,,-^^) 7 △ 一 △リ 1 + 2" oos2A( ^o — ^/x) + /z2 C Wenn wir jetzt aimebmen, dass die Grösse cos 2 A (>0— 0/t) bei jedem Wertlie, welchen A amiimmt, das Vorzeichen nicht wechselt, oder was auf dasselbe Lilian«- Yerhiiltniss ^ siel, nicht durch eiucii einfachen BrucL tlarstelleu lässt, dann ist 1 + “ cos 2 A ( 0o 一 0 认） 一 1 + 2(/z)cos2A(^o— 0^) + /z2 mithin e ein positiver echter Bruch und die Grösse 去 + e (噠- も） atellt daun das reciproke Quadrat einer gewissen Welleiilkiige dar, weiche zwibclieu (len Wellenliinge, der spectraleu Endsfcralilen der Lichtquelle Jiegfc. Daun erselieu wir aus der Gleichung ( 26 ), dass der Quotient ! 二' in der That die Dreluuig eines gewissen mittleren Liclitskraliles giebt, vorausgesetzt；, dass die Quarzplatte eiue üinrecliend grosse Dicke habe, und gelangen zugleich zur Erkeunfcuiss, dass die Drehung das mittleren Strahles unter Anwendung einer grossen Quarzdicke niclit eine für jede Lichtquelle cliaracteristisclie Coustante, Bondern von der Dicke der Quarzplatte abliiingig ist, und dass um so uiiher einem gewissen mittleren AVer the dev Drehung gleich konimeu muss, je grösser die Differenz 厶一 V genommen wird. Die Drehuug des mittleren Strahls ist mu】, wie aus der Gleiclmiig (20) ersichtlich, unter gleichen Jlmständei), lim so kleiner, je grösser ß isfc d. li., die Wellenlänge des mittleren Strahls ist um so grösser, je grösser ^ il. h., ge- mäss der Vorstelluug, welche wir über den ersten DiÖerentralquotieuten der Em- pfiiidungsrunctionen gebildet haben, jo mehi* die Lichtquelle Strahlen grösserer Wellenlänge im Vergleich mit den Strahlen kleinerer Wellenlänge aussendet. Je kleiuer ]iingegen ß isfr, d. li.; je grösser die Menge der Strahlen kleinerer Wellen- länge ist, welelie die Lichtquelle aus.sfcrahlt, desto grosser wird dio Drehung des mittleren Strahls d. i., desto kleiner wird die Wellen limge des mittlereia Strahls sein, löt eine Lichtquelle so bescliafiou, dass für bic — 82 —— 入1^ (ilr)A = 和 し 昏)。 d. h. “ = 1 isf, was auch fur eine nahezu monochromatisclio Lichtquelle der Fall sem würde, so wird ( 2G ) = a + 去)— 乃- 2 eine Gleiclnmg, die immittelbar hätte hingeschrieben werden können. jj 一 jfr Ich liatto clio W ertlio von für verschiedene Lichtquellen bestimmt, und mittelst dei* Metliode der kleinsten Quadrate gefunden, dass 一：” , wenn (A — A — A) innerhalb, Eiues iviilli meters negh, als einer Con st ante gleich betrachtet Averden können. Allein ; me die Rechnung zeigt, ist —5 eine Function von der ein- A — Ar geschalteten Quarz dicke, so klein man auch (△ 一 △’) wühlen mag. 00 kann tier Quotient R _ 1_5_ mu. in so fern einer Cou staute gleich erschieuen sein, △ 一 Ar aid der Fehler, welclier durch die Annalimo einer linearen Beziehung zwischen V und △ begangen wurde, aller Walirscheiiilidikeit uaoli weit unter dem- jenigen liegt, welclier von der Schwierigkeit der Einstellung in die Maximal- blässe lieiTiibrt. Walilk man liiu gegen (△ — △') gross, so zeigten die Werth e •tj 乃, von in cler That deutlich ilire Abliiiugigkeit von der eingesclialteten Quarzdicke ; sie zeigten aber auch, dass tier Worth ? — im Allgemeinen um so • • • △ — mehr einem gewissen arifclimeti sehen Mifctelwerfche aller für die zwischen A und △' liegenden Quarzdicke ermittelten Wer the nähren, je grösser A 一 genom- 111 eil wird, indem -5 beim waclisentlen A innerhalb gewisser Grenzen zu oscilliren sclieint uiul bald über, bald unter einem gewissen mittleren Wertlie zu liegen kommt;, eine Tliatsaclie, welche auch aus der Gleichung ( 26 ) gefolgert werden kam]. Dei. Bruch ,V ist in Bezug auf A periodisch, e kann daher je nach dem Wertlie von △ innerhalb der Integrationsgrenzcn positiv oder negativ bleiben oder eben so oft negativ, oder positiv sein, woraus dann folgt, dass der Quotient : mich der Gleichung (26) zu beurtheilen, für gewisse "Wertlie von △ = p/t cl. h., der Drehung der rotlien Euclsfrablen wird oder = der Drehung eines Liclitstmliles welclie« jenseits der l.otlieu Endstralilen liegt, uucl davum unsichtbar ist. Allein : so weit icli 乃一 für verscliieclenste Quarzdicke, imd für ver- A 一 A scliiedene Liclit(j[uellen bestimmt habe, waren solche Wertlie für bei keinem noch so grossen Werth von △ aufzuüiulen gewesen, welche eben liinreiclien, die Maximalblässo liorzustelleu, ohne darum die vollständige Eutfärbung bei jeder Lage des Ocularnicolö herbeiz ufüliren. Die Wertlie für 卫 entsprach eu immer