,,handbook ,,of ,,railroad ,,construction2 ,,for ,,the ,,use ,,of ,,american ,,engineers4 ,,containing ,,the ,,necessary ,,rules1 ,,tables1 ,,and ,,formul ,,for ,,the ,,location1 ,,construction1 ,,equipment1 ,,and ,,management ,,of ,,railroads1 ,,as ,,built ,,in ,,the ,,united ,,states4 ,with #aeh ,illustrations ,,by ,,george ,l4 ,,vose1 ,,civil ,,engineer 8,,rules ,,themselves ,,oblige ,,us ,,to ,,reflect1 ,,that ,,we ,,may ,,see ,,whether ,,we ,,have ,,not ,,departed ,,from ,,them40--,,napoleon4 ,,boston ,,and ,,cambridge3 ,,james ,,munroe ,,and ,,company4 #aheg4 ,entered according to ,act of ,congress1 in the year #aheg1 by ,,james ,,munroe ,,and ,,company1 ,in the ,clerk's ,office of the ,district ,court of the ,district of ,massachusetts4 ,,cambridge3 ,,allen ,,and ,,farnham1 ,,printers4 ---------------------------------------- -------------------------------- ,,preface4 ,the object of this work is to give in the plainest possible manner all instructions1 rules1 and tables necessary for the location1 construction1 equipment1 and management of railroads4 ,as a general thing1 ,american engineers are not educated for their business2 and when they do possess a knowledge of pure science1 they are at a loss how to apply it4 ,the reader is presumed acquainted with the elements of arithmetic1 geometry1 algebra1 and mechanics3 being thus provided1 he will1 by a perusal of what follows1 be enabled to correctly proportion bridges1 of wood1 stone1 and iron3 abutments1 piers1 retaining walls1 superstructure1 and locomotive engines2 and to plan and lay out1 execute1 and estimate any description of work occurring upon railroads4 ,as the object has been more to be useful than original1 the best engineering writers and experimenters have been consulted2 among whom are1--,gauthey1 ,navier1 ,vieat1 ,tredgold1 ,barlow1 ,totten1 ,fairbairn1 ,hodgkinson1 ,clark1 and ,lardner4 ,also a great number of reports by ,american civil engineers upon railroad matters4 ,if assumptions take the place of demonstration1 it will be on good authority4 ,readers will bear in mind that the work is a 8handbook10 and not a 8treatise40 ,it is intended more as an office companion than as a text-book for students4 ,it will give in all cases the actual numerical result needed1 whether it be the scantling of a bridge chord1 the thickness of a wall1 or the dimensions of a locomotive boiler4 ,in connection1 it will be found convenient to use the works of ,trautwine and ,henck1 on ,field ,work3 of ,lieutenant ,smith1 on ,topography2 ,davies1 on ,surveying2 and ,gurley1 on the ,use of ,instruments4 ,any one wishing a complete treatise on the principles of bridge construction is referred to the excellent work of ,hermann ,haupt4 ,i take this opportunity of heartily thanking the engineers who in many ways have aided in making the work1 as it is believed1 of some worth4 ,g4 ,l4 ,v4 ,,general ,,table ,,of ,,contents4 ,page ,,introduction #a ,,chapter ,i4-- ,,reconnoissance #ab ,,ii4-- ,,survey #bd ,,iii4-- ,,location #da ,,iv4-- ,,preliminary ,,operations #ee ,v4-- ,,laying ,,out ,,work #hi ,,vi4-- ,,earthwork #ig ,,vii4-- ,,rockwork #aae ,,viii4-- ,,wooden ,,bridging #abb ,,ix4-- ,,iron ,,bridging #aib ,x4-- ,,stone ,,bridging #bcc ,,xi4-- ,,masonry #bdh ,,xii4-- ,,foundations #bfa ,,xiii4-- ,,superstructure #bgb ,,xiv4-- ,,equipment #cjb ,,xv4-- ,,stations #djc ,,xvi4-- ,,management #dac ,,appendix #dei ,,analytical ,,index4 ,,introduction4 ,,page ,rise and progress of railroads #a ,influence of railroads #c ,safety of railroad travelling #e ,preliminary operations #e ,mechanical principles of locomotion #f ,determination of character of road #g ,gauge #h ,general establishment of route #aj ,,chapter ,i4 ,,reconnoissance4 ,general topography #ab ,barometrical levelling #ah ,,chapter ,,ii4 ,,survey4 ,topographical sketching #bd ,general establishment of grades #cb ,equating for grades #cd ,comparison of surveyed lines #ci ,,chapter ,,iii4 ,,location4 ,alignment #da ,final adjustment of grades #df ,comparison of located lines #dg ,,chapter ,,iv4 ,,preliminary ,,operations4 ,specification #ee ,contract #ha ,solicit #hd ,bid #he ,comparison of bids #hg ,,chapter ,v4 ,,laying ,,out ,,work4 ,slopes #hi ,culverts #ij ,masonry #ia ,tunnels #ie ,,chapter ,,vi4 ,,earthwork4 ,form of railroad sections #ig ,excavation and embankment #ajd ,transport of material #ajf ,average haul #ajf ,drainage #aji ,method of conducting construction operations #aaa ,,chapter ,,vii4 ,,rockwork4 ,rock excavation #aae ,blasting and quarrying #aae-aag ,tunnelling #aah ,,chapter ,,viii4 ,,wooden ,,bridging4 ,of the forces at work in bridges #abb ,extension #abc ,compression #abc ,cross strain #abd ,detrusion #abf ,strength of materials #abf ,rules for practice #aca ,of the truss #aci ,of the arch #afi ,of the road-way #agd ,lateral bracing #age ,pile bridging #agh ,trestling #ahj ,draw bridges #aha ,centres #ahb ,,chapter ,,ix4 ,,iron ,,bridges4 ,nature and strength of iron #aib ,classification of iron bridges #aid ,iron truss frames #aie ,suspension bridges #bjc ,boiler plate bridges #bbc ,,chapter ,x4 ,,stone ,,bridging4 ,of the water-way #bcc ,form of the arch #bcf ,thickness of voussoirs #bch ,form and thickness of abutments #bci ,form and dimensions of piers #bde ,,chapter ,,xi4 ,,masonry4 ,stone #bdh ,cements1 mortars1 and concretes #bdi ,construction of arches1 wings1 and parapet #bec ,culverts and drains #bee ,retaining walls #bef ,,chapter ,,xii4 ,,foundations4 ,pile driving1 common system #bfb ,mitchell's screw pile #bff ,potts's atmospheric system #bff ,coffer-dam #bfg ,caisson #bfi ,,chapter ,,xiii4 ,,superstructure4 ,timber work #bgc ,rail section #bgf ,chairs and joints #bhb ,frogs #bij ,switches #bid ,sidings and crossings #bih ,elevation of exterior rail #bih ,,chapter ,,xiv4 ,,equipment4 ,,part ,i4 ,,locomotives4 ,introduction #cjb ,birth and growth of the locomotive #cjb ,the ,english locomotive of #ahej #cjd ,the ,american locomotive of #ahee #cje ,general description #cjf ,mechanical and physical principles #cab ,resistance to the motion of trains #cab ,traction and adhesion #caf ,fuel #cag ,generation of steam #ccj ,application of steam #ccf ,boiler proportions and dimensions #cdj ,rules and tables for practice #ced ,adaptation of locomotives to the movement of trains #cfj ,classification of engines #cga ,,part ,,second4 ,,cars4 ,wheels and axles #cif ,classification of cars #djj ,retarding of trains #dja ,,chapter ,,xv4 ,,stations4 ,classification of buildings #djc ,location of buildings #djc ,terminal passenger house #djc ,terminal freight house #dje ,engine house and appurtenances #dje ,way passenger and freight house #djg ,wood shed and tank #djg ,,chapter ,,xvi4 ,,management4 ,organization of employees #dac ,duties of employees #dae ,number of trains to be used #dah ,amount of service of engines #dah ,expenses1 receipts1 profits #dbj ,express trains #dbh ,comparative cost of working heavy and light trains #dcd ,branch roads #dcf ,reproduction of road and of stock #dcg ,working railroads by contract #dci ,classification of freight #dci ,time tables #ddc ,locomotive registers #ddd ,electric telegraph #ded ,new ,york and ,erie ,railroad #def ,,appendix4 ,a4--,decimal ,arithmetic #dei ,b4--,algebraic formul #dfa ,c4--,weights and measures #dfd ,d4--,value of the ,birmingham gauges #dfe ,e4--,locomotive boilers #dff ,f4--,effect of grades on the cost of working #dfh ,g4--,form for a locomotive specification #dga ,h4--,relative cost of transport by railroad and by stage #dgf ,i4--,form for experimental trips with locomotives #dgh ,k4--,proper weight for locomotives #dgi ,,additions1 ,,alterations1 ,,and ,,corrections4 ,the reader is particularly requested to apply the following errata before perusing the work4 ,they are partly mistakes in printing1 and partly errors in the original ,,ms4 ,the only excuse the writer can offer for the number is1 that1 being engaged in ,missouri1 while his publishers were in ,boston1 he has been prevented from seeing a single proof-sheet in time for its correction4 ,page #e1 line #g1 for 8#dii4iii10 read 8#dii1iii40 -- #e1 l4 #i1 for 8#di4iii10 read 8#di1iii40 -- #aj1 l4 #a1 for 8can be10 read 8can never be40 -- #ab to #bc1 headings1 for 8reconnoitre10 read 8reconnoissance40 -- #ah1 l4 #bd1 for 8#cf4i10 read 8#cf4h40 -- #ai1 l4 #f1 for 8table ,b10 read 8table ,d40 -- #bd1 l4 #a1 for 8any thing10 read 8every thing40 -- #be1 l4 #ag1 for 8horizontal line m m m10 read 8line #a1 #b1 #c10 etc4 -- #bf1 l4 #b1 for 8land10 read 8level40 -- #bg1 l4 #a1 for 8at the place10 read 8at the right place40 -- #bh1 l4 #bi1 for 8reconnoitre10 read 8reconnoissance40 -- #cj1 l4 #c1 for 8,a c d ,b10 read 8,a ,c ,d ,b40 -- #cb1 l4 #b1 the point m in the cut1 is one whole division above ,c2 it should be only three fourths of a division4 -- #ch1 l4 #aj from bottom1 for 8#bgf10 read 8#bfh40 -- #ci1 l4 #aj from bottom1 for 8#adb4ac10 read 8#adc4ac02 and last line1 for 8#eh4df10 read 8#dh4df40 -- #dj1 l4 #g1 for 8#ajcaj1ffg10 read 8#aj1bgg1ccc40 -- #db1 l4 #i1 for 8,thus10 read 8,these40 -- #db1 l4 #h from bottom1 for 8#b4ha or #b #dh4f0 read 8#b4hf or #b4ea4f40 -- #dc1 l4 #bg1 for 8,hencke10 read 8,henck40 -- #dg1 #dh1 #di1 for 8,mc,cullum10 read 8,mc,callum40 -- #dg1 l4 #ah1 for 8distance10 read 8resistance40 -- #dh1 l4 #f1 for 8infringing10 read 8impinging02 line #i1 for 8slacking10 read 8shackling02 l4 #h from bottom1 for 8increased10 read 8increases40 -- #ej1 l4 #ag1 for 8#aaj #ae4fj10 read 8#aaj #ae4fb40 -- #eb1 l4 #ae1 for 8#de4ei10 read 8#de4di02 also l4 #ag1 for 8#aacb10 read 8#aa4cb40 -- #eh1 l4 #aj1 for 8of size10 read 8and size40 -- #eh1 l4 #e from bottom1 for 8one cent10 read 8_/#ajj of a cent40 -- #fa1 l4 #c1 for 8are necessary10 read 8are not necessary40 -- #fc1 l4 #bh1 for 8stretches10 read 8stretchers40 -- #fe1 l4 #ae1 for 8spanded10 read 8spandrel40 -- #ga1 l4 #f from bottom1 for 8left10 read 8let40 -- #gc1 l4 #ai1 for 8chains10 read 8chairs40 -- #gd1 l4 #e1 for 8across ties10 read 8on cross-ties40 -- #gd1 l4 #ab1 for 8#bh inches10 read 8#bg inches40 -- #ge1 l4 #ah1 for 8land10 read 8haul40 -- #gf1 l4 #h1 for 8top10 read 8bottom10 and for 8charred when10 read 8charred where40 -- #gf1 l4 #aa1 for 8twopenny10 read 8tenpenny40 -- #gh1 l4 #a and #b1 for 8base10 read 8basis40 -- #hd1 l4 #ac1 for 8as10 read 8or40 -- #hi1 l4 #f1 for 8,whenever10 read 8,wherever02 l4 #ab1 for 8,letting10 read 8,setting40 -- #ij1 l4 #d1 for 8cost10 read 8cut40 -- #ic1 l4 #f1 for 8#cg and #ch10 read 8#cf and #cg40 -- #ie1 l4 #a1 for 8beach10 read 8bench02 l4 #c1 for 8to so10 read 8so to02 l4 #ac1 for 8b being #aj ft4 back of #b is 444 #ajj4jj10 read 8b being #aj ft4 back of #b is #j4a ft4 higher than #b1 or 444 #ajj4aj40 -- #ajb1 l4 #a1 head of middle col41 for 8,slopes #a10 read 8,slopes #a40 -- #ajc1 l4 #d from bottom1 for 8and ten feet10 read 8and one end ten feet40 -- #ajd1 l4 #i1 for 8any10 read 8very40 -- #ajh1 l4 #i1 for 8,elwood10 read 8,ellwood40 -- #aae1 l4 #e1 for 8a loam10 read 8a berm02 l4 #af1 for 8a rent10 read 8a vent40 -- #aag1 l4 #g1 for 8volcanic10 read 8voltaic40 -- #aag1 l4 #i1 for 8,round ,drum10 read 8,round ,down40 -- #aag1 l4 #ah1 for 8,col4 ,puseling10 read 8,col4 ,pasley40 -- #aah1 l4 #b1 for 8,maillefaut10 read 8,maillefert40 -- #aah1 l4 #af1 for 8insert10 read 8invert40 -- #aah1 l4 #be1 for 8quointed10 read 8grouted40 -- #aai1 l4 #cj1 for 8furnished10 read 8finished40 -- #abj1 ,table1 for 8,nochistingo10 read 8,nochistongo02 for 8,supperton10 read 8,sapperton02 and for 8,black ,rock1 ,w4 ,s40 read 8,black ,rock1 ,u4 ,s40 -- #aba1 l4 #ai1 for 8,belchingly10 read 8,blechingly40 -- #abe1 in table at bottom1 for 8#ij_/fi10 read 8#ij_/ff10 and for 8#adj1 #bj_/adj1 #bj_/afj or #j4ac10 read 8#aaa1 #bj_/aaa1 #bj_/aca1 or #j4ae40 -- #abf1 l4 #a1 for 8extensive10 read 8extensile40 -- #abg1 l4 #aj1 for 8#fg1bjj10 read 8#fe1bea40 -- #abg1 l4 #bf1 for 8,hodgekinson10 read 8,hodgkinson40 -- #abh1 l4 #d1 for 8#abjjj10 read 8#aajjj40 -- #abh1 l4 #ae and #bb1 for 8,hodgekinson10 read 8,hodgkinson40 -- #abi1 l4 #e1 for 8#abjjj10 read 8#aajjj40 -- #abi1 l4 #b from bottom1 for 8,sun ,wood10 read 8,ironwood40 -- #acj1 l4 #g1 for 8,,wl#b #d,sbd#b10 read 8,,wl #d,sbd#b40 -- #aca1 l4 #i1 for 8wood #adc10 read 8wood #acc40 -- #acd1 in art4 #afd1 for 8#gjj10 read 8#ieb40 -- #acf1 for example there given1 place the following3-- ,span #cj feet1 ,whence-- ,length #cd feet1 ,length #cd feet1 ,load #aj tons at centre4 ,span #cj feet1 ,depth #be inches1 ,lower flange #cb4eh square inches1 ,upper flange #e4cd square inches1 a 7#f #aj #ab #cj7_/7bf 7#cd #ab7_/af7 #cb4eh and #cb4eh_/f4a #e4cd4 -- #ada1 last line1 ,fig4 #fc ,a was omitted2 it is the same as fig4 #ajb1 page #bjj1 inverted4 -- #adb1 last line1 for 8span10 read 8spans40 -- #adf1 head of col4 #g1 for 8,top ,washer10 read 8,thickness of ,washer40 -- #aej1 after line #i1 ,figs4 #fg ,d and #fg ,e 7page #aec7 should be inserted4 -- #aea1 l4 #c1 for 8,w #bbdi10 etc41 read 8,w #bbdj10 etc4 -- #aea1 l4 #ah1 for 8opposite to #ca1daf1 is the diam4 #a10 read 8opposite to #da1dae1 is the diam4 #a40 -- #aea1 l4 #ai1 for 8#a10 read 8#a40 -- #aed1 last line1 for 8tubular10 read 8tabular40 -- #aef1 l4 #d from bottom1 for 8washer band10 read 8washer used40 -- #afd1 l4 #aj to #ad1 inclusive4 ,the first number of ratios should be #bj instead of #ae4 -- #aff1 l4 #aa1 for 8#fi ,b10 read 8#fi ,a40 -- #aga1 head of col4 #e of table1 for 8,rod of ,arch10 read 8,rad4 of ,arch40 -- #agc1 l4 #be1 for 8ability10 read 8stability40 -- #agc1 l4 #cb1 for 8,whence10 read 8,where40 -- #age1 l4 #h1 for 8triangular10 read 8diagonal40 -- #agh1 l4 #c1 for 8article10 read 8outside40 -- #ahd1 l4 #d from bottom1 for 8barriers10 read 8voussoirs40 -- #ahg1 fig4 #if is upside down2 also1 fig4 #ig1 page #ahh1 and fig4 #ih1 page #ahi4 -- #aic1 l4 #d1 col4 #c of table1 for 84#jjjjjfge10 read 84#jjjjjfhe02 also1 l4 #af1 col4 #e1 for 8straining10 read 8shearing02 l4 #g from bottom1 for 8#ae1jjj10 read 8#ah1jjj20 and l4 #f from bottom1 for 8#ge1jjj10 read 8#aje1jjj40 -- #aii1 l4 #g from bottom1 for 8#bj1acb10 read 8#bj1cab40 -- #bjj1 l4 #d1 for 8,a ,c10 read 8,a ,g02 and l4 #f1 for 8that on ,a ,r10 read 8that on ,a ,k40 -- #bjb1 l4 #g1 for 8on page #aic10 read 8on page #ach40 -- #bjd1 l4 #e from bottom1 for 8varied line10 read 8versed sine40 -- #bjg1 l4 #e and #f1 for 8,f ,g1 ,g ,e1 in place of ,e ,f1 ,e ,c10 read 8,g ,l1 ,g ,e1 in place of ,f ,l1 ,f ,c40 -- #baj1 in place of 8f 7,f7_/7#dph710 put 8,d 7,v#b - d#b7 - 7l#b - d#b74 where ,d depression1 l half length of curve before elongation1 ,v half length of curve after elongation1 d half distance between points of suspension40 ,omit the remainder of the paragraph4 -- #baa1 omit the #fth and #gth lines1 and in place of formula there given1 use that on page #baj1 7as corrected17 ,v being the length of semi-curve as elongated by heat instead of by tension2 the elongations1 both by heat and tension1 being found by table on page #aic4 -- #bab1 l4 #b1 for 8#eaj4fi10 read 8#eaj4hj10 which result1 of course1 runs through the whole example4 -- #bac and #bad4 ,the remarks under 8,anchoring ,masonry10 are evidently wrong throughout3 #ast1 the whole tension should be divided by two1 instead of four1 as half of the whole tension acts at each point of suspension2 #b;d1 no reduction should be made for the direction of the pulling force4 ,one half of the tension is #c1cba1bej lbs42 which is resisted by a column of masonry of #c1cba1bej_/afj #bj1geh cubic feet1 or #bj #bj #eb feet1 or by a mass #ae #ae #ia feet4 -- #bad1 l4 #f1 for 8#efa1ebg10 read 8#efb1edb40 -- #bae1 l4 #ad from bottom1 for 8,,stiffening ,,towers10 read 8,,stiffening ,,trusses40 -- #bbe1 l4 #ad1 for 8#aid10 read 8#aic40 -- #bbf1 l4 #c1 for 8see page #abh10 read 8see page #aic40 -- #bbg1 l4 #d1 for 8detensional10 read 8detrusional40 -- #bbh1 in place of equations at l4 #af1 put 8,r a ,r 7#b d t701 whence d 7,r a7_/7#b,r t72 where a area of rivet1 d distance1 t plate thickness4 -- #bbi1 in art4 #bdb1 the strengths of 8wrought iron10 have been taken for those of 8boiler plate02 that is1 #aa1jjj for #g1ejj1 and #ae1jjj for #ab1gdj1 which is wrong4 -- #bca1 l4 #ba1 for 8chopped10 read 8dropped40 -- #bcd1 l4 #d1 for 8joint10 read 8just40 -- #bce1 l4 #ad1 for 8#j4jaf feet10 read 8#j4jdg feet40 -- #bcf1 l4 #i1 for 8care10 read 8ease40 -- #bcg1 l4 #c from bottom1 for 8representing10 read 8separating40 -- #bda1 l4 #b1 for 8localities10 read 8locality40 -- #bdb1 l4 #g1 omit 8and c e1 the parapets40 -- #bdc1 l4 #i1 for 8embankment10 read 8abutment40 -- #bdd1 l4 #i1 for 8is thus10 read 8is found thus40 -- #bde1 l4 #ag1 for 8latter10 read 8batter40 -- #bdi1 l4 #bc1 for 8common hydraulic10 read 8common mortar1 hydraulic40 -- #bdi1 l4 #bg1 for 8argyle magnesia10 read 8argil1 magnesia40 -- #bea1 l4 #af1 for 8#g to #b10 read 8#a to #b40 -- #bed1 last l41 for 8corners10 read 8courses40 -- #bef1 l4 #ac1 for 8formed10 read 8found40 -- #beh1 art4 #bgf1 in place of 8#bj_/b #ae #a #ajj #bj_/c10 put 8#bj #ae #a #ajj #b #bj_/c10 where #b represents the ratio between ,ca #f1 and #f-b2 thus1 #bj #ae #a #ajj #f4f_/ab #bj_/c #aaa1aaa1 for the overthrowing force in place of #ajj1jjj4 ,the overthrowing force is thus large1 because the maximum weight of earth has been assumed to press against the wall with its whole force1 no allowance being made for friction4 ,in practice1 #d_/aj of the height has been found amply thick for walls retaining ordinary earth4 -- #bfb1 last l4 but one1 for 8superstratum10 read 8substratum40 -- #bfd1 in example1 l4 #e1 for 8#bf1ffg10 read 8#dh1jjj40 -- #bff1 l4 #be1 for 8,godwin10 read 8,goodwin40 -- #bff1 l4 #bf1 for 8,there1 sands10 read 8,these sands40 -- #bfg1 l4 #bb1 for 8bottom10 read 8proper level40 -- #bha1 l4 #d from bottom1 for 8curve10 read 8cone40 -- #bhb1 l4 #bj1 for 8,daniel10 read 8,david40 -- #bhb1 l4 #d from bottom1 for 8cup10 read 8cap40 -- #bhd1 l4 #aj1 and #bhe1 l4 #h1 for 8compressed rails10 read 8compound rails40 -- #bhe1 l4 #e1 for 8extension10 read 8extensile40 -- #bhi1 invert col4 #a of table1 so that it shall read-- ,at #ajj place the rails in contact4 ,at #ij at a distance of 4#jjacf feet1 or #j4jaf inches4 ,at #hj at a distance of 4#jjbgb feet1 or #j4jcb inches ,etc4 -- #bhi1 last l41 for 8levelled10 read 8bevelled40 -- #bia1 last l41 for 8a c1 #d4h10 read 8a c1 ,l #h40 -- #bib1 l4 #i1 for 8e h and d k10 read 8e ,l and d k02 same p4 l4 #f from bottom1 for 8a1 #i is three1 etc40 read 8a b is three10 etc4 -- #bic1 l4 #f and #g1 for 8i g1 e h1 b b1 #h1 #i1 ,a s #gi10 read 8i g1 e h1 a c1 b c40 -- #bif1 l4 #ad1 for 8,r#b - 7,r - #h7b10 read 8,r#b - 7,r - g7#b40 -- #cjc1 art4 #bii1 for 8,m4 ,leguire10 read 8,m4 ,seguin40 -- #cjf1 l4 #b1 for 8,r4 ,r4 ,g410 read 8,r4 ,k4 and ,g40 -- #cad1 l4 #b1 for 8,d4 ,r4 ,clark10 read 8,d4 ,k4 ,clark40 -- #cbj1 l4 #a1 for 8,railroad1 three pounds 7,pennsylvania710 read 8,railroad 7,pennsylvania71 three pounds40 -- #cbj1 l4 #g1 for 8coal10 read 8coke40 -- #cca1 near bottom1 for 8,the area is1 therefore1 ,sides1 twice length1 etc41 read 8,sides1 twice length by height1 etc41 ,back1 twice height1 etc41 ,back1 height by width1 etc41 ,front1 twice height1 etc41 ,front1 height by width1 etc41 ,top1 twice length1 etc410 ,top1 length by width1 etc40 -- #ccd1 l4 #ae1 for 8#dd4g lbs410 read 8#ad4g lbs40 -- #cce1 l4 #g1 for 8,railway ,mechanics10 read 8,railway ,machinery40 -- #cce1 l4 #aj1 for 8two velocities10 read 8low velocities40 -- #ccf1 last l41 for 8entering part10 read 8entering port40 -- #cda1 l4 #aa1 for 8properties10 read 8proportions40 -- #cda1 last l41 for 8,nollan10 read 8,nollau40 -- #cdf1 l4 #ag1 for 8part10 read 8port10 and for 8construction10 read 8contraction40 -- #cee1 l4 #g1 for 8#fcjj10 read 8#eagj02 and l4 #i1 for 8#af1ije10 read 8#ae1gge40 -- #cfc1 l4 #ag1 for 8#dd #b #hj10 read 8#dd #b #hh40 -- #cfc1 l4 #ah1 for 8#ed #c #ajc10 read 8#ed #c #afc40 -- #cfg1 l4 #af1 for 8#ae4j_/aj10 read 8#ae4j_/af10 -- #cfh1 l4 #ae1 for 8u #ace10 read 8n #ace10 etc4 -- #cgj1 l4 #g1 for 8feet10 read 8per cent40 -- #cgf1 for 8#aijij10 read 8#aijej40 -- #chd1 in last part of example1 for 8#ebhj_/7d #c4adaf7 #d #cgcjj10 read 8#be #ebhj_/7d #c4adaf7 #d #cgcdh40 -- #dba1 bottom line1 for 8decision10 read 8division40 -- #dbc and #dbd1 in table1 for 8count10 read 8cost40 -- #dbg1 l4 #cb1 for 8which10 read 8we40 -- #dbh1 l4 #d1 transpose 8,dr4 ,lardner1 7#ahej170 to the end of line #c4 -- #ddc1 l4 #bh1 for 8valuation10 read 8solution40 -- #ddf1 l4 #aa1 for 8attained10 read 8obtained40 -- #dei1 l4 #bj1 for 8,hectametre10 read 8,hectometre40 -- #dei1 l4 #ba1 for 8,ridometre10 read 8,kilometre40 -- #dfa1 l4 #g1 for 8less than a1 or o10 read 8less a1 or #j40 -- #dfh1 l4 #cj1 for 8fractions10 read 8functions40 -- #dgd1 l4 #ah1 for 8,balbett10 read 8,babbitt40 -- #dgi1 l4 #aj1 for 8one sixth1 with much less10 read 8one sixth2 with sand1 much less40 ,,handbook ,,of ,,railroad ,,construction4 ,,introduction4 8,they build not merely roads of earth and stone1 as of old1 but they build iron roads3 and not content with horses of flesh1 they are building horses of iron1 such as never faint nor lose their breath40--,,dr4 ,,bushnell4 ,,rise ,,and ,,progress ,,of ,,railroads4 #a4 ,in #ahbe1 the ,stockton and ,darlington ,railroad 7,england71 was opened4 ,in #ahbg1 the ,quincy 7of ,massachusetts71 and ,mauch-,chunk 7,pennsylvania71 were completed4 ,in #ahbi1 the ,liverpool and ,manchester road1 7,england71 was finished4 ,in #ahcc1 a road was opened from ,charleston1 7,south ,carolina71 to ,augusta 7,georgia74 ,in #ahdj1 ,belgium opened #aij miles of railroad4 ,in #ahdc1 the railroad from ,paris to ,rouen 7,france71 was completed4 ,in #ahdd1 ,belgium finished her system of #cdg miles4 ,in #ahdf1 ,russia opened a railroad from the ,wolga to the ,don4 ,in #ahdg1 ,germany had in operation #b1hbh miles4 ,in #aheb1 the ,moscow and ,st4 ,petersburg road was finished4 #b4 ,in #ahef1 the ,united ,states of ,america had in operation #bc1jjj miles1 and in progress #ag1jjj miles2 employing #f1jjj locomotive engines1 #aj1jjj passenger and #gj1jjj freight cars2 costing in all about #gej1jjj1jjj of dollars2 running annually #aad1jjj1jjj miles1 and transporting #abc millions of passengers1 and #cj millions of tons of freight per annum2 performing a passenger mileage of #d1gej1jjj1jjj1 and a freight mileage of #c1jjj1jjj1jjj4 #c4 ,by mileage is meant the product of miles run1 by tons or by passengers carried4 ,thus1 #ejj persons carried #ajj miles1 and #gej persons carried #ge miles1 give a passenger mileage of #ejj #ajj #gej #ge #ajf1bej4 #d4 ,the rate of progress in the ,united ,states has been as follows3-- ,in #ahbh1 there were #c miles4 ,in #ahcj1 #da miles4 ,in #ahdj1 #b1afg miles4 ,in #ahej1 #g1cee miles4 ,in #ahef1 #bc1bdb miles4 ,at the present time1 ,january #a1 #aheg1 there is probably1 in round numbers1 #be1jjj miles of completed road1 or enough to extend entirely around the world4 ,as regards the ratio of completed road to population1 and as regards the actual length of railroad in operation1 the ,united ,states stand before any other country4 ,,influence ,,of ,,railroads4 #e4 ,the effect of a judicious system of railroads upon any community is to increase consumption and to stimulate the production of agricultural products2 to distribute more generally the population1 to cause a balance between supply and demand1 and to increase both the amount and safety of travelling4 ,it is stated that within two years after the opening of the ,new ,york and ,erie ,railroad1 it was carrying more agricultural produce than the entire quantity which had been raised throughout the tributary country before the road was built4 #f4 ,the following table1 cut from a ,chicago paper1 shows the effect of railroad transport upon the cost of grain in that market3-- ,,wheat4 ,,corn4 ,by ,r4 ,r4 ,by ,wagon4,by ,r4 ,r4 ,by ,wagon4 ,at market1 #di4ej #di4ej #be4fj #be4fj #aj miles1 #di4be #dh4jj #bd4be #bc4bf #ej miles1 #dh4ge #db4jj #bd4jj #ag4be #ajj miles1 #dh4jj #cd4ej #bc4be #i4ge #aej miles1 #dg4be #bg4jj #bb4ej #b4be #bjj miles1 #df4ej #ai4ej #ba4ge #j4jj #bej miles1 #de4ge #ab4jj #ba4jj #j4jj #cjj miles1 #de4jj #d4ej #bj4be #j4jj #ccj miles1 #dd4ee #j4jj #ai4hj #j4jj ,thus a ton of corn carried two hundred miles1 costs1 per wagon transport1 more than it brings at market2 while moved by railroad1 it is worth #ba4ge per ton4 ,also wheat will not bear wagon transport of three hundred and thirty miles2 while moved that distance by railroad it is worth #dd4ee per ton4 #g4 ,by railroads1 large cities are supplied with fresh meats and vegetables1 butter1 eggs1 and milk4 ,an unhealthy increase of density of population is prevented1 by enabling business men to live five1 ten1 or fifteen miles away from the city and yet do business therein4 ,the amount of this diffusion is as the square of the speed of transport4 ,if a person walks four miles per hour1 and supposing one hour allowed for passing from the house to the place of business1 he cannot live at a greater distance than four miles from his work4 ,the area1 therefore1 which may be lived in1 is the circle of which the radius is four1 the diameter eight1 and the area fifty and one quarter square miles4 ,if by horse one can go eight miles per hour1 the diameter becomes sixteen miles1 and area two hundred and one square miles2 and1 if by railroad he moves thirty miles per hour1 the diameter becomes sixty miles1 and the area #b1hbg square miles4 ,the effect of such diffusion is plainly seen about ,boston1 7,massachusetts74 ,people who in #ahcj were mostly confined to the city1 now live in ,dorchester1 ,milton1 ,dedham1 ,roxbury1 ,brookline1 ,brighton1 ,cambridge1 ,charlestown1 ,somerville1 ,chelsea1 ,lynn1 and ,salem2 places distant from two to thirteen miles4 #h4 ,in railroads1 as in other labor saving 7and labor producing7 machines1 the innovation has been loudly decried4 ,but though it does render some classes of labor useless1 and throw out of employment some persons1 it creates new labor far more than the old1 and gives much more than it takes away4 ,twenty years of experience shows that the diminished cost of transport by railroad invariably augments the amount of commerce transacted1 and in a much larger ratio than the reduction of cost4 ,it is estimated by ,dr4 ,lardner1 that #cjj1jjj horses working daily in stages would be required to perform the passenger traffic alone1 which took place in ,england during the year #ahdh4 ,it is concluded1 also1 from reliable returns1 that could the whole number of passengers carried by railroad1 have been transported by stage1 the excess of cost by that method above that by railroad would have been #dj1jjj1jjj4 ,,safety ,,of ,,railroad ,,travelling4 #i4 ,if we know that in a given time the whole distance travelled by passengers was #ejj1jjj miles1 and that in such time there occurred one fatal accident1 it follows that when a person travels one mile1 the chances are #dii1iii against one of losing life4 ,if he travel ten miles1 the chances are #di1iii against one1 or ten times as many of meeting with loss of life2 and generally the chances of accident are as the distance travelled4 ,in #ahee1 the whole number of miles run by passengers in the ,united ,states was1 in round numbers1 #d1gej1jjj1jjj1 while there were killed one hundred and sixteen2 or one in every #da1jjj1jjj1 very nearly4 7,the ratio in ,england is one in every #fe1jjj1jjj47 ,now if for each #djj1jjj miles travelled by stage passengers1 7a distance equal to sixteen times round the world17 one passenger was killed1 and if the whole railroad mileage could be worked by stages1 there would be annually #aa1hge lives lost2 or one hundred times the number annually lost by railroad4 ,thus it would be one hundred times safer to travel by railroad than by stage4 ,the danger of steamboat travelling is far greater than by stage4 ,,preliminary ,,operations4 #aj4 ,the first step to be taken in starting a railroad enterprise1 is the choice of a board of directors 7provisional71 whose duty is to find all that can be known of the commercial1 financial1 and agricultural nature of the country to be traversed4 ,to determine as near as possible its ability to build and support a road2 and to obtain the necessary legislative enactments4 #aa4 ,the determination of the increase of traffic which the road may be expected to excite1 is a difficult matter4 ,there can be few rules given for proceeding in such an inquiry4 ,it seems very easy to prove by what roads have done1 that any project will be profitable4 ,an abstract of a report lately published1 tries to prove that a road will pay forty-five and one half per cent4 net2 the working expenses being assumed at only thirteen and one half per cent4 of the gross receipts4 ,the error here lies in assuming the working expenses too low1 as few roads in the country have been worked for less than forty per cent42 a more common ratio being fifty one-hundredths of the gross receipts4 ,not one half of railroads are built for the original estimate4 ,in few cases has sufficient allowance been made for the sacrifice undergone in negotiating the companies' securities4 ,all general instructions that can be given relating to the determination of prospective profits1 are1 to keep the estimate of constructing and working expenses high1 and that of the assumed traffic low2 not so low1 however1 as to require a too lightly built road4 ,,mechanical ,,principles ,,of ,,locomotion4 #ab4 ,the superiority which the modern railroad possesses over the common1 ,mc,adam1 plank1 or turnpike-road1 consists1 first1 in the reduction of the resistance to motion1 and second1 in the application of the locomotive steam-engine4 #ac4 ,the effect of grades of a given incline upon a railroad is relatively more than upon common roads2 for as the absolute resistance on a level decreases1 the relative resistance of grades augments3 whence to obtain the full benefit of the system1 we must reduce much more the grades and curvature upon a railroad1 than on a common road4 ,for example1 if the resistance to moving one ton upon a level upon a railroad was ten pounds1 and upon a common road forty pounds1 where a twenty-three feet grade would be admissible upon the former1 we might use an incline of ninety-three feet per mile upon the latter4 #ad4 ,the resistance to the motion of railroad trains increases rapidly with the speed2#a whence the grades of a passenger road where a high average speed is used1 may be steeper than those of a road doing a freight business chiefly4 ,footnote #a3 ,see chapter ,,xiv4 ,,determination ,,of ,,character ,,of ,,road4 #ae4 ,upon a correct idea of what the road ought to be1 depends in a great degree its success4 ,the amount of capital expended upon the reduction of the natural surface1 depends upon the expected amount of traffic4 ,the traffic remaining the same1 the greater the capital expended in reducing grades and curvature1 the less will be the working expense2 and the less the construction capital1 the greater that for maintenance4 ,the limit of expenditure must be such as to render the sum of construction and maintaining capital a minimum4 ,the bad effect of grades upon the cost of maintaining and of working railroads1 is not so great as many suppose4 ,of the whole cost of working1 only about forty per cent4 can be charged to locomotive power2 and of this1 not more than sixty-two per cent4 is effected by grades4#b ,footnote #b3 ,see appendix ,f4 #af4 ,the degree of curvature to be admitted upon any road depends somewhat upon the speeds at which trains are to be run4 ,the larger the radius of curvature1 the greater may be the speed2 at the same time the elevation of the exterior rail upon curves may be less1 and therefore more adapted to freight trains4 ,high rates of speed are considered upon some competing roads necessary2 but are1 even in such cases1 necessary evils4 ,the wear of cars and of engines1 of permanent way and of bridges1 increase in a rapid ratio with the velocity4 ,the maximum speed for freight trains should never exceed fifteen miles per hour1 or for passenger trains from twenty to twenty-five miles per hour4#c ,footnote #c3 ,see chapter ,,xvi4 #ag4 ,the agricultural nature of the country and its commercial position1 will determine the nature of the traffic1 whether passenger or freight1 and also the amount4 ,the amount and nature of the traffic will limit the curvature1 and will partially determine the arrangement of grades4 ,,gauge4 #ah4 ,the question of broad and narrow gauge has led to much discussion1 and both plans claim among their advocates some of the best engineers4 ,the narrow gauge 7,american and ,english17 is four feet eight and one half inches 7from inside to inside of rail74 ,the maximum adopted1 is 7the ,great ,western of ,england7 seven feet4 ,the ,american maximum 7,new ,york and ,erie1 and ,ohio and ,mississippi7 is six feet4 ,there is also in ,america four feet ten inches1 five feet1 and five feet six inches4 ,the advantage of the broad gauge for a road doing an extensive business1 is the increased stowage room in freight cars1 thus rendering admissible shorter trains2 by which the locomotive power is more directly applied on curves4 ,more comfortable passenger cars1 7the same length of car of course accommodates the same number of passengers74 ,the disadvantages of a wide gauge are1 increased expense of cutting1 embanking1 bridging1 and masonry2 increased expense of engines1 cars1 rails1 sleepers1 and all machinery2 more wear and tear upon curves1 by reason of greater difference between the lengths of inner and outer rails1 and increased atmospheric resistance to fast trains1 from increased bulk4 #ai4 ,the general conclusion arrived at by a commission appointed by the ,great ,western ,railway ,company1 7,england17 consisting of ,messrs4 ,nicholas ,wood1 ,j4 ,k4 ,brunel1 and ,john ,hawkshaw1 was1 that four feet1 eight and one half inches was rather narrow1 but still enough for a certain class of roads2 that two or three inches made no material difference2 that seven feet was too wide for any road2 that the weight of the broad gauge engine1 compared with the small increase of power1 was a serious evil2 that engines could be run with perfect safety upon the narrow gauge at any speed from thirty to sixty miles per hour1 and that no more had been attained upon the broad2 that rolling friction was less upon the broad1 owing to the increased diameter of wheels1 but that friction from curves and atmospheric resistance was greater4 #bj4 ,d4 ,k4 ,clark1 in 8,railway ,machinery10 p4 #cjj1 #cja1 makes the resistance as deduced from experiments made upon both the four feet1 eight and one half inches1 and the seven feet gauge1 considerably greater upon the former than on the latter2 but as the narrow gauge trials were made upon a curved road1 with rails in a bad state1 in average weather1 while those upon the broad were made in good weather1 upon a good and straight line1 he leaves the gauge question open1 and uses the same formula for all widths4 #ba4 ,want of increased power1 can be an apology for increased gauge1 until the capacity of the narrow gauge has been filled4 ,the strongest engines in the world are upon the four feet1 eight and one half inch gauge4 ,no engines in ,america surpass or compare for absolute strength1 with those upon the ,baltimore and ,ohio ,railroad4 ,the most powerful passenger engine ever built for high speeds1 is ,crampton's engine 8,liverpool10 7,london and ,north-western ,railroad1 ,england17 gauge four feet1 eight and one half inches4 ,,general ,,establishment ,,of ,,route4 #bb4 ,the straight and level line connecting any two points1 is of course the best for the completed road2 but this is seldom practicable4 ,way towns must be accommodated to a certain extent2 but the main line should not be lengthened on that account1 unless the traffic and capital furnished by such town is not only sufficient to pay for the construction and maintenance of the extra length1 but also to carry the entire through traffic over such increased distance4 ,if the town is unable to support such a burden1 it may be able to build and maintain a branch4 #bc4 ,routes placed upon the immediate bank of a large stream1 are generally crossed by a great number of deep gorges1 which serve to drain the side lands4 #bd4 ,routes placed upon sloping land1 when the axis of the road and the natural descent are at right angles to each other1 are more subject to slides than when placed upon plateaus or 8bottoms40 #be4 ,lines crossing the dividing ridges of separate waters1 rise and fall a great deal2 thus rendering necessary a strong motive power to work the road4 ,such roads are the ,western of ,massachusetts1 passing from the valley of the ,connecticut at ,springfield1 to the ,hudson ,river valley at ,greenbush4 ,also those roads crossing the ,alleghanies4 ,and such will be the ,pacific road1 crossing first the ,rocky ,mountains to the ,great ,basin1 and second1 the ,sierra ,nevada into the ,sacramento valley4 ,,chapter ,i4 ,,reconnoissance4 #bf4 ,the object of the reconnoitre is to find approximately the place for the road1 7i4 e4 within half of a mile17 to find the general form of the country1 and to choose that part which with reference to the expected traffic1 shall give the best gradients2 to determine the elevations of summits upon competing routes2 and1 in fine1 to prepare the way for the survey4 ,,general ,,topography4 #bg4 ,the general topography of a country may be ascertained by reference to ,state maps1 where such exist1 and when not1 by riding over the district4 ,the direction and size of watercourses1 will show at once the position of summits4 ,illustration3 ,fig4 #a4 #bh4 ,water flowing as in fig4 #a1 indicates a fall from ,b to ,e2 and also traverse slopes from a a and c c to d d4 ,illustration3 ,fig4 #b4 #bi4 ,fig4 #b shows a broken ridge a a a from which the water flows in both directions2 and in general1 the sources of streams point towards the higher lands4 ,illustration3 ,fig4 #c4 #cj4 ,if it be required to join the points ,a and ,d by railroad1 7fig4 #c47 it may be better to pass at once from ,a through ,b and ,c1 than to go by the streams ,f ,e1 ,f ,e4 ,by the latter route the road would ascend all of the way from ,a to ,e2 and descend from ,e to ,d4 ,by the first if it requires steep gradients to rise from ,a to ,b1 and to fall from ,c to ,d1 still if the section ,b ,c is a plateau1 and if the rise between ,a and ,b and ,a and ,e is the same1 by grouping the grades at ,b and ,c we may so adapt the motive power1 as to take the same train from ,a to ,d without breaking4 ,the general arrangement of grades by the line ,a ,b ,c ,d is then as fig4 #d2 and ,a ,f ,e ,e ,f ,d1 as in fig4 #e4 ,the saving in this case is by length1 as the same amount of power is required to overcome a given ascent4 ,illustration3 ,fig4 #d4 ,illustration3 ,fig4 #e4 #ca4 ,valleys generally rise much faster near their source1 than at any point lower down2 also the width increases as we approach the debouch4 ,fig4 #f shows the cross sections of a valley from its source to the mouth4 ,illustration3 ,fig4 #f4 #cb4 ,in the case of parallel valleys running in the same direction1 the form will be as in fig #g4 ,let #a #b1 #a #b1 etc41 represent a datum level1 or a horizontal plane passing through the lowest point4 ,the line a b1 shows the height of the bottom at ,b2 c d that at ,d1 e f that at ,e1 and g h that at ,c4 ,the broken lines i1 k1 l1 m1 n1 show the general form of the land4 ,now by the route m m m m1 from ,a to ,f1 we have the profile m m m m1 fig4 #h1 by n n n n1 the profile n n n n1 and by o o o1 the profile o o o4 ,illustration3 ,fig4 #g4 ,illustration3 ,fig4 #h4 ,illustration3 ,fig4 #i4 #cc4 ,in the case of parallel valleys running in opposite directions1 as in fig4 #i1 we have the form there shown2 and the profiles corresponding to the several lines are shown in fig4 #aj4 ,as we should always adopt the line giving the least rise and fall1 other things being equal1 it is plain which line on the plan we must follow4 ,illustration3 ,fig4 #aj4 #cd4 ,in passing from ,a to ,b1 figs4 #aa and #ab1 by the several lines c1 d1 e1 f1 we have the profiles shown at c1 d1 e1 f1 from which it appears1 that the nearer we cross to the heads of streams1 the less is the difference of heights4 ,illustration3 ,fig4 #aa4 ,illustration3 ,fig4 #ab4 ,illustration3 ,fig4 #ab 7a74 #ce4 ,if we wish to go from ,a to ,b1 fig4 #ab 7a71 we should of course take first the straight line2 but being obliged to avoid the hill ,c1 on arriving at d1 we should not try to recover that line at e1 but proceed at once to ,b4 ,also as we are obliged to pass through d1 we ought to go directly to d and not by the way of c2 and the same idea is repeated between ,a and d2 the last line being ,a b d ,b4 ,few rules can be given in the choice of routes4 ,practice only will enable the engineer to find the best location for a railroad4 ,,barometrical ,,levelling4 #cf4 ,the relative height of summits1 the rate of fall of streams1 and absolute elevation1 within a few feet1 may be easily1 rapidly1 and cheaply found by the barometer4 ,this also affords an excellent check upon subsequent levelling operations4 ,the results thus obtained depend upon the physical property1 that the density of the air decreases as the square of the height4 #cg4 ,the barometer is a glass tube1 partly filled with mercury1 having a vacuum in the upper part4 ,by it the exact density of the air at any point is determined4 ,accompanying are two thermometers2 one attached1 showing the temperature of the barometer2 the other detached1 showing the atmospheric temperature4 #ch4 ,knowing now the manner of finding the density of the air at any two points1 and also the relation between density and height1 the operation of levelling by the barometer is very simple4 ,the modus operandi is as follows1 7see tables ,a1 ,b1 ,c1 and ,d73-- ,let us have the notes4 ,barom4 ,attached ,therm4 ,detached ,therm4 ,upper ,station1 #bi4ge #bh4e #bg4i ,lower ,station1 #bf4hj #cf4h #cf4c ,latitude #df ,n4 ,we have by table ,a1 against the bar4 point1 #bi4ge1 #fajh4f also by table ,a1 against the bar4 point1 #bf4hj1 #ebgf4f ------------ ,the difference #hcb4j ,diff4 of attached therm4 #cf4h- #bh4e #h4c 7table ,b7 -#ab4b ------------ #hai4h ,double the sum of detached thermometers multiplied by #a_/ajjj of #hai4h is #b7bg4i #cf4c7 4#haih #aje4c ------------ #ibe4a ,correction 7see table ,c7 for lat4 #df ,n4 and approximate height #ibe4a #c4a ------------ #ibh4b ,final correction by table ,d4 ,the barometer at the lower station being #bf4hj1 and the tabular number against #bg4ef being #j4bb1 that for #bf4hj will be #j4ca1 and we have #ajjj to 4#ca as #ibh4b to #j4bhg1 or #j4c1 which add to #ibh4b and we have as the final height #ibh4e metres1 or #ibh4e #c4bh #cjde4dh feet4 ,the tables above referred to1 are those of ,mr4 ,oltman1 and are considered as the most convenient and reliable of any published4 ,,table ,a4 ,english ,inches4 ,metres4 #ad4ef #dah4e #ad4fa #ddj4j #ad4fe #dfa4e #ad4fh #dhb4i #ad4gb #ejd4b #ad4gf #ebe4d #ad4hj #edf4f #ad4hd #efg4h #ad4hh #ehh4i #ad4ib #fji4i #ad4if #fcj4i #ae4jj #fea4h #ae4jd #fgb4g #ae4jh #fic4e #ae4ab #gad4c #ae4af #gce4j #ae4bj #gee4f #ae4bd #ggf4b #ae4bh #gif4h #ae4ca #hag4c #ae4ce #hcg4h #ae4ci #heh4b #ae4dc #hgh4e #ae4dg #hih4h #ae4ea #iai4j #ae4ee #ici4b #ae4ei #iei4c #ae4fc #igi4d #ae4fg #iii4e #ae4ga #ajai4e #ae4ge #ajci4d #ae4gi #ajei4c #ae4hc #ajgi4a #ae4hg #ajih4i #ae4ia #aaah4f #ae4ie #aach4c #ae4ih #aaeg4i #af4jb #aagg4e #af4jf #aaig4a #af4aj #abaf4f #af4ad #abcf4j #af4ah #abee4d #af4bb #abgd4h #af4bf #abid4a #af4cj #acac4c #af4cd #accb4e #af4ch #acea4g #af4db #acgj4h #af4df #achi4i #af4ej #adjh4i #af4ed #adbg4i #af4eg #addf4h #af4fa #adfe4g #af4fe #adhd4g #af4fi #aejc4d #af4gc #aebb4b #af4gg #aedj4h #af4ha #aeei4e #af4he #aegh4b #af4hi #aeif4h #af4ic #afae4c #af4ig #afcc4h #ag4ja #afeb4b #ag4je #afgj4f #ag4ji #afhi4j #ag4ac #agjg4c #ag4ag #agbe4f #ag4bj #agdc4h #ag4bd #agfb4a #ag4bh #aghj4c #ag4cb #agih4d #ag4cf #ahaf4e #ag4dj #ahcd4e #ag4dd #aheb4e #ag4dh #ahgj4d #ag4eb #ahhh4c #ag4ef #aijf4b #ag4fj #aibd4j #ag4fd #aida4h #ag4fh #aiei4f #ag4gb #aigg4c #ag4gf #aiid4i #ag4gi #bjab4f #ag4hc #bjcj4b #ag4hg #bjdg4h #ag4ia #bjfe4c #ag4ie #bjhb4h #ag4ii #bajj4b #ah4jc #baag4f #ah4jg #bace4j #ah4aa #baeb4c #ah4ae #bafi4f #ah4ai #bahf4i #ah4bc #bbjd4a #ah4bg #bbba4c #ah4ca #bbch4d #ah4ce #bbee4e #ah4ci #bbgb4f #ah4db #bbhi4f #ah4df #bcjf4f #ah4ej #bcbc4f #ah4ed #bcdj4e #ah4eh #bceg4d #ah4fb #bcgd4b #ah4ff #bcia4a #ah4gj #bdjg4i #ah4gd #bdbd4f #ah4gh #bdda4c #ah4hb #bdeh4j #ah4hf #bdgd4f #ah4ij #bdia4c #ah4id #bejg4i #ah4ih #bebd4c #ai4jb #bedj4h #ai4je #beeg4c #ai4ji #begc4g #ai4ac #beij4b #ai4ag #bejf4f #ai4ba #bfbb4i #ai4be #bfci4b #ai4bi #bfee4d #ai4cc #bfga4f #ai4cg #bfhg4i #ai4da #bgjd4a #ai4de #bgbj4b #ai4di #bgcf4c #ai4ec #bgeb4c #ai4eg #bgfh4c #ai4fa #bghd4d #ai4fe #bhjj4d #ai4fh #bhaf4c #ai4gb #bhcb4b #ai4gf #bhdh4a #ai4hj #bhfd4j #ai4hd #bhgi4h #ai4hh #bhie4f #ai4ib #biaa4c #ai4if #bibg4j #bj4jj #bidb4g #bj4jd #bieh4d #bj4jh #bigd4j #bj4ab #bihi4f #bj4af #cjje4b #bj4bj #cjbj4g #bj4bd #cjcf4b #bj4bh #cjea4g #bj4ca #cjfg4b #bj4ce #cjhb4f #bj4ci #cjig4i #bj4dc #caac4c #bj4dg #cabh4f #bj4ea #cadc4i #bj4ee #caei4b #bj4ei #cagd4d #bj4fc #cahi4g #bj4fg #cbjd4i #bj4ga #cbbj4j #bj4ge #cbce4a #bj4gi #cbej4b #bj4hc #cbfe4c #bj4hg #cbhj4c #bj4ij #cbie4c #bj4id #ccaj4c #bj4ih #ccbe4c #ba4jb #ccdj4b #ba4jf #ccee4a #ba4aj #ccgj4j #ba4ad #cchd4h #ba4ah #ccii4f #ba4bb #cdad4d #ba4bf #cdbi4b #ba4cj #cddc4i #ba4cd #cdeh4f #ba4ch #cdgc4c #ba4db #cdhg4i #ba4df #cejb4e #ba4ej #ceag4b #ba4ed #ceca4h #ba4eg #cedf4c #ba4fa #cefj4h #ba4fe #cege4c #ba4fi #cehi4h #ba4gc #cfjd4b #ba4gg #cfah4f #ba4ha #cfcc4j #ba4he #cfdg4d #ba4hi #cffa4g #ba4ic #cfgf4j #ba4ig #cfij4c #bb4ja #cgjd4f #bb4je #cgah4h #bb4ji #cgcc4j #bb4ac #cgdg4b #bb4ag #cgfa4c #bb4bj #cgge4d #bb4bd #cghi4e #bb4bh #chjc4f #bb4cb #chag4g #bb4cf #chca4g #bb4dj #chde4g #bb4dd #chei4g #bb4dh #chgc4g #bb4eb #chhg4f #bb4ef #cija4e #bb4fj #ciae4d #bb4fd #cibi4c #bb4fh #cidc4a #bb4gb #cief4i #bb4gf #cigj4g #bb4hj #cihd4e #bb4hc #ciih4b #bb4hg #djaa4i #bb4ia #djbe4f #bb4ie #djci4c #bb4ii #djeb4i #bc4jc #djff4f #bc4jg #djhj4b #bc4aa #djic4h #bc4ae #dajg4c #bc4ai #dabj4h #bc4bc #dacd4c #bc4bg #dadg4h #bc4ca #dafa4c #bc4ce #dagd4g #bc4ci #dahh4a #bc4dc #dbja4e #bc4df #dbad4i #bc4ej #dbbh4b #bc4ed #dbda4f #bc4eh #dbed4i #bc4fb #dbfh4b #bc4ff #dbha4d #bc4gj #dbid4g #bc4gd #dcjg4i #bc4gh #dcba4a #bc4hb #dccd4c #bc4hf #dcdg4d #bc4ij #dcfj4e #bc4id #dcgc4g #bc4ih #dchf4g #bd4jb #dcii4h #bd4jf #ddab4h #bd4ji #ddbe4i #bd4ac #ddch4i #bd4ag #ddea4i #bd4ba #ddfd4h #bd4be #ddgg4g #bd4bi #ddij4g #bd4cc #dejc4f #bd4cg #deaf4d #bd4da #debi4c #bd4de #dedb4a #bd4di #deed4i #bd4ec #defg4g #bd4eg #dehj4e #bd4fa #deic4b #bd4fe #dfjf4j #bd4fh #dfah4g #bd4gb #dfca4d #bd4gf #dfdd4j #bd4hj #dfef4g #bd4hd #dffi4c #bd4hh #dfhb4j #bd4ib #dfid4e #bd4if #dgjg4a #be4jj #dgai4g #be4jd #dgcb4b #be4jh #dgdd4g #be4ab #dgeg4b #be4af #dgfi4g #be4bj #dghb4a #be4bd #dgid4f #be4bh #dhjg4j #be4ca #dhai4d #be4ce #dhca4g #be4ci #dhdd4a #be4dc #dhef4d #be4dg #dhfh4g #be4ea #dhha4j #be4ee #dhic4c #be4ei #dije4f #be4fc #diag4h #be4fg #dicj4j #be4ga #didb4b #be4ge #died4d #be4gi #diff4f #be4hc #digh4g #be4hg #diij4i #be4ia #ejjc4j #be4id #ejae4a #be4ih #ejbg4b #bf4jb #ejci4c #bf4jf #ejea4b #bf4aj #ejfc4b #bf4ad #ejge4c #bf4ah #ejhg4b #bf4bb #ejii4b #bf4bf #eaaa4b #bf4cj #eabc4a #bf4cd #eace4j #bf4ch #eadf4i #bf4db #eaeh4h #bf4df #eagj4f #bf4ej #eahb4e #bf4ed #eaid4c #bf4eg #ebjf4a #bf4fa #ebag4i #bf4fe #ebbi4g #bf4fi #ebda4d #bf4gc #ebec4b #bf4gg #ebfd4i #bf4ha #ebgf4f #bf4he #ebhh4c #bf4hi #ecjj4j #bf4ic #ecaa4f #bf4ig #ecbc4b #bg4ja #eccd4h #bg4je #ecdf4d #bg4ji #eceh4j #bg4ac #ecfi4f #bg4ag #echa4a #bg4ba #ecib4g #bg4be #edjd4b #bg4bh #edae4f #bg4cb #edbg4b #bg4cf #edch4g #bg4dj #edej4a #bg4dd #edfa4e #bg4dh #edgb4i #bg4eb #edhd4c #bg4ef #edie4g #bg4fj #eejg4a #bg4fd #eeah4d #bg4fh #eebi4h #bg4gb #eeda4a #bg4gf #eeeb4d #bg4hj #eefc4g #bg4hd #eege4j #bg4hg #eehf4b #bg4ia #eeig4e #bg4ie #efjh4g #bg4ii #efai4f #bh4jc #efca4a #bh4jg #efdb4b #bh4aa #efec4d #bh4ae #effd4f #bh4ai #efge4g #bh4bc #efhf4h #bh4bg #efig4i #bh4ca #egji4j #bh4ce #egbj4a #bh4ci #egca4a #bh4dc #egdb4a #bh4df #egec4a #bh4ej #egfd4b #bh4ed #egge4a #bh4eh #eghf4a #bh4fb #egig4a #bh4ff #ehjh4j #bh4gj #ehai4j #bh4gd #ehbi4i #bh4gh #ehdj4h #bh4hb #ehea4g #bh4hf #ehfb4e #bh4ij #ehgc4d #bh4id #ehhd4b #bh4ih #ehid4i #bi4jb #eije4h #bi4jf #eiaf4g #bi4ji #eibg4e #bi4ac #eich4b #bi4ag #eidi4j #bi4ba #eiei4g #bi4be #eigj4d #bi4bi #eiha4b #bi4cc #eiia4i #bi4cg #fjjb4e #bi4da #fjac4b #bi4de #fjbc4h #bi4di #fjcd4d #bi4ec #fjde4a #bi4eg #fjee4g #bi4fa #fjff4c #bi4fe #fjgf4i #bi4fi #fjhg4e #bi4gb #fjih4j #bi4gf #fajh4f #bi4hj #faai4a #bi4hd #fabi4f #bi4hh #fadj4a #bi4ib #faej4f #bi4if #fafa4a #cj4jj #faga4e #cj4jd #fahb4j #cj4jh #faib4d #cj4ab #fbjb4h #cj4af #fbac4b #cj4bj #fbbc4f #cj4bd #fbcd4j #cj4bh #fbdd4d #cj4cb #fbed4g #cj4ce #fbfe4j #cj4ci #fbge4d #cj4dc #fbhe4g #cj4dg #fbif4j #cj4ea #fcjf4b #cj4ee #fcaf4e #cj4ei #fcbf4g #cj4fc #fccg4j #cj4fg #fcdg4b #cj4ga #fceg4d #cj4ge #fcfg4f #cj4gi #fcgg4h #cj4hc #fchh4j #cj4hg #fcih4b #cj4ia #fdjh4c #cj4id #fdah4e #cj4ih #fdbh4f #ca4jb #fdch4g #ca4jf #fddh4h ,,table ,b4 ,deg4#d ,met4 #j4b #j4c #j4d #j4f #j4f #j4i #j4h #a4b #a4j #a4e #a4b #a4h #a4d #b4a #a4f #b4c #a4h #b4f #b4j #b4i #b4b #c4b #b4d #c4e #b4f #c4h #b4h #d4a #c4j #d4d #c4b #d4g #c4d #e4j #c4f #e4c #c4h #e4f #d4j #e4i #d4b #f4b #d4d #f4e #d4f #f4h #d4h #g4a #e4j #g4d #e4b #g4f #e4d #g4i #e4f #h4b #e4h #h4e #f4j #h4h #f4b #i4a #f4d #i4d #f4f #i4g #f4h #aj4j #g4j #aj4c #g4b #aj4f #g4d #aj4i #g4f #aa4b #g4h #aa4e #h4j #aa4h #h4b #ab4a #h4d #ab4d #h4f #ab4f #h4h #ab4i #i4j #ac4b #i4b #ac4e #i4d #ac4h #i4f #ad4a #i4h #ad4d #aj4j #ad4g #aj4b #ae4j #aj4d #ae4c #aj4f #ae4f #aj4h #ae4i #aa4j #af4b #aa4b #af4e #aa4d #af4h #aa4f #ag4a #aa4h #ag4d #ab4j #ag4f #ab4b #ag4i #ab4d #ah4b #ab4f #ah4e #ab4h #ah4h #ac4j #ai4a #ac4b #ai4d #ac4d #ai4g #ac4f #bj4j #ac4h #bj4c #ad4j #bj4f #ad4b #bj4i #ad4d #ba4b #ad4f #ba4e #ad4h #ba4h #ae4j #bb4a #ae4b #bb4d #ae4d #bb4g #ae4f #bb4i #ae4h #bc4b #af4j #bc4e #af4b #bc4h #af4d #bd4a #af4f #bd4d #af4h #bd4g #ag4j #be4j #ag4b #be4c #ag4d #be4f #ag4f #be4i #ag4h #bf4b #ah4j #bf4e #ah4b #bf4h #ah4d #bg4a #ah4f #bg4d #ah4h #bg4g #ai4j #bh4j #ai4b #bh4b #ai4d #bh4e #ai4f #bh4h #ai4h #bi4a #bj4j #bi4d ,footnote #d3 ,the degrees refer to the centigrade thermometer4 ,,table ,c4 ,approximate #j #ae #dj #ee ,height4 #bjj #a4b #a4j #j4f #j4d #djj #b4d #b4b #a4d #j4h #fjj #c4d #c4b #b4j #a4b #hjj #d4e #d4c #b4h #a4g #ajjj #e4g #e4c #c4d #b4b #abjj #g4j #f4d #d4b #b4f #adjj #h4b #g4f #d4h #c4j #afjj #i4b #h4h #e4f #c4d #ahjj #aj4d #i4h #f4c #c4h #bjjj #aa4f #aa4j #g4j #d4b #bbjj #ab4h #ab4a #g4f #d4f #bdjj #ad4j #ac4c #h4d #e4a #bfjj #ae4b #ad4d #i4b #e4f #bhjj #af4e #ae4f #aj4j #f4b #cjjj #ag4g #af4h #aj4h #f4f #cbjj #aj4a #ah4j #aa4e #g4j #cdjj #bj4e #ai4c #ab4d #g4g #cfjj #ba4h #bj4d #ac4d #h4b #chjj #bc4a #ba4f #ad4c #h4g #djjj #bd4f #bb4i #ae4a #i4d #dbjj #be4i #bd4c #ae4i #aj4a #ddjj #bg4e #be4h #af4i #aj4h #dfjj #bh4i #bg4a #ah4j #aa4e #dhjj #cj4d #bh4d #ai4j #ab4a #ejjj #ca4h #bi4h #ai4i #ab4g #ebjj #cc4j #ca4j #bj4h #ac4c #edjj #cd4c #cb4d #ba4g #ac4i #efjj #ce4g #cc4g #bb4f #ad4e #ehjj #cg4a #ce4j #bc4f #ae4a #fjjj #ch4e #cf4c #bd4f #ae4g ,,table ,d4 ,barometrical ,metres ,height #ae4ge #a4ga #ag4gb #a4ci #ai4fh #a4aa #ba4fe #j4hf #bc4fb #j4fc #be4ei #j4db #bg4ef #j4bb #bi4ec #j4jc ,,chapter ,,ii4 ,,survey4 ,,topographical ,,sketching4 #ci4 ,topographical drawing includes every thing relating to an accurate representation upon paper1 of any piece of ground4 ,the state of cultivation1 roads1 town1 county1 and state boundaries1 and all else that occurs in nature4 ,the sketching necessary in railroad surveying1 however1 does not embrace all of this1 but only the delineation of streams and the undulations of ground within that limit which affects the road1 perhaps #ejj feet on each side of the line4 ,the making of such sketches consists in tracing the irregular lines formed by the intersection of the natural surface1 by a system of horizontal planes1 at a vertical distance of five1 ten1 fifteen1 or twenty feet1 according to the accuracy required4 ,illustration3 ,fig4 #ac4 #dj4 ,suppose that we wish to represent upon a horizontal surface a right cone4 ,the base m m1 fig4 #ac1 is shown by the circle of which the diameter is m1 m4 ,if the elevation is cut by the horizontal planes a a1 b b1 c c1 the intersection of these planes with the conical surface is shown by the circles a1 b1 c1 in plan4 ,the less we make the horizontal distances1 on plan1 between the circles1 the less also will be the vertical distance between the planes4 ,wishing to find the elevation of any line which exists on plan1 as #a1 #b1 #c1 #c1 #b1 #a1 we have only to find the intersection of the verticals drawn through the points #a1 #b1 #c1 #c1 #b1 #a1 and the elevation lines a a1 b b1 c c2 this gives us the curve #d1 #e1 #f1 #g1 #f1 #e1 #d4 ,illustration3 ,fig4 #ad4 #da4 ,again1 in fig4 #ad1 the cone is oblique1 which causes the circles on plan to become eccentric and elliptic4 ,having given the line #a1 #b1 #c1 as before1 we find it upon the elevation in the same manner4 #db4 ,in the section of regular and full lined figures1 the horizontal and vertical projections are also regular and full lined2 but in a broken surface like the ground1 the lines become quite irregular4 ,suppose we wish to show on plan the hill of which we have the plan1 fig4 #ae1 and the sections figs4 #af1 #ag1 and #ah4 ,let ,,ad be the profile 7made with the level7 of the line ,,ad on plan1 fig4 #ae4 ,b ,e that of ,b ,e1 and ,c ,f that of ,,cf4 ,illustration3 ,fig4 #ae4 ,illustration3 ,fig4 #af4 ,illustration3 ,fig4 #ag4 ,illustration3 ,fig4 #ah4 ,to form the plan from the profiles proceed as follows3-- ,intersect each of the profiles by the horizontal planes a a1 b b1 c c1 d d1 equidistant vertically4 ,in the profile ,a ,d1 fig4 #ah1 drop a vertical on to the base line from each of the intersections a1 b1 c1 d1 d1 c1 b1 a4 ,make now ,a #a1a #b1 #b #c1 #c #d1 etc41 on the plan equal to the same on the profile4 ,next draw1 on the plan1 the line ,b ,e1 at the right place and at the proper angle with ,a ,d2 and having found the distances ,b #a1 #a #b1 #b #c1 etc41 as before1 transfer them to the line ,b ,e on plan4 ,proceed in the same manner with the line ,c ,f4 ,the points a a a1 b b b1 c c c1 are evidently at the same height above the base upon the profiles1 whence the intersections of these lines with the surface line or #a #a #a1 #b #b #b1 #c #c #c1 etc41 on the plan1 are also at the same height above the base2 and an irregular line traced through the points #a #a #a1 or #b #b #b1 will show the intersection of a horizontal plane1 with the natural surface4 ,when as at ,a we observe the contour lines near to each other1 we conclude that the ground is steep4 ,and when the distances are large1 as at #f1 #g1 #h1 we know that the ground falls gently4 ,this is plainly seen both on plan and profile4 ,illustration3 ,fig4 #ae4 ,having now the topographical sketch1 fig4 #ae1 we may easily deduce therefrom at any point a profile4 ,if we would have a profile of ,g ,e1 on plan1 upon an indefinite line ,g ,e1 fig4 #ai1 we set off ,g #a1 #a #b1 #b #c1 #c #d1 etc41 equal to the same distances on the plan4 ,from these points draw verticals intersecting the horizontals a a1 b b1 c c2 and lastly1 through the intersections draw the broken line 7surface line or profile7 a1 b1 c1 d1 d1 c1 b1 a4 ,thus we see how complete a knowledge of the ground a correct topographical sketch gives4 ,illustration3 ,fig4 #ai4 #dc4 ,field sketches for railroad work are generally made by the eye4 ,the field book being ruled in squares representing one hundred feet each4 ,when we need a more accurate sketch than this method gives1 we may cross section the ground either by rods or with the level4 ,by making a very detailed map of a survey1 and filling in with sketches of this kind1 the location may be made upon paper and afterwards transferred to the ground4 ,so far we have dealt with but one summit2 but the mode of proceeding is precisely the same when applied to a group or range of hills1 or indeed to any piece of ground4 #dd4 ,as a general thing1 the intersection of the horizontal planes with the natural surface 7contour lines7 are concave to the lower land in depressions1 and convex to the lower land on spurs and elevations4 ,thus at ,b ,b ,b b b1 fig4 #bj1 upon the spurs1 we have the lines convex to the stream2 and in the hollows c c c1 the lines are concave to the bottom4 #de4 ,having by reconnoissance found approximately the place for the road1 we proceed to run a trial line by compass4 ,in doing this we choose the apparent best place1 stake out the centre line1 make a profile of it1 and sketch in the topography right and left4 ,illustration3 ,fig4 #bj4 ,illustration3 ,fig4 #ba4 ,illustration3 ,fig4 #bb4 ,suppose that by doing so we have obtained the plan and profile shown in figs4 #ba and #bb1 where ,a a a ,b is the profile of ,a ,c ,d ,b1 on the plan4 ,the lowest line of the valley though quite moderately inclined at first1 from ,a to ,c1 rises quite fast from ,c to the summit2 and as the inclination becomes greater1 the contour lines become nearer to each other4 ,now that the line may ascend uniformly from ,a to the summit1 the horizontal distances between the contour lines must be equal2 this equality is effected by causing the surveyed line to cut the contours square at #a1 #b1 #c1 #d1 and obliquely at #e1 #h1 #aj4 ,thus we obtain the profile ,a #e #e ,b4 ,illustration3 ,figs4 #bc and #bd4 #df4 ,having given the plan and profile1 figs4 #bc and #bd1 where ,a ,c ,d ,b represents the bed of the stream1 in profile1 if it were required to put the uniformly inclined line ,a m m ,b1 upon the plan1 we should proceed as follows4 ,take the horizontal distance ,a m from the profile1 and with ,a 7on plan7 as a centre1 describe the arc #a1 #c4 ,the point m on the profile is evidently three fourths of a division above the bed of the stream4 ,so on the plan we must trace the arc #a1 #c1 until we come to a1 which is three fourths of b c1 from b4 ,again1 m is nine and one half divisions above m4 ,from a1 with a radius m n on profile1 describe the arc #d1 #e1 #f4 ,now1 as on the profile1 in going from m to m1 we cross nine contour lines1 and come upon the tenth at m1 so on the plan we must cross nine contour lines and come upon the tenth1 and at the same time upon the arc #d1 #e1 #f4 ,proceeding in this way1 we find ,a1 a1 b1 ,b1 on the plan1 as corresponding to ,a m m ,b on the profile4 ,to establish in this manner any particular grade1 we have first to place it upon the profile1 and next to transfer it to the plan4 #dg4 ,it may be remembered as a general thing1 that the steepest line is that which cuts the contour line at right angles2 the contour line itself is level1 and as we vary between these limits we vary the incline4 ,,general ,,establishment ,,of ,,grades4 #dh4 ,considerable has been written upon the relation which ought to exist between the maximum grade1 and the direction of the traffic4 ,some have given formul for obtaining the rate and direction of inclines as depending upon the capacity of power4 ,this seems going quite too far1 as the nature of the ground and of the traffic generally fix these in advance4 #di4 ,between two places which are at the same absolute elevation1 there should be as little rise and fall as possible4 #ej4 ,between points at different elevations1 we should if possible have no rise while descending1 and consequently no fall while on the ascent4 #ea4 ,some engineers express themselves very much in favor of long levels and short but steep inclines4 ,there are cases where the momentum acquired upon one grade1 or upon a level1 assists the train up the next incline4 ,the distance on the rise during which momentum lasts1 is not very great4 ,a train in descending a plane does not receive a constant increase of available momentum1 but arrives at a certain speed1 where by increased resistance and by added effect of gravity1 the motion becomes nearly regular4 ,up to this point the momentum acquired is useful1 but not beyond4 ,any road being divided into locomotive sections1 the section given to any one engine should be such as to require a constant expenditure of power as nearly as possible2 i4 e41 one section1 or the run of one engine1 should not embrace long levels and steep grades4 ,if an engine can carry a load over a sixty feet grade1 it will be too heavy to work the same load upon a level economically4 ,it is best to group all of the necessarily steep grades in one place1 and also the easy portions of the road2 then by properly adapting the locomotives the cost of power may be reduced to a minimum4 ,as to long levels and short inclines the same power is required to overcome a given rise1 but quite a difference may be made in the means used to surmount that ascent4 ,illustration3 ,fig4 #be4 #eb4 ,suppose we have the profiles ,a ,e ,d and ,a ,b ,d1 fig4 #be4 ,the resistance from ,a to ,d by the continuous twenty feet grade is the same as the whole resistance from ,a to ,b and from ,b to ,d4 ,the reason for preferring ,a ,e ,d is1 that an engine to take a given load from ,b to ,d would be unnecessarily heavy for the section ,a ,b2 while the same power must be exerted at each point1 of ,a ,e ,d4 ,also the return by ,a ,e ,d is made by a small and constant expenditure of power1 being all of the way aided by gravity2 while in descending by ,b1 we have more aid from gravity than we require from ,d to ,b1 after which we have none4 ,when the distances ,a ,b1 ,b ,c1 are sixty and twenty miles in place of six and two1 we may consider the grades grouped at ,b ,d1 and use a heavier engine at that point1 as we should hardly find eighty miles admitting of a continuous and uniform grade4 ,,equating ,,for ,,grades4 #ec4 ,in comparing the relative advantages of several lines having different systems of grades1 it is customary to reduce them all to the level line involving an equal expenditure of power4 ,the question is to find the vertical rise1 consuming an amount of power equal to that expended upon the horizontal unit of length4 ,this has been estimated by engineers all the way from twenty to seventy feet4 ,for simple comparison it does not matter much what number is used if it is the same in all cases2 but to find the equivalent horizontal length to any location1 regard must be had to the nature of the expected traffic4 ,the elements of the problem are1 the length1 the inclination or the total rise and fall1 and the resistance to the motion of the train upon a level1 which latter depends upon the speed and the state of the rails and machinery4 ,from chapter ,,xiv4 we have the following resistances to the motion of trains upon a level3-- ,velocity1 in miles1 per hour4 ,resistance1 in lbs4 per ton4 #aj #h4f #ae #i4c #bj #aj4c #be #aa4f #cj #ac4c #dj #ag4c #ej #bb4f #fj #bg4a #ajj #ff4e ,the power expended upon any road is of course the product of the resistance per unit of length1 by the number of units4 ,calling ,r the resistance per unit upon a level1 and ,r the resistance per unit on any grade1 and designating the lengths by ,l and ,l1 that there shall be in both cases an equal expenditure of power1 we must have ,,rl ,r,l1 whence the level length must be ,l 7,l,r7_/,r4 ,thus assuming the resistance on a level as twenty lbs4 per ton1 that on a fifty feet grade is #bj #ej_/ebhj of #bbdj1 or #bj #ba4b or #da4b1 and if the length of the inclined line is ten miles1 the equivalent level length is ,l 7#da4b #ebhjj7_/bj #ajhgfh feet1 or #bj4f miles4 ,also #aj miles #da4b lbs4 #dab1 and #bj4f miles #bj lbs4 #dab4 #ed4 ,the above may be somewhat abridged as follows3 ,let ,r be the resistance on a level4 ,the resistance due to any grade is expressed by ,w #a_/;a1 where #a_/;a is the fraction showing the grade1 and ,w the weight of the load4 ,the vertical height in feet1 to overcome which we must expend an amount of power sufficient to move the train one mile on a level1 must be such that ,w #a_/;a ,r1 or #a_/;a ,r_/,w2 and to find the number by which to equate1 we have only to place the values of ,r and ,w in the formula4 ,for example1 let the speed be twenty miles per hour1 the corresponding resistance is #aj4c lbs4 per ton4 ,w being one ton1 or #bbdj lbs41 we have #a_/;a ,r_/,w #aj4c_/bbdj #a_/bah of #ebhj1 7the number of feet in one mile17 #a_/bah of #ebhj #bd feet4 ,in the same manner we have ,speed1 in miles1 per hour4 ,equating number4 #ae #bb #bj #bd #cj #cb #dj #da #ej #ec #fj #fg #ajj #aee ,thus when we take the speed as thirty miles per hour1 for each thirty-two feet rise we shall consume an amount of power sufficient to move the train one mile on a level4 ,in descending1 the grade instead of being an obstacle1 becomes an aid2 indeed the incline may be such as to move the trains independently of the steam power4 ,thus if on account of ascending grades we increase the equated length1 so also in descending we must reduce the length4 ,the amount of reduction is not1 however1 the reverse of the increase in ascending1 as after thirty or forty feet any additional fall per mile instead of being an advantage is an evil2 as too much gravity obliges us to run down grades with brakes on4 ,twenty-five feet per mile is sufficient to allow the train to roll down1 and any more than this is of very little use4 ,therefore for every mile of grade descending at the rate of twenty-five feet per mile we may deduct one mile in equating1 and for every mile of grade descending twelve and one half feet per mile deduct a proportional amount2 but for any more fall per mile than twenty-five feet1 no allowance should be made2 i4 e41 if we descend at the rate of forty feet per mile1 we may deduct one mile in equating for the twenty-five feet of fall1 and throw aside the remaining fifteen feet4 #ee4 ,this is a common method of equating for grades1 and represents a length which is proportional to the power expended1 but not proportional to the cost of working1 as the ratios of power expended and cost of working under different conditions are very different1 double power requiring only twenty per cent4 more working capital4 ,the above rules1 therefore1 require a correction4 ,the cost of working a power represented by unity being expressed by #ajj2 ,that of working a power #b is expressed by #abe2 ,that of working a power #c is expressed by #aej2 ,that of working a power #d is expressed by #age2 ,that of working a power #e is expressed by #bjj4 7,see ,appendix ,f47 ,now the resistance on a level being at a velocity of twenty miles per hour1 #aj4c lbs4 per ton by the formula #a_/;a ,r_/,w1 the vertical height in feet causing a double expenditure of power is twenty-four2 but as above1 the whole expense of a double power is increased by only twenty-five per cent42 we should not add one mile for twenty-four feet rise1 but one fourth of a mile only1 or one mile for each ninety-six feet2 and by correcting our former table in this manner1 we have the following table3-- ,speed1 in miles1 per hour4 ,equating number4 #ae #hh #bj #if #be #aaj #cj #abh #dj #afd #ej #bab #fj #bfh #ajj #fbj ,so much for equating for the ascents4 ,in descending1 we have allowed one mile reduction for each mile of twenty-five feet of descending grade2 but as in ascending we correct the first made table1 so in descending we must also correct as follows4 ,if we needed no steam power either while descending or afterwards1 we should only save wood and water2 as a general thing the fire must be kept up while descending1 and the only gain is a small part of the expense of fuel2 so small1 in fine1 that with the exception of roads which incline for the whole or a great part of their length1 no reduction should be made4 ,,comparison ,,of ,,surveyed ,,lines4 #ef4 ,the requisite data for an approximate comparison of lines are1 the measured length1 total rise1 total fall4 ,let the length of line ,a be #ajj miles1 ,let the length of line ,b be #ij miles1 ,whole rise on ,a #bjjj feet1 ,whole rise on ,b #eajj feet1 ,whole fall on ,a #abjj feet1 ,whole fall on ,b #dcjj feet4 ,assume the number by which to equate1 as ninety-six1 and we shall have ,line ,a4 ,ascending1 #ajj #bjjj_/if #abj4hc ,descending1 #ajj #abjj_/if #aab4ej ------------ ,sum #bcc4cc ,mean #aaf4ff ,line ,b4 ,ascending1 #ij #eajj_/if #adc4ac ,descending1 #ij #dcjj_/if #acd4hj ------------ ,sum #bgf4ic ,mean #ach4df ,the mean equated length of ,a is #aaf4ff ,the measured length of ,a is #ajj4jj ------------ ,the difference #af4ff ,the mean equated length of ,b is #ach4df ,the measured length of ,b is #ij4jj ------------ ,the difference #dh4df4 ,the cost of construction being assumed as the actual length1 and that of working as the equated length1 we have the final approximate comparison thus3-- ,assume the construction cost as #be1jjj per mile1 and the cost of maintenance #d1jjj per mile1 and we have ,the line ,a to the line ,b as #ajj #bejjj 7#aaf4ff #djjj7 #ajj_/f #aj1bgg1ccc1 is to #ij #bejjj 7#ach4df #djjj7 #ajj_/f #aa1dhj1ffg2 or ,a is to ,b as #aj4c to #aa4e nearly1 although the line ,a is ten miles longer than ,b4 ,,chapter ,,iii4 ,,location4 ,,alignment4 #eg4 ,the broken line furnished by the survey is of course unfit for the centre line of a railroad4 ,the angles require to be rounded off to render the passage from one straight portion to the other easy4 ,illustration3 ,fig4 #bf4 #eh4 ,let ,a ,x ,b1 fig4 #bf1 represent the angle formed by any two tangents which it is required to connect by a circular curve4 ,it is plain that knowing the angle of deflection of the lines ,a ,x1 ,b ,x1 we obtain also the angles ,a ,c ,x1 ,x ,c ,b4 ,the manner of laying these curves upon the ground is by placing an angular instrument at any point of the curve1 as at ,a1 and laying off the partial angles ,e ,a a1 ,e ,a ,m1 ,e ,a ,g1 etc41 which combined with the corresponding distances ,a a1 a ,m1 ,m ,g1 fix points in the curve4 ,these small chords are generally assumed at one hundred feet1 except in curves of small radius 7five hundred feet7 when they are taken less4 ,the only calculation necessary in laying out curves1 is1 knowing the partial deflection to find the corresponding chord1 or knowing the chord1 to get the partial angle4 ,as the radius of that curve of which the angle of deflection is #a is #egcj feet1 the degree of curvature for any other radius is easily found4 ,thus the radius #bhfe has a degree of curvature per one hundred feet of #egcj_/bhfe #b2 again1 #egcj_/bjjj #b4hf or #b #ea4f4 ,the radius corresponding to any angle is found by reversing the operation4 ,if the angle is #c #cj1 or #baj1 we have 7#egcj #fj7_/baj #afcg feet radius4 ,the following figures show the angle of deflection for chords one hundred feet long1 corresponding to different radii3-- ,angle of deflection4 ,radius1 in feet4 or #ae #bbibj4j or #cj #aadfj4j or #de #gfdj4j #a or #fj #egcj4j #a #dehe4j #a #chbj4j #a #cbgd4j #b #bhfe4j #b #bbib4j #c #aiaj4j #c #afcg4j #d #adcc4j #d #abgd4j #e #aadf4j #e #ajdb4j #f #iee4d #f #hbb4j #g #hai4j #g #gfd4e #h #gaf4h #aj #egc4g ,points in any curve may also be fixed by ordinates1 as a b1 ,m ,d1 ,g ,f1 or by ,e a1 ,k ,m1 etc4 ,for the details of locating1 of running simple and compound curves1 and of the calculations therefor1 the reader is referred to the works of ,trautwine1 and of ,henck4 ,illustration3 ,fig4 #bg4 #ei4 ,suppose now that we have the surveyed lines m m1 and n n1 fig4 #bg1 one of which is to be finally adjusted to the ground4 ,the shortest line is the straight one1 which is generally impracticable4 ,the most level line is the contour line1 which is also impracticable4 ,between these two lies the right line1 which is to be found by an instrumental location4 ,the line ,a n n n n ,b1 on the plan1 gives the profile ,a n n n n ,b4 ,the line ,a m m m m ,b gives the profile ,a m m m m ,b1 while the finally adjusted line ,a #a #b #c #d #e #f gives the profile ,a #a #b #c #d #e #f ,b4 ,illustration3 ,fig4 #bh4 #fj4 ,again1 in fig4 #bh1 the straight line ,a n n n ,b gives the profile ,a n n n ,b1 requiring either steep grades or a great deal of work4 ,by fitting the line to the ground1 as by the line ,a a b c d 444 m n o ,b1 we obtain the profile ,a a b c 444 m n o ,b4 ,,final ,,adjusting ,,of ,,grades4 ,illustration3 ,fig4 #bi4 #fa4 ,the general arrangement of inclines must not be interfered with to save work1 but a large part of the excavation and embankment may be saved by breaking up long grades so as not to affect materially the character of the road4 ,upon some lines the grades must necessarily undulate1 as in fig4 #bi4 ,the difference in the amount of work is plainly seen4 ,the steepest grades thus applied must not be greater than the ruling grade upon the travel of one engine4 #fb4 ,in long and shallow cuts and fills1 the best plan is to place the grade line quite high1 avoiding much cutting1 and to make the embankments from side cuttings1 7ditching74 ,banks must at least be placed two or three feet above the natural surface1 first to prevent the snow from lodging too much upon the rails1 second1 to insure draining4 #fc4 ,snow fences are much used in the northern parts of the ,united ,states4 ,these are high pieces of lattice-work1 made roughly1 but well braced2 from eight to twelve feet high1 and standing from sixty to one hundred feet from the road4 ,the object of the fence is to break the current of the wind1 and cause it to precipitate its snow4 ,close fences effect the object no better than the open ones1 are more liable to blow down1 and cost more4 #fd4 ,in locating a road which is to have a double track eventually1 regard must be paid to this fact in side-hill work4 ,the first track should1 if possible1 be so placed as not to require moving when the double line is put on4 ,,comparison ,,of ,,located ,,lines4 #fe4 ,in this comparison there is an element which does not enter the approximate comparison of surveyed lines1 curvature4 ,the resistance arising from this cause has never been accurately determined4 ,mr4 ,mc,callum estimates the resistance at one half pound per degree of curvature per one hundred feet2 i4 e41 the resistance due to curvature on a #d curve1 would be two lbs4 per ton1 7see report of ,september #cj1 #ahee74 ,mr4 ,clark estimates the resistance due to curves of one mile radius and under1 as #f4c lbs4 per ton1 or twenty per cent4 of the whole resistance4 ,the average radius encountered1 therefore1 by ,mr4 ,clark1 would be1 at ,mr4 ,mc,callum's estimate1 #f4c_/j4e #ab nearly1 or #dgg4e feet4 ,so small a radius is by no means allowable upon ,english roads2 thus the estimate of ,mr4 ,clark and of ,mr4 ,mc,callum differ considerably4 ,experiments might easily be made with the dynamometer upon different curves1 by which we might find very nearly the correct resistance caused by curves4 ,the curvature on any road cannot be adjusted to trains moving at different speeds4 #ff4 ,the tractive power acts always tangent to the curve at the point where the engine is1 and thus tends to pull the cars against the inner rail4 ,the tangential force1 generated by the motion of the cars1 tends to keep the flanges of the wheels against the outer rail2 and only when a just balance is made between the tractive and tangential forces1 the wheel will run without impinging on either rail1 7the wheel being properly coned74 ,for these forces to balance1 there must be a fixed ratio between the weight of a car and the speed1 7not the weight of a train1 as the shackling allows the cars to act nearly independently1 some indeed rubbing hard for a moment against the rail1 while the next car is working at ease74 ,whenever the right proportion is departed from1 as it nearly always is1 7and perhaps necessarily in some cases17 upon railroads1 the wheels will rub against one rail or the other4 ,thus on any road where the speed on the same curve1 or the radii of curvature under the same speed1 differ1 there must be loss of power1 and dragging or pushing against the rails4 #fg4 ,we are obliged to elevate the outer rail 7see chapter ,,xiii471 for the fastest trains1 and the slower trains on such roads will therefore always drag against the inner rails4 ,thus in practice we generally find the inside of the outer rail most worn on passenger roads1 and the inside of the inner rail upon chiefly freight roads4 #fh4 ,it has been the practice of some engineers in equating for curvature1 to add one fourth of a mile to the measured length for each #cfj of curvature1 disregarding the radius1 as the length of circumference increases inversely as the degree of curvature4 #fi4 ,now in equating for grades1 in doubling the power we do not double the expense of working4 ,we however increase it more by curvature than we do by grades1 because besides requiring double power1 the wear and tear of cars and rails and all machinery is increased upon curves1 which is not the case upon grades4 #gj4 ,the analysis of expense 7in ,appendix ,f47 upon the ,new ,york system of roads1 gives the following3-- ,locomotives1 #dj per cent4 ,cars1 #bj per cent4 ,way and works1 #ae per cent4 ---- or in all1 #ge per cent4 ,now each #cfj will be equal to #ge_/ajj of one quarter of a mile1 or #ge_/djj of a mile2 whence the number of degrees which shall cause an expense equal to one straight and level mile1 will be #aibj4 #ga4 ,the number of degrees by ,mr4 ,mc,callum's estimate would be thus3-- ,the resistance upon a level being ten lbs4 per ton1 and that due to curves one half pound per ton1 per degree per one hundred feet2 the length of a #b curve to equal one mile will be #aj lbs4_/#a lb41 or ten miles4 ,also ten miles1 or #ecj hundred feet by #b is #ajfj4 #gb4 ,again1 by ,mr4 ,clark's resistance of twenty per cent4 of the level resistance1 upon curves averaging #b1 we have as the length of #b curve #aj_/b #e miles1 or #bfe hundred feet1 which by #b gives #ecj4 #gc4 ,averaging the first and last1 we have as the number of degrees which should be considered as causing an amount of expense equal to one straight and level mile1 #abbe1 which averaging with the estimated resistance by ,mr4 ,mc,callum1 gives finally #aadb as causing an expense equal to one straight and level mile1 or1 in round numbers1 #aadj4 #gd4 ,suppose now that we would know which of the lines below to choose4 ,line ,a4 ,line ,b4 ,description4 #ajj miles1 #aaj miles1 ,actual length1 #ejjj feet1 #cjjj feet1 ,rise1 #cejj feet1 #aejj feet1 ,fall1 #cfjj #ijjj ,degrees of curvature4 ,assuming the speed as twenty miles per hour1 the number by which to equate for grades1 see chapter ,,ii41 is ninety-six1 also the number of degrees for curvature #aadj1 whence1 ,line ,a ascending #ajj #eb4a #c4af #aee4bf #adg4df ,line ,a descending #ajj #cf4e #c4af #aci4ff ,line ,b ascending #aaj #ca4be #g4hi #adi4ad #ada4ca1 ,line ,b descending #aaj #ae4fb #g4hi #acc4di and if the cost of construction is as the actual1 and the cost of maintaining and working as the mean equated length1 we have1 as a final comparison1 ,a to ,b as #ajj #adg4df to #aaj #ada4ca1 or as #bdg4df to #bea4ca4 ,here the extra grades on the one hand nearly equal the curvature and the extra length on the other hand4 #ge4 ,as a further example in the comparison of competing lines1 let us take the actual case of the location of the eastern part of the ,new ,york and ,erie ,railroad4 ,it was questioned which of the two lines between ,binghampton and ,deposit should be adopted1 and also between the mouth of ,callicoon ,creek and ,port ,jervis4 ,illustration3 ,fig4 #cj4 ,between ,a and c1 fig4 #cj1 were located the lines shown in the sketch1 one following the ,susquehanna river from ,a to ,b1 thence crossing the dividing ridge between that river and the ,delaware to ,deposit 7c74 ,the other passing up the ,chenango river to a1 thence crossing first the summit ,m to the ,susquehanna at ,l1 and second the summit ,k1 to ,deposit 7c74 ,the elements of the two lines are as follows3-- ,a route1 ,a ,b c4 ,b route1 ,a ,m ,k c4 ,length1 #ci4bi #dc4eh ,rise ,a to c1 #edj4jj #ajhg4jj ,rise c to ,a1 #cie4jj #icf4jj ,whole rise and fall1 #ice4jj #bjbc4jj ,degrees of curvature1 #bcga4jj #cbec4jj ,estimated cost1 #gdf1ijj4jj #fbh1fjj4jj ,assuming the number by which to equate for grades1 as #if1 and the equating number of degrees of curvature as #aadj2 equating for grades and curvature in both directions1 we have1 ,route ,a4 ,a to c4 ,mean1 #df4be4 #ci4bi #edj_/if #bcga_/aadj #ci4bi #e4fc #b4jh #dg4jj ,route ,a4 c to ,a4 #ci4bi #cie_/if #bcga_/aadj #ci4bi #d4ab #b4jh #de4di ,route ,b4 ,a to c4 ,mean1 #ef4if4 #dc4eh #ajhg_/if #cbec_/aadj #dc4eh #aa4cb #b4he #eg4ge ,route ,b4 c to ,a4 #dc4eh #icf_/if #cbec_/aadj #dc4eh #i4ge #b4he #ef4ah ,assuming the cost of working and of maintaining as #d1jjj per mile1 we have ,the cost of building ,a to ,b as #gdf1ijj to #fbh1fjj ,the cost of operating ,a to ,b as 7#df4be #djjj7 #ajj_/f to 7#ef4if #djjj7 #ajj_/f1 or as #c1jhc1ccd to #c1gig1ccd -------------------- -------------------- and the sum as #c1hcj1bcd #d1dbe1icd giving the preference of #eie1gjj to the route ,a ,b c1 notwithstanding that the estimate thereon exceeds that on ,b by #aah1cjj4 ,the route ,a ,b c was adopted4 ,again1 it was doubtful whether to adopt the route ,e ,f1 in going from ,d to ,g1 or the line ,i ,h4 ,the following are the elements of the two lines3-- ,i ,h4 ,e ,f4 ,measured length1 #fa4ad #eh4ec ,rise ,d to ,g1 #aahg #ded ,rise ,g to ,d1 #ajdi #caf ,degrees curve1 #gfji #dehh ,estimated cost1 #a1jid1iej #a1dif1dcj ,the mean equated lengths are as follows3-- ,line ,i ,h4 ,d to ,g4 ,mean1 #gi4df1 #fa4ad #aahg_/if #gfji_/aadj #fa4ad #ab4cf #f4fh #hj4ah ,line ,i ,h4 ,g to ,d4 #fa4ad #ajdi_/if #gfji_/aadj #fa4ad #aj4ic #f4fh #gh4ge ,line ,e ,f4 ,d to ,g4 ,mean1 #ff4ef4 #eh4ec #ded_/if #dehh_/aadj #eh4ec #d4gc #d4jb #fg4bh ,line ,e ,f4 ,g to ,d4 #eh4ec #caf_/if #dehh_/aadj #eh4ec #c4bi #d4jb #fe4hd ,the comparison as to cost is ,i ,h to ,e ,f as #a1jid1iej to #a1dif1dcj1 and as to working1 ,i ,h to ,e ,f as 7#gi4df #djjj7 #ajj_/f to 7#ff4ef #djjj7 #ajj_/f1 and the sum as #a1jid1iej to #a1dif1dcj #e1big1ccd #d1dcg1ccd -------------------- -------------------- or #f1cib1bhd to #e1icc1gfd ,although the cost of ,e ,f is #dja1dhj more than that of ,i ,h1 the line ,e ,f was adopted4 ,,chapter ,,iv4 ,,preliminary ,,operations4 ,,specification4 #gf4 ,the object of this paper is to define exactly the terms of the contract as regards execution of work4 ,every thing therein should be expressed in a manner so plain as to leave no room for misunderstanding4 ,a ,,and ,b ,,railroad4 #gg4 ,specification for ,graduation4 ,,line4 ,the centre of the road-bed to conform correctly to the centre line of the railroad1 as staked out or otherwise indicated on the ground1 and to its appropriate curvatures and grades as defined and described by the engineer2 and the contractor shall make such deviations from these lines or grades at any time1 as the said engineer may require4 ,the road-bed to conform to the cross section which shall be given or described1 or to such other instructions as may be given as hereinafter limited2 and the same of the ditches and slopes of the work1 and of all operations pertinent to the satisfactory performance of the graduation or masonry on the part or parts of the line contracted for4 ,,clearing4 ,the ground forming the base of all embankments1 and five feet beyond the foot of the slopes of all embankments1 to be cleared as close to the surface as practicable1 of all timber1 saplings1 brush1 logs1 stumps1 or other perishable material4 ,the valuable timber to be laid aside1 beyond the clearing as directed by the engineer1 the rest to be burned1 if this can be done safely1 otherwise to be moved beyond the limits of the cleared ground4 ,the ground for ten feet beyond the top lines of all slopes of cuttings shall be cleared in like manner1 of all timber and saplings4 ,wherever additional ground has to be taken in widening excavations to obtain materials1 or in widening embankments to dispose of surplus material1 or in grading for turnouts or depot grounds1 an additional amount of ground shall be cleared in like manner2 and when directed by the engineer1 wherever additional space is required for outside ditching1 or for alterations of roads or watercourses1 or otherwise4 ,,grubbing4 ,all stumps and large roots within ten feet of the grade line shall be grubbed out to the entire width of the work1 and moved at least ten feet beyond the slopes4 ,the cost of all clearing and grubbing is included in the price for earth work1 which price is also understood to include all clearing and grubbing necessary in borrowing pits1 spoil banks1 road crossings1 alterations of roads and watercourses1 the formation of ditches or otherwise4 ,the necessary clearing and grubbing in all cases to be kept completed five hundred feet in advance of any work in progress4 ,,mucking4 ,wherever mud1 muck1 or similar soft material occurs in excavations or embankments1 within two feet of subgrade1 it shall be removed and replaced by compact earth or gravel4 ,,grade4 ,the grade lines on the profiles show the true grade1 and correspond with a line two inches below the bottom of the iron rail of the superstructure4 ,what is called subgrade corresponds with a line placed eighteen inches below the grade4#e ,footnote #e3 ,the distance between grade and subgrade depends somewhat upon the climate1 but is generally between one and two feet4 ,see chap4 ,,xiii4 ,,width ,,of ,,road1 ,,and ,,slopes4 ,the width of road-way1 unless otherwise directed1 shall be twenty-two feet wide at grade in earth excavations1 and eighteen feet wide in rock excavations4 ,both rock and earth shall be taken out eighteen inches below grade for the entire width of road-way4 ,the bottoming to be replaced by gravel1 broken stone1 or spawls1 in such manner as shall be directed by the engineer1 leaving the necessary ditches of the width and depth directed on either side4 ,the contractor will not be paid for any rock excavated beyond the slope lines of one to eight from the required width1 or for any earth excavated beyond slope lines of one and one half horizontal to one vertical1 unless directed by the engineer to move additional rock or earth4 ,,blasting4 ,all blasting shall be done at the risk of the first party1 who shall be liable to the second parties1 or to the railroad company1 for any damages incurred in consequence1 to dwelling-houses1 individuals1 or otherwise4 ,,ditches4 ,whenever required1 ditches shall be cut along the tops of the slopes1 of the form and size and in the position directed4 ,,surplus ,,material4 ,whenever the earth or rock required for the adjoining embankments exceeds the amount in the neighboring excavations1 the contractor1 when required1 shall increase the width of said excavations1 as directed by the engineer1 to a sufficient width for a double track1 provided that this additional width shall not be extended so as to produce an average haul of more than eight hundred lineal feet1 on said borrowed stuff4 ,and whenever the earth or rock to be moved from any cut exceeds in amount the adjoining embankments1 7unless elsewhere wanted17 it shall be applied to widening the embankment to a width for a double track1 within the same limits of haul2 but for a greater haul than eight hundred feet1 the contractor shall be paid _/#ajj of a cent per yard per hundred feet of excess4 ,,borrow ,,pits4 ,where the excavation does not furnish sufficient material to make the adjoining embankments1 borrow pits may be opened4 ,but no earth shall be deposited in spoil banks nor borrow pits opened without the knowledge and consent of the superintending engineer1 who shall take care that such operations are arranged so as not to damage the road or its slopes1 nor interfere with the widening of the road-bed at a future time for additional tracks4 ,,material ,,to ,,be ,,saved4 ,if materials be found in the excavations applicable to useful purposes1 such as building stone1 limestone1 gravel1 minerals1 etc41 they shall be laid aside in such place as the engineer may direct1 for use1 to be applied then or subsequently to the construction of the road under the conditions of these specifications and of the contract4 ,,classification ,,of ,,materials4 ,earth--every thing except solid and loose rock4 ,loose rock--all boulders and detached masses of rock measuring over one cubic foot in bulk and less than five cubic yards4 ,solid rock1 includes all work in ledge1 which requires drilling and splitting1 and all loose rocks containing more than five cubic yards4 ,the prices for excavation include all earth or rock excavated in ditching1 bottoming1 borrowing1 road crossings1 alterations of road crossings and water channels1 and the construction of temporary roads1 provided the average distance hauled on each section1 be the same as stated on the schedule here annexed2 but if the actual average haul on any section is found1 on completion1 to have been greater or less than the distance stated1 a corresponding addition or deduction shall be made1 of one cent per cubic yard per hundred feet which the actual haul exceeds or falls short of that stated4 ,,embankments4 ,the embankments to be formed fifteen feet wide on the surface1 unless otherwise directed1 with slopes of one and one half horizontal to one vertical4 ,wherever the embankment is formed from ditching on either side1 such ditching1 and the crest of the slopes thereof shall in no case approach within six feet1 nor within double the depth of ditch1 of the foot of the proper embankment slope1 allowing always on one side for a double track2 and no soft mud or muck shall be allowed to enter the bank4 ,wherever watercourses or new channels for rivers require to be formed1 they shall not approach within once and one half of the depth of such stream1 plus twenty-five feet4 ,care shall be taken in forming embankments to exclude all perishable material4 ,,subsidence4 ,to allow for the after settlement of materials on embankments1 they shall1 when delivered to and accepted by the second parties1 be finished to the full width to the following heights above subgrades1 namely3 all banks below five feet in height to be finished three inches above subgrade2 at ten feet in depth1 five inches2 at twenty feet1 six inches2 and twenty-eight feet1 seven inches2 at thirty-five feet1 eight inches2 and at forty feet in depth1 nine inches above grade2 and intermediate heights in proportion2 the engineer having the power to change these proportions at his discretion4 ,,extra ,,excavation ,,and ,,embankment4 ,whenever it is considered necessary to increase the width of the road-way for turnouts1 water stations1 or depot grounds1 whether in excavation or embankment1 such work shall be done at the contract prices1 as may be directed4 ,the opening of foundation pits in simple excavation1 where coffer-dams or such like expedients are not necessary1 and in places where such expedients are necessary1 all excavation above the water line shall also be done at such increase or decrease of the contract price as shall be deemed proper by the engineer4 ,,embanking ,,at ,,bridges ,,and ,,culverts4 ,the contractor for earthwork shall not carry forward in the usual way any embankments within fifty feet of any piece of masonry1 finished or in progress1 7counting from the bottom of the slopes17 but shall in every such case have the earth wheeled to the walls or abutments1 and carefully rammed to such width and depth1 and in such manner as may be directed1 when the embankment may be carried on as usual4 ,the expense attendant upon any damage or rebuilding of mason work1 consequent on neglect of these directions1 shall be charged to the account of the first party4 ,in case the mason work shall not be finished when the embankment approaches it1 the contractor shall erect a temporary structure to carry over the earth1 and proceed with the embankment on the opposite side2 and the expense of said structure shall be paid by1 and charged to1 the contractor for masonry1 in case such contractor shall have delayed beyond the proper or required time1 the construction of the mason work2 but if the mason work could not have been ready in season for the bank1 then shall the expense belong to the contractor for the earthwork1 whose price for graduation is understood to comprehend all such contingencies4 ,for the above work of wheeling and ramming efficiently the earth around any piece of masonry1 the contractor shall be paid ---- cents per cubic yard1 by the engineer's measurement4 ,,roads ,,and ,,watercourses4 ,the first party is to make good and convenient road crossings wherever directed1 and shall also make such alterations of existing roads1 or watercourses1 or river channels1 or such new pieces of these pertinent the section undertaken by him1 as may be required1 and shall be paid for such work1 whether earth1 rock1 or masonry1 the prices1 and no more1 applicable to this contract4 ,and such road crossings or other alterations referred to1 he shall make at and within such times and in such form and manner as the engineer shall direct2 and whenever the operations of the first party interfere with a travelled road1 public or private1 either by crossing or by making required alterations on it1 the first party shall so operate as to afford at all times a safe and free passage to the public travel2 and the first party shall be liable for any damage to which the second parties or the railroad company may become lawfully liable by reason of his neglect to maintain a safe and properly protected passage for the current travel4 ,,ballasting4 ,where gravel is used for the ballasting of the road-bed1 it shall be of a quality satisfactory to the engineer1 and shall be spread upon the road-bed to the width and depth required4 ,when broken stone is used1 it shall be of durable quality1 and shall be broken so as to pass through a ring of three inches in diameter4 ,the quantity will be measured in the road-bed as finished1 and the contractor will be required to keep the ditches trimmed and clear4 ,,rip-,,rap1 ,,or ,,rubble ,,slopes4 ,the first party shall distribute rubble stone over the slopes of earth embankments1 whenever required to do so1 to protect said slopes from the action of water4 ,such stone to be arranged by competent hands1 and laid to such thickness1 and with stones of such size1 as shall be directed4 ,where the contractor has rock in the neighboring cuttings which is available1 it shall be reserved and applied to this purpose2 and when not1 good rock shall be obtained where the contractor can conveniently get it4 ,,measurements4 ,all earth or rock necessarily moved to complete the grading of this contract according to direction1 will be measured in excavation only2 and if the contractor 7with the consent of the engineer17 should find it convenient to waste earth from an excavation1 instead of carrying it to its proper embankment1 and to borrow at some nearer point earth for said embankment to replace that which was wasted1 he shall be paid for the earth from the original excavation in the order of its most economical arrangement for the second parties4 ,all earth moved from borrowing pits shall also be measured in excavation only4 #gh4 ,specification for ,masonry4 ,,first ,,class ,,masonry4 ,first class masonry will apply to bridge abutments exceeding twenty-five feet in height1 to the ring stones of arches1 and to the piers of bridges in running water4 ,the stone shall be laid at the rate of one header to two stretchers1 disposed so as to make efficient bond4 ,no header to be less than forty inches long1 and no stretcher to be less than eighteen inches in width4 ,no stone less than twelve inches in thickness1 no stone to have a greater height than width1 all stones to be placed upon the natural bed4 ,the masonry throughout to have hammer dressed beds and joints4 ,vertical joints to be continued back at least ten inches from the face of the wall4 ,the mortar joints on the face not to exceed one fourth of an inch in thickness4 ,the stone to be laid with regard to breaking joints in the adjoining courses4 ,the stone must be dressed complete before laying1 and not be moved after being placed in the mortar4 ,the face will not be tooled1 but only roughly hewed1 except for one half inch from the beds and joints1 where it will be hammered4 ,the ring stones of arches shall have beds to conform to the radius of the arch1 with the end joints vertical1 and be made to set smoothly on the centering1 with the beds with the proper inclination4 ,each stone must extend through the whole thickness of the arch1 and not be less than eight inches thick on the intrados4 ,no spawls or pinners will be admitted4 ,the ring stone shall be dimension work1 according to the plans furnished1 the beds and joints being truly dressed1 but the faces left rough4 ,all first class work shall be carefully laid in good cement mortar1 7see ,art4 ,cement74 ,each stone before being laid shall be carefully cleaned and moistened2 and masonry built in hot weather shall be protected from the sun as fast as laid1 by covering with boards4 ,copings shall be built of stone of equal thickness1 neatly dressed and laid4 ,all first class masonry shall be well pointed with cement pointing4 ,,second ,,class ,,masonry4 ,to be applied to abutments less than twenty-five feet high1 ring and face walls of bridges and culverts1 and to piers not in running water1 shall consist of stones cut in bed and build to a uniform thickness throughout1 before being laid1 but not hammered2 they shall be laid on a level bed1 and have vertical joints continued back at right angles at least eight inches from the face of the wall4 ,the work need not be carried up in regular courses1 but shall be well bonded1 having one header for every three stretchers1 and not more than one third of the stones shall contain less than two cubic feet1 or be less than nine inches thick2 and none of that third shall contain less than one and one half cubic feet1 or be less than six inches thick4 ,no more small stones shall be used than necessary to make even beds1 the whole to be laid in cement mortar and pointed4 ,,third ,,class ,,masonry4 ,applicable to culverts1 and to the spandrel backing of arches1 shall consist of strong and well built rubble masonry1 laid dry for culverts1 but wet for backing4 ,the culverts to be of such form and dimensions as the engineer may direct4 ,the foundation courses of the side walls to consist of large flat stones1 from eight to ten inches in thickness1 laid so as to give a solid and regular basis for the side walls4 ,the side walls to be laid with sound stone1 and of sufficient size1 and with beds having a fair bearing surface and good bond4 ,the covering stone for culverts being not less than ten inches thick for two feet culverts1 twelve inches for three feet culverts1 and fifteen inches for four feet culverts2 to be free from flaw or defect1 and to have a well bedded rest upon each side wall1 of not less than twelve inches for two and three feet culverts2 and not less than fifteen inches for larger ones4 ,in case such stone cannot be obtained1 a dry rubble arch may be thrown instead1 well pinned and backed2 but the price for the arch shall not be more than the general price for third class masonry1 with an allowance for the centering4 ,,fourth ,,class ,,masonry4 ,applicable to cattle-guards1 pavement of culverts1 and slope and protection walls1 shall consist of stones of not less than one cubic foot in contents1 so laid and bonded as to give the greatest degree of strength in preference to appearance2 being laid when directed with beds perpendicular to the inclined face4 ,pavements under culverts shall be made by excavating one foot in depth of that part to be paved1 which space shall be filled with flat stones one foot wide1 set on edge1 close together1 and made to present an even upper face4 ,,timber ,,and ,,plank ,,foundations4 ,timber and plank foundations require the beds to be perfectly well levelled1 and timber of such dimensions1 and so laid1 as shown by the plans2 to be well bedded and brought to an even and level top surface4 ,the spaces between them to be filled and well rammed with such material as the engineer may direct4 ,on these timbers planks shall be laid1 and trenailed or spiked if required4 ,the materials shall be of quality and shape approved by the engineer1 and the price shall be in full for material and labor in laying the whole in a thorough and workmanlike manner4 ,,piling4 ,piling may be used either as bearing piles for foundations1 or for piled bridges4 ,in the former case they will be bid for by the running foot driven1 and in the latter by the stick of twenty-five feet in length4 ,the piles in either case must be straight round timber1 of a quality approved by the engineer1 not less than ten inches in diameter at the small end1 barked1 and properly banded and pointed for driving4 ,they shall be driven in such places1 and to such depths as required1 and the heads cut off square1 or finished with a tenon to receive caps1 as may be required4 ,bearing piles will be cut off so far below the lowest water that any timber foundation laid thereon shall be at all times entirely immersed4 ,,cement4 ,cement when used shall be of the best quality1 hydraulic1 newly manufactured1 well housed and packed1 and so preserved until required for use4 ,and none shall be used in the work until tested and approved by the engineer4 ,,cement ,,mortar4 ,the proportion of sand and cement for construction shall be one of cement1 to two of clean1 sharp sand1 unless in special cases the engineer direct otherwise1 for which due allowance shall be made4 ,it shall be used directly after mixing1 and none remaining on hand over night shall be remixed4 ,,lime ,,mortar4 ,lime mortar 7which in all cases shall contain cement71 will consist1 unless otherwise directed1 of two parts of best quick lime1 one of cement1 and five of sand2 the ordinary mortar of lime and sand being first properly made1 and the cement thrown in and thoroughly mixed immediately before using4 ,,concrete4 ,whenever concrete is required to be used1 it shall be formed of clean broken stone1 cement1 and sharp1 clean sand4 ,the stone1 which shall be of satisfactory quality1 shall be broken so as to pass through a ring three inches in diameter4 ,the cement and sand shall be thoroughly mixed in the proportions already described for cement mortar4 ,thus prepared1 it shall be carefully mixed with the broken stone in the proportion of one of mortar to two or two and one half of broken stone1 as the engineer upon experiment shall determine1 and shall be immediately laid carefully in its place1 and well rammed4 ,the concrete shall be protected on the sides by boards1 and be allowed to remain undisturbed after laying until it is properly set2 and in special cases the engineer shall direct the mode of application4 ,for the proper preparation and laying of such concrete1 there shall be paid the price applicable to second class masonry4 ,the contractor shall furnish all tools and plank necessary to the operation4 ,,pointing4 ,all masonry in cement or lime will be finished with a good pointing of cement1 without extra charge4 ,,brickwork4 ,when bricks are required1 or allowed to be used1 they shall consist of sound1 hard-burned brick1 laid in cement1 or common mortar1 as directed1 and no soft or salmon brick will be admitted2 and none but regular bricklayers must be employed4 ,,centering ,,and ,,backing4 ,the whole top of all arches1 whether brick or stone1 shall be finished by plastering with a good coat of cement1 so as to prevent the percolation of water1 and turn it away from the arch4 ,the centering shall be such as the engineer approves of in every respect1 and shall not be removed until he directs4 ,the cost of backing to be included in the price bid4 ,for arches of more than twenty-five feet span1 compensation shall be made1 at the engineer's estimate1 for the extra value and cost of the centering proper for large arches4 ,,general ,,provision4 #gi4 ,the engineer reserves the right to require the whole or any part of the above described work of masonry to be laid in cement1 lime1 mortar1 or dry1 at his discretion4 ,first and second class masonry1 and brickwork1 will be bid for at prices for laying in cement1 from which will be deducted fifty cents per yard if laid in lime mortar1 and one dollar if laid dry4 ,third and fourth class masonry at prices for laying dry1 to which will be added fifty cents per yard if laid in lime mortar1 and one dollar if laid in cement4 ,,scaffolding4 #hj4 ,nothing shall be allowed for workmanship or timber of any scaffolding used in the construction of timber bridges1 or in carrying up abutments1 piers1 coffer-dams1 or otherwise4 ,should the timber used in any coffer-dam be carried away by floods1 the renewal of it shall fall upon the first party4 ,,foundations4 #ha4 ,the foundations for all structures shall be executed by the contractor for masonry in such manner and to such depth as to secure a safe and secure foundation1 of which the engineer will judge4 ,if a natural foundation cannot be procured at a reasonable depth1 then the contractor shall prepare such artificial foundation as the engineer may direct4 ,the stuff moved from the foundations1 if of the proper quality1 shall be deposited in the adjoining embankment1 provided the site for said embankment has been cleared of all perishable material4 ,so much of the stuff as shall not be fit for the embankment1 and all roots1 stumps1 etc41 shall be deposited beyond the limits of the clearing1 so as not to obstruct roads1 watercourses1 or ditches4 ,for the earth moved from such foundations1 and for all earth used according to direction1 in the construction of coffer-dams1 there shall be paid ---- cents per cubic yard4 ,whenever it may be necessary to pump or bale water in the foundations1 the contractor shall furnish the pumps or buckets1 and all scaffolding and apparatus necessary to work them4 ,he shall be allowed the net cost of all labor employed in the operations of pumping or baling water1 and shall make a monthly return to the engineer of the value of such labor1 provided that these operations are conducted in an economical manner1 with efficient men1 pumps1 and tools1 under the direction and to the satisfaction of the engineer4 ,he shall also be allowed such compensation for the use of the pumps and apparatus1 and for superintendence1 as the engineer shall judge to be fair and reasonable4 ,,trestle ,,work4 #hb4 ,includes all wooden structures commonly used as substitutes for abutments and piers1 and for farm passes1 etc41 etc4 ,these shall be built according to the plans furnished1 and directions given by the engineer1 of sound1 durable material1 to be approved by him4 ,the price bid shall be by the thousand feet board measure1 and will be considered as in full for all material except iron1 and for the labor of building and erecting complete4 ,the iron used will be of the best ,american1 and the workmanship of approved quality4 ,the bids will be by the pound1 and will cover all cost of material and the labor incident to its use4 ,spikes and nails when used will be furnished by the contractor at cost4 ,,bridging4 #hc4 ,contractors may submit plans for bridging in connection with1 or separate from their bids2 but the engineer of the company may reject such plans if he choose1 and substitute others1 which if the contractor decline building at the approved prices1 may be let to other parties4 ,in every case1 the exact manner of building1 erecting1 adjusting1 and finishing bridges1 and the determination of the nature and amount of material1 will be specified by the engineer4 ,the price bid must be by the running foot of the whole length of bridge1 as erected and finished complete4 #hd4 ,specifications for ,superstructure4 ,,subsills4 ,to maintain the track in good adjustment until embankments are settled1 subsills will be laid on certain banks1 and likewise in cuts where the imperfect nature of the bottoming may1 in the opinion of the engineer1 render them expedient4 ,these subsills to be fairly bedded in the earth or ballasting1 and carefully adjusted and rammed so as to correspond with the grade lines given by the engineer4 ,an additional piece of sill1 four feet long1 shall be laid at each joint of the subsill1 either under the sill1 or alongside1 as may be directed4 ,the sills will be of #c #i plank1 in length of twelve1 fifteen1 eighteen1 and twenty-one feet2 of which one fourth may be below fifteen1 one fourth below eighteen1 and one fourth below twenty-one feet4 ,the plank must be square at the ends1 and of sound1 durable material1 and not have more than two inches wane on one end only4 ,there will be about #be1jjj feet1 board measure1 laid per mile where it may be required1 and #ffj joint sills1 #c #i inches1 and four feet long4 ,when the depth of stuff to be moved to admit the subsills exceeds six inches1 an allowance shall be made for extra labor1 the amount of which shall be noted by the assistants on their receiving notice of such extra labor from the contractor or his agent4 ,,cross ,,ties4 ,the cross ties shall be of white1 black1 or yellow oak1 burr oak1 chestnut1 red elm1 black walnut1 or other sound timber of suitable character in the opinion of the engineer4 ,eight feet long1 and not more than three inches out of straight1 hewn to a smooth surface on two parallel plane faces six inches apart1 the faces being not less than seven inches wide for at least half of the number1 and the remainder not less than six inches wide4 ,the ties shall be carefully and solidly laid on the subsills1 or ballasting1 or earth previously properly prepared1 so as to give the true planes required by the rails1 whether on straight or curved lines4 ,they shall be laid at the rate of eight ties to each eighteen feet rail4 ,all imperfect ties shall be excluded by the tracklaying party4 ,the surface of the ties to be faithfully adjusted to the grades given1 and to the web of the rail2 and the rail to be truly laid and firmly spiked so as to correspond neatly to the alignment of the road4 ,there will be about #b1ejj ties required per mile of road4 ,,chairs ,,and ,,joints4 ,when chairs are used1 they shall be such as directed by the engineer1 and furnished by the company1 and shall be well and accurately placed and spiked in such manner and position as required4 ,when chairs are used1 the largest ties shall be selected for the joints4 ,when the joint is made by fishing1 there will be no tie directly under the joint4 ,,rails4 ,the rails will weigh about sixty pounds per lineal yard4 ,no rail shall be laid on the tangents which is in any way twisted or bent4 ,it shall be the duty of the first party to correct and make true any crooked rails received by him1 also to bend to the proper curve1 and in such a manner as not to affect the strength of the bar1 all rails laid in curves4 ,punching of rails1 and cutting1 will also be done by the contractor4 ,,track ,,laying4 ,the materials composing the track will be furnished by the company1 and it will be laid in the best manner according to the conditions following4 ,the track will be laid on cross-ties1 and the ties at the proper places on subsills4 ,where the sills are used1 they will be laid with four feet blocks at the joints1 and with six feet blocks at the rail joints1 the whole being set to their places by stakes1 and by the engineer's directions1 and mauled down to a perfect bearing1 being settled at least half an inch by mauling4 ,the cross ties will be placed uniformly distant1 7twenty-eight inches from centre to centre74 ,the iron must be so cut or selected that the joints of the parallel rails shall be within two inches of being opposite to each other2 no joint tie being allowed a greater amount of askew than this1 whether on tangents or curves4 ,a slip of metal shall be inserted at the rail joints while laying1 to keep the rails apart sufficiently to allow for expansion1 which thickness1 7depending upon the temperature17 shall be fixed by the engineer4 ,notches to be cut at the centre of each bar1 to correspond with half a spike1 to prevent longitudinal motion of the rails4 ,each joint chair to be fastened with four spikes4 ,two spikes at each end of each tie upon straight lines and upon curves of less than #a1ejj feet radius at the outer end of the tie two spikes outside and one inside1 and at the inner end two spikes outside and one inside of the rail4 ,upon curves the outer rail to be raised by such an amount1 depending on the radius of curvature1 as the engineer may direct4 ,,turnouts4 ,the contractor to put in such turnouts and sidings1 with the necessary frogs and switches1 as may be required2 the frogs and switches to be firmly and truly placed in position so as to work easily4 ,,filling ,,and ,,ditching4 ,the stuff moved in bedding the sills and ties1 to be placed between the latter4 ,the ditches to be properly cleaned out after the track is laid2 the filling never to rise higher than the top of the cross tie4 ,any surplus stuff to be moved out of the cuts1 or if on embankment1 to be thrown over the bank1 leaving the track and road-bed in a neat and workmanlike shape4 ,,delivery ,,of ,,materials4 ,the ties and sills to be delivered at some point on the road as near as possible to the places where they are to be used1 in no case requiring more than one thousand feet of haul2 to be so piled as easily to be counted and inspected4 ,the bids for ties will be by the piece2 the proposal stating the number and conditions2 the sills to be bid for by the thousand1 board measure4 ,all material furnished in connection with track laying to be delivered in such manner and time as to comply in good season with the contract for laying the rails4 ,,measurement ,,of ,,track4 ,the measurement of track laid shall include the turnouts1 measuring from heel to heel of switch4 ,no extra allowance being made for putting in frogs or switch machinery4 #he4 ,specification for ,fencing4 ,bids for fencing will be by the running foot1 or mile1 including both sides of the road4 ,where required1 it will consist of posts placed eight feet apart from centre to centre1 set three feet into the ground1 either by digging or boring1 and not by mauling4 ,the posts shall be of oak1 elm1 chestnut1 or other durable wood1 not less than eight inches in diameter at the bottom1 barked and charred where put into the ground4 ,the boards to be #f #a inches1 and to square sixteen feet long1 to be placed six inches apart vertically1 and fastened to the posts with tenpenny nails at each bearing1 and breaking joint with each other4 ,there will be five bars in depth1 the top of the uppermost being five feet from the ground4 ,in side hill and in ground liable to slide1 particular care shall be taken to place the posts firmly in the ground4 ,at cattle guards1 the fence will be turned in to the proper distance1 and such arrangement made as to prevent the passage of animals4 #hf4 ,general ,provisions4 ,,classification4 ,the classification of material excavated will be referred to the engineer1 in all cases where the nature of the material is questioned1 and his judgment taken thereon4 ,also all material used in structures will be submitted to the inspection of the engineer or his assistants4 ,,quantities ,,and ,,qualities ,,approximate4 ,the quantities and qualities of work presented in the schedule are merely approximate1 and the information given on the maps and profiles in relation thereto is according to the best present knowledge4 ,the company retains the right to change at any time during the progress of the work1 the alignment1 grades1 and width of the road1 or any part thereof2 and also the limits of the sections1 or to alter the character1 vary the dimensions1 or change the location of structures1 or substitute one kind of work or material for another1 or to omit entirely1 when found necessary1 or to require to be built where not now contemplated2 and the contractor shall carry into effect all such alterations when required1 without the contract prices being thereby affected1 unless the aggregate value of all work contemplated by the contract be changed full twenty per cent41 in which case a fair allowance1 either for the company or the contractor1 shall be made by the engineer4 ,in case1 however1 the aggregate value of the work be changed by over twenty per cent4 of the original amount1 and the contractor be not satisfied with the altered compensation1 then said contractor may throw up said contract1 on condition1 that within ten days after receiving notice from the engineer of such alteration1 he give written notice to the engineer or the company of his desire to do so4 ,in which case1 as in other cases of throwing up the contract1 he shall as soon as desired1 give peaceable possession to the company or their agents2 leaving also in their possession any tools or machinery upon which they have advanced any thing2 and the company may then settle with the contractor on the measure of damages which either shall suffer4 ,,basis ,,for ,,estimating ,,effect ,,of ,,changes4 ,the basis for estimating any changes as above mentioned is understood to be the schedule exhibited at the letting4 ,,no ,,liquor1 ,,and ,,good ,,order4 ,the contractor shall not sell1 or allow to be sold or brought within the limits of his work any spirituous liquors1 and will in every way discountenance their use by persons in his employ4 ,he will do all in his power by his own act1 or by assisting the officers of the county1 or of the corporation1 in maintaining the laws and such regulations as conduce to good order and peaceable progress1 and prevent encroachment on the rights of persons or property2 and he shall discharge from his service1 when required by the engineer1 any disorderly1 dangerous1 insubordinate1 or incompetent person1 and refuse to receive into his employ any who may have been discharged for such cause from other parts of the work4 ,,monthly ,,estimates4 ,measurements and estimates shall be made by the engineer once in each month1 by means of which may be known approximately the amount of work done1 and the contractor shall be entitled to payment therefor at such rates below his contract prices as the engineer or president of the company deems expedient2 it being understood that the contractor has no claim on account of any material not laid in its place in the road-way1 or for labor bestowed thereon2 and the quantities shall be estimated from the dimensions when so laid1 though on the advice of the engineer1 advances may be made on such material when delivered for use1 in which case it becomes the property of the company1 in the contractor's care and keeping1 and he becomes liable for its loss or injury4 ,,extra ,,work4 ,no claim for extra work or for work not provided for in the contract shall be allowed1 unless a written order to perform such work shall have been given by the engineer2 or that the work be subsequently certified by him1 and the certificate produced at the time of demanding the payment of the monthly estimate next after such work shall have been performed4 ,,sub-,,contracts4 ,the contractor will be required to perform the work himself1 and no sub-contracts relieving him from the responsibility of a proper performance of his contract will be permitted1 unless by the written consent of the president of the company4 ,and no moneys shall be paid to any such sub-contractor for work or materials1 without sufficient authority from the principal contractor4 ,,when ,,work ,,to ,,be ,,commenced4 ,on the acceptance of a proposal1 the chief engineer will give notice thereof to the person proposing1 by letter directed to his stated address2 and in twenty days from the date of such notice1 provided there be no impediment on the part of the company1 or in twenty days after such impediment is removed if there be1 the work shall be begun with an adequate force1 and from that time be prosecuted vigorously until its completion4 ,,how ,,to ,,progress4 ,it shall be understood that proper progress is not made1 if the amount of work done in each month is not in due proportion to the total amount to be done up to the time fixed for completion by the contract2 in which case the engineer shall call the attention of the contractor 7or whoever may be in charge of the work if the contractor be absent17 to the fact1 and state to him what additional exertion is necessary to be made1 and what further force is required1 in such reasonable time as may be prescribed4 ,,putting ,,on ,,more ,,force4 ,in default of the contractor's making such additional exertion1 and supplying such force1 the chief engineer1 or president of the company may have such force sent to the work1 and the necessary buildings may be erected to receive them at the contractor's charge and expense1 who shall receive the said force in his employ1 and work it at whatever price it may have been found necessary to employ it1 without diminishing the previous force of the work1 and regarding always such extra force as if employed by himself4 ,,causes ,,for ,,detention4 ,there shall be no claim for detention on account of work not being laid out1 unless a written notice three days in advance1 that it is required1 shall have been given to the engineer2 and the damage for such detention shall be estimated by the engineer4 ,the right of way shall be furnished by the company1 but if it fail to do so for any particular place1 damages for detention shall not be claimed unless the contractor be detained full twenty days after he shall have given written notice to the engineer of his wish to commence work at such place4 ,then the engineer may either estimate to him the amount of damage which he shall take as satisfactory1 or he may extend the time of the completion of such work by as many days beyond the contract time1 as the contractor is detained beyond the twenty days following his notice to the engineer4 ,,the ,,engineer4 ,in all cases where the word 8engineer0 is used1 the engineer in charge of construction is meant2 but the directions of any subordinate engineer shall be obeyed when given in regard to any of the ordinary operations1 or where they are evidently in accordance with the specifications1 or when transmitting the orders of his superiors4 ,in other cases they may be referred to the resident engineer1 and finally to the chief engineer1 he being the authorized officer1 at the time acting in that capacity4 ,,contractor4 ,the word 8contractor0 applies to and includes all persons contracting jointly1 any one of whom shall be considered the authorized agent for and in behalf of his associates1 and empowered to receipt payment of moneys1 receive and act upon orders4 ,,the ,,contract4 #hg4 ,this is the mutually binding legal article of agreement between the contractor and the company1 specifying the times of completing1 manner of payment1 and describing the work which is to be done4 ,thus3-- ,a ,,and ,b ,,railroad ,,company4 ,contract4 ,graduation on sections ,a ,c ,d1 ,masonry on sections ,a ,c ,d1 ,ballasting on sections ,a ,c ,d1 ,bridging on sections ,a ,x ,t1 ,fencing on sections ,o ,o ,o1 ,sills and ties on sections ,o ,o ,o1 ,track laying on sections ,o ,o ,o4 ,contractors4 ,articles of agreement made and concluded this first day of ,january1 ,a4 ,d4 #aheg1 between ---- of the first part1 and the ,a and ,b ,railroad ,company of the second part1 being a company duly incorporated by the ,state of ---- of the second part1 whereby it is mutually agreed as follows1 namely3 ,the said party_/parties of the first part hereby agree to and with the said party of the second part that he_/they will perform in a substantial and workmanlike manner the following work1 namely3-- ,the work here described4 ,the said work to be performed and completed agreeably to the directions and to the approval of the chief engineer of said company for the time being1 and subject to all the general provisions of the specification attached to and forming a part of this agreement1 and also subject to such of the special provisions of said specifications as are applicable to the work hereby contracted for4 ,and in consideration of the full and faithful performance by the said party_/parties of the first part of this agreement on his_/their part1 the said party of the second part hereby agrees to pay for the same in the time and in the manner hereinafter mentioned1 at the rates as follows1 namely3-- ,here insert the items and corresponding prices4 ,it is mutually agreed that this contract applies only to those items to which prices are attached1 and that where it embraces both labor and materials introduced in the work1 such prices are in full compensation therefor when introduced in the manner required4 ,when it embraces materials only1 such prices are in full compensation for the materials and the labor necessary to deliver the same to the company1 and when it embraces labor only1 such prices are in full compensation for such labor1 and every incident to its complete and proper performance4 ,in every case the estimate for ascertaining the amount of compensation shall be made by the engineer from the actual work1 from the material furnished1 or from that on which the labor contracted for is bestowed4 ,it is also agreed that partial payments shall be made from time to time during the progress of the work as follows3-- ,times and manner of payment4 ,and that in thirty days after the contract is fully completed to the satisfaction of the chief engineer of the company for the time being1 and the work is surrendered to and accepted by the company1 a final measurement and estimate thereof shall be made under the direction of the chief engineer1 and be duly certified by him1 on the return of which to the president of the company the whole amount then found to be due to the said party_/parties of the first part shall be paid to him_/them on demand as follows3-- ,insert mode of payment4 ,and it is also hereby further agreed1 that bank-bills current in the ,state of ---- shall be accepted for cash in payment for all claims under this contract4 ,and the said party_/parties of the first part further agree_/agrees that in twenty days after he_/they shall be notified to do so1 as provided for in said specifications1 he_/they will begin the work hereby contracted to be performed1 with a force of all kinds sufficient for its completion in the time herein prescribed1 and that he_/they will finish and deliver the same to the company fully completed in all its parts as follows3-- 99 99 99 99 99 ,and the said specifications hereunto annexed are hereby made a component part of this contract and 7except so far as any provision therein may not be pertinent to the subject-matter of the contract or may be specially modified herein17 shall be looked to in ascertaining the meaning1 extent1 and purport of this agreement1 and in determining the rights1 powers1 duties1 privileges1 and obligations of the contracting parties as to any particular embraced therein4 ,in virtue whereof the said party_/parties of the first part has_/have hereunto set his_/their hand and seal1 and the said party of the second part have caused their president to subscribe his name and affix the corporate seal of the company hereto1 all done in triplicate the day and year first above written4 ,contractor's name1 ,,seal4 ,president's name1 ,,seal4 ,,solicit ,,for ,,bids4 #hh4 ,the approximate estimates1 plans1 and profiles being made1 and other preliminaries settled1 proposals for executing work are solicited by the public papers4 ,thus3-- ,,new ,,york1 ,january #a1 #aheg4 ,office of the ,a and ,b ,railroad ,company4 ,proposals for executing the graduation1 bridging1 masonry1 and track laying1 and for the supply of materials upon the ,a and ,b railroad will be received at this office until the #cast day of ,january1 #aheg4 ,plans1 profiles1 and schedules of amounts of work may be seen1 and blank bids obtained by application at this office4 ,all proposals must be directed to the chief engineer of the ,a and ,b ,railroad ,company4 ,no bids will be received after ,january #cast1 at #ab1 ,m4 ,per order1 ,c4 ,d41 ,secretary ,a and ,b ,r4 ,r4 ,co4 ,,form ,,for ,a ,,bid4 #hi4 ,that proposers may make their bids in a convenient form for comparison1 a blank1 somewhat like the following1 is given them to fill out4 ,number of ,section4 ,sec4 ,sec4 ,sec4 ,sec4 #a4 #b4 #c4 #d4 ,length in miles4 #a #a #a #a ,graduation4 ,clearing and grubbing1 ,price per acre1 ,cost on the section1 ,earth excavation1 ,price per yard1 ,cost on the section1 ,loose rock excavation1 ,price per yard1 ,cost on the section1 ,solid rock excavation1 ,price per yard1 ,cost on the section1 ,average haul on section1 ,ballasting1 ,price per yard1 ,cost on the section1 ,whole cost of graduation1 ,masonry4 ,first class masonry1 ,price per yard1 ,cost on the section1 ,second class masonry1 ,price per yard1 ,cost on the section1 ,third class masonry1 ,price per yard1 ,cost on the section1 ,foundation timber1 ,cost per ,m41 b'd measure1 ,cost on the section1 ,excavation for foundation1 ,price per yard1 ,cost on the section1 ,rip rap1 ,price per yard1 ,cost on the section1 ,whole cost of masonry1 ,bridging4 ,detailed as above1 ,track laying4 ,fencing4 ,this form being filled out1 evidently gives the cost of each or all of the items upon any one or all of the sections1 the cost of all the items upon any one section being at the foot of that section1 and the whole cost of any one item at the extreme right and on the line of that item4 ,on the bottom of the form is printed1 8,the undersigned having read the specifications1 and made due examination1 hereby proposes to the ,a and ,b ,railroad ,company1 to perform the work in the above schedule1 to which he_/they has_/have set figures1 at those prices and under the conditions described1 and upon acceptance of this proposal by the company1 binds_/bind himself_/themselves to enter into a written contract to that effect1 and to furnish the required security4 ,name1 ,address1 ,name of ,surety1 ,address of ,surety40 ,,comparison ,,of ,,bids4 #ij4 ,the bids being received1 are compared as follows3-- ,name of ,graduation4 ,masonry4 bidder4 ,sec4 ,sec4 ,sec4 ,sec4 ,total4,sec4 ,sec4 ,sec4 ,sec4 ,total4 #a4 #b4 #c4 #d4 #a4 #b4 #c4 #d4 ,a ,b ,c ,name of ,bridging4 ,superstructure4 bidder4 ,sec4 ,sec4 ,sec4 ,sec4 ,total4,sec4 ,sec4 ,sec4 ,sec4 ,total4 #a4 #b4 #c4 #d4 #a4 #b4 #c4 #d4 ,a ,b ,c ,name of ,fencing4 ,grand bidder4 ,total4 ,sec4 ,sec4 ,sec4 ,sec4 ,total4 #a4 #b4 #c4 #d4 ,a ,b ,c ,from which the names may be easily selected either for one or more sections1 for any or all of the items1 that shall give the least cost4 ,,chapter ,v4 ,,laying ,,out ,,work4 #ia4 ,the running of the line consists in placing a stake at every one hundred feet upon tangents1 and at every fifty feet distance upon sharp curves2 also a permanent post at each tangent point1 and at points of compound and reversed curvature4 ,this is the centre line1 the axis of the road1 and the base of all field operations4 ,wherever the work is going on1 the centre pins should be referred to fixed points outside of the ground occupied by the road4 #ib4 ,the first operation in preparing for excavation is to place side stakes at one half the width of road-bed plus the ditch1 on each side of the centre line4 ,,slopes4 #ic4 ,setting out slopes is a term applied to laying off upon the ground1 on each side of the centre1 the distance to which the slope1 commencing at the outer edge of the ditch1 will extend1 depending upon the angle of slope1 width of road-bed and ditch1 and depth of cutting4 ,there are here five distinct cases which may occur3-- ,in embankment when the natural surface is horizontal4 ,in embankment when the natural surface is inclined4 ,in excavation when the natural surface is horizontal4 ,in excavation when the natural surface is inclined4 ,in mixed work 7side hill17 when the road-bed is partly in cut and partly in fill4 ,in both excavation and embankment1 when the natural surface is horizontal1 we have only to add the cut1 in feet and decimals1 multiplied by the slope1 to one half the width of road-bed plus ditch4 ,thus suppose the cut is #bj4ee feet1 half the road-bed1 #aj4be feet1 ditch1 #c4jj feet1 slope #a horizontal to #a vertical1 and we have 7#bj4ee #a7 #aj4be #c4j #dd4jge feet4 ,when the ground is inclined transversely to the axis of the road1 first assume a point upon the ground1 7apparently right7 find its height above grade with the level1 multiply this by the slope and add one half the distance between the outer edge of ditches1 and see how near it comes to the measured distance from the centre to the assumed point2 if within a foot1 it will answer2 if not1 a second trial will fix the place4 ,,culverts4 #id4 ,the length of any structure passing under a railroad embankment is ,l - #b,rh1 where ,l is the distance between slope stakes1 ,r inclination of slopes1 h the height of structure from the natural surface4 ,thus1 suppose the distance between slope stakes to be #ajj feet1 slope #a to #a1 and h #aj feet1 we have ,l #ajj - 7#aj #a #b7 #ajj - #cj #gj feet4 ,the length of an oblique structure will of course be greater than that of one at right angles to the road2 the length depending upon the obliquity4 ,,masonry4 #ie4 ,there are eight general cases which may occur in laying out such structures as bridge abutments with wings4 #a4 ,a right bridge on a level tangent4 #b4 ,a right bridge on a level curve4 #c4 ,a skew bridge on a level tangent4 #d4 ,a skew bridge on a level curve4 #e4 ,a right bridge on an inclined tangent4 #f4 ,a right bridge on an inclined curve4 #g4 ,a skew bridge on an inclined tangent4 #h4 ,a skew bridge on an inclined curve4 ,and these eight cases will vary again according to the natural surface of the ground1 whether horizontal1 or inclined transversely4 #if4 ,the general position of wing walls and general form of the line inclosing the base of the bridge1 is shown from fig4 #ca to fig4 #ch4 ,fig4 #ca represents case one4 ,the points ,a1 ,b1 ,c1 ,d1 are fixed by squares from the centre line at ,e ,f1 ,g ,h4 ,illustration3 ,fig4 #ca4 ,fig4 #cb represents case two4 ,the wings #c;c1 #d;d1 must evidently have a different inclination from ,a#a1 ,b#b4 ,the points ,a1 ,b1 c1 d1 #a1 #b1 #c1 #d1 as before1 are laid off by squares from a tangent to the curve4 ,illustration3 ,fig4 #cb4 ,fig4 #cc explains itself4 ,illustration3 ,fig4 #cc4 ,illustration3 ,fig4 #cd4 ,fig4 #cd1 case five4 ,here the wings ,a#a1 ,c#d1 are the same1 as also ,b#b1 ,d#c1 the former being longer1 on account of the greater depth of the fill4 ,illustration3 ,fig4 #ce4 ,fig4 #ce1 case seven4 ,here each wing is peculiar2 the figure being a compound of figs4 #cc and #cd4 ,illustration3 ,figs4 #cf and #cg4 ,figs4 #cf and #cg1 case #h4 ,this is the most difficult of all4 ,no two wings have the same length or inclination on plan4 ,the natural surface being horizontal1 the line inclosing the bridge is ,a ,b ,c ,d4 ,if the natural surface descended from ,c to ,a1 the position taken would be ,a1 ,b1 ,c1 ,d4 ,fig4 #cg is the elevation of the position ,a ,b ,c ,d4 ,the several points are laid off from the line n1 n4 ,the general manner of fixing the lines of figures #ca to #ch1 is to assume the angle of some one wing1 as ,a #a1 in fig4 #cd1 to draw ,a ,c parallel to ,e ,f2 and from ,c1 the intersection of ,a ,c with the base of the embankment1 ,c #d gives the other wing4 ,local circumstances will of course often fix at once the length and angle of the wings4 ,upon simple curves1 as in fig4 #cb1 the lines ,a c and ,b d are made radial4 #ig4 ,in curving a viaduct1 the axes of the piers are made radial to the centre of the located curve1 and the planes of the springing lines are made parallel to the axes of the arches4 ,the pier thus becomes a wedge1 and should be strengthened by a starling1 upon the outside of the curve1 to resist the resultant of the thrusts of two adjoining arches4 #ih4 ,we should never try to stake out the exact horizontal projection of a complicated piece of work upon rough ground1 but only the trenches1 which being cut1 give a horizontal surface to work upon4 ,in placing the stakes1 we must be careful to have them so far outside of the work that they will remain undisturbed while operations are going on4 ,the pegs for cutting pits and trenches may be placed at the angles of the latter1 but the working pegs must be so placed that the lines stretched from one to the other will define the masonry4 ,all measurements made in laying out work should be made by graduated rods1 and carefully checked4 #ii4 ,in founding piers1 and in aquatic operations generally1 two stakes upon the shore1 or a fixed transit1 will define any line in the water4 ,two transits will define points4 #ajj4 ,a permanent bench mark should be carefully fixed at each structure1 from which its levels may be obtained4 #aja4 ,in adjusting oblique bridges1 care must be taken so to place the bridge seats that the floor beams shall lie in a correct plane1 and not be at all warped or winding4 ,illustration3 ,fig4 #ch4 #ajb4 ,as an example of laying out work with regard to heights1 take the case of fig4 #ch4 ,let the grade of the centre line be one in #ajj1 the angle of obliquity #de1 the width of bridge twenty feet1 and span on the skew one hundred feet4 ,required the elevations of the points a1 b1 c1 d4 ,assume the height of 7#b7 as #ajj4jj ,that of 7#c7 will be #ii4jj b being #aj ft4 back of #b is #j4a ft4 higher than #b1 or #ajj4aj and d #j4a feet less than 7#b7 or #ii4ij also a #ii4jj #j4aj1 or #ii4aj and c #ii4jj - #j4aj1 or #ih4ij ,,tunnels4 #ajc4 ,the maintaining a correct centre line through tunnels is generally considered difficult4 ,the fixing of the line in deep shafts requires great care1 owing to the short distance between the only two fixed points1 that can be transferred from the surface to the bottom of the pit4 ,this is a matter of manual skill and of instrumental manipulation4 ,there is no difficulty in aligning the upper ends of two plumb-lines2 and the lower ones will certainly be governed by their position4 ,the following method has been found to answer every purpose4 ,let the opening of the shaft be ten feet in diameter4 ,place two horizontal bars at right angles to the road across the opening1 upon which slide blocks holding the upper end of the plumb-lines4 ,adjust these lines1 at the surface1 with a transit2 and when fixed1 place iron pins at the point marked by the plumbs at the bottom of the shaft4 ,upon these pins fix the exact centres4 ,for keeping the line in the shaft headings1 a straight rod1 with steel points at each end1 should be used1 which being placed upon the iron centre pins1 fixes the centre line of the tunnel4 ,when the tunnel is curved1 the line should be laid off by offsets from the tangent to the curve at the shaft4 ,by this method points at ten feet distance may be fixed within #a_/ajj of an inch1 a difference of which would cause an error of of an inch per one hundred1 or an inch per thousand feet4 ,,chapter ,,vi4 ,,earthwork4 ,,form ,,of ,,railroad ,,sections4 #ajd4 ,the reader is presumed to be acquainted with the manner of finding the areas and cubes of simple geometric figures and bodies4 ,the following fifteen figures show the forms which may be taken by the cross section of a railroad in cutting2 for embankment invert the same4 ,they are easily separable into simple figures4 ,illustration3 ,fig4 #ci4 ,illustration3 ,fig4 #dj4 ,illustration3 ,fig4 #da4 ,illustration3 ,fig4 #db4 ,illustration3 ,fig4 #dc4 ,illustration3 ,fig4 #dd4 ,illustration3 ,fig4 #de4 ,illustration3 ,fig4 #df4 ,illustration3 ,fig4 #dg4 ,illustration3 ,fig4 #dh4 ,illustration3 ,fig4 #di4 ,illustration3 ,fig4 #ej4 ,illustration3 ,fig4 #ea4 ,illustration3 ,fig4 #eb4 ,illustration3 ,fig4 #ec4 ,illustration3 ,fig4 #ed4 #aje4 ,the formation of tables for the amount of earth in level cutting is very simple4 ,the area of the following section1 where ,b is the base1 and ,r the horizontal dimension of the slope1 is 7,b ,b #b,r7_/#b h1 or 7#b;,b #b,r7_/#b h1 or finally 7,b ,r7 h1 i4 e41 the base of a rectangle by its height4 ,multiply this by #ajj and divide the product by #bg2 or divide by #bg_/ajj1 and we have the cubic amount in a prism one hundred feet long4 ,the road-bed being nineteen feet wide1 and slopes one and a half to one1 the formula for the amount of a prism one hundred feet long is 77#ai #a;h7h7_/#j4bg1 and assuming the base of rock cutting as eighteen feet1 and slope one quarter to one1 and embankment eighteen feet at subgrade1 we have1 rock1 77#gb h7h7_/#a4jh1 and embankment1 77#ah #a;h7h7_/#j4bg1 the figure being inverted for embankment4 ,for a prism of ten or of one thousand feet in length1 we have only to move the decimal point4 ,in forming a table1 proceed as follows3-- h ,b #a;h 7,b #a;h7 h 77,b #a;h7 h7_/#j4bg a b c d a b c d an bn cn dn4 ,illustration3 ,fig4 #ee4 ,it is evident from inspection of fig4 #ee1 that c exceeds co by h #br2 and that c exceeds c by h #br2 and so on as far as we go2 this increase being constant1 we have then to find the area of c1 and for the area c c double c1 and add the increment2 whence the rule3-- ,having found the increase 7which varies with the angle of the slope7 for the second section1 add the increase to twice the first4 ,for the third1 add twice the increase to three times the first2 and for the nth1 add n - #a times the increment to n times the first area1 or algebraically calling a the first area1 a the second1 a the third1 an the nth area1 and we have ,the first area a a2 ,the second area #b;a i a2 ,the third area #c;a #b;i a2 ,the nth area na 7n - #a7;i an4 ,we might operate at once upon the cubic contents1 but for the length to which some decimals run2 some indeed circulating4 #ajf4 ,the table thus made may be of the following form3-- ,cut 7or fill71 in feet4 ,cubic yards ,earth4 ,cubic yards ,rock4 ,slopes #a to #a4 ,slopes to #a4 #a #gf #fh #b #afc #acg #c #bfa #bjh #d #cga #bhb #e #dia #cef #f #fbb #dcc #g #hjb #eab #h #iai #eic #i #ajhc #fge #aj #abfj #gei i4 e41 cut being eight feet1 each one hundred feet length gives nine hundred and nineteen cubic yards2 one thousand feet1 #iaij yards1 and ten feet of length #ia4i cubic yards4 #ajg4 ,the preceding system is intended only for approximate estimates4 ,let one person read off the cuts or fills from the profile1 a second give the corresponding number of yards by the table made as above1 while a third sets the figures down2 being careful to separate the cuts from the fills4 ,for final measurements1 none but the prismoidal formula should be used2 the length of the prismoids being taken at each one hundred feet1 and nearer when the ground is rough4 #ajh4 ,as an example of the comparative amounts given by the above formula1 and by the common method of averaging end areas1 take the following1 the slopes being #a to #a4 ,base4 ,distance4 ,cut4 ,end ,area4 ,mean ,area4 ,middle ,area4 #bj #j #j #jjj #jjj #jjj #bj #ej #e #acg #jfi #jei #bj #ej #aj #cej #bdd #bcf #bj #ej #ae #fcg #dic #dhc #bj #ej #jj #jjj #cah #bcf ,by averaging end areas we have #ej #fi #c1dej #ej #bdd #ab1bjj #ej #dic #bd1fej #ej #cah #ae1ijj ,sum1 #ef1bjj4 ,and by the prismoidal formula1 #ej #cje #ej #a1beg #ej #b1ffi #ej #a1gee ,sum #bii1cjj #f #di1jjj1 and #ef1bjj - #di1jjj #g1bjj cubic feet in favor of the method of end areas4 #aji4 ,the prismoidal formula is algebraically 77a a #d;a7_/#f7,l c1 when ,l length1 c cubic contents1 a area of one end1 a area of other end1 a middle area2 or1 verbally1 to the sum of the end areas add four times the middle area1 and multiply the result by one sixth of the length2 the middle area being the area made upon the mean height of the two ends4 ,thus if the length is one hundred feet1 and one end ten feet high1 the other twenty feet high1 and slopes one and a half to one1 the cubic amount is1 7the base being twenty-two feet17 77#bb #bb #cj7_/b #aj7 77#bb #bb #fj7_/b #bj7 77#bb #bb #de7_/b #ae #d7 #ajj4_/f ,,excavation ,,and ,,embankment4 #aaj4 ,some writers have considered that the grades of a road should be so adjusted as to equalize the cutting and the filling4 ,the total rise and fall might not be much affected by this1 but the mechanical effect of grades might4 ,a perfect balance between the cuts and fills is not to be desired4 ,the whole cost of earthwork must be a minimum1 and it is often cheaper to waste and borrow1 than to make very long hauls1 and to form the grade line by interchange of material on the profile only4 #aaa4 ,the transverse slopes depend upon the nature of the soil in which the cut is made4 ,gravel will stand at a slope of one and a half horizontal to one vertical1 and in some cases one and a quarter1 or even one to one4 ,clay stands nearly vertical for some time1 but finally assumes a very flat slope1 in some cases two1 three1 and even four horizontal to one vertical4 ,in places where a stratum of clay underlies more reliable earth1 to avoid a very long slope1 it may be economical to support the clay by a wall1 and to slope the earth only4 #aab4 ,care should be taken in every case to secure good drainage and to protect the slopes by surface drains at the top4 ,the drains in long cuts should be slightly inclined to insure the running off of the water4 ,a fall of ten feet per mile is enough2 five will answer in many cases4 ,on side hill cuts a surface drain along the top of the upper slope will do good service4 ,on many high embankments1 catchwater drains1 commencing at the road-bed and gradually sloping to the base1 will prevent1 in a great degree1 cutting of the bank4 #aac4 ,embankments1 when made rapidly1 should be finished to the full width1 somewhat above true grade1 to allow for the after settlement4 7,see specification47 #aad4 ,the following allowances have been made for the shrinkage of material in some parts of ,america4 ,light1 sandy earth #j4ab ,clayey earth #j4aj ,gravelly earth #j4jh ,gravel and sand #j4ji ,loam #j4ab ,clay #j4aj ,clay puddled #j4be ,wet surface earth #j4ae ,the bulk of quarried rock on the contrary increases from twenty-five to fifty per cent4 #aae4 ,when embankments are carried up slowly1 in layers of three or four feet at a time1 the after settling is very little2 when carried up all at once it will be more4 ,the full width must be kept1 even above the required height4 ,fig4 #ef shows the forms of a bank both before and after settlement4 ,illustration3 ,fig4 #ef4 ,the best method of forming a bank of bad material is to ram the layers as in fig4 #eg2 thus the tendency is to consolidate by settling1 and not to destroy the work by sliding4 ,illustration3 ,fig4 #eg4 ,,transport ,,of ,,material4 #aaf4 ,in the formation of embankments it is not always advisable to make the whole bank from an adjoining cut or cuts4 ,the length of haul may be too long4 ,in this case it is customary to waste a part of the cut and to borrow earth from some nearer point for the bank4 ,that the transport shall be effected in the most economical manner1 the product of the cube of earth1 by the mean distance1 7the distance between the centres of gravity1 of excavation and embankment7 must be a minimum4 ,to determine the theoretical minimum expense1 the problem becomes very complicated on account of the great number of variable elements entering therein2 and the result obtained is applicable only to a particular case4 ,local circumstances more than any other thing1 determine the position of a borrow pit1 and the path over which the material is to be transported4 ,,of ,,the ,,average ,,haul4 #aag4 ,to find the cost of the movement of earth on any section1 we must have1 the total amount of earth to be moved1 and the average haul2 the latter being the distance through which1 if the whole amount were moved1 the cost would be the same as the sum of the costs of moving the partial amounts their respective distances4 ,to find the average haul proceed as follows3 ,first1 find the distance between the centres of gravity of each mass both before and after moving1 which may be done with sufficient accuracy for practice by inspection of the profile4 ,next1 #aah4 ,divide the sum of the products of the partial amounts by their respective hauls1 by the total amount2 the result is the average haul in feet4 ,or algebraically1 representing the partial amounts by m1 m1 m1 m1 the respective hauls by d1 d1 d1 d1 the total amount by ,s1 and the average haul by ,d1 we have 7md md md md7_/,s ,d4 ,example4--,let column #a show the partial amounts in cubic yards4 ,column #b the corresponding hauls4 #a1jjj #bjj #bjj1jjj #b1jjj #cjj #fjj1jjj #e1jjj #djj #b1jjj1jjj #h1jjj #fjj #d1hjj1jjj ------------ ------------------ #af1jjj #g1fjj1jjj and #g1fjj1jjj_/af1jjj #dge feet average haul4 ,proof4--,assume the cost of moving #a1jjj yards one foot as ten cents1 the costs of the separate masses are #a1jjj yards #bjj feet is #bj4jj #b1jjj yards #cjj feet is #fj4jj #e1jjj yards #djj feet is #bjj4jj #h1jjj yards #fjj feet is #dhj4jj -------------- ,sum1 #gfj4jj also the cost of moving #af1jjj yards #dge feet is #af #dge #aj #gfj4jj4 #aai4 ,the movement of earth is effected by shovels1 barrows1 horses and carts1 or by cars4 ,in round numbers we can move earth ,by shovels alone #aj to #bj feet1 ,by barrows alone #bj to #ajj feet1 ,by carts #ajj to #ejj feet1 ,by cars #ejj to #e1jjj feet1 ,as the haul increases1 the number of vehicles of transport remaining the same1 the number of excavators must decrease4 ,earths easily removed do not admit of so large a haul1 with a given number of excavators1 as hard earths4 ,the nature of the ground1 form of carts1 kind of horses1 season of the year1 and price of labor are some of the elements entering the problem of transport4 ,the best illustration of the matter will be found among the very able writings of ,ellwood ,morris1 ,esq41 ,c4 ,e41 in the ,journal of the ,franklin ,institute4 ,knowing the value of wages1 the nature of the earth and length of haul1 it is easy to see what mode of transport must have the preference4 ,,contractor',s ,,measurements4 #abj4 ,the price of executing any piece of work is paid to the contractor at stated intervals1 generally once each month4 ,the amount of work done at these partial payments is obtained by instrumental reference to the ground4 ,towards the completion of operations the most correct and easiest method of finding the rate of progress is to deduct the amount already done from the total as given by primary measurement4 ,the full price is not paid to the contractor1 but a percentage is kept back1 which insures a faithful performance of work4 ,it is impossible to establish a pro rata price at first1 owing to the uncertain nature of the work2 what appears to be earth may be rock4 ,by deducting a maximum price estimate for all but one of the items1 an approximate pro rata value for that one may be determined4 ,an analysis of cost will define the minimum limit for advantage to the contractor2 and the pro rata value less the percentage1 the maximum for the company's benefit4 ,,draining4 #aba4 ,when a level is to be drained1 or the water carried off from the surface of a swamp1 the first point to be ascertained is the location of the lowest outfall4 ,the direction in which aquatic plants lie show the natural fall of the water1 these always pointing down stream4 ,when the most available outlet has been decided upon1 a main drain should be set out1 from which oblique branches are to be cut1 pointing in the direction of the current2 into these all minor cuts are to be collected so that the whole district may be equally drained4 ,the fall should be greatest at the most remote points1 decreasing as the amount of water increases4 ,large and deep rivers run sufficiently fast when the fall is one foot per mile4 ,for small rivers1 double that is necessary4 ,ditches and ordinary drains require eight feet per mile4 ,when the water is made to pass away from the surface1 it should flow very gradually1 that the sides and bottom of the ditches may not be worn away by friction2 it should be in constant motion that the channel may be kept clean and increase in velocity as it proceeds4 ,when the surface is a perfect level1 the drains should of course be made straight4 ,after the quantity of water has been determined by careful observation1 the section of the main and branches must be fixed1 so that regarding both their areas and velocities1 the main drain will not be overcharged4 ,to facilitate the current1 the sides should be inclined about one and a quarter to one2 and the breadth of base should be two thirds of the depth of water4 ,these results are obtained from the practice of ,english engineers1 who have given a great deal of attention to the subject4 ,drains cut through bogs1 may have sides nearly1 if not quite vertical1 as the fibres of plants forming the soil resist the action of the water4 ,,subsoil ,,draining4 ,geology has assisted this operation very materially by rendering us acquainted with the quality and nature1 as well as of the succession of strata4 ,the soils which are impervious are usually the heaviest1 and the porous are those of lighter quality4 ,clays1 when they receive water1 will only part with it by evaporation1 when left in a natural state2 and therefore to make such a surface fit for a useful end requires considerable ingenuity1 and often great expense4 ,such a soil is not rendered unstable by underground springs1 and may be effectually drained by boring through1 and letting the water off into an under stratum1 when this is of a porous nature4 ,when land abounds with springs1 or is subject to the oozing out of subterraneous water1 draining is effected in a different manner4 ,springs have their origin in the accumulation of rain water1 which falling upon the earth1 after passing the porous strata1 lodges upon the impervious1 and glides along the sloping surface until it crops out1 generally in some valley where it forms a watercourse4 ,descending streams are easily taken care of by collecting them into a body before they reach the low lands4 ,when a morass is to be drained1 the strata upon which it reposes should be examined1 and if1 as is often the case1 a layer of clay intervenes between the substratum and the mossy covering1 which holds the water1 by tapping this in well chosen places1 the whole will sink away4 ,a fine example of embankment upon a bad bottom was performed by ,mr4 ,stephenson1 on the ,great ,western ,railroad1 ,england1 at the crossing of ,chatmoss4 ,this moss was so soft that cattle could not walk upon it1 and an iron bar sank into it by its own weight4 ,the moss was first thoroughly drained by a system of longitudinal and cross drains1 and the embankment made of the lightest material possible--the dried moss itself4 ,without this treatment1 the moss would have sank beneath the bank alone2 it now supports the passage of the heaviest railroad trains4 ,,method ,,of ,,conducting ,,operations4 #abb4 ,the organization of the engineer corps upon a railroad is as follows1 differing somewhat in different parts of the country4 ,the ,chief ,engineer has entire charge of all the work1 of all assistants1 appointing and dismissing members of the corps1 designing of all structures1 making of specifications1 and of all mechanical operations incident to the thorough1 correct1 and timely construction of the road2 and should be able also to specify1 generally1 the amount and character