der Drelumg eine Lichtstrahles, welcher zwischen den beiden Etuis trahlon des Spectrums liegen, bic 'Viu’eu albu der Art, diiss £ in der Glcicluiug (26) als ein echter durchaus — 83 — Bi.ucli sich lierausstellfc— was oöeubar darauf liiudeutet, dass das VerlntHiiiss im Allgemeinen nicht durch einen eintuclien Bruch darstellbar sein wird, um! dass (klier 2A(^0 — p，x) nur danii einen Vielfachen von tt gleich wird, mithin cos 2a (j^0 - y,ß) mu* dann durch Null hin duvcbgeiieud sein Vorzeichen wachse! fc, wenn A so gross geworden ist, dass ihr Werth weit jeuseits derjenigen Greuze liegt, imierhalb deren nicht die EntiJirüiuig bei jeder Lage des Ocularnicols ein tritt, und so die Ermitteluug des Quotienten unmöglich macht. Wir sehen somit, dass die Young- Helmlioltz'sche Farben tlieorie vollständig die Fii r b c n er sch ein ungen in dem Lenkoskop und sein Verl 1 alten gegen verschieden zusammengesetzte Lichter zu erklären im Stande ist, wenn man gewisse Amiabmen in Betreff der Eigenschaften der Empfindiiügsfunctionen an den Grenzen des Spectrums als Conseqnenzcn der Young- Helmlioltzen Hypothese gelten lässt. Wir sehen aber auch zugleich, dass es von einer Messung der Drehung eino« bestimmten mittleren Stro-lilcs, welcher im Spectrum der Licht(]uo]le eine bestimmte imveiTüclc- bai.e Lage behiilfc, wie die Rede sein kann, sondern von einer Messung der Drehung eines gewissen mittleren Strahles, dessen Lage im Spectrum der Lichtquelle mit dem Wer the der eingeschalteten Quarzclicke veränderlich iöt, und demnach keine fiii. die Lichtquelle und ihren Emissionszustand characktei-is tische Coustante bildet. Soll aber die Drehung eines solchen mittleren Str；i.]jls eine solche Coustante sein, so braucht man zu dem Ende die Dicke der eingeschalteten. Quarzplatte und die Diöerenz (A — △’) ein für alle Male constant zu jielimen, und den Compensations- winkel (7) -Tl，') zu beobachten, claim giebt der Quotient ■■クニ” unter allen Um- ständen eine für die Lichtquelle und für das Stadium ihrer Lichtemission charak- teristische Grosse ' aü+ ベ 去- i)] - 乃 BEDINGUNGEN" DER MAXIMALBLAESSE BEI V E RSCII WINDENDER QUARZDICKE. Iüli will jetzt zu zeigen suchen, dass die Maximalblässe auch bei einer ver scliwindeiKlen Quarz dicke entsteht. Wir setzen wieder |,(f ■ M ■ — — I^)d\ b : ^ _f^rWX + Wr J^\)d\+Wa bf J ¢1 X)dX+Wv ,n-f^)dX-\Vr J^WdX-W, ろ" ,r^(^)dx-wv wo W wieder ein Integral von der Form ブ 0 ( 入） cos 2( 厶 0 — り） d 凡 bedeutet. Jedes der drei Integrale W r W Q und Wv verschwindet, wenn A verschwindet mitl 71 den speciellen Werth ^ ei.liiiU; claun wird ar = au = at und bf bn ~ b uiul es winl gleichzeitig die Bedingung der gleichen Helligkeit erfüllt. Ver- schwindet aber A nicht, sondern wird sie nur unendlich klein, so künuen die Integ- rale W rW g und W v durcli einen von uneudlicb wenig verschiedenen Wertli von V verschwiiuleud klein gemacht werden, wie dass Integral J 0 (A.) cos2 ( — 7)) sdböi;. Wird dieses bei verscliwiiulendem A durch einen passenden Wertli von j] zum Verschwinden gebracht d. li.» wird die Bedingung der gleichen Helligkeit erfüllt, so lasst sich zeigen, dass die Summe cler Mengungsverliiiltnisse der Gnmd färben in (len beiden Spaltenbilder (af + und (a" 十み") dann dem absoluten Wertlie nach amicilireiid um eine imd dieselbe im endlich kleine Grösse von der Summe eleu Meugmigsverhiiltmäse cler Gnmdfarben im urspri'uigliclicn Licht (a + b) abweicht. — S5 — Wir entwickeln ar, a' // bn nach den steigenden Potenzen von △, und denlcen uns A so klein, dass wh* mit dem Glied erster Ordnung ims begnügen können, wobei über 0(入) nur das vorausgesetzt werden möge, dass sie nirgends zwischen 入 o und so unstetig wird, dass das Integral W nicht mehr als eine stetige Function von A angesehen werden kann. Wir finden 1. h., + A け, dl/ \ " 厶 ノ丨， v A / da,f + △し A ) も" = & + a ( db,r \ メ △人 2 Asia 2t/ (J 0r( X)^fdX — a/0g{ X)^dX) 1 +cos 2j) S 似え）《 u 2Asin2^ (/ 0/ X) 屮 d\ — h f X)yjdX) (1+COS27；) 2 ABin2^ (/ 成. (凡) 叫ん— a f (2 — cos 如） 2 Asin2^ — b f 0/ 入) 中 (IX) a" : ar = (i 1/ = b an- b h，，==h - (l-cos2^) - ' oder indem wir die neuen Cons tan ten einf ähren = f^r( y — f ス) 料 入 -T __ / 0v[ X)U>dX /ル (入) 从 ^ 一 ~70gWca トー 成 X>u— 一 (も -ん)） - ¥„)) ほ-も)） ( V>v — Pa) ) Entwickelt man ferner W = 〇, so findet man mit \r eruachliissigimg der Glieder höherer Ordnung cos2^ I (0( 入) 似 + 2Asin2^ j <^(X)Y>dX = o oder, da 0 hierin — 0,. -f- + 0V zu setzen ist, so ist cos2/y (l + a + &) + 2 Asin2^ 、apr + bpv + ^) = 〇 (27) die Bedingung dafür, dass die beiden Spalfceubilder gleiche Helligkeit zeigen. Wenn wir jetzt die Summen ar -{- brf und a,f + V bilden und uns vor stellen, dass die af V b,r + a (1 — 2 Asin2；7 (1 + cos 如） _2Asin2^ (1 + cos2,7J) i 2Asin2?