of the equipment needed4 ,the ,resident ,engineer has charge of the detailed construction of from twenty-five to fifty miles of road1 according to the nature of the work1 being responsible to the chief engineer for the proper execution of the orders from headquarters2 he returns to the chief engineer a monthly account of the exact condition of his work1 both as to the amount executed1 and also that remaining to be done4 ,the assistants of the resident engineer are a leveller and transit man2 to whom1 under his supervision1 is the duty of laying out1 measuring1 and estimating the work4 ,the leveller has with him one or more rodmen4 ,the transit man1 two chainmen1 and one or more axemen4 ,in some cases1 added to the above are inspectors of masonry1 bridging1 and superstructure4 ,these are necessary only when the road embraces a great number of mechanical structures2 too many to leave the proper time to the resident engineer for his other duties4 ,once each month the exact amount of graduation1 bridging1 and masonry executed is obtained by the resident and his assistants4 ,the chief engineer applies the prices to these amounts1 and the percentage deduction being made1 the estimate is ready for the treasurer4 #abc4 ,the abstract prepared from the monthly estimate should show clearly1 without unnecessary figures1 the amount of work completed1 and also that remaining to be done4 ,for convenience1 the various blanks used on railroads should fold to the same form and size4 ,the blanks are1 ,the ,contract1 ,the ,specification1 ,the ,resident ,engineer's ,monthly ,return1 ,the ,assistant's ,weekly and ,monthly ,returns1 ,the ,force ,return1 ,the ,pay ,roll1 ,vouchers4 ,the contract and specification are given in chapter ,,iv4 ,the resident's monthly return to the chief engineer is somewhat as follows3-- ,monthly return of work done on the first division of the ,a and ,b ,railroad1 for the month ending ----1 showing also the whole amount of work up to ----2 also the present estimate for completion4 ,section4 ,contractor4 #a ,,graduation4 ,clearing and ,grubbing4 ,excavation4 ,in ,july4 ,total to date4 ,in ,july4 ,total to date4 ,acres4,price4,am't4,acres4,pr4,am't4,ya rds4,pr4,am't4,yards4,pr4,am't4 #ae #ajj #aejj #cjj #ajjcjjjjddjjj #aj #ddjj #ajjjjjaj #ajjjj ,,masonry4 ,foun- ,foun- ,first ,class4 ,second ,third dation in dation ,class4 ,class4 ,excava- ,timber4 tion4 ,in ,tot4 ,in ,tot4 ,in ,tot4 ,in ,tot4 ,in ,july4 ,total to date4,ju- to ,ju- to ,ju- to ,ju- to ly4date4ly4date4ly4date4ly4date4 ,yds4,pr4,am't4,yds4,pr4,am't4 ,,bridging ,,and ,,timberwork4 ,truss ,bridges4 ,pile ,stringer ,trestling4 ,bridges4 ,bridges4 ,in ,july4 ,total to date4 ,feet4 ,c4 ,am't4,feet4 ,c4 ,am't4 ,,superstructure ,,and ,,fencing4 ,superstructure4 ,fencing4 ,in ,total ,in ,july4 ,total to date4 ,july4 to date4 ,miles4 ,price4 ,am't4 ,miles4 ,price4 ,am't4 ,,value ,,of ,,work ,,and ,,payments ,,made4 ,value of ,work ,amount paid ,whole value ,whole amount ,amount left in ,july4 in ,july4 to date4 paid4 due4 ,,value ,,of ,,labor4 ,foreman and ,laborers4 ,carts with ,carts with ,whole value4 ,mechanics4 ,horses4 ,oxen4 ,,recapitulation4 ,value of work done in ,value of work up to ,remaining ,value4 ,july4 date4 ,the resident engineer's assistants return to him weekly a statement of the amount and value of the force employed upon the several sections1 and monthly the exact amount of work done on the same1 for each of which there should be a blank4 ,the above forms may be printed and folded in #hvo41 or may be the continuous headings of a large sheet4 ,,chapter ,,vii4 ,,rockwork4 ,,rock ,,excavation4 #abe4 ,the sides of rock excavation are sometimes cut to a small slope1 as one fourth or one fifth horizontal to one vertical1 and sometimes cut quite perpendicularly4 ,the earth1 when it occurs1 which covers the rock1 is first taken out at the proper slope2 a berm of one or two feet being left between the foot of the earth and the crest of the rock4 #abf4 ,rock is taken out one or two feet below grade1 as well as earth1 to allow the introduction of the necessary ballast4 ,,blasting ,,and ,,quarrying4 #abg4 ,the most common mode of removing rock is by blasting2 for this holes are drilled by steel-edged jumpers1 worked either by hand or by steam4 ,the first object in cutting a passage through rock1 is to open a working face1 so as to get the necessary lines of least resistance1 7this line is that by which the powder finds the least opposition to a vent at right angles to the length of the drill72 these lines should1 if possible1 be at right angles to the beds of stratification2 the holes should be drilled parallel to the seams of the rock1 as the powder will then lift off the strata4 ,in working a vertical face1 it may be best to blast out the lower part first1 and so undermine the overhanging mass4 #abh4 ,the amount of powder in different charges to produce proportional results should be as the cube of the line of least resistance2 for example3-- #bc is to #d oz4 as #cc is #ac oz41 or #h to #d as #bg to #ac2 and generally1 ,l#c 3 w 33 ,l#c 3 w2 whence w 7w,l#c7_/,l#c4 #abi4 ,the following charges corresponding to lines of least resistance are from the works of ,sir ,john ,burgoyne4 ,line of least resistance4 ,charge of powder4 #b feet1 #j lbs4 #d oz4 #d feet1 #b lbs4 #j oz4 #f feet1 #f lbs4 #ab oz4 #h feet1 #af lbs4 #j oz4 #acj4 ,after the powdered stone is removed1 the powder is placed in the lower part of the hole2 after which a wad of turf1 or some other light material1 follows2 next the tamping of powdered brick1 dried clay1 or something similar1 and finally a stopper of wet clay1 or some other firm substance4 ,a hole is left through all1 communicating with the powder by ramming the tamping around a wire2 through this hole a fuse is inserted by which to light the charge4 ,the most perfect tamping would offer a resistance as great as that by the natural rock4 ,a great improvement upon the above method is the sand blast2 the powder is put in1 and the hole filled with loose1 dry sand1 simply poured in and settled by a gentle stirring1 but not at all rammed2 the explosion of the powder spreads the sand as a wedge1 and causes the power of the blast to be exerted sideways4 ,in some cases a small cone of wood has been placed 7base down7 in the hole with the sand1 which aids very much in stopping the exit of the blast through the drill4 #aca4 ,of late years an admirable method of lighting large charges simultaneously has been employed1 namely1 voltaic electricity4 #acb4 ,a gigantic example of the application of this method has been furnished by the ,english engineers in overthrowing a portion of ,round ,down ,cliff1 about two miles from ,dover1 7,england74 ,two chambers1 #ac #e #d1 and one #aj #e #d feet were cut in the rock4 ,within these were placed fifty bags of powder1 amounting in all to eight and one half tons4 ,the charges were lighted by the voltaic system1 by which operation a mass of rock 7chalk7 #chj #cfj #hj feet1 amounting to #djj1jjj cubic yards1 was thrown into the sea1 and by which there was estimated to have been saved nearly #dj1jjj4 #acc4 ,the following table from ,colonel ,pasley's memoranda on mining1 shows the capacity of different drills for powder1 by weight1 and also the depth of holes of different diameters1 to contain one pound of powder4 ,diameter of hole ,ounces of powder ,powder in one ,depth of hole in in inches4 in one inch foot deep4 inches to contain depth4 one pound4 lbs4 oz4 #a #j4d #j #e4j #ch4b #a #j4i #j #aa4c #af4i #b #a4g #a #d4a #i4e #b #b4f #a #ae4d #f4a #c #c4g #b #ac4b #d4b #c #e4a #c #ac4e #c4a #d #f4g #e #j4d #b4d #d #h4d #f #e4g #a4i #e #aj4e #g #ac4f #a4e #e #ab4g #i #h4j #a4c #f #ae4a #aa #d4i #a4j #acd4 ,blasting under water has been practised to some extent1 and with great success by ,messrs4 ,maillefert and ,raasloff1 both in ,new ,york harbor and in the ,st4 ,lawrence ,river4 ,the method is merely to explode bodies of powder upon the surface of the rock1 the water itself being a sufficient source of reaction to the blast4 ,,tunnelling4 #ace4 ,tunnels are driven through hills to avoid very deep cutting4 ,when in rock of a solid nature1 the roof supports itself2 but when in earth or in loose rock1 an artificial arched lining becomes necessary4 ,figs4 #eh and #ei show sections in both rock and earth2 the invert b b is placed in a bed of concrete4 ,in excavating earth1 a temporary roof is made use of while the work is in progress1 which is afterwards replaced by an arch of brick or stone4 ,the back of the arch must be closely wedged1 grouted1 and the earth well rammed in4 ,illustration3 ,fig4 #eh4 ,illustration3 ,fig4 #ei4 ,the great disadvantages attending the construction of tunnels are want of air1 light1 room1 and drainage4 ,to facilitate the latter requirement1 a very light grade may be introduced2 this may easily be done1 as they generally occur on summits1 or on the approach to summits2 #a_/ajjj or five feet per mile is sufficient4 ,in working a tunnel which is upon a grade1 one end naturally drains itself if the approach is taken out2 the other drains the wrong way1 to meet which obstacle we must resort to pumps which follow the work1 keeping always in the lowest place1 or by sinking a well at the shaft through which the water is raised to the surface4 ,the ventilation of tunnels is effected by drawing off the bad air when a fresh supply must enter4 #acf4 ,in taking out the rock1 the expense will depend much upon the nature and stratification of the rock encountered4 ,,shafts4 #acg4 ,in tunnels of considerable length1 a long time would be consumed in working from the ends only4 ,in such cases it is customary to sink shafts at the most convenient places 7the shallowest when at the proper distance17 and to commence at the bottom of these to work both ways4 ,this operation involves considerable expense1 as all draining1 ventilating1 and removal of excavated materials must be effected through the shaft4 ,in leaving openings for the exit of smoke and for admission of light in artificial arches1 regard must be had to their position4 ,they should be at the springing rather than at the crown of the arch1 as they will thus less affect the strength of the masonry4 ,the approaches of tunnels in cities and in other places where appearance is of importance1 are finished with face coping and wings4 #ach4 ,tunnels1 when conducted in the most expeditious manner1 require for their completion a long time4 ,the following table shows the rate of progress upon some of the most important tunnels of ,america4 ,name of ,tunnel4 ,average daily ,length in advance1 in feet4 ,time in days4 feet4 99,penn ,railroad1 #c1fab #fig #e4ah 99,kingwood ,b4 ,o4 ,r4 ,r4 #d1ajj #gej #e4dg ,board ,tree ,b4 ,o4 ,r4 ,r4 #b1bej #fge #c4cb 99,welling1 ,b4 ,o4 ,r4 ,r4 #a1bdj #ebd #b4cg ,pacific ,railroad1 #gjj #baj #c4cc ,pittsburgh and ,connelsville1 7estimated7 #d1ejj #haj #e4ef ---------- ,general average daily advance1 in feet1 #d4bje ,those marked 99 being for a double track4 ,the following table also gives the time and cost of other tunnels in different parts of the world4 ,name and ,material4 ,daily location of ,length,time average ,cost tunnel4 in in in per feet4 days4 feet4 ,section4 foot4 ,nerthe1 ,france1 ,hard limestone#ae1aec ---- #bi #bf ,riqueral1 ,chalk ,france1 #ah1fbcb1aci #h4gbf #bf #ci4hi ,pouilly1 ,france1,chalk clay #aj1ibhb1ejd #d4dbj #bjaac4if ,arscherville1 ---- ,france1 #g1cdha1hgh #c4ibf #bf #fh4ch ,maurage1 ,france1---- #ae1gebb1jhe #g4ebe #be #id4dc ,rolleboise1 ,chalk ,france1 #h1fgj #fbf #ac4ibe #be #fb4ih ,roule1 ,france1 ---- #e1fde #ebb #aj4hbe #be #fb4ih ,lioran1 ,france1 ---- #d1edhb1jhg #b4bba #ba #ef4ih ,kilsby1 ,england1,clay and sand #g1bcca1beb #e4hbg #bcaid4ca ,belchingly1 ,blue clay ,england1 #c1igb #fbf #f4cbd #be #ajb4hf ,thames ,medway1,chalk ,eng'd1 #aa1hhj #ici #ab4fcj #ch #de4ei ,box1 ,england1 ,marble1 freestone and marl #i1fhja1beb #g4gce #ci #adh4ae ,harecastle1 ,rock and sand ,england1 #h1ggh #ici #i4cad #af #eg4je ,nochistongo1 ,clay and marl ,mexico1 #ba1fei #bhg #ge4dac #aa ---- ,blisworth1 ,rock and clay ,england1 #i1bdjb1aia #d4baf #ah #bc4ah ,sapperton1 ,rock ,england1 #ab1ijja1hgh #f4iae #ae #ab4dd ,black ,rock1 ,u4 ,greywacke ,s4 slate #a1icb ---- ----#ai #ag #gg4ah ,blaisy1 ,france1 ,chalk and clay#ac1deea1jdc #ab4ibf #bfacf4jf ,edge ,hill1 ,clay ,england1 freestone #f1fjj ---- ----#bb #af #cj4ae ,littlebourg1 ---- ,england1 #h1fjg #eij #ad4fbg #bd #abi4fa ,woodhead1 ,millstone ,england1 #ae1hdja1hjj #h4h ---- ---- ,the cost per cubic yard for excavating tunnels in some places has been as follows3-- ,name4 ,material4 ,cost per cubic yard4 ,blackrock1 ,u4 ,s4 hard greywacke slate1 #f4fj ,lehigh1 ,u4 ,s4 very hard granite1 #d4cf ,schuylkill1 ,u4 ,s4 slate1 #b4jj ,union1 ,u4 ,s4 slate1 #b4jh ,blue ,ridge1 ,u4 ,s4 ----1 #d4jj ,the ,blue ,ridge tunnel on the ,virginia ,central ,railroad is #d1bhj feet long1 made for a single track1 #ba #ae feet4 ,lining about four feet thick4 ,excavation where lining is used is #bf #bc4 ,the ,hoosac tunnel 7,massachusetts7 is proposed to be four and one half miles long1 #bc #bb feet section4 ,to have two shafts eight hundred and fifty and seven hundred and fifty feet deep1 and ten feet in diameter4 ,artificial ventilation becomes necessary in headings over four hundred and fifty or five hundred feet in length4 ,the cost of the shafts of the ,blechingly tunnel1 7,england17 ninety-seven feet deep1 and ten and one half feet in diameter1 cut through blue clay1 and lined1 was #fh4dd per yard down4 ,the shafts of the ,blaisy tunnel average five hundred feet deep1 through clay and chalk and loose earth1 7being lined17 cost #aci4aa per yard down4 ,the shafts of the ,black ,rock tunnel1 one hundred and thirty-nine feet deep1 in hard slate1 cost #ah4gb per cubic yard4 ,,chapter ,,viii4 ,,wooden ,,bridges4 #aci4 ,wooden bridging1 owing to its cheapness and fitness for universal application1 has been and is being adopted in all parts of the country4 ,almost any variety of form may be seen upon our railroads1 and though less durable than stone or iron1 it may with proper precaution be made to last a long time4 ,,of ,,the ,,forces ,,at ,,work ,,in ,,bridges4 #adj4 ,there are four distinct strains to which a piece of timber or a bar of metal may be exposed1 each of which tends to destroy the piece in a different manner4 ,the amount and character of these strains1 depend upon the position of the bar or beam1 and upon the direction of the force4 ,a beam may be pulled apart by stretching1--,tension4 ,it may be destroyed by crushing1--,compression4 ,it may be broken transversely1--,cross strain4 ,it may be crushed across the grain1--,detrusion4 ,,tension4 #ada4 ,if one thousand pounds were hung from the end of a suspended timber1 so that the direction of the weight coincides with the axis of the timber1 then will the tension upon the beam be one thousand pounds4 ,if the direction of the force is vertical1 and the beam is inclined1 then the strain is increased by as much as the diagonal of inclination exceeds the vertical2 for example1 let one thousand pounds be suspended from the lower end of a beam ten feet long1 inclined at an angle of #de4 ,the diagonal being ten1 the vertical will be #g4jg feet1 and the strain is increased as follows3-- #g4jg to #aj as #a1jjj to #a1dad lbs4 ,as the angle of inclination1 from the horizontal1 increases1 the strain from a given load decreases1 until the beam is vertical1 when a weight acts with its least power4 ,,compression4 #adb4 ,if a vertical post is loaded with one thousand pounds1 the compressive strain upon that post will also be one thousand pounds4 ,if a post is inclined1 the amount of strain is increased1 as noticed in the case of tension1 and to the same amount1 that is1 depending upon the inclination4 ,a piece of wood or metal acting as a post1 or pillar1 must not only be able to resist crushing1 but also bending or bulging laterally4 #adc4 ,a cylinder of which the length is only seven or eight times the diameter1 will not bulge by any force that can be applied to it longitudinally1 but will split4 ,when the length exceeds this1 it will be destroyed by a similar movement to that produced by a cross strain4 ,when the length of a cast-iron pillar is thirty diameters1 the fracture is produced by bending alone2 when less1 partly by bending and partly by fracture4 ,when the column is cast hollow1 and enlarged towards the middle1 the strength is increased in a very great ratio4 #add4 ,the formula for finding the weight which any beam acting as a post1 will support before bending1 is1 according to ,barlow1 who considers the weight as varying inversely as the length1 as follows3-- 7,,wl#b7_/7hj;,e7 bd#c1 and the value of ,w is 7bd#c #hj;,e7_/7,l#b71 and the weight being given1 and the sectional dimensions assumed1 we have d 77,,wl#b7_/7hj;,eb771 and b 7,,wl#b7_/7hj;,ed#c71 ,where ,w represents the weight in pounds1 ,l represents the length in feet1 ,e represents a constant1 d represents the depth in inches1 b represents the breadth in inches4 ,,cross ,,strain4 #ade4 ,the amount of strain caused by any weight applied in a transverse direction1 to a beam supported at both ends1 is as the breadth1 as the length inversely1 and as the square of the depth4 ,whatever depression takes place1 tends to shorten the upper1 and to extend the under-side2 whence the fibres of the top part suffer compression1 and those of the bottom extension4 ,the amounts of compression and extension must of course be equal1 and therefore if any material resists these two strains in a different degree1 the number of fibres opposing each will also be different4 ,the top being compressed1 while the bottom is extended1 of course at some point within the beam there exists a line which suffers neither compression nor extension4 ,the position of this line 7the neutral axis7 depends upon the relative power of the material to oppose the strains1 upon its form and upon its position4 ,thus if wood resists two thousand pounds per square inch of extension1 and one thousand pounds of compression1 the axis will be twice as far from the top as from the bottom4 ,in some materials the neutral axis changes its place while the bar is at work2 thus wrought iron1 after being a little compressed1 will bear a great deal more compression than when in its original state2 also the lower fibres1 after being extended1 will resist less than at first2 the effect of which two actions is to move the neutral axis up4 #adf4 ,the following table shows the relative resisting powers of wood1 wrought and cast-iron2 with the corresponding positions of the axis1 with sufficient accuracy for practice4 ,distance of axis ,material4 ,resistance to ,resistance to ,ratio4 from top1 in extension4 compression4 fractions of the depth4 ,wrought iron1 #ij #ff #ij_/ff #ij_/aef or #j4eh ,cast-iron1 #bj #aaa #bj_/aaa #bj_/aca or #j4ae ,wood1 #b #a #b_/a or #j4ff ,thus in beams subjected to a cross strain1 as well as to a direct extensile or compressive one1 the resistance is effected by the incompressibility and inextensibility of the material4 #adg4 ,the formula for dimensioning any beam to support a given weight transversely is ,s 7#d;bd#b7_/;e1 ,where ,s represents the ultimate strength in lbs4 b represents the breadth in inches1 d represents the depth in inches1 e represents the length in inches1 ,,detrusion4 #adh4 ,detrusion1 or crushing across a fixed point1 is such as occurs wherever a brace abuts against a chord1 or where a bridge bears upon a bolster or wall plate2 also the shearing of bolts1 pins1 and rivets4 ,,general ,,resistance ,,of ,,materials4 #adi4 ,the resistance to extension1 to compression1 7as regards simple crushing17 and to detrusion1 is as the area of cross section2 i4 e41 if we double the area1 we double the strength4 ,the resistance to a cross strain is as the breadth1 as the length inversely1 and as the square of the depth2 i4 e4 if we double the breadth we double the strength2 if we double the length1 we divide the strength by two2 and if we double the depth1 we multiply the strength by four4 ,,actual ,,strength ,,of ,,materials4 #aej4 ,any material will bear a much larger load for a short time than for a long one4 ,the weight that does not so injure materials as to render them unsafe1 is from one third to one fourth only of the ultimate strength4 ,throughout the present work one fourth will be the most that will in any case be used4 ,,wrought ,,iron4 #aea4 ,extension4 lbs4 per square inch4 ,mean of #ag experiments by ,barlow 7p4 #bgj7 #fb1gbj ,weisbach's ,mechanics 7,vol4 ii41 p4 #ga7 #fj1ejj ,overman's ,mechanics1 7p4 #djh1 #dji7 #fa1ccc ,brown1 ,rennie1 and ,telford1 7mean7 #fe1bea ------------ ,the mean #fb1dea ------------ ,reducing by #d for safety #ae1fac ,or in round numbers #ae1jjj lbs4 per square inch1 is the resistance of wrought iron to extension1 to be used in practice4 #aeb4 ,compression4--,great discrepancies appear among writers on the strength of materials1 as to the compressive strength of wrought iron4 ,though all estimate the resistance to compression1 as great as to extension1 yet no one in summing up the general result of experiment1 places the former at more than from #ej to #ge per cent4 of the latter4 ,william ,fairbairn gives1 as the relative resistances to extension and compression in bars applied as girders1 #b to #a4 ,we have by ,weisbach #ef1jjj ,we have by ,rondelet #gj1jjj ,we have by ,hodgkinson #fe1jjj ------------ ,the mean #fc1ffg ------------ ,reducing by #d #ae1iag ------------ ,in round numbers #af1jjj lbs4 per square inch4 ,as far as practice is any guide1 from #h1jjj to #ab1jjj pounds per inch is the most to be used4 ,the ratio of #ij to #ff1 seems to express very nearly the action as in the most reliable structures2 which will1 therefore1 be adopted1 or #aa1jjj pounds per square inch nearly4 ,the resistance to compression is very much greater after wrought iron has been somewhat compressed4 ,,cast-,,iron4 #aec4 ,extension4--,this material is seldom used to resist a tensile force4 ,that the tables may be complete1 however1 the following is given3-- ,by ,weisbach #bj1jjj pounds4 ,by ,barlow #ah1bcc pounds4 ,by ,overman #bj1jjj pounds4 ,by ,rennie #ah1jjj pounds4 ,by ,hodgkinson #af1egg pounds4 ,by the ,british ,iron ,commission #ae1gaa pounds4 ------------ ,the mean #ah1jhg pounds4 ------------ ,reducing by #d #d1ebb pounds4 ------------ ,in round numbers #d1ejj pounds4 #aed4 ,compression4 ,by ,weisbach #aji1hjj pounds4 ,by ,hodgkinson #ajg1ebj pounds4 ,by ,iron ,commission #ajj1jjj pounds4 ,stirling's toughened #acj1jjj pounds4 -------------- ,mean of ,common #aje1ggc pounds4 -------------- ,mean of ,stirling's #acj1jjj pounds4 -------------- ,reducing by #d for safety 7,common7 #bf1ddc pounds4 -------------- ,reducing by #d for safety 7,stirling's7 #cb1ejj pounds4 -------------- ,in round numbers 7,common7 #be1jjj pounds4 -------------- ,in round numbers 7,stirling's7 #cj1jjj pounds4 #aee4 ,following are given the condensed results of the preceding figures1 which may be relied upon as giving perfectly safe dimensions in practice4 ,wrought ,iron4 ,cast-,iron4 #ae1jjj #d1ejj ,tensile strength1 #aa1jjj #be1jjj ,compressive strength4 ,for additional remarks on iron1 see chap4 ,,ix4 #aef4 ,nature and ,strength of ,american ,woods4 ,name of the ,weight per ,resistance ,resistance ,value of wood4 cubic foot4 to to ,s4 ,elasticity4 ,extension4 ,compression4 ,white ,pine #bf #ab1jjj #f1jjj #a1bbi ---- ,yellow ,pine #ca #ab1jjj #f1jjj #a1ahe ---- ,pitch ,pine #df #ab1jjj #f1jjj #a1gbg #d1ijj ,red ,pine #ce #ab1jjj #f1jjj #a1ebg #g1cei ,virginia ,pine #cg #ab1jjj #f1jjj #a1def ---- ,spruce #dh #ab1jjj #f1jjj #a1jcf ---- ,larch #cc #ab1jjj #f1jjj #ijg #b1dfe ,tamarack #bf #ab1jjj #f1jjj #ijg ---- ,white ,cedar #bb #h1jjj #d1jjj #gff ---- ,canada ,balsam #cd #ab1jjj #f1jjj #a1abc ---- ,white ,oak #dh #ae1jjj #g1ejj #a1gdc #h1eie ,red ,oak #da #ae1jjj #g1fjj #a1fhg ---- ,live ,oak #gb #ae1jjj #g1bjj #a1hfb ---- ,white ,beech #dd #ah1jjj #i1ajj #a1chj #e1dag ,red ,beech #dh #ah1jjj #i1jjj #a1gci ---- ,birch #dd #ae1jjj #g1jjj #a1ibh ---- ,black ,birch #da #ae1jjj #g1bjj #b1jfa ---- ,yellow ,birch #cf #ae1jjj #g1bjj #a1cce ---- ,ash #ch #af1jjj #h1ajj #a1gie #f1eha ,black ,ash #ce #af1jjj #h1jjj #hfa ---- ,swamp ,ash #eg #af1jjj #h1jjj #a1afe ---- ,hickory #ea #ae1jjj #g1bjj #b1abi ---- ,butternut #ed #ae1jjj #g1fjj #a1dfe ---- ,ironwood #ed #af1jjj #h1ajj #a1hjj ---- ,rock ,elm #de #af1jjj #h1jaa #a1igj #b1gii ,the mean tensile strength of wood is #ad1jhj lbs4 ,reducing by #d for safety #c1ebj lbs4 ,reducing for want of seasoning #b1jjj lbs4 ,the reduced mean compressive strength #a1jjj lbs4 ,reduced resistance to detrusion #aej lbs4 ,ratio of tensile to compressive strength #b to #a4 ,mean value of ,s in formula 7,,wl #d,sbd#b7 for the woods most used in practice #a1bej4 #aeg4 ,the lateral adhesion of fir was found1 by ,barlow1 to be six hundred pounds per square inch4 7,lateral adhesion is the resistance which the fibres offer to sliding past each other in the direction of the grain2 as1 in pulling off the top of a post where it is halved on to the chord47 #aeh4 ,as regards the nature of timber1 seasoning1 time of cutting1 etc41 although these are important items1 still1 generally1 commercial considerations outbalance all else4 ,the most complete treatise on the nature of woods1 is 8,du ,hamel1 ,lexploitation des bois20 from which it appears that the best oaks1 elms1 and other large trees1 are the product of good lands1 rather dry than moist4 ,they have a fine1 clear bark1 the sap is thinner in proportion to the diameter of the trunk1 the layers are less thick1 but more adherent the one to another2 and more uniform than those of trees growing on moist places4 ,the grain of the latter may look very fine and compact1 but microscopic examination shows the pores to be full of gluten4 ,the density of the same species of timber1 in the same climate1 but on different soils1 will vary as #g to #e2 and the strength1 both before and after seasoning1 as #e to #d4 ,in trees not beyond their prime1 the density of the butt is to that of the top1 as #d to #c2 and of centre to circumference1 as #g to #e4 ,after maturity1 the reverse occurs in both cases4 ,oak1 in seasoning1 loses from to of its weight2 but its strength is increased from #cj to #dj per cent4 ,,general ,,table ,,of ,,the ,,nature ,,of ,,materials4 #aei4 ,the tensile strength of wrought iron assumed as #a1jjj4 ,weight ,sum divided ,material4 ,tension4 ,compression4 ,cross ,sum4 per by weight ,strain4 cubic per cub4 ft4 ft4 ,cast-,iron #cjj #a1fff #ca4fh #a1iig4fh #dej #d4d ,wrought ,iron #a1jjj #gcc #ee4dj #a1ghh4dj #dhj #c4g ,wood #acc #ff #e4fj #bjd4fj #cj #f4h ,the advantage possessed by iron over wood1 is in durability only4 ,the above figures show how much more of the strength of the material is consumed by its own weight in iron than in wood4 ,in actual practice1 however1 the method of making joints and other details often render iron the lightest material4 ,,rules ,,for ,,practice4 ,,tension4 #afj4 ,the tensile strength of any material1 is expressed by the formula ,t ,sa1 ,where ,t represents the whole strength1 ,s represents the strength per square inch1 a represents the area of section in inches4 whence the necessary area of section of any material to resist a tensile strain1 is found by the following rules3-- ,wrought ,iron a ,w_/#ae1jjj1 ,cast-,iron a ,w_/#d1ejj1 ,wood a ,w_/#b1jjj4 ,,compression4 #afa4 ,wrought ,iron a ,w_/#ab1jjj1 ,cast-,iron a ,w_/#be1jjj1 ,wood a ,w_/#a1jjj4 ,,cross ,,strain4 #afb4 ,the power of any material to resist a cross strain1 is shown by the formula ,w 7#dsbd#b7_/,l1 ,where ,w represents the breaking weight in pounds1 s represents the constant in the table of woods1 b represents the breadth in inches1 d represents the depth in inches1 and ,l represents the length in inches1 and to reduce the load to one fourth of the breaking weight ,w 7#dsbd#b7_/7d,l71 and finally1 by substituting for #ds1 #d #a1bej1 7#a1bej of the table of woods17 we have ,w 7#ejjj;bd#b7_/7d,l74 ,also1 knowing the weight to be supported1 and requiring the dimensions1 we take out the values of d and b1 and have d 77,w #d,l7_/7#ejjj;b77 the depth1 b 7,w #d,l7_/7#ejjj;d#b7 the breadth4 ,as an example of the use of the formula1 take the following3-- ,let the span1 or length1 be #bj feet1 ,the breadth #ab inches1 and depth #ah1 required the load4 ,the formula ,w 7#ejjj;bd#b7_/7d,l7 becomes ,w 7#ejjj #ab #ahb7_/d #bdj #bj1bej lbs4 ,again1 the weight to be supported being #ae1jjj lbs41 length #cj feet1 breadth #af inches1 the formula for the depth becomes d 77#aejjj #addj7_/7ejjj #af77 7#bgj7 #af inches1 also1 b 7#aejjj #addj7_/7ejjj #bef7 #bafjjjjj_/abhjjjj #af inches4 ,,cast-,,iron4 #afc4 ,the formula1 expressive of the strength of a cast-iron beam1 is #hej;bd#b ,,wl1 from which we have b 7,,lw7_/7#hej;d#b7 the breadth1 and d 77,l ,w7_/7#hej;b77 the depth4 ,,wrought ,,iron4 #afd4 #ieb;bd#b ,,wl1 whence b 7,,wl7_/7#gjj;d#b7 the breadth1 and d 77,,lw7_/7#gjj;b77 the depth4 ,illustration3 ,fig4 #fj4 #afe4 ,mr4 ,hodgekinson found1 that by arranging the material in a cast-iron beam1 as in fig4 #fj1 that the resistance per unit of section was increased over that of a simple rectangular beam1 in the ratio of #dj to #bc4 ,he makes the general proportion of such girders as follows3-- ,length #af ,height #a ,area of top flange #a4j ,area of lower flange #f4a ,in this consummate disposition of material1 the areas of top and bottom flanges are made inversely proportional to the power of cast-iron to resist compression and extension4 #aff4 ,mr4 ,fairbairn found1 that in wrought iron flanged girders1 7under which come the various rails1 chap4 ,,xiii417 the top web should contain double the area of the lower one4 ,this agrees with the conclusion adopted on page #abi1 as wrought iron resists more extension than compression4 #afg4 ,in cast-iron girders1 on no account should there be introduced webs1 or openings of any kind1 either from economic or ornamental motives2 as the uniformity of cooling is thereby very much opposed4 #afh4 ,mr4 ,hodgekinson gives1 as the result of his experiments1 the following formula for dimensioning the cast-iron girder above referred to4 ,w 7#bf;ad7_/,l1 ,where ,w is the breaking weight in tons1 a the area of the bottom flange1 d the depth of the girder in inches1 ,l the length in inches4 ,as it is not considered safe to load a cast-iron beam with more than one sixth of the breaking load1 the formula may be expressed as follows3-- ,w 7#bf;ad7_/#f,l1 for the weight in tons which may be safely borne1 and transforming a 7#f,,wl7_/#bf;d for the area of the lower flange4 ,example4--,required the dimensions of a cast-iron beam1 of ,mr4 ,hodgekinson's form1 for a span of thirty feet1 to support a load of ten tons at the centre4 ,span #cj feet1 ,whence-- ,length #cd feet1 ,length #cd feet1 ,load #aj tons at centre4 ,span #cj feet1 ,depth #be inches1 ,lower flange #cb4eh square inches1 ,upper flange #e4cd square inches1 a 7#f #aj #ab #cj7_/7bf 7#cd #ab7_/af7 #cb4eh and #cb4eh_/f4a #e4cd4 and the area of the top flange will be #cf_/f #f1 whence the following dimensions3-- ,length #cj feet1 ,depth #bc inches1 ,lower flange #cf square inches1 ,upper flange #f square inches1 ,,of ,,posts4 #afi4 ,a post may be very well able to resist the compressive strain thrown upon it by any load1 but may bulge1 or bend1 laterally4 ,the formula by which beams are dimensioned for this requirement1 changes with the material1 and with the form of section4 ,for rectangular posts of wood1 we have the formula below4 ,w 7#bbdj;bd#c7_/7,l#b71 ,where ,w represents the weight in lbs41 which may be safely borne1 b represents the breadth in inches1 d represents the depth in inches1 and ,l represents the length in feet4 #agj4 ,the value of the formula for the strength of cast-iron posts1 seems to depend more upon the authority consulted than upon the nature of iron4 ,for example1 assume the length of a post as twenty feet1 and the diameter as ten inches2 the load which may be safely borne is1 according to six different authorities1 as follows3-- ,a #d1jjj1jjj ,b #aha1ajj ,c #cgj1jjj ,d #idj1jjj ,e #cjg1bdb ,f #cjj1jjj and assuming the length as ten feet1 and diameter as ten inches1 we have ,a #h1jjg1ejj ,b #bjd1ejj ,c #a1ddb1ejj ,d #c1fdj1jjj ,e #a1agj1jjj ,f #fjj1jjj showing not only a great difference in the unit resistance taken1 but also in the effect of the ratio between the length and diameter4 ,such being the discrepancy1 there will be given no formula2 but in place of such1 the table following1 which is calculated from the rules least opposed to experimental evidence4 ,,table ,,showing ,,the ,,load ,,in ,,pounds ,,safely ,,borne ,,by ,,cast-,,iron ,,columns4 ,,hollow ,,cylinders4 ,diame- ,length or height in feet4 ter in inches #f #h #aj #ab #ae #ah #bj #bb #bd #b #fjjj #ejjj #djjj #cjjj #bejj #ahjj #aejj #acjj #aajj #c #afjjj #adjjj #acjjj #aajjj #ijjj #gjjj #fjjj #ejjj #ejjj #d #cjjjj #bijjj #bfjjj #bdjjj #bbjjj #ahjjj #afjjj #adjjj #acjjj #e #ejjjj #cgjjj #dejjj #dbjjj #cijjj #cgjjj #cajjj #bhjjj #bfjjj #f #eijjj #egjjj #eejjj #ebjjj #dijjj #ddjjj #dajjj #chjjj #cfjjj #gajajjj #iijjj #ifjjj #ibjjj #hhjjj #hajjj #gfjjj #gbjjj #fhjjj #hacajjjabijjjabfjjjabbjjjaahjjjajijjjaj ejjjajjjjj #ifjjj #iafijjjafgjjjafdjjjafjjjjaefjjjadfjjjad ajjjacfjjjacajjj #ajbajjjjbjjjjjbjjjjjbjjjjjaijjjjahjjjja hjjjjagjjjjagjjjj #aabejjjjbejjjjbdjjjjbdjjjjbdjjjjbcjjjjb bjjjjbbjjjjbajjjj #abcjjjjjcjjjjjbijjjjbijjjjbijjjjbgjjjjb gjjjjbfjjjjbfjjjj #addejjjjdcjjjjdajjjjchjjjjcgjjjjcejjjjc cjjjjcbjjjjcjjjjj #afebjjjjejjjjjdhjjjjdfjjjjddjjjjdbjjjjd jjjjjcgjjjjcejjjj #ahfejjjjfcjjjjfajjjjeijjjjefjjjjebjjjjd gjjjjdcjjjjdjjjjj #bjhjjjjjgfjjjjgdjjjjfijjjjfejjjjeijjjje djjjjdijjjjdejjjj ,diame- #f #h #aj #ab #ae #ah #bj #bb #bd ter in inches ,length or height in feet4 ,,table ,,showing ,,the ,,load ,,in ,,pounds ,,safely ,,borne ,,by ,,cast-,,iron ,,columns4 ,h ,,and ,,sections4 ,metal ,length or height in feet4 thick- ness4 #f #h #aj #ab #ae #ah #bj #bb #bd #djjj #cjjj #bdjj #ahjj #adjj #aajj #ajjj #ijj #hjj #abjjj #aajjj #ajjjj #ijjj #hjjj #gjjj #ejjj #djjj #cjjj #bejjj #bcjjj #bajjj #ahjjj #afjjj #acjjj #abjjj #ijjj #fjjj #cfjjj #cdjjj #cajjj #bhjjj #bejjj #bcjjj #bajjj #bjjjj #ahjjj #djjjj #chjjj #cgjjj #cfjjj #cejjj #cdjjj #cbjjj #cjjjj #bhjjj #ac_/af #fjjjj #eijjj #ehjjj #egjjj #efjjj #edjjj #ecjjj #eajjj #dijjj #ajjjjj #ihjjj #ifjjj #idjjj #iajjj #hhjjj #hcjjj #ghjjj #gjjjj #aadjjjjacjjjjabfjjjabjjjjaadjjjaajjjjaj fjjjajjjjj #ijjjj #aaijjjjahjjjjagjjjjafjjjjaejjjjadjjjjac jjjjabejjjabjjjj #abcjjjjbbjjjjbajjjjbjjjjjaijjjjahjjjjag jjjjafjjjjaejjjj #abhjjjjbfjjjjbejjjjbdjjjjbcjjjjbbjjjjbj jjjjaijjjjahjjjj #acfjjjjcbjjjjcajjjjcjjjjjbijjjjbhjjjjbg jjjjbfjjjjbdjjjj #bdfjjjjdcjjjjdjjjjjcgjjjjcejjjjccjjjjca jjjjcjjjjjbhjjjj #befjjjjecjjjjeajjjjdhjjjjddjjjjdajjjjch jjjjcejjjjccjjjj #cfjjjjjehjjjjeejjjjebjjjjejjjjjdfjjjjdc jjjjdjjjjjchjjjj ,metal #f #h #aj #ab #ae #ah #bj #bb #bd thick- ness4 ,length or height in feet4 ,,of ,,the ,,truss4 #aga4 ,the most simple bridge that could be built1 consists of a single piece of timber placed across the opening to be spanned4 ,this form is applicable to spans under twenty feet4 ,the proper dimensions are found by the formula3-- d 77#dw,l7_/7#ejjj;b77 the depth4 ,example4--,the depth of a beam of twenty feet span1 and twelve inches wide1 to support a load of twenty thousand two hundred and fifty lbs4 is d 77#d #bj1bej #bj #ab7_/7ejjj #ab77 #ah inches4 ,a beam #ab #ah1 and of #bj feet span1 will therefore bear safely a load of #bj1bej lbs41 applied at the centre4 ,in this manner is formed the following table1 giving the scantling of sticks for railroad stringer bridges1 of twenty feet span and under4 ,span4 ,breadth4 ,depth4 #e #ab #ab #aj #ab #ac #ab #ab #ae #ae #ab #ah #ah #ab #bj #bj #ab #ba inches4 ,the first scantlings exceed the requirement of the rule1 but are none too large to resist the shocks to which such sticks are exposed4 ,cross-ties of plank1 #b or #c by #f or #h inches1 and plank braces underneath1 7as shown in the fig4 at the end of chapter ,,viii417 should be bolted to the main timbers2 the same bolt passing through the tie beam and plank4 ,the longitudinal pieces should be firmly notched and bolted to the wall-plates1 and these latter either built in or scribed on to the masonry4 ,illustration3 ,fig4 #fa4 #agb4 ,for a span of from #bj to #ej feet1 we may use the combination shown in fig4 #fa4 ,the piece ,a ,b1 must be so strong as not to yield between ,a and ,d1 or ,d and ,b4 ,the pieces ,c ,e must be stiff enough to resist the load coming upon them which is as follows4 ,a locomotive engine of the heaviest class will not exceed fifty tons weight1 each pair of driving wheels will support ten tons1 and on each side five tons1 #bbdj #e #aa1bjj lbs42 or to allow for shocks and extra strains1 #ae1jjj lbs4 ,each brace1 then1 must support seven thousand five hundred pounds1 which for compression simply would require only seven and one half square inches of sectional area2 but the brace being inclined1 the strain is increased as follows3-- ,a ,e to ,e ,c as #g1ejj to ,x4 ,and ,a ,e being ten feet1 and ,a ,d fifteen feet1 ,e ,c becomes eighteen feet1 whence #aj to #ah as #g1ejj to #ac1ejj lbs42 which would require only thirteen and one half inches for compression1 or a piece #d #c4 ,but is this enough for flexure8 ,on page #abd the load which may be safely borne1 by a rectangular post of wood1 is shown by the formula ,w 7#bbdj;bd#c7_/7,l#b74 ,substituting for b and d1 the dimensions #d #d1 we have ,w 7#bbdj #d #dc7_/7ahb71 or #egc1ddj_/cbd1 #a1ggj1 which is evidently too small4 ,placing #f #g1 for b d1 we have ,w 7#bbdj #f #gc7_/7ahb7 #ad1bbg2 exceeding by a small amount the requirement4 ,illustration3 ,fig4 #fb4 #agc4 ,it is evidently immaterial whether we support the point ,d upon ,c1 or suspend it as in fig4 #fb1 provided we prevent any motion in the feet of the inclines ,a c ,b c4 ,abutting them against ,a ,b1 throws a tension against ,a ,b1 found as follows3-- ,representing by c ,d1 the applied weight1 draw ,d ,e parallel to c ,b2 also ,e f parallel to ,a ,b2 ,e f is the tension4 ,the graphic construction gives results near enough for practice4 ,rigorously we have ,a c ,d1 similar to ,e c f2 also1 ,a c1 to ,e c1 as ,a ,d1 to ,e f2 and ,ef 7,ec ,,ad7_/7,ac74 ,when a d and c d are differently inclined1 proceed as follows4 ,see fig4 #ajb1 p4 #bjj inverted4 ,illustration3 ,fig4 #fc4 ,let d b represent the weight2 e h shows the tension4 ,the triangles a c d1 and a b e1 are similar2 as also e b h and d b c2 whence b e 7a b1 c d7_/7a c71 and e h 7c b1 b e7_/7d c7 tension4 ,in practice place w for b d2 i4 e4 the actual weight4 ,in this plan1 if the chord is able to resist the cross strain between ,a and ,d1 it will also resist the tension4 ,this cross strain is found by the formula already given and illustrated4 #agd4 ,from what precedes1 we have the following dimensions for bridges such as are shown in figs4 #fa and #fb4 ,the details of #fb1 at f and c1 and at ,e1 #fa1 are shown in figs4 #fb ,a1 #fb ,b1 and #fa ,c4 ,illustration3 ,fig4 #fb ,a4 ,illustration3 ,fig4 #fb ,b4 ,illustration3 ,fig4 #fb ,c4 ,span4 ,rise4 ,a ,b4 ,c ,e4 ,rod b4 #bj #h #ab #ab 7#e #h7--b #a inches4 #be #aj #ab #ae 7#e #i7--b #a inches4 #cj #ab #ab #ah 7#e #aj7--b #a inches4 #ce #ac #ab #bj 7#e #aj7--b #a inches4 #dj #ad #ad #ba 7#e #ab7--b #a inches4 #de #ae #ad #bb 7#f #ab7--b #a inches4 #ej #af #ad #bd 7#f #ab7--b #a inches4 ,the braces1 7column #d17 being in pairs and blocked together4 ,in spans exceeding twenty-five feet1 the braces d f1 and the rods f g1 should never be omitted4 ,the size of the rod g f1 is found by considering ,a1 d1 f1 as a small bridge4 #age4 ,in all light bridges1 like the one under consideration1 all parts should be fastened by bolts1 to prevent springing by reaction4 ,a bridge with but little inertia1 or dead weight1 tends to jump up when the engine has passed over it4 ,fastening takes the place of weight in a large span4 ,as soon as the rise admits1 the points ,c1 on each side of the bridge1 should be connected to resist lateral motion4 ,when the height is not enough for this1 the same points may be joined to a floor beam extended out beyond the truss4 ,though the dimensions are given for this plan up to fifty feet span1 it is very seldom advisable to go beyond twenty-five or thirty feet2 as frames consisting of a few long timbers are not so rigid1 and free from vibration1 as those made of a greater number of short pieces4 #agf4 ,in extending this system one hundred or two hundred feet1 we see at once that the pieces ,a c1 ,b c1 would become very long and would need to be made large and heavy4 ,we should always so proportion any beam in a bridge that it is at once able to resist all of the several strains to which it may be exposed1 without being unnecessarily large4 ,as to compression1 the above system might be extended to almost any amount2 but the braces would yield by flexure4 ,instead of producing the braces ,a c1 ,a c1 fig4 #fd1 to their intersection1 we stop at c and c1 insert c c2 to prevent the approach of these points1 suspend the points ,b and ,b from c and c1 and commence again with the braces ,b ,d1 ,b ,d2 and so on as far as necessary4 ,to prevent the backward motion of the points ,b1 and ,b1 either the chord ,a ,a1 or the counter-braces m1 m1 are necessary4 ,illustration3 ,fig4 #fd4 ,the pieces ,a c1 ,ac must support all of the load1 including the weight of the bridge1 lying within the rectangle ,b c1 ,b c4 ,the next set of braces must sustain that part of the load only which comes over the centre of the bridge4 ,thus the braces should decrease in size as the centre is approached4 ,the rods c ,b1 c ,b1 must resist a tension equal in amount to the pressure on the braces1 only being vertical they do not need the increase given to the braces on account of their inclination4 #agg4 ,there is another method of stiffening a beam1 as shown in figs4 #fe and #ff1 by trussing rods1 and a post4 ,the dimensions being the same1 the forces in both cases will be equal4 ,the second1 fig4 #ff1 leaves the passage beneath the bridge clear4 ,illustration3 ,fig4 #fe4 ,the tension on the rods ,a c1 ,b c1 fig4 #ff1 tends to draw the points ,a and ,b together1 an effort which is resisted by the top chord ,a ,b4 ,in extending this system1 as in art4 #agf1 the rods become either very long1 or very large1 from the small angle of inclination2 evils which remedied as before1 by supporting the post c ,b1 fig4 #fd1 from the foot of the first rod1 fig4 #fd1 and commencing again from c4 ,illustration3 ,fig4 #ff4 ,to prevent the motion of the triangle c ,b ,g1 fig4 #fd1 about the angle ,b1 we must introduce either the upper chord c c1 or the counter rod c ,a4 ,if the lower chord is omitted the rod ,d ,b must be of the same size as ,e ,b4 ,in this truss1 either the top or the lower chord simply may theoretically be omitted1 due allowance being made in the size of the rods4 ,in practice it is never advisable to omit either1 as both are required for lateral bracing1 and for support of the road-way4 ,having said thus much of the general ideas that apply to all bridges1 let us now look at some of the plans most in use2 and to become familiar with the subject1 work out the dimensions of an example of each kind4 #agh4 ,as rods1 nuts1 and washers are used in all bridges1 the following table may not be out of place3-- ,column #a gives the diameter of rod4 ,column #b strength at #ae1jjj lbs4 per square inch4 ,column #c the weight per lineal foot4 ,column #d side of the square nut4 ,column #e the thickness of the same4 ,column #f the dimensions of washers4 ,column #g the thickness of washers4 ,column #h breadth 7side to side7 six-sided nut4 ,column #i breadth 7across angles7 six-sided nut4 ,column #aj thickness of six-sided nut4 ,column #aa number of screw threads per inch4 ,column #ab gives the diameter of rod4 #a #b #c #d #e #f ,diameter4,strength,weight,square,thickn ess4,square of ,rod4 per ,nut4 of ,foot4 ,washer4 #b1idj #j4ff #a #b #f1fcj #a4di #a #c #a #aa1gge #b4fe #b #a #d #a #ad1iaj #c4cf #b #a #d #a #ah1dje #d4ag #b #a #e #a #bb1bfj #e4jb #b #a #e #a #bf1eje #e4ig #b #a #f #a #ca1jie #g4ja #b #a #f #a #cf1jge #h4ac #c #a #g #a #da1dae #i4cc #c #a #g #b #dg1acj #aj4fb #c #a #h #b #ec1aij #ab4jj #c #b #h #b #ei1fdj #ac4dj #d #b #i #b #ff1dej #ae4jj #d #b #i #b #gc1fbj #af4gj #d #b #aj #a #b #c #d #e #f #a #g #h #i #aj #aa #ab ,diameter4 ,top ,six- ,six- ,six- ,screw4,diameter4 ,washer4,sided,sided ,sided ,nut4 ,nut4 ,nut4 #a #a #i_/af #ab #a #b #aj #a #a #b #a #h #a #a #b #bg_/af #a #g #a #a #bbaa_/af #ag_/ab #g #a #a #b #b #ag_/af #f #a #a #b #caaa_/af #f #a #a #b #ce_/afaac_/af #e #a #a #c #c #b #e #a #a #c #c #b #d #a #b #c #d #b #d #b #b #c #dc_/af #b #d #b #b #c #df_/af #b #d #b #b #d #d #b #d #b #b #d #d #b #c #b #a #g #h #i #aj #aa #ab #agi4 ,let us now assume the following data3-- ,span #bjj feet1 ,rise 7centre to centre of chords7 #be feet1 ,width #bj feet1 ,length of panel #ae feet1 ,weight 7bridge and load7 per lineal ft4 #d1jjj lbs4 ,,howe',s ,,bridge4 ,fig4 #fg4 ,illustration3 ,fig4 #fg4 ,lower ,chords4--,the tension1 at the centre of the lower chord1 is found by dividing the product of the weight of the whole bridge and load by the span1 by eight times the height1 or ,t 7,w ,s7_/7#h;h71 which becomes1 with the above data1 ,t 7#hjjjjj #bjj7_/bjj #hjj1jjj lbs4 ,here the tension and the total weight are equal1 a result which can occur only when the rise is one eighth of the span4 ,this is the best ration between these dimensions1 as then the horizontal and vertical forces are equal4 ,as to the proportion of the panel1 7or the rectangle inclosed by the chords and any two adjacent posts17 the ratio of base to height should be such as to make the inclination of diagonal about #ej from the horizontal2 if much less1 the timbers become large and heavy2 and if more1 the number of pieces is unnecessarily increased4 ,the braces at the end of a long span1 may be nearer to the vertical than those near the centre1 as they have more work to do4 ,if the end panel be made twice as high as long1 and the centre panel square1 the intermediates varying as their distance from the end1 a good architectural effect is produced4 ,to determine the size of the lower chords1 to resist the above #hjj1jjj pounds of tension1 proceed as follows3 ,each side truss will support one half of the whole load1 or #djj1jjj pounds2 which1 at #b1jjj pounds per inch1 will require #bjj square inches of section4 ,four sticks of #h #ab inches1 give an area of #chd square inches1 which must be reduced as follows3 ,deduct #gb square inches for the area cut out by the splicing blocks1 #dj inches for the bolts connecting the pieces1 #bh inches for inserting the foot blocks1 and #aj inches for inserting the washer1 and we have remaining #bcd square inches2 which exceeds by a little the exact demand4 ,this excess 7about one seventh7 is a necessary allowance for accidental strain1 to which all bridges are subjected4 ,illustration3 ,fig4 #fg ,a4 ,the splices used in bridge framing are shown in fig4 #fg ,a and fig4 #fg ,b4 ,for the first1 the depth of insertion and length of the block depend upon the tension upon the chord4 ,the following dimensions have been much used and are perfectly reliable3-- ,span of ,bridge4 ,a ,c ,b ,c ,c ,d ,feet4 ,feet4 ,inches4 ,feet4 #ej #a4jj #a #a4ej #ajj #a4be #b #b4jj #aej #a4ge #b #b4be #bjj #b4jj #c #b4ge ,there is no need of cutting more than one notch1 as in the figure2 the resistance of the triangles is thereby lessened1 and the work increased4 ,illustration3 ,fig4 #fg ,b4 ,in fig4 #fg ,b1 the rods must of course be able to resist the tension upon the one piece which is cut4 ,upper ,chord4--,the upper chords of a bridge suffer compression1 to the same amount numerically1 as the tension on the lower chord2 as whatever tension is thrown by any brace upon the lower chord1 reacts as just so much compression upon the upper4 ,in the case at hand1 #hjj1jjj lbs4 in all1 or #djj1jjj on each chord4 ,the resistance to compression being one thousand pounds per inch1 renders necessary four hundred inches of section to each chord2 four pieces #h #ab give in all three hundred and eighty-four inches of section1 which requires no reduction1 as the whole chord pressing together and being properly framed is not weakened by splicing4 ,the splicing blocks in the upper are merely plain pieces1 inserted one half inch1 the only duty being to keep the sticks at the proper horizontal distance4 ,the spaces between the pieces should be large enough to allow the rods to pass without cutting the chords2 7two inches answers every purpose74 ,the bolts for splicing1 have no very great strain to bear4 ,in small spans from to 1 and in large bridges from to an inch is enough4 ,the object in framing a built beam for a bridge chord1 is to make a stick which shall be uniformly strong4 ,this is done by cutting the pieces in the centre of the panel1 and by having no two joints in either chord in one panel2 though in long spans this cannot always be done4 ,figs4 #fg ,d and #fg ,e 7page #aec7 ,,braces4 ,the whole load being #hjj1jjj pounds1 ,each truss supports #djj1jjj pounds1 ,each set of braces #bjj1jjj pounds1 ,each brace 7there being #d7 #ej1jjj pounds1 which must be increased for inclination as follows3 ,the length of diagonal is twenty-nine feet1 7the height being twenty-five and length #ae17 whence #be to #bi as #ej1jjj to #eh1jjj lbs42 which would need fifty-eight square inches1 or #g #h for compression2 which1 however1 is quite too small for flexure4 #ab #ab placed in the formula gives ,w 7#bbdj bd#c7_/7,l#b71 or ,w 7#bbdj #ab #agbh7_/hda #ee1bif lbs4 ,in practice1 smaller braces than #ab #ab would answer1 because the four braces in a set may be fastened together1 making a post of four pieces #h #ab1 or in all a built post of #dd #ab inches2 twelve being the depth1 whence ,w 7#bbdj #dd #agbh7_/hda #bjb1eaa lbs42 the forty-four inches being made by blocking the braces four inches apart4 ,the second set of braces are to be treated in the same manner1 the weight to be supported being only the rectangle included by those braces2 i4 e4 the whole bridge and load less the two end panels4 ,as the centre of the span is approached1 the pressure on the braces becomes very small2 and the scantling of the braces will be reduced to about #f #g inches4 ,,rods4 ,the weight upon the first set of rods is the same as that upon the end sets of braces2 in the present case #hjjjjj #b #djjjjj on each side truss1 and #djjjjj #b #bjjjjj on each end2 and if there are five rods in each set1 each rod bears #dj1jjj lbs4 ,referring to the table on p4 #adf1 opposite to #da1dae lbs41 is the diameter #a inches2 whence the first set must contain five rods1 of #a inches diameter4 ,the second set decrease in size as the weight is lessened by the two end panels4 ,the nut and washer for the rod are also found in the same table4 ,,counterbracing4 #ahj4 ,when a load is placed on the point ,c1 fig4 #fd1 the truss tends to sink at that point1 and a corresponding rise takes place at ,c4 ,this motion changes the figure ,a ,b ,c ,e1 from a rectangle to an oblique angled figure2 the diagonal ,e ,b being shortened1 and ,a ,c lengthened4 ,this motion is easily checked by the introduction of the counter brace ,e ,b4 ,illustration3 ,fig4 #fd4 ,the action which this timber is called upon to resist1 being caused by the moving or variable load on one panel1 the brace must resist the load coming thereon1 7say fifteen feet17 and is thus the same size as the brace at the centre of the span4 ,the counter braces may be so confined between the braces1 at the intersection1 as not to move laterally or vertically1 but must not be fastened to the braces2 because the action of the separate timbers is thus trammelled4 ,illustration3 ,fig4 #fg ,c4 ,the manner of adjusting the braces and counter braces to the chord is shown in fig4 #fg ,c4 ,it was formerly the custom to abut the braces against a block on one side of the chord1 and to screw the rod against a block on the opposite side2 the whole strain acting to crush the chord crosswise4 ,this has been remedied by the arrangement shown in the figure1 the two blocks being cast in one piece and connected by a small hollow cylinder passing between the chord sticks4 ,illustration3 ,fig4 #fg ,d4 ,fig4 #fg ,e4 ,this system is known as ,howe's bridge1 and may be seen in almost any section of the country2 and though in many cases badly proportioned1 and of bad material1 if properly made answers a very good end4 ,the following table has been formed for the use of engineers and builders1 giving1 together with the table of nuts and washers1 all dimensions required4 ,span4 ,rise4 ,panel4 ,chords4 ,end ,centre ,end ,centre braces4braces4 rod4 rod4 #ej #aj #gb--h #aj #gb #e #e #b--a #b--a #ge #ab #ib--h #aj #hb #e #e #b--a #b--a #ajj #ae #aac--h #aj #ib #f #f #b--a #b--a #aej #bj #acd--h #ab #ajb #f #g #c--b #c--a #bjj #be #aed--h #af #abb #g #g #e--b #e--a ,,pratt',s ,,bridge4 ,illustration3 ,fig4 #fh4 #aha4 ,assume the following data for an example3-- ,span #ajj feet4 ,rise #ab feet4 ,panel #aj feet4 ,weight per lineal ft4 #b1ejj lbs4 ,the tension on the lower1 or the compression on the upper chord1 will be 7#bejjjj #ajj7_/if #bfj1dag lbs4 ,the manner of dimensioning the chord1 and of splicing1 is the same as already described for ,howe's4 ,,suspension ,,rods4 ,the first sets of rods1 ,a ,b1 ,a ,b1 must sustain the whole weight of the bridge and load2 which is #bej1jjj lbs4 ,each side #abe1jjj lbs42 and each end set of rods #fb1ejj lbs42 and if each set has four rods1 each rod must support #ae1fbe lbs4 ,the rod being inclined1 this amount is increased by the following proportion3-- #ab 7height7 to #ae4h 7diagonal7 as #ae1fbe to #bj1egc lbs4 ,this is half-way between the tabular numbers for rods of #a and #a inches in diameter2 #a will therefore answer4 ,the next set of rods must be considered as supporting the whole load1 less the two end panels1 and so on as already explained for ,howe's bridge4 ,the manner of applying the rods to the chords is shown in fig4 #fh ,a4 ,the bevel block should be connected with the block at the foot of the post1 so as to prevent crushing the chord4 ,illustration3 ,fig4 #fh ,a4 ,,counter ,,rods4 ,as both top and bottom chords are always used in this bridge1 the counter rods have only the variable load on one panel to resist4 ,the action is1 in amount1 the same as that on the counter braces in ,howe's bridge2 but acts in a different direction1 and in the other diagonal4 ,the weight of a passing load cannot be more than two thousand pounds per lineal foot4 ,the panel being ten feet long1 the whole weight coming on two sets of counter rods1 7one set in each side truss17 is twenty thousand pounds2 or ten thousand pounds on each set2 and if there are put three rods in each set1 we have #c1ccc pounds per rod1 which increase for inclination as follows3-- #ab 3 #ae4h 33 #cccc 3 #dchi lbs41 requiring a rod of three fourths inch diameter4 ,the posts in this structure1 correspond to the braces in the ,howe bridge2 only being vertical1 they need not be so large4 #ahb4 ,the following table gives all the dimensions necessary for proportioning this truss4 ,span4 ,rise4 ,chords4 ,end ,c post4 ,end ,c rod4 ,counter post4 rod4 rod4 #ej #ajb--h #aj #e #e #db #b--a #b--a #a--a #ge #abb--h #aj #f #f #eb #b--a #b--a #a--a #ajj #aec--h #aj #g #g #fb #b--a #b--a #b--a #abe #ahc--h #aj #h #h #fb #c--a #c--a #b--a #aej #bad--h #ab #i #i #fb #c--b #c--a #c--a #bjj #bdd--h #afaj #aj #fb #e--a #e--a #c--a ,and the following1 the sizes of counter rods1 for different panels4 ,length of ,height of ,approximate panel4 panel4 diagonal of ,diameter of the rod4 panel4 ,one in a ,two per ,three per set4 set4 set4 #aj #ab #af #a #a #aa #ac #ag #a #a #a #ab #ad #ah #a #a #a #ac #ae #bj #a #a #a #ad #af #ba #a #a #a #ae #ah #bc #a #a #a #af #ba #bf #b #a #a #ah #be #bg #b #a #a ,the advantage possessed by this bridge1 over ,howe's plan1 is that the panel diagonals may be adjusted by the screws2 by which control is had over the form of the truss1 and of the duty done by the several parts4 ,change of form cannot be had by working upon verticals4 ,howe's bridge must be adjusted by wedging the braces and the counter braces4 #ahc4 ,the manner of drawing the bevel block in this bridge1 is shown in fig4 #fh b4 ,the proportions of the block depend upon the proportions of the panel2 and the dimensions1 upon the size of washer used4 ,let ,c ,c be the centre line of the post1 and ,a ,b the chord4 ,let o m1 and o n1 be the panel diagonals1 and ,h and y1 the length of the washers4 ,illustration3 ,fig4 #fh ,b4 ,the depth of insertion of the block into the chord1 depends upon the horizontal strain upon it4 ,in a span of one hundred and fifty feet1 with the rods at an angle of #ej1 two inches have been found ample at the end of the truss1 and one half inch at centre4 ,from ,d1 perpendicular to m m1 lay off ,d ,e2 equal to ,h1 also from ,e1 at right angles to n n1 make ,e ,e y4 ,from ,e draw the vertical ,e ,l4 ,the strain upon the rod o m1 being represented by o m2 and that upon o n1 by o n1 the resultant is shown1 both in direction and amount1 by o ,v4 ,it is not necessary that this should pass through the centre of the post1 as the excess of tension on o m1 over that on o n1 is absorbed by the lower chord4 ,,note4--,screwing up truss bridges1 is a more scientific operation than is generally supposed4 ,many builders commence at each end1 and lift the bridge from the scaffolding4 ,by this method the greater part of the load is often borne by a few of the end sets of rods4 ,the better method is to begin at the centre and work both ways towards the ends1 being sure that each set of rods does its duty before the next is touched4 ,the lift to be made by each set of rods1 should first be calculated1 and tested while screwing up1 with the level4 ,,lattice ,,bridges4 #ahd4 ,town's lattice1 consists of a simple lattice-work of plank1 #c #ab inches1 treenailed together at an angle of forty1 forty-five1 or fifty degrees4 ,it possesses great stiffness1 without by any means having the material disposed in the best manner4 ,such bridges might well be made by the mile1 and cut off to order according to the span4 ,the improved lattice1 by ,hermann ,haupt1 ,esq41 ,c4 ,e41 avoids all of the evils attendant upon the common lattice1 and gives a very cheap1 strong1 and rigid bridge4 ,in this plan the braces are placed in pairs1 with vertical tie planks between them2 by which the twisting seen in the common lattice1 is removed4 ,the braces are also brought to the vertical1 as the point of support is reached1 by which a good bearing is given to the end sets of timbers4 ,to vary the size of the braces1 as the strain upon them decreases1 would be both inconvenient and expensive2 but the same effect may be produced by varying the distance between them1 making it greater as the centre is approached4 ,s4 ,w4 ,,hall',s ,,wooden ,,truss ,,and ,,arch ,,bridge4 ,inverting ,mr4 ,haupt's design for a lattice of improved construction1 7which consists of vertical ties and inclined braces17 we have the base of the above-named bridge2 where the inclined timbers are used to resist tension1 as below4 ,this being a very good plan1 and the arrangement for building being such as to secure the thorough execution of the work in its most minute detail2 it is thought best to extract at some length from a letter from the inventor1 dated ,july #cast1 #ahef1 not however being confined to the matter therein4 ,the first claim1 is for a new form of truss1 formed of posts vertical1 or nearly so1 and tension pieces1 inclining downwards toward the centre2 thus differing from nearly all other plans4 ,timber resists double as much extension as compression2 and when large enough to resist the simple tension1 does not have to be increased as in resisting compression for flexure2 but requires a larger allowance for joints1 as tension tends to pull the joints apart1 while compression forces them together4 ,the following result was obtained1 showing the superior strength of timber work in resisting by tension4 ,two models1 containing the same amount of timber1 were tested4 ,the one built with vertical ties and braces1 broke by crippling the brace1 under #b1djj lbs42 while that constructed with verticals and suspenders1 inclining towards the centre1 sustained #d1bjj lbs4 with no visible change of form4 ,the second claim is for more efficient bearings and connections than common1 and this with less cutting away of timber4 ,the arch and arch braces have a full1 fair bearing at top and bottom4 ,the first sets of tension braces1 7those extending from the top of the arch braces towards the centre17 are sustained by two pins at each joint2 which gives six pin bearings1 or twelve for one set of braces1 of six inches each1 7the pin being two inches in diameter1 and plank three inches thick17 equal in all1 to seventy-two inches of bearing surface at least1 for each five feet lineal of bridge1 or one hundred and forty-four inches for ten feet4 ,the third claim1 is that the bearings1 at joints1 are central1 and that the shrinkage of the timber is towards and not from them as in many plans4 ,the pin holes are bored by machinery smooth and true2 the treenails when of wood are of seasoned oak or locust1 turned to a perfect fit1 and when of iron are made hollow4 ,these bridges1 after three years1 stand within an inch of their shape as framed without exception4 ,one indeed supporting an aqueduct1 which throws upon the truss a constant load of #b tons per foot1 not including the weight of the bridge1 without any apparent settling4 ,the connections being fast1 prevent reaction and vibration from variable loads1 the strains in this case are reversed1 the bridge tending to spring up instead of settling4 ,the fourth claim1 is for the small brace connecting the lower with the intermediate chord2 by which additional connections are obtained1 and smaller timbers rendered available4 ,the fifth claim1 is the formation of a stronger chord than by the plan of using a few large sticks4 ,the chord being made of a great number of small pieces1 the strength is of course less affected at any one point1 by a joint1 than when only a few pieces are used4 ,in the bridges built by the above engineer1 are to be seen some of the most perfect built beams in the country4 ,the following conditions being observed1 the most uniform1 and highest average strength possible is obtained4 ,first4 ,to cut but one stick in any one panel4 ,second4 ,to cut no stick at the centre of the bridge4 ,third4 ,to place every joint in the middle of the collateral piece4 ,the chords are cut by two rows of pins1 two inches each2 and if the chord be fifteen inches1 the cutting at centre1 where there is no joint1 is but four fifteenths of the whole section4 ,to resist the parting of any two sticks1 there is the resistance to shearing of ninety-six pins2 and the section of each being three square inches1 the whole resistance is two hundred and eighty-eight inches of area4 ,if the intermediate chord has the same number1 the whole area to resist shearing1 in the lower chord1 is five hundred and seventy-six square inches4 ,the bearing surface of each pin in the chord stick is #b #c inches1 or six inches2 and #if #f #egf3 and in both chords #aaeb inches4 ,sq4 in4 ,the whole chord timber1 7both chords17 is 7#f #c #ad71 #beb ,in the intermediate chord1 7#f #c #ab71 #baf ------ ,whole timber section1 #dfh ,deduct #d pins for both chords1 #dfh - 7#d #b #c #f7 or #dfh - #add #cbd ,deduct for joints #c #aj #c #h or #cbd - #ed1 ,square inches of available area4 #bgj ,comparing the amount thus cut away with that cut away in other plans1 we have the following figures2-- ,a4 ,hall's ,bridge1 7actual bridge17 #cj_/ajj ,b4 ,howe's bridge1 7actual bridge17 #ce_/ajj ,c4 ,page #afc1 7,handbook ,r4 ,r4 ,construction17 #ci_/ajj ,d4 ,mc,callum's1 7,susquehanna bridge17 #eh_/ajj ,the sixth claim1 is the peculiarly convenient form for applying an arch1--the superiority consisting in convenience for attachment2 in the connections being less affected by shrinkage than when posts are locked into arches2 in the timbers not being weakened by cutting4 ,the arch is loaded with the tension timbers1 inwardly1 and acts as a general arch brace1 transferring at once all of the several tensions to the abutment1 thus really combining the arch with the truss4 ,the liability of this plan to decay1 certainly appears to be less than that of most plans of wooden bridges now in use2 as will be plainly seen by observing the position of the joints2 falling rain finds a much easier access to almost any other joint than the pin hole4 ,the timber work being made of plank1 all the timbers are small1 and are thus much more likely to be sound4 ,illustration3 ,fig4 #fi4 ,the bridges built upon this plan upon the ,alleghany ,valley1 and upon the ,williamsport and ,elmira roads1 illustrate plainly the design4 #ahe4 ,applying arch braces to lattice bridges1 has suggested ,the ,arch-brace truss bridge1 in which the whole strength lies in a series of differently inclined braces1 extending from the abutment to the head of each post2 a very light lattice being used to prevent reaction1 or as a counter-brace or stiffener4 ,see fig4 #fi4 ,in trusses consisting of a series of triangles1 when the span is large1 7#aej to #bjj feet17 the immense weight coming at the feet of the second and third sets of braces1 causes settling or depressing at twenty or thirty feet off from the abutment1 which can hardly be removed4 ,the remedy for such settling1 is to transfer the load at once to the abutment2 which is completely done in the above-named bridge4 ,each brace does its duty directly and well4 ,before the lattice-work is fastened1 the bridge should be loaded with a maximum load4 ,then by fastening the diagonals1 the recoil is prevented2 and the effect of a passing load is to ease the counterbracing lattice1 without otherwise affecting the truss4 ,,note4--,a model of this bridge1 made by the writer1 of the following dimensions3-- ,length1 #g feet4 ,height1 #a foot4 ,width1 #a inch4 ,chords1 inch4 ,braces1 inch4 ,lattice1 #a_/af inch4 ,supported #b1ejj lbs4 at centre1 besides a variable load of #aej lbs4 applied as a rolling weight in the most disadvantageous manner4 ,it represented a span of one hundred and fifty feet1 and according to ,weisbach's formula for testing a model1 proved the actual structure1 7as far as can be proved by a model17 both strong and rigid to any desired amount4 ,the longest bridge ever built upon this principle1 was that of ,schaffhausen1 over the ,rhine1 which had a single span of three hundred and ninety feet4 ,this bridge was not stiff1 having no lattice1 but was very strong4 ,b4 ,h4 ,latrobe1 ,esq4 has adopted this form upon the ,baltimore and ,ohio ,railroad4 ,the calculations for the parts of this bridge are as follows3-- ,the ,span being #aej feet1 ,the ,rise #bj feet1 ,the ,panel #ae feet1 ,weight per foot of bridge and load #c1jjj lbs4 ,the half number of panels is five2 the diagonals of which1 neglecting fractions1 are 7#bjb #aeb7 #be feet1 7#bjb #cjb7 #cg feet1 7#bjb #deb7 #di feet1 7#bjb #fjb7 #fd feet1 7#bjb #geb7 #gh feet4 ,the weight upon each of these sets of braces1 is the weight of the length of one panel2 which1 in the present case1 is #c1jjj #ae #de1jjj lbs4 ,as there is a brace under each chord stick1 and assuming four sticks in each chord1 we divide by eight1 and have1 in round numbers1 #f1jjj lbs4 per brace2 and correcting for inclination1 as follows1 we have the numbers below4 #bj 3 #be 33 #fjjj 3 #ajjjj #bj 3 #cg 33 #fjjj 3 #aejjj #bj 3 #di 33 #fjjj 3 #bjjjj #bj 3 #fd 33 #fjjj 3 #bejjj #bj 3 #gh 33 #fjjj 3 #cjjjj4 ,the last column has the several weights coming upon the different braces at their several inclinations2 to resist which1 the scantling might be very small1 for compression1 but flexure requires larger dimensions4 ,these braces should be confined laterally and vertically1 as they pass each post1 but not connected therewith2 as this would not permit a free action of the brace1 without straining transversely the post4 ,the length of beam1 therefore1 in which flexure is to be checked1 is the distance between posts in any panel4 ,in panel ,no4 #a1 it will be #be feet4 ,in panel ,no4 #b1 it will be #ah feet4 ,in panel ,no4 #c1 it will be #ag feet4 ,in panel ,no4 #d1 it will be #af feet4 ,in panel ,no4 #e1 it will be #af feet4 and applying the formula 7#bbdj;bd#c7_/7,l#b7 ,w we get1 in round numbers1 the following dimensions1 the braces being bolted and blocked together3-- ,for the #ast panel1 #be feet long1 #h #aj ,for the #b;d panel1 #cg feet long1 #h #aj ,for the #c;d panel1 #di feet long1 #h #aj ,for the #dth panel1 #fd feet long1 #h #aj ,for the #eth panel1 #gh feet long1 #h #aj4 ,for the lattice-work1 a double course on each side of each truss1 in long spans1 7#aej to #bjj feet72 and a single course in shorter spans1 of #c #f plank1 treenailed at intersections1 is ample4 ,,general ,,table ,,of ,,dimensions ,,for ,,arch ,,brace ,,truss4 ,span4 ,rise4 ,chords4 ,ties4 ,braces4 ,lattice4 #ej #aj #b-h #aj #a-h #aj #b-f #fb #i or #c #f #ge #ab #b-h #aj #a-h #aj #b-f #fb #i or #c #f #ajj #ae #c-h #aj #b-h #aj #c-f #fb #i or #c #f #aej #bj #d-h #ab #c-h #aj #d-f #hb #i or #c #f #bjj #be #d-h #af #c-h #aj #d-f #ib #i or #c #f ,illustration3 ,fig4 #fi ,k4 ,fig4 #fi ,a4 ,fig4 #fi ,a1 shows the method of bringing the arch braces to the chord4 ,to find the dimensions of the cast-iron block1 make a complete drawing of all of the braces1 at their proper angles1 and then draw in the block around the feet1 as shown in fig4 #fi ,a4 ,,note4--,the centre of pressure of the braces in fig4 #fi ,a1 is not1 as might seem1 at ,c2 because the vertical components of the forces1 coming down the brace1 are much less in the braces at small angles than in those at the end of the span4 ,the load applied to each brace being the same1 and the inclines being found1 we find the centre of pressure1 or the centre of bridge seat as follows3-- ,the length of the brace is to the vertical height1 as the applied load to the vertical pressure4 ,in fig4 #fi ,a1 we have the following lengths of braces3 a1 #be2 b1 #cg2 c1 #di2 d1 #fd2 e1 #gh2 f1 #ib2 and g1 #ajf2 and the weights corresponding thus1 a1 #be 3 #bj 33 #fjjj 3 #dhjj4 b1 #cg 3 #bj 33 #fjjj 3 #cbdc4 c1 #di 3 #bj 33 #fjjj 3 #bdej4 d1 #fd 3 #bj 33 #fjjj 3 #ahgj4 e1 #gh 3 #bj 33 #fjjj 3 #aedj4 f1 #ib 3 #bj 33 #fjjj 3 #acjd4 g1 #ajf 3 #bj 33 #fjjj 3 #aacb4 ,in fig4 #fi ,a1 assume the foot of the fifth brace 7,b7 as the centre of pressure1 and adding the moments1 7or products of vertical components on the braces by their distance from ,b17 and we have the sum on the land side #ah1ibh1 and on the water side #af1icj2 showing that the centre is taken too far from the land side4 ,in the same manner ,a will be found too far from the land side4 ,a third trial will give the place4 ,illustration3 ,fig4 #fi ,b4 ,fig4 #fi ,c4 ,illustration3 ,fig4 #fi ,d4 ,fig4 #fi ,e4 ,fig4 #fi ,f4 ,fig4 #fi ,g4 ,fig4 #fi ,h4 ,fig4 #fi ,b1 shows the manner of splicing the arch braces3 being subjected to compression1 they are spliced in the same manner as the upper chords4 ,fig4 ,c1 shows the lower chord spliced4 ,figs4 ,d and ,e1 the connection of the posts1 chord1 and lattice4 ,figs4 ,f1 ,g1 and ,h1 the casting for applying the upper end of the arch brace to the chord4 ,fig4 #fi ,k1 the method of supporting the tracks at the end of the span1 where the arch braces will not allow the floor beams to bear upon the lower chord4 ,,mccallum',s ,,patent ,,railroad ,,bridge4 ,illustration3 ,fig4 #gj4 #ahf4 ,this bridge represents a class of structures in which the upper chord is curved upwards 7#g feet in #bjj in the ,susquehanna bridge1 ,new ,york and ,erie ,railroad71 which curved chord has the effect of distributing an applied load at once to all of the braces directly1 by means of the chord1 as well as indirectly1 by means of the braces1 as in the common trusses4 ,to this bridge is applied the arch braces ,a ,b1 ,a ,b1 fig4 #gj1 which serves to aid the #b;d1 #c;d1 and #dth pair of diagonal braces in bearing their load4 ,the great distributing power of the curved chord1 is shown by the fact that a bridge of #abe feet span1 actually supported a railroad train before the diagonal bracing was introduced4 ,the whole strain was thrown through the curved chord and arch braces to the abutments4 ,the bridge is counterbraced by the pieces d d and d d1 adjustable by screws at the ends4 ,the following test was applied to a span of #aij feet of this plan of bridge4 ,placing the load as near as possible to the centre1 the following deflections were produced4 ,load4 ,deflection4 #da4dj tons1 #j4jac feet1 #ie4ce tons1 #j4jch feet1 #adj4gj tons1 #j4jfa feet1 #ahg4bj tons1 #j4jfa feet4 ,upon removing the load1 the bridge entirely recovered its form4 #ahg4 ,as the span increases1 the benefit derived from the curved chord also augments2 and though in the latter part of the present chapter its application to small spans is shown1 it may not be worth while to adopt it4 ,bridges transferring the load directly1 from each panel to the abutment1 would not be aided1 to an amount worth the increased expense1 by adopting the curved top chord4 ,in case of any settling at the centre of the span1 the reverse effect is seen from that produced in a truss with horizontal chords2 i4 e41 when the ends of the upper chords in the latter draw in1 those of the former push out2 and when in such bridges1 arch braces are not used1 the top chords of adjoining spans must be wedged apart1 in place of tying together as in common plans1 over the centre of the piers4 ,,the ,,arch4 #ahh4 ,the arch has been applied to long spans for a great while1 and when care has been taken to prevent flexure1 answers very well4 ,the repair of such bridges1 if any of the arch timbers decay1 is difficult2 but is effected1 in the largest arches4 ,the most correct ideas on wooden arch bridge building1 are to be found in ,weibeking's ,traite d'une parte essential de construire les grandes pents en charpente4 ,this engineer1 7,general ,director of ,roads and ,bridges in ,bavaria17 has built a great number of wooden arches of the best description1 which show him to be master of both the science and the art4 ,illustration3 ,fig4 #ga4 ,the general plan of his bridges is shown in fig4 #ga4 ,they consist of curved ribs formed of long pieces scarfed and bolted together1 from which the road-way is supported by posts4 ,the bridges of ,neucettringin1 ,freysingin1 ,bamberg1 ,scharding1 ,wertach1 ,vilshoven1 and ,altenmarkt1 all testify to the good judgment of this man4 ,the spans vary from one hundred to two hundred feet2 and the width from twenty-five to thirty-two feet4 ,the proportions which he gives for the ratio of rise to span1 are valuable2 as they are the result of his own experience4 ,he states1 generally1 that one tenth of the span is the best rise2 but that for convenience1 it is better to keep it lower4 ,the following table shows the dimensions he has adopted in practice4 #ahi4 ,name4 ,span4 ,rise4 ,width4 ,rad4 of ,scantling ,arch4 of ,arch4 ,bamberg1 #bjh #af4icb #dbb #ac #ae ,scharding1 #aid #ah4hbe #beh #ab #ae ,vilshoven1 #agi #aa4abg #cgh #ac #ae ,freysingin1 #aec #aa4fbe #bdf #ab #ad ,ettringin1 #aci #h4jbe #cje #ab #ae ,ersingin1 #abf #g4jbe #bhe #aa #ad ,augsberg1 #aad #aj4fbe #aeh #ab #ad ,neucettringin1 #ajc #f4hbe #bjj #ac #ae ,the last column shows the scantling of the arch timbers2 these being placed three deep1 in spans of less than #aej feet2 and in larger spans1 #c deep at centre1 and #e deep at ends4 ,mr4 ,weibeking's formula for determining the scantling of ribs1 is as follows3-- 77,w 7,s_/#b7b7_/,rn74#jjaa ,scantling in sq4 ft4 ,where ,r is the rise of the arch2 n1 the number of ribs2 ,w1 width of bridge2 and ,s1 span of bridge4 ,,example4--,required the scantling of the ribs of a bridge of #cjj feet span1 #bj feet wide1 and #cj feet high4 ,the formula becomes1-- 7#bj #bbejj7_/cj 4#jjaa #af sq4 feet of section1 of all of the arches2 or two parallel arches1 #b feet wide1 by #c feet deep each4 ,from #ajj to #aej feet span1 he makes the rise #a_/bj span1 ,from #aej to #bjj feet span1 he makes the rise #a_/ah span1 ,from #bjj to #cjj feet span1 he makes the rise #a_/ae span1 ,from #cjj to #djj feet span1 he makes the rise #a_/ad span1 ,from #djj to #ejj feet span1 he makes the rise #a_/ac span4 #aij4 ,the bridge built by ,mr4 ,burr across the ,delaware at ,trenton1 ,new ,jersey1 is a good specimen of an arch4 ,it is composed of white pine planks1 from thirty-five to fifty feet long1 and of a scantling #d #ab4 ,these planks are laid close together1 breaking joint1 having an entire depth of three feet4 ,the arches are stiffened by horizontal tie beams1 supporting the road-way1 and by diagonal bracing4 ,the spans are #afj1 #ahj1 and #bjj feet1 and the rise twenty-seven feet4 #aia4 ,the bridge over the ,susquehanna1 at ,columbia1 built in the same manner1 consists of twenty-nine arches1 each two hundred feet clear span1 supported on two abutments and twenty-eight stone piers4 ,the clear water-way of this bridge is #e1hjj feet2 and the entire length1 including piers and abutments1 one and one fourth miles4 ,there are three sets of arches1 which allow of two carriage roads and one railroad1 the whole width being thirty feet4 #aib4 ,an arch to support a passing railroad train must be very rigid4 ,it is customary to connect them with a light truss1 which effectually counter braces