； (1 一 cos2^) 2Asiu27? (1 一 cos2^) — 86 — Gleichung (27) durch geeignete von A und Tj erfüllt sei, so fm len wir für diesen Punkt (a + 心） (1 + cos2^) (a -f b) 1 一 cos2 TJ (1 - e) (i-O wo cos (2 々 ） 2 (1 ä •卜 />) sin 2 tj (a + h) ist. Cos 27} ist gemäss der Gleicliung (27) eine unendlich kleine Grösse derselben Ordnung wie △ ; mithin ist e auch eine uiiendlich kleine Grosse derselben Ordnung, wie Mit Yernacliltissigung unendlich kleiner Grösse zweiter Ordnung können die letzten Gleichungen aucli so geschrieben werden : af + レ = (« + &) ( 1 — cos2”） (1 — ^) == (a + b) (1 — e — cos 2 了/) a” + f = ( rt 4* ^ ) ( 1 + 0082 々） （1 一 c) = (^a H- (1 一 s + cos 2”） Genüge demnach eine verschwindend kleine Quarzdiclie und ein entsprechender Winkel des Ooularnicols der Bedingungsgleichung der gleichen Helligkeit (27), so unterscheiden sich («’ + り und (a/; + b,f) von (a + b) dem absoluten Wer the nacli um eine mul dieselbe verscliwindentl kleine Grösse ; und da (a + b) ebenso gut die Qualität cles von einer Lichtquelle ausgeBtralüten Lichtes cliaraktcrisirt, wie a uucl b selbst, so folgt hieraus, dass die beiden Spaltenbilde r irnter diesem Umstand nahezu dieselbe Färbung zeigen müssen und zwar wie die des ursprünglichen Lichtes d. h., es findet in den beulen Spaltenbilder die Maximalblässe statt. BESTIMMUNG DEU DKEHÜNG DES MITTLEREN STRAHLS UNTER ANWENDUNG VEKSCH^ WINDENDER QUAKZDICKE. Wie 、\ii göböbßii liSibei】， liisst nicli die ^Jtixiiuftlblässo bei vcrscliwiiiclei)dör Quarzilickö ebenso gut zur Bestimmung der Drehung eines gewissen mittleren Strahls benutzen, wie die Maximalblässe bei grosser Quarzdicke. Es liegt mir mm ob， einen Ausdruck liierfüi «ibzuleiteii, und zu versuchen, ob die clurcligangigo 、 ö^scliiedoubeifc der unter Bouutzung kleiner und grosser Quarz dioke enoittelteu Wer the von S. ?L si(Jj nicht theoretisch deuten hisst, ム ー ヽ Vk deuken uns : die Gleicliung W = 0 'vei’de erfüllt durch einen sehr kleinen Werth von A und einen dazu eutspreclienden Werth von 7)f oder was dasselbe ist , n /’が 凡） cos 2 △叫 凡 tag. 2j) = ~ /扒; g Sin 2 △叫え Weuu wii， bilden, uiuT clabei bemerken, dass 00^(27]) = j + tagia(2^) ist, so folgt (]± = öiu 2A^a. Jfi(V) sin 2A^ca dA (/0(^) sin~2A^ayJ 一 + /p( X) cos 2A^(l^ ノ X 又） p cos + (/ 0(A) cos 2 A oder indem man ia dem einen Integrale ?ur für X mul pr füv y> schreibt, edaäU man durch Integration 1) + coubt. = f ^rm clA wo — 88 — //バ 入') 0( 入,）— s2A 〇 — r/jf)dXd^ = //0 ( A.) 0 f ^ ) cos 2 A — ^ ) d\ d\r gesetzt worden ist. Diese Grosse ^ m ist eine stetige endliche Fancfcion von A allein und kann daher nach den steigenden Potenzen von A iu eine convevgirende Reihe entwickelt werden, so dass wir erhalten, 0WI + △2 可 r CCi + △4 TT wo die Cüustiuiteu ^in und an durcli [¢(70 か a 斗、、 (28) い (-1 ド^^ m 織^» oder was dasselbe ist an = (-l)’T [〇2„ 02 ( 0‘-’u - 2 一ん i 一 1) 一 (I 2// (2/i 一 1) 2! ^än l) - 2ll^l{^>.：n_1 - 02„) 211 (2 u — 1) (2m — 2) 8! U + etc. bestimmt sind, wenn im Allgemeinen / 0( X)^vdX J 叭 ^1 = ^VI gesetzt wird. Die Con stauten an sind bei eiicllidiem n darchaus endliche Grössen, (leim die Grössen % レ stellen gewisse mittlere Wcutlie von 蛉レ dar, sind also durchaus end liehe Grössen. AVenn nun daher dio Grerjzeu, innerlialb deren A sich bewegt, sehr klein siud, mul alle mit höheren Potenzen von A2 multiplizirtcn Glieder als unendlich klein vevnacbliissigt werden dürfen, so dass inan amiiilirend setzen kami • △ 2 ^>,rin == + — jjj — tl. ]i., — 2A2(^3-~5^2 一 れん 一 ^oJ ) dann erhalten wir als Eolation zwischen Tj mul △ für sein* kleine B erthe von A Tj 4- const. = 厶 — ÜA:3 (Pa — Pu A 一 2 [あ 一^ ■」 ) — so — . Wir sehen hieraus, dass, wenn 7/ mul △' ein amlerGs Worth paar der beiden Vavia- beln sind, welches diese Gleicliung befriedigt cl. li., die Maximalbliisse lierstellt, die Drelnmg eines bestimmten mittleren Stralils untei* allen Strahlen, welche die betreffende Lichtquelle aussendet, bestimmt wird durch die Gleiclmng V — V1 一/ △ 一 zV /0 ( ^) ^ ^ und zwar bis eine Grosso höchstens von der Ordnung ^ 2 genau, wobei os glcicligiltig ist, ob die betreffende Lichtquelle ein contimiirliclies oder ein disconthmirlichos Spectrum besitzt, oder ol) die In tegfation sgren zen ス0 und 又 弘 die Wellenli'mgon derjenigen Strahlen sind, denen die Empfiiulungen Roth und Violett entsprechen, oder nicht tl. li., clor Qaotieut . Tl 一 ■ろ: r giebt die Drehung eines beslitnruten mitt- A — ~ A leren Strahls einer Lichtquelle für jede Beschaffenheit und jedes Stadium ilivor ijiclitemission. Wenn A yicli zwischen 0 und 0,2 臟 bewegt, wie bei den von mir ausgoführtc» Messungen der Fall 'vai.