the arch1 and prevents that change of form which would otherwise take place2 depending entirely upon the arch for strength4 ,wherever the load is applied1 the arch tends to sink1 and a corresponding rise takes place at the opposite point4 ,a load placed at ,e1 fig4 #ga1 settles the arch at that point and causes it to rise at ,c4 ,a load placed at the curve of the arch depresses the centre1 and elevates the haunches4 ,to counteract these movements a light1 stiffening frame may be used1 its strength being able to resist the variable load passing over the bridge4 ,the strain thrown by the arch upon the truss1 advances from the opposite end to meet the train1 passes it at the centre1 and finally goes off from the bridge behind the load4 ,when the arch is the truss1 or when a truss is made with curved chords1 the counteracting effect of the truss is not completely obtained4 ,we should not depend upon the curved chord as an arch1 but only as a member of the truss4 #aic4 ,many combinations of arch and truss have been built in ,america for railroad bridges4 ,the principle of connecting the two systems is by some thought bad1 as they can hardly be made to bear equal parts of the load2 whence each must have more than half the necessary strength of the whole4 ,others maintain that by a proper arrangement of parts a perfect adjustment may be made1 by which the load may be placed more or less on either4 ,there seems to be no very good reason why the two systems should be combined1 as either may be made strong enough to bear the largest loads4 ,both arches and arch braces1 however1 are very usefully applied to bridges which have been made too light4 #aid4 ,the manner of applying arches is well shown in the bridges of the ,pennsylvania ,central ,railroad1 built by ,hermann ,haupt1 ,esq4 ,these bridges are on ,howe's plan1 to which have been added strong wooden arches4 ,the systems are connected by adjusting the counter braces against the arch by set screws4 ,the arrangement is simple and effectual4 ,the name of the builder is sufficient to warrant the stability of the bridge4 #aie4 ,however nicely we may form an arch1 it will settle more or less when the scaffolding is removed1 according to its flatness2 which depression increases with time4 ,mr4 ,weibeking expresses it in inches as follows3-- #j4hjf,r_/,s ,where ,r1 shows the rise1 and ,s1 shows the span4 ,to allow for this settling1 the curve when laid down on the platform for building the arch1 should be made a little more convex than the completed arch is required to be2 the amount of excess being that shown by the formula4 ,illustration3 ,fig4 #gb4 ,as a bridge composed of a curved rib when the span is large yields at ,d1 ,c1 and ,e1 fig4 #ga1 when the load is applied in the middle1 the strength must of course be increased by increasing the depth of the rib2 and not to make this too heavy1 a framed or built beam should be used as in fig4 #gb4 ,here it must be remembered that the two ribs must be so framed as to resist both tension and compression2 for when a load is placed at ,d1 the lower rib will be extended at d1 and compressed at c1 and e2 while the upper one will be compressed at ,d1 and extended at ,c and ,e4 ,,of ,,the ,,road-,,way4 #aif4 ,the flooring of any system is about the same2 consisting of transverse floor beams1 placed either on the top or bottom chords1 7according as the road-way is more or less elevated above the water-way17 which support longitudinal timbers1 upon which are placed cross-ties4 ,in some cases1 two curves of diagonal plank have been placed across the floor beams1 spiked at right angles to each other1 by which the bridge is considerably stiffened laterally4 ,general dimensions for the floor may be thus3-- ,transverse timbers1 #c feet from centre to centre1 #h #ad ,track strings1 notched #b inches to floor beams1 #ab #ad ,cross-ties placed one foot apart1 7clear17 #c #f ,illustration3 ,fig4 #gc4 ,,lateral ,,bracing4 #aig4 ,to prevent vibration in a horizontal direction1 a system of diagonal bracing is necessary4 ,the chief pressure upon these braces is caused by wind2 and may be found by considering the bridge as turned over upon the side1 and loaded with a weight equal to the maximum pressure of the wind1 which may be taken as forty pounds per square foot4 ,it is unnecessary to vary the size of these braces1 except in very long spans1 when they should increase from the centre to the ends4 ,for short spans1 7less than one hundred feet17 a brace #e #e is large enough4 ,for larger spans #g #g is sufficient4 #aih4 ,diagonal bracing1 when it can be introduced1 is a very desirable part of a bridge4 ,when the road is on the lower chord this cannot have place in full1 but may be applied as in fig4 #gd4 ,illustration3 ,fig4 #gd4 ,by increasing the height of truss in any bridge1 the tension and compression on the chords is lessened2 but the length of posts and rods is increased4 ,as a general thing1 one eighth of the span gives the best results4 #aii4 ,in framing a large bridge1 it is customary to cut the top chord sticks a little longer than to dimension2 to allow for compression in settling4 #bjj4 ,bridges in exposed situations have been sometimes blown off from the masonry4 ,if a bridge slides off from the masonry1 the whole force of the wind must be fifteen twenty-fourths of the whole weight of the bridge2 but if1 as is generally the case1 the masonry is rough1 7and not hammered17 no amount of wind will cause the bridge to slide4 ,the bridge will upset1 turning about its lower edge1 when the whole pressure of the wind1 multiplied by half the height of truss1 overbalances the whole weight1 multiplied by the half width4 ,in very exposed places the rod ,a ,d1 fig4 #gd1 answers a very good end2 when the road is upon the upper chord1 and a rod from ,b to the masonry1 when upon the lower4 ,,oblique ,,bridges4 #bja4 ,the effect of running a train over a skew bridge1 is to depress one side before the other2 as the load comes upon the centre of one truss before it does upon the opposite one4 ,this produces a side rocking in the engine1 dangerous alike to the bridge and to itself4 ,the floor timbers transferring the load to the chords should not be at right angles to the axis of the road1 but parallel to the abutment4 ,thus in fig4 #ge1 a wheel at ,b1 throws one third of its weight upon the abutment at ,e2 and two thirds upon the chord at ,c2 while in fig4 #ge ,a1 the wheel at ,b1 throws two thirds of the load upon ,c1 but one third also upon ,d4 ,illustration3 ,fig4 #ge4 ,fig4 #ge ,a4 #bjb4 ,in a very long1 oblique span1 the floor timbers may be arranged as in fig4 #gf1 that is1 inclined at the entrance and exit of the bridge1 but at right angles at the middle of the span4 ,illustration3 ,fig4 #gf4 #bjc4 ,the preservation of timber in wooden bridges may be accomplished by covering with boards1 whitewashing1 painting1 and by ,kyanizing4 ,covering and whitewashing are the best1 if care is taken to prevent dry rot by giving a good circulation of air about the timbers4 ,the oil in paints prevents the escape of moisture from within as well as the entrance of that from without2 and should not be used unless the wood is well seasoned4 ,the best plan is to thoroughly whitewash and cover the frame of the bridge1 and to paint the outside of the covering4 #bjd4 ,in framing two or more continuous spans1 the chords should always be connected over the piers2 as there is thus given something for the upper chords to pull against1 and a counter thrust for the lower4 #bje4 ,bridges should never1 when it can be avoided1 be placed either upon a curve or upon a grade2 particularly upon the former1 as the effect of a load is thereby very much increased1 in the first case causing a lateral1 and in the second a vertical shock4 ,,pile ,,bridging4 #bjf4 ,in shallow water1 in marshes1 and in similar situations1 where an embankment would be expensive1 pile bridging is very useful4 ,indeed1 whenever we are at liberty to obstruct the passage beneath the road1 it is well to adopt this system1 unless over twenty feet high4 ,it is cheaper than any other1 easier to repair1 the parts are quite independent of each other1 and such bridges last full as long as other wooden structures4 ,illustration3 ,fig4 #gg4 ,illustration3 ,fig4 #gh4 ,different plans for pile bridging are given in figs4 #gg to #hb4 ,figs4 #gg to #ha show plans for temporary pile work1 to be used during construction4 ,nothing lighter than fig4 #hb1 ought to be permanently used4 ,a pile bridge upon a curve may need stronger lateral bracing upon the convex1 than upon the concave side of the curve2 and also in running water2 in which cases1 such a form as fig4 #ha may do good service4 ,illustration3 ,fig4 #gi4 ,illustration3 ,fig4 #hj4 ,illustration3 ,fig4 #ha4 ,illustration3 ,fig4 #hb4 ,illustration3 ,fig4 #hb ,a4 7,for pile-driving1 and for proper dimensions1 see chap4 ,,xii47 ,,trestling4 #bjg4 ,trestling is a system of vertical posts1 and of caps and braces1 used both for temporary and for permanent works2 temporarily to pass a road over low ground where embankments are to be made1 and permanently over deep1 dry gorges1 where the amount of earthwork or masonry would be too great4 ,illustration3 ,fig4 #hc4 ,american railroads show all sizes and arrangements of trestling1 from twenty to two hundred feet high4 ,figs4 #hc and #hd show temporary works1 and fig4 #he permanent4 ,the main part of the design in trestles is to connect the several posts and caps by well-formed triangles2 the equilateral being the best4 ,illustration3 ,fig4 #hd4 ,the finest example of this system of building is the ,genesee high bridge1 over ,genesee ,river near ,portageville1 on the ,buffalo and ,new ,york ,railroad2 built by ,h4 ,c4 ,seymour1 ,esq4 ,it is eight hundred feet long1 and two hundred and thirty feet above the river4 ,it has eight stone piers1 thirty feet high1 upon which are placed trestles one hundred and ninety feet high1 seventy-five feet wide at base1 and twenty-five at top4 ,upon the top of all is placed a bridge fourteen feet high4 ,to build this viaduct was used #a1ejj1jjj feet1 board measure of timber1 which covered1 when standing1 two hundred and fifty acres2 also1 sixty tons of bolts4 ,the whole time occupied in building was but eighteen months1 the whole cost being #adj1jjj4 ,illustration3 ,fig4 #he4 ,,drawbridges4 #bjh4 ,in crossing rivers or bays open to navigation1 it is required from any companies building a bridge1 to leave a free passage for shipping4 ,this is done by making that part of the bridge over the channel movable2 7a draw74 ,illustration3 ,fig4 #hf4 ,draws may lift up1 7being counterbalanced17 may slide back upon the fixed part of the bridge1 or may turn on a pivot4 ,fig4 #hf shows a draw much used at present1 and answering every purpose4 ,each half of the movable part must be calculated as a small bridge4 ,the rods c c c support the overhanging part of the draw while open4 ,the whole revolves upon a centre pin and a set of rollers4 ,,centres4 #bji4 ,centres are temporary wooden frames1 used in the construction of stone arches4 ,their duty is to hold the masonry1 while it is unable to support itself4 ,for arches from five to fifteen feet span1 a centre made of boards or planks1 fig4 #hg1 is all that is necessary4 ,for longer spans1 when the ground beneath the arch can be used1 the form1 fig4 #hh1 answers well4 ,when there is no support but the abutments or piers1 something similar to fig4 #hi must be adopted4 ,this is the plan adopted by ,george ,rennie1 chief engineer at the ,waterloo bridge over the ,thames at ,london4 ,illustration3 ,fig4 #hg4 ,illustration3 ,fig4 #hh4 ,centres are strained in a different manner as the arch progresses2 first at the haunches1 and last at the crown4 ,excess of weight at any point causes a settling at such1 and a rise takes place at some other place4 ,by loading the arch temporarily1 such motions are checked4 ,illustration3 ,fig4 #hi4 ,these frames are placed vertically upon the pieces ,f ,f1 which being connected with the braces ,d ,d by the folding wedges c c1 admit of adjustment of the height of the centre4 ,the distance between the ribbed frames depends upon the form of the arch1 and the span1 or upon the weight to be supported2 varying from one to four feet4 ,the centres are covered with a course of narrow plank1 placed parallel with the axis of the arch1 upon which the voussoirs rest4 #baj4 ,the method of putting a bridge upon the masonry is shown in figs4 #ij1 and #ia2 the former when the road-way is upon the upper1 and the latter when upon the lower chord4 ,illustration3 ,fig4 #ij4 ,illustration3 ,fig4 #ia4 #baa4 ,in figs4 #ib to #ajj1 are given several plans for spans from five to seventy-five feet4 ,fig4 #ib1 shows the simple beam braced beneath with diagonal plank2 the bolts passing through the ties1 stringers1 and braces4 ,the stringers are bolted to the wall plates1 and when the bridge is upon a curve notched also1 by cutting the bolster4 ,fig4 #ib ,a shows the plan4 ,this form answers for openings from five to twenty feet4 ,from fifteen to thirty feet1 we may use figs4 #id1 #ie1 #if1 and #ig4 ,from twenty-five1 to fifty and sixty feet1 figs4 #ic1 #ig1 and #ih4 ,and from fifty to seventy-five feet1 figs4 #ii and #ajj4 ,the following tables give reliable dimensions for bridges upon the above plans4 ,illustration3 ,fig4 #ib4 #e to #bj feet4 ,fig4 #ib ,a4 ,span4 ,bolsters4 ,stringers4 ,ties4 ,braces4 ,bolts4 #e #ab #ab #ab #ab #f #aj #b #aj #a inch #aj #ab #ab #ab #ac #f #aj #b #aj #a inch #ae #ad #ad #ab #ah #f #aj #b #aj #a inch #bj #ad #ad #ab #bd #f #aj #b #aj #a inch ,the ties being notched three inches on to the stringers1 without cutting the latter4 ,illustration3 ,fig4 #ie4 #ae to #cj feet4 ,span4 ,rise4 ,bolster4 ,stringer4 ,braces4 ,rod4 #ae #f #ab #ab #ab #ab #b--e #f #a inch #bj #g #ad #ad #ab #ab #b--e #h #a inch #be #h #ad #ad #ab #ae #b--e #i #a inch #cj #aj #ae #ae #ab #ah #b--e #aj #a inch ,illustration3 ,fig4 #if4 #ae to #cj feet4 ,span4 ,rise4 ,stringer4 ,post4 ,rod4 #ae #e #ab #ab #h #h #a #bj #f #ab #ac #i #i #a #be #g #ab #ae #aj #aj #a #cj #h #ab #ah #aj #ab #a ,illustration3 ,fig4 #id4 #ae to #cj feet4 ,span4 ,rise4 ,stringer4 ,braces4 ,rods4 ,lattice4 #ae #e #b--h #h #b--e #e #a #b #f #bj #f #b--h #i #b--e #f #a #b #h #be #g #b--h #aj #b--e #h #a #b #i #cj #i #b--h #ab #b--e #i #a #b #aj ,illustration3 ,fig4 #ig4 #ae to #cj feet4 ,span4 ,rise4 ,stringer4 ,post4 ,rods4 ,braces4 #ae #e #b--h #h #h #h #a #d #e #bj #f #b--h #i #i #i #a #d #f #be #g #b--h #aj #aj #aj #a #e #f #cj #i #b--h #ab #aj #ab #a #f #f ,illustration3 ,fig4 #ic4 #be to #ej feet4 ,span4 ,rise4 ,chords4 ,braces4 ,posts4 ,rods4 #be #h #b--f #h #f #f #f #h #a #dj #aj #b--g #i #f #g #h #h #a #ej #aj #b--h #aj #f #h #h #aj #a ,illustration3 ,fig4 #ig4 #be to #ej feet4 ,span4 ,rise4 ,chords4 ,posts4 ,braces4 ,rods4 #be #h #b--f #h #h #h #e #e #a or #b-- #dj #aj #b--g #i #i #i #e #h #a or #b--a #ej #aj #b--h #aj #aj #aj #f #h #a or #b--a ,illustration3 ,fig4 #ih4 #be to #ej feet4 ,span4 ,rise4 ,chords4 ,posts4 ,braces4 ,rods4 #be #h #b--f #h #f #h #e #e #b--a or #a--a #dj #aj #b--g #i #f #i #e #h #b--a or #a--a #ej #aj #b--h #aj #f #ab #e #aj #b--a or #a--a ,illustration3 ,fig4 #ii4 #ej to #ge feet4 ,span4 ,rise4 ,chord4 ,posts4 ,braces4 ,lattice4 #ej #h #b--h #aj #a--h #aj #b--f #g #b #f #fj #i #b--h #aj #a--h #aj #b--f #g #b #f #ge #aj #c--h #aj #b--h #aj #c--f #h #b #f ,illustration3 ,fig4 #ajj4 #ej to #ge feet4 ,span4 ,rise4 ,chords4 ,posts4 ,braces4 ,centre ,rods4 braces4 ,no4 #a4 ,no4 #b4 #ej #h #b--h #aj #a--h #aj #b--f #g #e #e #a #a #fj #i #b--h #aj #a--h #aj #b--f #g #e #e #a #a #ge #aj #c--h #aj #b--h #aj #b--f #h #e #f #a #a #bab4 ,in dimensioning small bridges1 like the above1 in estimating the maximum load1 more regard must be given to the weight of momentary loads than 7as in large bridges7 the weight per lineal foot1 as the weight of the bridge itself1 when under fifty or sixty feet span1 is inconsiderable4 ,the greatest load that can come upon a single post or rod1 is that from the driving wheels of a locomotive4 ,if the whole engine weighs forty tons1 there will be ten tons on each pair of drivers1 or five tons or #aa1bjj lbs4 on each wheel2 which1 being applied over a length of ten feet only1 may be considered as at a single point1 and all parts must be able to bear such load4 ,in large spans1 where the weight is great1 if the truss is strong enough to support the bridge and load1 it will safely resist the effects of a sudden application of passing trains4 ,,note4--,on the ,static and ,dynamic deflection of ,bridges4 ,considerable variance of opinion exists as to the relative deflection of bridges1 produced by stationary and by moving loads4 ,neither experiment nor theory has exactly settled the point4 ,experiments upon the ,elwell bridge1 7,epsom and ,croydon ,railway1 ,england74 ,velocity in feet per second4 ,deflection in inches4 #j #j4bae #be #j4bae #ca #j4bcj #cb #j4bbe #ed #j4bde #ge #j4bce ,the bridge being a cast-iron girder of forty-eight feet span1 load thirty-nine tons4 ,experiments on the ,godstone bridge1 7,s4 ,e4 ,r4 ,r4 ,england74 ,velocity in feet per second4 ,deflection in inches4 #j #j4ai #bb #j4bc #dj #j4bb #gc #j4be ,cast-iron girder1 thirty feet span1 load thirty-three tons4 ,mr4 ,w4 ,h4 ,barlow1 7,eng47 observed1 8that in case of a timber viaduct1 a freight train1 at a low speed1 produced a certain deflection2 but an extra train1 with a much lighter engine1 seemed to push the bridge like a wave before it40 ,the ,britannia tubular bridge was depressed three fourths of an inch by two locomotives and a train of two hundred and eighty tons standing still2 but at seventy miles per hour1 the deflection was sensibly less4 ,,chapter ,,ix4 ,,iron ,,bridges4 8,a little knowledge is a dangerous thing40 #bac4 ,within the past ten years iron has been brought extensively into use for railroad bridging2 and when employed by those who understand its chemical and mechanical nature is unequalled for strength1 durability1 and elegance of appearance2 but when1 as is too often the case in ,america1 it is intrusted to men who neither know nor care for any thing but the price they get for it1 nothing can be more unsafe4 ,no material requires so complete a knowledge of its properties1 to be safely used1 as cast-iron4 ,,nature ,,and ,,strength ,,of ,,iron4 #bad4 ,the table below shows the properties of the several descriptions of iron used in engineering4 ,wrought ,cast-,iron4,iron ,wire4 ,boiler ,designation of the ,iron4 ,plate4 quality4 #dhj #dej ---- #dhj,weight per cubic foot in lbs4 ,resistance to #aejjj #dejj #bejjj #abgdj extension in lbs4 per sq4 inch4 ,resistance to #aajjj #bejjj ---- #gejj compression in lbs4 per sq4 in4 ,expansion per degree 4#jjjjjff 4#jjjjjfjh 4#jjjjjfhe 4#jjjjjff ,fahrenheit in lengths4 4#jjjjjjjdbd4jjjjjjajf4jjjjjjjddf4jjjjjj jebd;,extension per lb4 per square inch4 4#jjjjjjadi4jjjjjjjhc ---- 4#jjjjjjahi;,compression per lb4 per square inch4 ,ratio of extensive to #ij to #ff #bj to #aaa ---- #abg to #ge compressive strength4 ,resistance to #abejj #agejj ---- ---- detrusion1 or shearing4 #ee #ca ---- ----,relative transverse strength4 ,column four refers to boiler plate when built into tubes4 ,after wrought iron has become a little compressed1 its power to resist a crushing force is very much increased4 #bae4 ,the tenacity of wrought iron is increased by heating4 ,experiments upon thirty varieties gave the following mean result1 the temperature ranging from #ejj to #gjj ,fahrenheit4 ,strength when ,cold4 ,hot4 ,cooled4 #fj1jjj #fd1jjj #gj1jjj #baf4 ,stirling's process of toughening cast-iron1 by the addition of malleable scrap1 increases the strength in the following ratio3-- ,the mean tensile strength of cast-iron being #ah1jjj lbs4 ,and the compressive strength being #aje1jjj lbs4 ,when ,stirling-toughened the tensile strength is #bc1jjj lbs4 ,and the compressive strength #acj1jjj lbs4 ,the strength of cast-iron increases rapidly up to the twelfth or fifteenth recasting1 when it is nearly doubled2 after the fifteenth melting the strength decreases4 #bag4 ,wrought iron exposed for some time to vibration1 as in the case of railroad axles1 or iron which has been wrought with light hammers1 loses its toughness and becomes 8short10 7crystalline74 ,the fibre may be restored in such cases by reheating and cooling slowly4 #bah4 ,,general ,,ratios ,,of ,,the ,,strength ,,of ,,iron4 ,tension4 ,compression4 ,cross ,strain4 ,cast1 #cjj #a1fff #ca4fh ,wrought1 #a1jjj #gcc #ee4dj ,,of ,,the ,,strength ,,of ,,boiler ,,plates4 #bai4 ,the strength of rolled boiler plates is no greater in the direction of the fibres than crosswise1 but is more regular2 whence the length of the fibre must be placed as nearly as possible with the direction of the force4 ,a mean of twelve experiments1 by ,mr4 ,fairbairn1 gives the tensile strength of wrought iron plates as #ej1ifj lbs4 per square inch2 and the compressive strength of plates1 when built into tubes1 as #cj1dfd lbs41 or for safe use in practice1 for extension1 #ab1gdj lbs41 and for compression1 #g1ejj lbs4 ,in the remarks upon girder bridges the matter of riveting will be considered4 ,,classification ,,of ,,iron ,,bridges4 #bbj4 ,iron bridges may be classified as follows3-- ,those entirely of cast-iron1 or ,arch and ,girder bridge4 ,those of wrought iron alone1 or ,tubular and ,girder4 ,those of iron wire1 or ,suspension bridges4 ,those of cast and wrought iron1 or ,trussed bridges4 ,the order in which these bridges may be placed as regards cost of construction1 and extent of application1 is as follows3-- ,number4 ,span4 ,description of bridge4 #a #aj to #ej feet ,cast-iron girder4 #b #ej to #bjj feet ,cast and wrought combinations4 #c #bjj to #bjjj feet ,suspension4 #d #bjj to #ejj feet ,cast arch4 #e #be to #ajj feet ,boiler plate girder4 #f #ajj to #ejj feet ,tubular4 ,numbers #b1 #c1 and #e1 are the forms which are in use upon ,american roads4 ,no4 #a1 is very liable to failure1 requires much more knowledge and care in building1 and is far more expensive than a wooden truss1 or trussed girder4 ,no4 #d1 is very expensive1 and causes a greater obstruction to the water-way than any other4 ,the enormous expense of ,no4 #f1 should1 and will prevent its adoption in the ,united ,states4 ,let us look at the principles of construction of numbers #b1 #c1 and #e4 ,,combinations ,,of ,,cast ,,and ,,wrought ,,iron4 #bba4 ,under this head come all of the iron trussed frames used in this country4 ,as before observed1 skill in bridge construction consists in using always that material which with the least expense is the best able to resist the particular strain to which it may be exposed4 ,thus wrought iron must always be used to resist tension1 and cast-iron compression4 ,posts1 braces1 and upper chords should always be cast1 while ties and lower chords should be made of wrought iron4 ,the strength of a railroad bridge must be such as to resist all extra shocks and strains1 such as are produced by derailment of engines1 and breakage of axles2 also incidental strains arising from change of form by expansion and contraction of the metal1 and from high winds and gales4 ,illustration3 ,fig4 #aja4 ,every part of a bridge not resisting some force is worse than useless1 as it adds to the weight4 ,lightness not only increases the economy directly1 but indirectly by removing a part of the permanent load4 #bbb4 ,foremost in class number two stands ,wendel ,bollman's ,iron ,suspension and trussed bridge4 ,for simplicity of construction and directness of action1 this bridge is unsurpassed4 ,the weight at each post is transferred at once to the abutment or pier4 ,the upper chord is of cast iron1 hollow1 octagonal without1 and circular within4 ,the posts consist of an casting1 the central web cast open and the flanges whole4 ,the top is adjusted to the chord1 and the bottom to the tension or suspending rods4 ,these latter are of wrought iron1 rectangular in section1 joined when the length requires it by an eye bolt4 ,each set after leaving the foot of the post1 passes through the chair at ,a ,b1 fig4 #aja1 and is secured by a nut4 ,the junction of the tension rod ,a ,c1 and the counter rod ,b ,c1 is attached indirectly to the foot of the post by a pendulum or link2 which serves to equalize the effect of expansion upon the rods4 ,vibration and reaction are prevented by the panel diagonal ties ,d ,h1 and ,c ,e4 ,the floor is supported by flanges at the foot of each post4 ,the lateral bracing consists of a system of hollow cast-iron posts1 and of wrought diagonal tie rods4 ,a lower chord is plainly unnecessary1 its place being taken by the rods ,c ,b1 ,f ,b1 ,f ,a1 ,g ,a4 ,a bridge of this description upon the ,baltimore and ,ohio ,railroad of the following dimensions1 ,clear span1 #abd feet ,length of top chord1 #abh feet ,length of panel1 #ae feet ,height of truss1 #ag feet ,width1 #af feet ,lbs4 of cast-iron1 #fe1acg ,lbs4 of wrought iron1 #cc1ebg ,whole weight1 #ih1ffd ,weight per lineal foot1 #gif was subjected to the following tests4 ,three locomotives with tenders attached1 and weighing in all one hundred and twenty-two tons1 7nearly one ton per foot17 were run over the bridge at eight miles per hour1 when the deflection at centre was one and three eighths inches1 and at the first post nine sixteenths of an inch4 ,the following tests were applied to a bridge of seventy-six feet span upon the ,washington branch of the same road3 ,an engine and tender weighing forty tons1 caused a deflection of five eighths of an inch4 ,a fast passenger train deflected the bridge nine sixteenths of an inch4 ,two engines and tenders1 back to back1 at rest1 and weighing in all #gg tons1 caused a deflection of #aa_/af inch1 ,the same at ten miles per hour1 #ac_/af inch1 ,engines head to head at four miles per hour1 #ac_/af inch1 ,engines head to head at eight miles per hour1 #ac_/af inch1 ,engines head to head at twenty miles per hour1 #ad_/af inch4 ,the extreme expansion of the one hundred and twenty-eight feet chord from heat1 was five sixteenths of an inch at each end1 or five eighths of an inch in all1 or #a_/bdegth of the length2 and that without the slightest derangement of masonry4 ,the rod ,c ,b1 being five times as long as ,c ,a1 expands five times as much1 but at the same time the lengths ,d ,a1 ,d ,b1 being so nearly proportional to ,c ,a1 and ,c ,b1 expand also in the ratio of one to five2 and thus no bad result is experienced4 ,the estimate of strains upon this bridge is extremely simple2 the whole consisting of as many separate systems as there are posts4 ,each set of rods sustain a rectangle equal to one panel1 i4 e41 the two adjacent half panels4 ,thus ,a ,c1 and ,c ,b1 support the rectangle m m1 m m1 the rods ,a ,f1 ,f ,b1 the rectangle n n1 n n4 ,allowance must of course be made for the inclination of the rods4 ,the dimensions of the central pair will of course be the same2 but those of the other sets will vary4 ,the diagonals ,d ,h1 and ,h ,l1 prevent reaction2 and must be able to resist the action produced by the variable load upon one panel 7as noticed in ,chapter ,,viii74 ,any load1 one at ,c ,d for example1 gives to the posts a tendency to revolve on ,a1 as a centre towards the abutment2 to oppose which1 there must be a force in the opposite direction4 ,the most proper direction in which to resist such motion is the line ,c ,k1 i4 e41 the line of the lower chord4 ,in this bridge there is no lower chord1 but in place of such are put the rods ,a ,g1 ,a ,k1 ,b ,h1 and ,b ,c2 which prevent the change of form 7by the motion of the triangle7 and act against the upper chord4 ,as an example of the estimate of strains upon this bridge take the following4 ,span1 #ij feet4 ,rise1 #ah feet4 ,panel1 #ae feet4 ,weight per lineal foot1 #b1ejj lbs4 ,whole weight1 #bbe1jjj lbs4 ,weight on each side truss1 #aab1ejj lbs4 ,weight on each post1 #ah1gej lbs4 ,the weight borne by each system1 i4 e41 one post and the two supporting rods1 is #ah1gej lbs4 ,the strain to be resisted by any one rod depends upon its inclination4 ,the following figures show the elements of the truss in question3-- ,section ,rod4 ,length4 ,applied weight4 ,increased of the strain4 bar in inches4 ,a ,b #ij4j ,c ,d #ah4j ,a ,c #bc4d 7#ahgej - #cabe7 #aefbe which by #bc4d_/ah #bjcab #a ,a ,h #ce4j 7#ahgej #fj7_/ij #abejj which by #ce_/ah #bdcjf #a ,a ,f #dh4e 7#ahgej #de7_/ij #icge which by #dh4e_/ah #bebfj #a ,a ,k #fb4f 7#ahgej #cj7_/ij #fbej which by #fb4f_/ah #bagcf #a ,a ,g #gg4f 7#ahgej #ae7_/ij #cabe which by #gg4f_/ah #acdgb #a ,column #a1 gives the name of the rod2 col4 #b1 the calculated diagonal length2 col4 #d1 the applied weight1 7the varying weight by reason of the varying inclination7 found by multiplying the whole weight upon one panel or post by the distance of that post from the abutment1 and dividing the product by the span4 7,thus the load applied to ,a ,g is 7,w ,,ib7_/,s1 that on ,a ,k is 7,w ,,bx7_/,s1 and so on47 ,col4 #f1 shows the increase found by col4 #e on account of inclination as noticed in ,chap4 ,,viii42 and finally1 col4 #d gives the necessary sectional area of the bars or rods4 ,the compression on the top chord is evidently the sum of the compressions of the separate systems2 the compression from any one system is as follows1 fig4 #ajb4 ,illustration3 ,fig4 #ajb4 ,let a d1 c d be the rods1 and a b c the chord2 also b d1 the post2 now if d b represents the weight1 e h shows the tension on a lower1 or the compression on an upper chord2 the triangles a c d and a b e are similar2 as also e b h and d b c2 whence be 7ab cd7_/7ac72 and eh 7cb be7_/7dc7 compression4 ,numerically we have the following figures3-- ,in the first system1 be 7#ae #gg4f7_/ij #ac1 also eh 7#ge #ac7_/gg4f #ab4 ,in the second system1 be 7#cj #fb4f7_/ij #ba1 also eh 7#fj #bj7_/fb4f #bj4 ,in the third system1 be 7#de #dh4e7_/ij #bd1 also eh 7#de #bd7_/dh4e #bc1 that is1 the compression from the system ,a ,c ,b1 is to the weight on the post1 as twelve is to the length of the post2 or actually #ah to #ab as #ah1gej to compression2 whence compression 7#ahgej #ab7_/ah #abejj in system one1 and in the second system #ah to #bj as #ahgej to #bjhcc4 ,in the central system1 #ah to #bc as #ahgej to #bdjjj4 ,doubling the sum of the first and second systems1 and adding thereto the central1 we have #b7abejj #bjhcc7 #bdjjj #ijfff lbs41 as the whole compression upon one side of the bridge4 ,as to compression only1 this would require a section of about four square inches of cast-iron1 which may be obtained by a tube of four and one half inches inside1 and five inches outside diameter4 ,we may however need to increase this amount to resist flexure1 or transverse strains2 in which case the length of tube in one panel is to be regarded as the height of a post1 or the length of a beam2 and the size will be found by the table on page #ach4 ,each post must bear #ah1gej lbs41 and these being of cast-iron1 to resist flexure1 by the same table above referred to1 should1 if made as a hollow cylinder1 be a little over four inches in diameter1 and one half inch thick2 and if of or section1 should have a square of nearly five inches4 ,the flooring will be dimensioned by the rules given in ,chapter ,,viii4 for single beams4 ,there is nothing about this bridge to burn1 in case of fire1 except the floor2 and that might easily be made of iron4 ,to use the words of the inventor1 8,the permanent principle in bridge building sustained throughout this mode of structure1 and in which there is such gain in competition with any other1 namely1 the direct transfer of weight to the abutment1 renders the calculation simple1 the expense certain1 and facilitates the erection of secure1 economical1 and durable structures40 ,,whipple',s ,,iron ,,bridges4 #bbc4 ,the bridges built by the above-named engineer are in all respects well proportioned1 rigid1 safe1 and durable4 ,cast-iron is used as a top chord1 and wrought iron is employed to resist the tensile forces4 ,the plan put up upon the ,new ,york and ,erie ,railroad1 consists of a hollow cast-iron top chord1 circular in section4 ,lower chords of wrought iron rods4 ,posts cast cruciform in section4 ,diagonal tension rods1 as in ,pratt's bridge1 7,chapter ,,viii474 ,the whole structure is in iron exactly what the above-named bridges are in wood2 and the method of calculation is the same4 ,for spans not exceeding one hundred feet1 this form answers every purpose as a railroad bridge4 ,it is open to the same objection in larger spans as are all trusses transferring the load by a series of triangles through which the weight passes successively1 namely1 the effect of an enormous pressure at the feet of the second and third pairs of braces1 which should be taken up by arch braces1 as in fig4 #fi2 or by rods from the top of the abutment pillars to the feet of the second and third sets of posts4 ,a span of this plan1 upon the ,new ,york and ,erie ,railroad1 of forty feet1 and which weighed only three tons1 supported a load of fifteen hundred pounds per lineal foot for two days2 when the bridge had settled nearly one half inch4 ,a load of rails weighing #acah lbs4 per foot 7of bridge7 was then rolled over1 upon a truck without springs1 thus making the whole load upwards of #b1hjj lbs4 per foot1 when the whole deflection was three fourths of an inch4 ,upon removing the load the bridge returned to its original position1 within one fourth of an inch4 ,,suspension ,,bridges4 #bbd4 ,suspension bridges of large span have been generally considered as entirely unfit for railroad purposes2 but ,john ,a4 ,roebling has proved the contrary by erecting a wire suspension railroad bridge of eight hundred feet clear span across ,niagara ,river2 which with heavy loads and violent gales has shown itself to be both stiff and strong to any desired amount4 ,the construction of a bridge upon any other plan would have been hardly possible at the site of ,mr4 ,roebling's ,niagara bridge1 there being no opportunity for scaffolding or for piers1 pontoons or hydraulic presses4 ,the simple road-way supported by cables1 possesses great strength with very little stiffness4 ,it must be accompanied by stays and trusses to check vibration4 ,no bridge involves more simple calculations1 and in none can we proceed with more absolute safety1 than in the wire suspension4 ,european suspension bridges are generally formed of cables made by linking bars of wrought iron together4 ,this method is more expensive and more liable to failure than the ,american plan of forming cables of iron wire4 ,an apparently good bar may be defective inside1 while we are sure of every component fibre of the cable2 indeed it is very little trouble to test each wire as it is laid into the cable4 ,the parts to be considered in proportioning a suspension bridge are ,the anchoring masonry1 ,the anchor chains1 ,the towers and plate1 ,the suspension cables1 ,the suspending rods1 ,the stiffening arrangement1 ,the road-way4 ,the data given in the construction of a bridge of this description are ,the span1 ,the load to be supported4 ,the assumed data ,the versed sine of the cable1 ,the width4 ,and the required elements ,the length of cable1 ,lengths of suspending rods1 ,angle of tangent of cable at point of suspension with axis of tower1 ,tension upon the cables1 ,section of the anchor irons1 ,amount of anchoring masonry1 ,size of the towers1 ,dimensions of trussing and of road-way4 ,,of ,,the ,,cables4 #bbe4 ,the curve formed by the cable of a suspension bridge lies between the parabola and the catenary4 ,when loaded the curve is nearly the former1 and when unloaded the latter4 ,problem #a4 ,given the horizontal distance between the points of suspension and the versed-sine1 to find the length of the cable1 fig4 #ajc4 ,illustration3 ,fig4 #ajc4 ,represent ,c ,e by b1 and ,e ,f by a1 and the length of the semi-curve is ,l b#a 7a_/b7#b4 ,let the half span be five hundred feet1 and the versed-sine or deflection eighty feet1 the formula becomes ,l #ejja 7#hj_/ejj7b #ejj #a4jaga #ejh4ee feet1 which is the half length of cables between towers4 ,problem #b4 #bbf4 ,to find the length of the suspending rods4 ,calling ,e the horizontal distance between the vertical suspenders1 we have the formula ,x 7,y#b7_/7;b#b7 a1 in which we place ,e1 #b;,e1 #c;,e1 etc41 in place of ,y1 thus calling the rods one hundred feet apart1 we have ,centre4 ,rod #a4 ,rod #b4 #j 7,e#b7_/7;b#b7 a 7#d;,e#b7_/7;b#b7 a #j 7#ajjb7_/7ejjb7 #hj 7#bjjb7_/7ejjb7 #hj #j #c4bj #ab4hj ,rod #c4 ,rod #d4 ,rod #e4 7#i;,e#b7_/7;b#b7 a 7#af;,e#b7_/7;b#b7 a7#be;,e#b7_/7;b#b7 a 7#cjjb7_/7ejjb7 #hj 7#djjb7_/7ejjb7 #hj 7#ejjb7_/7ejjb7 #hj #bh4hj #ea4bj #hj4jj ,problem #c4 #bbg4 ,to find the angle ,e ,c ,g1 fig4 #ajc4 ,the formula for the angle between the axis of the tower1 and the tangent to the curve of the cable at the point of suspension is tang a ,e ,c ,g 7#b;a7_/b4 ,span being one thousand feet1 b is five hundred2 and a being eighty feet1 we have tang ,e ,c ,g #afj_/ejj log #afj - log #ejj3 or #b4bjdabj - #b4fihigj tang #i4ejeaej #ag #de ,e ,c ,g4 ,also1 #ij - #ag #de #gb #ae angle ,g ,c ,a1 or ,a ,c ,h4 ,when the points of suspension are not at the same elevation1 we proceed in the same manner3 only using ,g ,l1 ,g ,e1 in place of ,f ,l1 ,f ,c1 in fig4 #ajc ,a4 ,illustration3 ,fig4 #ajc ,a4 ,that the resultant of the forces acting upon the top of the tower may be vertical1 the angles ,g ,c ,a1 and ,a ,c ,h1 fig4 #ajc1 must be equal2 if not1 the masonry must be so arranged as to cause the resultant to pass through the centre of gravity4 ,when more than one span is used1 and the openings are unequal1 that the intermediate pier or piers shall not be pulled over1 the cable of the largest1 and consequently heaviest span1 must have a greater inclination from the horizontal than that of the shorter span2 the product of the tensions by their respective inclinations must be equal4 ,mr4 ,roebling's plan in connecting several spans1 is to attach the cables of adjacent spans to a pendulum upon the pier1 by which arrangement the difference in tension upon the different cables swings the pendulums1 without racking the masonry4 ,problem #d4 #bbh4 ,given the weight per foot of bridge and load1 to find the tension at the lowest point of the curve4 ,the formula for the minimum tension1 that at the vertex ,f of the curve1 is ,t 7ph#b7_/7b;f72 where p is the weight per foot of bridge and load1 h the half distance between the points of suspension1 and f the versed-sine4 ,thus the span being one thousand feet1 the versed-sine eighty feet1 and the load per lineal foot six thousand lbs41 the formula becomes ,t 7#fjjj #ejjb7_/afj #icgejjj lbs4 or #dahe tons4 ,the maximum tension is at the points of support1 and is expressed by the formula ,t 77ph7_/7#b;f77h#b #d;f#b3 which1 in the case before us1 becomes ,t 77#fjjj #ejj7_/afj7ejjb #d #hjb #dcie tons4 #bbi4 ,the object of the anchoring is to connect the cable with a resistance upon the land side1 which shall more than balance the weight and momentum of the bridge and load upon the opposite side4 ,the anchoring of the ,niagara bridge consists of an iron chain made of flat links1 #g feet long1 #g inches wide1 and #a4d inches thick2 the chain links consist alternately of six and of seven of these bars2 see fig4 #ajd4 ,illustration3 ,fig4 #ajd4 ,in the ,fribourg bridge 7,switzerland7 the anchorage is made as in fig4 #aje1 7see p4 #bbj17 by a cable in place of the chain4 ,in ,m4 ,navier's suspension bridge at ,paris1 over the ,seine1 the anchorage depended somewhat upon the natural cohesion of the earth forming the bank of the river1 and this being destroyed by the bursting of a water-pipe in the vicinity1 the bridge fell4 ,when there is no natural rock for an anchorage1 the masonry of the shaft must1 by its own weight1 resist the tension4 #bcj4 ,the height of the towers must be at least as much as the versed-sine of the cable4 ,their duty is to support the whole bridge and load4 ,the breadth and thickness of these columns must be determined more with a view to opposing lateral1 than downward strains4 ,the former result from the horizontal vibrations of the bridge caused by the action of the wind4 ,tremor and vibration caused by a passing load1 tend to pull the towers into the river4 ,the section for weight only might be very small4 ,from the practice of the best builders1 a mean section of one fifth of the height seems to give the best results2 thus1 if a tower is sixty feet high1 the mean thickness should be twelve feet2 or the top being #h #h feet1 the bottom should be #af #af feet4 ,if the bridge is so little braced laterally as to swing1 a dangerous momentum will be generated which would very much increase the strain1 both upon the masonry and upon the cables4 #bca4 ,the object of the stiffening truss is to transfer the weight applied at any one point over a considerable length1 and to prevent vibration4 ,its dimensions should1 therefore1 be those of the counterbracing in an ordinary truss4 ,any applied load produces a certain depression in the bridge3 to use the words of ,mr4 ,roebling1 8every train that passes over the bridge causes an actual elongation of the cables1 and consequently produces a depression4 ,if the train is long1 and covers nearly the whole length of the bridge1 and is uniformly loaded1 the depression will be uniform4 ,if the train is short1 and covers only a part of the floor1 the depression will be less general and more local2 and will be the joint result of an elongation of the cables1 and of a disturbance of the equilibrium4 ,depressions will be in direct proportion to the loads1 and indirectly as the length of train40 ,the amount of depression depends on the elongation of the cables2 the elongation upon the length4 ,the depression is shown by the formula ,d 7,v#b - d#b7 - 7l#b - d#b74 where ,d depression1 l half length of curve before elongation1 ,v half length of curve after elongation1 d half distance between points of suspension40 ,the effect of heat1 by expanding the cables1 is also to depress the road-way2 the amount being shown by the expression ,d 7,v#b - d#b7 - 7l#b - d#b74 ,v being the length of semi-curve as elongated by heat instead of by tension2 the elongations1 both by heat and tension1 being found by table on page #aic4 ,upon the top of the towers is placed a pair of cast-iron plates separated by rollers2 the upper plate 7the saddle7 is thus enabled to move over the lower one when pulled either way by the movement of the cables4 ,the length of the half cable between towers being generally greater than the distance from the top of the tower to the anchoring1 expands more1 when the saddle moves towards the land side4 ,the dimensions of these castings must be sufficient to resist the whole weight of bridge and load4 #bcb4 ,as an example of the preceding formula1 take the following3-- ,assume the span as #a1jjj feet4 ,height of towers #ajj feet4 ,deflection of cables #ij feet4 ,weight per foot 7lineal7 of bridge #b1ejj lbs4 ,weight per foot 7lineal7 of load #b1jjj lbs4 ,whole weight per foot #d1ejj lbs4 ,total weight #d1ejj1jjj lbs4 ,,cables4 ,the formula for the half length of cables between tops of towers is ,l b#a 7a_/b7#b1 which becomes ,l #ejja 7#ij_/ejj7b #eaj4hj1 which doubled1 is #ajba4ch4 ,to this add double the distance from the top of tower to the anchorage1 7see page #bjf17 which is found as follows3-- tang ,e ,c ,g 7#b;a7_/b4 ,also1 tang ,e ,c ,g log #b;a - log b1 or #b4beebgc - #b4fihigj tang #i4eefcjc of which the angle is #ai #dh and #ij - #ai #dh is #gj #ab angle ,g ,c ,a or ,a ,c ,h4 ,the height of the tower being one hundred feet1 and the angle at the tower #gj #ab1 we have ,sin #ai #dh #i1ebi1hfd ,sin #ij #jj #aj1jjj1jjj log height 7#ajj7 #b1jjj1jjj log distance 7#bie4b7 #b1dgj1acf which double1 and we have #eij4d2 finally1 add twice the breadth of the tops of the towers1 and the whole length of cable is1 from anchorage to anchorage1 #ajba4ch #eij4dj #af #afbg4gh feet4 ,the formula for the maximum tension1 7that at the point of suspension17 is ,t 77ph7_/7#b;f777h#b #d;f#b71 which becomes ,t 77#dejj #ejj7_/ahj77bejjjj #cbdjj7 #biff tons4 ,number #aj iron wire 7#bj feet per lb47 will support #a1fdh lbs4 per strand2 this is the ultimate strength2 the maximum load for safety is #djj lbs4 per strand2 whence #b1iff tons1 or #f1fdb1ejj lbs4 will require #af1fjf strands2 and if we use two cables1 each must have #h1cjc wires2 or four cables of #d1aea each4 ,the permanent load on suspension bridges should never be more than one sixth of the ultimate strength2 one eighth is a good standard4 ,the accidental load should never exceed one fifth of the whole strength of the cables4 ,the permanent weight supported by the ,niagara bridge is only one twelfth of the ultimate strength of the cables4 ,,anchor ,,chains4 ,the maximum tension being #f1fdb1ejj lbs4 the whole section of the four anchorings will need to be #ffdbejj_/aejjj #ddc inches1 or #aaa square inches for each shaft2 which is obtained by eleven links ten inches wide and one inch thick4 ,if we so attach the anchor chains to the masonry as to reduce the tension one fourth at the first arch1 7see ,fribourg anchoring17 we may fasten three bars of the chain at that point1 and descend from the first to the second arch with eight bars2 and leaving two bars at that point1 proceed to the bottom with the remaining six4 ,where there is no natural rock to build the masonry into or against1 enough artificial stone must be put down to balance the bridge and load4 ,,anchoring ,,masonry4 ,the entire weight of the bridge and load being #d1ejj1jjj lbs4 and the whole tension1 as above found1 #f1fdb1ejj lbs41 or upon each tower #c1cba1bej lbs42 this is the tension tending to draw the masonry out of each shaft4 ,this tension must be reduced on account of the inclination of the pulling force4 ,the tower is one hundred feet high4 ,the distance on the line of tension from the top of the tower to the anchoring1 as already found1 is #bie4b feet2 whence the actual effort to move the anchor masonry1 is thus1 #bie4b to #ajj as #a1ffj1fbe to the effort or #efb1edb lbs4 ,if rock weighs #afj lbs4 per cubic foot1 which is resisted by a column of masonry of #c1cba1bej_/afj #bj1geh cubic feet1 or #bj #bj #eb feet1 or by a mass #ae #ae #ia feet4 ,,towers4 ,the height of towers being one hundred feet1 and the mean thickness being one fifth of the height1 we have mean section #bj #bj2 or top #ab #ab1 and base #bh #bh4 ,,suspending ,,rods4 ,assuming the horizontal distances between the centres of the vertical suspenders as five feet1 their lengths1 then1 will be found by formula ,x 7,y#b7_/7;b#b7 a2 and placing for ,y#b the distances #e1 #aj1 #ae1 #bj1 etc41 we have1 commencing at the centre1 ,centre4 #e #aj #ae #j #eb_/ejjb #ijajb_/ejjb #ijaeb_/ejjb #ij #j 4#jji 4#jcf 4#jha ,centre4 #bj #be #cj #j #bjb_/ejjb #ijbeb_/ejjb #ijcjb_/ejjb #ij #j 4#add 4#bbe 4#cfj ,centre4 #ce #dj #de #j #ceb_/ejjb #ijdjb_/ejjb #ijdeb_/ejjb #ij #j 4#dij 4#egf 4#gbi ,centre4 #ej d #j #ejb_/ejjb #ij7;d#b7_/7;b#b7 a #j 4#ijj h and so on1 until we arrive at the tower4 ,whatever distance above or below the vertex of the curve the road-way is placed1 is of course constant1 to be added to or taken from the above lengths4 ,the manner of putting in any camber is simple both in theory and practice4 ,the strain upon the suspenders is merely the direct weight of the road-way and load4 ,if this is #c1ejj lbs4 per foot1 the five feet supported by two rods 7one each side7 will weigh #ag1ejj lbs42 each rod or wire rope must hold #h1gej lbs42 this can be done by a section of one half inch area4 ,for extra strains1 however1 on so large a span as #a1jjj feet1 one inch of area is not too large4 ,,of ,,the ,,stiffening ,,trusses1 ,,girders1 ,,and ,,stays4 ,the object of the girders supporting the rails is to diffuse the applied weight2 these girders may be made of a ,howe truss four or five feet deep1 by trussed girders1 only simply deep and stiffly framed track strings4 ,they should be able to distribute the load applied at one point at least fifteen or twenty feet4 ,the side trusses transfer to a still greater extent any applied load4 ,mr4 ,roebling estimates the combined effect of trusses and girders in the ,niagara bridge as transferring the weight of a locomotive over a length of two hundred feet4 ,this transferring counteracts the local depression4 ,the ,niagara truss is formed by a system of vertical posts1 five feet apart1 and diagonal rods passing from the top of the first post to the foot of the fifth2 the inclination being #de1 spreads the weight placed upon any one pair of posts over twice the height of the truss1 or about forty feet4 ,as to the actual dimensions of the girders supporting the rails1 if we intend them to spread an applied weight over forty feet1 they must be as stiff as a bridge of forty feet span4 ,and as regards the truss1 if we would effectually distribute the applied weight and check vibration1 the trussing should be as strong as the counterbracing in a large span upon the ordinary plans4 ,the principle of trussing a suspension bridge may be thus explained4 ,see fig4 #ajf4 ,suppose that in place of supporting the three trusses ,d s w1 s m m1 and m m d1 upon piers at w and m1 we suspend these points from the cable ,a c ,b4 ,the cable is flexible1 and when we apply a load at m1 the truss will assume the position ,d s c n d1 but between ,d and s1 s and n1 n and d1 the truss will be quite stiff4 ,what we require1 then1 is to make the figure o p m m1 incapable of changing its form1 which is done by diagonal bracing4 ,illustration3 ,fig4 #ajf4 #bcc4 ,undoubtedly the finest specimen of a bridge of large span upon the suspension principle1 or indeed upon any principle1 is that built by ,john ,a4 ,roebling1 across the ,niagara ,river1 a short distance below the falls4 ,the dimensions below of this admirable structure are from the final report of the above-named engineer4 ,length of bridge from centre to centre of tower #hba #d ,length of floor between towers #hjj ft4 ,number of wire cables #d ,diameter of each #aj ,solid wire section of each cable #fj4dj sq4 in4 ,total section of four cables #bda4fj sq4 in4 ,whole section of lower links of anchor irons #bgf sq4 in4 ,whole section of upper links of anchor irons #cgb sq4 in4 ,ultimate strength of chains #aa1ijd tons4 ,whole number of wires in cables #ad1efj ,average strength of a wire #a1fdh lbs4 ,ultimate strength of four cables #ab1jjj tons4 ,permanent weight supported by cables #a1jjj tons4 ,resulting tension #a1haj tons4 ,length of anchor chains #ff ft4 ,length of upper cables #a1bfa ft4 ,length of lower cables #a1aic ft4 ,deflection of upper cables 7mean temperature7 #ed ft4 ,deflection of lower cables 7mean temperature7 #fd ft4 ,number of suspenders #fbd ,aggregate strength of suspenders #ah1gbj tons4 ,number of over-floor stays #fd ,aggregate strength #a1ibj tons4 ,number of river stays #ef ,aggregate strength #a1fhj tons4 ,elevation of grade above mean water #bde ft4 ,depth of river #bjj ft4 ,cost of the bridge #djj1jjj4 #bca4 ,the following items are extracted from the report above referred to3-- 8,the trains of the ,new ,york ,central1 and ,canada ,great ,western ,railroads have crossed regularly at the rate of thirty trips per day for five months4 7,at present over two years47 8,a load of forty-seven tons caused a depression at the centre of five and a half inches4 8,an engine of twenty-three tons weight1 with four driving wheels1 depressed the bridge at the centre #j4c feet4 ,the depression immediately under the engine was one inch2 the effect of which extended one hundred feet4 8,the depression caused by an engine and train of cars is so much diffused as scarcely to be noticed4 8,a load of three hundred and twenty-six tons produced a deflection of #j4hb feet only4 ,the ,conway tubular bridge deflects #j4be feet under three hundred tons2 the span being only one half that of the ,niagara bridge4 8,the specified test for the wire was1 that a strand stretched over two posts four hundred feet apart should not break at a greater deflection than nine inches2 also1 that it should withstand bending square and rebending over a pair of pliers without rupture4 ,this test corresponds to a tensile strain of #ij1jjj lbs4 per square inch1 or ,i1#cjj lbs4 per wire of twenty feet per pound40 ,the wire is preserved from oxidation by coating with linseed oil and paint4 ,upon the durability of wire cables employed for suspension bridges the following fact came to light3 ,upon taking down the cables of the footbridge1 put up in #ahdh1 by ,mr4 ,ellet1 the wire was found so little impaired that ,mr4 ,roebling did not hesitate to work it into the new cables2 also1 the original oil was found to be still soft and in good condition1 having been up six years4 ,that iron-work lying under ground has been completely covered with cement grout1 as this is found by the above-named engineer to be an effectual guard against oxidation4 ,engineers wishing to study the details of the ,niagara bridge1 will find the final report of ,mr4 ,roebling full of valuable matter1 both as regards the making of cables1 anchoring1 stiffening1 and the effect of passing trains4 ,,note4--,this engineer is at present engaged upon a still greater work1 namely1 a railroad suspension bridge across ,kentucky ,river1 of #a1bbd feet span1 #cjj feet above the water4 ,there is no lower road-way in this bridge1 the cross section being a triangle base upwards4 #bce4 ,,note4--,the ,britannia tubular bridge1 across the ,menai ,straits1 is doubtless a great work1 and also an enormously extravagant one4 ,if no other structure were possible it would be admissible2 but it is equalled in strength and by far surpassed in economy by ,mr4 ,roebling's system of trussed suspension bridges4 ,the cost of material alone in one span of the ,britannia bridge1 of #dfj feet1 exceeds the entire cost of the ,niagara bridge of #hjj feet span2 add to this that we are sure of the strength of wire cables1 but not of tubes1 and that the #hjj feet span of the ,niagara bridge weighs only #a1jjj tons in itself against #a1djj in a #dfj feet span of tube1 and it will not be difficult to prove the superiority of the suspension over the tubular system2 thus1 ,a suspension bridge of #hjj feet span costs #djj1jjj4 ,a tubular bridge of #dfj feet span costs #ejj1jjj4 ,when we double the linear dimensions we increase the weight by the cube2 and the cost of a tube is very nearly as the weight2 whence a tubular bridge of #hjj feet span will cost #b #b #b1 or eight times #ejj1jjj1 or #d1jjj1jjj against #djj1jjj4 ,thus1 ,suspension #djj1jjj #a ,tubular #d1jjj1jjj #aj ,illustration3 ,fig4 #aje4 ,fig4 #aje1 shows the anchoring of the ,fribourg bridge4 ,illustration3 ,fig4 #ajg4 ,illustration3 ,fig4 #ajh4 ,fig4 #ajg1 the manner of fastening the ground stays of the ,niagara bridge4 ,fig4 #ajh1 connection between cable and suspender4 ,illustration3 ,fig4 #aji4 ,illustration3 ,fig4 #aji ,a4 ,figs4 #aji1 #aji ,a1 another method of effecting the same4 ,illustration3 ,fig4 #aaj4 ,illustration3 ,fig4 #aaa4 ,fig4 #aab4 ,fig4 #aaj1 floor beam attachment to suspender4 ,figs4 #aaa1 #aab1 floor beam attachment in ,niagara bridge4 ,illustration3 ,fig4 #aac4 ,fig4 #aac1 connection of land and water cables in ,fribourg bridge4 ,illustration3 ,fig4 #aad4 ,fig4 #aad ,a4 ,figs4 #aad1 #aad ,a1 fastening of cables at ,g1 7fig4 #aje74 ,illustration3 ,fig4 #aae4 ,fig4 #aae1 ,mr4 ,roebling's pendulum connection for the cables of two adjacent spans4 ,,boiler ,,plate ,,bridges4 ,spans from #be to #ajj feet4 #bcf4 ,these structures fulfil every requirement of safe1 durable1 and rigid bridges2 being open however to the contingency attendant upon all similar structures of wrought iron1 namely1 the becoming crystalline when exposed to vibration4 ,time only will show whether this is a sufficient cause for their non-adoption4 ,each side truss consists as it were of a top and bottom chord connected by a vertical web4 ,the whole being of wrought iron1 requires that the section of the upper chord should be to that of the lower1 as ninety to sixty-six4 ,the general plan of such bridges is shown in fig4 #aaf4 ,this is the patent wrought iron girder bridge of ,mr4 ,fairbairn4 ,the upper chord is formed by connecting the four plates a a a a1 by angle irons4 ,the web is formed either by a single or a double plate1 stiffened laterally by ,t iron placed at the vertical plate joints1 as shown generally at ,b1 and detailed at ,c and ,d2 or by a pair of plates separated by a space as at ,b1 thus forming a rectangular tube4 ,the lower chord is made by bending horizontally the lower part of the web1 and to the flanges thus formed riveting the plate m m4 ,the suspending rod f is applied to the upper chord by a washer as at ,e4 ,illustration3 ,fig4 #aaf4 ,the central connecting web1 acting as do the braces and ties in a wooden truss1 should be more stiff at the ends of the span than at the centre4 ,this is easily effected by joining the web plates towards the end by stronger ,t irons than at the centre4 ,the joints for the rib1 or the vertical plates1 either single or double1 are shown in figs4 ,c and ,d4 ,an example of the need of such increased stiffness towards the ends1 was given to the experimenters upon the ,britannia model tube1 which 7tube7 was found to yield by buckling near the ends of the span sooner than elsewhere4 ,thus advised1 the vertical plates were made thicker as the end of the span was approached4 ,examination of the principles of proportioning a common wooden truss would have shown this without experiment4 ,the tensile and compressive strength of rolled boiler plates 7by the table on page #aic17 is1 extension #ab1gdj lbs4 per square inch1 compression #g1ejj lbs4 ,the strength of such work depends in a very great measure upon the size and disposition of rivets4 ,in plates exposed to compression1 the strength is not so much affected by riveting as in those subjected to tensile strains2 as to whatever amount the plate is cut away1 by the same amount is the resistance to tension reduced4 #bcg4 ,mr4 ,fairbairn found that to obtain the maximum strength of riveted plates1 the section of the rivets should equal that of the plates1 that is1 in a plate four inches wide1 if there are two rivets1 the area of each must be one inch2 or the diameter #a inches2 thus leaving a section of #d - #b #a inches1 which divided by four gives seven sixteenths of an inch as the distance from the edge of the plate to the side of the first rivet2 and seven eighths of an inch between rivets4 ,if the bolt yields by shearing1 the rim is destroyed by detrusion1 or crushing across the fibres4 ,that the rivets and plates may be equally strong1 their products of area of section by the actual strength per unit of area must be equal4 ,the detrusive strength of wrought iron 7see page #aic7 is #ab1ejj lbs4 per inch1 whence the proportion #ab1ejj 3 #ae1jjj 33 #a 3 d where #a is the resisting length of the plate at right angles to tension1 and d1 the sum of rivet diameters4 ,thus suppose we have a plate #ac4b inches wide1 to be fastened with nine rivets of #j4h inch diameter2 we have #i #j4h #g4b d1 and the above proportion becomes #ae1jjj 3 #ab1jjj 33 #g4b to #f inches1 which is the length of plate section at right angles to tension4 ,as there are nine rivets1 there will be eight spaces between them1 and one space at each edge of the plate1 half as large as those between2 or reducing all to the same size1 #h #b #af1 #af #b #ah2 and as the whole plate section after punching is six inches1 #f_/ah 4#cc or inch for the edge space1 and two thirds inch between rivets4 ,proceeding thus1 the result compares with the practice of ,mr4 ,fairbairn as follows3-- ,diameter of rivet4 ,distance between rivets4 ,mr4 ,fairbairn inch1 or #j4fbe inch1 #j4h ,handbook inch1 or #j4fff inch1 #j4h ,the difference between the results1 or #j4jda inch1 less than one sixteenth inch1 will be partially absorbed by the remark of ,mr4 ,fairbairn that the area of the rivet should be nearly as much as that of the plate1 and partly by the difference in results showing the detrusional force of iron4 ,illustration3 ,fig4 #aag4 #bch4 ,in experimenting to determine the resistance of rivets1 ,mr4 ,fairbairn found that by the common plan of riveting1 fig4 #aag1 the strength of plates when whole1 single1 and double riveted1 was as follows1 the section of the punched plate being in each case equal to that of the whole one4 ,whole plate1 #ajj4 ,single riveted1 #ef4 ,double riveted1 #gj4 ,this loss of strength made him fearful of the ability of the tension plates of the ,britannia bridge to do their duty2 and he was led to adopt what he terms 8chain riveting10 which consists in placing the rivets as in fig4 #aah1 or in the same line of tension4 ,the strength of plates thus made he considers as great at the joints as elsewhere4 #bci4 ,as to the diameter of rivets1 we have the following results of the practice of the best ,english engineers4 ,thickness of plate1 1 #e_/af1 1 #g_/af1 1 #i_/af1 1 #aa_/af1 4 ,diameter of rivet1 1 #f_/h1 1 #a1 #a1 #a1 #a1 #a1 #a4 #bdj4 ,as to the distance in the direction of the force from rivet to rivet1 also from the first rivet to the plate end1 we gather the following from the best executed works in boiler plate4 ,see fig4 #aah4 ,plates exposed to compression1 cb #b diam41 df #a diam4 ,plates exposed to extension1 cb #b diam41 df #b diam4 the diameter being that of the rivet4 ,the distance at right angles to the force has already been given4 #bda4 ,if we knew the lateral adhesion of rolled plates1 that is1 the resistance of the fibres to sliding horizontally past each other2 we should determine the distance of rivets in the direction of tension as follows3-- ,let ,r1 equal the resistance per unit of area for detrusion or shearing1 ,r the lateral adhesion of rolled plates1 and we should have ,r a ,r 7#b d t72 whence d 7,r a7_/7#b,r t72 where a area of rivet1 d distance1 t plate thickness4 also #b;d d 7,r d7_/7,r72 and #b;d 7,r d7_/7,r7 - d2 whence d 7,r d7_/7,r7 - d_/#b and finally d 7,r d7_/7,r7 - d supposing the piece #a1 #b1 #c1 #d1 fig4 #aah1 to split out4 ,the diameter of the semi-spherical head of the rivet should be three times the thickness of the plate to be riveted2 that of the conical head four times2 and the height of both of the heads1 one and one half the plate thickness4 #bdb4 ,examples of the application of the preceding remarks4 ,suppose we wish to build a boiler plate bridge of one hundred feet span1 twelve feet rise1 weight of bridge and load #ccjj lbs4 per lineal foot4 ,the tension by formula ,t 7,,ws7_/7#h;h7 7see ,chap4 ,,viii47 becomes #ccjjjjjj_/if #cdc1gej lbs4 ,each side truss will bear one half of this or #aga1hge lbs41 and as wrought iron resists eleven thousand pounds of compression per square inch1 the required section of the top chord will be #agahge_/gejj #bb4i square inches4 ,also the lower chord resisting fifteen thousand pounds per square inch1 must have #agahge_/abgdj #ac4e square inches of area nearly4 ,if we make the tube at top of one fourth inch iron1 and #h #aj inches2 fastening the plates by one fourth inch angle iron1 four inches on the side1 the section becomes ,one top plate #aj #b square inches4 ,one bottom plate #aj #b square inches4 ,two side plates #h #d square inches4 ,four angle irons #h #h square inches4 -- ,in all1 #ag square inches4 ,in the lower chord1 if we bend the web plates 7of inch7 so as to form a flange of eighteen inches in width1 and to that rivet a bottom plate #ah 1 we shall have ,in the flanges1 #ah #f ,bottom plate1 #ah #d ------ ,in all1 #aa ,the web acting as both ties and braces1 must be able to support the following load4 ,whole weight of bridge and load is1 in round numbers1 #cdd1jjj lbs4 ,one half1 #agb1jjj lbs4 ,and upon each end of the truss1 #hf1jjj lbs4 to resist which1 at eleven thousand pounds per square inch1 requires eight inches nearly1 regarding the plate as a brace4 ,now the side of the bridge being one hundred feet long1 and twelve feet wide1 will contain any system of bracing that we choose to draw thereon4 ,suppose1 for example1 that we chalk a line upon the erected bridge representing an arch-brace1 extending from the end to the centre4 ,such a brace has actual existence in the bridge2 and the same idea holds good for any system of braces that may be assumed4 ,we ought1 therefore1 to take the most disadvantageous system that can have place1 and giving such a good bearing upon the abutment1 estimate its width and thickness4 ,suppose that we draw a natural size representation of ,howe's bridge1 the end braces must support a load of eighty-six thousand pounds1 which at eleven thousand lbs4 per inch1 requires a section of nearly eight inches2 and if the plate is one half inch thick1 the brace must be sixteen inches deep4 ,the manner1 however1 in which the plate would yield is by bulging laterally2 which is to be checked by the before-mentioned ,t connecting irons at the sides4 ,it may be thought that the above method of considering the plates as braces1 would give very little thickness by assuming very wide plates4 ,the answer to this is1 that the side plates must not be so thin as to need more stiffening angle irons by weight1 than a thicker plate with less stiffening4 ,of course the weight should be minimum4 #bdc4 ,as an actual example of this plan we have the following1 built by ,mr4 ,fairbairn for the ,blackburn and ,bolton ,railroad1 across the ,leeds and ,liverpool ,canal4 ,span1 #fj feet1 ,length1 #ff feet1 ,end bearings1 each1 #c feet1 ,rise1 #e feet1 ,width1 #bh feet1 for a double track4 ,top chord of three eighths iron1 web of five sixteenths1 lower flange of three eighths1 and vertical web plates stiffened by ,t irons4 ,this bridge was tested as follows3-- ,three engines1 weighing twenty tons each1 running from five to twenty-five miles per hour1 deflected the bridge 4#jbe feet4 ,two wedges1 one inch high1 being placed upon the rails1 and the engines being dropped from that height1 the bridge was deflected at the centre 4#jce ft42 with wedges of one and one half inches the deflection was 4#jde ft4 ,the cost of this bridge 7in ,england7 was estimated by ,mr4 ,fairbairn at #d1ejj1 while that of a cast-iron bridge of the same span was #g1aej4 #bdd4 ,example #b4--,manchester1 ,sheffield1 and ,lincolnshire ,railroad 7,england7 ,bridge1 at ,gainsborough1 on the river ,trent4 ,two spans1 each one hundred and fifty-four feet4 ,rise twelve feet4 ,top chord1 double rectangular tube1 #cf #af inches1 vertical web as before1 and horizontal plate for the lower chord4 ,the floor beams are wrought iron girders1 cruciform in section1 ten inches wide1 and one foot three inches 7#ae7 deep1 placed four feet apart4 #bde4 ,example #c4--;,fifty-five feet boiler plate bridge1 built by ,james ,millholland1 in #ahdg1 for the ,baltimore and ,susquehanna ,railroad ,company4 ,each truss consists of two vertical plates #ee #f feet1 formed of plates thirty-eight inches wide by six feet deep1 the plates being fastened together by bolts passing through cast-iron sockets4 ,the lower chord is formed by riveting two bars #e inches to each side of each truss plate2 making in all eight4 ,top chord--one bar of the same size on each side of each plate1 compression being made up by a wooden chord between the plates4 ,height of bridge1 six feet2 length1 fifty-five feet2 width1 six feet2 weight1 fourteen tons2 cost1 #b1bjj1 or forty dollars per foot4 ,the inventor thinks thirty dollars per foot enough when a considerable amount of such bridging is wanted4 ,,note4--,white1 buff1 or some light color should be used in painting iron bridges1 as such throw off1 and do not absorb heat from the sun4 ,,chapter ,x4 ,,stone ,,bridges4 ,a complete treatise on stone bridging would be of little practical value to the ,american engineer1 and would occupy too much of the necessarily small space allowed here4 ,the object in the present chapter is to give the manner of dimensioning stone arches of from ten to sixty feet span1 and of proportioning retaining walls1 piers1 and abutments4 ,,contraction ,,of ,,the ,,water-,,way4 #bdf4 ,in building a bridge across a stream1 we must be careful not to obstruct the water-way so as to prevent free passage to the highest floods4 ,regard must be had to this in fixing the size of the spans1 and the thickness and number of the piers4 ,by contracting the width of the stream the velocity is increased beneath the arches1 the same amount of water being obliged to pass through a smaller space1 and when the bottom is of such a nature as to yield to this action1 there is danger of the foundation being undermined4 ,if the form and size of the piers be so arranged as not to increase the velocity1 such danger will be avoided and floods will pass without harm4 ,in bridges crossing navigable streams1 if the bottom is not destroyed the velocity may be made so great as to impede navigation4 #bdg4 ,the following table is from ,gauthey1 ,construction des ,ponts1 showing the velocities which are just in equilibrium with the material composing the bottom of the stream4 ,state of the water4 ,velocity in feet per second4 ,nature of bottom4 ,torrents1 #aj #j ,large rocks4 ,floods1 #c #c ,loose rocks4 ,common1 #c #j ,gravel and stones4 ,regular1 #b #j ,fine gravel4 ,moderate1 #a #j ,sand4 ,slow1 #j #f ,clay4 ,very slow1 #j #c ,common earth4 #bdh4 ,if b represents the width of the natural water-way2 c1 that as reduced by the structure2 ,v1 the velocity of the stream in the natural state2 then the augmented velocity is expressed by ,w m,v7b_/c72 and c 7mb,v7_/,w2 where m is a constant quantity expressing the contraction which takes place in passing the narrow place1 which1 according to ,du-,buat1 is #a4ji2 but depending somewhat upon the form of the bridge piers2 adopting which value1 we have ,w #a4ji,v7b_/c72 and c 7#a4ji;b,v7_/,w4 ,example4--,let the bottom be gravel1 the width of the natural water-way one hundred feet1 the velocity one foot per second3 now for a gravel bottom the velocity must not exceed two feet per second1 whence c 7#a4ji #ajj #a7_/b #ed feet2 which is the width of the contracted water-way2 and #ajj - #ed1 or #de feet may be occupied by piers or other obstructions4 ,the amount of fall which the water suffers in passing the pier is found by the following formula1 the notation being the same1 fall 77,v#bm#b;b#b7 - c#b7_/7fd;c#b7 ,thus the velocity being one foot per second1 m being #a4ji and b #ajj2 also1 c #ed1 we have 7#a #a #a4ji #a4ji #ajj #ajj7 - 7#ed #ed7 fall ---------------------------------------- ---------------------------------------- -------------- #j4jdg ft4 #fd #ed #ed ,the velocity of a river is greatest at its surface and at the centre of the stream4 ,in the same river the velocity is nearly as the square root of the depth2 thus the surface velocity being known1 that for any other depth may be easily found4 ,the velocity of streams should always be noted at the times of the highest floods4 ,for measuring the velocity of running water a bottle enough filled with water to maintain an upright position1 with a small rod placed through the stopper having a red flag upon the upper end1 answers very well4 ,velocities of undercurrents may also be measured by so loading the bottle as to cause it to float two1 four1 six1 or ten feet below the surface4 ,,of ,,the ,,form ,,of ,,the ,,arch4 #bdi4 ,there are three general forms which may be given to the intrados of a stone arch4 ,semicircular1 or one hundred and eighty degrees4 ,segmental1 less than one hundred and eighty degrees4 ,basket handle1 nearly elliptical1 being formed by a number of circular curves4 ,full centre 7semicircular7 arches offer the advantages of great solidity and ease of construction2 but unless the springing lines are high1 contract considerably the water-way4 ,segmental arches give the freest passage to the water1 are easily built1 but throw a great horizontal strain upon the abutments4 ,the basket handle gives free passage to the water1 when not too flat are very strong1 are easily adjustable to different ratios between the span and the distance between grade and the spring line1 and except making the centres1 are easily built4 ,whatever the form of the arch1 the line of arch springing should not be below high water4 ,the manner of tracing the full centre and segmental curves is too simple to need remark4 #bej4 ,in tracing the basket handle curve1 the following conditions must be observed3-- ,the tangents at springing must be vertical4 ,the summit tangent must be horizontal4 ,the curve at springing must inclose the ellipse4 ,the radius of summit must not be greater than the span4 ,the number of arches composing the curve must not be less than three1 nor more than eleven2 and must be uneven4 ,perronet's fine bridge of ,neuilly1 over the ,seine at ,paris1 has eleven centres4 ,in spans of sixty feet and under1 it is unnecessary to use more than five centres4 ,illustration3 ,fig4 #aai4 #bea4 ,the three centred curve is described as follows1 fig4 #aai3-- ,let ,a ,b represent the span1 and c ,d the rise1 with c as a centre and c ,a as radius1 describe the quadrant ,a ,f ,e2 make the angle ,a ,c ,f #fj4 ,parallel to ,f ,e draw ,d ,g1 and parallel to ,f ,c draw ,g ,k4 ,h is the centre1 and ,a ,g the arc of the springing curve2 also ,,gd is the arc1 and ,k the centre of the summit curve4 ,,the ,,five ,,centred ,,curve4 #beb4 ,the common construction of the five centred curve leaves the radii of the extreme curves to be assumed4 ,the following method fixes all of the dimensions when the span and rise are given3-- ,let c ,b be half the span and c ,d the rise4 ,join ,d ,b4 ,draw n ,k through n perpendicular to ,d ,b4 ,make ,b a equal to c ,d4 ,also c e to c a4 ,draw e ,k o and ,k a m4 ,k ,h and ,k are the centres1 and ,h m and ,h o the lines separating the several curves4 ,for spans of from twenty-five to one hundred feet1 the five centred arch answers every purpose2 making a strong and well proportioned structure4 ,,thickness ,,of ,,voussoirs1 7,,ring ,,stones74 #bec4 ,the thickness of the voussoir1 or arch stone1 depends upon the form and size of the arch1 the nature of the masonry1 and the character of the stone4 ,no authority gives more reliable results than ,gauthey1 who1 for stone of average quality1 with hammer dressed beds1 laid in cement1 gives the following proportions between the span and depth of key3-- ,for spans under six feet the depth should be thirteen inches4 ,from six to fifty feet1 #ac inches plus #a_/dh of the span4 ,from fifty to one hundred feet1 #a_/bd of the span4 ,for over one hundred feet1 #a_/bd of #ajj plus #a_/dh of the remainder4 ,thus for a span of one hundred and ninety-six feet we have 7#ajj #ab7_/bd 7#if #ab7_/dh1 or1 #ej #bd equal in all to seventy-four inches1 or six feet and two inches2 whence the following table3-- ,span of arch in feet4 ,thickness of voussoir in inches4 #f #ac #j #ac #h #ac #b #ae #aj #ac #c #af #ab #ac #c #af #ae #ac #d #ag #ah #ac #e #ah #bj #ac #f #ai #be #ac #g #bj #cj #ac #h #ba #ce #ac #i #bb #dj #ac #aj #bc #de #ac #aa #bd #ej #ac #ac #bf #fj #cj inches4 ,,thickness ,,and ,,form ,,of ,,abutments4 #bed4 ,the above depend upon the span and form of the arch1 the height of the abutment1 and character of the masonry4 ,different methods of determining the thickness of an abutment have from time to time been given2 several very correct rules have been arrived at1 but difficult of application4 ,the most simple rule is given by ,hutton in the course of mathematics edited by ,rutherford2 it is as follows3-- ,illustration3 ,fig4 #abj4 ,let ,a ,b1 ,c ,d1 fig4 #abj1 be one half of the arch and ,a ,g ,f the abutment4 ,from the centre of gravity ,k of the arch1 draw the vertical ,k ,l2 then the weight of the arch in the direction ,k ,l will be to the horizontal thrust1 as ,k ,l to ,l ,a4 ,for the weight of the arch in the direction ,k ,l1 the horizontal thrust ,l ,a1 and the thrust ,k ,a will be as the three sides of the triangle ,k ,l1 ,l ,a1 ,k ,a2 so that if m denotes the weight of the arch1 7,,la7_/7,,kl7 m1 will be its force in the direction ,l ,a1 and 7,,la7_/7,,kl7 ,,ga m its effect on the lever ,g ,a to overturn the wall1 or cause it to revolve about the point ,f4 ,again1 the weight or area of the pier is as ,,ef ,,fg1 and therefore ,,ef ,,fg ,,fg1 or ,,fg#b ,,ef1 is its effect upon the lever ,,fg1 to resist an overthrow4 ,now that the abutment and the arch shall be in equilibrium these two effects must be equal to each other2 whence we must have ,,fg#b ,,ef 7,,la7_/7,,rl7 ,,ga m2 whence ,,fg 77#b;,,ga ,,la7_/7,,ef ,,rl7 m74 ,the following table has been calculated for the use of builders and engineers1 giving the thickness of abutments for different spans and heights4 #bee4 ,,thickness ,,of ,,rectangular ,,abutments4 ,semicircular arch4 ,basket-handle arch4 ,the height being4 ,span4 #e #h #aj #ae #e #h #aj #ae #f #c #c #c #c #c #d #d #e #h #c #d #d #d #d #d #e #f #aj #d #e #e #e #d #e #f #g #ae #d #e #e #f #e #f #g #h #bj #e #e #f #g #f #g #h #i #be #e #f #f #g #g #g #h #i #cj #f #g #h #h #h #h #i #aj #ce #f #g #h #i #i #i #aj #aa #dj #g #g #h #i #i #aj #aa #ab #de #g #h #i #aj #aj #aj #aa #ab #ej #h #i #aj #aa #aj #aa #ab #ac ,illustration3 ,fig4 #aba4 ,fig4 #aba ,b4 ,fig4 #aba ,a4 #bef4 ,the form of a bridge abutment will depend upon the locality and upon the use to which the bridge is to be put1 whether used for a railroad1 or for common travel2 whether near a large city1 or in a location where appearance need not be regarded4 ,where a river acts dangerously upon a shore1 wing walls will be necessary4 ,these wings may be curved or straight1 and may be simply the abutment produced1 or may be swung around into the