， so betrügt die Grösse des felilorliaften Glietle es 0,0266 (^3—5^0 — 2 (わ 一 ㈣) Grad. Wie gross nun, oder wie klein dieses Glied ist, (Irs lässt sich auf keinerlei Weise schätzen, da die Grenzen, innerhalb deren A variiren kann, ohne dass Herstellung der Maximalbliisse unmöglich wird, zu klein sind, da ferner bei den Messungen dieser Art un vermeid! iclie Beobaclituugsfeliler zu gross sind, als dass dio Methode der kleinsten Quadrate Latte mit Erfolg ziu* Auwenduug gebracht weiden können. Indossöu ist os walivscheiulich, dass dio Grösse [0S — — 2 (#••，一 ^l)} aucli eine kleine Grösse ist, denn , J^3 und stellen die erste zwei to mul dritte Potenz der Ih’duingen wenn, fiucli nicht; eines und desselben mittleren Strahls, doch gewisser Stralileii mittlerer Wellenlnjigc dar, sodass die Wer the der Drehungen sich nicht viel von einander unterscheiden werden. Da von derselben Ordnung, wie und von derselben Orclnnng, wie ¢»3 ist, so darf man folgern, dass も 一 ^2 — 2 f^2 — ) nicht， einen nil zu l)et.rächtlicliGD Werth besitzen kann. DIE PHYSIKALISCHE BEDEUTI 腦 DER COXSTANTE Es bleibt nur noch übrig, zu mitersuclien, ob nicht aus dem experimentell ermittelten Weitlio fiii* rückwürts auf tlen Emissionszustand der Lichtquelle geschlossen werden kann. Indem ich dieses unternehme, werde ich mich lediglich auf tlie Botraclitung solcher Lichtquellen bescliriinkon, welche ein continuirliches •spectrum besitzen, fiii* welche also die K idj) fi n d u ngßciu* ven nirgends Unterbrechung ilu.es stcticfen A erlaufs erleiden ； sclion dosslialb, weil Betrachtungen, wie die folgenden, mchb für eine Lichtquelle mit oinem discontinnirliclicm Spoctrum an- gestellfc worden können, wenn nicht eine besondere specialisiremle Annahmo über die Art und Weise gemacht wird, wie die Lichtstrahlen in dem Rpectrum der Lichtquelle vertlieilt sind. Indem wir in (28) wieder ^>==^2-/3 ßetzon, so können wir auch so schreiben, Die Grösse : J f0_O) 凡2 — dX /0 w 一 ß /0 U) stellt mm das receproke Quadrat eines bestimmten mittleren W ellenlänge dar ； denn : setzt man (29) Strahls von der so dass dU JX = 0 ( 入） mid 凡 （ス〇 凡） = [ 0 ( >1) d^f ノ入〇 1 尨 A-ju 入 o ist- Indem man den Zähler partiell integvirt und beobachtet, dass U eine durchaus positive Function von X ist, und leeinerlei Zeicliemveclisel unterworfen ist, ßo kann der Zähler nach dem bekannten Satz aus der Lehi.e von dem bestimmten Integrale auch so darstellfc werden. wo 入’ einen gewissen zwischen und liegenden Werth von X bedeutet. Es folgt hieraus, dass wenn man, U(7mX) ク， £/(^Ao) macht ^ = Ä + W.(+Ö — Ä) C80) ist. Die rechte Seite bedeutet das reciproke Quadrat oinor bestimmten mittleren Wellenlänge, denn u ist ein positiver echter Bruch tla V { 7^n 又 0) = U X ) -r ist und constant. Sein Wei.Üi liiingt aber offenbar von der Beschaffen- Iieifc der Function 0(^,) ab, d. li., von der Natur der Lichtquelle, und dem Stadium ilu’ei’ Liclitemissiou. Allein ; da n im übrigen nicht näher bekannt ist, müssen wir der Grösse /0(^) ^ eine andere, der Discussion weniger unzugängliche Form zu ertlieilen suchen. Zu dem Ende denken wir uns die Function 0( 又)， da sie der Voraussetzung zu Folge überall innerhalb ^.〇 mul ^ stetig und endlicli bleiben soll, so entwickelt, dass oo 0 ( 凡） = X A sin ist, wo die Constanten und q durch die Gleichungen =J^r^-ao)iAf(a) sin レ o- 抑） ぬ bestimmt sind. Diese Sinusreihe ist nun so gebildet, dass sie mit 多 (凡） die Eigenschaft theilt, ハ •■ば 久 = ス〇 imcl 久 = 凡/ ^ zu rerscliwinfleu, so darf dann — 92 — 人 M 〇〇 CQ 入# / X ^ V (2) — 2 入） f? 入 =Z X f ^v »in V {v—q\) d\ 入 0 1 1 •ん〇 gesetzt werden. Es ist zunächst Kß ( 0(凡)议 ス 2 hfl 入 o t Avj sin v (p-qX) d\ 1 「— 入 0 ocler indem man alle Glieder mit geraden, und ungeraden Indices besonders sum- mirt, sodass ^ ん 从 f.ps^ = 室々 ?v + り ㈣生ナ 4| ■ヒ逆 入 〇 入2 d\ A-o 九 0 Aju- und über dies setzt. (2p + 1) 。 (2y + l)= Kfi - 2V iS12v =y* sin 2v 01 - 170 dx ( 30„) ん /X so folgt Kii [ 0 (X) 00 CC '~7\j2 — ぶ 入 =2/^1 (2 レ +i) (2 v + 1 ) iß/ (2v 十 i) —乂ふ レ 2p. \Qj2v (31 〕 入 〇 Die Integrale (30«) können auf andere Form ge))rac]it werden durch die Einführung (les dom äquivalenten Integrals GO Xx ß x dx Indem wiv dies tlmn, und die auf \ bozi\ gliclic Intogrfition ans füliren, finden wir GO e +e \H (2 ド +i) = ィ (為ね… 一 occlx 0 2+ (2v+])2^2) cc — 98 — iQi — Ai)X - e 一 e 心 x) xdv (x2 + 如2 g2) Wir wollen jetzt statt dieser Transceudenten, an genährte Austlriickc dafür in die Gleichung (31) einscfczeu. Es ist nämlich der Werth eines Integrals von der Fon» co ( — 凡ぶ e x dx ノ （a?2- 卜 m2 j Ideiner als co 1 /* — Aa? m-J e x dx iltum der Unterscliiecl co - 7a co Xx m 2 e x dx 一 e x dx 00 Oj if? cl.v (?n2 + x2) ノ 7/i2(w2 + it (p — ^ 入） JA 1 Au 丄 S 』(2レ:+1) q « (2^ + 1) iöfc, folgt liierau-s, dass — 1)4 — 瓦 = /0U>a ^ Hi + 'k) ~ t~ (ü- ) ⑼ wenn die von der Beschafieulieifc der Function 0(a.) abhängige Coustante S 々2v) H C9-», \ : K w g d(2 レ +2) o ( 2 p + 1 ) gesetzt wird. Vergleicht man mm diese Gleichuug (82) mit der Gleicliuug (80), so ergiebt sich sofort die Eelation n und K 1 一 2u= K mitliin -K 2 Dui.elx diese Belation ist der Charaktei* der Constante u bestimmt, wenn der Charakter der Constante K für verscliieclene Erniäsionszustiinde der Lichtquelle ermittelt ist. Um daher den Charakter von K niilier zu imtersuclieu, setzen wir statt Ajy und A (2y i i) ihre Integralausdvücke eiu so (lass, K= t 人 メ⑻ siu 2 p (p—qX) dX A-M- F. W+vL^ U) sin (2v + l){p-q\)ca. ludem wir V — q 入 = Q setzen und die Integrale so wohl im Neuner als im Zähler nach dem Schema -7T f zerlegen, ündet man, nachdem im zweiten Integral statt g, (? + 7T gesetzt worden i«t, K= ^ S', fo (P デ) - 奋 sin 2vdd0 Es ist aber \ {2v+T)l [ベ〜^) + ^ ] sin^2 ,0 cos 2i?6 dö a sin IvO 2v ft 伽 +1) ⑽ sin (2u + l)0 (2^ + 1) und bekaimtlicli ^ ^ sin (如 +1) ク 1 ^ /0 ，- , N Ä sin ( 4v 4-1 ) 0 系 刪 2vÖ= 2 sin 0 "2 X ^(^ + n^ = — 2^7 - Es folgt hieraus Kz lim./f[0(^)+0(^_)] [/ ’ク sin (4y +1) 夕 sin 0 dd I (10 Nun iaifc bckamitlich der Werth cloy tutegrals 广— ぼ 去;.) 夕 d0 a für eiu in’s Unendliche wachsendes v = ¥, wo c eiue beliebige positive Grässe ist, welche jedoch der Bedingung unterworfen ist Da 6 in o < c < 7T. 0 sin ( グ + 1)0 dO. immer zwischen o und 7r spielt, so wird sich der Werfcli dieses 丄 litegfals bei doiu in’8 Unendliche wachsenden v von If um eine kleinere Grösse unfcerscbeiden als jede noch so kleine Grösse. Mithin erhalten wir •Tür* ，一、 ，£±^L)] (レ） 抓 K / 屮 (午: M — 吾/ fl> (午 )ィ中)] Bestituirt man hierin statt 0 die Variabel 凡， so kommt zunäclxst, 九 於 [0( 又) 一 0(1+ 心- 凡) 1 ( 久， ( ?\jß + D、 2 J d\ K Kß ~\- A-o 2 (n) 卞 • f [ 0 ( 入） + 0 ( ス Ü 十 入 パー 入） 0 び (又 w + 入)， mithin muss Kg eiu positiver kleiner Bruch sein. Ist 0( 又） aber die Empfindungsfunction für Roth, so muss für jedes X die Ungleichung (入 m + 又） > 0,，( 凡饥 一入） stattfiiulen, weil ^r{X) ihr Maximum nur für eine grössere Welleulänge, als erreichen kann. K ist dann ein durchaus posi- tiver Brncli, welcher um so grösser ausfallen wird, je grössere Menge die Licht- quelle Strahlen von grösserer Wellenlänge aussendefc, denen die Einpnmuuig Roth entspricht. Ist endlich が (又） die Empfindungsfunction für Violett, claim muss für jedes 入 da ^v( \ ) nur fiir eine kleinere Wellenlänge als Xm Maxiraalwerth erhiilfc, die Ungleiolumg ^v{\m + X) < 0v[Xm - Tu bestehen ; mithin muss K für diesen Fall ein echter aber negativer Bruch sein, dessen Wertli um so grösser sein wird, je mehr die Lichtquelle Lichtstrahlen von kleinerer Wellenlänge ausstralilt, die in der Netzhaut die Empfindung Violett erregen. Wenn wir die Constante K und den Wovtli von — für jede der drei Fascrart mit entsprechenden Buchstaben r, fj und r bezeichnen, so lässt sich das bisher Erörterte in die Gleicliungen zusammenfassen. 1 1 (l— X,.)( l— - M ÄV -JF^ + 2 U:o 1 U 1 -巧十 2 V”o め J (33) 1 冗 = 1 =瓦+ (や) (备- 一; so dass 1 . 1 〆 —i れ く 兄く i isfc. Wenn nun die Lichtquelle, Avie es bisher vorausgesetzt wurde, nicht alle sicht, baren Strahlengat tun gen aussendet, olme dass ihr Spectrum cliacontinuirlioh wird, so gilt das Erörterte auch fiir diesen Fall. Gesetzt : die Lichtquelle sende keine Strahlen aus, welche die Empfindung Violett erregen, so dass 入 〇 jetzt (lie W ellenlange eines Strahls bedeutet, welchem etwa die Empfindung Blau entsprechen würde. Die Wellen- lange des Mittelstrabls—0 ^ = Xm imt jetzt einen grösseren Werth als in dem Fall, wo die Lichtquelle alle Stralilcngattungen aussendot. Es ist klar, (lass da (ßg mu* in der Nähe von Xm ihren grössten Werth besitzt, und 0( Vm — X) naher an dem Maximalwerthe (f>J^ Tjn ) liegt, als + X)j im Allgemeinen — 7〇 > X) sein muss. Es folgt hieraus, dass Kü für diesen Fall em negativer — 98 — Bruch sein muss. Dio Cons tan ten K,. una ]{0 bleiben allet'dings von derselben Natur, wie in dem Fall, so die Lichtquelle ein vollständig aasgeb ild^tes Spectrum besitzt, da auch liier, wie dort, die Ungieicliungen (入 ’m + 入） > 0, •(九〜 n ■—久） und 0t.( Xvi + 久） < 0 ノス' m + ?w) stattfinden ； allein, die absoluten Wer the der Oonstiuiten Averclen grüsser far diesen Fall ausfalleu, als fiu* jenen, tla die Untcu.- schiede ^r( ^rm \) 一 0，( 入' m + 入) vmd 认.( A/m —入) 一 0V( 7Jm + 入) lii^v im Allgemeinen grässci. sein werden, als für jenen Fall ( vergl. Fig. 4 Ta.fel.) Aolmliclie Betvaclitung lässt sich auch fiir don Fall anstellen, wo die Lioht- nolle z. 13.， keine Strahlen anssendet, tlencn die Empfindung Roth entspricht-, und sie orgiebt, dass, da die Wellenlänge dos Mittel stralils -^2 (vergl. Fig. 4. Taf.) füi* diesen Fall kleiner sein muss als , Kg ein positiver echter Bruch ist, mul dass Kr untev diesem Umstand einen positiven kleineren mul Kv liingegen fiineu negafciveu grosseren Werth besitzen muss, als in dem Falle, wo die Lichtquelle Lichtstralilen von jeder Gattung aussen de t. Wir sehen hieraus, class das reciproke Quadrat clev Wellen] iin go des mittleren Strahls d. i., tlie Drehung dos mittloren Strahls für jede der drei Faserartcn wächst, oder abniinmt, je nach dem die Lichtquelle grössere Menge Liclitstmlileu von Ideinerer Wellen] jingo, odor von grösserer Welloiiliinge ausstrahlfc. Könnten daher die Drei mii gen rler mittleren Strahlen für die drei E'aserarten einzeln gemessen wertlen, so konnte inan aus iliren Wertlien rückwiirts sell] lessen, welche Stralilen- gattung die l)et reffende .Lichtquelle in einem Stadium ihrer Ijiclitemission in grösserer Menge entwickelt, als in einem anderen Stadium. Nun gostattet die in der Timt raessl)are Grosse derartige Schlussfolgerung. Denn es ist w, 一/ [0八 んノ + 0/a) + 1 一 1 ß. (入） + 0/ /l J~ + 0t.( \) ] d\ In dem wir die Festsetzungen (12a) berücksichtigen, ist auch so darstellbar. 1 一 ^ 4 -一 1 玉 4* ゐ 玉 /qo/y \ 竑 —（l + a + り； 二卞 (l+a + &) X\ (l+a + 6) \\ い洲) (l. h., mit Eucksiclifc auf die Gleichungen (38) = 長 + し1~ )(を 一 i) (84，) wenn man 7C— KP~hKr ~ ~JlT^+b)~ setzt. Wenn wir annelimen, dass Kt, im Allgemeinen ein kleiner Bruch ist, was walir- sclieinlich immer der Fall ist, wenn die Lichtquelle Strahlen jeder Gattung aussendet, so ist K negativ, wenn aK,. < />A"ydas lieisst wenn dio Lichtquelle grössere Menge Licht- strahlen von Ideinerer AVellenlänge, und wenn umgekehrt aKr > bKv das lieisst, wenn die Lichtquelle eine grössere Menge Jjiclitstrahlen von grösserer Wellenlänge ausRonclet, als diejenigen von Ideinerer Wellenlänge ; dann ist K positiv, da Kv in — 99 — diesem Fall ein positiver ldomer, und in jenem Fall liingegen ein negativer ldeinoL* Bruch ist. Es geht dann aus der Form der Gleichung (84) unmittelbar hervor, dass wenn der Werth vou 土- in einem Stadium der Licbtentwickelnng der Lichtquelle grösser ausfällfc. als in dem* anderen, die Lichtquelle jetzt eine grössere Menge Licht- strahlen kleinerci1 Wellenliinge aussenden muss. Füllt 】iingegen dev "Wertli vou 一- Ivlemer ans, als sonst., so kann man (laraus sei ili essen, dass dio betreffende Lichtquelle jetzt eine gvössero Menge Liclitstrnlilen von grösserer Wolleuliinsro aus- sivnlilt Es leuchtet auch mmiittolbav ein dass man aus dem Werthe der Drehung de» mifctlorpn Strahls uicht allein nuf die Emissionsstarlien einer und derselben Liclitquello sclilicsseii kann, sondern aucli anf die Lichtemission verscbiecleiu'i, Lichtquellen . ül)erhaupt, da. zwei Lichtqudlen, bei denen eine Vcrachiedenlieit der Liclitemissiou Torausgeset/t- werden muss, als versclnedene Emis.sioiiflsfcadion einer und derselben Jjichtrjuello aufgofasst werden können, so dass ich glaube, das Ergebniss der bis- Irrigen Erörfcornngon daiim ausspreclion zu könueu, dass die Drelmtif/ des minieren Straldrs um so fjrusscr sein 7mmf je (/ rosse re Moujc eine j Acht quelle Strahlen von kleine rer WellenVinfje aussendet, wenn m Licht Strahlen von jeder Gattunfj rollständiri d. h” cii\ iremes Licht aussendet. Die Werthe der