bank at any required angle1 until the winged abutment1 as in figs4 #aba1 #aba ,a1 #aba ,b1 becomes the ,u abutment1 fig4 #abd2 or by moving the walls1 ,w and ,w1 parallel to themselves1 takes the form of the ,t abutment1 fig4 #abb4 ,illustration3 ,fig4 #abb4 ,the curved wing1 in fig4 #aba1 being arched1 requires a little less thickness1 but at the same time is longer4 ,b ,b1 show the bridge seats4 ,the slope of the wings may be battered with an inclined coping1 or off-setted at each course4 ,wing walls1 subjected to special strains or to particular currents of water1 require positions and forms accordingly4 ,in skew bridges1 as in ,chap4 ,v41 the wing1 at the acute angle1 is longer and inclines less from the face of the abutment than that at the obtuse angle4 ,the more the wing departs from the face line and swings round into the slope1 the greater the thrust becomes upon it1 as the centre of pressure is raised2 the thrust becomes a maximum when the wing is inclined from forty-five to seventy degrees from the face of the abutment4 ,the body of an abutment1 as well as any other retaining wall1 may be much stronger by giving it a trapezoidal instead of a rectangular section1 as the resisting leverage is thereby much increased4 ,abutments may be to advantage buttressed in order to resist special strains1 as in case of the arches or braces of wooden bridges4 ,illustration3 ,fig4 #abc4 ,illustration3 ,fig4 #abd4 #beg4 ,railroad abutments except for a double track1 require but little breadth on top1 except where the truss itself rests4 ,the common ,t abutment originated by ,captain ,john ,childe1 and now in very extensive use1 seems to fulfil any requirement of a good abutment1 see fig4 #abb1 page #bdb4 ,b ,b is the bridge seat1 and the mass ,t ,t takes the place of wings4 ,the difference of level of the top and of the bridge seat depends upon the difference between the height of the bearing of the lower chord of the bridge1 and grade4 ,the line of contact between the earth and the wall is shown by s s s s4 ,the length of the top of the masonry is found thus4 ,suppose the slope to be one and one half to one1 and the whole height thirty feet1 the whole horizontal length of slope is then forty-five feet2 from this we take the sum of the horizontal distances1 s s and s s1 and suppose these to be1 respectively1 six and eight feet1 we have the whole operation thus3-- #cj #a - #f #h #de - #ad #ca feet4 ,it may be advisable in very high abutments to lighten the masonry by an arched opening as in fig4 #abc4 ,the walls1 also1 of the ,u abutment 7see fig4 #abd71 when large1 may be pierced with arches to save masonry4 ,probably the cheapest mode of bringing a bridge to the embankment is that shown in fig4 #abe2 ,a being the bridge seat for the main truss1 and ,b that for the trussed girder4 ,illustration3 ,fig4 #abe4 ,,piers4 #beh4 ,the thickness of a pier may be considered either as depending upon the weight of the superstructure1 or as resisting the thrust of arches or braces4 ,for the first requirement1 very little thickness would suffice2 for the second1 it may require to be considerable4 ,the objection to thick piers is the expense1 and the contracting too much the water-way2 the benefit1 a large bearing surface1 and in stone bridges where there are several continuous spans1 a saving of centring2 as where the piers are not able to resist the thrust of the arches1 they must all be carried up at once4 #bei4 ,piers supporting truss bridges1 require very little thickness provided a good foundation is obtained4 ,the following table shows the sufficient dimensions for the piers of wooden or iron trussed bridges1 when the masonry is good4 7,see ,first ,class ,masonry1 specification1 ,chap4 ,,iv47 ,from ten to twenty feet in height the batter is assumed at one twelfth2 from twenty to fifty feet in height at one twenty-fourth4 ,span4 ,length of bridge seat4 ,width of seat4 #bj to #dj feet1 #bj feet1 #d feet1 #dj to #fj feet1 #bj feet1 #d feet1 #fj to #hj feet1 #bb feet1 #e feet1 #hj to #ajj feet1 #bc feet1 #e feet1 #ajj to #abe feet1 #bc feet1 #f feet1 #abe to #aej feet1 #bd feet1 #f feet1 #aej to #bjj feet1 #bd feet1 #g feet4 #bfj4 ,upon the form of the up-stream end of the pier1 or the starling1 depends1 in a considerable degree1 the contraction of the water-way4 ,in sluggish water the form is not of much importance1 but in swift flowing rivers a great deal depends upon the choice4 ,the forms in use are the rectangle1 the rectangle terminated by right-lined triangles1 and the same terminated by curved-lined triangles1 and finally the ellipse4 ,the latter is that which causes the least disturbance to the water1 but is also the most costly4 ,the effect of gyration at the shoulder1 deserves notice1 as it may be the cause of the ruin of the foundation when the bottom is of yielding material4 ,river beds being porous1 springs work up through them with a force equal to the whole depth of water2 and whenever there is a means of escape for such1 its pressure will act upwards against any structure that comes within its reach2 and if four or five feet deep1 is capable of moving enormous weights4 ,such springs gave a great deal of trouble at the foundation of the ,united ,states ,dry ,dock1 at ,brooklyn1 ,n4 ,y4 ,when checked in one place they burst up in another1 and to proceed with the work it was necessary to allow them a passage through which to flow4 ,illustration3 ,fig4 #abf4 #bfa4 ,however proper it may be to give to piers the proper form to cause as little contraction as possible to the water1 it is no less necessary to give them strength to oppose the shocks to which they are subject from floating ice1 timber and shipping4 ,the best method of breaking up ice1 when it comes in large masses1 is by inclining the front of the pier1 as shown in fig4 #abf4 ,the angle of the front being inclined from #cj to #ej4 ,the ice running up this slope breaks by its own weight1 and falls off on either side4 ,the foundations of piers may be protected by sheet piling1 7see chap4 ,,xii417 or the bottom1 if soft1 may be dredged out for a few feet and filled in with loose rock4 ,the form of the down-stream end is not of so much importance as of the upper one1 but deserves consideration2 as when the water is swift or the bottom soft and yielding1 the eddies caused by sharp angles wear upon the soil in a dangerous manner4 ,,chapter ,,xi4 ,,masonry4 ,,stones4 #bfb4 ,the varieties of this material most commonly used in engineering operations are granites1 limestones1 sandstones1 slates1 brick1 and artificial stones2 the latter being made by compounding clays1 limes1 and cements4 ,rock taken from the surface1 which has been exposed to the atmosphere1 is of an inferior quality to that found at a depth where it has been exposed to a strong pressure2 and is consequently denser4 ,therefore1 in opening a quarry it is advisable to excavate upon a hill-side and come at once to the sound stone4 ,rock is generally found in beds1 divided by joints or seams1 at which the natural adhesion is broken and the layers are easily separated4 ,when the quarry shows no natural line of separation1 one may be produced by drilling a line of holes at equal distances from each other1 into which conical steel pins are driven1 and the stone splits2 the pins being placed in the plane of the required seam4 #bfc4 ,stone is used almost entirely to resist a compressive strain2 as in the voussoirs of an arch1 or in the courses of a pier4 ,the resistance of stone to crushing1 is as follows3-- ,pounds per square inch4 ,granite #aj1jjj to #af1jjj ,limestone #ab1jjj to #ad1jjj ,sandstone #aj1jjj ,marble #i1jjj to #ad1jjj ,firm1 hard burned brick #b1fjj ,yellow burned brick #a1ejj ,red brick #a1bjj ,pale-red brick #ijj ,chalk #gej #bfd4 ,when stone cannot be found1 brick forms an excellent substitute2 being made from clay earths1 which can be found in almost any locality4 ,bricks are well fitted for nice work1 are cheap1 and easy of transport4 ,the ,french1 at ,algiers1 have used concrete1 rammed in boxes so as to make large cubes and other shapes4 ,the structures built of this material are found to be very nearly if not quite as strong as those of natural rock4 ,,limes1 ,,cements1 ,,mortars1 ,,and ,,concretes4 #bfe4 ,nothing is more important in the construction of masonry than good cement2 and generally1 no part of construction is intrusted to more ignorant persons4 ,under the above head are to be considered limes1 cements1 sands1 common mortar1 hydraulic mortar1 and concrete4 #bff4 ,lime is obtained by burning off the carbonic acid from the pure limestones2 when it is put up in air tight barrels and is unslacked lime4 ,natural cements are composed of pure lime mixed with argil1 magnesia1 iron1 and manganese4 ,artificial cements are prepared by mixing with pure lime1 calcined clay1 forge scales1 powdered bricks which are underburnt1 and other materials of like nature4 ,cements made thus artificially1 are as good as those naturally hydraulic4 ,lime is termed rich1 poor1 hydraulic1 and eminently hydraulic1 according to its properties4 ,rich or fat limes are those which double their volume in slacking and dissolve in fresh water to the last particle4 ,they absorb about #cjj per cent4 of their weight of water4 ,poor limes do not much increase their volume1 do not dissolve completely1 and absorb #bjj per cent4 of water4 ,hydraulic limes set in fifteen or twenty days after immersion1 and continue to harden as they grow older4 ,after one year their consistency is about that of hard soap4 ,eminently hydraulic limes set in five or six days1 and continue to harden4 ,limes are said to set when they will bear1 without depression1 a rod of #a_/bj of an inch diameter loaded with ten or twelve ounces4 ,,note4--,the following test was applied to every tenth cask of ,rosendale cement used upon the masonry of the ,united ,states ,dry ,dock at the ,brooklyn 7,n4 ,y47 ,navy ,yard4 ,cakes two inches in diameter and three fourths of an inch in thickness1 after being immersed five days1 were required to bear a rod of one twenty-fourth of an inch diameter loaded with fifty lbs4 ,two bricks united with the cement and immersed five days1 were required to resist one hundred lbs4 before separating4 ,the following shows the progress of hardening4 ,the force required to thrust a rod one twenty-fourth of an inch in diameter through a cake three fourths of an inch in thickness1 was1 after #bd hours1 #fe lbs4 #dh hours1 #gj lbs4 #gb hours1 #ge lbs4 #ae days1 #aej lbs4 #ej days1 #cij lbs4 ,,sand4 #bfg4 ,sand is the product of the decomposition of granitic and schistose rocks1 and weighs1 per unit of bulk1 somewhat less than one half of the rock producing it2 owing to the spaces between the grains4 ,the amount of lime necessary to fill these spaces must be known before we can form a solid mass with the least lime4 ,the amount of void may be found by filling a measure with sand1 and then pouring in water3 the volume of water is that of the spaces4 ,in pebbles of one half inch in diameter the void amounts to about one half1 in gravel about five twelfths1 in common sand two fifths1 and in very fine sand1 one third4 ,clean sharp sand obtained from the beds of rivers is the best for mortars4 #bfh4 ,in mixing the ingredients for mortar1 the lime is first spread on a platform and wet by sprinkling with water1 which causes it to give off a great deal of heat and vapor1 and fall into a powder4 ,the sand is then applied1 and the whole brought with water to a consistent paste4 ,the proportions for common mortar for dry work are ,sand1 #a to #b ,lime1 #a ,it is well always to use a small quantity of cement2 the parts which have in practice been found perfectly satisfactory are ,cement1 #a ,lime1 #c ,sand1 #f ,for hydraulic mortar the following proportions have been used with success3-- ,cement1 #b ,sand1 #c #bfi4 ,concrete is made by mixing broken stone1 brick1 or shells1 with cement mortar2 it is used for foundations1 backing of arches1 and for making artificial stone4 ,the common proportions are ,cement1 #a or #b ,sand1 #a or #c ,broken stone1 #e or #aj ,the cement and sand are first mixed as for cement mortar2 the broken stone is added and the whole well mixed and immediately applied before it has time to set4 ,both concrete and cement mortar should be made as required for use1 and in no case applied after standing over three hours4 ,,flashing ,,mortar4 #bgj4 ,flashing consists of a thin coat of cement mortar made with a very large part of cement4 ,it is used to protect the face of walls exposed to the wet2 such as the top of arches4 ,stone liable to disintegration may be protected by flashing4 ,,pointing ,,mortar4 #bga4 ,pointing is used to protect the joints of masonry1 and is made by mixing cement and sand with a minimum of water4 ,the joint is first cut out to the depth of from one half to one inch1 carefully brushed clean1 moistened with water1 and filled with the mortar1 which is well rubbed with a steel tool4 ,to give architectural effect1 plaster of ,paris 7,gypsum7 is sometimes used in pointing4 ,,grout4 #bgb4 ,grout is thin-tempered mortar1 composed almost entirely of cement and water4 ,it is run into the joints1 and is useful in filling crevices in masonry which cannot be filled with mortar4 ,,construction ,,of ,,arches4 #bgc4 ,the foundations being secured1 and the piers and abutments being carried up to the springing line of the arch1 the centres are carefully adjusted to their places and the arch is commenced4 ,when the voussoirs begin to bear upon the centre 7which is when the angle of the joint with the horizontal is greater than the angle of repose of one stone upon another71 the frame is liable to change of form1 7particularly when the arch is flat17 which must be provided for by counter loading the centre in various points as the work proceeds4 ,great care should be taken to make each stone point in the direction of the radius of the arch4 ,to do this effectually1 their thickness should be marked upon the outer rib of the centre4 ,the line of the joint may then be fixed by a straight-edge placed both on the centre and the rib mark1 or by a template so cut that when one side is level the other shall stand at the proper angle4 ,excess of weight upon one side of the centre causes a depression at that point1 and a corresponding rise at the opposite side of the arch4 ,both sides being loaded1 the haunches settle1 and the crown rises4 ,the point where the centre is first loaded will determine the point where the frame is to be temporarily weighted4 ,such precautions1 however1 need only to be taken in arches of over fifty feet span1 unless the curve is quite flat4 ,the keystone should be put into the proper place1 but not driven until the rest is finished4 ,the back joints are then closely wedged and cemented with thin tempered mortar1 and the whole is left to set4 ,the masonry of the spandrels is brought up to about one fourth the height of the arch1 or enough to prevent by their weight any change of form of the curve4 ,the centres are then struck and the soffit and voussoir joints cleaned and pointed4 ,the facing and road-way may next be carried up2 the parapet coping and drains finished off2 and the whole pointed4 ,parapets are shown in figs4 #abg and #abh4 ,the spandrels1 fig4 #abi1 may be carried up solid or hollow2 their weight must be enough to stiffen sufficiently the arch4 ,it should1 at least1 be carried up solid to the line c c c2 the shaded mass being of well-cemented rubble4 ,above this the filling may be of masonry1 solid or arched1 or even of well-rammed layers of earth4 ,the road-way should1 in all cases1 be well drained1 that the water may not sink through to the masonry4 ,illustration3 ,fig4 #abg4 ,fig4 #abh4 ,illustration3 ,fig4 #abi4 ,the apparatus for handling stone 7cranes1 lewises1 and derricks7 is much better understood by inspection than by description4 ,wherever walls support masses of earth1 the thrust may be somewhat lessened by ramming the earth behind the wall in layers inclining backward4 ,in laying up the courses each should be well cleaned and moistened before the mortar is laid upon it4 ,when a stone has been once placed upon the mortar bed1 it should not be moved at all laterally1 but may be gently mauled on top4 ,,culverts ,,and ,,drains4 #bgd4 ,small culverts are made by covering two side walls with large flat stones2 the bottom being paved with stone at least nine inches deep1 laid dry4 ,the general dimensions of such structures depend somewhat upon the class of masonry1 but as this is generally the third or fourth1 will not vary much4 ,opening4 ,side walls4 ,cover4 ,heads4 #b #b #c #b #ab #b #aj #b #c #c #c #ab #c #aj #c #c #c #c #ab #c #aa #c #d #c #d #ae #d #ab #d #d #c #d #ae #d #ac #d #e #c #e #ah #e #ae #e #e #d #e #ah #e #af #e #f #d #f #ah #f #ah ,figs4 #acj1 #aca1 and #acb1 show plans for culverts of from #e to #be feet span4 ,illustration3 ,fig4 #acj4 ,illustration3 ,fig4 #aca4 ,fig4 #acb4 ,,retaining ,,walls4 #bge4 ,a wall made to sustain a mass of earth or water1 to resist overthrow1 requires a certain thickness4 ,a body of earth assumes what is termed the natural slope1 the inclination of which depends upon the adhesion of the soil1 but may be taken as one and one half horizontal1 to one vertical1 7#a to #a71 as an average4 ,the problem is1 knowing the height of the wall and the form of the mass of earth to be supported1 to find the thickness of the wall4 ,let ,a ,b #f ,f1 represent the thickness of the wall4 ,its centre of gravity is at ,o1 and is horizontally projected at m4 ,the centre of gravity of the thrusting triangle of earth1 ,b #d #f1 is ,c1 7found by the cutting of lines joining any two angles to the centre of the opposite sides17 is horizontally projected at ,ca1 and the horizontal component of the thrust is exerted at #b1 tending to overthrow the wall with a leverage1 #f #b4 ,illustration3 ,fig4 #acc4 ,the overthrowing power is1 then1 the area of the triangle ,b#df the weight of the unit of area the leverage #f #b4 ,and the resisting power1 the area ,,ab ,b#f the weight of a unit of area by one half breadth1 or m #f2 or1 calling w the weight of the wall1 and w that of the triangle1 ,b #d #f1 and ,l and ,l the leverage respectively of the wall to resist and of the earth to overthrow2 we must have at least w,l w,l1 and to insure stability1 w,l w,l or1 ,l 7w,l7_/w1 and as ,l half base finally1 the thickness1 or #b,l 7#bw,l7_/w #bgf4 ,example4--,let the height of wall be twenty feet1 slope one and one half to one2 if a cubic foot of earth weighs one hundred lbs41 and of masonry1 one hundred and sixty lbs41 we have the overthrowing force1 #bj #ae #a #ajj #b #bj_/c1 and the resisting force1 7assuming the thickness as eight feet1 in order to get the area71 #bj #h #a #afj #h_/b4 ,or performing the operations1 ,for overthrowing1 #ajj1jjj lbs4 ,for resisting1 #ajb1djj lbs4 ,if the wall in place of retaining only the mass ,b #d #f1 retains the bank ,b ,e ,fa1 the pressure will evidently be increased4 ,the centre of gravity of the trapezoid ,b ,e ,fa #f1 is at ,c1 which is horizontally projected at ,ca1 and the horizontal component of the thrust acts at #c with the leverage #fc4 ,any superincumbent load1 as a train of cars at ,e ,fa1 will again increase the pressure1 not only by reason of weight1 but from shocks and vibration4 ,for resisting lateral pressure1 the beds of masonry are best when rough dressed4 ,for vertical loads1 hammer dressed beds are the best4 ,the leverage of resistance is very much increased by battering the wall in front1 as at ,a ,d4 ,the centre of gravity is then horizontally projected at m1 but the distance ,d m is much greater than ,f m4 ,illustration3 ,fig4 #acd4 ,the amount of masonry remaining the same1 by decreasing the top1 and increasing the base1 the strength is very much increased4 ,when retaining walls are exposed to shocks or pressures special directions1 they may be very much aided by buttresses opposing directly such forces1 as in fig4 #acd4 ,the increase of strength thus made by a small bulk of masonry is very great4 ,all abutments1 wing-walls1 and side walls of culverts1 come under the head of retaining walls4 ,when the face of the wall does not by its position admit of buttresses1 as in fig4 #acd1 it may be dovetailed into the earth2 the latter being firmly rammed around the masonry1 as in fig4 #ace4 ,illustration3 ,fig4 #ace4 #bgg4 ,the weight of the different earths and stones are shown in the following table4 ,name of material4 ,weight per cubic foot4 ,brick1 common #ig to #abe ,brick1 stock #aae to #ace ,brickwork1 7average17 #ij to #ie ,chalk1 #add to #aff ,granite1 #afd to #ahg ,marble1 #aaa to #aag ,mortar1 7hair17 dry #hj to #hf ,puzzolano1 #afj to #agh ,slate1 #aeg to #ahj ,stone1 7average17 #adj to #aej ,clay1 7common17 #aaj to #abe ,clay and gravel1 #aej to #agj ,earth1 common1 #ie to #abf ,gravel1 #ajj to #aaj ,quick-lime1 #ej to #ee ,quartz sand1 #agj to #age ,common sand1 #hh to #ic ,shingle1 #hh to #ib ,earth1 loose #ij to #ie ,stone work1 7hewn17 in wall1 #afj to #age ,stone work1 7unhewn17 in wall1 #abe to #adj ,,chapter ,,xii4 ,,foundations4 #bgh4 ,foundations may be divided into four classes4 ,those on firm1 dry land4 ,those on unfirm dry land4 ,those on solid bottom1 under water4 ,those on unfirm bottom1 under water4 ,foundations upon firm dry land require only to be placed at a sufficient depth to be out of the way of frost2 varying from one foot in the ,southern1 to two and three feet in the ,middle1 and four and five feet in the ,northern ,states4 ,the first course should consist of small1 flat stones placed dry1 but well packed by hand1 upon the bottom2 upon the top of this layer1 the mortared or cement masonry should be commenced4 ,the object of the first course of small stones is to apply the weight of the superincumbent masonry as equally as possible to the ground4 ,all boulders and rounded stones should be carefully kept out of the foundation4 ,unfirm soils are prepared by driving piles1 upon which a platform holding the masonry is placed2 or by placing the lower courses directly upon the heads of the piles4 ,sand piles are made either by driving and withdrawing a wooden pile and filling the hole thus made with sand2 or by digging trenches and filling such with sand4 ,the applied weight is thus spread over the entire surface of the sides and bottom1 instead of being placed upon the bottom only4 ,when the weight of a heavy structure is thrown upon a few small points of support1 they may be made the piers and abutments of a series of inverted arches1 by which the whole surface beneath the structure is made to assist in bearing the load4 ,foundations upon yielding or sandy and wet soils may be secured by piling around the whole structure2 by which the earth is kept from spreading4 ,foundations upon dry land do not generally give much trouble to the engineer2 but operations carried on under water require all the science and patience that he is master of4 #bgi4 ,three methods of founding under water may be noticed1 ,by driving piles4 ,by coffer-dam4 ,by caisson4 ,in very shallow water1 where no danger arises from contracting the water-way1 we may throw in loose stones until the surface is reached2 and commence thereon the lower courses of the masonry4 ,this is termed 8,enrockment40 ,,pile ,,driving4 ,this operation has for its object the consolidation of naturally weak bottoms2 for piles driven close together tend to prevent that compression that might take place under a heavy structure4 ,piles may resist either by friction against the soils through which they are driven1 or by bearing upon a firm substratum at too great a depth to be reached by uncovering4 ,piles driven in clay have sometimes acted as a conductor to water1 which1 insinuating itself along the side of the wood1 produced settling which would not otherwise have taken place4 ,experience has shown that four feet apart from centre to centre1 when there is a good substratum1 is near enough to bear the heaviest loads4 ,the fact that a pile refuses to enter further1 does not show that it has reached a bed strong enough to bear the required load2 for though it may bear upon a solid bottom1 or resist penetration by side friction1 when the load has been for some time upon the pile1 it may be found too weak to stand4 ,piles have in some cases refused to enter the ground from the blow of a #a1ejj lbs4 ram1 falling twenty feet1 when first driven1 and have afterwards gone down three feet from a ram of #a1jjj lbs4 ,the following formula1 showing the resistance which a pile should offer1 is given by ,weisbach in ,mechanics of ,engineering1 ,vol4 ,i4 p4 #bhe4 ,first1 when the ram remains upon the pile after the blow1 ,p s 7,g#b ,h7_/7,g ,g74 ,and1 second1 when the ram does not remain upon the pile1 ,p s 7,g_/7,g ,g77#b ,,gh ,example4--,a pile weighing five hundred lbs4 is driven two feet1 by forty blows of a #a1jjj lbs4 ram falling six feet4 ,required the weight which may be safely supported by the pile without further penetration4 ,the notation in the formula above is thus1 ,g the weight of the pile4 ,g the weight of the ram4 ,h the fall of the ram4 s penetration per blow4 ,p the weight in lbs4 ,the penetration per blow will be #b_/dj or 4#je feet2 and the formula for the second case 7#ajjj_/7ajjj #ejj77b 7#ejj #f7_/4je #dh1jjj lbs4 ,of which one tenth or one twelfth only is the maximum load which should be placed upon the pile permanently4 ,the surest test of the power of a pile is to load it temporarily1 when the time and place admit4 ,perronet considered fifty tons1 or #aab1jjj lbs4 as not too great for a twelve inch pile2 and allowed twenty-five tons for a pile of nine inches in diameter4 ,that the point of the pile may not be shattered by contact with the hard earth1 an iron shoe is sometimes fitted to the lower end2 and that the head may not split1 an iron ring is driven on to the top4 ,the force of the blow given by a ram depends upon the weight of the ram or monkey1 and upon the velocity at which it strikes the pile2 the velocity depends upon the height from which it falls4 ,the velocities of bodies falling freely being as the times1 and the spaces fallen through as the squares of the times1 we have the following rules2 and from them the table succeeding4 ,given the velocity of a body to find the space through which it must fall1 77,velocity in feet per second7_/#h7b space in feet4 ,thus a weight to acquire a velocity of two hundred feet per second1 must fall through a height of 7#bjj_/h7b #fbe feet4 ,given the space fallen through1 to find the velocity4 7height in feet #fd4c7 velocity in feet per second4 ,thus the velocity of a body falling twenty feet will be 7#bj #fd4c7 #cf feet per second4 ,momentum is the product of weight by velocity2 therefore1 to find the force of the blow given by a ram of given weight1 falling a given height1 we find1 first1 the velocity by rule two4 ,also1 given the weight of ram1 the necessary velocity to produce any required effect being found1 it is easy to find the height1 and the reverse4 ,examples4--,suppose we have a ram weighing #b1jjj lbs4 and wish to strike a blow of #be1jjj lbs42 the velocity must be #bejjj_/bjjj #ab feet per second2 and to acquire that velocity1 the height fallen must be 7rule one7 7#ab_/h7b #b4dc feet4 ,again1 if we have a pile-engine which admits of a fall of fifteen feet1 and we wish to strike a blow of #ah1jjj lbs41 we first find the velocity 7rule two7 thus3-- 7#ae #fd4c7 #ca feet per second nearly1 whence the weight #ahjjj_/ca #eha lbs4 ,the form of the common pile-engine is too well known to need description4 ,mr4 ,nasmyth's system of pile-driving consists in forcing the pile into the ground by a great number of blows following each other in rapid succession4 ,piles were driven by his engine at the ,united ,states ,dry ,dock1 at ,brooklyn1 7,n4 ,y417 as follows3 ,a pile was sunk fifty-seven feet by a hammer of #d1ejj lbs42 it was driven forty-two feet in seven minutes by three hundred and seventy-three blows4 ,,mitchell',s ,,screw ,,pile4 ,mitchell's screw pile is a cast-iron column1 around the lower part of which is a spiral flange4 ,it is screwed into the ground1 and offers great resistance to vertical pressure1 on account of the large bearing surface obtained4 ,,dr4 ,,potts',s ,,atmospheric ,,system4 #bhj4 ,all methods of placing foundations in difficult positions must yield to the above plan1 which consists in exhausting the air from a hollow cast-iron cylinder2 when the pressure upon the surface of the ground1 outside of the cylinder1 forces the earth immediately under the pile to its interior2 at the same time the pile sinks into the opening thus made1 both by its weight and by the atmospheric pressure from the outside4 ,the earth is moved from the interior of the pile2 and when sunk to the necessary depth1 the interior is filled with concrete4 ,a very successful application of the above system was made at the ,goodwin ,sands1 at the mouth of the ,thames ,river1 7,england74 ,these sands change their position with every violent storm1 and are yet so compact that a steel bar could be driven only eight feet with a sledge hammer2 and a pointed rod three inches in diameter1 when sunk thirteen feet deep1 required forty-six blows from a one hundred lbs4 ram falling ten feet to drive it one inch4 ,but a hollow pile two and a half feet in diameter was sunk seventy-eight feet1 at the rate of ten feet per hour for a part of the time4 ,in case of meeting with rock1 the pile may be converted into a diving-bell1 and the obstruction moved4 ,the pile is cast in lengths of ten or twelve feet1 and flanged together with cemented joints4 ,in founding a bridge at ,rochester1 7,england17 a pile of this nature was loaded with thirty tons of iron rails1 which caused a settlement of three fourths of an inch4 ,the rails being removed and the air exhausted1 by a single effort the pile descended six and a half feet4 ,one hundred tons of rails were then placed upon the pile1 when the settlement was again three fourths of an inch4 7,this small depression was owing to the compression of the soil47 ,the piles supporting the ,shannon bridge1 on the ,midland ,great ,western ,railroad1 7,england17 were sunk by this system2 and are ten feet in diameter1 and filled with concrete4 ,after wooden piles have been driven1 they are cut off at the proper level to receive the lower courses of the masonry4 ,in some cases square timber caps are placed upon the pile heads1 and thereon a plank floor4 ,in others1 the spaces between the piles are filled with cement and concrete4 ,,coffer-,,dam4 #bha4 ,in founding in water from five to twenty-five feet deep1 a contrivance called a 8coffer-dam10 is sometimes used4 ,it is formed by driving a double or triple row of piles around the foundation2 which rows are made water tight1 either by tongued and grooved square piles1 or by round piles1 to which is fastened a sheathing of plank4 ,the space between the courses of piling is emptied of water and packed closely with clay or other material impervious to water4 ,the interior of the dam is then pumped dry and the masonry laid as on dry land4 ,the thickness of the dam depends upon the depth of water2 the pressure upon the lower part being of course much greater than that at the upper4 ,if it was considered as a mass resisting by its weight1 overthrow from the pressure of the water1 the thickness would be easily calculated4 ,thus1 if the water is twenty feet deep the whole hydrostatic pressure upon each lineal foot of the dam is #bj #a #aj #fb #ab1ejj lbs42 and as the weight of water increases in the order of the terms of an arithmetical progression1 as also the pressure1 it may be expressed by the elements of a triangle1 of which the height is the depth2 and as the centre of gravity of a triangle is at two thirds of the height from the vertex1 the pressure may be regarded as concentrated at one third of the depth from the bottom2 and the leverage of the above #ab1ejj lbs4 is #bj_/c #f4fg feet2 and the overthrowing force is #hc1cge lbs4 ,the resisting force of a clay dam twenty feet high and ten feet thick1 would be #bj #aj #aaj #aj_/b #aaj1jjj lbs4 ,determining the thickness thus1 would make the dam1 when in deep water1 very thick2 and it is generally best to brace the inside against the ground1 and when the masonry will admit1 against that4 ,dams of the following thickness have proved perfectly secure3-- ,depth of water4 ,thickness4 #f feet4 #c feet4 #aj feet4 #e feet4 #ae feet4 #h feet4 #bj feet4 #ab feet4 #be feet4 #ad feet4 ,the best form for a large coffer-dam is circular1 or elliptical2 as the pressure is thus resisted more equally in all places than when there are flat sides and angles in the plan4 ,to keep the dam dry while the work is going on1 pumps are rigged along one side of the dam the lower ends of which are placed in a trench or well which drains the bottom4 ,the piers of the ,victoria bridge at ,montreal1 7,canada17 are put down by coffer-dams4 ,some of the piers being in but few feet of water1 and upon a rocky bottom1 which did not admit of the driving of piles2 the dams for such were built in sections1 floated to the site and anchored4 ,,foundation ,,by ,,caisson4 #bhb4 ,in deep water the coffer-dam becomes very expensive1 on account of the size and length of the piling1 and the quantity of bracing required4 ,in such cases recourse is had to the caisson2 which is simply a box in which the masonry is built1 and afterwards sunk to the proposed site4 ,the manner of putting down a piece of masonry by caisson will best be shown by an example4 ,suppose we wish to sink a pier thirty feet long1 twenty feet high1 and six feet wide1 in twenty feet of water4 ,let the caisson bottom be of two courses of square #ab #ab timbers1 fastened strongly at right angles to each other4 ,let the courses of masonry be two feet thick4 ,assume the weight of a cubic foot of stone as one hundred and sixty lbs41 a cubic foot of wood at thirty1 and of water sixty-two lbs4 per foot4 ,every floating body will sink until it has displaced a quantity of water equal to its own weight4 ,if the bottom is ten feet wide and thirty-five feet long1 it will weigh #ce #aj #b #cj #ba1jjj lbs4 one course of masonry weighs #cj #f #b #ajj #eg1fjj lbs4 one course of side timbers1 #ab #ab1 which are laid upon the sides of the raft1 7#b #ce #b #h7 #cj #b1ehj lbs4 ,now load the bottom with one course of masonry and three courses of side timbers1 and we have ,stone #eg1fjj lbs4 ,bottom of caisson #ba1jjj lbs4 ,three side courses #g1gdj lbs4 ------------ ,in all3 #hf1cdj lbs4 which divided by #fb1 gives #a1cib2 which divided by the area of the caisson bottom1 gives #acib_/cej #c4ih or nearly four feet1 for the depth at which the caisson will float4 ,this leaves the sides one foot above the water surface4 ,putting on a second course of masonry and three more side courses of timber1 we have ,floor #ba1jjj lbs4 ,two courses masonry #aae1bjj lbs4 ,six side courses #ae1dhj lbs4 -------------- ,in all #aea1fhj lbs4 which divided by #fb1 and by #cej1 gives seven feet very nearly2 leaving the top one foot above the surface4 ,in the same manner we proceed until the caisson grounds upon the bed1 which has been previously prepared1 either by pile-driving or by dredging4 ,the bottom being reached1 the sides are taken off1 and the masonry remains upon the floor4 ,the caisson may at any time be grounded by filling with water1 and may be raised again by pumping out4 ,the masonry may be laid either from barges or rafts at the site1 or at the shore4 ,guide piles are necessary to insure the descent in the proper manner1 and to prevent overturns4 ,in laying stone under water1 it is to be remembered that masonry submerged loses #fb_/ajj nearly of its weight1 and is consequently more liable to be injured by shocks than when above the surface4 ,,chapter ,,xiii4 ,,superstructure4 #bhc4 ,nothing aids more the proper accomplishment of any object than a correct idea of what is wanted4 ,the following definition is given by ,mr4 ,w4 ,b4 ,adams1 of what good superstructure should be3-- 8,the principal requirements of permanent way are3 ,that it shall be well drained1 especially in contiguity to the substructure2 that the weight and damaging power of the locomotives and rolling stock should be considered the data for calculation2 that the strength1 hardness1 and tenacity of rails1 and the immobility of the substructure should be adapted to the hardest work to which the railway is to be subjected2 that the substructure should have an amount of bearing surface proportioned to the load to be borne1 and the nature of the rail and ballast2 and a sufficiently fair hold in the ground to prevent looseness or lateral motion1 from the side lurches of the engines and trains2 that the rails should possess so much vertical and lateral stiffness1 either in themselves or in their fastenings1 as to prevent all deflection2 and have sufficient hardness of surface not to laminate or to disintegrate beneath the rolling loads2 also1 to have sufficient breadth or tread surface to diminish the crushing effect of the wheels4 8,they should be as smooth as possible1 to prevent concussion1 and be laid at the proper angle1 and the curves regularly bent1 so as to insure the accurate tread of the wheels4 ,the joints should be so made that the rails may practically become continuous bars1 yet with freedom to contract and expand without being too loose4 ,and with all this there should be interposed between the rails and the solid ground1 some medium sufficiently elastic to absorb the effect of the blows of the wheels1 without being crushed or forced down into the ballast1 and yet stiff enough to keep the upper surface of the rails in a uniform plane40 ,,timberwork4 #bhd4 ,the timber-work supporting the rails consists either of cross ties of wood1 hewn flat on top and bottom1 of dimensions from #f #g to #g #i1 and #b or #c feet longer than gauge2 or of longitudinal sawed timbers rectangular in section1 placed directly beneath the rail1 and giving it a bearing throughout the whole length4 ,longitudinal bearings seem to possess no advantage over cross ties1 but are subject to some decided disadvantages4 ,in case of removal1 two rails at least must be taken up to admit of the replacing a timber2 while with cross ties any one may be taken out and replaced without even affecting the immediate passing of a train4 ,a continued bearing is no better than a broken one1 as the strength of the timber itself offers very little resistance to the weight of a locomotive4 ,strength is not to be expected in the timber-work2 it is only the elastic medium between the rail and the ground serving to maintain the rail in a proper position4 ,the strength is in the rail4 ,the distance at which to place cross ties depends upon the weight of engines traversing the road1 the nature of the ballast1 and the strength of the rail2 somewhere between two and four feet from centre to centre4 ,the amount of superficial bearing which the timber-work ought to give per lineal foot of rail1 is differently estimated by different engineers4 ,upon the #d #h gauged roads of ,america1 #a square feet per lineal foot of rail has been allowed4 ,several of the ,english roads give the following3-- ,name of road4 ,gauge4 ,square feet per lineal foot of rail4 ,london and ,n4 ,w4 ,railway1 #d #h #c ,great ,western1 #g #j #b ,s4 and ,w4 of ,ireland1 #e #c #c ,midland ,g4 ,w4 of ,ireland1 #e #c #bg_/ab ,if ties are made eight inches wide1 and eight feet long2 we have the following amounts of bearing surface per lineal foot of the rail with different distances of the ties4 ,distance ,c to ,c of tie4 ,superficial feet per lin4 foot4 #b #b4ff #b #b4ac #c #a4gh #c #a4ec ,of course the longer the tie is made the greater may be the distance between1 provided the rail will bear it4 ,mr4 ,peter ,barlow1 in his report of ,august1 #ahce1 to the directors of the ,liverpool and ,manchester ,railway1 fixes the following dimensions for superstructure4 ,distance between insides of ties being #c #c #i #d #e #f ,weight in lbs4 per yard4 #ej #ei #fa #fg #gi ,depth of rail in inches4 #d #d #d #e #ee_/af ,at the time these dimensions were given1 however1 much less weight was applied to the rails than at the present day4 ,as the bearing is increased1 the rail must become heavier and more expensive2 but the number and cost of the ties is lessened4 ,the report above referred to1 concludes that five feet bearings1 involving heavier rails1 would cost no more1 after the road bed is consolidated1 than shorter ones2 but that on embankments and soft subsoils1 it would be at first somewhat more expensive4 #bhe4 ,the object of the ballast is1 first1 to transfer the applied load over a large surface2 second1 to hold the timber-work in place1 horizontally2 and third1 to carry away the rain water from the superstructure2 it also furnishes the means of adjusting the timber-work to the proper position4 ,it should be at least one half way up the depth of the tie1 and deep enough below the under surface to prevent the timber being forced down by the passing weight4 ,from various observations it appears that there should be one and a half times the depth of the tie of ballast1 beneath the under surface2 or the whole depth of ballast should be from two to two and one half times the depth of tie4 ,for ballast1 broken stone1 gravel1 or other dry1 durable1 and porous material1 is suitable4 ,a perfectly inelastic road bed is not to be desired4 ,something is necessary to absorb the shocks given by the wheels1 and prevent their reaction against the machinery4 ,to supply this amount of elasticity1 and to transmit the weight evenly to the ground1 is the duty of the ballast and timber-work4 ,of late years there has been applied1 in ,england1 cast-iron hemispherical bowls1 designed to take the place of both tie and chair4 ,such answers very well when there is no lack of ballast1 and where wooden ties are worth from seventy-five cents to one dollar each4 ,,section ,,of ,,the ,,rail4 #bhf4 ,a good rail must be able to act as a girder1 or supporter1 between the ties1 as a lateral guide upon curves2 and must possess a top surface of sufficient hardness and size to resist the rolling wear of the wheels4 ,lbs4 per yard4 ,tons per mile4 7#b1bdj lbs474 ,one square inch of rail section weighs1 #i4i #ae4gb ,two inches of rail section weighs1 #ai4h #ca4db ,three inches of rail section weighs1 #bi4g #dg4ad ,four inches of rail section weighs1 #ci4f #fb4hd ,five inches of rail section weighs1 #di4e #gh4ef ,six inches of rail section weighs1 #ei4d #id4bh ,seven inches of rail section weighs1 #fi4c #aaj4jj ,eight inches of rail section weighs1 #gi4b #abd4ej ,nine inches of rail section weighs1 #hi4a #adj4ja ,ten inches of rail section weighs1 #ii4j #aee4eg ,single line of ,double line of rails4 rails4 ,thus1 at sixty dollars per ton1 each square inch of section costs #idc4bj per mile1 or #id1cbj per one hundred miles1 whence the necessity of rolling the rail to the form which shall give the greatest strength with the least weight4 ,the sections most in use in ,america are shown in fig4 #acf1 and #acg4 ,illustration3 ,fig4 #acf4 ,fig4 #acf gives the most direct bearing1 is compact1 and brings the fibres at top and bottom more directly in opposition with the compressive and extensive strains4 ,the top of the rail being curved to a radius of ten or twelve inches1 the load is applied nearly to a single point2 whence the whole resistance in fig4 #acg1 depends upon the lateral resistance of the piece a b c d to being pushed down4 ,an objection is sometimes made to fig4 #acf1 on the ground that it splits off on the line n n3 this will not be the case when the head is joined to the web by a proper curve1 as in fig4 #acf4 ,this splitting off happens full as often in fig4 #acg as may be seen where it is in use2 and it might be supposed to act in that manner2 because if the weight is transferred at all from the point of application to the web1 it must be in the direction e f4 ,illustration3 ,fig4 #acg4 ,the rails in present use upon our roads1 weigh from fifty to seventy-five lbs4 per lineal yard2 and are laid upon cross ties placed at a distance of from two and one half to four feet from centre to centre4 ,,of ,,the ,,actual ,,dimensions ,,of ,,rails4 ,digesting carefully the results of the experiments of ,barlow1 ,fairbairn1 and ,hodgekinson1 and the experience of ,mr4 ,w4 ,b4 ,adams1 and other ,english engineers2 also the conclusions arrived at by the ,berlin ,convention of #ahej1 appointed to determine the best form of section1 we come to the following limiting dimensions4 ,,the ,,head4 ,mr4 ,barlow limits the width of head at two and one half inches as the maximum2 the ,berlin ,convention1 at two and one fourth inches2 ,w4 ,b4 ,adams1 at two and one half2 and all of the above recommend supporting the edges of the head well from the rib4 ,,the ,,vertical ,,rib4 ,the experiments of the ,prussian engineers fix the thickness for a rail four inches high1 at one half of an inch1 and a rail four and one half inches high1 at #j4f or #f_/aj inch4 ,mr4 ,barlow makes it six tenths of an inch for a four and one half inch rail1 and #j4ge1 or three fourths inch for a rail four and five eighths inches high1 and for four and three fourths inches high1 #j4h1 eight tenths inch4 ,,the ,,bottom ,,flange4 ,the use of this is more for bearing and fastening1 than for supporting strength4 ,the ,prussian engineers make three and one half inches an ample base for a rail five inches high4 ,the edge for one half or three fourths of an inch1 should be nearly horizontal1 or parallel with the base1 to allow the spike to have a good bearing4 ,,of ,,the ,,inclination4 ,as the tread of the wheel is conical1 the top of the rail must be inclined to fit this cone1 otherwise the wear will come upon the inner edge of the rail only4 ,this may be done in two ways2 by placing the rail base level1 and inclining the vertical axis of the cross section of the rail1 and making the tread square with that axis2 or by making the rail section true1 and inclining the base1 either by cutting the tie1 or by a wedge placed between the rail and the tie4 ,,of ,,the ,,head ,,curvature4 ,if the top surface of the rail were perfectly flat1 and the wheel tire does not happen to fit it exactly1 7from want of the proper position of the rail1 by settling1 or other cause17 the wheel will bear entirely upon one edge1 and would soon destroy the rail4 ,to remedy this1 a slight convexity is given to the top4 ,mr4 ,clark 7in ,r4 ,r4 ,mach471 recommends the top to be curved to a radius of ten or twelve inches4 ,,of ,,the ,,vertical ,,depth 7,,height7 ,,of ,,the ,,rail4 ,mr4 ,barlow's general results are as follow3-- ,distance from inside to inside of tie4 ,height of rail4 #c #j #d #c #i #d #d #j #d #e #j #e #f #j #ea_/af ,in the ,london edition 7#ahcf7 of ,barlow's ,strength of ,materials1 page #djb1 in a report to the ,london and ,birmingham ,railway ,co41 upon the best form and upon the strength of rails2 after a carefully conducted set of experiments1 and an elaborate theoretical deduction of results1 the writer comes to the following five sections of rails possessing the maximum strength1 with the least weight4 ,dimensions4 ,no4 #a4 ,no4 #b4 ,no4 #c4 ,no4 #d4 ,no4 #e4 ,height1 #d #d #d #e #ee_/af ,breadth at top1 #b #b #b #b #b ,depth of top1 #a #a #a #a #a ,thickness of rib1 #j4f #j4ge #j4h #j4he #a4j ,width of lower flange1 #a #a #a #a #a ,depth of lower flange1 #a #a #a #a #a ,weight per yard1 #ea4d #eh4h #fa4b #fg4d #gi ,distance ,c4 to ,c4 of ties1 #c #ci #d #e #f ,this table shows the ratio of material which should be placed in the top and bottom4 ,with the above dimensions1 and joining the curve of the head to the rib at two and one fourth inches from the top of the head1 we obtain a strong and well-shaped rail1 with the least material possible4 ,see fig4 #acf4 ,as an example of the application of the above1 the table below has been formed1 showing four standard forms1 which will be found to unite all of the requirements of good rails2 the general form being that of fig4 #acf4 ,dimensions4 ,the weight of the rail being1 in lbs41 #fj #fe #gj #ge ,width of head1 #b #b #b #b ,rad4 of top1 #ab #ab #ab #ab ,height of rail1 #d #d #d #d ,thickness of rib1 #j4f #j4f #j4fe #j4g ,breadth of base1 #c #c #c #d ,depth of head at point ,a ,b1 #b #b #b #b ,thickness at edge of lower web1 and the following figures show the weights which should be applied to differently spaced sleepers4 ,distance centre to centre of tie4 ,distance clear4 ,weight of rail4 #a feet1 #a feet1 #fj lbs4 per yard4 #b feet1 #a feet1 #fj lbs4 per yard4 #b feet1 #a feet1 #fj lbs4 per yard4 #b feet1 #b feet1 #fj lbs4 per yard4 #b feet1 #b feet1 #fe lbs4 per yard4 #c feet1 #b feet1 #fe lbs4 per yard4 #c feet1 #b feet1 #gj lbs4 per yard4 #c feet1 #c feet1 #ge lbs4 per yard4 ,the amount of inclination or bevel to be given to the cross section of the rail1 depends directly upon the cone of the wheel1 and indirectly upon the gauge of the track4 7,see ,chapter ,,xiv4 part #b47 ,the radius of curvature being averaged at #b1 or #b1hfe feet1 ,feet or ,inches4 ,for the #d #h gauge it should be 4#jjag 4#jbj ,for the #e gauge1 4#jjag 4#jbj ,for the #e gauge1 4#jjai 4#jbb ,for the #f gauge1 4#jjba 4#jbe in the width of the rail1 or two and one half inches4 ,the above dimensions embrace all of the best results of experiment and experience1 and at the same time satisfy the conditions demanded by the mechanical and physical nature of the material--iron4 ,,chairs ,,and ,,joints4 #bhg4 ,the chairs most common at present are made of a wrought iron plate1 with two lips1 either cut and punched up1 or forged up1 to hold the lower web of the rail4 ,such chairs weigh from six to ten pounds each1 and are less liable to break than the common form of cast-iron chairs4 ,it is probable that a cast-iron chair may be made1 however1 with properly shaped lips1 and so hollowed out as to be at once strong and light4 7,see ,clarke's ,r4 ,r4 ,machinery1 8,permanent ,way407 ,of late the chair of ,mr4 ,david ,l4 ,davis1 of ,dedham1 ,mass41 has attracted considerable attention1 and bids fair to be the means of obtaining a better rail surface than has heretofore been possible4 ,this gentleman has been for twenty years ,road-master of the ,boston and ,providence ,railroad1 and has had ample opportunity for considering the subject of track laying in every respect4 ,the rail bears upon a cap of wrought iron1 which rests upon a piece of rubber1 lying in the chair4 ,the testimony of the leading managers of the ,new ,england ,railroads bears witness of the excellence of the arrangement4 ,the practice of notching each end of the rail causes the expansion to be exerted directly against the fastenings1 which should not be the case4 ,some point should be fixed longitudinally1 to resist the end shocks from the wheel4 ,this point should be either the centre or one end of the rail4 ,end chairs may hold the rail laterally1 and vertically1 but not longitudinally4 ,the weakest part of the track is that1 where1 to resist the concussions of the wheels it should be strongest1 namely1 at the joint3 here we lose the strength of the rail and depend entirely upon the tie4 ,the flattened ends of rails which have been laid for a few years show the bad effect of the common joint4 ,the complete remedy for this is1 so splicing the rail that it is as strong at the joint as elsewhere4 ,the method termed 8fishing10 is not much more expensive than the ordinary method of jointing1 it is perfectly effectual1 and has had the test of long and successful use4 ,it consists in bolting a plate two and one half feet long1 two and one half or three inches wide1 and from one third to one half inch thick1 to the ends of both rails making the joint2 one plate being placed on each side4 ,the plates are convexed a little from the rail as in fig4 #ach1 so that being sprung by screwing on the nuts1 the latter shall not work loose by the vibration of the rail4 ,illustration3 ,fig4 #ach4 ,in the above arrangement there is no tie below the joint1 but the latter lies midway between two sleepers4 ,another method of 8fishing0 is1 to place a piece of or iron beneath the rail1 bolting it firmly to the lower flanges4 ,in bolting rails together at the ends1 the bolt holes must be cut a little larger than the bolt1 to allow for the expansion of the iron4 ,the effect of the joint upon the passing carriage1 is the jumping motion2 the middle of each rail being a summit1 and the end a depression1 7the strength at the joint being taken away72 and if the joints are not opposite to each other1 there is generated a very injurious and dangerous side rocking4 ,figs4 #ach1 #ach ,a1 and #ach ,b1 show the methods of fishing4 ,illustration3 ,fig4 #ach ,a4 ,fig4 #ach ,b4 ,illustration3 ,fig4 #aci4 ,to avoid the wear caused by frequent joints1 various forms of compound rails have been proposed2 consisting of two or more parts breaking joint4 ,one form has been contrived in which the section is vertically halved2 another of three parts1 a head placed on top of a double vertical web4 ,fig4 #aci shows what would seem to answer any purpose 7if compound rails are at all allowable74 ,the joint is here divided into four parts1 so that the strength of the bar at any point is reduced only one fourth4 ,in bolting the parts together the joints should be left open enough 7see in advance7 to allow for contraction2 and the bolt-holes1 as before noticed1 should be longer than the bolts4 7,this enlargement1 extending only in the direction of contraction1 and not in the line of the force47 ,the upper part of such a rail should be hardened to resist the rolling of the wheels1 while the webs must possess the strength to act as a girder4 ,it is questionable whether1 by dividing the rail1 particularly when it is done horizontally1 we do not prevent the mutual extensile and compressive actions which ought to have place in the top and bottom2 for we cannot make the bolts perfectly tight because of expansion4 ,some of the compound rails which have been laid in ,america have given good results1 others have not4 ,mr4 ,w4 ,b4 ,adams observes1 that a compressed rail to be as strong as a sixty pound whole rail1 must weigh ninety lbs4 per yard4 ,some engineers have proposed such a rail that when one side becomes worn it may be turned over so that the lower may become the upper table4 ,this is quite wrong in principle2 as when the lower fibres have been subjected for some time to extension1 they are entirely unfitted to oppose compression4 ,,of ,,the ,,life ,,of ,,rails4 #bhh4 ,the time which a rail will last1 depends upon the form and weight1 and on the quality of the iron2 and upon the number1 weight1 and speed of engines and cars passing over it4 ,,note4--,the effect of quality is altogether too little regarded in ,america4 ,how worthy of attention it is may be seen by the following4 ,upon the same road were used two kinds of seventy-two pound rails1 each five inches deep1 and having a bearing surface of #b4g inches in width4 ,the one was worn out with a tonnage of #da1jjj1jjj tons1 the other of #bb1jjj1jjj tons2 the difference being entirely in the quality of the iron4 ,upon the ,philadelphia and ,reading ,railroad there have been used forty-five pound rails of reheated and refined iron1 which have lasted for eighteen years2 and that with a very heavy traffic upon them4 ,while upon other ,american roads1 ,english sixty pound rails have required renewing in one1 two1 three1 and four years4 ,the durability of rails is practically independent of time1 and depends entirely upon the amount of work done4 ,the repairs of iron1 depending upon flaws and other physical defects1 will be greater at the commencement of operations than afterwards4 ,after the first one or two years the regular depreciation begins4 ,the first ,liverpool and ,manchester rail weighed thirty-five lbs4 per yard1 and the locomotive seven and a half tons4 ,as the traffic increased1 so did the necessary weight of engines1 and a corresponding increase in the strength and weight of rails was also rendered necessary4 ,in #ahca1 the average weight of engines with tenders was eighteen tons4 ,in #ahee1 the maximum engine with tender1 fuel1 and water weighed sixty tons2 and in like manner the rails increased from thirty-five to eighty-five lbs4 per yard4 ,messrs4 ,stephenson and ,locke1 in a report to the ,london and ,north-western ,railroad ,company1 in #ahdi1 recommend the adoption in future of an eighty-five lb4 rail4 ,upon the roads of ,belgium are used rails of fifty-five and sixty-four lbs4 per yard2 but it is asserted that an eighty lb4 rail would allow of ten times more traffic4 ,for the average of ,american roads1 when the iron is good1 7in quality17 fifty-five1 sixty1 and at most sixty-five lbs41 will probably be found ample for the heaviest traffic3 the rail being of the form already given1 and supported on ties not more than two and a half feet from centre to centre4 ,mr4 ,belpaire1 7of the ,belgium engineers17 concludes1 from many experiments1 that in sixty miles1 each engine abrades #b4b lbs42 each empty car #d oz42 and each ton of load #a4d oz42 the amounts being in direct ratio to the several weights4 ,captain ,huish1 of the ,london and ,north-western ,railroad1 7,england17 estimates 7,report of ,april1 #ahdi7 that fifty trains per day1 or #ah1bej trains per annum1 for twenty years1 would wear out a seventy lb4 rail4 ,the ,belgian engineers have concluded that #c1jjj trains per annum1 for one hundred and twenty years1 would wear out a fifty-five lb4 rail4 ,now #abj #c1jjj #cfj1jjj ,belgian1 and #bj #ah1bej #cfe1jjj ,english1 a very satisfactory coincidence1 as the different observers did not know of each other's proceedings4 ,the difference1 #e1jjj trains1 being accounted for by the use of heavier engines upon the roads of ,england4 ,from the above results the following table is formed1 showing the life of rails under from two to one hundred trains per day4 ,american roads being less nicely finished1 as regards the road-bed1 will of course wear out rails faster than the roads of ,europe4 ,the table will serve as a base for estimates4 ,trains per day4 ,trains per year4 ,no4 of years' life of rails4 #b #fjj #fjd #d #a1bjj #cjb #f #a1hjj #bja #h #b1djj #aea #aj #c1jjj #aba #ab #c1fjj #ajj #ad #d1bjj #hf #af #d1hjj #ge #ah #e1djj #fg #bj #f1jjj #fj #cj #i1jjj #dj #dj #ab1jjj #cj #fj #ah1jjj #bj #hj #bd1jjj #ae #ajj #cj1jjj #ab ,probably one half of the above numbers of years would show the full life of rails upon ,american roads4 ,as those rails which are most used wear out the soonest1 they should be made accordingly heavier4 ,such are those at depot grounds and at sidings4 ,,note4--,from the reports of the ,reading 7,penn47 ,railroad it appears that in #ahdf #aec_/bji of the damaged rails were split2 and that in #ahde #bhe_/bie were split4 ,as regards the quality of railroad iron1 it is generally notoriously bad1 and its makers know it as well as those who buy it4 ,railroad companies are not willing to pay for good iron4 ,comparisons between ,american and ,english iron amount to little4 ,first rate iron can be made in ,england or in ,america1 and so can that which will last about two years4 ,time will convince companies that the most expensive iron is the cheapest4 ,,table ,,of ,,the ,,weight ,,per ,,mile ,,of ,,different ,,rails4 ,weight in lbs4 ,tons per mile4 ,tons per mile4 per yard4 7#b1jjj lbs47 7#b1bdj lbs47 #ej #dd4jj #ci4bi #ee #dh4jj #dc4ba #fj #eb4hj #dg4ai #fb #ed4ef #dh4ga #fd #ef4cb #ej4bh #ff #eh4je #ea4hf #fh #ei4hd #ec4dc #gj #fa4fj #ee4jj #gb #fc4cf #ef4eg #gd #fe4ab #eh4ad #gf #ff4hh #ei4ga #gh #fh4fd #fa4bh #hj #gj4dj #fb4hf ,,track-,,laying4 #bhi4 ,as wrought iron expands #j4jjjjjfh of its length per degree 7,fahrenheit7 of heat1 a change of #acj will cause the following expansions3-- ,in a #ae feet rail 4#jace ft4 ,in a #ah feet rail 4#jafb ft4 ,in a #bj feet rail 4#jagf ft4 and that the track may be kept in the right vertical and horizontal line1 rails laid in cold weather must not be placed in contact2 but separated by space enough to allow expansion to take place4 ,in hot weather they may be placed close together4 ,calling #ajj the maximum and -#cj the minimum1 we form the following table for the average lengths of rail1 7#bj feet74 ,at #ajj place the rails in contact4 #ij at a distance of 4#jjacf feet 4#jaf inches4 #hj at a distance of 4#jjbgb feet 4#jcb inches4 #gj at a distance of 4#jjdjh feet 4#jdi inches4 #fj at a distance of 4#jjedd feet 4#jfe inches4 #ej at a distance of 4#jjfhj feet 4#jhb inches4 #dj at a distance of 4#jjhaf feet 4#jib inches4 #cj at a distance of 4#jjieb feet 4#aad inches4 #bj at a distance of 4#jajhh feet 4#aca inches4 #aj at a distance of 4#jabbd feet 4#adg inches4 #j at a distance of 4#jacfj feet 4#afc inches4 -#aj at a distance of 4#jadif feet 4#agi inches4 -#bj at a distance of 4#jafcb feet 4#aif inches4 -#cj at a distance of 4#jagfh feet 4#bab inches4 ,illustration3 ,fig4 #adj4 ,the proper distance of rails may be fixed by the use of the steel plates shown in figs4 #adj and #adj ,a1 which are marked with the temperature1 according to their thickness1 as in the above table4 ,to incline the rail base may be used1 when the rail is not bevelled1 wedges one foot long and six inches wide1 spiked with the rail to the tie4 ,when the chairs are of cast-iron1 they may be cast to the required slope4 ,illustration3 ,fig4 #adj ,a4 ,,frogs4 #bij4 ,when one line of rail crosses another1 a contrivance called a frog is used2 see figs4 #ada and #adb4 ,illustration3 ,fig4 #ada4 ,that the wheel may run smoothly from a to c1 fig4 #ada1 the rail b f must be cut at ,d1 and the rail a c must be cut at the same point4 ,cutting the two gives the form shown in the figure1 and further developed in fig4 #adb4 ,in order that the flange of the wheel shall not leave the line a c1 when at the break ,d1 the guard rail m m is used to confine the opposite wheel4 ,it should be placed at a distance of two inches from1 and parallel with1 the main rail g g1 from opposite six inches below the frog point at s1 to six inches above the shoulder at s4 ,from the ends of the parallel line n n the guard rail should gently curve away at both ends4 ,thus the wheel will be gradually brought into the right line1 kept so until the break in the rail is passed1 and finally easily released4 ,to place and maintain the guard rail in the right position1 it is well to put both it and the main rail into a double chair1 which is spiked to the sleeper4 ,illustration3 ,fig4 #adb4 ,the form and dimensions of the cast-iron frog depends upon the angle at which the cutting rails cross1 and upon the size of the wheel tire4 ,to draw the frog1 proceed as follows3-- ,illustration3 ,fig4 #adb ,a4 ,let a c b be the angle4 ,parallel with and two inches from b c draw d e1 e being in a c produced4 ,in the same manner fix the point g4 ,at the width of the rail head 7from #b to #b inches7 draw1 parallel to a c1 ,l #h4 ,the point #h is the limit to the solid steel4 ,at double the rail width1 or #d inches1 draw1 also1 parallel to a c1 #af4 #f2 #e4 #f is the limit of the flat steel1 generally about half an inch in thickness4 ,this is the least amount of steel allowable2 it is best to steel the whole tongue1 and all of that part of the wings acted upon by the wheels4 ,the geometric point is generally very thin1 and is omitted to a distance far enough back to make the point a third or half an inch wide1 which is rounded off2 e ,l and d k are made two and a half inches2 as also f m and g n2 k #aj and m #aa are made six or seven inches1 and joined to d and f by a curve1 abrupt at first1 but afterwards more gentle4 ,the distances1 #e a and #f b must be such that a #i is three and one eighth inches1 7depending upon the breadth of rail base17 o m is from three to four inches4 ,at the other end of the frog e h must be enough to make s t at least an inch1 when e h and i g are from three to four inches2 i m being1 as at the other end1 three or four inches4 ,the steel plates ,n ,n are one half inch in thickness4 ,the surface1 ,n1 is two inches above the bottom1 ,m4 ,the lower plate1 ,m1 is two inches thick4 ,a ,b1 ,c ,d1 and ,e ,f are six or seven inches wide1 and one inch thick4 ,the spike holes #aa_/af square1 the spike being one half inch4 ,the sharp edges1 i g1 e h1 a c1 b c1 should be rounded off to fit the wheel at ,a1 fig4 #adb ,a4 ,the surface of the tongue ,n #i should be formed to a double incline to fit the wheel cone4 ,,note4--,fig4 #adb ,a gives the shape and dimensions of the largest tires4 ,another method of making a frog is to cut and weld the rails a and b of the track1 as in fig4 #adc4 ,the continuations of these rails are bent as shown in the figure4 ,illustration3 ,fig4 #adc4 ,the whole angle is placed upon a firm wooden bearing4 ,there is no weaker part of the track than the frog4 ,to make up the strength at such places a heavy longitudinal timber twelve feet long will answer a good end4 ,,switches4 #bia4 ,the object of the switch is to adjust a single line of rails to two or more pairs1 so that any two lines may be made continuous4 ,the form in general use consists of two rails1 as at a b1 a b1 fig4 #add1 moving upon a and a as centres4 ,here the tangent point of the turnout curve is at c4 ,the data given for the switch are the length of switch rail and the motion at the toe 7c7 7which determine the direction of the starting tangent7 and the radius of curvature of the turnout curve4 ,the required elements are1 the angle of frog at b and the distance from a to the point of the frog4 ,illustration3 ,fig4 #add4 ,the following formula and table are by ,josiah ,hunt1 ,esq41 7at present chief engineer of the ,hannibal and ,st4 ,joseph ,railroad1 ,mo474 ,the formula was first published in ,appleton's ,mechanics' ,magazine1 vol4 #a1 p4 #ege4 ,d #b7;g - s7 7cot4 ,s cot4 ,f7_/7cot4 ,s cot4 ,f74 ,where ,s angle of switch4 ,f angle of frog4 s the movement4 g the gauge4 ,example4--,how far from the toe of the switch is the point of the frog1 the gauge being #d #h1 the rail twenty feet long1 and moving five inches2 the frog being six feet long1 six inches wide across the head1 and three inches at the mouth8 ,we have ,d #b7d4gjh - 4#dag7 7#bdj_/e #gb_/7f #c77_/7bdj_/e #gb_/7f #c77 or1 ,d #h4ehb 7#dh #h7_/7dh #h7 #eh4he feet4 ,in laying the rails1 the distance from the point to the end of the frog 7towards the switch7 is to be taken from the above4 ,table showing the distance between the frog and switch1 gauge #d #h1 movement of switch-rail five inches4 ,frog six inches across head1 and three inches at mouth4 ,main track being straight4 ,length of frog4 ,,length ,,of ,,switch ,,rail4 #ab #ad #af #ah #bj #bb #c #bi4abi4gcj4acj4dcj4gcj4i #c #cc4ccd4jcd4ece4jce4cce4f #d #cg4cch4bch4hci4dci4hdj4b #d #da4adb4bdc4jdc4gdd4cdd4g #e #dd4hdf4adg4adg4idh4edi4a #e #dh4cdi4hea4jea4ieb4gec4b #f #ea4gec4ded4hee4ief4heg4f #f #ee4jef4ieh4eei4hfj4hfa4g #g #eh4afj4cfb4afc4dfd4gfe4g #g #fa4bfc4ffe4ffg4bfh4efi4f #bib4 ,when the switch rail is short1 the angle between the main line and the switch rail1 when switched1 is considerable2 and causes quite a shock to the passing engine4 ,the switch shown in fig4 #ade remedies the evil1 makes the machinery compact1 and the calculation simple4 ,the tangent point of the turnout curve is at n n 7the usual heel74 ,in place of adjusting the single to the double line of rails1 the double is adjusted to the single line4 ,the data given are the gauge and radius of curve2 and as before1 the elements required the frog angle and distance from switch to frog point4 ,illustration3 ,fig4 #ade4 ,now ,rad4#b - 7,rad4 less gauge7#b distance#b1 or ,r#b - 7,r - g7#b ,d#b1 and ,d 7,r#b - 7,r - g7#b74 ,the angle of frog is also ,sin angle of frog 7,sin #ij log ,d7_/7log ,r74 ,the length of this switch rail depends upon the radius of curvature4 ,the distance between the two rails at ,s must be enough to admit the wheel flange1 that is1 at least two inches4 ,let ,a ,b1 fig4 #adf1 be the straight rail2 ,e ,d the curved one4 ,draw ,g ,h parallel with and two inches distant from the inner edge of ,a ,b4 ,no point of the curved rail must fall within ,g ,h2 whence ,e is the turning-point1 and ,e ,d the length1 found as follows4 ,let ,r equal the radius of curve to outside of outer rail2 d equal two inches plus width of rail1 or i e1 and ,d equal ,d ,e4 ,then ,d 7,r#b - 7,r - d7#b74 ,illustration3 ,fig4 #adf4 ,example4--,let the radius of outer rail be five hundred feet1 and the gauge five feet4 ,we have1 then1 the distance 7,a47 ,d 7#ejjb - #dieb7 #gb feet1 very nearly4 ,also1 ,sin ,e ,c ,d 7,sin #ij log ,d7_/7log ,r71 7,b47 or 7,sin #ij log #gb7_/7log #ejj7 #h #ag1 and the length of switch 7,c47 7#ejjb - #dii4feb7 #ah feet nearly4 ,five hundred feet is1 therefore1 about the longest radius for which such switches should be used4 ,,sidings ,,and ,,crossings4 ,crossings occur where two tracks cross1 and consist of four frogs1 with the corresponding guard rails1 as in fig4 #adg4 ,illustration3 ,fig4 #adg4 ,,elevation ,,of ,,the ,,exterior ,,rail4 #bic4 ,the motion of a train of cars around a curve is accompanied by a tangential force1 depending in amount upon the velocity of the train and the radius of curvature4 ,this force tends to throw the cars from the track2 and is counteracted by elevating the exterior rail4 ,the centrifugal force of any body in motion in a curved line is shown by the formula 7,,wv#b7_/7cb,r74 ,where ,w is the weight in lbs4 ,v the velocity in feet per second4 ,r the radius of curvature1 and #cb the accelerating force of gravity4 ,the force tending to throw the car from the rail is not centrifugal but tangential1 but it matters not whether the body is kept in position by tension upon the inside or by compression on the outside2 the amount of the force is the same4 ,illustration3 ,fig4 #adh4 ,the horizontal projection of the centre of gravity of the car1 when at rest1 is at c1 fig4 #adh1 and when in motion the direction of the weight should be a b2 and the inclination1 c a b1 must be such that a b will be perpendicular to c a2 to effect which1 c b should be to a b as the weight to the tangential force2 or ,e being the elevation of the rail1 g the gauge1 ,w the weight1 and c the tangential force2 we have ,e 3 g 33 c 3 ,w1 or ,e 7cg7_/,w1 and c being 7,,wv#b7_/7cb,r72 finally ,e 77,,wv#b7_/7cb,r77g_/,w or 7,v#b;g7_/7#cb,r7 ,e4 ,where ,w weight of a car4 ,v speed of train in feet per second4 g gauge of road4 ,r radius of curve4 ,e elevation of outer rail in feet and decimals4 g and ,r are the only fixed quantities in the formula2 and the average weight and speed of a car must be assumed4 ,examination of the formula shows how important it is that all trains should run at such a velocity as to demand the same elevation of rail4 ,the absolute elevation must be arranged to meet the requirement of the fastest trains2 and other trains must conform1 even at a disadvantage4 ,,note4--,the subject of the mechanics of traversing railroad curves1 is yet quite in the dark4 ,the action of the train1 as caused by its own momentum1 is tangential2 while the action of the engine tends to pull the cars against the inner rail1 being opposed to the first motion4 ,this might require a reduction of the elevation given by the formula when the engine is exerting a strong tractive power1 but when running without steam the full elevation is needed1 7see chapter ,,iii47 ,illustration3 ,fig4 #adi4 ,in laying and maintaining the rails to the proper elevation1 a clinometer attached to a rail gauge1 as in fig4 #adi1 answers a good end3 the small arc being graduated according to the different elevations required by curves of different radii4 ,thus the index of the level being placed at #b1 when the rails are fitted to ,a and ,b1 the elevation is correct for a #b curve2 or for a curve of #b1hfe feet radius4 ,the difference in gauge of one foot makes a difference in the elevation of but #j4jji feet1 or about of an inch4 ,the following table is calculated for the average of the different gauges in use1 thus1-- #d4g #e4j #e4e #f4j ------------ #d7ba4b ------------ ,average gauge1 #e4c feet4 ,,table ,,of ,,elevation ,,of ,,outer ,,rail4 ,radius of curve ,,elevation ,,of ,,outer ,,rail ,,in ,,feet ,,and ,,decimals1 ,,the in feet1 being ,,velocity ,,in ,,miles ,,per ,,hour ,,being #aj4 #ae4 #bj4 #be4 #cj4 #dj4 #bej 4#acj #ejj 4#jgj #a1jjj 4#jcg 4#jgi #b1jjj 4#jah 4#jdj 4#jgd 4#aaa #c1jjj 4#jac 4#jbf 4#jdh 4#jgd 4#ajf #d1jjj 4#jji 4#jbj 4#jcg 4#jeh 4#jgi 4#aed #e1jjj 4#jjg 4#jaf 4#jca 4#jde 4#jfe 4#aai #f1jjj 4#jjf 4#jac 4#jbd 4#jcg 4#jec 4#jie #g1jjj 4#jje 4#jaa 4#jba 4#jcc 4#jdf 4#jhf #h1jjj 4#jjd 4#jaj 4#jah 4#jbi 4#jci 4#jgg #aj1jjj 4#jjc 4#jjh 4#jaj 4#jbb 4#jcb 4#jei ,,chapter ,,xiv4 ,,equipment4 ,,part ,i4 ,,locomotives4 ,as the locomotive engine is the power by which railroads are worked1 and as its proportions and dimensions are so intimately connected with the physical character of the road1 it is thought proper to take space enough at this point to examine the general principles of its construction1 and of its adaptation to the work required of it upon railroads4 ,under the general principles1 we recognize the production and consumption of steam1 the disposition of weight upon the several pairs of wheels which shall secure the necessary adhesion1 the application of the power generated in the boiler to the moving of the wheels1 and that general arrangement of parts which shall render the use of power economical4 ,,birth ,,and ,,growth ,,of ,,the ,,locomotive4 #bid4 ,the first idea of the application of steam to locomotion1 is due to the unfortunate ,solomon de ,caus1 of ,normandy 7,france71 who was confined in a madhouse for insisting that steam could be made to move wheeled carriages4 #bie4 ,in the year #aghd1 ,william ,murdoch1 the friend and assistant of ,james ,watt1 built a non-condensing steam locomotive engine1 on a scale of about one inch per foot1 having ,cylinders1 #b inches1 ,wheels1 #i inches1 and ,weight1 #aj lbs4 ,this little engine1 however1 accomplished the speed of ten miles per hour4 #bif4 ,in #ahjb1 ,richard ,trevethick patented the application of the non-condensing steam-engine to the propelling of carriages on railroads2 his engine was fitted with one horizontal cylinder1 which applied its power to the wheels by means of spur gear4 #big4 ,in #ahbe1 the truck was first applied1 to relieve the driving wheels of a part of the weight1 and to enable the engine to pass freely around curves4 #bih4 ,in #ahbg1 ,timothy ,hackworth applied the blast pipe1 for the purpose of draft4 ,he applied1 also1 spring balances to the safety-valves1 and used the waste steam to heat the feed water4 ,this engine drew one hundred tons1 at five miles per hour1 and forty-five tons on a fifty feet grade4 #bii4 ,in #ahbh1 ,m4 ,seguin 7,france7 introduced the multitubular boiler4 #cjj4 ,in #ahbi1 the directors of the ,liverpool and ,manchester ,railroad offered a premium for the best locomotive1 which should draw three times its own weight1 at ten miles miles per hour4 ,the 8,rocket10 by ,robert ,stephenson1 of ,newcastle on ,tyne1 was the successful competitor1 and drew the load required1 seventy miles1 at an average speed of #ac4h miles per hour2 its maximum velocity was twenty-nine miles per hour2 it evaporated #e4d lbs4 of water per pound of coke1 and #ah4bd cubic feet per hour of water4 #cja4 ,from #ahcj to #ahdj1 the changes that were made were rather those of dimension1 proportion1 and arrangement1 than of essential elements of steam producing4 #cjb4 ,in #ahdj1 several truck frame engines were sent to ,england from the ,norris ,works of ,philadelphia4 ,these locomotives would draw a load of one hundred and twenty tons over a sixteen feet grade1 at the rate of twenty miles per hour4 #cjc4 ,in #ahde1 the ,great ,western ,railroad1 of ,england1 was supplied with an engine of twenty-two tons weight1 having cylinders #ae #ah1 wheels #g feet1 heating surface #hbi square feet4 ,this locomotive carried seventy-six and one half tons at a velocity of fifty-nine miles per hour4 ,the consumption of coke was #ce4c lbs4 per mile1 and of water1 #bja4e cubic feet per hour4 ,,the ,,english ,,locomotive ,,of #ahej4 #cjd4 ,the 8ne plus ultra0 for the seven feet gauge 7,great ,western ,railway7 by ,gooch1 has inside cylinders #ah #bd inches1 one pair of eight feet driving wheels1 grate area twenty-one square feet4 ,fire-box surface1 one hundred and fifty-three feet4 ,three hundred and five two inch tubes1 giving #a1gii feet of surface4 ,total heating surface1 #a1ieb square feet4 ,weight of engine1 empty1 thirty-one tons2 of tender1 eight and one half tons2 whole weight with wood and water1 fifty tons4 ,evaporating power1 three hundred cubic feet of water per hour4 ,this engine can draw two hundred and thirty-six tons1 at forty miles per hour4 ,the maximum for the ,london and ,north-western ,railroad1 four feet1 eight and one half inches gauge 7,crampton's patent71 has cylinders #ah #bd inches2 wheels1 eight feet2 two hundred two and three sixteenths inch 7outside diameter7 tubes2 grate1 twenty-one and one half square feet2 fire surface1 one hundred and fifty-four feet2 tube surface1 #b1acf feet2 whole heating surface1 #b1bij square feet2 weight1 loaded1 thirty-five tons2 twelve tons upon driving wheels2 tender1 twenty-one tons1 loaded2 whole weight1 fifty-six tons4 ,,the ,,american ,,locomotive ,,of #ahee4 #cje4 ,the engine 8,charles ,ellet1 ,jr410 drew on the #ith of ,august1 #ahed1 forty tons1 over a grade of two hundred and seventy-five feet per mile1 and over grades of two hundred and thirty-eight feet1 upon curves of three hundred feet radius4 ,this engine has wheels four and one half feet in diameter coupled seven feet apart2 cylinders #ad #bf inches2 and weighs1 including wood and water1 #ec1jeh lbs4 ,this is a tank locomotive1 the tender is dispensed with1 and in its room a tank containing one hundred cubic feet of water1 and one cord of wood is used4 ,this engine was built by ,richard ,norris and ,son4 ,an engine built by the ,cuyahoga ,steam ,furnace ,co4 of ,cleveland1 ,ohio1 performed the following feat4 ,an ordinary passenger train was carried one hundred and one miles1 over a total ascent of #a1bee feet of grades1 making twenty stops1 at an average speed of twenty-five miles per hour1 with a consumption of only ninety cubic feet of wood4 ,the same engine drew an average load of three and one third cars four hundred and thirty miles1 making seventy-five stops1 surmounting a total ascent of #e1dci feet1 averaging twenty-five miles per hour1 with one tender full of wood only4 ,in the months of ,july and ,august1 #ahef1 two engines upon the ,pacific ,railroad 7,missouri71 one by ,r4 ,k4 and ,g41 and one by ,palm ,robertson1 ran each one hundred and twenty-five miles1 with three passenger and one baggage cars1 using only one cord of wood4 ,,note4--,for an interesting example of what can be done by the ,american locomotive1 and an illustration of engineering peculiarly ,american1 the reader is referred to a description of the 8,mountain top track0 at the ,rock-fish ,gap crossing of the ,blue ,ridge 7,va471 by the ,virginia ,central ,railroad1 given by the engineer under whose direction the work was proposed and executed 7,charles ,ellet1 ,esq471 from which is extracted the following3-- 8,the eastern slope is #ab1ejj feet long1 and rises #faj feet2 the average grade being #begd_/aj feet1 and the maximum #biefh_/ajj feet per mile4 ,the least radius of curvature #bcd feet2 upon which curve the grade is #bcgf_/aj feet per mile4 ,the western slope is #aj1fej feet long1 and falls #dej feet2 the average grade being #bbc1 and the range #bgihd_/ajj feet per mile4 8,the engines1 which have taken loads ranging from twenty-five to fifty tons up one slope at seven and one half miles per hour1 and down the opposite one at six miles per hour1 making four trips of eight miles per day for three years1 were designed and built by ,m4 ,w4 ,baldwin ,co41 ,philadelphia1 and have three pair of forty-two inch wheels all coupled1 the flange base being #i #d1 cylinders #af #bj inches1 weigh1 with wood and water1 #ee1jjj lbs41 or twenty-seven and one half tons4 ,they run without a tender1 the engine carrying its own feed2 thus gaining the double advantage of increasing the adhesion of the engine1 and avoiding the resistance of a tender40 ,,general ,,description4 #cjf4 ,the locomotive is a non-condensing1 high pressure engine1 working at a greater or less degree of expansion1 according to the labor to be performed1 and placed upon wheels which are so connected with the piston1 that any motion of the latter is communicated to the former1 by which the whole is moved4 ,the power exerted in the cylinder and referred to the circumference of the driving wheel1 is called traction2 its amount depends upon the cylinder diameter and steam pressure1 upon the diameter of wheel and stroke1 this latter being the distance between the wheel centre and point of application of power4 ,the means by which the 8traction0 is rendered available for moving the engine and its load1 is the resistance which the wheel offers to slipping on the rail1 or its bite1 and is called adhesion2 it is directly as the weight applied to the wheels1 but depends also upon the state of the rails4 ,it varies from nothing1 when there is ice on the rail1 to one fifth of the weight upon the driving wheels when the rail is clean and dry1 and in some cases has reached as high as nearly one third4 ,it should be enough to resist the maximum force of traction1 that is1 the wheel should not slip when the engine is doing its greatest work4 ,steam producing1 ,traction1 and ,adhesion1 are the three elements which determine the ability of an engine to perform work4 ,the proportions and dimensions of the machine depend upon the duty required of it2 sufficient adhesion for a required effect should be obtained rather by a proper distribution1 than by increase of weight4 ,fig4 #aej shows the relative position of parts in the locomotive engine as at present constructed in ,america4 #a #b1 ,grate upon which the fuel is placed4 #a #b #c #d1 ,interior fire-box4 #e #f1 ,exterior fire-box4 #g #g #h #h1 ,shell of the boiler4 #i #i1 ,boiler flues4 #aj #aa #ab #ac1 ,exhaust chamber1 or smoke box4 #ad1 ,steam dome1 entrance to steam pipe4 #ae1 ,steam pipe4 #af1 ,piston4 #ah1 ,piston rod4 #ai1 ,connecting rod4 #bj1 ,crank4 #ba1 ,driving wheel4 #bb1 ,blast pipe4 #bc1 ,chimney4 #bg #bh1 ,leading wheels1 supporting the front end of the engine1 turning on a swivel1 #bi4 #cj1 8,blow off0 safety-valve4 ,illustration3 ,fig4 #aej4 #cjg4 ,the operation of generating and applying steam for the production of motion is as follows3-- ,the boiler and the space between the two fire-boxes being filled with water1 7high enough at least to cover the flues and the top of the inner box17 fire is applied to the fuel placed upon the grate2 the heat which fills the fire-box and tubes1 is communicated to the water and converts the same to steam2 which entering the mouth of the pipe1 #ae1 flows to the cylinder1 where it forces the piston to the end of the stroke4 ,this motion is transferred through the connecting rods and cranks to the wheels1 which revolving1 move the engine upon the rails4 ,at the same time the eccentrics1 placed upon the driving axle1 give a motion to the valve gear1 and thence to the valves1 by which the admission of steam is stopped at the first end of the cylinder1 and commenced at the other4 ,the volume of steam which entered during the first half stroke is forced out of the cylinder by the returning piston1 up the blast pipe1 and out at the chimney1 where a vacuum is produced1 which can be supplied with air only from the chamber #aj #aa #ab #ac2 after a few strokes the air is exhausted from the chamber1 which can be refilled only by the external air drawn through the fuel1 furnace1 and tubes4 ,the more complete this vacuum1 the stronger the current of air drawn through the fire1 which 7current7 is the draft4 ,the admission of fresh air is regulated by a damper placed at #b4 ,the fuel is placed upon the grate by means of a door in the rear of the fire-box4 ,the necessary height of water is maintained in the boiler by pumps worked by the engine1 in such a manner as to secure at all times the proper supply4 ,the proportions and dimensions of the boiler1 the engine1 and the carriage1 with the rules for obtaining the same will be considered shortly4 ,,duties ,,expected ,,of ,,locomotive ,,engines4 #cjh4 ,the work required of any engine depends upon the nature and amount of traffic1 and upon the physical character of the road4 ,the nature of the traffic1 whether bulky or compact1 and whether requiring quick or slow transport1 determines somewhat the number and size of the trains1 and consequently the number and power of the engines4 ,a road with steep grades and sharp curves1 with the same amount of traffic1 will need stronger engines than a road with easy grades and large curves4 ,the amount of motive power and cost of working it1 depends in a great degree upon the disposition of grades as regards the direction of the traffic movement4 ,the most economically worked road will be either a level one1 or one where the bulk of the traffic is moved down hill4 ,the mineral1 commercial1 or agricultural nature of the country1 determines the direction of the traffic1 and the physical nature1 the arrangement of the grades4 ,the different kinds of labor required of locomotives1 necessitate the employment of engines of different proportions2 and the different classes of railways1 require engines possessing different amounts of power4 #cji4 ,the classification of locomotives should be determined according to the following relations4 ,department depends upon commercial duty4 ,division depends upon character of road4 ,order depends upon weight of trains4 ,class depends upon speed of trains4 ,,note4--,the general classification is given at the end of this chapter4 ,high rates of speed are generally combined with light loads1 and heavy trains are required to move at the lower velocities4 ,great speeds require the rapid production and consumption of a large bulk of steam of but little density2 large wheels and short stroke1 that the ratio of velocities of piston and wheel may be as great as possible4 ,heavy trains consume less steam by bulk1 per mile1 but of a much greater density1 and combine a long stroke with a small wheel1 by which great leverage is obtained4 ,in general1 engines for winter use should be heavier than those for summer1 upon the same ground1 as natural causes are more liable to resist adhesion in the winter4 ,the locomotive engine may be so proportioned as to run at any speed from ten to sixty miles per hour1 over grades from ten to two hundred feet per mile1 and to carry loads from two hundred to two thousand tons4 ,the rules by which the necessary dimensions to perform any required duty are fixed1 depend upon the very simplest mechanical laws4 ,,note4--,the formul expressing the most proper relations to exist between the several steam-producing and steam-consuming parts are more reliable than the assertions of any machinist in ,america1 and though taken from books1 are the result of the experience of the most able and practical men for twenty years4 ,operatives are too apt to despise book knowledge1 forgetting that the very knowledge so despised is the result of more practice than a lifetime can afford them4 ,railroad managers are too apt to receive as indisputable1 the opinions of men who are practical1 simply because they understand nothing of principle4 ,since the work of ,d4 ,k4 ,clark 7,england7 has appeared1 any dimension from the beginning to the end of a locomotive may be fixed1 to the eighth of an inch1 with absolute correctness1 and there is no excuse for departing from the proper proportions4 ,it does not follow that because a locomotive does actually start off and draw the train1 that it is properly made4 ,a race-horse can draw a plough1 and a yoke of oxen a 8trotting buggy10 but this is by no means the correct adaptation of power4 #caj4 ,the elements which govern the requirements of power are ,the maximum grades4 ,the weight of the train4 ,the required speed4 ,and the elements which govern our ability to produce the power needed1 ,the grate area4 ,the heating surface4 ,the cylinder diameter4 ,the steam pressure4 ,the stroke4 ,the diameter of wheels4 ,the weight upon driving wheels4 ,,mechanical ,,and ,,physical ,,principles ,,governing ,,the ,,construction ,,of ,,the ,,locomotive ,,engine4 ,,resistance ,,to ,,the ,,motion ,,of ,,railroad ,,trains4 #caa4 ,the exact resistance to the motion of a railroad train cannot be determined1 as some of the elements are so variable2 for example1 the state of the weather4 ,an approximate estimate1 near enough for practice1 is easily obtained4 ,to arrive at correct data the observations must be made upon trains working under the same conditions that they are subject to in practice4 ,the whole resistance is made up of several partial resistances1 some of which are constant at all speeds1 and some of which increase with the velocity4 ,the engine and tender resistance is composed of the friction of pistons1 cross heads1 slide valves1 cranks1 eccentrics1 pumps1 the back pressure of the blast1 and various erratic movements1 rolling1 twisting1 and pitching together with both wheel and axle friction1 which is common to the engine and tender4 ,the atmospheric resistance is not due to the direct action of the air upon the front and sides of the train entirely1 but chiefly to the exhausting action in the rear4 ,the train has1 as it were1 to pull along a large column of air like the water in the wake of a ship2 form or amount of frontage has little or no effect4 ,the resistance depends upon the bulk of the train and its velocity4 ,a train with the same frontage offers more resistance as its bulk increases4 ,oscillatory resistance is caused by irregularities in the surface of the rails1 and increases with the velocity1 and also with increase of height of the centre of gravity of the car or engine4 ,frictional resistance may be divided into wheel and axle friction4 ,that of the axle is composed of two parts1 the direct vertical friction on the journal1 and the side friction on the collar1 consequent upon lateral motion4 ,the vertical friction is independent of the surface pressed or of velocity1 but is directly proportional to the pressure1 and the same remark applies to that of the collars4 ,as the diameter of wheel increases1 the oscillation is increased1 the centre of gravity being raised4 ,the direct cause of the vertical friction is the weight of the car or engine1 and of the lateral irregularities in the surface of the rails1 which cause the car to sway from side to side4 ,wheel friction which acts between the periphery of the wheel and the surface of the rail increases with the load1 and decreases as the wheel diameter augments4 ,for the total resistance to the motion of a railroad train1 ,d4 ,k4 ,clark gives the following formula3-- 7,v#b7_/aga #h ,r1 ,where ,r is the resistance in lbs4 per ton1 and ,v the velocity in miles per hour4 ,from this expression we form the following table3-- ,velocity in miles per hour4 ,resistance in lbs4 per ton4 #aj #h4ehe #ab #h4hdb #ae #i4cae #bj #aj4cci #be #aa4fee #cj #ac4bfc #dj #ag4cef #ej #bb4fbj #fj #bi4jeb #ajj #ff4dhj ,from a great number of experiments made by ,mr4 ,clark1 the relative resistance to the motion of inside and outside connected engines is as follows3-- ,inside connections #ag ,outside connections #ad ,the effect of curves1 bad state of the road1 and adverse winds1 amounts 7according to the same author7 to the following percentages3-- ,bad state of the road #dj ,curves #bj ,strong head and side winds #bj -- ,in all #hj ,the resistance due to grades depends entirely upon the rate of incline1 and is quite independent of all other considerations4 ,the relative effect of grades decreases with the absolute increase of resistance on a level4 ,thus common roads admit of steeper grades than do railroads1 because the level resistance is much more upon the former than on the latter4 ,the exact determination of the resistance due to any grade depends upon the very simple mechanical principle1 regulating motion upon the inclined plane4 ,for each foot rise of grade per mile1 the resistance per ton is #bbdj #a_/ebhj4 ,thus the resistance to one ton upon a forty feet grade is #bbdj #dj_/ebhj or #ag lbs4 ,and if we are moving at thirty miles per hour the sum of all other resistances is1 by the formula1 or the table at the end of ,chapter ,,xiv41 part ,i41 #ac4c lbs4 per ton2 whence the whole resistance to the motion of one ton1 at thirty miles per hour1 upon a forty feet grade1 is #ag #ac4c or #cj4c lbs4 and one hundred tons would be one hundred times as much4 ,table #a1 at the end of ,chapter ,,xiv41 part ,i41 gives the whole resistance to the motion of trains of from fifty to one thousand tons1 moving at speeds varying from ten to one hundred miles per hour1 and table #b gives the resistance upon grades from ten to one hundred feet per mile4 ,,traction ,,and ,,adhesion4 #cab4 ,the whole steam pressure upon both pistons1 referred by means of the crank1 connecting1 and piston rods1 and wheel1 to the rail1 is called 8traction40 ,it is the drawing power of the engine4 ,its amount depends upon the diameter of cylinder1 steam pressure1 stroke1 and diameter of wheel4 ,by increasing the steam pressure1 we increase the power4 ,by increasing the cylinder diameter1 we increase the power4 ,by increasing the stroke1 we increase the power4 ,by decreasing the wheel diameter1 we increase the power4 ,and by adjusting the dimensions of the above parts1 we may give any desired amount of power to the engine4 ,the formula expressing the tractive power of an engine1 of any dimensions1 is 77#b;,a7 ,p #b,s7_/,c4 ,where ,a the area of one piston4 ,p the steam pressure in cylinder per square inch1 ,s the stroke in inches4 ,c the circumference of the wheel in inches4 ,the formula is expressed verbally as follows3 ,double the stroke and multiply it by the total steam pressure on both pistons2 divide the product by the circumference of the driving-wheel in inches4 ,,adhesion4 #cac4 ,as observed on page #cjg1 the adhesion or the bite of the wheels upon the rail is1 as an average1 from one fifth to one sixth of the weight2 one fifth when the rail is in a good state1 and less when wet or greasy2 we cannot depend upon more than one sixth in practice4 ,therefore1 if the tractive power of an engine is #c1jjj lbs4 we must1 to make it available1 place #c1jjj #f or #ah1jjj lbs4 upon those wheels which are connected with the machinery1 7driving wheels74 ,,fuel4 #cad4 ,the fuels employed in the locomotive engine for the evaporation of water are wood1 coal1 and coke4 ,in ,england the latter is used exclusively4 ,in ,america the first has1 on account of its cheapness1 been quite generally adopted2 but of late railroad companies have been turning their attention to coal and coke4 ,the immense beds of coal distributed throughout the ,united ,states will furnish fuel to railroad companies almost without limit4 ,its position as well as its amount will render its adoption practicable in nearly all of the ,states4 ,ohio alone contains more coal than all of ,great ,britain4 ,the following table is from the iron manufacture of ,frederick ,overman4 ,name of ,state4 ,area of ,coal-fields4 ,georgia #aej square miles4 ,maryland #eej square miles4 ,alabama #c1djj square miles4 ,tennessee #d1cjj square miles4 ,michigan #e1jjj square miles4 ,missouri #f1jjj square miles4 ,indiana #g1gjj square miles4 ,ohio #aa1ijj square miles4 ,kentucky #ac1ejj square miles4 ,pennsylvania #ae1dcg square miles4 ,virginia #ba1aie square miles4 ,illinois #dd1jjj square miles4 -------------- ,in all #acc1acb square miles4 #cae4 ,the following table 7also from the works of ,overman7 gives the nature and evaporative power of the different ,american coals4 ,state ,steam of ,quantity,percentage ,name of ,coal4 where ,percentage #bab of heat of coke by found4of carbon4evaporated by weight4 per lb4 volume4 ,anthracite4 ,beaver ,meadow1 ,pa4 #hh4i #aj4d #id ,forest ,improvement1 ,pa4 #ij4g #aj4h #id ,lehigh1 ,pa4 #hi4a #i4f #id ,lackawanna1 ,pa4 #hg4g #aj4g #id ,coke4 ,midlothian1 ,va4 #aj4c #ib 4#ff ,cumberland1 ,md4 #aj4c #ib 4#ge ,bituminous4 ,maryland1 ,md4 #gc4e #aa4b #he ,cumberland1 ,md4 #gd4c #aa4j #he ,blossburg1 ,pa4 #gc4d #aj4i #he 4#hc ,karthans1 ,pa4 #gc4h #i4h #he 4#hh ,cambria ,county1 ,pa4 #fi4d #aj4b #he ,clover ,hill1 ,va4 #ef4h #h4e #he 4#fh ,tippecanoe1 ,va4 #fd4f #h4e #he ,pittsburgh1 ,pa4 #ee4j #h4i #he 4#fh ,missouri1 ,mo4 4#eg #caf4 ,the employment of the several varieties of wood depends more upon the commercial than the chemical character4 ,the following table shows the specific gravity1 the nature and the evaporative value of the different species4 ,species4 ,specific,specific,specific,degrees of ,species4 gravity gravity gravity heat which green4 air kiln may be dried4 dried4 generated4 ,hickory1 #cjjj ,hickory4 ,white ,oak1 #a4jg #j4ga #j4ff #cjjj ,white ,oak4 ,black ,oak1 #cjjj ,black ,oak4 ,red ,oak1 #a4je #j4fh #j4ff #cjjj ,red ,oak4 ,beech1 #j4ih #j4ei #j4eh #cjjj ,beech4 ,birch1 #j4ij #j4fc #j4eg #cjjj ,birch4 ,maple1 #j4ij #j4fd #j4fa #cjjj ,maple4 ,yellow ,pine1 #bhjj ,yellow ,pine4 ,chestnut1 #cjjj ,chestnut4 ,pitch ,pine1 #bhjj ,pitch ,pine4 ,white ,pine1 #j4hg #j4dg #j4ch #bhjj ,white ,pine4 ,species4 ,specific,specific,specific,degrees of ,species4 gravity gravity gravity heat which green4 air kiln may be dried4 dried4 generated4 ,species4 ,percentage,quantity,weight,relative ,species4 of of heat of onevalue as ,charcoal4 as to cord fuel4 volume4 in lbs4 ,hickory1 #dd4fi #be #ddfi #a4jj ,hickory4 ,white ,oak1 #ba4fb #be #chba #j4ha ,white ,oak4 ,black ,oak1 #bc4hj #be #cbed #j4ga ,black ,oak4 ,red ,oak1 #bb4dc #be #cbed #j4fi ,red ,oak4 ,beech1 #cb4cf #be #cbcf #j4fe ,beech4 ,birch1 #be ,birch4 ,maple1 #bg4jj #be #bgjj #j4eg ,maple4 ,yellow ,pine1 #bd4fc #bc #bdfc #j4ed ,yellow ,pine4 ,chestnut1 #be4be #be #bccc #j4eb ,chestnut4 ,pitch ,pine1 #ai4jd #bc #aijd #j4dc ,pitch ,pine4 ,white ,pine1 #ah4fh #bc #ahfh #j4db ,white ,pine4 ,species4 ,percentage,quantity,weight,relative ,species4 of of heat of onevalue as ,charcoal4 as to cord fuel4 volume4 in lbs4 ,of the relative value of wood and coal1 we have the following results of experience4 ,in the engines of the ,baltimore and ,ohio ,railway #b4ee lbs4 of pine wood were found equal to one pound of ,cumberland coal4 ,on the ,reading ,railroad 7,pennsylvania71 three pounds of pine wood equal to one pound of ,anthracite coal4 ,mr4 ,haswell estimates the best varieties of wood fuel to contain twenty per cent4 of carbon4 ,walter ,r4 ,johnson found that one pound of wood1 upon an average1 evaporated two and one half pounds of water4 ,the average percentage of coke from ,american bituminous coal from the above table is seventy-three per cent41 and the average percentage of carbon1 sixty-seven and one half per cent4 #cag4 ,the following table shows the relative properties of good coke1 coal1 and wood4 ,name of fuel4 ,coke4,coal4,wood4 ,weight per cubic foot1 in lbs4 #fc #hj #cj ,degrees of heat generated4 #dcjj #djjj #bhjj ,percentage of carbon1 in the fuel4 #ie #hh #bj ,economic bulk1 or cubic feet required to stow one #hj #dd #ajg ton4 ,economic1 or stowage weight per cubic foot4 #bh #ea #ba ,cubic feet of air to evaporate one lb4 of water4 #bb4d #cb #af ,equivalent economic bulk1 to evaporate the same #ac #aj #fj weight of water4 ,weight of water evaporated per lb4of fuel in #h #f #b ordinary practice4 ,relative value as fuel1 disregarding the actual #ajj #ga #bi cost4 ,the power of fuel depends upon the amount of carbon in it4 ,pure coke is solid carbon4 ,hence its superior value as a heat generator4 ,,of ,,the ,,process ,,of ,,coking4 #cah4 ,anthracite coal is used for locomotive fuel in its natural state4 ,it is employed chiefly upon those roads on the eastern slope of the ,alleghanies4 ,the bituminous coal lies in the ,mississippi valley1 and may be found anywhere between the summits of the ,alleghanies and the ,rocky ,mountains4 ,this1 in its natural state1 contains so much pitchy matter as to render it unfit for locomotive purposes4 ,upon being heated1 it melts1 runs into a mass1 and clogs the grate2 requiring frequent poking and a strong draft4 ,but when the bitumen is burnt off by slow and careful baking1 7as described below17 no fuel equals it4 ,just as carbonized wood is charcoal1 so carbonized coal is coke4 ,coke is bituminous coal deprived of its bitumen1 the raw coal being baked in ovens having vents so regulated as to admit air enough to char1 without consuming the coal4 ,the ovens being closed at the proper time1 the fire is gradually extinguished1 and the coke1 compacted into large masses1 requiring to be broken up before taken out4 ,coal may be coked by piling loosely in heaps1 covering with earth1 and firing through openings1 which1 after forty or fifty hours1 are closed4 ,in preparing coke1 however1 in the large quantities required for railroads1 and that it may be of the very best quality1 a good deal of care must be taken4 ,probably in no place more or better coke is made1 or the operation more skilfully carried on1 than at the ,camden-town station of the ,london and ,north-western ,railroad1 7,england74 ,the company have built eighteen ovens1 in two rows1 all discharging their volatile gases into a horizontal flue terminating in a chimney one hundred and fifteen feet high2 having an internal diameter of eleven feet1 and being three feet thick1 7making the external diameter seventeen feet74 ,the ovens are elliptical1 #aa #ab feet inside1 with walls three feet thick4 ,the height is ten feet1 the first three feet from the ground being solid1 and furnished with a fire brick floor1 on which the coal is placed4 ,each oven communicates with the flue by an opening in the top two and one half feet by twenty-one inches2 which opening is closed by an iron damper1 to regulate the draft4 ,the openings for the doors are three and one half feet square outside1 and two and three fourths inside1 being closed with iron doors four and one half by five feet1 lined with fire brick1 and balanced in opening by counterweights4 7,the object of the chimney and horizontal flue is to carry the smoke and unburned gases so far up that they shall not be a nuisance4 ,in ,america we might allow the smoke of each oven to escape through a low chimney of its own1 7ten or twelve feet high17 and save the cost of a large stack2 like the coking ovens in our foundries74 ,the operation of coking is carried on as follows3--,each alternate oven is charged between eight and ten ,a4 ,m4 every day1 with three and one half tons of good coals4 ,a whisp of straw is then thrown in1 which takes fire from radiation from the top1 and inflames the smoke then arising from the surface1 by the reaction of the hot sides and bottom upon the body of the fuel4 ,in this way the smoke is consumed at the very point of the process1 where it would otherwise be the most abundant4 ,the coking process is a complete combustion of the volatile principles of the coal4 ,the mass of coal being first kindled at the surface1 where it is supplied with an abundance of oxygen1 because the doors in front and vents in the rear are open1 no more smoke goes from the chimney than from that of a common kitchen fire4 ,the gas generated from the slightly heated coal cannot escape destruction in passing up to the bright flame of the oven4 ,any deficiency in oxygen for consuming the smoke is supplied by the air entering the grooves of the dampers4 ,as the coking process advances most slowly from the top to the bottom1 only one layer is consumed at a time2 while the surface is covered with red-hot cinders1 ready to consume any particles of carburetted or sulphuretted hydrogen gases which may escape from below4 ,the greatest mass cannot emit more gases than the smallest heap4 ,the coke being perfectly freed from all smoky and volatile matters1 by a calcination of forty hours1 is cooled down to a moderate ignition by sliding in the dampers and opening the doors1 which had been partly closed during the latter part of the operation4 ,the coal is now converted into a clean1 crystalline1 porous1 columnar mass1 of a steel-gray color1 and so hard as to cut glass4 ,this is broken up and taken out--coke4 ,it is sometimes extinguished by a watering-pot4 ,this is wrong1 it ought not to be wet1 and even more1 ought to be immediately shut up in fire-proof boxes and bins4 ,even left to itself in the air1 it absorbs moisture rapidly1 which must be burned off in the boiler2 it should by all means be kept in a dry place4 ,mr4 ,woods 7,england7 observes1 that coke may absorb as much as eight per cent4 of water in going from the oven to the storehouse4 ,the amount of absorption depends upon the nature of the coke4 ,d4 ,k4 ,clark records the following1 the coke being immersed in water4 ,no4 #a4 ,close-grained and good1 absorbed #ad4e per cent4 of water4 ,no4 #b4 ,porous and ordinary1 absorbed #ba per cent4 ,no4 #c4 ,very close-grained and good1 #i per cent4 ,the time of coking may be stated generally as fifty hours1 though it is somewhat improved by being allowed forty hours more2 this gives time for a better consolidation1 and gives a firmer1 brighter1 and more crystalline mass4 ,mr4 ,gooch1 of the ,great ,western 7,england7 ,railroad1 experimented upon the time of coking with the following results4 ,in oven4 ,yield per ton of ,water evaporated ,result4 coal4 per lb4 of coke4 #dh hours #ab4ga cwt4 #g4a lbs4 #ijb4 #gb hours #ab4jj cwt4 #g4g lbs4 #ibd4 ,thus1 though the yield per ton is decreased by a greater time1 the value of the coke per pound is augmented1 and the increase overbalances the decrease4 ,firstrate coal gives from seventy-five to eighty per cent4 by weight1 of compact glistening coke1 weighing about #ad cwt4 per chaldron1 7thirty-six bushels74 ,the bulk is increased from ten to fifty per cent4 ,in breaking out the coke from the ovens1 a great deal is unavoidably reduced too fine for use in the locomotive furnace under a strong draft2 such may1 however1 be used in firing up1 in standing still1 and at the stations4 ,in taking the coke from the ovens it should be separated into the three following classes4 ,large coke4 ,cubes of #i inches to the side4 ,medium coke4 ,cubes of #f inches to the side4 ,small coke4 ,cubes of #c inches to the side4 ,pittsburgh coal carefully coked for forty-eight hours1 gives seventy-five per cent41 by weight1 and one hundred twenty-five per cent4 by bulk1 of firstrate1 firm1 bright1 clean coke4 ,the best test for coke is to place it in water4 ,water1 weighing sixty-two and one half pounds per cubic foot1 should not float good coke1 which ought to weigh sixty-three pounds per cubic foot1 therefore if the coke floats it is too light4 ,much of the bituminous coal in the ,mississippi valley does not coke1 but burns up4 ,a large part cokes moderately well1 but not so well as the ,pittsburgh coal4 ,in estimating for a comparison of fuels1 the particular coal of any location must be tested4 ,,of ,,the ,,comparative ,,value ,,of ,,wood1 ,,coal1 ,,and ,,coke4 ,this question divides itself into two parts1 ,the relative cost of the different fuels1 and ,the relative power to produce heat4 #cai4 ,it does not follow that because coke in ,england1 anthracite in ,pennsylvania1 or wood in ,new ,england1 is the most economical fuel1 that either of the above will be so in ,ohio1 ,indiana1 or ,illinois1 or because wood is the cheapest in some parts of a ,state1 that it is so throughout1 or even that one fuel should be applied to the whole length of a single road4 ,the heat used to evaporate water in the locomotive boiler is developed by combustion2 combustion is produced by chemically combining the oxygen of the air with the carbon of the fuel2 whence1 that material containing in a given cost the largest amount of carbon will produce heat the most economically4 ,from the table on page #cbj1 we see that1 by bulk1 thirteen of coke are equal to sixty of wood2 that one pound of coke evaporates eight and one half pounds of water2 that one pound of wood will evaporate two and one half pounds of water4 ,tables of specific gravity give as an average weight per cubic foot of hard wood1 thirty pounds4 ,a cord of wood1 by very careful measurement1 contains one hundred cubic feet solid1 or one hundred twenty-eight feet as piled1 taking the average size of wood2 whence a cord will weigh three thousand pounds4 ,and we have as the relative evaporative efficiency of a cord of wood and a ton of coke1 #bbdj #h #aijdj1 #cjjj #b #gejj4 ,now if the cost of a cord of wood is to the price of a ton of coke as #g1ejj to #ai1jdj1 it is immaterial which we use4 ,as an example of the use of the above proportion1 when the absolute cost of wood1 coal1 coke1 and labor are known1 take the following4 ,if wood1 cut and ready for burning1 costs #c4jj per cord1 how much may be given for a ton of coke8 ,as #g1ejj is to #ai1jdj1 so is #cjj to #gfb1 or #g4fb4 ,from the same proportion we form the following table4 ,cost per cord of wood ,price that may be paid ready for burning4 per ton for coke4 7,cents47 7,cents47 #bjj #ejh #bbe #ega #bej #fce #bge #fih #cjj #gfb #cbe #hbe #cej #hgg #cge #ieb #djj #ajaf #dbe #ajgi #dej #aadc #dge #abjf #ejj #abgj ,in the comparison above1 the maximum evaporative power of wood has been used1 #b lbs41 and the ordinary power of coke1 #h lbs4 of water per pound of fuel4 #cbj4 ,in making coke in large quantities1 the ovens should be at the mines1 as we thus save transporting the extra weight of coal over coke4 ,the cost of making coke1 exclusive of the cost of the coal1 is approximately as follows3-- #aj ovens capable of making annually #e1jjj tons of coke1 #e1jjj ,sheds1 and apparatus to correspond1 #c1jjj ------------ ,in all1 #h1jjj ,annual interest at #f per cent41 #dhj ,annual cost of attendance1 #b men1 #a1jjj ------------ ,the sum of which is1 #a1dhj ,and the cost per ton1 #j4bif_/aj or in round numbers1 thirty cents per ton2 and if coal is #a4ej per ton1 adding twenty-five per cent4 we have #a4hg as the cost of coal that will make one ton of coke1 to which add the cost of making per ton1 thirty cents1 and we have as the whole cost of one ton of coke #b4ag2 and from the rule on page #cbg we see that wood must not cost over #j4he per cord to be as economical as coke at #b4ag2 of course inferior qualities of coal will give less good coke and change the comparison4 ,,combustion4 #cba4 ,the combustible element in all fuels is carbon2 the heat necessary for steam producing1 is obtained by combining the carbon of the fuel with the oxygen of the air1 forming carbonic acid gas4 ,carbonic acid gas consists of ,oxygen #af ,parts by ,carbon #f weight4 ,atmospheric air consists of ,oxygen #h ,parts by ,nitrogen #bh weight4 ,whence1 for the combustion of one pound of carbon1 we require ,carbon #a4jj ,oxygen #b4ff ,but to obtain #b4ff of oxygen from the atmospheric air1 we also use nitrogen in the proportion of #bh nitrogen to #h oxygen2 whence1 for converting one pound of carbon to carbonic acid1 we require ,oxygen #b4ff ,nitrogen #i4ca ---------- ,or #aa4ig lbs4 of atmospheric air4 ,from careful observations on the gases passing through the chimneys of well-constructed boilers1 oxygen is found free1 varying in amount from one quarter to one half of the quantity necessary for combustion2 this is owing to the mechanical obstructions to the perfect conversion of the air arising from leakage through the fuel4 ,more than the above #aa4ig lbs4 of air should1 therefore1 be applied to the fire for each pound of carbon consumed4 ,twenty-five per cent4 is found by experience to be a sufficient surplus allowance to convert the carbon4 ,whence1 to #aa4ig add #c4jc ---------- and we have #ae4jj lbs4 of atmospheric air per lb4 of carbon4 ,air weighs 4#jge lbs4 per cubic foot1 whence #ae_/4jge or #bjj cubic feet of air are necessary for the proper combustion of one lb4 of pure carbon4 ,knowing the necessary amount of air for one lb4 of carbon1 and also the percentage of carbon in the different kinds of fuel1 it becomes a simple arithmetical operation to fix the bulk of air required for any species of coal1 coke1 or wood4 ,the result of such a calculation is shown in the seventh column of the table on page #cbj4 8,there are two causes why all the heat which fuel may furnish is not obtained4 ,first1 that the inflammable gases evolved by the heat are not all consumed from want of a sufficient supply of oxygen1 the air drawn through the fire being only sufficient to decompose more fuel than when decomposed it could burn1 or supply with oxygen4 ,the thick smoke that escapes from a chimney when fresh fuel is thrown on a hot fire1 is unconsumed gas2 decomposed from the fuel1 but without oxygen enough to burn--although there may have been a sufficient supply of heat4 ,from this cause it is1 perhaps1 that flame is seen coming from the top of a steamboat chimney which appears to be continuous from the furnace2 but which1 in fact1 is ignited by contact with the air1 having retained sufficient heat for that purpose4 8,all smoke-consuming furnaces are simply means of admitting fresh air to the unconsumed gases above the fire1 which1 in a common chimney1 will effect the object1 as so large a mass of smoke retains the necessary amount of heat4 ,this only prevents the nuisance of smoke4 ,to render the gases thus reheated useful in evaporating water1 this supply of oxygen must be added while the gases are yet in the flues40 ,this might seem difficult4 ,mr4 ,mc,connell 7,england7 divides the flues of his locomotives into two parts1 connecting the front ends of the first part and the back ends of the second part by a space of twelve or fifteen inches1 7called by him a #8combustion chamber1'7 into which he admits any required amount of fresh air4 7,see appendix ,e47 8,a second cause why the full value of the fuel produced is not obtained is1 that so much is abstracted from the gases in passing through long tubes1 that there is not enough left to continue combustion1 although the inflammable gas is still there4 ,that a tube or any substance in the way of the hot gases does absorb the heat enough to prevent the burning of the gas1 is proved by the action of ,davy's ,safety ,lamp2 this is a common light surrounded by a wire gauze1 which so absorbs the heat from the flame as to extinguish the latter at the wire2 by applying fire above the gauze1 the gas is again kindled1 showing plainly that want of heat above had quenched the flame40 ,see ,stckhardt's ,chemistry2 translation by ,c4 ,h4 ,peirce1 ,m4 ,d41 ,cambridge1 ,mass41 #aheb1 page #aje4 ,we require1 then1 in every boiler1 first1 to have a sufficient supply of oxygen to decompose the fuel2 next1 a quantity above the fire to consume the produced gases2 third1 such an arrangement of communicating surface that so much heat shall not be abstracted from the gases as to deaden their combustion1 until just as they are discharged1 at which period they ought to be consumed4 7,see appendix ,e47 ,,generation ,,of ,,steam4 #cbb4 ,the means of producing the power is of course of the first importance4 ,the heat generated in the fire-box is conducted through the tubes to the exhaust chamber2 during which passage it is imparted to the metal1 and from thence absorbed by the adjacent water1 which being thereby made lighter1 rises to the surface and gives place to a new supply4 ,the duty of the furnace is to generate1 and of the tubes to communicate1 heat4 ,the power of a plain surface to generate steam1 depends upon its position and on the ability of the material to transmit heat ,an experiment recorded in ,clark's ,railway ,machinery1 gave the following results3 ,a cubic metallic box submerged in water and heated from within1 generated steam from its upper surface more than twice as fast as from the sides when vertical1 while the bottom yielded none at all4 ,by slightly inclining the box the elevated side produced steam much faster1 while the depressed one parted so badly with it as to cause overheating of the metal4 ,acting upon this result1 most builders of engines of the present day give an inclination of from one inch to one quarter of an inch per foot to the sides of the inner fire-box4 ,that the heat should be applied in the most effectual manner to the water1 the latter should circulate freely around the hot metal1 carrying off the heat as soon as it reaches the surface4 ,as the heat is applied to the inside of the furnace and tubes1 it must1 therefore1 be the inside dimensions which determine the amount of heating surface4 ,,note4--,if we multiply the interior surface of a tube by the intensity of heat applied1 and divide the product by the exterior surface1 we shall have the intensity at the outside4 ,we also apply more heat to the outside of a tube1 which1 passing to the inner surface1 augments in intensity per unit of area4 ,the area of the inner fire-box is not all available for heating1 but requires to be reduced as follows3-- ,for the fire-door4 ,for the ferrule area4 ,for the top stays4 ,for the side stay bolts4 ,the area is1 therefore1 ,sides1 twice length by height1 less stay bolts4 ,back1 height by width1 less fire-door4 ,front1 height by width1 less ferrule area4 ,top1 length by width1 less top stays4 ,,tubes4 #cbc4 ,the tubes or flues1 varying in number from one hundred to three hundred1 in diameter from one and a half to three inches1 and in length from eight to sixteen feet1 furnish the real communicating surface4 ,the amount of heating surface thus obtained for any length1 number1 and diameter1 is given in table #aj1 ,chapter ,,xiv41 ,part ,i4 ,the surface of a single tube is found by the formula 7,ld#c4adaf7_/add4 ,where ,l the length1 and d the diameter1 both in inches4 ,the efficiency of circular tubes is a matter not yet fully understood4 ,they certainly give a large amount of surface in a small boiler4 ,pambour considered the value of tube area per unit of surface1 in terms of the furnace area1 as one third only2 that is1 three square feet of tube surface as equal to one foot of furnace area1 in power of generating steam4 ,d4 ,k4 ,clark makes no distinction between the two surfaces1 but observes 8there is reason to believe that in the upper semicircular part of each tube the efficiency principally resides4 ,the winding progressive motion1 observable in tubes of considerable diameter1 confirms this conclusion1 as it is with much probability due to the cooling of the upper portion of the gases of combustion1 which1 as they cool also1 become heavier and descend laterally1 to make room for the hotter smoke next the bottom of the flue2 the general result of which is the spiral motion of the current in its progress onwards40 ,certainly the upper half of the tube would part much easier with the steam than the under one1 even supposing the applied heat to be the same4 ,at page #cdj of 8,overman's ,mechanics10 is the following3 8,the application of heat to a concave surface is wrong in principle4 ,the heat in gases is conducted to other bodies1 and among themselves by convection only4 ,this quality of gases causes the convex form of a vessel to be the most profitable in absorbing the heat of ascending gases1 because the motion of the gas causes a constant change of particles on the convex body4 ,on a concave surface exposed to the influence of moving gases1 but little effect is produced2 because the particles of gas in the concavity are at rest4 ,a plane surface is for the same reason an imperfect form for absorbing heat2 it must be exposed at an angle of #de to obtain the best effect of the heating gases4 ,in all cases if we wish to obtain the best effect from the fuel1 we should expose a convex surface to the current of hot air4 ,the direction of the motion of the hot gases decides the position of the metal which is to absorb the heat2 if the current is horizontal the pipes must be vertical4 ,gases do not convey heat by radiation4 ,tubes and other vessels containing water must be so placed that the hot gases play around the outside4 8,if we lead a current of hot air around a cylinder we shall observe that a particle of air plays but a short time upon its surface1 when it gives way to another2 the particles play almost around the cylinder1 and a concentration or increase of density behind the pipe is the result4 ,the relative position of pipes in the range is not indifferent1 and the distance of one from the other must be related to their diameter40 ,the conducting power of the metal composing the fire-box and tubes1 is one condition which limits the rate of evaporation1 when the heat is abundant on the one side and circulation free on the other1 as the water certainly carries off the heat as fast as it arrives at the outer surface4 ,all the heat should be extracted if possible from the gases before they enter the smoke box4 ,we should so arrange the flues1 that without so much contracting the passage for the exit of the gases as to need too strong a blast1 yet to confine the gases until their full value is extracted4 ,several attempts have been made to apply the ideas of ,clark and ,overman1 but as yet they have been very indirect and have met with only moderate success4 7,see ,appendix1 ,e47 ,,evaporation1 ,,pressure1 ,,temperature1 ,,and ,,density4 #cbd4 ,the character of work to be done determines the nature of the steam to be used4 ,the quantity of work to be done shows the amount of steam to be produced4 ,the amount and character of the steam required1 fixes the dimensions and proportions of the boiler4 ,a cubic foot of water1 at a temperature of #fb1 weighs #fb4cba lbs4 ,a cubic foot of steam1 generated at #bab ,fahrenheit1 under the atmospheric pressure 7#ad4g lbs4 per square inch7 weighs 4#jcfff lbs4 ,whence one cubic foot of water boiled at #bab1 makes #a1gjj cubic feet of steam4 ,the total heat of saturated steam 7steam produced in contact with the water71 consists of two parts at all temperatures2 the latent and the sensible4 ,the sensible heat is that shown by the thermometer1 and varies with the pressure4 ,the latent heat absorbed during the generation of steam1 amounts to three fourths of the whole4 ,as the temperature at which the steam is produced increases1 the bulk produced from a given unit of water decreases1 but the pressure and the total heat increase4 7,see ,c4 ,r4 ,m4 p4 #ei1 #fa1 ,regnault's experiments47 ,table #h1 ,chapter ,,xiv41 ,part ,i41 gives the properties of saturated steam1 produced under pressures varying from fifty to one hundred and fifty pounds per square inch4 ,the steam produced over water is called saturated1 and an application of heat to an isolated volume of this steam1 raises both the temperature and pressure1 the volume and density remaining the same4 ,the saturation is then no more1 and the steam is surcharged4 ,if the heat be withdrawn1 pressure and density fall1 and a precipitation of water takes place4 ,the priming of steam in a cylinder is an illustration of this4 ,d4 ,k4 ,clark1 in ,railway ,machinery1 urges the necessity of thoroughly drying the steam before applying it to the pistons in this manner1 he says1 ten per cent4 may be gained at low velocities1 and in some cases forty per cent4 at high speeds4 ,,motion ,,of ,,steam ,,in ,,pipes4 #cbe4 ,steam may flow from any vessel into a vacuum1 into the open air1 or into steam of a less density4 ,the velocity of efflux of steam is the same as that of a stream of water flowing under a pressure equal to that of the steam4 ,steam flowing into the atmosphere of course has #ad4g lbs4 per inch resistance to meet1 which is equivalent to a reduction of #ad4g lbs4 of its pressure4 ,the following numbers show the velocity of efflux of steam into the open air under different pressures4 ,pressure4 ,velocity1 in feet per second4 #ej #agia #fj #ahch #gj #ahgg #hj #aiai #ij #aicf #ajj #aieg #aaj #aigb #abj #aiij #acj #bjjd ,,loss ,,of ,,pressure ,,caused ,,by ,,the ,,motion ,,of ,,steam4 #cbf4 ,the loss of power suffered by the steam during its motion from the boiler to the cylinder is caused by condensation in passing through cold pipes1 and by friction and sharp bends4 ,the total fall that may be caused by a combination of circumstances is from ten to fifteen per cent4 at low velocities1 and from fifty to sixty per cent4 at high speeds4 ,the fall of pressure decreases as the square of the velocity of motion1 that is1 the fall at a velocity of #a1fjj feet per second is four times as great as the fall at a velocity of eight hundred feet4 ,by well protecting the steam pipes and cylinders1 and by drying1 it may be worked at nearly its initial pressure4 ,,application ,,of ,,steam4 #cbg4 ,the steam being generated in the boiler1 and conveyed to the cylinders1 is admitted alternately to the opposite sides of the piston1 by which its reciprocations are produced4 ,the first valve applied to regulating the admission of steam to the cylinder was so arranged that the steam was admitted during the whole stroke2 at the end of which1 ingress stopped and egress commenced at the first end1 and ingress commenced at the second end simultaneously2 this caused an unnecessary resistance to the return movement1 by preventing the quick escape of the first cylinder-full1 which had to be pushed out1 instead of flowing out4 ,the continuance of the full pressure upon the piston also1 until the end of the stroke1 caused a dangerous momentum to be given to the reciprocating machinery4 ,these evils are obviated by causing the exhaust passage to open1 and the entering port to close a little before the end of the stroke4 ,this is effected by moving the valve bodily forward4 ,now it is well ascertained1 that with very free steam entrances1 if we allow the cylinder to be only partially filled1 and then cause the steam to expand itself1 more work is accomplished with a given bulk than when the cylinder is completely filled4 ,that the steam may have time thus to expand itself1 the return of the piston must not take place until after the suppression 7the stopping of admission74 #cbh4 ,there are four positions of the valve during each half stroke1 and three distinct actions of steam in the same period1 which are as follows3-- ,position of valve4 ,action of steam4 ,admission 7,a74 ,entrance4 ,suppression4 ,expansion4 ,release4 ,compression4 ,admission 7,b74 ,the longer the time between suppression and release1 of course the more complete will be the expansion4 ,the entire force of the steam should not 7even if possible7 be extracted1 as a certain force is necessary to produce a blast4 ,the time of expansion is regulated by the proportions of the valve cover2 which may be so adjusted as to fix suppression or release at any desired part of the stroke4 ,by the above means any rate of expansion may be established1 but when once fixed will remain the same1 the valve being invariably connected with the eccentric1 and thus partaking of its motion4 #cbi4 ,the great step which has been taken in locomotive construction since #ahdj is the invention of the 8link motion10 by ,williams1 which1 perfected by ,howe1 admits of varying the travel of the valve1 and thus using the steam under any desired rate of expansion4 ,by this arrangement1 the power of regulating the force applied to the piston1 according to the work to be done1 is placed in the engineer's hands1 to be used at any time under whatever conditions the engine may be working4 ,by this arrangement1 two eccentrics to each cylinder are required1 7and in some dispositions of the link1 only one74 ,fig4 #aej shows the general plan of varying the expansion4 ,a fixed relation evidently exists between the points ,a and ,b1 two distinct motions are communicated by the eccentrics ,c and ,d through the rods ,e and ,f1 to the two ends ,g ,h1 of the curved link ,l2 the eccentrics are so adjusted upon the driving axle as to cause the two ends of the link to move in opposite directions1 whence at some point midway there is no motion2 the link is movable 7vertically7 upon the suspended point ,l1 so that by bringing ,l to one end or the other1 the motion given to the rod m partakes of the motion of that eccentric which is nearest to it4 ,thus the movement of the valve may be checked1 or even reversed in a second1 while the engine is in motion1 and that without sudden shocks4 ,the link is moved by the levers n n n terminating in the bar ,o1 placed at the foot board of the engine in reach of the engineer4 ,applied to this is an iron sector h h h made fast to the frame of the engine4 ,now when the point ,l is in such a part of the link as to place the valve in a position admitting steam for any fraction of the stroke1 let the point at which the bar ,o stands upon the sector be marked for that admission2 and so also for any number of different degrees of expansion4 ,it is plain that the engineer may thus1 by fixing the lever ,o1 use any percentage of admission that is required2 and may always know just what duty the engine is doing4 ,five minutes' examination of the reversing gear upon an engine will render the operation plain4 #ccj4 ,if we cut the steam off at half stroke and then allow it to expand1 of course the mean pressure during the whole stroke is less than that at entering4 ,the effective mean pressure obtained by any degree of expansion is shown by the following formula1 deduced from a mean of forty-nine experiments with the ,great ,britain locomotive1 7,great ,western ,railroad1 ,england17 having cylinders #ah #bd4 #ac4e77;a7 - #bh7 mean pressure where a is the percentage of admission4 ,from this formula1 table #aa is made4 #cca4 ,mr4 ,clark deduces as general results1 from a very extensive and carefully conducted system of experiments1 the following4 ,that the maximum useful admission is seventy-five per cent4 ,the minimum useful admission is ten per cent4 ,the greatest possible gain by working expansively is one hundred per cent41 which is effected by an admission of ten per cent4 ,the best admission for engines having ports #a_/ad of the area of the piston1 and blast area from #a_/ac to #a_/af of piston1 at high speeds 7from thirty to sixty miles per hour7 and with considerable loads1 is from sixty to sixty-six per cent4 ,with a wider port and blast area1 the best admission is seventy-five per cent4 ,the resistance due to the back pressure of the blast1 varies as the speed squared1 and inversely as the square of the area of blast orifice4 #ccb4 ,from the experiments made by ,daniel ,gooch1 with the engine 8,great ,britain10 the following results appear4 ,the loss of fuel at seventy-five per cent4 admission1 the blast orifice being from to #a_/aa of piston at sixty miles per hour1 is from to 2 at thirty or forty per cent4 admission1 the loss is from to #a_/ej2 and at thirty miles per hour1 7seventy-five per cent4 admission17 from #a_/aa to #a_/dj4 ,the resistance from steam compressed in the cylinder1 increases with the speed1 and also with the degree of expansion2 it varies from eight per cent4 in full gear1 7seventy-five per cent417 to twenty-eight per cent4 at an admission of forty per cent4 ,at the highest velocities1 the whole resistance from back pressure is nearly the same for all expansions2 for compression increases as blast pressure decreases4 ,the above deductions hold good for speeds under forty miles per hour1 with steam ports at least #a_/ad1 and blast orifice from #a_/ab to #a_/ae of the piston area4 ,,of ,,boiler ,,proportions4 #ccc4 ,the dimensions of ,american locomotives seem to depend more upon the shop whence they come1 than upon any special duty required of them4 ,it is not surprising that the utmost economy is seldom attained when a railroad president orders a lot of locomotives1 from the cheapest builder1 to suit his own ideas of an engine2 or when engines are ordered by a superintendent of machinery who does not know the difference between a sixty foot grade and a level4 ,it is the affair of the company's agent and not of the machinist to know just what a railroad needs4 ,it is a common1 and most absurd practice1 for a man who is completely ignorant of machinery to order five or ten engines1 without the least regard to the character of the road or of the traffic4 #ccd4 ,the particular characteristics of each class of engines is entirely a matter of figures4 ,there is no reason why a general table should not be formed embracing all divisions1 orders1 and classes of locomotives1 in which the requirements and general dimensions corresponding thereto should be laid down for machine shop reference4 ,such a table would at once establish a mutual understanding between railroad companies and builders4 ,such a general classification is shown hereafter4 ,the dimensions of engines are not given1 as it was thought best to let each person fill it up according to his own ideas4 ,by so doing some valuable general proportions may be arrived at4 #cce4 ,thus far experience has been the only guide to proportion 7in ,america at least74 ,practice1 in many things1 is the only correct path to the right results1 but locomotives are too expensive for philosophical apparatus2 correct experiments upon imperfect machines will lead to the means of avoiding errors4 ,the following is the modus operandi of ,d4 ,k4 ,clark in his 8,railway ,machinery40 ,a number of engines of different proportions are chosen1 and observations made upon the amounts of fuel and water consumed upon the work done1 and under what conditions4 ,these results are so tabulated as to show the effect in difference of construction upon the performance of the engine1 whence the proportioning of parts becomes a simple arithmetical operation4 ,the reduction of experiments to tables1 and the deduction from tables of formul1 is a simple operation compared with the skill and care required in observing the operation of a machine1 subject to so many disturbances as a locomotive engine in rapid motion4 ,none have had a better opportunity of observing1 have conducted experiments with more care1 or have obtained results which show fewer discrepancies than the ,english engineers ,clark and ,gooch1 and the ,french and ,german observers ,le ,chatlier and ,nollau4 #ccf4 ,three essential parts of the locomotive are the grate area1 heating surface1 and cylinders4 ,no two writers upon this subject arrive at the same dimensions to perform the same work4 ,they not only differ1 but differ widely4 ,they cannot all be right2 all but one1 or all must be wrong4 ,american builders have fixed the dimensions of their engines by observing the performance of constructed machines1 not by rules deduced from any systematic experiments1 but upon a system of remedying visible errors4 ,if a chimney diameter of ten inches is found too small and twenty too large1 fifteen has been assumed as about right4 #ccg4 ,as an example of the difference in the results obtained by different authors1 take the following3-- ,an engine to do the same work must have1 according to ,zerah ,norris4#g ,d4 ,k4 ,d4 ,k4 ,colburn4#f ,clark4#h ,clark4#i #ah #bb #ah #bb #ah #bb #ah #bb ,cylinders4 #e #e #e #e ,wheels4 #ac4jj #ac4hf #ad4jj #ai4fj ,grate area4 #aaad #hab #acbg #acbg ,heating surface4 #bej #cbd #acd #acd ,area of chimney4 #d #bc #bh #bh ,area of blast4 #ei #gc ---- ---- ,steam room4 #ajj #gc ---- ---- ,water room4 ,footnote #f3 ,colburn on the ,locomotive ,engine4 ,footnote #g3 ,norris's ,handbook for ,locomotive ,engineers and ,machinists4 ,footnote #h3 ,d4 ,k4 ,clark's ,railway ,machinery1 calculated for coke4 ,footnote #i3 ,d4 ,k4 ,clark's ,railway ,machinery1 calculated for wood4 ,from these figures1 the work done being the same1 ,mr4 ,clark gives forty per cent1 more grate area than either ,colburn or ,norris1 an easier blast1 and greater heating surface4 ,norris makes the steam and water room equal1 while ,colburn makes the latter almost double the former4 ,it is to be observed that ,colburn gives only rules adopted by different builders1 not vouching for their correctness1 while ,norris lays down his rules as fixed and right4 ,the engines used by the ,english experimenters in their observations1 vary in dimension between the following wide limits1 whence the universal application of their results4 ,grate area #i to #bd square feet4 ,fire surface #ej to #ajj square feet4 ,tube surface #djj to #a1jjj square feet4 ,whole surface #dej to #a1ajj square feet4 ,blast orifice #aj to #bj sq4 inches1 area4 ,speed of engine #ab to #bj miles per hour4 #cch4 ,the result of some sixty experiments upon forty-five different engines 7detailed in ,clark's ,railway ,machinery1 page #aef71 gives the following formula1 expressing the relations which ought to exist between grate area1 heating surface1 and consumption of water2 that evaporation may be carried on in the most economical manner4 ,s 7ac7 #ba4b surface4 ,where ,s is the heating surface in square feet4 a is the grate area in square feet4 c is the hourly consumption of water in cubic feet4 ,from which we deduce the value of a or c thus1 a 77,s_/#ba4b7b7_/;c grate area2 and c 77,s_/#ba4b7b7_/;a hourly water consumption4 ,the maximum evaporation which should be carried on per square foot of grate is found1 by ,mr4 ,clark1 to be sixteen cubic feet per hour4 ,thus1 if we wish to evaporate #afj cubic feet of water per hour1 we must have a grate area of at least #afj_/af or ten square feet4 #cci4 ,the above formula for the grate area gives the dimension for a coke-burning furnace4 ,locomotives burning wood or coal require a modification of the above1 as follows3-- ,to produce a given amount of heat1 a certain amount of carbon must be burnt4 ,as wood contains much less carbon than coke1 a correspondingly larger bulk must be burnt1 and a larger grate is necessary2 not1 however1 larger in proportion to the larger bulk of fuel1 as we may have a deeper wood than coke fire4 ,the relative depth of fire being as the stowage bulk1 and the actual depth of a coke fire being #a4i feet1 that of a wood fire will be #b4e feet4 ,now let ,a be the number of lbs4 of coke per foot of water evaporated4 ,b the number of lbs4 of coal per foot of water evaporated4 ,c the number of lbs4 of wood per foot of water evaporated4 ,call d the depth at which if is the most economical to burn coke2 d the same depth for coal1 and the depth for wood d4 ,then will the area of a coke grate be ,a_/d2 ,of a coal grate ,b_/d2 ,and of a wood grate ,c_/d4 ,to be able to fix the proper grate area for any fuel1 we must know its evaporative power1 and a depth of a layer in the furnace4 ,knowing the absolute value for coke1 it remains only to obtain the relative value for any other4 ,thus far we have disregarded the difference in time of burning wood and coke4 ,to produce a given amount of heat1 we burn a certain chemical value of fuel2 a much larger bulk of wood than of coke is needed4 ,if we burn wood and coke at the same depth and in the same time1 the grate areas would be proportional to the bulks of fuel to produce the same heat2 but1 first1 we burn fuel in a depth proportioned to the economic stowage bulk1 or as #b4e to #a4i1 which decreases the wood area2 and1 second1 a layer of coke #a4i feet deep burns in one hour1 while a layer of wood #bd feet deep burns in fifteen minutes2 whence #fj m4 divided by #ae m4 #d layers of #b feet deep each1 or in all ten feet1 which into the bulk 7equal to a mass of coke #a foot square #a4i high7 or #a foot square by #ad high1 gives #ad #aj #a4d2 or1 finally1 the area of the wood grate should be #a4d times that of a grate to burn coke4 ,,of ,,the ,,size ,,and ,,use ,,of ,,the ,,smoke ,,box4 #cdj4 ,the smoke box is the general termination of the flues1 and the place where the vacuum is produced1 which causes the draft4 ,the size of the boiler being the same1 the vacuum varies directly as the blast pressure4 ,the power of the blast is of course affected by the capacity of the smoke box4 ,mr4 ,clark fixes the capacity of the exhaust chamber at three cubic feet per square foot of grate4 ,the vacuum in the furnace varies from one to two thirds of that in the smoke box4 ,the less the resistance to the hot gases experienced in the flues1 the less may be the vacuum4 ,upon the vacuum depends the amount of air drawn through the grate2 upon the bulk of air drawn through the grate depends the combustion2 upon the combustion the evaporation4 ,whence the evaporation cet4 par4 depends the vacuum in the smoke box4 ,the velocity of any fluid depends upon the power applied to it1 7being as the square root17 the pressure applied to the gases in the furnace of a locomotive is the vacuum in the smoke box2 thus the combustion or rate of evaporation is as the square root of this vacuum4 ,to double the evaporation it is necessary to quadruple the vacuum4 ,,blast ,,pipe4 #cda4 ,the blast pipe conducts the waste steam from the cylinder1 which drives the air from the chimney and produces the vacuum in the smoke box2 its form should permit the freest escape of the steam from the cylinder4 ,the blast pipe area should nowhere be smaller than the exit port1 except at the contraction at the top4 8,too much care10 says ,mr4 ,clark1 8cannot be taken to adjust the blast pipe concentrically with the chimney2 one half inch has been known to spoil the draft of a locomotive40 8,the area of orifice is the most critical and most important item in the composition of the locomotive40 ,for the form1 dimensions1 and influence of this important member1 the reader is referred to ,clark's ,railway ,machinery4 ,as the grate area increases1 the blast may decrease4 ,the greater the flue area the easier may be the blast2 decrease of smoke box capacity and of chimney diameter1 both allow a milder blast4 #cdb4 ,the following proportions are collected from the work of ,mr4 ,clark4 ,the order in which the different parts of the engine stand in importance with relation to the blast1 is shown in column #a4 ,the figures show the ratios 7the best7 which may be had under the most favorable circumstances4 ,grate area #a ,ferrule area 7area of section of tubes at back flue sheet7 ,tube1 sectional area ,capacity of smoke box1 cubic feet #c ,chimney1 height four diameters1 area of section #a_/ae ,blast orifice #a_/ge ,the vacuum in the smoke box is somewhat regulated by a damper placed in front of the ash pan1 by a valve in the chimney1 or by a ,venetian blind covering the front ends of the tubes4 ,,tube ,,section ,,and ,,length4 #cdc4 ,the section of the tubes 7crosswise7 is the space through which the hot gases pass off4 ,by increasing the length or decreasing the diameter1 we of course require a stronger blast4 ,that the steam may escape as soon as generated1 there must be a certain clearance between the tubes1 which ,mr4 ,clark fixes as follows3-- ,divide the number of tubes by thirty and the result is the clearance in eighths of an inch2 or algebraically ,c 77,n_/#cj77_/h clearance in inches2 ,or otherwise ,c ,n_/#bdj clearance in inches4 ,,proportions ,,of ,,cylinders ,,and ,,wheels4 #cdd4 ,the above proportions depend entirely upon the nature and amount of work to be done1 and upon the character of the road4 ,small wheels and long stroke are to be applied to heavy trains and steep grades4 ,short stroke and large wheels to fast trains and level roads4 ,there are some advantages in a long cylinder1 even with a constant ratio between the stroke and wheel diameter4 ,the steam has more time to expand2 the action of the machinery is slower1 and the erratic movements of the engine caused by the movement of the reciprocating machinery are lessened1 at the same time the centre of gravity is raised and oscillation increased4 ,,of ,,the ,,carriage4 #cde4 ,the arrangement of the wheels1 axles1 springs1 and draw-link1 and the distribution of the weight of the engine upon its several bearings so as to provide the necessary adhesion1 and to run steadily upon the rails1 is a matter well worthy of more attention than is commonly given to it4 ,the frame is the base of the engine1 to which every thing should be attached4 ,the cylinders and the wheel both being attached to it1 it of course becomes the counterpart to the piston and connecting rod2 the former holding the cylinder and wheel together1 while the latter pushes them apart4 ,the frame should form a rigid connection between the piston and the wheel2 and its strength must be able to resist the whole power of the engine1 applied alternately as compression and as extension4 ,the wheels of a locomotive answer three several purposes1 and are classed as follows3-- ,leading wheels4 ,driving wheels4 ,trailing wheels4 ,the duty of the driving wheels is to transfer the power of the engine to the rails1 by which the motion is produced4 ,that of the leading wheels1 to guide the engine2 and that of the trailing wheels1 to support the after end of the engine4 ,the weight upon the driving wheels must be enough for sufficient adhesion4 ,that upon the leading wheels1 sufficient to guide the engine upon curves1 7decreasing as their distance from the centre of gravity becomes greater1 and increasing with the speed47 ,the centre of gravity of an engine is generally at a distance of from one quarter to one sixth of the length of the barrel from the furnace horizontally and forwards1 and in the lower part of the barrel1 vertically4 ,the weight upon any one pair of wheels is as their distance from the centre of gravity2 by changing their position we change the applied weight4 ,the flange base#aj must increase as the engine becomes heavier1 when applied to fast trains1 as more leverage is necessary to keep it on the rails4 ,heavy freight engines with four or five pairs of wheels1 and no truck1 wear the rails and strain themselves very much4 ,we should make the wheels of such very small and near together1 in order to contract the flange base4 ,footnote #aj3 ,wheel base1--,horizontal length between centres of extreme wheels4 ,flange base1--,horizontal length between centres of extreme fixed flanged wheels4 ,,distribution ,,of ,,weight4 #cdf4 ,suppose the whole load upon the wheels is #fj1jjj lbs4 ,if the centre of gravity is half-way between the wheels 7there being two pairs71 each will support #cj1jjj lbs4 ,if the centre of gravity is twice as near to one axle as to the other1 the furthest one will support #bj1jjj lbs41 and the nearest one #fj1jjj-bj1jjj1 or #dj1jjj lbs4 ,suppose the engine has six points of support1 or three points in the side elevation1 7the ordinary four driving wheels and a truck engine74 ,let the centre of gravity be one foot behind the middle axle and the distances between the wheel centres eight feet4 ,the weight upon the middle axle being ,h1 that upon the hind axle is ,h_/#g1 because that axle is seven times more distant from the centre of gravity than the middle one1 and for the same reason the weight upon the front axle is ,h_/#i4 ,now ,h ,h_/#g ,h_/#i #fj1jjj lbs4 ,whence ,h #dg1igf lbs4 ,also1 ,h_/#g #f1hec lbs4 ,and ,h_/#i #e1cca lbs4 ,and the same laws 7see article ,lever1 in any work on ,mechanics7 apply to any arrangement of wheels and to any position of centre of gravity4 ,springs are employed to absorb the shocks received by the wheels from irregularities in the surface of the rails4 ,they must be equally stiff on both sides of the engine1 or lateral rocking will be generated4 ,when1 as is generally the case1 the springs are connected by compensating levers1 their stiffness being as the load upon them1 the arms of the connecting lever must be inversely proportional to the applied weights4 ,the shock received by one wheel is by the lever communicated to the whole four1 7or even more when there are such74 ,the truck springs of some builders are also connected by an equalizing lever4 ,according to ,mr4 ,clark1 not more than twelve tons should ever be placed upon one axle2 whence engines requiring a tractive power of twelve tons and less may be of the form shown in fig4 #aea4 ,between twelve and twenty-four tons1 of the form fig4 #aeb2 and over the forms figs4 #aec1 #aed1 and #aee4 ,illustration3 ,fig4 #aea4 ,the weight upon the leading wheels of fast passenger engines should be as much as one fifth of the whole weight4 ,upon freight engines it need not be more than one sixth4 ,illustration3 ,fig4 #aeb4 ,the line of traction of a locomotive ought to be as near as possible at the same vertical height as the driving wheel centres4 ,if much below this the load will tend to lift the engine off from the leading wheels1 upon the drivers as a fulcrum1 thus increasing the adhesion and lessening the leading power4 ,illustration3 ,fig4 #aec4 ,if the traction bar 7draw link7 is above the wheel centres1 it will tend to lift the rear of the engine from the rails4 ,illustration3 ,fig4 #aed4 ,the general form of engines used in ,america are shown in figs4 #aea1 #aeb1 #aec1 #aed1 and #aee4 ,illustration3 ,fig4 #aee4 ,fig4 #aea is the express passenger locomotive4 ,fig4 #aeb is the ordinary passenger1 mail1 and mixed engine4 ,fig4 #aec is the heavy freight engine4 ,we have1 also1 engines with three1 four1 and five pairs of small wheels without a truck1 for heavy grades and large amounts of work4 ,,of ,,erratic ,,movements4 #cdg4 ,the erratic movements of a locomotive in motion are due to three separate causes4 ,to the motion of the machinery4 ,to the arrangement of the frame and wheels4 ,to the state of the surface of the rails4 ,those caused by the motion of the machinery are as follows3 ,longitudinal fore and aft movement1 generated by the reciprocations of the piston rod1 cross head1 connecting rod1 and crank2 and depending in amount upon the weights of the moving parts1 steam pressure1 and velocity of motion4 ,pitching of the engine1 arising from the oblique action of the cross heads upon the guides1 which tends to lift the front end of the engine from the rails2 and depends in amount upon the ratio between the stroke and length of connecting rod4 ,rocking laterally1 arising from the difference of time of action of the cross heads2 one acting with its greatest vertical power1 when the opposite one acts with none4 ,vibration in plan about the centre of gravity of engine1 produced by the pressure between the piston and crank pin1 and by the momentum of the reciprocating machinery4 ,this last1 combined with lateral rocking1 produces sinuous or spiral motion4 ,the amounts of these several irregularities depend considerably upon the arrangement of carriage2 that is1 upon the position of wheels2 being less as the base included by the bearing points is greater4 ,the influence of the state of the rails is shown by the vertical and lateral shocks arising from the rail joints and from bad adjustment1 both horizontally and vertically4 ,the amounts of these irregularities increase very rapidly with the speed4 ,le ,chatelier's experiments make them increase nearly as the square of the velocity4 ,longitudinal fore and aft motion is nearly balanced by applying a counterweight to the wheel1 opposite the point to which the connecting rod is attached4 ,the remedy for pitching consists in placing the guide bars under the heaviest part of the engine2 by which1 a great weight is opposed to the vertical action of the cross heads4 ,crampton's engine is quite free from this disturbance1 as the guide bars are almost directly under the centre of gravity4 ,the only counteracting effort 7remedy it is not7 for sinuous motion yet applied1 is extension of wheel and flange base1 thus giving the guiding wheels more control over the mass of the engine4 ,the remedy1 however1 which applies at once to all of the erratic movements1 is reduction of speed1 as when we divide the velocity by two we decrease the disturbances nearly fourfold4 ,,review ,,of ,,the ,,formul ,,and ,,formation ,,of ,,the ,,tables4 ,no4 #a4 #cdh4 ,given the weight and velocity of a train1 to find the necessary traction on a level4 ,formula4 ,w ,r1 ,w being the weight of the train in tons1 and ,r the resistance in lbs4 per ton2 found by the formula 7,v#b7_/aga #h ,r4 ,by this formula is formed table #a1 giving the traction required to move trains of from fifty to one thousand tons weight1 at speeds from ten to one hundred miles per hour4 ,no4 #b4 #cdi4 ,to find the traction due to a grade4 ,formula4 ,w ,r_/,l1 where ,w is the weight of the train in tons1 ,r the rise1 and ,l the length of the incline4 ,by this rule is formed table #b1 giving the necessary traction to overcome grades from ten to one hundred feet per mile1 with loads from one to one thousand tons4 ,to obtain the whole traction required1 add the amounts taken from tables #a and #b2 thus the traction necessary to draw five hundred tons at twenty miles per hour over fifty feet grades is1 ,by table #a1 #e1agj lbs4 ,by table #b1 #aj1fje lbs4 ------------ ,in all1 #ae1gge lbs4 or1 algebraically1 7,w ,r7 7,,wr_/,l7 ,t1 the letters standing for the same quantities as above4 ,no4 #c4 #cej4 ,to find the weight to place on the driving wheels4 ,formula4 #f,t1 where ,t is the whole tractive power4 7,table #c47 ,nos4 #d and #e4 ,the tractive power of an engine is expressed by ,t 77#b;,a7,p #b,s7_/,c1 ,where ,t is the tractive power4 ,p1 steam pressure in lbs4 per square inch4 ,s1 stroke in inches4 ,c1 circumference of wheel in inches4 ,a1 area of one piston in inches4 ,from this formula we get the values of the several factors as follows3-- ,the steam pressure1 or ,p 7,,tc7_/77#b;,a7#b,s74 7,a47 ,the stroke1 or ,s 7,,ct7_/77#b;,a77#b,p774 7,b47 ,the piston area1 or ,a 7,,tc7_/7#d,,sp74 7,c47 ,the wheel circumference1 or ,c 7#b;,a ,p #b,s7_/,t4 7,d47 ,and from 7,c7 we get the diameter of piston by the following3-- d 7area_/4#ghed74 ,and in like manner from 7,d7 the diameter of wheel by d c_/#c4adaf4 7,see tables #d and #e47 ,no4 #g4 #cea4 ,to find the capacity of cylinders of any dimension4 ,formula4 7,d#b 4#ghed ,stroke7_/#agbh4 ,this gives the capacity in cubic feet4 ,the dimensions above 7see ,d and ,s7 being in inches4 7,table #g47 ,no4 #f4 #ceb4 ,to find the hourly steam consumption in terms of the capacity of one cylinder1 7that is1 the number of cylinderfuls per hour74 ,formula4 ,n7#ebhj_/;c7 #d1 where ,n is the number of miles per hour1 c the wheel circumference4 7,table #f47 ,no4 #h4 #cec4 ,knowing the hourly consumption of steam1 to reduce it to water4 ,formula4 ,b_/,n1 ,b being the bulk of steam in cubic feet1 and ,n the relative volume of steam and water4 7,the values of ,n are given in table #h47 ,no4 #i4 #ced4 ,knowing the hourly water consumption1 to find the grate area and heating surface4 ,first1 7,cubic feet of water per hour7_/#af grate area in square ft4 ,second1 ,s 7ac7 #ba4b heating surface1 where a is the grate area1 and c the hourly consumption of water in cubic feet4 ,from the same formula1 ,grate area1 or a 77,s_/#ba4b7b7_/;c ,also water consumption1 or c 77,s_/#ba4b7b7_/;a 7,see table #i47 ,no4 #aj4 #cee4 ,to find the necessary number of tubes to give any amount of heating surface4 ,formula4 ,n ,s_/7,ld71 when ,n is the number1 ,s the required surface1 ,l the length1 d the diameter1 both in feet1 and #c4adaf4 7,see ,table #aj47 ,no4 #aa4 #cef4 ,to find the mean cylinder pressure for any percentage of admission4 ,formula4 #ac4e7;a7 - #bh1 where a is the percentage of admission4 7,see ,table #aa47 ,as to the internal arrangement of the barrel of the boiler1 