Drcliung des mittleren Straiils für verschiedene Lichtquellen, welche ich mittelst der ]\laxiraalblässo bei versclnvindender Quarzdioke gemessen habe, wurden bereits mitgetlieilt ; sic stehen mit dem Ergebniss unserer bisherigen Auseinandersetzung nicht im Widerspruch. Dass sie aber durchaus vorseliieden von den mittelst der Maximalblässo bei grossor Quarzdicko gemessenen Wer then sein müssten, ist unmittelbar aus den füi* dio beiden Falle erhaltenen Ausdrücken flu. die Drehung dos mittleren Sfcrabls ersichtlich. Per Ausdruck für die boi grosser Quarzdicke gemessene Drehung hängt im Wesen tliclien nur von der Em- pfiiKlmigsfunction für die rotli- uml viole tfcempli ndon do Faserart ab, wiibrencl (lei- Ausdruck für die bei der veracliwindenclen Quarz dicke gemessene Drehung auch von tier Empfinduugsfimction für die grünempfindende Faserart abhiingig ist-, lind zwar so dass clio bei der Terschwindcuclen Quarzdicke gemessene Drehung des mittleren Strahls der Gleichung ( 88« ) zu Folge einem bestimmten mittleren Wertho der Drehungen für die drei Faserarton gleich isfc. Die Coustanto K in der Gleichung (34) kann nur ein kleiner Bruch sein, wenn wir annehmen dürfen, dass bei einer Lichtquelle, welche vollständig ausgebildetes Spectrum besitzt, die Mengen der von der rotli- und violettempfindendcn Faseravt empfundenen Farben niclifc allzu von einander diftcriren, und tlasa dio Erapfindungs- curven für die rotli- tmd violettemiifindende Faserar t unter diesem Umstand nahezu dieselbe, aber umgekelirte Gestalt haben. Dann unterscheiden sich a und />, und auch Kr nnd Kv von einander nicht erheblich ; mithin wird K d. i., aKt - IKV ± Ku — 100 — nm. ein kleiner Bruch sein Kuinion, d；x Kv ein solcher sein so]lfco ； d. li., tlic mittelst der Maximalblässe bei verscliwinclender Quarzdiclco gemessene Prellung des mittleren Strahls kann nicht viel von der Drelmug des mittleren Strahls für die grün- empfindende Fasorart ab weichen, d. li” eines Strahls, welchem die Empfintluug Grün entsprechen würde ; eine Folgerung, deren Bestätigung ich in den bereits oben angegebenen, oxperimontoll bestimmten Werthen für die Drehung des mittleren Strauls der woissen Licntquelleu zu finden glaube ； denn die daraus berechneten Wellenlängen des mittleren Strahls sind m der That diojcnigen, bei (Ionen ein Liclitstralil in unserem Scliorgan die Einpfindung Grün hervorruft. Dass die Maximalbliis.se bei verscliTvinclendcr Quarzdicke der Maximalblässe bei grosser Quarz dicke vorzuziehn ist, da, wo es sich darum handelt, die Drehung des mittleren Strahls als oiuo von der Natur dor Licntquelle und ihrem Emissions- zustand ul) li äugige Constantc zu bestimmen, kann os, meiner Meinung nach, bezweifelt werden ; denn os darf liiclit verschwiegen bloiben, dass die Beobaclitmig bei jener we^eii ilcu Jvlemlieit clor ein- oder abz lisch altenclen Quarz di cko, mi(l dev Gering fiigigkeifc der dadurch bewirkten Farbeniindernng in den beiden Spalten- Mlclorn mit bei weitem grösserer Schwierigkeit verknüpft ist, als bei dor durch grosse Quarzdicke bewerkstelligten Maximalljliisse. Allein ; jene Maxiinalbliisse bietet den unleugbaren Yortlieil, dass sic uns gestattet, die Drehung des mittleren Strahls auch für solche Lichtquellen v.w bestimmen, welche continuirliches Spectrum nicht besitzen, wie glühende Gase und Dämpfe, oder durch farbige Medien absorbirte leichter. Die Wertlie der für solche Lichtquellen gemessenen Drehung des mittleren Strahls und seiner Wellenlänge sind bereits mitgetlieilfc ; auch sie stclin, aus- genommen glilbende Gase und Diimpfo, zum wenigsten mit der unmittelbar sinnlichen Wahrnehmung nicht im 'Widersprucli. Was immer also für eine Zusammensetzung der Strahlen eine Lichtquelle auch haben mag; der Quotient gemessen A 一 A mittelst der Maximalbliisso bei verschwindonder Quarzdicke, giebt immer eine für die Natur der Lichtquelle und für ihre Farbe charakteristische Constantc% ZUR GESCHICHTE DES LEUKOSKOPS. Währeml der Ausarbeitung dieser Abhaxidliiug erschien 011 von einem der Laboranten im physikalischen Institut zu Berlin einige Arbeiten"' über das von Professor von Helmholtz verbesserte Leukoskop. Es macht sicli in diesen Ablmiul- luugeii das befremde))de Streben geltend, dem Herrn }?rofessor von Helmholiz die unbedingte Autorschaft dieses Instrumentes zu viudicireu. so dass ich midi da/u geckäugt sei), im Folgeiulen der Entstell