we must of course have the length of tubes the same as that of the barrel1 7that is1 in the general plan of boiler1 some makers have moved the back flue plate ahead74 ,the length of tubes will of course be the same as the distance between the tube sheets4 ,the number is governed by their diameter and by the proper clearance1 which is found by the formula1 7,n_/#cj7_/h in eighths of inches1 or ,n_/#bdj inches4 ,the upper fifteen to eighteen inches of the barrel must be left for steam room4 ,,of ,,the ,,diameter ,,of ,,barrel4 #ceg4 ,to find the diameter of a barrel to contain a given number of tubes1 ,represent the inside diameter of boiler by ,d1 ,diameter of one tube d1 ,clearance between tubes c1 ,number of tubes n1 ,sectional area of boiler1 in inches ,a1 ,water section1 in inches ,b1 we shall have as the area of water room per tube1 7d c7#b1 and the whole area of water room1 7d c7#b n1 the whole section of the barrel1 ,a_/,b7d c7#bn1 and the diameter of that area1 ,d 777d c7#bn,a_/,b7_/4#ghed7 which is the boiler diameter in inches1 to which add ,d_/#af on each side1 or in all ,d_/#h as the room to be left between the sides of the boiler and first tube4 ,the diameter finds its maximum limit in the gauge less the two half breadths of tire1 and two or three inches allowance for attachment to the frame and other mechanical incidentals4 ,the length must be enough to carry the leading wheels a sufficient distance from the centre of gravity of the engine4 ,,adaptation ,,of ,,the ,,locomotive ,,engine ,,to ,,the ,,movement ,,of ,,railway ,,trains4 #ceh4 ,first1 as regards the nature of the traffic4 ,there are certain necessary causes of a bad application of power upon railroads2 for example1 when the trains are very much heavier in one direction than in the other1 as we are obliged to use the same engine both ways1 because when it arrives at one end of the road it must go back to start again4 ,where the traffic requires to be worked chiefly up hill1 we use an engine much heavier to ascend with the load than is necessary to descend without a load4 ,different objects of transport require different speeds4 ,perishable freight1 such as ice1 beef1 pork1 cattle1 c41 requires to be moved in much less time than grain1 lumber1 flour1 coal1 and manufactured articles4 ,as a general thing1 the difference between the characters of freight engines1 as regards the nature of the traffic1 can be adapted only with a view to amount1 disregarding the nature4 ,with passenger traffic1 however1 there is a great variety of speeds made use of1 and consequently may be a greater difference in the proportions of engines depending entirely upon the nature of the traffic4 ,,adaptation ,,as ,,regards ,,the ,,physical ,,character ,,of ,,the ,,road4 ,the best adaptation of locomotive power to any system of grades1 would be that which should render the mileage a minimum2 and this will be done1 as nearly as possible1 by applying engines1 the strength of which shall be proportional to the resistance to be overcome4 ,the best mode of comparing different adaptations of power is by reducing the grades to a level2 or by equating for grades by means of the capacity of motive power4 ,this is done as follows3-- ,the length of an incline being ,l1 ,the resistance on a level being ,r1 ,the ratio of the resistance due to the grade to the resistance on a level by r1 ,the equivalent horizontal length by ,l1 and we shall have1 7,r r7,l ,l4 ,example4--,let the length of a grade be seventy-five miles2 the value of r ,r_/#c2 and we have 7#c_/c,r,r_/#c7,l 77#d,r7_/#c7ge #ajj miles4 ,let us now compare the mileage of some of the large roads of ,america1 as given by a good1 and also by a bad adaptation of power4 ,the ,massachusetts ,western ,railroad may be divided into the four sections below 7including the ,boston and ,worcester road74 ,length miles4 ,maximum grade4 ,boston to ,worcester1 #dd #cj ,worcester to ,springfield1 #ed #ej ,springfield to ,pittsfield1 #eb #hc ,pittsfield to ,albany1 #di #de ,assume the speed of freight trains as fifteen miles per hour1 the resistance on a level will be #i4c lbs41 or for simplicity call it ten pounds per ton4 ,the resistance due to a #cj feet grade is #ac lbs4 per ton4 ,the resistance due to a #ej feet grade is #ba lbs4 per ton4 ,the resistance due to a #hc feet grade is #ce lbs4 per ton4 ,the resistance due to a #de feet grade is #ai lbs4 per ton4 ,and the value of r for a #cj feet grade is #ac_/aj lbs4 per ton4 ,and the value of r for a #ej feet grade is #ba_/aj lbs4 per ton4 ,and the value of r for a #hc feet grade is #ce_/aj lbs4 per ton4 ,and the value of r for a #de feet grade is #ai_/aj lbs4 per ton4 ,and the relative length of the several sections will be1 ,boston to ,worcester1 #aj_/aj #ac_/aj #bc_/aj of #dd #aja ,worcester to ,springfield1 #ca_/aj of #ed #afi ,springfield to ,pittsfield1 #de_/aj of #eb #bcd ,pittsfield to ,albany1 #bi_/aj of #di #add ------ ------ ,and the sums1 #bjj #fdh the equated distance being #c times the actual length4 ,this length assumes the resistance of the several sections to be for their whole length that given by their maximum grade4 ,this might seem erroneous2 but its correctness will be seen when it is remembered that the greatest load that can be taken over any section is limited by its maximum grade4 ,now suppose that the engine employed is of the following dimensions 7as it is very nearly74 ,cylinders #af #bj inches1 ,wheels #ed inches4 ,assume the cylinder pressure #aaj lbs41 and the tractive power of the engine is #e1bhg lbs4 ,a load of #ejj tons1 upon a #cj feet grade1 requires a #aa1ejj lbs4 traction of ,upon a #ej feet grade1 #ae1ejj lbs4 ,upon an #hc feet grade1 #bb1ejj lbs4 ,upon a #de feet grade1 #ad1ejj lbs4 ,to move the above load from ,boston to ,worcester we should #b engines1 require ,from ,worcester to ,springfield1 #c engines1 ,from ,springfield to ,pittsfield1 #e engines1 ,from ,pittsfield to ,albany1 #c engines1 ,and the products of the number of engines by the lengths of the corresponding divisions1 are ,boston to ,worcester1 #dd #b #hh ,worcester to ,springfield1 #ed #c #afc ,springfield to ,pittsfield1 #eb #e #bfj ,pittsfield to ,albany1 #di #c #adh -------- #ffj ,suppose that by making the engines on the several sections strong in proportion to the resistance of those sections1 one engine is capable of taking the whole load over all of the grades4 ,the mileage becomes as follows3-- ,boston to ,worcester1 #dd #a #dd ,worcester to ,springfield1 #ed #a #ed ,springfield to ,pittsfield1 #eb #a #eb ,pittsfield to ,albany1 #di #a #di ------ #bjj miles4 ,the mileage before was #ffj miles1 ,and the saving therefore #djj miles4 or about #gj per cent4 of the first mileage4 #cei4 ,from a recent report of the ,new ,york and ,erie ,railroad it appears that the same power will draw #bh tons on the ,western division1 #hj tons on the ,susquehanna division1 #he tons on the ,delaware division1 and #bj tons on the ,eastern division1 neglecting the assistance required from ,susquehanna to ,deposite4 ,in the following table are given the actual lengths of the several divisions1 and the sum of the products of three lengths both by the relative and a uniform resistance on each4 ,miles run ,miles run by ,division4 ,length4 by an an engine ,difference4 engine not adapted4 adapted4 ,western1 #abh #abh #c4jd #abh #a4j #bfa4ab ,susquehanna1 #aci #aci #a4jf #aci #a4j #h4ce ,delaware1 #ajd #ajd #a4jj #ajd #a4j #j4jj ,eastern1 #hh #hh #d4be #hh #a4j #bhf4jj ------------ ,sum of differences1 #eee4dg miles1 that is1 the miles run by engines adapted to the work on the several divisions will be #eee4dg less than the miles run by engines not adapted4 7,see ,appendix ,f47 ,,pennsylvania ,,central ,,railroad4 #cfj4 ,the physical character of this road is as follows3-- ,length4 ,max4 grades4 ,philadelphia to ,harrisburg1 #ajf #de ,harrisburg to ,altoona1 #aca #ba ,altoona to ,johnstown1 #dh #ib ,johnstown to ,pittsburgh1 #gh #ec ,the value of r will be here #de feet grades1 #ai_/aj #ba feet grades1 #i_/aj #ib feet grades1 #ci_/aj #ec feet grades1 #be_/aj ,whence the equation1 #ajf 7#aj_/aj #ai_/aj7 #cjg #aca 7#aj_/aj #i_/aj7 #bdi #db 7#aj_/aj #ci_/aj7 #bjh #gh 7#aj_/aj #be_/aj7 #bge ------ ------ ,sum1 #ceh ,sum1 #ajci and #ajci - #ceh #fha4 #cfa4 ,on the ,baltimore and ,ohio ,railroad we have1 ,miles4 ,max4 grade4 ,baltimore to ,harper's ,ferry1 #hj #hb ,harper's ,ferry to ,cumberland1 #ih #dj ,cumberland to ,raccoon1 #hh4b #aaf ,raccoon to #adh miles1 #fj4e #dj #adh miles to ,wheeling1 #ea4c #hj ,and as before1 #hj 7#aj_/aj #ce_/aj7 #cfj #ih 7#aj_/aj #ag_/aj7 #bfe #hh4b 7#aj_/aj #di_/aj7 #ebj #fj4e 7#aj_/aj #ag_/aj7 #afc #ea4c 7#aj_/aj #ce_/aj7 #bca ,sum of ,col4 #a #cgh1 ,sum of ,col4 #c #aeci2 difference #aafa4 ,thus by the most correct adaptation of power1 upon the above-named railroads1 the following percentages of mileage may be saved4 ,massachusetts ,western1 #gj ,new ,york and ,erie1 #ee ,pennsylvania ,central1 #fh ,baltimore and ,ohio1 #ge ,of these roads the ,baltimore and ,ohio is that which has actually the best adaptation2 and the ,western road of ,massachusetts that which has the worst4 #cfb4 ,to determine the actual dimensions of the engines which should be used upon any road1 from the tables1 proceed as follows3--,let the load be one hundred tons1 the maximum grade thirty feet per mile1 and speed twenty-five miles per hour4 ,referring to the tables in succession we have1 ,by table #a1 ,traction for #ajj tons1 on a level1 at #be miles #a1eej lbs4 per hour1 ,by table #b1 ,traction for #ajj tons1 on a #cj feet grade1 #a1bgc lbs4 ---------- ,whole traction required1 #b1hbc lbs4 ,by the formula1 table #c1 the weight upon the drivers must be #bhbc #f #afich lbs41 or #h tons4 ,by table #d1 with a wheel five feet in diameter1 and a stroke of twenty inches1 we have the decimal 4#babb4 ,by table #e1 the mean cylinder pressure being sixty pounds per inch1 and piston twelve inches in diameter1 we have as the total pressure ,on both pistons1 #ac1egb lbs4 ,and finally1 #acegb 4#babb #b1hhj lbs4 ,the requirement being #b1hbc lbs4 ,by table #f1 we see that five feet wheels at twenty-five miles per hour1 use #cc1fjj cylinders of steam per hour4 ,by table #g1 the capacity of a cylinder #ab #bj is #a4ca cubic feet2 also #ccfjj #a4ca #ddjaf cubic feet of steam per hour4 ,assuming the mean cylinder pressure at sixty pounds1 and the entering pressure at eighty pounds1 also the loss in passing from the boiler at twenty pounds1 we must generate the steam at one hundred pounds per square inch4 ,by table #h1 we see that when steam is produced under one hundred pounds pressure per inch1 each cubic foot of water makes #bic cubic feet of steam2 whence #ddjaf_/bic #aej1 is the number of cubic feet of water to be evaporated per hour4 ,at sixteen cubic feet of water per hour per square foot of grate1 we thus require #ae4j_/af or #i4d feet1 nearly2 and by table #i1 we find the heating surface necessary to evaporate #aej cubic feet of water per hour1 with nine square feet of grate surface1 to be #ggi square feet2 and by the formula1 with #i4d square feet1 we have1 ,s 7#i4d #aej7 #ba4b #gig square feet1 the fuel being coke2 for wood1 multiply the grate area 7as mentioned before7 by #a4d and the grate area will be #a4d #i4d #ac4af4 ,the tube surface of course remains the same1 as1 when the necessary amount of heat is developed1 the same surface only is enough to apply it to the water4 ,to obtain #ggi square feet of heating surface1 we see1 by table #aj1 that it is given by #ajj tubes #ag feet long and #a inch diameter1 or #ajj tubes #af feet long and #a inch diameter1 or #ajj tubes #ae feet long and #b inch diameter1 or #ajj tubes #ad feet long and #b inch diameter1 or #ajj tubes #ab feet long and #b inch diameter1 or #ajj tubes #ab feet long and #b inch diameter1 or by consulting the table1 and having given the number and length1 the number and diameter1 or the length and diameter1 we may easily find the third factor of the surface4 ,thus the length being eleven feet1 and diameter two inches1 #ggi feet is obtained by #ggi_/7aa #c4adaf #afg7 #ace tubes4 ,to obtain the diameter of barrel to contain #ace two inch tubes1 we use the formula ,d 77,a_/,bn7dc7#b7_/74ghed774 ,we have already found d #b inches1 n #ace1 whence c will be by formula1 c ,n_/#bdj #j4ed1 and d c #b4ed1 also1 7d c7#b #f4de1 and #ace #f4de #hga2 and allowing three fourths of the boiler cross section to be filled with tubes1 we have1 #d_/c of #hga #aafa2 also1 #aafa_/4ghed #adgh1 the square root of which is #ch4e nearly1 to which add #ch4e_/h or #d4h inches1 7see page #cei71 and we have #ch4e #d4h #dc4c inches1 as the inside diameter of boiler1 whence the following locomotive to meet the requirement as stated4 ,weight upon driving wheels1 #af1ich lbs41 ,cylinders1 #ab #ab inches1 ,wheels1 #e feet1 ,tubes1 #ace--aa feet #b inches1 ,grate1 #ac4af square feet1 ,barrel1 7inside diameter17 #dc4c inches1 and under the most favorable circumstances1 the chimney may be #dj inches high1 #ab4g inches in diameter2 the blast orifice #e4h inches in diameter2 and the capacity of smoke box #ci cubic feet4 #cfc4 ,we may vary the tractive power of an engine by using the steam at a greater or less degree of expansion1 but the adhesion remains the same4 ,if an engine was built able to work a road partly level1 and partly on steep grades1 varying the power simply by varying the expansion1 it would be unnecessarily heavy for the easy parts of the road4 ,the expansive principle may be advantageously employed in adjusting the power to the difference of resistance on any one division of a road1 and also to the varying load which each day's traffic will present4 ,suppose we would move a load of two hundred tons over the road below2 and suppose1 also1 that we require the cylinder pressures set opposite the several divisions4 #aj miles1 level1 #fj lbs41 #aj miles1 #aj feet per mile1 #hj lbs41 #aj miles1 #bj feet per mile1 #ajj lbs41 #aj miles1 #cj feet per mile1 #abj lbs4 ,the boiler pressure being #aej lbs41 and the pressure at entering the cylinder #ade lbs41 ,an admission of #ga per cent4 gives a mean pressure of #abj lbs41 ,an admission of #ee per cent4 gives a mean pressure of #ajj lbs41 ,an admission of #dj per cent4 gives a mean pressure of #hj lbs41 ,an admission of #bh per cent4 gives a mean pressure of #fj lbs41 ,and if the #ast notch of the sector admits1 #ge per cent1 ,and if the #b;d notch of the sector admits1 #gj per cent1 ,and if the #c;d notch of the sector admits1 #fe per cent1 ,and if the #dth notch of the sector admits1 #fj per cent1 ,and if the #eth notch of the sector admits1 #ee per cent1 ,and if the #fth notch of the sector admits1 #ej per cent1 ,and if the #gth notch of the sector admits1 #de per cent1 ,and if the #hth notch of the sector admits1 #dj per cent1 ,and if the #ith notch of the sector admits1 #ce per cent1 ,and if the #ajth notch of the sector admits1 #cj per cent4 ,we should work the engine as follows3-- ,from #j to #aj miles1 use the #ajth notch1 ,from #aj to #bj miles1 use the #hth notch1 ,from #bj to #cj miles1 use the #eth notch1 ,from #cj to #dj miles1 use the #b;d notch1 ,,application ,,of ,,locomotive ,,engines ,,to ,,railroads4 #cfd4 ,department #a4 ,freight4 ,,general ,,classification4 ,order,order,order,order,order,order ,number of ,maximum ,designation #a #b #c #d #e #f division4 grades4 of parts4 #ej #ajj #bej #ejj #gej #a1jjj tons4tons4tons4tons4tons4tons4 ,grate area4 ,tube #a ,level4 surface4 ,cylinders4 ,wheels4 ,weight4 #b #aj feet per mile4 #c #bj feet per mile4 #d #dj feet per mile4 #e #fj feet per mile4 #f #hj feet per mile4 #g #ajj feet per mile4 ,the speed is assumed from twelve to fifteen miles per hour4 ,the mean cylinder pressure is assumed at sixty lbs4 per square inch2 the initial pressure at ninety pounds1 and the boiler pressure at #abj lbs4 per square inch4 ,the grate areas are designed for coke2 for wood multiply the same by #a4d4 #cfe4 ,department #b4 ,passenger4 ,order #a,order #b,order #c,order #d ,designation ,classification4 #ej #ajj #aej #bjj of parts4 tons4 tons4 tons4 tons4 ,grate area4 ,division #a #be miles ,tube surface4 ,level4 per hour4 ,cylinders4 ,wheels4 ,weight4 ,division #b #be miles #bj grades4 per hour4 ,division #c #be miles #dj grades4 per hour4 ,division #d #be miles #fj grades4 per hour4 ,division #e #be miles #hj grades4 per hour4 ,division #f #be miles #ajj grades4per hour4 ,the engines in the ,northern ,states require more power in winter than in summer4 ,to the above classification might be added1 an engine for 8making up trains10 and similar station work2 such an engine should be able to start easily the extreme weights of trains1 from fifty to one thousand tons1 and should be fitted with a power of varying its adhesion4 ,,formula4 ,w 7,v#b7_/aga #h ,r4 ,example4 ,the speed being thirty miles per hour1 and load #bej tons4 ,r will be 77#cj #cj77_/aga #h #bej #ccae lbs4 #cff4 ,table #a4 ,showing the required traction on a level for loads from fifty to one thousand tons1 and for velocities from ten to one hundred miles per hour4 ,velocity4 #ej #ge #ajj #bej #ejj #gej #ajjj ,tons4 ,tons4 ,tons4 ,tons4 ,tons4 ,tons4 ,tons4 #aj #dbi #fdc #heh #badf #dbib #fdce #hehe #ab #ddb #ffc #hhd #bbaj #ddba #ffcj #hhdb #ae #dfe #fih #ica #bcbh #dfeg #fihb #icae #bj #eag #ggc #ajcd #behe #eagj #ggce #be #ehb #hgd #aafe #biab #ehbe #cj #ffc #iid #acbf #ccae #ffcj #dj #hfh #acjb #agcf #dcdj #ej #aaca #afif #bbfb #efee #fj #adeb #bahj #bije #ajj #ccbd #dihf #ffdh ,,formula4 ,,wr_/,l4 ,example4 ,the tractive power to overcome the resistance of #gej tons upon a sixty feet grade is #gej #fj_/ebhj #aijej4 #cfg4 ,table #b4 ,showing the tractive power necessary to overcome grades from ten to one hundred feet per mile with loads from one to one thousand tons4 ,grade4#a ,ton4 #ej #ge #ajj #bej #ejj #gej #ajjj ,grade4 ,tons4 ,tons4 ,tons4 ,tons4 ,tons4 ,tons4 ,tons4 #aj #d #bab #cah #dbd #ajfa #baba #caha #dbdj #aj #bj #h #dbd #fcf #hdh #babb #dbdb #fcfb #hdhj #bj #cj #ac #fcf #iee #abgc #cagj #fcfc #iede #abgcj #cj #dj #af #hdh #abgb #afif #dbdd #hdhd #abgbd #afifj #dj #ej #bj #ajfj #aeij #babj #ecje #ajfje #aeije #babjj #ej #fj #bf #abgb #aiaj #bedf #fcdj #abgbf #aijej #bedfj #fj #gj #cj #aejj #bbdj #cjjj #gejj #aejjj #bbdjj #cjjjj #gj #hj #cc #afig #bede #ccic #hdhi #afifi #bedei #cciej #hj #ajj #dj #babj #cahj #dbdj #ajfaj #babaj #cahaj #dbdjj #ajj ,grade4#a ,ton4 #ej #ge #ajj #bej #ejj #gej #ajjj ,grade4 ,tons4 ,tons4 ,tons4 ,tons4 ,tons4 ,tons4 ,tons4 ,,formula4 #f,t4 ,example4 ,required traction #e1jjj lbs42 upon driving axles the weight is #ejjj #f #cj1jjj lbs4 #cfh4 ,table #c4 ,giving the weight which should be placed upon the driving axles to secure any amount of adhesion2 the latter being one sixth of the weight4 ,required ,weight in,weight in traction4 pounds4 tons4 #ejj #cjjj #a4cd #ajjj #fjjj #b4fi #bjjj #abjjj #e4cf #cjjj #ahjjj #h4jd #djjj #bdjjj #aj4hj #ejjj #cjjjj #ac4dj #fjjj #cfjjj #af4jg #gjjj #dbjjj #ah4ge #hjjj #dhjjj #ba4dc #ijjj #edjjj #bd4aa #ajjjj #fjjjj #bf4hj #abjjj #gbjjj #cb4ad #adjjj #hdjjj #cg4ej #afjjj #ifjjj #db4hf #ahjjj #ajhjjj #dh4bb #bjjjj #abjjjj #ec4fj ,,formula4 7#b,s7_/c4 ,where ,s stroke4 c circumference of wheel1 7both in inches47 ,example4 ,let stroke be twenty inches1 and diameter of wheel five feet1 the ratio will be #dj_/ahh4d #j4babb4 #cfi4 ,table of decimals1 which1 multiplied by the total piston pressures 7table #e7 will give the traction in pounds1 or ratio between double stroke and wheel circumference4 ,table #d4 ,wheel4 ,,stroke ,,in ,,inches4 ,wheel4 #ah #bj #bb #bd #bf #bh #cj #cb #cd #cf #c #bgbhcjcacccdcfch #c #c #beecbhcgcabjcdjdcfhh #c #d #bchfbfebbiahcahbcdddcgjh #d #d #bbejbejjbgejcjjjcbejcejjcgej #d #d #baeabcijbeicbhcjcjgacbidcebicgfd #d #d #bjabbbcebdeibfhbbijecabiccebcegechjj #d #e #aiajbabbbccdbedfbgffbigicaibcdjecfagchc je #e #agcfaibibabbbcaebejjbfibbhhecjggcbgccdg ce #f #aeiaagfhaidebabbbcbabejjbfghbhegcjcfcba ef #f #adfhafcbagifaiehbacabbiebdeibfbcbgijbie af #g #acfdaeafaffgahaiaigjbababbgcbdbdbegfbgb gg #g #abgbadadaeefafiaahcaaigbbaadbbedbcidbec eg #h #aaidacbfadagaeibafhhahahaidhbjghbbjhbcc gh ,wheel4 #ah #bj #bb #bd #bf #bh #cj #cb #cd #cf ,wheel4 ,,stroke ,,in ,,inches4 ,,formula4 #b7;d#b 4#ghed p7 ,p4 ,where d diameter4 p pressure per inch4 ,example4 ,the whole pressure at one hundred pounds per inch on two sixteen inch pistons will be #baf #af #j4ghed #ajj #djbab4 #cgj4 ,table #e4 ,total pressures upon pistons from ten to twenty-four inches in diameter1 and for steam pressures from fifty to one hundred and fifty pounds per square inch4 ,diam4 ,area of ,,whole ,,piston ,,pressure ,,on ,,both ,diam4 of one ,,pistons1 ,,at ,a ,,per ,,inch ,,pressure ,,of of cyl'r4,piston4 cyl'r4 #ej #fj #gj #hj #ij #aj #gh4e #giej #idbj #ajiij #abefj #adacj #aj #aa #ie4j #iejj #aadjj #accjj #aebjj #agajj #aa #ab #aac4a #aacaj #acegb #aehcd #ahjif #bjceh #ab #ac #acb4g #acbgj #aeibd #ahefd #babcb #bcijf #ac #ad #aec4i #aecij #ahdfh #baedf #bdfbd #bggjb #ad #ae #agf4g #agfgj #babjd #bdgch #bhbgb #cahjf #ae #af #bja4a #bjaaj #bdacb #bhaed #cbagf #cfaih #af #ag #bbg4j #bbgjj #bgbdj #caghj #cfcbj #djhfj #ag #ah #bed4e #bedej #cjedj #cefcj #djgbj #dehaj #ah #ai #bhc4e #bhcej #cdjbj #cifij #decfj #eajcj #ai #bj #cad4b #cadbj #cggjd #dcihh #ejbgb #efeef #bj #ba #cdf4d #cdfdj #daefh #dhdif #eedbd #fbceb #ba #bb #chj4a #chjaj #defab #ecbad #fjhaf #fhdah #bb #bc #dae4e #daeej #dihfj #ehagj #ffdhj #gdgij #bc #bd #deb4d #debdj #edbhh #fcccf #gbchd #hadcb #bd ,diam4 ,,pistons1 ,,at ,a ,,per ,,inch ,,pressure ,,of ,diam4 of of cyl'r4 cyl'r4 #ajj #aaj #abj #acj #adj #aej #aj #aegjj #agbgj #ahhdj #bjdaj #baihj #bceej #aj #aa #aijjj #bjijj #bbhjj #bdgjj #bffjj #bhejj #aa #ab #bbfbj #bdhhb #bgadd #bidjf #cagfh #ccicj #ab #ac #bfedj #biaid #cahdh #cdejb #cgaef #cihaj #ac #ad #cjghj #ccheh #cfgef #djjad #dcjib #dfagj #ad #ae #cecdj #chhgd #dbdjh #eeidb #didgf #ecjaj #ae #af #djbbj #ddbdb #dhbfd #ebjfb #efcjh #fjccj #af #ag #dedjj #diidj #eddhj #eijbj #fcefj #fhajj #ag #ah #ejijj #eeiij #fajhj #ffagj #gabfj #gfcej #ah #ai #efgjj #fbcgj #fhjdj #gcgaj #gichj #hejej #ai #bj #fbhdj #fiabd #gedjh #hafib #hgigf #iebfj #bj #ba #fichj #gfbjh #hcacf #ijjfd #ifiibajcibj #ba #bb #ggjbj #hcfbb #iabbd #ihhbfajfdbhaadjcj #bb #bc #hcajj #iadaj #iigbjajhjcjaafcdjabdfej #bc #bd #ijdhj #iiebhajhegfaagfbfabffgbacegbj #bd ,,formula4 ,n #ebhj_/;c #d4 ,where ,n the number4 c wheel circumference4 ,example4 ,speed twenty-five miles per hour1 wheels four and a half feet1 the number of cylinders per hour is #be #ebhj_/7d #c4adaf7 #d #cgcdh #cga4 ,table #f4 ,showing the hourly consumption of steam in terms of the capacity of one cylinder1 with wheels from three and a half to eight feet1 and speeds from ten to sixty miles per hour4 ,wheel4 ,wheel ,revolutions in per mile4 inches4 #c #db #dhj #c #de #ddi #d #dh #dba #d #ea #cig #d #ed #cgc #d #eg #cfa #e #fj #ccf #e #ff #cjf #f #gb #bha #f #gh #bei #g #hd #bdj #g #ij #bbd #h #if #baa ,wheel4 ,,number ,,of ,,cylinders ,,per ,,hour ,,at ,a ,,velocity ,,of #aj #ab #ae #bj #be #cj #dj #ej #fj #c #aibjjbcjdj #c #agifjbaeebbfidj #d #afhdjbjbjhbebfjccfha #d #aehhjaijefbchbjcagfjcigjj #d #adibjagijdbbchjbihdjcgcjj #d #adddjagcbhbaffjbhhhjcfajj #e #bjafjbfhhjccfjj #e #ahcfjbddhjcjfjjcfgbj #f #bbdhjbhajjccgbjddifj #f #bjgbjbeijjcajhjdaddjeahjjfbafj #g #aibjjbdjjjbhhjjchdjjdhjjjegfjj #g #bbdjjbfhhjcehdjddhjjecgfj #h #baajibecbjccgfjdbbjjejfdj ,,formula4 7,d#b 4#ghed ,stroke7_/#agbh ,c4 ,example4 ,cubic content of a cylinder #ae #bd is 7#ae #ae #j4ghed #bd7_/agbh #b4dd cubic feet4 #cgb4 ,table #g4 ,capacity of cylinders in cubic feet of from ten to twenty-four inches in diameter1 and from eighteen to thirty-six inches stroke4 ,diam4 ,,capacity ,,of ,,cylinders ,,in ,,cubic ,,feet1 ,diam4 of ,,stroke ,,being of cyl'r4 cyl'r4 #ah #bj #bb #bd #bf #bh #cj #cb #cd #cf #aj #jhbjiaajjajiaahabgacfade #aj #aa #jicajdaaeabfacgadhaeiagjaha #aa #ab #aahacaaddaegagjahcaifbjibbbbce #ab #ac #accadiafeahaaigbacbbibdebfabgg #ac #ad #afjaghaifbadbcbbejbfhbhfcjdcbb #ad #ae #ahdbjdbbdbddbfdbhdcjdcbdcddcfd #ae #af #bjhbcbbeebghcjacbdcdgcgjcicdaf #af #ag #bcebfcbhicaecdacfgcicdaiddedga #ag #ah #bfcbidcbccebchadajdcidfhdigebf #ah #ai #cfaciddbgdfjdicebfeeieib #ai #bj #djjdcgdgdeaaedhehefbbfei #bj #ba #dhaebaefafjafdafhagba #ba #bb #ebhegbfafffjgjdgdhgib #bb #bc #fbefgdgbcggbhbahgf #bc #bd #fhagccghehcghhiida #bd #cgc4 ,table #h4 ,giving the volume1 pressure1 temperature1 and density of steam4 ,relative volume or ,weight of ,steam cubic feet,temperature4 ,total a cubic ,steam pressure4 of steam1 heat4 foot4 pressure4 water being #a4 #ej #eeb #bha #abjj #aabi #ej #fj #dfg #bic #abjc #acce #fj #fe #dcd #bih #abje #adcf #fe #gj #djf #cjc #abjf #aece #gj #ge #cha #cjg #abjh #afcf #ge #hj #cei #cab #abji #agcf #hj #ij #cbc #cbj #abab #aibi #ij #ajj #bic #cbh #abad #babg #ajj #aaj #bfi #cce #abaf #bcag #aaj #abj #bdi #cda #abah #beje #abj #acj #bca #cdg #abbj #bfih #acj #adj #baf #cec #abba #bhhe #adj #aej #bjc #ceh #abbc #cjgj #aej ,,formula4 ,s 7ac7 #ba4b4 ,where ,s surface4 a grate area4 c cubic feet of water per hour4 ,example4 ,grate area sixteen square feet1 cubic feet of water per hour two hundred1 surface is 7#af #bjj7 #ba4b #aaii4ib4 #cgd4 ,table #i4 ,showing the necessary amount of grate area and heating surface for an hourly consumption of water4 ,cubic ft4 of water ,,grate ,,areas ,,in ,,square ,,feet4 evap'd per hour4 #g #h #i #aj #aa #ab #ac #ad #ae #af #ag #ah #ai ,,heating ,,surface ,,corresponding ,,to ,,above ,,grate ,,areas ,,and ,,to ,,side ,,column4 #ajjefaeiifcf #fgj #gjc #gcd #gfd #gic #hba #hdh #hgd #ijj #ibd #aajehhfbhffg #gjb #gcg #ggj #hjb #hca #hfa #hhh #iaf #idc #ifi #abjfadfegfig #gcd #ggj #hje #hcg #hfi #ijj #ibg #ieg #iheajac #acjfcifhcgbe #gfd #hja #hcg #hga #ijd #icf #ife #iifajbeajec #adjffcgjigeb #gic #hca #hfi #ijd #ich #igbajjcajcdajfdajic #aejfhfgcdggi #hba #hfj #ijj #ice #igaajjfajchajgjaajaaaca #afj #gehhje #hdh #hhi #ibg #iffajjdajciajgcaajfaachaafi #agj #ghbhbi #hgd #iaf #ieg #iifajcdajgaaajfaadjaagcabje #ahj #hjehec #ijj #idc #iheajbeajfdaajbaachaagcabjgabdj #aij #hgg #ibd #ifiajacajecajicaacbaafiabjeabdjabgd #bjj #ijj #idh #iieajciajhaaabbaafaaaiiabcfabgbacjg #baj #ibh #igdajaiajfdaajgaadiaahiabbiabfdabihaccf #bbj #ajjjajdbajhiaaccaagfabagabehabiaacbdacf e #bcj #ajaiajfgaaadaaeiabjcabdeabhfacbcaceiaci h #bdj #ajiaaachaahdabbiabgbacadacedacicadca #bej #aaaaaafbabjhabedabihacdaachjadbbadeh #bfj #aahdabcbabghacbcacfgadjfadejadhd #bgj #abjgabefacjcacdiadjaadccadghaeae #bhj #abgiacbgacgdadceadfjaejeaedf #bij #acjbaceaadjjadebadhfaecbaegc #cjj #acgdadbeadfiaeabaeehafjj #cbj #adfiaeafaefdafajafed #cdj #aefdafabafehagjd #cfj #afehagjfaged #chj #agecahjb #djj #ahjjahdh #dbe #dej #dge #ejj ,cubic ft4 of water ,,grate ,,areas ,,in ,,square ,,feet4 evap'd per hour4 #bj #ba #bb #bc #bd #be #bf #bg #bh #bi #cj ,,heating ,,surface ,,corresponding ,,to ,,above ,,grate ,,areas ,,and ,,to ,,side ,,column4 #ajj #idh #igb #iieajagajciajfjajhaaajbaabbaadbaafa #aaj #iidajahajdbajffajhiaaaaaaccaaeeaagfaaig abag #abjajciajfdajhiaaadaachaafbaahdabjgabbi abeaabgb #acjajhaaajgaaccaaeiaahdabjhabcbabeeabgh acjjacbc #adjaabbaaejaaggabjcabbiabedabgiacjcacbg aceaacgd #aejaafaaaijabahabdeabgbabihacbcacejacgc acihadbb #afjaaiiabbiabehabhfacadacdaacfgacicadai adddadfi #agjabcfabffabifacbeacedachbadjiadcfadfb adhhaead #ahjabgbacjcaccdacfdacicadbbadejadghaeje aecbaeeh #aijacjgacciacgjadjaadcaadfaadijaeahaedf aegcafjj #bjjacdaacgdadjfadcgadfhadiiaebiaeehaehf afadafdb #bajacgdadjhaddaadgcaejeaecfaeffaeifafbe afedafhc #bbjadjfaddaadgeaejhaedaaegbafjcafcdaffd aficagbb #bcjadcgadgcaejhaedbaegeafjgafciaffcagja agbdagfa #bdjadfhaejeaedaaegeafjiafdbafgeafibagch agedagii #bejadiiaeccaegbafjfafdbafgeagjiagccaggd agigahcf #bfjaebiaefjafjcafcfafgeagjhagdcaggdahji ahdjahgb #bgjaeegaeibafcdaffhafibagdaaggfahjhahdc ahgeaijh #bhjaehfafbdaffdagjjagchaggdahjiahdbahgg aiajaidc #bijafadafecaficagbiagedahjdahdaahgcaiaj aiciaigg #cjjafdbafhbagbbagehagiiahcdahgbaijdaidc aifhbjaa #cbjafifagchagghahafaheiahidaicbaigjbjjh bjbdbjgh #cdjagdhagibahccahgbaiaeaiedaiicbjcbbjfi bjifbada #cfjahjjahddahhfaibhaigabjabbjejbjijbabh baffbbjd #chjahdhahidaichaihbbjbebjffbajgbadhbahg bbbfbbfd #djjaijjaiddaiijbjcdbjggbabjbafbbbjdbbdd bbhdbcbb #dbeaiejbjadbjefbjggbadbbahgbbbfbbfhbcag bcecbcif #dejbjadbjefbabjbaejbaijbbjjbcjjbccbbcgd bdagbdei #dge #bagebbajbbfhbcajbcecbdafbddebdhjbebc #ejj #bccbbcgjbdabbdeibebcbefebfjh ,,formula4 ,n ,s_/7,ld7 or ,s_/7,ld#c4adaf74 ,where ,s whole surface1 ,where ,l length1 ,where d diameter1 in feet1 ,where #c4adaf1 ,where ,n the number4 ,example4 ,diameter two inches1 surface #adff1 length fourteen feet1 we have1 ,n #adff_/7ad #j4afg #c4adaf7 #bjj4 #cge4 ,table #aj4 ,giving the number and dimensions of tubes to obtain any given amount of surface4 ,l'gth4,diam4 ,diam4 ,diam4 ,diam4 ,diam4 ,diam4 ,diam4 ,diam4 ,l'gth4 #a #a #a #b #b #b #b #b #h #cad #ccf #cig #dai #dde #dga #ejd #ebc #h #h #ccd #chi #dbb #dde #dgc #ejj #ece #eef #h #i #ceb #daa #ddg #dga #ejg #ecj #eff #ehh #i #i #cgb #dce #dga #dig #ebc #eei #eig #fba #i #aj #cib #deg #dif #ebd #eef #ehi #fbh #fee #aj #aj #daa #dhj #eba #edi #ehd #fah #fei #fhg #aj #aa #dca #ejc #ede #egf #fab #fdg #fij #gbj #aa #aa #dea #ebf #egj #fjb #fdj #fgg #gba #gec #aa #ab #dga #edi #eie #fbh #ffg #gje #geb #ghf #ab #ab #dij #egb #fbj #fed #fie #gce #ghc #hah #ab #ac #eaj #eie #fde #fha #gbc #gfd #had #hea #ac #ac #ecj #fag #ffi #gjg #gej #gic #hde #hhd #ac #ad #edi #fdj #fie #gcc #ggh #hbc #hgf #iaf #ad #ad #efi #ffc #gai #gei #hjf #heb #ijg #idi #ad #ae #ehi #fhf #gdd #ghe #hcd #hhb #ich #ihb #ae #ae #fjh #gjh #gfi #haa #hfa #iaa #ifi #ajae #ae #af #fbh #gca #gid #hcg #hhi #ida #ajjj #ajdh #af #af #fdh #ged #hai #hfc #iag #iga #ajca #ajha #af #ag #ffh #ggg #hdc #hhi #ide #ajjj #ajfb #aaad #ag ,,formula4 #ac4e7;a7 - #bh1 where a is the percentage of admission4 ,example4 ,what is the mean pressure1 with an initial pressure of one hundred pounds1 and sixty per cent4 admission4 #ac4e7fj7 - #bh 7#ac4e #g4g7 - #bh #gf_/ajj of #ajj1 or #gf lbs4 #cgf4 ,table #aa4 ,showing the mean cylinder steam pressure for any percentage of admission1 the initial pressure being from #ej to #aej lbs4 per inch4 ,initial pressure ,,mean ,,cylinder ,,pressure1 ,,admission ,,being ,,in ,,hundredths in ,,of ,,the ,,stroke4 pounds4 #aj #ae #bj #be #cj #ce #dj #de #ej #ee #fj #fe #gj #ge #ej #g #ab #af #bj #bc #bf #bh #ca #cc #cf #ch #dj #db #dd #fj #i #ad #ai #bd #bh #ca #cd #cg #dj #dc #df #di #ea #ec #gj #aj #ag #bb #bh #cc #cf #dj #dc #dg #ej #ed #eg #ei #fb #hj #ab #ai #bf #cb #ch #db #da #di #ed #eh #fb #fe #fh #ga #ij #ac #bb #bi #cf #db #dg #ea #ed #fj #fe #fi #gc #gf #hj #ajj #ae #bd #cb #dj #dg #eb #eg #fb #fg #gb #gg #ha #he #hi #aaj #af #bf #ce #dd #eb #eg #fc #fh #gd #gi #he #hi #ic #ih #abj #ah #bi #ch #dh #ef #fb #fh #gd #hj #hf #ia #igajbajg #acj #ai #ca #db #eb #fa #fh #gd #ha #hg #id #iiajeaajaaf #ade #ba #cd #de #ef #fe #gc #hj #hg #idajaajgaacaaiabe #afj #bb #cf #dh #fj #gj #gh #he #icajjajhaadabaabgacd ,,part ,,ii4 ,,cars4 ,,wheels ,,and ,,axles4 #cgg4 ,of the mechanical details of car building it is not necessary here to speak2 but of those matters which fit a car for special duty1 and depend upon particular characteristics of any road1 such as the gauge1 something must be said4 ,the trend of the wheel tire1 as remarked in ,chapter ,,xiii41 is not turned cylindrical1 but conical4 ,a perfectly straight road would of course require no cone upon the wheels2 the object of the latter being to vary the wheel diameter when upon curves4 ,the general practice is to give a certain standard cone to all wheels1 for all gauges4 ,this is quite wrong1 as will be seen by the following formula1 which is from 8,pambour on the ,locomotive ,engine40 ,illustration3 ,fig4 #aef4 ,let m m1 fig4 #aef1 represent the outer rail1 and n n the inner one4 ,the circumferences upon the same axles must evidently vary as the length of these curves1 which are included between the same radii4 ,let ,d1 be the diameter of the first wheel1 and d1 that of the second2 and we shall have1 7mm7_/7nn7 7,d7_/7d71 or otherwise mm #c4adaf ,d1 and nn #c4adaf d4 ,we have also1 7mm7_/7nn7 7mo7_/7no74 ,expressing the radius of curvature by r1 and the half gauge by e1 the above proportion may be expressed by 7mm7_/7nn7 7r e7_/7r - e71 and also ,d_/d 7r e7_/7r - e71 and finally ,d - d 7#b;e,d7_/7r e74 ,this equation shows the difference in diameters that ought to exist between the inner and outer wheels1 that the required effect1 7no dragging of the outer and no slipping of the inner wheel17 is produced4 ,example4 ,let the radius of curvature be #a1jjj feet4 ,the gauge of the road1 #f feet4 ,the wheel diameter1 #d feet4 ,and the formula becomes 7#b;ed7_/7r e7 #bd_/ajjc 4#jbd feet1 or 4#bhh inch on both wheels1 or #j4add inch for each wheel2 which for four inches breadth1 gives a curve of #a_/bh of the width1 or decimally1 #j4add1 and vulgarly1 of an inch4 ,for a three feet wheel1 the rule gives a cone of #j4aa inch4 ,,note4--,messrs ,bush and ,lobdel cone their wheels #j4jh inches in a four inch tire2 or inch per foot4 ,the formula above for a three feet wheel1 and #d #h gauge1 gives a curve of #j4ji inches4 ,the wheel most used upon ,american roads is made of cast-iron1 in one piece1 and consists either of two side plates1 connected by a hub and rim1 or of a central plate ribbed on the sides4 ,messrs ,whitney and ,son1 7,philadelphia17 pass all their wheels through an annealing process1 which renders them much less liable to fracture from shocks and from cold than when the wheel is allowed to cool at once1 when hot from the foundery4 ,the wheels used upon ,english roads are made with a wrought iron rim and spokes1 with a cast hub1 the tire being1 put on separately4 ,such wheels are less liable to fracture1 but cost more than the ,american wheel4 #cgh4 ,a very frequent cause of accident upon railroads1 is the breakage of axles4 ,experiments made at ,wolverhampton1 7,england17 upon differently formed axles1 show very plainly that it is quite wrong to reduce the diameter of the axle at the middle4 ,that if any variation exists it should be in making the middle the largest4 ,that the effect of a shoulder behind the wheel was to decrease very much the strength4 ,probably the strongest and most economical railroad axle1 would be a wrought iron tube4 ,certainly a hollow axle is much stronger in resisting tension than a solid one containing the same amount of material4 ,,note #a4--,thomas ,thorneycroft1 of ,wolverhampton1 ,england1 an educated man1 and a manufacturer of railway axles1 observes3--,that the various forms of axles1 as generally made1 possess within themselves the elements of destruction4 ,that there are certain fixed principles to be observed in proportioning axles1 and that just as such principles are departed from1 just so much is liability to failure increased4 ,he says3--,it is doubtful whether the wheel is the support and the journal the loaded part1 or the reverse4 ,if the latter is the case1 then the cone of the wheels causes a lateral strain1 tending to bend the axle2 and should that bending extend no further than one half of the elastic limit1 if long continued1 fracture must result2 and should the elastic limit be exceeded1 the plane of the wheel will be removed from that in which it ought to revolve4 ,the object of the first experiment was to determine the effect of the form of the longitudinal section of the axle upon its elastic limit4 ,by reducing the diameter of the axle from #de_/af inches at centre1 to #c inches2 the limit of elasticity was reduced from 4#cdc to 4#bcb inches2 and the load1 to produce that elasticity1 from fourteen to seven tons4 ,experiment second was to ascertain the effect of a reduction of diameter at the centre1 upon the ability to resist sudden shocks4 ,one half of the axle was made #d inches in diameter from middle to end1 and the other half was reduced from #d to four inches at centre4 ,the wheel being fixed1 and a ram allowed to fall upon the journal1 when the following result was obtained4 ,under forty-six blows1 the unreduced end was bent to an angle of eighteen degrees4 ,under sixteen blows1 the reduced end was bent to twenty-two degrees4 ,experiment third was to ascertain the effect of a shoulder behind the wheel1 one end being turned with a shoulder of one eighth of an inch1 as a stop to the wheel1 the other end turned plain4 ,tested by hydraulic pressure1 the shouldered end broke with sixty tons1 the plain end with eighty-four tons4 ,the object of the fourth experiment was to find the influence of the position of the wheel1 as regards the end of the journal4 ,an axle was fastened into a cast-iron frame1 in a line with the neck of the journal1 when the latter was broke with seven blows of a ram falling ten feet4 ,the other end was keyed into the frame1 with the neck of the journal projecting #a inch1 and broke at the twenty-fourth blow of the same ram1 falling ten feet4 ,the results of the trials are thus summed up by the experimenter3--,that axles should never be smaller at the centre than at the ends1 but on the contrary1 that if a difference in size is made1 the centre should be the largest4 ,the best authorities on the strength of materials1 give the hollow tube as three times stronger in resisting twisting1 than the solid bar possessing the same weight4 ,thus an axle with an external diameter of five inches1 and an internal diameter of #c inches1 is three times as strong as a solid axle of #c inches diameter4 99 99 99 99 99 ,,note #b4--,the following experiments were prepared by ,m4 ,bourville1 and executed by the ,austrian government4 ,the apparatus consisted of a bent axle1 which was firmly fixed up to the elbow in timber1 and which was subjected to torsion by means of a cog-wheel connected with the end of the horizontal part4 ,at each turn the angle of torsion was twenty-four degrees4 ,a shock was produced each time that the bar left one tooth to be raised by the next4 ,an index adapted to the apparatus1 indicated the number of revolutions and shocks4 ,seven axles1 submitted to this trial1 presented the following results3-- #ast4 ,the movement lasted one hour2 #aj1hjj revolutions and #cb1djj shocks were produced4 ,the axle1 two and six tenths inches in diameter1 was taken from the machine and broken by an hydraulic press4 ,no change in the texture of the iron was visible4 #b;d4 ,a new axle1 having been tried four hours1 sustained #abi1jjj torsions1 and was afterwards broken by means of an hydraulic press4 ,no alteration of the iron could be discovered1 by the naked eye1 on the surface of rupture2 but tried with a microscope1 the fibres appeared without adhesion1 like a bundle of needles4 #c;d4 ,a third axle was subjected1 during twelve hours1 to #chh1jjj torsions1 and broken in two4 ,a change in its texture1 and an increased size in the grain of the iron1 was observed by the naked eye4 #dth4 ,after one hundred and twenty hours1 and #c1hhh1jjj torsions1 the axle was broken in many places2 a considerable change in its texture was apparent1 which was more striking towards the centre2 the size of the grains diminished towards the extremities4 #eth4 ,an axle1 submitted to #bc1cbh1jjj torsions during seven hundred and twenty hours1 was completely changed in its texture2 the fracture in the middle was crystalline1 but not very scaly4 #fth4 ,after ten months1 during which the axle was submitted to #gh1gcb1jjj torsions and shocks1 fracture1 produced by an hydraulic press1 showed clearly an absolute transformation of the structure of the iron2 the surface of rupture was scaly like pewter4 #gth4 ,finally1 as a last trial1 an axle submitted to #abh1cjd1jjj torsions1 presented a surface of rupture like that in the preceding experiment4 ,the crystals were perfectly well defined1 the iron having lost every appearance of wrought iron4 ,,classification ,,of ,,cars4 #cgi4 ,railroad cars come under three general heads1 ,those for passenger transport1 ,those for freight traffic1 ,those for repairs of the road4 #chj4 ,the ,american passenger car consists of a body about fifty feet long1 ten feet wide1 and seven feet high1 containing seats for about sixty passengers1 being cushioned1 warmed1 lighted1 and ventilated4 ,except for emigrants1 second and third class cars are but little used in ,america4 ,house1 box1 or covered freight cars1 differ from the 8flat10 or platform car1 only in having a simple rectangular house1 about six feet high and nine feet wide1 built upon the floor4 ,this is used for the protection of such freight as will not bear exposure2 as furniture1 books1 dry goods1 hardware1 and small machinery4 ,carriages1 boxes1 bales1 masts1 lumber1 and fuel are carried by platform cars4 ,bulky machinery1 and first and second class freight too large for the box cars1 should be protected by tarpaulins4 #cha4 ,the general arrangement of wheels1 springs1 and brakes1 is the same for the several classes of cars1 the chief difference being in the ease of springs4 ,each car rests upon two 8trucks10 consisting of four1 six1 or eight wheels1 so connected by levers and springs1 as best to absorb shocks1 and connected with the body by a pin only1 by which the passage of curves is made quite easy4 ,cars used for the movement of earth are so arranged as to allow the body to be tipped up1 that the contents may be quickly 8dumped10 either at the sides1 ends1 or middle1 as desired4 #chb4 ,upon some roads1 a continuous draw bar is passed under the whole train1 the several cars being attached to it1 and to each other by safety chains only4 ,by adopting this1 and at the same time by springing the buffer beams tight upon each other1 the whole train becomes one piece2 and the jerks at stopping and at starting are in a great measure avoided4 ,as lightness combined with strength is a desideratum in all cases1 it will be found best to truss the longitudinal frame pieces of the car with rods1 rather than to use large and heavy beams1 as done by many builders4 ,,retarding ,,of ,,trains4 #chc4 ,as regards the mode of retarding trains of cars1 the practice of applying blocks to the wheels is justly considered by many as quite wrong4 ,the brake should be applied to the rail and not to the wheel4 ,blocks drawn against the wheel are supplied with friction by means of levers worked by a brakeman1 who can at pleasure cause the wheels to slide upon the rail4 ,a shoe1 sliding upon the rail1 may be supplied with friction from the whole weight of the car4 ,the retarding force should be applied at once to every car alike2 if too much in front1 the rear cars are driven against those in advance2 if too much behind1 the train is liable to break4 ,the proper place for the brakeman is upon the top of the train1 where all signals may be quickly seen4 ,,chapter ,,xv4 ,,stations4 ,,classification ,,of ,,buildings4 #chd4 ,the entire establishment of buildings for operating a railroad1 consists of the ,terminal1,passenger1,stations4 ,freight1 ,way1,passenger1,stations4 ,freight1 ,engine houses4 ,repair shops1 7for engines74 ,repair shops1 7for cars74 ,wood sheds4 ,water tanks4 ,and appertaining to these1 scales for the weighing of cars and freight2 turntables1 transfer tables1 switch and gate houses4 ,,location ,,of ,,buildings4 #che4 ,the location of the several buildings mentioned above will depend upon the situation of the terminus1 the character of the traffic1 and the number of trains arriving and departing4 ,,terminal ,,passenger ,,house4 #chf4 ,the passenger house should be at the most convenient point of access to the persons using it4 ,the freight buildings should be at the most convenient point for receiving1 shipping1 and distributing merchandise4 ,the engine and car houses1 with the shops for repair1 may be placed where the land is cheap1 and so distant from dwelling-houses as not to cause inconvenience to the inmates thereof by smoke and noise4 ,the wood sheds1 tanks1 turntables1 etc41 etc41 are generally at the engine houses2 weigh scales1 etc41 at the freight buildings4 #chg4 ,a railroad which connects the interior with a seaport1 would probably bring two classes of freight2 one for export and one for home consumption4 ,the first should be carried at once to the wharves and loaded into the ships with one transshipment2 while the second should be delivered as near as possible to the centre of home trade4 ,the departments of arrival and departure should be kept quite distinct1 when the amount of business transacted is considerable2 otherwise operating will become complicated4 ,the arrival part of a large passenger house requires a great number of doors1 that exit may be easy to the large number of passengers that arrive at once4 ,the departure rooms require few doors1 as departing passengers come singly or in small bodies4 ,thus1 in large cities the front of a long rectangle is given to departure1 while a long side1 communicating with an outside platform1 forms the arriving room4 ,one thing in particular ought to be looked to by ,american railroad companies1--the arrangement of public vehicles that shall secure travellers from the impositions and extortions of hack-drivers4 ,no person whatever should have access to any building except passengers and the railroad officials4 ,the places of the several carriages1 and the rates of pay for the same1 should be fixed by the company2 the fare being paid by checks bought by the traveller from a company agent at the station4 ,,terminal ,,freight ,,house4 #chh4 ,the terminal freight house should contain all of the apparatus necessary for receiving and embarking freight4 ,when the central part of the building is occupied by tracks1 and the sides by platforms1 the landing platform should incline gently from the car to the door2 and that for loading1 from the door to the car4 ,this arrangement facilitates the handling of freight4 ,the interior of the building may be divided into departments1 either according to the destination or the class of the freight4 ,,engine ,,house ,,and ,,appurtenances4 #chi4 ,a terminal engine house1 with a table in the centre1 to contain #aj engines1 must be #ade feet in diameter4 #ae engines1 must be #aej feet in diameter4 #bj engines1 must be #afg feet in diameter4 #be engines1 must be #ahc feet in diameter4 #cj engines1 must be #bjj feet in diameter4 #ce engines1 must be #bag feet in diameter4 #dj engines1 must be #bcc feet in diameter4 #de engines1 must be #bej feet in diameter4 #ej engines1 must be #bfg feet in diameter4 ,the diameter of the table being forty-five feet1 and the engine occupying1 when off from the table1 fifty feet4 ,again1 thirty-two engines would require a diameter of 7#cb #aj7_/c4adaf 7#b #ej7 #bjb nearly4 ,the engines within the house may be supplied with water from small tanks between each alternate pair of pits1 7each tank holding five thousand gallons17 or the entire building may be furnished from a cast-iron pipe running around the whole1 and being in connection with a large tank4 ,in such pipe there should be a gate over the centre of each pit1 and near its upper end4 ,it may be convenient to connect all to a series of small tanks1 by a pipe1 that the water level may be kept nearly constant4 ,repair shops for engines and for cars1 may be plain1 rectangular buildings1 so arranged as to accommodate the necessary machinery4 ,turntables consist of simply a circular framework of wood or iron1 placed at the centre upon a solid iron pintle which bears the whole weight1 and guided at the circumference by a series of fifteen1 eighteen1 or twenty wheels fourteen or fifteen inches in diameter4 ,the wheels are placed in an independent spider frame1 and run upon a curved rail placed on the bottom masonry1 and the table runs upon the top of the wheels1 so that the motion of the circumference of the table is double that of the wheels4 ,the frame consists1 first1 of a pair of timbers ten or twelve inches wide and fifteen or sixteen inches deep1 upon which the rails are placed1 strongly trussed so as to throw the load upon the centre4 ,at right angles to these are placed1 at a distance of eight or ten feet1 timbers #e #aj1 also trussed1 which serve to connect the load more completely with the wheels4 ,the whole is stiffened by diagonal bracing1 and is strongly floored4 ,the table is turned by a pinion upon itself1 working into a rack fastened to the foundation or to the side masonry4 ,the trusses1 as also the centre bearing1 should be capable of adjustment vertically4 ,the cost of the table1 exclusive of masonry1 is from #a1bjj to #a1hjj4 ,weigh scales are made similar to1 but stronger than1 the ordinary hay-scales1 being rigid and strong enough to bear the weight of a locomotive4 ,every car 7freight7 placed upon the road should have the number and the exact weight painted upon it in some conspicuous place1 so that the contained load may1 at any time1 be found by placing the car upon the scale4 ,,wood ,,shed ,,and ,,tank4 ,at way stations the freight and passenger houses1 wood and water station1 may all be combined2 the plan and size depending upon the location and importance of the station4 ,the relative position of the tank1 wood shed1 and passenger house should be such that when the tender is at the proper place for receiving its supplies the centre of a passenger train of ordinary length shall be at the passenger door4 ,,of ,,the ,,water ,,supply4 #cij4 ,the number of engines leaving the terminus of a road determines the amount of water necessary at the principal stations2 and the character of the road and of the traffic fixes the location and size of the way water stations4 ,the amount of traffic being pretty equally distributed over the length of the road1 the tanks should be placed at equal equated distances2 thus the engines will need to water at closer points upon steep grades than upon level roads4 ,generally1 however1 the water is taken where it can be got1 the location of streams and springs fixing the place4 ,steam1 hydraulic1 wind1 human1 or animal power may be employed to raise the water to the tank4 ,oftentimes high springs will fill the tanks without the application of artificial power4 ,as we find the liquid water in nature it is more or less impregnated with vegetable1 gaseous1 and saline matter1 which often impairs its fitness for mechanical purposes4 ,these admixtures are derived from the rocks and ground over or through which the water flows4 ,the incrustations which form in boilers are caused by the precipitation of the impurities in consequence of the concentration of water in the boiler4 ,they may be effectually removed1 no matter what their nature1 by boiling charcoal in the water4 ,if the water1 previous to filtration1 can be heated1 to expel all the air and carbonic acid gas1 which is often the solvent of the foreign matter1 the filtering process will be accelerated1 and will be more effectual4 ,rain water is more pure than any other2 practically1 perfectly so4 ,river water comes next to it4 ,spring water is generally adulterated with basic salts in various forms1 most of which may be precipitated by gently heating and filtering through charcoal4 #cia4 ,fig4 #aeg shows a convenient form for a tank house1 with pump and heater4 ,illustration3 ,fig4 #aeg4 ,a shows half interior section of the tank4 ,b1 half elevation of tank4 ,c1 pump2 ,c1 supply pipe2 d1 suction pipe and strainer4 ,e1 heater4 e1 the short1 and h1 the long pipe4 ,h1 the discharge pipe4 ,g1 discharge valve4 ,i1 counter weight for discharge pipe4 ,k1 wheel for weight rope4 ,l1 scale showing amount of water in the tank4 ,the heater shown in the cut is made of a coil of two inch pipe of iron4 ,the short pipe descends from within six inches of the bottom of the tank to within two or three feet of the floor2 then bending four or five times around spirally1 turns up through the centre of the coil1 and runs three or four feet into the tank4 ,a small grate is placed in the lower part of the coil1 and the whole apparatus is cased in sheet iron4 ,by such an arrangement of pipe1 circulation is obtained1 and the water in the tank is kept quite warm4 ,the following rules and tables may be found convenient4 #cib4 ,the velocity of water in any pipe necessary to discharge a given quantity1 in a fixed time1 is expressed by 7#add;,c7_/a4 ,where ,c is the number of cubic feet per hour1 and a the area of the pipe4 #cic4 ,the head necessary to send water through a given length of pipe1 of any diameter1 is shown by the formula ,c_/7,d ,c7 ,h4 ,where ,c a constant4 ,c constant for diameter of pipe4 ,d diameter of pipe4 ,h heads required4 ,the experimental values of ,c and ,c are as follows3 ,let ,v equal the velocity in feet per minute1 and we have ,v4 ,c4 #fj #h4fb #gj #aa4dj #hj #ad4eh #ij #ag4ie #ajj #ba4ef #abj #bi4gj #adj #ch4ij #aej #dd4jj #ahj #fb4ac ,also1 the values of ,c are ,diameter of pipe4 ,c4 #b 4#jjj #c 4#jjf #d 4#jbh #e 4#jec #f 4#jgh #g 4#ajd #h 4#acd ,,example ,,of ,,use ,,of ,,preceding ,,rules4 ,required the head of water necessary to send #a1ccc cubic feet of water1 or #aj1jjj gallons per hour1 through an eight inch pipe one thousand feet long4 ,the velocity by rule one will be 7#accc #add7_/7hb 4#ghed7 #chah feet per hour1 or #fd feet per minute4 ,by rule two 7the value of ,c for #fj being #h4fb1 and for #gj #aa4dj1 that for #fd is #aj nearly71 we have #aj_/7h #j4acd7 #a4bc1 which multiplied by ten 7the number of times that one hundred is contained in one thousand feet1 the distance71 gives the result1 twelve inches or one foot1 which is the required head2 and if the entrance to the tank is twenty feet high1 we have1 as the necessary head1 #bj #a #ba feet4 #cid4 ,the formula expressing the power of an engine to raise a given amount of water is 7,,wv7_/#ccjjj4 ,where ,w is the weight of a column of water1 and ,v the velocity in feet per minute2 also #cc1jjj the expression of a horse-power4 ,for example1 how many horse-power must an engine possess to raise one thousand cubic feet of water per hour through a six inch pipe fifty feet high8 ,the velocity will be 7#ajjj #add7_/7fb #j4ghed7 #ejic feet per hour1 or eighty-five feet per minute4 ,the weight of a column of water fifty feet high and six inches in diameter is 7#fb #j4ghed #ej #ab7_/agbh #fb #fac4f lbs4 ,also1 7#fab #hc7_/ccjjj #a horse-power nearly4 #cie4 ,among the pumps now in use for raising water at railroad stations are ,carpenter's rotary1 ,worthington's1 ,mc,gowan's1 and that of ,messrs4 ,perkins and ,bishop1 either of which answers every purpose4 #cif4 ,,table ,,showing ,,the ,,weight ,,and ,,cost ,,per ,,foot ,,of ,,cast-,,iron ,,pipe4 ,diameter of ,thickness of ,weight of pipe ,cost of pipe bore4 metal4 per lineal foot4 per lineal foot4 ,inches4 ,inches4 ,lbs4 ,cents4 #a #c4jf #ae #a #c4fg #ah #a #d4bi #ba #a #g4ha #ci #b #h4gc #dd #b #i4fe #dh #b #ad4gj #gc #b #ae4ic #hj #c #ag4ae #hf ,the weight of a cubic foot of cast-iron being #dej lbs41 and the price being five cents per lb4 ,,table ,,showing ,,the ,,capacity ,,of ,mc,g,o,w,a,n',s ,,double ,,acting ,,pumps4 ,time required to ,explanation4 ,no4 #a4 ,no4 #b4 fill a #ffjj gallons tank4 ,stroke in inches1 #e #h ,hours4 ,diameter of plunger1 #b #c ,area of plunger1 #e4bgh in4 #g4gj in4 ,small ,large ,cube of half stroke in #j4aad #j4bhcpump1 ,no4pump1 ,no4 gallons1 #a4 #b4 ,discharge ,at #aj ,full #acf4h #cci4f #di #ai in ,at #bj strokes #bgc4f #fgi4b #bd #aj gallons ,at #cj per #daj4d #ajah4h #af #g per hour4 ,at #dj minute4 #edg4b #aceh4d #ab #e ,at #ej #fhd4j #afih4j #aj #d ,at #fj #hbj4h #bjcg4f #h #c ,at #gj #ieg4f #bcgg4b #g #c ,at #hj #ajid4d #bgaf4h #f #b ,at #ij #abca4b #cjeh4d #e #b ,at #ajj #acfh4j #ccif4j #e #b ,,chapter ,,xvi4 ,,management4 ,all that is required to render the efforts of railroad companies in every respect equal to that of individuals1 is a rigid system of personal accountability through every grade of service4--,d4 ,c4 ,mc,callum4 ,,organization ,,of ,,employees4 #cig4 ,railroad management may be divided into two grand departments1-- ,financial management4 ,operating management4 ,the first of these does not properly come into a work of the present kind4 ,it embraces the entire system of accounts4 ,its officers are a president1 secretary1 treasurer1 attorney1 and directors4 #cih4 ,the operating management is subdivided as follows3-- ,the mercantile department4 ,the mechanical department4 ,the first embracing every thing relating to the adjusting of tariffs1 the transport of passengers and freight1 the embarking and delivering of goods1 and the weighing and measuring1 ticket and receiving offices1 steamboat1 stage1 and railroad connections4 ,the second1 the maintaining the road-bed1 superstructure1 bridging1 masonry1 buildings1 and fixed stock in working order2 making all repairs1 renewals1 enlargements1 and alterations1 and the purchase1 inspection1 maintaining1 and operating of the rolling stock4 ,these departments are again divided and subdivided until we come to the minutest details4 ,,note4--,that part of ,chapter ,,xvi4 in italics is extracted1 by permission1 from the elaborate ,report of ,d4 ,c4 ,mc,callum to the stockholders of the ,new ,york and ,erie ,railroad1 7,march #be1 #ahef74 #cii4 ,the following general principles govern the formation of an efficient system of operations4 ,first4 ,a proper division of responsibilities4 ,second4 ,sufficient power conferred to enable the same to be fully carried out1 that such responsibilities may be real in their character4 ,third4 ,the means of knowing whether such responsibilities are faithfully executed4 ,fourth4 ,great promptness in the report of all derelictions of duty1 that evils may at once be corrected4 ,fifth4 ,such information to be obtained through a system of daily reports and checks that will not embarrass principal officers nor lessen their influence with their subordinates4 ,sixth4 ,the adoption of a system1 as a whole1 which will not only enable the general superintendent to detect errors immediately1 but will also point out the delinquent4 #djj4 ,a system of operations to be efficient and successful should be such as to give to the principal and responsible head of the running department a complete daily history of details in all their minuti4 ,without such supervision the procurement of a satisfactory annual statement must be regarded as extremely problematical4 ,the fact that dividends are made without such control does not disprove the position1 as in many cases the extraordinarily remunerative nature of an enterprise may insure satisfactory returns under the most loose and inefficient management4 ,all subordinates should be accountable to1 and directed by1 their immediate superiors only4 ,each officer must have authority1 with the approval of the general superintendent1 to appoint all persons for whose acts he is held responsible1 and to dismiss any subordinate when in his judgment the interests of the company demand it4 #dja4 ,the following table shows the rate and direction of subordination for a first class railroad3-- ,section men4 ,superintendent ,road-master4,section men4 of ,road4 ,road-master4,section men4 ,section men4 ,foreman ,machine shop1 ,machinists4 ,foreman ,blacksmith shop1 ,blacksmiths4 ,superintendent ,foreman ,car shop1 ,carpenters1 of ,machinery4 ,foreman ,paint shop1 ,painters4 ,engineers 7not on trains71 ,firemen4 ,car-masters1 ,oil men and cleaners4 ,conductors ,brakemen4 ,mail agents4 ,engineers 7on trains74 ,ticket collectors4 ,general ,superintendent,general passenger,station agents4,hackmen4 agent4 ,switchmen4 ,express agents4 ,police4 ,conductors4 ,brakemen4 ,engineers 7on trains74 ,general freight ,station agent4 agent4 ,weighers4 ,gaugers4 ,yard-masters4 ,supply agent4 ,clerks1 ,teamsters furnishing supplies4 ,fuel agent4 ,all men employed about the wood sheds4 ,,duties ,,of ,,employees4 #djb4 ,the ,general ,superintendent has entire control of all of the heads of departments2 he issues his orders to the heads only1 and is the main agent for transferring the resolves of the directors to the operating department1 and the channel through which the reports of the departments go to the directory4 ,the ,superintendent of the ,road has complete charge of the road-bed1 superstructure1 bridging1 masonry1 and buildings2 also all removals1 enlargements1 and alterations4 ,he should be a thorough civil engineer1 able in every respect to build a railroad from beginning to end4 ,the ,superintendent of ,machinery has charge of the purchase1 inspection1 repair1 and operating of all of the rolling and fixed machinery1 of shops1 engine houses1 turntables1 tanks1 and weigh scales4 ,he is responsible for the good condition1 proper adaptation and efficiency of the entire equipment of engines and cars4 ,the ,general ,passenger ,agent fixes1 under the direction of the president and general superintendent1 the prices of passenger transportation1 has charge of all conductors1 ticket sellers1 station police1 mail and express agents1 of stage1 steamboat1 and railroad connections1 and of all operations incident to transporting passengers4 ,the ,general ,freight ,agent has charge of all persons occupied at all of the stations in forwarding and receiving merchandise1 in measuring and weighing1 in receiving money1 and bookkeeping1 station agents1 and train hands4 ,he makes and regulates1 with the approval of the president and general superintendent1 the tariff for freights2 contracts with connecting roads1 and insures the benefits of such agreements1 examines all claims for damages to freight1 and sees that such are properly settled4 ,the ,agent for ,wood contracts1 with the approval of the general superintendent1 for the supply of the necessary amount of fuel2 attends the measurement1 inspection1 and delivery at the proper places2 registers each month the amount of fuel supplied and used1 and the location and amount on hand4 ,the ,supply ,agent has charge of the supply of all materials in use in all departments2 iron1 timber1 engines1 rails1 bridges1 and every thing in use upon the road2 charging each department with its correct quantity and quality of material received4 ,road-masters will have charge1 under the superintendent of the road1 of the maintenance of the road-bed and superstructure of divisions of from twenty-five to fifty miles in length1 depending upon the care that the road-way may need4 ,they will have charge of gravel trains1 and of wood trains1 which run under the orders of the superintendent of the road4 ,they should pass over their divisions at least once per day4 ,under them are placed section men1 having care of ten miles each1 being supplied with the proper tools and signals4 ,they must pass over their respective sections at least once per day in a hand car4 ,they should see that every switch1 frog1 chair1 and rail on their section is in proper order1 and report at once any defects1 which cannot be remedied by them1 in the track1 to the road-master4 ,engineers are subject to the superintendent of machinery when off1 and to the conductor when on1 the trains4 ,none but a man well acquainted with the details of machinery1 and who has served in a locomotive machine shop1 and is in every respect temperate and steady1 should fill this berth4 ,foremen of the blacksmith1 machine1 carpenter1 and car shops1 are subject to the superintendent of machinery1 and have charge of the repairs and cleaning of the engines1 cars1 and other machinery4 ,car-masters have charge of the men employed in cleaning1 oiling1 and examining the cars and their wheels4 ,the cars should be thoroughly examined at the end of each trip1 and at each stop1 by an inspector who accompanies the train and looks to the wheels1 axles1 boxes1 and brakes4 ,conductors4--,a conductor of a train should be a machinist1 a prompt1 active man1 who should station himself on the top of the cars in such a position as to see the whole train1 and able at any moment to communicate with the engineer4 ,he should direct the running of the train1 and control the engineer and the person who takes the fares4 ,the latter should confine himself to the inside of the cars4 ,,number ,,of ,,trains ,,to ,,be ,,used4 #djc4 ,this is determined by the quantity and quality of the material to be transported1 and by the character of the road4 ,the train should not be so heavy as to be beyond the power of the engines upon the steepest grades1 nor so light as to increase unnecessarily the number4 ,a road doing a large passenger business must accommodate the public as far as possible as regards the time of departure and arrival1 and the connections with other roads4 ,a freight road must regard more the character of the road4 ,some classes of freight 7ice1 beef1 etc47 do not admit of delay4 ,as we increase the number of trains1 the ratio of time employed in actual work to the whole train under steam is decreased1 as there must be much time lost on sidings in waiting for trains to pass4 ,liability to accidents is also incurred4 ,commercial circumstances1 more than any other1 will determine the proper number and class of trains4 ,,amount ,,of ,,service ,,of ,,engines4 #djd4 ,this is much less than is generally supposed4 ,the number of engines required to perform any amount of work is considerably greater than the number actually in motion1 because of liability to accident1 time required for cleaning and repair4 ,the ,new ,york ,state ,engineer's ,report for #ahed gives1 as the number of engines on #b1ejj miles1 #ffh1 or one engine per #c miles4 ,also1 #ffh engines run per annum #aa1cic1jjj miles1 or #ag1jee miles per annum per engine2 thus requiring 4#jjjjehfc of an engine per mile run per annum4 ,this is very nearly fifty-five miles per day1 7#cac days per annum74 ,also1 #ifh_/bejj gives #bg_/ajj of an engine per mile of road1 and the same report gives the following3-- ,one locomotive for #c miles of road4 ,one passenger car for #b miles of road4 ,one freight car for #cb_/ajj miles of road4 ,or each mile needs #bg_/ajj of a locomotive4 #dj_/ajj of a passenger car4 #c freight cars4 ,or to one engine #gha_/ajj passenger cars1 and #ajgb_/ajj freight cars4 ,from ,lardner's ,railway ,economy it appears that the average daily run of an engine is forty-two miles1 or seventy-five miles per day1 working four days in the week4 ,that the daily service is two hours working1 and three and three quarters hours standing with steam up4 ,the maximum annual mileage mentioned by ,lardner is that upon the ,belgium lines1 and was #ba1gcg4 ,the maximum in ,america has been1 as far as we have been able to ascertain1 #bb1jjj1 and this for eighteen years4 ,,note #a4--,two little eight ton1 four wheeled1 ,stephenson engines1 cylinders #aj #af1 four and a half feet drivers1 inside connection1 copper fire-boxes1 have averaged #bb1jjj miles per annum1 with trains weighing forty tons exclusive of engine and tender1 for eighteen years1 costing about #gjj per annum each for repairs1 or #c4ah cents per mile run1 upon the ,bangor and ,oldtown ,railroad 7,maine74 ,,note #b4--;,in the ,report of the ,railroad ,commissioners of the ,state of ,new ,york for the year ending ,september #cj1 #ahee1 is the following3-- ,one engine is required for each three and a half miles2 or one engine in constant use for five and a quarter miles4 ,the average run per annum by each engine in actual use is #bb1hbc miles2 or #af1cjb to all of the engines4 ,also1 as regards the work done by cars4 ,effective in ,miles per car4 ,distance run per constant use4 annum per car4 ,passenger1 #fej #d #de4abf ,baggage1 #bdf #aa ---- ,freight1 #gejj #j4ce #aa4igj the number of miles being #b1fae4 ,,expenses1 ,,receipts1 ,,profits4 ,,expenses4 #dje4 ,american railroad reports as a general thing do not analyze the cost of working4 ,the gross expense is given1 and in some cases is primarily divided4 ,besides the retrospective use of a minute division of expenses1 which enables us to see what system is the most economical1 there is a prospective use1 namely1 the formation of estimates for future operations and a correct base for establishing tariffs4 ,if the circumstances of the traffic remain the same1 an estimate of what the cost will be at any time is easy2 but if they change1 the data for the estimate change also4 ,that we may at all times possess these data1 we should know every year just the cost of working each article of traffic4 ,it is not enough that the gross receipt exceeds the whole expense2 even then the road may be working unprofitably4 ,unless each item of transport pays for itself1 we are taxing unjustly some other item1 7except1 indeed1 in such cases as adopting low rates in order to fill trains running in one direction which would otherwise run empty74 ,an analysis of cost will also show whether or not it is best to attract an increased amount of business by a reduction of rates4 #djf4 ,the whole cost of operating and of maintaining a railroad may be generally and specially divided as follows3-- ,cost of ,road-bed4 ,cost of ,superstructure4 7,a7 ,interest on construction and equipment ,cost of ,buildings4 capital4 ,cost of ,engines4 ,cost of ,cars4 ,fixed machinery4 ,road-bed4 ,material4 ,labor4 7,b7 ,maintenance of way and works4 ,buildings4 ,material4 ,labor4 ,superstructure4 ,material4 ,labor4 ,fuel1 oil1 and ,working4 waste4 ,passenger4 ,salaries4 ,maintaining4 ,material4 ,labor4 ,locomotives4 ,fuel1 oil1 and ,working4 waste4 ,freight4 ,salaries4 ,maintaining4 ,material4 ,labor4 7,c7 ,maintenance of the fixed and ,warming1 rolling stock4 ,working4 lighting1 and cleaning4 ,passenger4 ,oil and waste4 ,cars4 ,maintaining4 ,material and labor4 ,working4 ,oil and waste4 ,freight4 ,maintaining4 ,material and labor4 ,fixed ,in shops4 ,machinery4 ,oil and waste4 machinery4 ,on road4 ,tanks and ,materials and tables4 labor4 ,conductors4 ,ticket ,sellers4 ,passenger4 ,clerks4 ,brakemen4 7,d7 ,salaries of hands employed in ,porters4 and about trains4 ,conductors4 ,freight4 ,station agents4 ,brakemen4 ,weighers and gaugers4 ,passenger4 ,warming and lighting4 ,police4 7,e7 ,station expenses4 ,freight4 ,warming and lighting4 ,police4 ,salaries4 ,travelling expenses4 7,f7 ,general superintendence4 ,office expenses4 ,stationery4 ,advertising1 c41 c4 ,the actual general division of the operating expenses upon the ,new ,york ,state system of roads was1 for #ahed1 as follows4 7,see ,state ,engineer's ,report74 ,way and works1 #a1abc dollars per mile of road4 ,machinery1 #b1jgb dollars per mile of road4 ,salaries on and about trains1 #fdj dollars per mile of road4 ,stations1 #cj dollars per mile of road4 ,general superintendence1 #ccc dollars per mile of road4 ---------- ,total1 #d1aih dollars per mile of road4 ,that the detailed expenses may be charged to the proper departments1 and that we may be able to take out the exact cost of working any one class of trains1 or of carrying any article of transport1 the following form should be filled4 #djg4 ,,table ,,showing ,,the ,,general ,,and ,,detailed ,,expenses ,,of ,,working ,,and ,,maintaining ,,the ,,railroads ,,of ,,new ,,york ,,state1 ,,for #ahed1 ,,and ,,the ,,new ,,york ,,and ,,erie ,,railroad ,,for ,,the ,,year ,,ending ,,september #cj1 #ahee4 ,,way ,,and ,,works4 ,nature of the item is shown ,road-bed4,superstructure4,buildings4,to tal4 in horizontal columns4 ,name of railroad4 ,cost1 in dollars1 per mile1 #cea #adj #bb;,f4 #eac upon ,n4 ,y4 ,state ,railroads #dec #hh #bg,p4 #efh ,cost in cents1 per ton1 or per ,f4 passenger 4#jbj 4#afa 4#jaj 4#aia per mile run1 ,n4 ,y4 and ,erie ,railroad4 4#jce 4#bjg 4#jaa ,p4 4#bec ,,notes4 #djg4 ,,table ,,showing ,,the ,,general ,,and ,,detailed ,,expenses ,,of ,,working ,,and ,,maintaining ,,the ,,railroads ,,of ,,new ,,york ,,state1 ,,for #ahed1 ,,and ,,the ,,new ,,york ,,and ,,erie ,,railroad ,,for ,,the ,,year ,,ending ,,september #cj1 #ahee4 ,,locomotive ,,engines1 ,,cars1 ,,and ,,fixed ,,machinery4 ,nature of the item is shown ,,locomotive ,,engines4 in horizontal columns4 ,passenger ,locomotives4 ,name of ,oil railroad4 ,fuel4 and ,salaries,whole4,repairs4,total4 waste4 ,cost1 in dollars1 per mile1 upon ,n4 ,y4 ,state ,railroads #cie #ej #adj #ehe #bcg #hbb ,cost in cents1 per ton1 or per passenger per mile run1 ,n4 ,y4 and ,erie ,railroad4 4#aeg 4#jba 4#ajg 4#bhe 4#aji 4#cid ,,recapitulation4 #djg4 ,,table ,,showing ,,the ,,general ,,and ,,detailed ,,expenses ,,of ,,working ,,and ,,maintaining ,,the ,,railroads ,,of ,,new ,,york ,,state1 ,,for #ahed1 ,,and ,,the ,,new ,,york ,,and ,,erie ,,railroad ,,for ,,the ,,year ,,ending ,,september #cj1 #ahee4 ,,locomotive ,,engines1 ,,cars1 ,,and ,,fixed ,,machinery4 ,nature of the item is shown ,,locomotive ,,engines4 in horizontal columns4 ,total ,freight ,locomotives4 cost4 ,name of ,oil railroad4 ,fuel4 and ,salaries4,whole4,repairs4,total4 waste4 ,cost1 in dollars1 per mile1 upon ,n4 ,y4 ,state ,railroads #bjb #ca #abb #cee #aia #edf #acfh ,cost in cents1 per ton1 or per passenger per mile run1 ,n4 ,y4 and ,erie ,railroad4 4#bje 4#jah 4#jhj 4#cjc 4#jha 4#chd 4#ggh #djg4 ,,table ,,showing ,,the ,,general ,,and ,,detailed ,,expenses ,,of ,,working ,,and ,,maintaining ,,the ,,railroads ,,of ,,new ,,york ,,state1 ,,for #ahed1 ,,and ,,the ,,new ,,york ,,and ,,erie ,,railroad ,,for ,,the ,,year ,,ending ,,september #cj1 #ahee4 ,,locomotive ,,engines1 ,,cars1 ,,and ,,fixed ,,machinery4 ,nature of the item is shown ,,cars4 in horizontal columns4 ,passenger cars4 ,name of railroad4 ,operating4,maintaining4,total4 ,cost1 in dollars1 per mile1 upon ,n4 ,y4 ,state ,railroads #ej #ade #aie ,cost in cents1 per ton1 or per passenger per mile run1 ,n4 ,y4 and ,erie ,railroad4 4#jbj 4#jgi 4#jii ,,summary4 #djg4 ,,table ,,showing ,,the ,,general ,,and ,,detailed ,,expenses ,,of ,,working ,,and ,,maintaining ,,the ,,railroads ,,of ,,new ,,york ,,state1 ,,for #ahed1 ,,and ,,the ,,new ,,york ,,and ,,erie ,,railroad ,,for ,,the ,,year ,,ending ,,september #cj1 #ahee4 ,,locomotive ,,engines1 ,,cars1 ,,and ,,fixed ,,machinery4 ,nature of ,whole the item cost of is shown ,,cars4 ,,fixed machinery in ,,machinery4oiling on horizontal the road4 columns4 ,total ,repairs1 cost oil and ,freight ,cars4 of waste1 cars4 labor1 and machinery4 ,name of railroad4 ,operating4,maintaining4,total4 ,cost1 in dollars1 per mile1 #dd ,f4 #hda upon ,n4 ,y4 ,state ,railroads #de #bjf #bea #ddf #ee ,p4 #ajgb ,cost in cents1 per ton1 or per passenger 4#jae ,f4 4#dff per mile run1 ,n4 ,y4 and ,erie ,railroad4 4#jbb 4#jde 4#jfg 4#aff 4#jah ,p4 4#eaa #djg4 ,,table ,,showing ,,the ,,general ,,and ,,detailed ,,expenses ,,of ,,working ,,and ,,maintaining ,,the ,,railroads ,,of ,,new ,,york ,,state1 ,,for #ahed1 ,,and ,,the ,,new ,,york ,,and ,,erie ,,railroad ,,for ,,the ,,year ,,ending ,,september #cj1 #ahee4 ,salaries of ,station employees ,general ,grand expenses4 in and superintendence4 ,total4 about trains4 ,cost per ,nature of ,repairs ,conductors4 ,stationery4 passenger the item and ,brakemen4 ,salaries4 or per is shown material4 ,weighing4 ,offices4 ton1 per in ,warming ,loading4 ,travelling4 mile run1 horizontal and ,porters4 ,advertising4 or cost columns4 lighting4 ,watchmen4 ,agencies4 per mile of road4 ,name of railroad4 ,cost1 in dollars1 per mile1 -- #cga #ahj #aije upon ,n4 ,y4 ,state ,railroads -- #bdf #agj #bjef ,cost in cents1 per ton1 or per passenger 4#jbc 4#bdj 4#jde 4#ife per mile run1 ,n4 ,y4 and ,erie ,railroad4 4#jbf 4#aei 4#jec #a4jjb ,,deductions4 #djh4 ,the following general measures are recommended by ,lardner in his ,railway ,economy1 as being the means of obtaining increased economy in the working of railroads4 #ast4 ,so to manage the traffic as to cause the cars to carry more complete loads4 #b;d4 ,to encourage the transport to long distances4 #c;d4 ,to regulate the tariff so as to give the largest possible number of cars to each engine4 #dth4 ,to adjust the tariffs where the business is chiefly in one direction1 so as to attract return traffic1 that the cars may not run without a load4 #eth4 ,not to increase the number of trains beyond a reasonable accommodation of traffic4 #fth4 ,to diminish as far as possible express trains1 if it be not practicable to abolish them altogether4 ,,receipts ,,and ,,profits4 #dji4 ,the distribution of expenses1 as we have seen1 is somewhat complicated1 and is systematically done upon a very few roads4 ,the classification of receipts is1 however1 very easy1 and is properly detailed in nearly all railroad reports4 ,upon the ,new ,york ,state railroads1 the following was the division for the year #ahed4 ,average receipts per mile of road1 ,passengers1 #d1jgd4af ,freight1 #c1ggf4gb ,extras1 #dbg4bh ------------------ ,whole1 #h1bgh4af ,whole expense1 #d1gaj4ad or fifty-seven per cent4 of the receipts4 ,receipts per mile run by trains1 ,passengers1 #a4cb ,freight1 #b4jb ,extras1 #a4fg ---------- ,whole1 #e4ja ---------- ,average1 #a4fg ---------- ,whole expense per mile run by train1 #j4ig ,average receipts per passenger and per ton1 per mile1 ,passenger1 #a4ie cents1 ,ton1 #b4gi cents1 -------- ,average of passenger or ton1 #b4cg cents1 -------- ,average expense of passenger or ton1 #a4ch cents1 #daj4 ,upon the ,new ,york and ,erie ,railroad for the year ending ,september #cj1 #ahef4 ,receipts per mile of road1 ,passengers1 #c1cig4cd ,freight1 #g1adc4db ,express and mail1 #cig4hd -------------------- ,whole1 #aj1ich4fj ,whole expense per mile of road1 #e1bfc4jj or forty-eight per cent1 of the receipts4 ,receipts per mile run by trains1 ,passengers1 #a4af ,freight1 #b4ac ,average receipts per passenger and per ton1 per mile1 ,passenger1 #b4jb cents1 ,ton1 #b4cg cents4 #daa4 ,upon the ,new ,york ,state roads1 ,average number of passengers per mile run1 #eg4d ,average distance travelled by passengers1 #ha4d ,average tons per mile run1 #ij4j ,average distance1 whole number of tons carried1 #agg4j ,length1 #dif miles1 ,freight tonnage1 #aej1fgc1iig miles1 ,passenger1 #hd1jfi1cih miles4 #dab4 ,it is of course an object on every railroad to make the gross receipts overbalance the gross expense by the largest possible amount4 ,the elements which determine the gross receipts are1 ,the charge per mile1 for transport1 ,the number of units transported1 ,the distance carried1 of which the company's directors can control the first only1 except as adjustment of rates may attract business4 ,reduction of tariff1 to a certain degree1 has the effect of increasing the receipts by augmenting the number of fares2 but the reduction may be carried too far4 ,so1 also1 for a certain distance1 increased rates will increase the whole receipts2 but in this case1 also1 the extreme must be avoided4 ,the point to be arrived at is1 evidently1 that at which the difference of expense and receipt is the greatest1 and this is not necessarily when receipts are the greatest4 ,we can make the receipts nothing either by making the charges so large that nothing can bear them1 or so small as to vanish4 ,even when the receipts are #j1 we still have the expense of moving the empties4 ,by forming a table in which one column shall show the different charges1 and the second the corresponding amounts transferred1 with the consequent receipts and cost of working1 we shall find which rate of charge will give the greatest difference between expense and receipt4 ,,express ,,trains4 #dac4 ,express trains are a source of vast expense1 directly and indirectly1 which can never be repaid by any practicable tariff to be levied upon them4 ,dr4 ,lardner1 7#ahej73-- ,resolved1 ,that this meeting recommend the adoption of a higher rate of fare upon express passenger trains1 corresponding in some degree to the increased cost of such trains4--,american ,railroad ,convention of #ahed4 ,,increased ,,cost ,,of ,,working4 ,this is due to the extra wear and tear of engines1 cars1 and road1 from increased speed1 and also to the delays occasioned to other trains in motion at the same time4 ,the influence of express trains is felt not only by themselves1 but by nearly all the trains upon the road4 ,,note4--,to determine the most economical speed1 regard need only be had to the variable elements of cost1 namely3 cost of power1 and maintenance of superstructure1 and rolling stock2 assuming the power expended as the resistance1 and the cost of repairs of machinery and superstructure as the velocity1 we form the following table3-- ,velocity in ,resistance ,hours con4 ,product of ,cost of miles per in pounds in going column #b repairs4 ,result4 hour4 per ton4 #cjj miles4 #c4 #aj #h4f #cj #beh #ajj #ceh #ae #i4c #bj #ahf #aej #ccf #bj #aj4c #ae #aed #bjj #ced #be #aa4f #ab #aci #bej #chi #cj #ac4c #aj #acc #cjj #dcc #ce #ae4b #h4fj #aca #cej #dha #dj #ag4c #g4ej #acj #djj #ecj #de #ai4h #f4fg #acb #ej #bb4f #f #acf #fj #bi4a #e #ade #ajj #ff4e #c #bjj ,the result is found by adding the product of columns #b and #c1 or column #d to column #e1 from which the minimum cost is seen to be produced by a very little more than fifteen miles per hour4 ,the variable 7and above assumed7 element is the rate of increase of cost of maintenance4 ,all trains in motion at the same time within a certain distance of the express1 must be kept waiting with steam up1 or be driven with extra velocities in order to keep out of the way4 ,where the time table is so arranged as to call for speed nearly equal to the full capacity of the engine1 it is very obvious that the risks of failure in 8making time0 must be much greater than at reduced rates2 and when they do occur1 the efforts made to gain time must be correspondingly greater and uncertain4 ,a single example will be sufficient to show this3-- ,a train whose prescribed rate of speed is thirty miles an hour1 having lost five minutes of time1 and being required to gain it1 in order to meet and pass an opposing train at a station ten miles distant1 must necessarily increase its speed to forty miles an hour2 and a train whose prescribed rate of speed is forty miles an hour1 under similar circumstances1 must increase its speed to sixty miles an hour2 in the former case it would probably be accomplished1 whilst in the latter it would more probably result in failure2 or1 if successful1 it would be so at a fearful risk of accident4 ,but a failure in either case would have the effect of retarding the movement of the opposing train1 deranging the time of those of the same and of an inferior class in both directions1 involving1 perhaps1 on the part of the latter1 the necessity of similar struggles for time1 and thus may prove the primary cause of accident to all trains whose movements may have been affected thereby4 ,the first cost of locomotives1 7assuming the cost to increase with the weight17 is thirty per cent4 greater for express trains1 than for those of the second or third class4 ,the cost of repairs being assumed as the product of the weight by distance run1 and this distance being the same1 is as the weight1 or increased thirty per cent4 7,this assumes the power to be equally well adapted47 ,the cost of cars does not 7though it ought71 differ much for express or slow trains2 the cost of repairs will certainly be increased4 ,the interest of construction capital to be charged to expresses1 will be1 their mileage proportion plus any expense which may have been incurred in reducing curves and grades2 the proportion of repairs of superstructure1 charged to expresses1 will depend on their weight4 ,the locomotive causes #be_/bi of the wear of rails1 and as the weight of the engines is increased thirty per cent41 the increased wear will be of #ae_/eh4 ,the use of stations and of employees costs no more for express than for accommodation trains4 ,the repairs of locomotives will be nearly1 if not quite1 as the product of their weight by the distance run2 and this1 from the above1 will be thirty per cent4 greater on an express than on an ordinary train1 the distance being the same4 ,the carriages for express trains ought to be at once stronger and more convenient than those for the slower work1 the shocks arising from irregularities in the rails being very much greater as velocity increases2 and the runs being very long1 passengers require easier seats1 even1 in some cases1 accommodation for sleeping4 ,the cost for repairs1 therefore1 of express cars1 would be somewhat greater than for any others4 ,,cost ,,and ,,maintenance ,,of ,,way ,,and ,,works4 ,as the speed is increased1 the relative effect of grade and curves is lessened1 but the absolute danger of passing curves is increased4 ,express trains require larger radius of curvature1 or greater elevation of exterior rail than others1 which extra elevation causes an unnecessary resistance to all other trains4 ,the rails to resist large and heavy wheels must be heavier and more firmly fastened4 ,all bridges and viaducts 7particularly if on grades or curves71 will require more strength to resist the increased shocks to which they will be subject4 ,the wear of rails is nearly as the weight passing over them2 the wear of rails consequent upon stopping and starting the trains depends upon the momentum of the train which is to be imparted to them4 ,the proportion1 in which the working expenses are distributed under the several heads on the larger railways of ,great ,britain1 is as follows3-- ,direction and management1 #g ,way and works1 #af ,locomotive department1 #ce ,cars1 #ch ,sundries1 #d ------ #ajj ,and the percentage of increase due to fast travelling1 to be applied to the several items of expense1 with the resulting increase in total expense1 is shown below4 ,direction and management1 #g #j #j4j ,way and works1 #af #bg #d4c ,locomotive department1 #ce #cj #aj4e ,cars1 #ch #aj #c4h ,sundries1 #d #j #j4j ------ -------- #ajj #ah4f or #ah per cent4 increase1 nearly4 ,express trains1 as worked on many roads1 run at an unnecessary speed1 to make up for frequent stops4 ,overcoming a long distance in a short time1 depends as much on decrease in the number of stops1 as increase in the speed4 ,the following figures show the effect of decreasing the number of stops4 ,a train running #djj miles1 and stopping once in fifty miles1 each stop being five minutes1 7including coming to rest and starting17 to pass over the whole distance in eight hours1 must run fifty-five miles per hour4 ,stopping once in twenty miles1 sixty-three miles per hour4 ,stopping once in ten miles1 eighty-six miles per hour4 ,the following table shows the velocities of the different classes of trains in ,england1 ,france1 and ,belgium1 including and excluding stops4 ,,excluding ,,stops4 ,express4 #ast class4 #b;d class4 #c;d class4 ,england1 #dc4i #cb4h #cb4h #be4b miles per hour4 ,france1 ---- #bg4e #bd4c #bh4a miles per hour4 ,belgium1 ---- #bf4b #be4g #bg4f miles per hour4 ,,including ,,stops4 ,express4 #ast class4 #b;d class4 #c;d class4 ,england1 #cf4e #bd4h #bd4h #ag4e miles per hour4 ,france1 ---- #bb4a #ag4i #ai4i miles per hour4 ,belgium1 ---- #bj4g #ai4c #ah4a miles per hour4 ,the distances at which the different classes of trains stop in the several countries1 are as follows3-- ,,trains ,,stop ,,once ,,in #ast class4 #b;d class4 #c;d class4 ,express4 ,england1 #h miles1 #h miles1 #e miles1 #bd miles4 ,france1 #aj miles1 #f miles1 #f miles1 ---- miles4 ,belgium1 #f4h miles1 #e4f miles1 #e miles1 ---- miles4 ,,of ,,the ,,increased ,,danger ,,of ,,fast ,,travelling4 ,the causes of accident1 beyond the control of passengers1 are ,collision by opposition4 ,collision by overtaking4 ,derailment by misplaced switches and draws4 ,derailment by obstacles upon the rails4 ,breakage of machinery4 ,failure of track or bridges4 ,fire4 ,boiler explosions4 ,those causes which are aggravated by fast travelling are the first1 second1 fifth1 and sixth2 the effects of all are worse at high speeds than at low4 ,the proportion of accidents due to each of these causes1 taken at random from one hundred cases on ,english railways1 are as follows3-- ,collision1 #ef ,breaking of machinery1 #ah ,failure of the road1 #ad ,misplaced switches1 #e ,obstacles on rails1 #f ,boiler explosion1 #a ------ #ajj ,in collision by opposition1 the engines1 tenders1 and baggage cars must be demolished before the shock reaches the passengers2 in collision by overtaking1 the engine of the rear train plunges at once into the last passenger car of the leading train2 the force in the last case is the difference of the speeds1 in the former the sum4 ,the increase of danger from this cause1 attendant upon express trains1 is due1 first1 to the longer time required in stopping1 and second1 in the greater shock if collision occurs4 ,breakage of machinery is more liable to take place while wheels are revolving #be1jjj times per hour1 than when the speed is less4 ,failure of the superstructure of bridges1 7particularly when on curves or grades17 is more liable to take place at high than at low velocities4 ,accidents from obstacles upon the track1 from fire1 boiler explosions1 and misplaced switches1 are no more attendant upon express than upon other trains1 but the consequences are worse with the high speeds4 ,from the analysis above1 of one hundred accidents1 it appears that eighty-eight per cent4 of the cases are due to the causes that are aggravated by increase of speed1 and if we assume the aggravation of collision1 and breakage of machinery1 to be 7speed being doubled7 as two to one1 the danger of travelling a fixed distance1 by express1 is eighty-eight per cent4 greater than by a slow train4 ,,comparative ,,cost ,,of ,,working ,,heavy ,,and ,,light ,,trains4 #dad4 ,the question is sometimes asked1 if it would not be better to run a greater number of trains and reduce the weight of engines4 ,a comparison of cost is easily made4 ,the cost of working trains consists of ,fuel1 oil1 and waste4 ,engine-men's wages4 ,wear of rails4 ,conductor and brakemen4 ,wear of cars4 ,suppose we have to move #a1jjj tons per day over any road4 ,if we do it by one engine and #ajj cars1 the whole cost will be ,one ,engineer #b4jj ,one ,fireman #a4ej ,one ,conductor #a4ge ,four ,brakemen #e4jj ------------ #aj4be ,and if we move #a1jjj tons by ten trains of one hundred tons each1 ,ten ,engine-men at #b #bj4jj ,ten ,firemen at #a #ae4jj ,ten ,conductors at #a #ag4ej ,ten ,brakemen at #a #ab4ej ------------ #fe4jj ,difference of salaries in favor of the heavy train1 of #ed4ge4 ,as the whole weight upon the drivers must be the same to move a given load by either method1 the only difference in weights of engines will be that upon the truck4 ,to lead well a truck must have five tons upon it4 ,the whole weight upon ten trucks is1 then1 fifty tons1 and that upon one1 five tons1 which leaves an excess of forty tons to be daily carried over the road by the small trains4 ,the heaviest freight engine will not cost over #ae1jjj2 the cost of an engine to draw one hundred tons cannot be less than #e1jjj4 #aj #ejjj #ejjjj less #aejjj is #cejjj4 #f_/ajj of #cejjj is #bajj4 ,add to this five times as much fuel used in firing up and standing with steam up1 ten times as much oiling1 cleaning1 and repairing1 ten times as much engine house and shop accommodation2 also that the cars in frequent trains are much less loaded than in seldom ones1 increased delay and chance of accident from increased number of trains1 and estimating all of them at #agj4jj per day1 7the cost of the large engine being assessed at #cj per day1 and that of each of the small ones as #bj1 the daily difference is #agj17 and we have1 as the whole daily increased cost of working ten small over one large train1 #agj4jj #ed4ge 7#f_/ajj of #cejjj7_/cac or #f4ga #bca4df per day1 or #gb1ddf4ih per annum1 which employs a capital of #a1bjg1ddi4 ,,branch ,,roads4 #dae4 ,these lines1 when belonging to the main road1 are generally worked at a loss2 and when independent1 are a poor investment4 ,at a meeting of the directors of the ,boston and ,worcester 7,mass47 ,railroad in ,february1 #ahee1 it was declared that out of six branches1 but one was profitable4 ,that four of them gave an income upon cost of from one and a quarter to one and three quarter per cent4 ,independent branch lines generally share a joint business by the mileage standard2 and here is where they lose1 for if the branch trains do not traverse the main line1 and the tribute passengers help to fill a train which runs at any rate upon the main1 then the branch expense of carrying the passengers is to that of the main1 as 7say ninety to ten71 and the branch should take #ij_/ajj of the receipts4 ,in this case the branch is charged with using both the cars and road of the main4 ,if it runs its own cars over the main1 7as when the branch is near the terminus17 it should be charged only with the wear of the road4 ,in like manner several roads1 forming a continuous line1 should not divide the receipts according to the mileage2 but according to the cost of working that mileage4 ,thus if we have the continuous line below1 column one shows the length2 column two1 the cost of building2 column three1 that of maintaining2 and column four1 the division of receipts4 ,division4 ,length4 ,construction ,maintaining ,result4 ,capital4 ,capital4 #a #h #aj #d #aj #d #ad #b #i #f #c #f #c #i #c #f #g #b #g #b #i #d #aj #d #a #d #a #e ,,reproduction ,,of ,,road ,,and ,,stock4 #daf4 ,besides the annual repairs necessary to maintain a road in proper working order1 there is needed a periodic expenditure for reproduction4 ,evidently the time will come1 upon all roads1 when rails and sleepers1 buildings1 bridges1 etc41 need to be replaced4 ,knowing the life of rails1 we also know the annual depreciation1 and from that can easily find what sum must annually be laid aside1 which being properly invested1 shall1 at the end of the life of the rail1 together with its interest1 be equal to the cost of renewing4 ,,rails4 ,suppose rails to last ten years1 the annual depreciation is ten per cent4 ,at sixty lbs4 per yard we have one hundred and five tons per mile1 which1 at #fj per ton1 amounts to #f1cjj4 ,let the cost of rerolling and relaying be #cj per ton1 the depreciation is then #cj per ton for ten years1 or #c per ton per annum1 or #cae per mile per annum4 ,,sleepers4 ,if sleepers last seven years1 and cost forty cents apiece1 their annual depreciation per mile 7at #b1djj per mile7 will be #ach per mile 7nearly74 ,,bridges4 ,if wooden bridges cost #cj per lineal foot1 and last twenty years1 the annual depreciation per foot will be #a4ej1 and if there is ten feet per mile of road1 #ae per annum per mile4 ,,extras4 ,allowing for the annual depreciation per mile of buildings1 fences1 etc41 #cc1 we have as the whole annual depreciation1 #ejj per mile2 and the amounts which yearly reserved and placed at compound interest for each of the ten years1 will pay for reproducing the road1 are as follows3-- ,at the end of the #ast year #bih ,at the end of the #b;d year #cae ,at the end of the #c;d year #ccc ,at the end of the #dth year #ced ,at the end of the #eth year #cgc ,at the end of the #fth year #cig ,at the end of the #gth year #dag ,at the end of the #hth year #ddf ,at the end of the #ith year #dgb ,at the end of the #ajth year #ejj which1 at six per cent41 gives1 at the end of the tenth year1 #ejj each4 ,,note4--,reproduction of rolling stock has been proved to be nothing more than repairs1 as a locomotive may be fitted with one and another new part until none of the original machine remains4 ,see ,lardner's ,railroad ,economy4 ,as the business upon a railroad increases1 so does the amount of station accommodation necessary1 and also of rolling stock1 which increase should be debited to capital1 and not to revenue4 ,the permanent investors in a railroad are in favor of having capital maintained1 even at the expense of revenue4 ,the temporary shareholders1 and the speculators in stock1 wish most to produce large dividends1 even at a sacrifice of capital1 and would charge nothing to revenue4 ,the rights of both of the above classes are to be regarded1 as the road is often built mainly by the efforts of the temporary investors4 ,,working ,,railroads ,,by ,,contract4 #dag4 ,an experiment has lately been tried upon the working of railroads which bids fair to reduce very considerably the cost of operating2 and to render the enterprises more profitable1 namely1 working the several departments by contract2 that is1 paying certain persons a fixed price for supplying the necessary amount of power1 cars1 or material per annum1 thus bringing into play private interest and individual enterprise4 ,there is no doubt but that by a judicious system of this kind1 correctly applied1 many roads which are now worthless could be made to pay1 while the value of good roads would be also increased4 ,,classification ,,of ,,freight4 #dah4 ,freight is classified according to its nature1 the commercial nature of the country traversed by the road1 and the direction of the principal market4 ,the distribution adopted upon some of the large roads is as follows3-- ,,classification ,,of ,,articles4 ,articles marked thus 99 at owner's risk4 ,double ,first ,class4 ,baskets1 99 ,band ,boxes2 99 ,camphene2 99 ,carboys1 and contents2 99 ,demijohns1 and contents2 99 ,eggs2 ,feathers1 in bags2 ,furs2 ,hobby ,horses2 ,musical ,instruments2 99 ,plaster of ,paris1 7ornaments72 ,pictures1 in frames2 ,teazles1 in casks2 ,wagons1 7children's72 ,willow ,ware4 ,first ,class4 99 ,ale1 in glass2 99 ,apples1 green1 pre-paid2 ,bacon1 loose2 ,batting2 ,bells2 99 ,berries1 pre-paid2 99 ,blinds1 7window7 in packages2 ,bonnets2 99 ,books1 in boxes2 ,boots2 ,bran1 in bags2 ,brass1 in sheets and pigs2 ,brass ,castings2 ,brass ,vessels2 ,bread and ,biscuit2 ,brooms1 in bales or bundles2 ,broom ,handles1 in boxes or bundles2 ,brushes2 ,buffalo ,robes1 packed2 ,buttons2 99 ,candies and ,confectionary1 canvassed2 ,cane2 ,cards2 ,carpeting2 ,caps2 ,china ,ware2 ,chocolate2 99 ,cigars1 in boxes2 ,cinnamon2 99 ,clocks1 in boxes2 ,cocoa2 ,cassia2 ,coffee1 ground2 ,collars2 ,combs2 ,copper1 in sheets and pigs2 ,copper ,vessels2 ,corks2 99 ,cotton1 in bales2 99 ,cotton ,waste2 ,covers and ,sieves2 99 ,cranberries2 99 ,cutlery2 ,deer ,skins1 in bundles2 ,doors2 ,dry ,goods2 ,fancy ,goods2 99 ,figs1 in boxes2 ,fire-arms2 99 ,fish1 fresh1 pre-paid2 ,flour1 in bags2 ,forks1 hay and manure2 99 ,fruits1 fresh1 pre-paid2 99 ,game1 pre-paid2 ,garden ,seeds2 ,ginger2 99 ,glass1 in boxes2 99 ,glass ,ware1 in boxes or casks2 ,glue2 99 ,grapes1 pre-paid2 ,gun ,stocks1 in boxes or bundles2 ,hair1 in sacks2 ,hams1 loose2 ,harness2 ,hides1 dry2 ,hoe ,handles2 99 ,hollow ,ware2 99 ,honey2 ,hops1 pressed2 99 ,ice1 pre-paid2 ,indigo2 ,ink2 ,iron ,castings1 light2 ,ivory2 ,japan ,ware2 ,joiners ,work2 99 ,lemons1 in boxes1 canvassed2 99 ,looking-glasses1 well boxed2 99 ,machinery1 boxed1 light2 ,marble1 wrought1 at owner's risk of breakage2 ,mats2 ,mattrasses1 double1 at #aej pounds each2 ,mattrasses1 single1 at #ajj pounds each2 ,mill ,stuffs1 in bags or casks2 ,measures2 99 ,meat1 fresh1 pre-paid2 ,meat1 in bulk1 salted2 ,medicines2 99 ,melons1 pre-paid2 ,moss1 in sacks2 ,nuts1 in sacks or casks2 99 ,oranges1 in boxes1 canvassed1 pre-paid2 99 ,oysters1 in cans or kegs2 ,palm ,leaf1 in bales2 ,paper1 brown wrapping and straw1 7light72 ,paper ,hangings2 ,pelts2 99 ,porter1 in glass2 99 ,poultry1 dressed1 pre-paid2 99 ,prunes2 ,rags1 7see second class72 99 ,raisins2 ,rake ,handles2 ,rattan2 ,rugs2 ,saddle ,trees2 ,saddlery2 99 ,sash1 in packages2 ,scale ,beams2 ,scythe ,snaths2 ,shoes2 ,shovel ,handles2 ,soap1 fancy2 ,soda2 ,spices2 99 ,spirits ,turpentine2 ,stationery2 ,straw ,goods2 ,teas1 7see third class72 ,tin ,ware1 in crates or hhds42 ,toys2 ,trunks1 empty1 #hj pounds each2 ,tubs2 ,turners' ,work2 99 ,vegetables1 pre-paid2 ,veneering2 ,wadding2 ,warp1 on beams2 ,warp ,beams2 ,waste1 woollen2 ,wax2 ,whalebone2 ,wheelbarrows2 ,whips2 ,wicking2 99 ,wines1 in baskets or boxes2 99 ,wooden ,ware2 ,wool2 ,woollens4 ,second ,class4 ,alcoholic ,liquors2 99 ,ale1 in casks2 ,apples1 dried2 ,alum2 ,anchors2 ,anvils2 ,ashes1 pot or pearl2 ,axes1 in boxes2 ,axles1 iron2 ,bacon1 packed2 ,bagging2 ,barilla2 ,bark1 tanner's1 #a cord per ton2 ,beans2 99 ,beef1 in casks or boxes2 ,beer1 in casks2 ,bleaching ,salts2 ,bones2 99 ,bottles1 packed1 7empty72 ,brimstone2 ,burr ,blocks2 ,burlaps1 in original packages2 99 ,butter1 in firkins2 99 ,candles1 in boxes2 ,cannon2 ,canvas2 ,castings1 heavy2 ,cement2 ,chains2 ,chalk2 ,chair and turned ,stuff in bales or bdls42 ,cider1 in casks2 ,cheese1 in boxes or casks2 ,clay1 ,coal1 and ,coke1 in casks or boxes2 ,clover ,seed2 ,coffee1 in sacks2 ,copperas2 ,cordage2 ,crockery ,ware1 well packed2 ,domestics1 in original packages2 ,dye ,stuffs1 in woods2 ,earthen ,ware1 well packed2 99 ,fire ,brick2 ,fish1 dried or salted2 ,flax ,seed2 ,flocks2 ,floor ,cloth1 painted2 ,flour1 in barrels1 #bj barrels or less2 ,furnaces2 ,grain1 of all kinds2 99 ,grindstones2 ,groceries1 generally heavy1 not otherwise specified2 ,gunnies1 in bales2 ,hoes2 ,hams1 shoulders or sides1 in casks or boxes2 ,hardware1 except ,cutlery2 99 ,hemp1 in bales2 ,hemp ,seed2 99 ,hides1 green2 99 ,high ,wines2 ,hoops1 shaved or split1 #c1jjj pounds per cord2 ,india ,rubber2 ,iron1 pig1 bloom1 boiler1 rod1 and bar2 ,iron1 hoop1 sheet1 or bolts2 ,iron1 nuts1 rivets1 and spikes2 ,junk2 ,lard1 in barrels or casks2 ,lead1 sheet1 pig1 or pipe2 ,leather2 ,liquors1 in barrels or casks2 ,lime1 in barrels or casks2 ,marble1 unwrought1 at owner's risk of breakage2 ,meal1 in bags or casks2 ,molasses2 ,moss1 pressed2 ,nails1 in kegs2 ,oakum1 in bales2 ,oil1 owner's risk of leakage2 ,oil ,cake1 ,oil ,cloth2 99 ,oysters1 in shell2 ,paints1 dry or in oil2 ,paper1 7white17 in boxes or bundles2 ,paper1 7heavy brown and hardware72 ,pasteboard2 ,pepper2 ,peaches1 dried2 ,peas1 in sacks or casks2 ,pickles1 in casks2 99 ,pipes1 in boxes2 ,pitch2 ,plaster1 in casks or barrels2 ,ploughs2 ,pork1 packed2 99 ,porter1 in casks2 ,potatoes1 in casks or sacks2 ,rags1 foreign1 pressed2 ,rakes2 ,railroad ,chairs and ,spikes2 ,rice2 ,rope2 ,rosin2 ,saleratus2 ,salt1 in bags or casks2 ,saltpetre2 ,scales1 in boxes2 ,scythes1 in bundles2 ,scythe ,stones2 ,shot1 in bags2 ,shovels and ,spades2 ,sizing2 ,slate2 ,soap1 7common17 in boxes2 ,soda3 ,spelter and ,zinc2 ,spikes1 in kegs2 ,spirits1 domestic2 ,starch2 ,steel1 in boxes or bundles2 ,steel ,springs2 ,stone2 99 ,stone ,ware1 well packed2 ,sugar2 ,sumac2 ,tallow1 owner's risk of heat2 ,tar2 ,tiles2 ,tin1 metal and plate2 ,tobacco1 in bales1 boxes1 or hhds42 ,tow1 pressed1 7in bales17 owner's risk of fire2 ,twine1 in bales2 ,vegetable ,roots1 in sacks or casks2 99 ,vinegar2 ,water1 ,mineral2 ,whiskey1 in casks2 ,white ,lead2 ,whiting2 99 ,wine1 in casks2 ,wire1 in rolls and casks2 ,woods1 in shape1 unfinished2 ,woods1 of value1 namely1 ,mahogany1 ,lignum ,vit1 ,rosewood1 ,cherry1 ,cedar1 ,walnut1 etc42 ,wool1 foreign1 pressed1 in bales2 ,yam1 pressed2 ,zinc and ,spelter4 ,third ,class4 ,includes the following articles in quantities of #h1jjj pounds1 and less than #af1jjj pounds1 in any one shipment from one consignor to one consignee4 ,same articles shipped in like manner1 in quantities of #af1jjj pounds and upwards1 will be taken at special rates4 ,anchors2 ,anvils2 ,ashes1 pot and pearl1 in casks2 ,axes1 iron2 ,bacon1 packed2 ,bark1 tanner's1 #a cord per ton2 ,beans1 in sacks or casks2 ,beef1 packed2 ,burr ,blocks2 ,cannon2 ,cement1 in barrels or casks2 ,chain ,cable2 ,cider2 ,clay2 ,coffee2 ,copper1 in boxes2 ,flaxseed1 in sacks or casks2 ,flour1 in barrels2 ,grain1 of all kinds2 ,grindstones2 ,hams1 packed2 ,high ,wines2 ,iron1 pig1 bar1 bloom1 sheet1 hoop1 or rod2 ,iron ,castings1 heavy2 ,lard1 in casks or barrels2 ,lead1 sheet1 pig1 or pipe2 ,lime1 in barrels2 ,marble1 unwrought1 at owner's risk of breakage2 ,molasses2 ,nails1 in kegs2 ,plaster1 in barrels2 ,pork1 packed2 ,potatoes1 in sacks or casks2 ,railroad ,iron1 ,chairs and ,spikes2 ,salt1 in sacks and barrels2 ,shot2 ,slate2 ,spikes1 in kegs2 ,sugar1 in casks2 ,teas2 ,tobacco1 in boxes or hhds42 ,vinegar1 in barrels2 ,whiskey1 in barrels4 ,besides the above regular articles1 are the following special objects of transport3-- ,stores2 ,cabinet ,ware2 ,brick2 ,charcoal2 ,pressed ,hay2 ,broom ,corn2 ,boxes of ,cigars2 ,barrels2 ,bags2 ,corn in the ,ear2 ,poultry2 ,looking-glasses2 ,trees and ,shrubbery2 ,safes2 ,mill-stones2 ,steam-engines2 ,machinery2 ,agricultural ,implements2 ,lumber2 ,live-,stock2 ,carriages2 ,coal and ,coke4 ,,time ,,tables4 ,fig4 #aeh1 7see end of volume74 #dai4 ,the most complete graphic solution of an engineering problem1 is doubtless the time table of ,s4 ,s4 ,post1 ,esq41 chief engineer of the ,new ,york and ,erie ,railroad4 ,let the vertical lines represent time in spaces of ten minutes each1 and the horizontals1 distances1 the heavy lines representing the several way stations4 ,suppose now that we leave station ,a at six1 ,a4 ,m41 and wish to arrive at ,k at two1 ,p4 ,m41 stopping ten minutes at each station2 the number of way stations being eight1 the whole time consumed in stops will be #aj #h #hj minutes4 ,from two1 ,p4 ,m41 and on the line ,k1 go back eighty minutes or to ,m1 and from ,a draw ,a ,b1 in the direction ,a ,m1 which cuts the line ,b ,b at ,b1 which is four miles1 or thirteen minutes from ,a4 ,now1 as we wait ten minutes1 pass along on the line ,b ,b one division 7ten minutes7 to ,b and start again parallel to ,a ,b1 arriving at ,c at one and a half hours from starting4 ,proceeding thus1 we arrive at ,k at the required time4 ,the inclination of the line shows the speed4 ,thus1 if it passes twenty horizontal spaces in six vertical divisions1 we have twenty miles in sixty minutes1 or twenty miles per hour4 ,suppose now we would start an express train at eight1 ,a4 ,m41 from ,a to arrive at ,k at one1 ,p4 ,m41 7see line #h ,f17 it will pass the first train at station ,f1 and will run at the rate of seventeen miles per hour from ,a to ,f1 at the same rate from ,f to ,g1 and at thirteen miles per hour from ,g to #a4 ,suppose also that we start a train from ,k at six1 ,a4 ,m41 to arrive at ,a at eleven1 ,a4 ,m41 we pass the before-mentioned trains at ,e and ,d4 ,also a freight train which is required to pass the above named trains1 leaving ,k at eight1 ,a4 ,m41 and arriving at ,a at one1 ,p4 ,m41 will stop ten minutes at ,g1 ten minutes at ,m1 pass the first train at ,l1 wait ten minutes on a siding at two and a half miles from ,l1 and run to ,a at nearly a uniform rate of speed4 ,so also may the motion of any train be laid down and traced through the hours of the day upon the table4 ,by plotting the profile of the road upon the line ,a ,k1 the places are shown at which grades will oblige us to use a less speed4 ,curves also may be shown by increasing the steepness of the grades2 or by making a grade on the profile when the road is level1 steep enough to involve an amount of power equal to that consumed by the curve4 ,,locomotive ,,registers4 #dbj4 ,american railroad reports are1 as a general thing1 quite destitute of detailed accounts of the performance of the power4 ,some of the large roads1 indeed1 are of late improving in this respect4 ,that fares and tolls may be properly applied to the different articles of transport1 the cost of moving each article should be known4 ,such items as the salaries of employees1 and repairs of machinery1 are easily distributed to the proper heads2 but the correct amount of fuel1 oil1 and waste1 to be charged to any department1 is not so evident4 ,what we require is1 the exact amount of fuel1 oil1 and waste used1 and work done by each engine2 to obtain which1 some system of registering these quantities must be adopted4 ,the following five blanks being filled1 we have all that is required3-- ,number #a is the engineer's weekly return to the master of machinery1 and gives1 as seen1 the times of arriving at1 and departing from1 each station4 ,the fuel should always be ready at each station for delivery1 in cords and half cords1 or in tons and fractions1 when coal or coke4 ,it may be delivered either from a small car placed on a pair of rails at right angles to the track1 or from a box hung upon a crane1 which may be at once swung over and lowered into the tender2 the box which is already in1 being first removed4 ,the latter method gives the most correct results1 as whatever fuel is left at the station may be credited to the engine4 ,the whole operation of wooding would not take longer than it does to describe it1 and would lead to a systematic and economical method of working4 ,the tanks and pumps being charged to construction1 we may1 without material error1 charge the cost of the water supply to the trains according to their mileage4 ,number #b is the wood register1 showing the amount of fuel delivered to the several engines from the different stations1 and should be weekly signed and returned by the station wood master to the fuel agent4 ,the engineer's fuel receipts 7,no4 #a7 check these reports4 ,number #c is the conductor's mileage account1 giving the exact weight left at1 and taken from1 each station2 and1 consequently1 the load carried between stations1 which is checked by the station master's return4 ,number #d is the monthly account of the performance of engines1 compiled from the weekly return by the superintendent of machinery1 and reported to the superintendent4 ,number #e gives the annual performance of each and all of the engines upon the road1 and is obtained from the monthly reports1 and from those of the repair and transportation departments4 ,the work done by different classes of cars should be registered in like manner4 ,knowing the amount of material used1 and also the work done1 it is easy to find the cost per mile of moving any article of transport1 regard of course being had to the character of the parts of the road traversed by the several engines4 ,an engine working a sixty feet grade should be allowed more fuel than one which works a level only4 ,,number #a4 ,a4 and ,b4 ,railroad4 ,report of amount of material consumed1 and of work done by ,engine ,no4 #ej1 during the week ending ,july #d1 #ahef4 ----------------1 ,engineer4 ,,monday4,name of train4 ,name of station4 ,time of arriving4 ,time of departing4 ,fuel taken4 ,whole cost fuel consumed -------- ,whole time under steam -------- ,whole time running -------- ,and the same for each day of the week4 ,,weekly ,,memoranda4 ,cords of wood used -------- ,gallons oil used -------- ,pounds tallow used -------- ,pounds waste used -------- ,miles run -------- ,whole time running -------- ,whole time under steam -------- ,time under repairs -------- ,cost of repairs -------- --------1 ,master of ,machinery4 ,,number #b4 ---- ,,railroad4 ,,amount ,,of ,,fuel ,,delivered ,,to ,,engines ,,from ---- ,,station ,,during ,,week ,,ending ----4 ,name of ,engine4 ,a4 ,b4 ,c4 ,d4 ,e4 ,f4 ,g4 ,h4 ,k4 ,total4 ,,monday4 ,morning4 ,afternoon4 ,,tuesday4 ,morning4 ,afternoon4 ,,wednesday4 ,morning4 ,afternoon4 ,,thursday4 ,morning4 ,afternoon4 ,,friday4 ,morning4 ,afternoon4 ,,saturday4 ,morning4 ,afternoon4 ,total to each engine4 ,wood ,station ,master ----4 ,,number #c4 ,a4 and ,b4 ,railroad4 ,conductor's mileage return1 for week ending ,july #d1 #ahef1 showing work done by ,engine ,no4 #ed4 ,,monday4 ,train4 ,station4 ,cars taken4 ,cars left4 ,cars in train4 ,weight of train4 ,eq'd distance4 ,eq'd mileage4 ,total equated mileage ---- ,and the same for each day of the week4 ,,number #d4 ,a4 ,,and ,b4 ,,railroad4 ,,performance ,,of ,,locomotive ,,engines ,,for ,,month ,,ending ----4 ,miles ,number4,use4run4 ,time4 ,wages4 ,fuel4 ,at ,under ,cost ,miles ,working4rest4repairs4,cost4 per ,cords4 per mile4 cord4 ,a4 ,,and ,b4 ,,railroad4 ,,performance ,,of ,,locomotive ,,engines ,,for ,,month ,,ending ----4 ,oil1 waste1 and tallow4 ,repairs4 ,totals4 ,cost ,cost of per ,gallons,miles,pounds,pounds oil1 mile of ,cost ,cost oil per of of waste1 oil1 ,cost4 per ,cost4 per used4 pint4waste4tallow4 and waste1 mile4 mile4 tallow4 and tallow4 ,a4 ,,and ,b4 ,,railroad4 ,,performance ,,of ,,locomotive ,,engines ,,for ,,month ,,ending ----4 ,comp1 ,work done4 work done4 ,freight4 ,passenger4 ,cost ,cost ,equated per ton ,equated per ton freight per passenger per mileage4equatedmileage4 equated mile4 mile4 ----1 ,general ,superintendent4 ,,number #e4 ,a4 ,,and ,b4 ,,railroad4 ,,annual ,,report ,,of ,,cost ,,of ,,maintenance ,,of1 ,,and ,,work ,,done ,,by ,,the ,,locomotive ,,power1 ,,also ,,the ,,cost ,,per ,,ton ,,and ,,passenger ,,per ,,mile1 ,,together ,,with ,,the ,,nature ,,and ,,amount ,,of ,,repairs1 ,,the ,,dimensions1 ,,the ,,present ,,state ,,of ,,the ,,stock1 #ahef4 ,name of the ,date of ,name orbuilder or ,use to commc'g ,number manufactorywhich it work of the from whence is upon engine4 bought4 applied4 the road4 ,,recapitulation1 ,,no4 #a4 ,cost per equated mile1 per ton1 of working freight engines4 ,engineer and fireman4 ,fuel4 ,oil1 tallow1 and waste4 ,repairs4 ,total4 ,a4 ,,and ,b4 ,,railroad4 ,,annual ,,report ,,of ,,cost ,,of ,,maintenance ,,of1 ,,and ,,work ,,done ,,by ,,the ,,locomotive ,,power1 ,,also ,,the ,,cost ,,per ,,ton ,,and ,,passenger ,,per ,,mile1 ,,together ,,with ,,the ,,nature ,,and ,,amount ,,of ,,repairs1 ,,the ,,dimensions1 ,,the ,,present ,,state ,,of ,,the ,,stock1 #ahef4 ,,general ,,character ,,and ,,principal ,,dimensions ,,of ,,the ,,engines4 ,capacity of ,weights4 tender ,cylind'rs4 ,mode of in connection4 gallons4 ,whole weight,weight ,weight of upon of the engine the tender ,diameter,stroke4 with driving with of bore4 fuel wheels4feed4 and water4 ,,recapitulation1 ,,no4 #b4 ,cost per equated mile1 per passenger1 of working engines4 ,engineer and fireman4 ,fuel4 ,oil1 tallow1 and waste4 ,repairs4 ,total4 ,a4 ,,and ,b4 ,,railroad4 ,,annual ,,report ,,of ,,cost ,,of ,,maintenance ,,of1 ,,and ,,work ,,done ,,by ,,the ,,locomotive ,,power1 ,,also ,,the ,,cost ,,per ,,ton ,,and ,,passenger ,,per ,,mile1 ,,together ,,with ,,the ,,nature ,,and ,,amount ,,of ,,repairs1 ,,the ,,dimensions1 ,,the ,,present ,,state ,,of ,,the ,,stock1 #ahef4 ,number ,,general ,,character ,,and ,,principal ,,dimensions ,,of ,,the of ,,engines4 miles run ,relative power1 or traction ,driv'g wheels4 at a ,boiler mean cylinder pressure of #ge lbs4 ,whole ,area of ,number4,diameter4 ,grateheating blast area4surface4orifice4 ,a4 ,,and ,b4 ,,railroad4 ,,annual ,,report ,,of ,,cost ,,of ,,maintenance ,,of1 ,,and ,,work ,,done ,,by ,,the ,,locomotive ,,power1 ,,also ,,the ,,cost ,,per ,,ton ,,and ,,passenger ,,per ,,mile1 ,,together ,,with ,,the ,,nature ,,and ,,amount ,,of ,,repairs1 ,,the ,,dimensions1 ,,the ,,present ,,state ,,of ,,the ,,stock1 #ahef4 ,,whole ,,expense ,,of ,,working ,,and ,,of ,,maintaining ,,the ,,locomotives1 ,,and ,,expense ,,per ,,mile4 ,cost of enginemen ,cost of oil1 waste1 and tallow4 and firemen4 ,miles ,cost run ,cost per ,gallons to ,pounds,poundsfor oil mile of oil one of of waste1 run for used4 pint waste tallow and oil1 of used4 used tallow4waste1 oil4 and tallow4 ,,recapitulation1 ,,no4 #c4 ,of ---- freight engines ---- are in working order1 or ---- per cent4 of the whole4 ,average work of an engine is ---- days per annum1 and for each day at work ---- days repairing and ---- at rest4 ,a4 ,,and ,b4 ,,railroad4 ,,annual ,,report ,,of ,,cost ,,of ,,maintenance ,,of1 ,,and ,,work ,,done ,,by ,,the ,,locomotive ,,power1 ,,also ,,the ,,cost ,,per ,,ton ,,and ,,passenger ,,per ,,mile1 ,,together ,,with ,,the ,,nature ,,and ,,amount ,,of ,,repairs1 ,,the ,,dimensions1 ,,the ,,present ,,state ,,of ,,the ,,stock1 #ahef4 ,,whole ,,expense ,,of ,,working ,,and ,,of ,,maintaining ,,time ,,of ,,service4 ,,the ,,locomotives1 ,,and ,,expense ,,per ,,mile4 ,time1 ,time1 in in ,time ,cost of fuel4 ,repairs4 ,total4 days1 days1 while of at under active rest4repair4 s'vice4 ,cost ,cost per ,total ,cords,cost per ,cost of mile cost of of mile repairsrun for,total per fuel fuel4 run of repairscost4mile used4 for engine4 of run4 fuel4 engine ,,recapitulation1 ,,no4 #d4 ,same as #c2 for passenger1 in place of freight engines4 ,a4 ,,and ,b4 ,,railroad4 ,,annual ,,report ,,of ,,cost ,,of ,,maintenance ,,of1 ,,and ,,work ,,done ,,by ,,the ,,locomotive ,,power1 ,,also ,,the ,,cost ,,per ,,ton ,,and ,,passenger ,,per ,,mile1 ,,together ,,with ,,the ,,nature ,,and ,,amount ,,of ,,repairs1 ,,the ,,dimensions1 ,,the ,,present ,,state ,,of ,,the ,,stock1 #ahef4 ,,receipts1 ,,or ,,amount ,,of ,,work ,,done ,,by ,,locomotives4 ,passenger4 ,merchandise4 ,mixed trains4 ,cost ,cost ,freight ,cost ,tons of per ton ,cars per cars per freight,cost per,mileage7gross7 carried car carried mile carriedton per of per one per one for one mile for mixed mile mile4 mile4 mile4 freight mile freight4trains4 for cars4 mixed trains4 ,,recapitulation1 ,,no4 #e4 ,relative cost per equated mile of gross to net tons of freight carried4 ,relative cost per equated mile of gross to net tons of passengers carried4 ,a4 ,,and ,b4 ,,railroad4 ,,annual ,,report ,,of ,,cost ,,of ,,maintenance ,,of1 ,,and ,,work ,,done ,,by ,,the ,,locomotive ,,power1 ,,also ,,the ,,cost ,,per ,,ton ,,and ,,passenger ,,per ,,mile1 ,,together ,,with ,,the ,,nature ,,and ,,amount ,,of ,,repairs1 ,,the ,,dimensions1 ,,the ,,present ,,state ,,of ,,the ,,stock1 #ahef4 ,total equated ,comparative ,nature ,present mileage effect of of condition of engines4 repairs4 of engines4 machinery4 ,gen'l ,superintendent4 ,,telegraph4 #dba4 ,the magnetic telegraph has lately come into use as a means of communication along the lines of long railroads1 and nothing serves better the purposes of adjusting the movement of trains1 of transmitting orders1 and of keeping the general superintendent informed at all hours1 of the exact condition in detail of the whole road1 and of all its trains4 ,the following is extracted from ,mr4 ,mc,callum's ,report1 before referred to3-- 8,a single track railroad may be rendered more safe and efficient1 by a proper use of the telegraph1 than a double track railroad without its aid1--as the double track can only obviate collisions which occur between trains moving in opposite directions1 whilst the telegraph may be used effectually in preventing them1 either from trains moving in an opposite1 or the same direction2 and it is a well established fact deduced from the history of railroads1 both in ,europe and in this country1 that collisions between trains moving in the same direction have proved by far the most fatal and disastrous1 and should be the most carefully guarded against4 ,i have no hesitation in asserting1 that a single track railroad1 having judiciously located turnouts1 equal1 in the aggregate1 to one quarter of its entire length1 and a well-conducted telegraph1 will prove to be a more safe and profitable investment than a much larger sum expended in the construction of a continuous double track1 operated without a telegraph4 8,collisions between fast and slow trains1 moving in the same direction1 are prevented by the application of the following rule3--#8,the conductor of a slow train will report himself to the superintendent of the division1 immediately on arrival at a station where by the time table he should be overtaken by a faster train2 and he shall not leave that station until the fast train passes1 without special orders from the superintendent of the division4' ,a slow train under such circumstances1 may1 at the discretion of the division superintendent1 be directed to proceed4 ,he1 being fully apprised of the position of the delayed train1 can readily form an opinion as to the propriety of doing so1 and thus1 whilst the delayed train is permitted to run without regard to the slow train1 the latter can be kept entirely out of its way4 8,,note4--,in moving trains by telegraph1 nothing is left to chance4 ,orders are communicated to the conductors and engineers of the opposing trains1 and their answers returned giving their understanding of the order before either is allowed to proceed4 8,their passing place is fixed and determined1 with orders positive and defined that neither shall proceed beyond that point until after the arrival of the other2 whereas1 in the absence of a telegraph1 conductors are governed by general rules and their individual understanding of the same2 which rules are generally to the effect1 that in cases of detention1 the train arriving first at the regular passing place1 shall1 after waiting a few minutes1 proceed cautiously1 #8expecting to meet the other train1' until they have met and passed1 the one failing to reach the #8half way post' between stations being required to back 7always a dangerous expedient71 and the other permitted to proceed2 the delayed train being subjected to the same rule in regard to all other trains of the same class it may meet1 thus pursuing its hazardous and uncertain progress during the entire trip4 ,the history of such a system furnishes a serious commentary on the imperfection of railroad regulations4 8,the liability to collision under the system referred to has prompted the invention of various expedients for suddenly arresting the progress of trains2 and which seem to have been conceived under the impression1 more imaginary than real1 that the difficulties they were designed to obviate1 are unavoidable in their character2 but which may1 by the exercise of ordinary care and the use of the telegraph1 be subjected to perfect control4 ,some of these inventions undoubtedly possess sufficient merit to entitle them to adoption under any circumstances1 whilst others1 for the above reasons1 are entirely valueless--indeed it is questionable whether a reliance on their use may not in many cases lead to danger1 by producing recklessness1 and thus increase instead of diminish the evils sought to be avoided40 ,,new ,,york ,,and ,,erie ,,railroad4 #dbb4 ,as a fine specimen of ,american railroad engineering1 and ,american railroad management1 stands the above-named line1 extending from ,jersey ,city to ,lake ,erie1 at ,dunkirk2 embracing with its branches #dif miles of road1 employing over #a1jjj1jjj dollars worth of labor per annum1 upwards of #bjj locomotive engines1 and about #c1jjj cars2 earning annually over #e1jjj1jjj1 and expending #b1fhj1jjj dollars4 ,the whole cost of the road up to ,september #cj1 #ahee1 was1 with the equipment1 nearly #cc1gej1jjj4 ,there are #abi truss bridges1 amounting in all to #ae1fib feet in length2 #fd trestle1 stringer1 and pile bridges1 of #e1dhi feet total length2 #c viaducts1 of length #a1bgd feet in all2 #afg arch culverts1 of from #c to #cj feet span2 #ebg box culverts1 from #a to #ab feet span2 #ib wood sheds1 #ad1bjj feet total length2 #dce buildings2 #dcc switches1 of #chg1iad feet available length1 and #ejd1bje feet total length4 ,notwithstanding the immense amount of business transacted by such a road1 so complete is the organization and management of employees1 that the general superintendent1 sitting in his ,new ,york office1 can at any moment tell1 within one mile1 where each car or engine is1 what it is doing1 with what loaded1 the consignor and consignee1 and the time of arriving and departing the several stations1 and other trains2 and thus at any moment may perceive and correct faults and remissness1 and in reality control the whole road4 ,,appendix4 ,a4 ,,decimal ,,arithmetic4 ,the advantage of a ,decimal system of ,arithmetic and of mensuration1 as applied to engineering1 can hardly be overstated4 ,civil and mechanical engineers both use 8per force0 some decimal expressions1 as #j4ghed1 #c4adaf1 etc41 etc4 ,why not adopt the system entirely8 ,all calculations are much easier made decimally1 and measurements made with more exactness4 ,the most perfect system of weights and measures is doubtless that of the ,french4 ,all lengths are based upon the meter as a unit1 and whether the mechanic is making a watch or a locomotive his scale is metrical4 ,the meter is exactly #a_/ajjjjjjj of the distance from the pole to the equator1 and was found1 by measuring a meridian line from ,rhodes to ,dunkirk 7,france71 #egj miles long4 ,the metrical scale is thus1 ,millimetre 4#jja or #a_/ajjj ,centimetre 4#ja or #a_/ajj ,decimetre 4#a or ,metre #a4 ,decametre #aj4 ,hectometre #ajj4 ,kilometre #ajjj4 ,myriametre #ajjjj4 ,the metre is #c4bhjhii ft41 or #ci4cgjghh ,english inches4 ,the ,english and ,american foot is of the yard2 the yard is #cejjj_/ceacic of a pendulum vibrating seconds at the latitude of ,london1 at the level of the sea1 in a vacuum4 ,the standard ,american scale is an eighty-two inch bar made by ,troughton of ,london for the ,united ,states ,coast ,survey4 ,in civil engineering the decimal division is almost entirely adopted2 indeed1 any other would lead to almost endless calculation4 ,the chain is one hundred feet long and divided into one hundred links4 ,the tape is graduated to feet1 tenths1 and hundredths4 ,the levelling rod to feet1 tenths1 hundredths1 and thousandths4 ,as the ,english foot is so universally adopted1 and as it may at any time be got from a pendulum1 it might not be best to attempt to introduce the metre1 but the foot should certainly be divided decimally4 ,the division should be thus1 4#jja or #a_/ajjj 4#ja or #a_/ajj 4#a or #a4 #aj4 #ajj4 #ajjj4 thus preserving a constant ratio1 and not changing the proportion at each increase or decrease as follows3-- #h_/h #a inch4 #ab inches #a foot4 #af feet #a rod4 #dj rods #a furlong4 #h furlongs #a mile4 #c feet #a yard4 #f feet #a fathom4 ,b4 ,,algebraic ,,formul4 ,as this work may come into the hands of those who are unacquainted with the solution of algebraic problems1 it was thought best to give the following3-- a a1 signifies a added to a1 or #b a4 a - a1 denotes a less a1 or #j4 a a1 a multiplied by a1 or a square1 a#b 7see below74 a a1 a divided by a1 or #a4 or a_/a a#b1 the square of a1 or a a a#c1 the third power of a1 or a a a4 7a71 the square root of a1 or a 7a71 the cube or third root of a1 or a 7a b c7_/d1 shows that the sum of a1 b1 and c1 is to be divided by d4 7a b c7 d or 7a b c7 d1 denotes that the sum of a1 b1 and c1 is to be multiplied by d4 ,generally in place of writing a b to express multiplication1 we put simply a b4 ,the above signs may be compounded in any manner2 thus1 777a b7c7_/d_/m74 ,here we have1 first1 the product of c by the sum of a and b2 this is divided by d1 and three quarters of the quotient is divided by m2 and1 finally1 the fourth root of the last result is extracted1 which is the value of the expression4 ,the following examples show the use of formul4 ,see ,chapter ,,vi41 on ,earthwork1 art4 ,average ,haul3-- ,required the average haul of several masses of earth4 ,let m m m mn represent the several masses1 and d d d dn the respective hauls2 ,s the sum of the masses1 ,d the average haul1 and we have ,d 7m d m d m d mn dn7_/,s4 ,if we make the values m #ajj also d #ajj m #bjj d #ej m #cjj d #ge mn #djj dn #bjj the sum is #ajjj1 and we have ,d 7#ajj #ajj #bjj #ej #cjj #ge #djj #bjj7_/ajjj #abb4e ft4 ,in ,chapter ,,viii41 ,wooden ,bridging1 we have the expression ,s 7#d;b d#b7_/l2 and if b #aj d #ab and l #bj ,s becomes 7#d #aj #add7_/bj #bhh4 ,in ,chapter ,,ix41 ,iron ,bridges1 we have ,t 7ph7_/7#b;f77h#b #d;f#b72 and making p #djjj h #ejj f #hj we have 77#djjj #ejj7_/7b #hj777ejjb 7#d #hjb77 #fefbbjb4 ,in ,chapter ,,xiii41 ,elevation of ,exterior ,rail1 ,e 77,,wv#b7_/7cb,r7_/,w7g1 and when ,w #ej ,v #bj g #e ,r #bjjj we have ,e 77#ej #djj7_/7cb #bjjj7_/ej7e #j4jc ,and finally1 in the latter part of ,chapter ,,xiv41 we have the formula ,d 77n7d c7#b7_/j4ghed7;,a_/,b1 and making n #bjj d #a c #a ,a #d ,b #c we have ,d 7#bjj7b #a7b_/j4ghed7d_/c1 ,now #a #a #e_/b and 7#e_/b7b is #be_/d1 also1 #bjj #be_/d #abej1 #abej #d_/c #afff1 #afff #j4ghed #baba1 finally1 7#baba7 #ddf very nearly4 ,c4 ,,weights ,,and ,,measures4 ,name of material4 ,weight per cubic foot4 ,air #j4jgg lbs4 ,earth #aab4 lbs4 ,water #fb4e lbs4 ,ice #eh4j lbs4 ,sand #acb4j lbs4 ,clay #abj4j lbs4 ,chalk #aee4j lbs4 ,brick #aaj4j lbs4 ,see ,chap4 ,,xi41 masonry4 ,brickwork #ie4j lbs4 ,dry mortar #if4j lbs4 ,sandstone #adj4j lbs4 ,limestone #adb4j lbs4 ,average #hf to #aih4 ,granite #age4j lbs4 ,coal1 ,bituminous #fj to #hj4j lbs4 ,coal1 ,anthracite #he to #ie4j lbs4 ,coke #ej to #fe4j lbs4 ,coal1 ,cannel #ge to #hj4j lbs4 ,wrought ,iron #dhj4j lbs4 ,cast-,iron #dej4j lbs4 ,steel #dhg4j lbs4 ,hard ,wood4 ,green #fb4j lbs4 ,air dried #df4j lbs4 ,kiln dried #dj4j lbs4 ,soft ,wood4 ,green #ec4j lbs4 ,air dried #cj4j lbs4 ,kiln dried #bh4j lbs4 ,weight per bushel4 ,wheat #fj lbs4 ,corn on the cob #gj lbs4 ,corn1 shelled #ef lbs4 ,rye #ef lbs4 ,oats #ce lbs4 ,barley #dg lbs4 ,potatoes1 ,irish #fj lbs4 ,potatoes1 ,sweet #ee lbs4 ,beans1 ,white #fj lbs4 ,beans1 ,castor #df lbs4 ,bran #bj lbs4 ,clover ,seed #fj lbs4 ,timothy #de lbs4 ,hemp #dd lbs4 ,flax #ef lbs4 ,buckwheat #eb lbs4 ,peaches1 ,dried #cc lbs4 ,apples1 ,dried #bd lbs4 ,onions #eg lbs4 ,salt1 ,coarse #ej lbs4 ,malt #ch lbs4 ,corn ,meal #dh lbs4 ,salt1 ,fine #ee lbs4 ,d4 ,,value ,,of ,,the ,,birmingham ,,gauges4 ,number4 ,size in inches4 #j #j4cdj #a 4#cjj #b 4#bhd #c 4#bei #d 4#bch #e 4#bbj #f 4#bjc #g 4#ahj #h 4#aje #i 4#adh #aj 4#acd #aa 4#abj #ab 4#ajj #ac 4#jie #ad 4#jhc #ae 4#jgb #af 4#jfe #ag 4#jeh #ah 4#jdi #ai 4#jdb #bj 4#jce #ba 4#jcb #bb 4#jbh #bc 4#jbe #bd 4#jbb #be 4#jbj #bf 4#jah #bg 4#jaf #bh 4#jad #bi 4#jac #cj 4#jab ,e4 ,,locomotive ,,boilers4 ,if the ideas of ,clark and ,overman are correct1 the value of vertical flues with the water inside1 as compared with horizontal flues with water outside1 is comparatively as follows3 ,one half of the surface of the horizontal tube 7the upper half7 is available1 but this half generates steam twice as fast as the same area of upright tube surface4 ,thus the amount of evaporation will be the same in either position1 for the same absolute tube surface1 not considering the increased diameter by applying the heat to the outside1 or the advantage1 so highly estimated by ,overman1 of applying the heat to the convex surface4 ,the following application of ,montgomery's vertical flue boiler to the locomotive engine for heat generation and application1 seems to satisfy nearly all requirements4 ,retaining the original furnace shell1 produce it forwards so that it shall just clear the driving axle1 let the sides drop to within two feet of the rail1 and close up the bottom4 ,next1 inside of this place a rectangular box which shall be a continuation of the inner box1 the top being about nine inches above the diametric chord of the semicircular crown1 leaving a water space of three or four inches between the sides and bottom of the two boxes4 ,fill the inner box with vertical tubes1 the top and bottom being flue plates1 the tubes being screwed in at one end and fitted with a screw thimble at the other1 may be removed for cleaning at any time and will effectually stay the inner box against the enormous pressure upon the top and bottom4 ,the pressure being inside of the tubes will tend to keep the end joints tight1 where1 in the common boiler1 the reverse is the case4 ,that the burning gases may retain sufficient heat to burn until they are discharged1 there should be less tube surface at the back than at the front end1 a requirement which is easily satisfied by decreasing the number and increasing the size of tubes from the front to the back end4 ,in the common boiler the ferrule area being less than the flue area1 a stronger blast is used than is really necessary to draw the hot gases through the tubes1 while in the vertical tube boiler the gas area may be equally large at all points4 ,again1 any amount of oxygen may be applied to the gases at any point of their passage from the furnace to the smoke box1 by the admission of fresh air to any part of the barrel4 ,thus the advantage of a combustion chamber 7if there is any7 is obtained without the sacrifice of a single inch of heating surface1 as we only require to admit air between the tubes and not into them2 this may be done either by hollow stay bolts or by larger openings1 to be open or shut at pleasure4 ,if the gases in passing through the boiler are left to themselves1 we get1 without an effort1 the effect produced by ,montgomery's third claim1 namely1 the application of the heat to the upper half of the tubes2 and1 however we wish to apply the passing heat to the flues1 complete control over the motion of the gases may be had by the use of a ,venetian blind damper in the smoke box1 in two parts2 the upper and the lower parts moving independently1 allow us to throw the heat upon any part of the length of the tubes4 ,of course1 by heating most the upper part of the flues1 we stand a better chance of getting circulation4 ,it might be objected that so much flat boiler surface would give a form more liable to explosion than the circular barrel4 ,experiments lately made by ,william ,fairbairn1 7,england17 induced by the bursting of a locomotive fire box1 show that the flat surfaces are the strongest forms of the boiler1 or1 to use his own words1 8are conclusive as to the superior strength of flat surfaces as compared with the top1 or even the cylindrical parts of the boiler40 ,his experiments show that two plates one fourth and three eighths inch thick1 connected by screw stay bolts four inches from centre to centre1 will resist over one thousand lbs4 per square inch4 ,by such a plan of engine we may always have any amount of heating surface with a moderate sized boiler1 and a low centre of gravity4 ,the excess of cost of the engine1 above described1 over the common form would be about #ejj1 the annual interest of which is #cj1 which must be saved by the new plan1 7say ten cords of wood74 ,any saving beyond this is pure gain4 ,f4 ,,effect ,,of ,,grades ,,on ,,the ,,cost ,,of ,,working ,,railroads4 ,the cost of working a railroad will be increased by augmenting the steepness of grades4 ,first1 because of the mechanical effect of the inclines2 second1 on account of decreased capacity of the road4 ,the cost of maintaining and working a road consists of items1 a few of which are functions of grades and many which are not4 ,the chief items which are affected by grades are1 fuel consumption1 first cost of locomotives1 and perhaps wear of rails1 where grades are so steep as to require sand ascending1 and application of brakes descending1 the rails will be somewhat more worn4 ,when not so steep as this the repair of superstructure will not be much increased4 ,steeper inclines involve the use of heavier engines1 or more of them4 ,heavy engines generally have no more weight on one pair of wheels1 and often not so much1 as lighter ones2 and though there is more abrasive power on increased total rolling weight1 there is less deflection of rails1 by means of less concentrated loads4 ,it would seem1 therefore1 that the effect of grades upon the wear of superstructure was but little1 if not inconsiderable4 ,the first cost of engines may be increased from #a1jjj to #b1ejj to enable them to work steep grades4 ,if the wheels are the same size in both engines1 we should require greater steam pressure1 consequently 7see ,chapter ,,xiv47 more fuel2 and if the steam power was the same1 smaller wheels or larger cylinders1 also requiring 7,chapter ,,xiv47 more fuel4 ,in doubling the work done by the engine we by no means double the amount of fuel consumed1 7see ,chapter ,,xiv417 but increase it by about ninety per cent4 ,the division of expenses upon five of the largest ,english railroads was for a certain time as follows3-- ,salaries #f4hc ,way and works #ae4gf ,locomotives #ce4ae ,cars #ch4ad ,sundries #c4fi -------------- #ajj4jj ,percentage for engines #ce4jj ,upon the roads of ,belgium1 ,salaries #e4dg ,way and works #bf4fb ,locomotives #di4if ,cars #ad4hj ,sundries #c4ae -------------- #ajj4jj ,locomotive percentage #ej4jj ,upon the railroads of ,new ,york ,state 7#b1bjj miles7 7,state ,engineer's ,report1 #ahed71 ,salaries #aj4jj ,way and works #ae4jj ,locomotives #dj4jj ,cars #bj4jj ,sundries #ae4jj -------------- #ajj4jj ,locomotive percentage #dj4jj ,average percentage of all of the above charged to locomotives #da of the whole locomotive expense2 fuel absorbs #fb percent42 and as a double amount of work requires ninety per cent4 more fuel1 we have1 as the cost of working a grade causing a double resistance 7say twenty-five feet per mile71 #ij_/ajj of #fb_/ajj of #db_/ajj1 or very nearly #bb per cent4 of the cost of working the train2 to which add more1 interest on locomotive capital1 and we have1 as the bad effect of a twenty-five feet grade1 when ,c locomotive capital1 ,d annual cost of working1 of #f_/ajj;,c #bb_/ajj;,d4 ,example4 ,locomotive capital #a1jjj1jjj ,cost of working #bjj1jjj ,annual expense of a level road 7at six per cent47 #fj1jjj #bjj1jjj ---------------- #bfj1jjj ,and upon a road with continuous #be feet grades #fj1jjj #f1jjj #bjj1jjj #bjj1jjj #bb_/ajj1 or #dd1jjj ---------------- ,total #caj1jjj or #abj per cent4 of the cost of working the level road1 the increase being twenty per cent41 or allowing five per cent4 for other contingencies1 twenty-five per cent42 also the increase due to a fifty feet grade1 fifty per cent42 and so on as long as only one engine is required to draw the full train1 7its power being increased by varying its dimensions74 ,when the train has to be broken and two or more engines are needed1 the percentage will of course increase4 ,the point at which the train ought to be broken may be found easily1 either as depending upon the load or the grade1 by a comparison of working expenses4 ,g4 ,,specification ,,for ,a ,,passenger ,,locomotive ,,engine ,,for ,,the ,a4 ,,and ,b4 ,,railroad4 ,requirement4 ,speed #bj miles per hour1 including stops2 fuel1 wood2 weight of train #aej tons2 maximum grade #fj feet per mile2 sharpest curve #c or #a1iaj feet radius2 rail #fj lbs4 per yard on ties #b feet from centre to centre4 ,general ,plan and ,dimensions4 ,outside connections2 four five feet driving wheels with best ,ames's tire1 all tires being flanged2 level cylinders #ae inches diameter of bore and #bj inch stroke4 ,centre-bearing truck1 with inside and outside bearings1 and ,lightener boxes4 ,square wrought iron frame well braced1 #d-cj inch ,whitney and ,sons' cast-iron truck wheels1 spread #fj inches centre to centre4 ,lifting link motion working through rockers1 valves described hereafter4 ,truck supplied with fore and aft safety chains1 and safety beams beneath axles4 ,weight on drivers #cj1jjj lbs41 on truck #aj1jjj lbs4 ,tender to be mounted on two trucks1 each of #d-cj inch ,whitney and ,sons' wheels1 spread #ed inches from centre to centre4 ,to have square iron frames well braced with outside ,lightener boxes2 tank to hold #a1fjj gallons4 ,detailed ,specifications4 ,boiler4--,grate #ch inches wide1 #ed inches long1 surface #bj above rail1 grate bars cast solid for #f inches of the front end1 to be #d inches deep1 and inch thick1 placed inch apart in the clear2 lower edges chamfered on each side by a chamfer of inch deep and inch wide2 centre of grate bars to be supported by a wrought iron bar #a inch thick and #d inches deep1 attached as in drawing4 ,fire-box4--,outer sides of furnace shell #ea inches wide by #fb inches long2 crown #h feet above rail1 to be made of inch iron plates with a #af inch necking of angle iron to carry the rear dome2 corners to be joined by flanges rounded to a #d inch radius4 ,the crown of the shell to be raised #i inches above the barrel crown1 the connection being made by a sloping offset #bj inches long on top4 ,end plates lap jointed to sides and top2 the seams joining the fire-box to the waist1 to be double riveted4 ,furnace to be made of inch copper plates1 inch at tubes1 lap jointed1 #db inches wide1 and #ea inches long inside2 side water spaces to be #c inches clear at the bottom1 widening 7by sloping inwards the sides of the furnace7 to #d inches at the top of inner box2 front spaces #d inches1 rear spaces #d inches at bottom and #e inches at top4 ,doorway made with a wrought iron ring fastened with inch rivets1 door of inch plate with inch shield4 ,furnace joined to shell with inch copper stay bolts1 screwed and riveted at both ends1 placed #dd inches from centre to centre4 ,eight roof-ribs laid widthwise of the crown of the furnace1 being each #f inches deep and inch thick1 double welded at the ends and riveted at the centre1 held down by ,t head bolts #e inches between centres1 bars to be raised above the crown sheet by inch thimbles4 ,dome opening1 neckling to be made of angle iron which shall be connected with the roof-ribs by #d-a inch stays1 connected and placed as in the drawing4 ,the back and tube sheets of the furnace are flanged over on top2 the crown is flanged downwards on the sides1 but not on the back and front4 ,one dome is placed on the crown of fire-box shell #bf inches diameter and #bd inches high2 opening of dome into boiler #af inches diameter4 ,lower part of dome of wrought1 top of cast-iron1 put on with a ground joint4 ,furnace and shell to be connected at bottom by a wrought iron bar #c inches wide1 #b inches deep4 ,the whole boiler to be thoroughly caulked inside and out4 ,barrel of inch best ,philadelphia stamped charcoal iron1 #dd inches diameter outside of main crown next the fire-box1 and #dc inches next the smoke box end1 #aj feet long with #c inch angle irons at ends4 ,front dome of inch plate worked in one piece1 #bc inches diameter4 ,end plates of boiler stayed with six #a inch rods1 cottered into blocks1 riveted to plates2 barrel plates riveted with inch rivets1 and #a inch pitch4 ,smoke box1 #b #d long1 same diameter as barrel1 of #c_/af inch plates well riveted1 bolted to the angle iron so as to be easily removed for inside repairs2 front tube sheet #f_/h inch4 ,tubes1 #adj two inch 7outside7 diameter ,no4 #i thickness at fire end1 ,no4 #ad at smoke end #aj feet long1 placed inch apart4 ,the smoke box end of tubes to be closed at pleasure by a venetian blind damper4 ,chimney of inch iron outside1 diameter #af inches1 top #f #f above crown of barrel1 fitted with proper stack1 cone1 and sparker4 ,ash pan of inch plate made with #a inch angle iron1 and band on upper edge1 fitted with doors both before and behind1 #g inches deep and riding #f inches clear of the rail4 ,steam pipes1 #f inch pipes of ,no4 #aj copper running the whole length of the boiler1 connected at the domes with #e inch cast-iron stand pipes4 ,cast-iron branch pipes in smoke box leading to valve chests1 #e inches diameter4 ,throttle to be in a cast-iron chest in smoke box1 as shown in drawing1 having an area at least as large as the steam port4 ,changes of direction in pipes to be made by curves and not by angles4 ,exhaust pipe of ,no4 #aj copper1 #e inches diameter at lower end1 fitted with a variable blast orifice1 ranging from eight to four square inches area1 to be inclosed in a petticoat pipe4 ,cylinders1 #ae inches bore1 and long enough for a #bj inch stroke1 or #bh inches from outside to outside of ground faces1 casting inch thick1 covers #a inch thick1 placed level and firmly bolted to main frame and to horizontal truss brace1 as shown in drawing2 heads to go on with ground joint4 ,valve seat to have steam ports #ad #a inches2 exhaust port #ad #b inches2 outside lap of valve inch1 inside nothing2 #a_/af inch lead on #d inch throw of valve1 gradually increasing as the throw is reduced1 to scant #e_/af4 ,steam chests bolted to a level face1 ground joint with inch bolts pitched #d inches4 ,valve motion4--,shifting link with lifting shaft1 sector1 lever1 rocker1 etc41 of the most approved form2 four solid eccentrics of #e inches throw1 fastened to axle by four square ended set screws pressing hardened steel dies1 cut with sharp grooves on their ends1 against the axle2 the friction of the dies against the axle holding the eccentric in place4 ,eccentric straps of cast-iron1 with oil caps cast on1 and grooved out inside so as to shut over the eccentric and exclude dust4 ,link forged solid and case hardened1 #ag inches by #b inches inside the slot2 thickness of iron all around the slot #a inches1 whole lateral thickness #b inches4 ,eccentric rods of iron #c inches deep1 #e feet between centres1 fastened to link and to eccentric1 as shown in the drawing4 ,link curved to a radius #f inches less than the distance between the centre of driving axle and centre of link at mid gear4 ,the links1 boxes1 stack1 etc41 to be of wrought iron1 case hardened4 ,pistons with one outside composition ring and two circumferential grooves filled with ,babbitt metal1 and one inside ring of wrought iron2 outside ring cut obliquely at one place with a small wrought iron flap on each edge to prevent leakage of steam at the point of division4 ,glands of piston and valve rod stuff boxes of cast-iron with tight brass or composition bushings4 ,frame forged from good scrap #db inches1 the main bar being straight from end to end with pedestals welded on2 the rear end piece to be a heavy forged foot plate1 the front end an oak beam #gad inches placed on the flat side4 ,all the pedestals on one side having adjustable keys4 ,flat boiler braces averaging #d inches with broad palms riveted to the boiler2 the attachment at the furnace to be made by the ,rogers expansion brace1 details of the frame as in the drawing2 frame to be placed true wherever needed to receive the working parts of the engine4 ,wheels1 axles1 and springs4--,four cast-iron driving wheels tired with best flanged ,ames's tires #b inches thick1 diameter with tire five feet1 tires to be turned to a true cone of 4#jgb inches per wheel1 wheels to be truly balanced4 ,rest scrap or bloom axles1 front #g and rear #f inches in diameter1 bearings #h inches long1 collars of cast-iron held by set screws1 axles to be cylindrical and not smaller at the centre than at the end4 ,four springs of seventeen steel plates1 each #d #dj inches2 equalizing lever between springs4 ,inside bearing springs of truck hung from equalizer1 which latter bears upon the axle boxes4 ,slides1 pumps1 connecting rods1 etc41 etc4--,slides1 flat wrought iron bars #c #a inches1 case hardened4 ,cross head bearing of cast-iron #af inches long and #b inches thick4 ,pumps1 full stroke brass pumps #e_/af inch thick with #a inch plungers1 ram of wrought iron with an eye fixed on cross head and worked by it4 ,waterways in body #b inches1 in valves #a inches4 ,three ball valves with #b inch hollow balls1 one for suction and two for delivery2 pipes inch thick1 #b inches diameter1 suction of iron1 delivery of copper1 cock of brass on delivery pipe worked by rod at cab4 ,air chamber on forcing side of pump equal to capacity of barrel2 on suction side half the same4 ,flat connecting rods forged from solid piles without welds4 ,babbett lined boxes upon all stub ends4 ,straps held on each by two bolts1 one key to each bearing4 ,safety-valves1 one to be #c inches diameter1 placed on the rear dome1 and one forward1 #d inches diameter1 both to be well fitted and supplied with the proper beams and spring balances4 ,barrel to be covered with hair felting inch thick1 to be furnished with a ,russia iron jacket4 ,cylinders to be protected by an inch felt coat and cased in brass4 ,the engine to have all the usual fixtures1 bell1 whistle1 gauges1 heater1 pet1 blow-off1 and other cocks1 name plates1 oil cups1 sandbox1 tools1 oil cans1 etc41 etc4 ,pilot to be #e feet long1 of flat horizontal wooden bars #b #d inches with a heavy centre piece1 the whole to be well hung and firmly braced4 ,cab to be neatly built1 with a projecting cornice1 and windows1 doors1 etc41 to be furnished in the best manner4 ,the whole engine to be well painted and varnished4 ,the draw bar to be strongly attached to the frame of the engine at #cj inches above the rail1 and connected by a double elliptical spring to the centre beam of the tender4 ,tender4--,tank to hold #a1fjj gallons1 top and side plates inch1 and bottom plate inch well riveted and caulked inside and out4 ,brakes to apply from a single wheel to each side of all of the wheels1 that is1 at sixteen points2 brake blocks hung with safety chains and springs to carry them away from the wheels4 ,one spring #bf inches long1 of ten levers #c #e_/af inches over each wheel4 ,frame of seasoned oak #aj #d inches1 centre beam #e #bj inches4 ,the whole to be thoroughly painted and varnished4 ,general ,provision4 ,all of the material1 both of engine and tender1 to be of the very best quality1 and all of the construction done in the most thorough and workmanlike manner4 ,the engine and tender being in every respect equal to the best that has heretofore been sent from the ---- shops4 ,for more detailed information1 see plans accompanying4 ,h4 ,,relative ,,cost ,,of ,,transport ,,by ,,railroad ,,and ,,by ,,stage4 ,too great a reduction of the cost of travel was both expected of and given by railroad companies at the commencement of the system1 as the following will show3-- ,voted1 8,that the directors are hereby earnestly and urgently requested forthwith to increase the rates of transportation1 both for passengers and freight1 in all cases in which1 in their opinion1 they are now too low1 and hereafter to decline all business that will not give to the corporation a full remuneration for expenses and a fair profit for its transportation40 ,why the railroad rates should have been placed so low1 it would be hard to show4 ,the cost of moving eight passengers by stage one hundred miles1 would be somewhat as follows4 ,let a common road cost one thousand dollars per mile1 and suppose the stage travel to use one tenth of the capital expended2 the daily interest for one trip is 7#ajj #ajjj #f_/ajj7_/cfe #aj or #a4fd ,ten horses and one stage1 7#aejj #ejj #f_/ajj7_/cfe or #j4cc ,daily salary of driver and stable hands1 #e4jj ,daily interest on stable cost1 repairs1 c41 c41 #a4jc ---------- ,whole cost of moving #h passengers #ajj miles1 #h4jj ,cost of moving one passenger one mile1 4#ja ,again4 ,let a railroad cost #be1jjj per mile1 one hundred miles cost #b1ejj1jjj1 and if we run ten trains per day the daily interest1 at six per cent41 for one train is 7#bejjjjj #f_/ajj7_/cfe #aj #da4aj ,a locomotive costs #aj1jjj1 ,two cars cost #d1jjj1 and 7#adjjj #f_/ajj7_/cfe is #b4cj ,and the daily cost of road and equipment1 #dc4dj divide by #ajj1 for the cent per mile1 #j4dc ,the average number of passengers carried in one car1 7see ,new ,york ,state ,engineer's ,report17 is #ag2 two cars1 #cd1 whence #dc_/cd #a cents ,the daily cost per mile1 per passenger1 is then1 for the use of the road and equipment1 #a cents ,the cost of maintaining and working is1 per passenger1 per mile1 7see ,new ,york ,state ,engineer's ,report for #ahed47 #a cents ,whence the whole cost of carrying one passenger one mile upon a railroad will be #bg_/ab cents ,the relative cost of transport is1 then1 thus1 ,by stage1 #a cent ,by railroad1 #bg_/ab cents and the relative charge thus1 ,by stage1 #e cents ,by railroad1 #c cents ,and the comparative profit as #e less #a1 or #d2 to #c less #bg_/ab1 or #e_/ab2 or as #a to #i4f4 ,i4 ,,form ,,for ,,recording ,,the ,,results ,,of ,,experimental ,,trips ,,with ,,locomotives4 ,in comparing the work done by different locomotives1 we must know not only the relative amounts of material consumed1 but also the exact nature of the work done1 as depending upon speed1 load1 curves1 and grades4 ,the following blank1 when filled1 has been found to give complete information1 for comparison4 ,station1 ---- ,time of arriving1 ---- ,time of departing1 ---- ,time running1 ---- ,time standing1 ---- ,distance1 ---- ,rise1 ---- ,fall1 ---- ,degrees of curvature1 ---- ,equated distance1 ---- ,cars taken1 ---- ,cars left1 ---- ,load between stations1 ---- ,equated mileage of train1 ---- ,gauge pressure1 ---- ,notch of sector1 ---- ,fuel used1 ---- ,water used1 ---- ,lbs4 of fuel per gallon of water1 ---- ,lbs4 of fuel per equated mileage1 per ton or per passenger1 ---- ,comparative effect1 ---- ,k4 ,,proper ,,weight ,,of ,,locomotives4 ,to move a given load the engine requires a certain amount of power2 to exert such power there is needed load enough on the drivers to prevent slipping on the rail4 ,this load varies from three times the tractive power1 7in the best state of the rails17 to ten times the tractive power1 and even more1 7in the worst state74 ,a fair working average 7without sand71 being one sixth2 with sand1 much less4 ,sand must be used upon grades and upon bad rails4 ,to find then the proper weight1 we have only to estimate the tractive power upon the hardest point of the road1 and multiply it by six4 ,examples4 ,how heavy an engine is needed to draw two hundred tons 7including engine and tender7 at twenty miles per hour over sixty feet grades8 ,the resistance on a level is #bjj 77#bj #bj7_/aga #h7 #b1jfj pounds4 ,the resistance due to the grade #bjj 7#fj_/ebhj #bbdj7 #e1bjj pounds4 ,the resistance due to curves #bjj #e #a1jjj pounds4 ------------ ,and the whole resistance1 #h1bfj pounds4 which multiplied by #f1 is #di1efj pounds4 or #bb4a tons1 to which add #e tons as the necessary load upon the truck1 and the whole weight is #bg4a tons1 which is the necessary weight of an engine to draw #bjj tons over #fj feet grades1 at #bj miles per hour4 ,or1 generally1 ,let ,w ,weight of engine1 tender1 and train1 in tons1 ,let ,v ,speed in miles per hour1 ,let a_/b ,fraction expressing the grade1 ,let c ,resistance1 in pounds per ton due to the sharpest curve1 which1 assume as #e lbs41 as we have no reliable data1 and we have1 as the weight of the engine1 ,w7,v#b_/aga #h7 a_/b #bbdj #ef_/bbdj weight of engine exclusive of weight on truck4 ,if we assume the adhesion as one fourth of the weight on the drivers1 and load #aej tons1 speed twenty miles per hour1 and grade forty feet per mile1 the above formula becomes1 #aej77bj #bj7_/aga #h7 7#dj_/ebhjbbdj7 #ed_/bbdj nine tons nearly4 ,to which add five tons1 and we have as the whole weight1 fourteen tons4 ,illustration3 ,fig4 #aeh4 ---------------------------------------- -------------------------------- ,,transcriber',s ,,notes #a4 ,made corrections listed in ,errata beginning on p4 xv4 #b4 ,did not correct the error for page #cb line #b as it referred to the cut rather than the text4 #c4 ,changed 8area #b1hbg miles0 to 8area #b1hbg square miles0 on p4 #d4 #d4 ,added 8,,general ,,topography0 subheading on p4 #ab4 #e4 ,changed 8#aadhj4ffg0 to 8#aa1dhj1ffg0 on p4 #dj4 #f4 ,changed 8 #e1big4ccd #d1dcg4ccd0 to 8 #e1big1ccd #d1dcg1ccd0 on p4 #ed4 #g4 ,added 8,,slopes0 subheading on p4 #hi4 #h4 ,added 8,,form ,,of ,,railroad ,,sections0 subheading on p4 #ig4 #i4 ,added 8,,rock ,,excavation0 and 8,,blasting ,,and ,,quarrying0 subheadings on p4 #aae4 #aj4 ,added 8,,sidings ,,and ,,crossings0 subheading on p4 #bih4 #aa4 ,changed 8#ah4bd cubic feet per hour0 to 8#ah4bd cubic feet per hour of water0 on p4 #cjd4 #ab4 ,changed all commas to decimals in the table's right-hand column titled 8,resistance in lbs4 per ton0 on p4 #cad to agree with the previous expression4 #ac4 ,added 8,,retarding ,,of ,,trains0 subheading on p4 #dja4 #ad4 ,added 8,,classification ,,of ,,buildings01 8,,location ,,of ,,buildings01 and 8,,terminal ,,passenger ,,house0 subheadings on p4 #djc4 #ae4 ,added 8,,terminal ,,freight ,,house0 and 8,,engine ,,house ,,and ,,appurtenances0 subheadings on p4 #dje4 #af4 ,added 8,,wood ,,shed ,,and ,,tank0 subheading on p4 #djg4 #ag4 ,silently corrected typographical errors4 #ah4 ,retained anachronistic and non-standard spellings as printed4 #ai4 ,enclosed italics font in underscores4 #bj4 ,enclosed bold font in pilcrow signs4 #ba4 ,superscripts are denoted by a caret before a single superscript character or a series of superscripted characters enclosed in curly braces1 e4g4 ,mr4 or ,mister4