migsgesclnchto dieses Instrumentes einige Worte r/A\ widmen, da ich lnclifc imverdientenveiso in den Huf eines Plagiatorö geratlien möchte. Herr Professor von Helmholtz hatte sein Iustruiueiifc, abgesehen von einigen AbiuuleningGn, nur liadi moinom Vefsuclisapparate liaclibiklen lassen, wie es ein Brief von ihm ausclrücklicli Ijezeugt, mul auch war er es nicht, der dom Instrument den Namen “ Lcukoakop ” gegeben hatte, wie Herr König iu jeder seiner Abhandlungen zu betonen nicht uuterliissk. Als ich Ende 1876 unter der immittcl- luu’eii Leitung des Hem] Prof, von Helmholtz zu arbeiten das Glück batte, bat ich mii* von meinem liocliverehrfcen Lolirer ein Thema ans, welcJics sioli zu einer Promo- tionss«Lrift eignen würde. Herr Professor von Helmholtz schlug mir vor, mittelst einer passenden Dicke tier senkrecht zur Axe gesclmittcuon Quavzplatte in den beiden Bildern eines Kal kspathrliomboiklcrs die Farbeugleichheit für das l.otlie Licht eines glühenden Platiuadrahtos zu bewerkstelligen. Als dieses aber sich als uiiausfitlirb^r lierausstellto, naaclito Herr Proiessor von Helmholtz mich auf eine ihm eigene, höchst auregemle Weise aufmerksam, days die Fiirbeugleicblieit der bei- den Bilder, wenn sie aucli t，i'u, das rotlie, Licht eines glüheuden Platinadrulites miss- lang, dennoch für ein weissea z. B., Tagosliclifc Iierges teilt werden könnte, weil es tluucli eine passende Quarz dicke nnd eine passende Drehung des Ocnlarnicols leicht üaliin gebracht werden lcünue, dass in dein einen Bilde Blau und Gelb und in dem anderen hingegen Both, Grüu und Violett im Maximum vorhanden sind. Diese Idee also mittelat einer geeigneten Quarz dicko dio beiden Bildci, des KalkspatbrlioDi- boütlers zu entfürben, eine Idee, tlurcli tlereu A^erfolgung spater das Leukoskop lxer- vonvuclis, rührt unbetliiigfc von Hoitji Prof, von Helmholtz lier, wa,s ich aucli niemals in Abrede gestellt habe. Zu Avas nun aber die An.sführung dieser Idee dienen sollte, hatte mir Herr Prof, von Helmholiz weder mitgefclieilt, noch in der Verfolgung dieser Idee micli irgend wie auf ein bestimmtes Ziel zu leiten gesucht. Es T\Tar also lediglich mir überlassen, aus dieser Idee zu machen, was ich wollte. #A Konig'. Wiodomann XVII. 1982, 991. Zeitschrift für die Instrumeutenkunclc JJeriiu 1833 (J amiarheft). — 102 — 丄 di stellte versuclisweise einen Apparat zasaminon, sogut es eben gehen wollte, und wandte den Quarzkoil an, um beliebige Quarzdicke einscli alten zu können. Die Entfärbung der beiden KalkspatLbilder gelang über Erwarten gut, wobei icli zuerst dio Walimelimung machte, dass zur Entfärbung der beiden Bilder eine andero Qtiarzdicke i’üi. das Lampenlicht erforderlich wav, tils für das Soimenliclit. Indem icli diese Erscheumug weiter untersuchte, überzeugte ich mich immer lueln* von der Anwendbarkeit des Apparates zur färben theoretischen Untersuchung 111111 (kmi ziu* Untersucbiiüg dev Liclitemission verschiedener Liclitquelleu. Allein : ein Umstand rein materieller Natur machto es damals unmöglich, meinen versuclisweise zusammengestellten Apparat ilurcli die Haucl eines Optikers in ein Instrumeufc venvandeln zu lassen imd damit auch jec|e weitere Untersuchung. Es war mir daher die mich enngci* Zeit von Herrn Prof, von Helmholtz mir zugekommene Mitthöiluug im höchsten Grade erfreulich, dass ein Apparat, wie ich versuchsweise zusammougesetzt liatte, bei der Firma Sclunidt und Haensch iu Berlin bestellt worden sei, und dass icli mit domsolben weitei.e Uiiterauchung vornelimen könne. Die liesultiile der mit cliosom Instrumente ausgeführt eu Untersucliungeu habe ich iu meiner doi* pliilosopliischeu Facultiit der Univeröitafc zu Güttingen vor- gelegten Dissertation uiedergelogt, iu welcher icli zuerst das Instrument, welchoa bisher namenlos geblieben war, mit dem Namen Leukoskop belegte. So entstand das Leukoskop, und e» möge dem Urtheile der Unbefangenen überlassen bloibou, ob qh nicht irrig ist, wenn Herr König dem Herrn Prof, von Helmlioltz die ausscliliesölicliü Urheber bchuffc cliesje« Iustnimenteö zasebreibt, und die Sache durchweg so darslellfc, iik habe Herr Professor von Uolmholtz von vorn herein an die Ausführung jener Idee die bewusste Absicht geknüpft, ein Leukoskop zu construiren, so dass er mich bloss dazu angehalten hatte, zu imtersuclieu, ob die dem Leukoskop zu Grund liegende Idee ausführbar sei. Fig 1 Fig 2. Fig 3. 八 年 年 八 五 月 月 廿 十 七 四 H 日 出