,,american ,,society ,,of ,,civil ,,engineers ,,instituted #aheb ,,transactions ,paper ,no4 #aagb ,,locomotive ,,performance ,,on ,,grades ,,of ,,various ,,lengths4 ,,by ,,beverly ,s4 ,,randolph1 ,m4 ,,am4 ,,soc4 ,c4 ,e4 ,,with ,,discussion ,,by ,,messrs4 ,c4 ,d4 ,,purdon1 ,,john ,c4 ,,trautwine1 ,,jr41 ,,and ,,beverly ,s4 ,,randolph4 ,in the location of new railways and the improvement of lines already in operation1 it is now well recognized that large economies can be effected by the careful study of train resistance due to grades and alignment1 distributing this resistance so as to secure a minimum cost of operation with the means available for construction4 ,while engaged in such studies some years ago1 the attention of the writer was attracted by the fact that the usual method of calculating the traction of a locomotive--by assuming from #bj to #be of the weight on the drivers--was subject to no small modification in practice4 ,in order to obtain a working basis1 for use in relation to this feature1 he undertook the collection of data from the practical operation of various roads4 ,subsequent engagements in an entirely different direction caused this to be laid aside until the present time4 ,the results are given in ,table #a1 from which it will be seen that the percentage of driver weight utilized in draft is a function of the length as well as the rate of grade encountered in the practical operation of railways4 ,in this table1 performance will be found expressed as the percentage of the weight on the drivers which is utilized in draft4 ,this is calculated on a basis of #f lb4 per ton of train resistance1 for dates prior to #ahhj1 this being the amount given by the late ,a4 ,m4 ,wellington1 ,m4 ,am4 ,soc4 ,c44 ,e41,a and #d4g lb4 per ton for those of #aijh-aj1 as obtained by ,a4 ,c4 ,dennis1 ,m4 ,am4 ,soc4 ,c4 ,e41,b assuming this difference to represent the advance in practice from #ahhj to the present time4 ,most of the data have been obtained from the ,catalogue of the ,baldwin ,locomotive ,works for #ahha1 to which have been added some later figures from ,record ,no4 #fe of the same establishment1 and also some obtained by the writer directly from the roads concerned4 ,being taken thus at random1 the results may be accepted as fairly representative of ,american practice4 ,attention should be directed to the fact that the performance of the #aj-cd ,e1 ,consolidation locomotive on the ,lehigh ,valley ,railroad in #ahga is practically equal to that of the latest ,mallet compounds on the ,great ,northern ,railway4 ,in other words1 in the ratio between the ability to produce steam and the weight on the drivers there has been no change in the last forty years4 ,this would indicate that the figures are not likely to be changed much as long as steam-driven locomotives are in use4 ,what will obtain with the introduction of electric traction is another story4 ,these results have also been platted1 and are presented in ,fig4 #a1 with the lengths of grade as abscissas and the percentages of weight utilized as ordinates4 ,the curve sketched to represent a general average will show the conditions at a glance4 ,the results may at first sight seem irregular1 but the agreement is really remarkable when the variety of sources is considered2 that in many cases the reputed rate of grade is doubtless given without actual measurement2 that the results also include momentum1 the ability to utilize which depends on the conditions of grade1 alignment1 and operating practice which obtain about the foot of each grade2 and that the same amount of energy due to momentum will carry a train farther on a light grade than on a heavy one4 ,there are four items in ,table #a which vary materially from the general consensus4 ,for ,item #i1 the authorities of the road particularly state that their loads are light1 because1 owing to the congested condition of their business1 their trains must make fast time4 ,item #aj represents very old practice1 certainly prior to #ahhb1 and is second-hand4 ,the load consisted of empty coal cars1 and the line was very tortuous1 so that it is quite probable that the resistance assumed in the calculation is far below the actual4 ,items #ae and #ag are both high4 ,to account for this1 it is to be noted that this road has been recently completed1 regardless of cost in the matter of both track and rolling stock1 and doubtless represents the highest development of railroad practice4 ,its rolling stock is all new1 and is probably in better condition to offer low resistance than it will ever be again1 and there were no foreign cars in the trains considered4 ,the train resistance1 therefore1 may be naturally assumed to be much less than that of roads hauling all classes of cars1 many of which are barely good enough to pass inspection4 ,as the grades are light in both cases1 this feature of train resistance is larger than in items including heavier grades4 ,attention should be called to the fact that a line connecting the two points representing these items on ,fig4 #a would make only a small angle with the sketched curve1 and would be practically parallel to a similar line connecting the points represented by ,items #ac and #af4 ,there is1 therefore1 an agreement of ratios1 which is all that needs consideration in this discussion4 ,illustration3 ,,fig4 #a4--;,,diagram ,,showing ,,percentage ,,of ,,weight ,,on ,,drivers ,,which ,,is ,,utilized ,,in ,,traction ,,on ,,grades ,,of ,,various ,,lengths ,wellington1 in his monumental work on railway location1 presents a table of this character4 ,the percentages of weight on the drivers which is utilized in draft show the greatest irregularity4 ,he does not give the length of the grades considered1 so that it is impossible to say how far the introduction of this feature would have contributed to bring order out of the chaos4 ,in his discussion of the table he admits the unsatisfactory character of the results1 and finally decides on #be as a rough average1 very approximately the safe operating load in regular service4 ,he further states that a number of results1 which he omits for want of space1 exceeds #cc per cent4 ,the highest shown in ,table #a will be found in ,item #a 7#j4jf mile1 #j4jff grade71 showing #cc per cent4 ,there is no momentum effect here1 as the grade is a short incline extending down to the river1 and the start is necessarily a dead one4 ,the reports of ,item #c1 which shows #ca1 and ,item #e1 which shows #bg1 state specifically that the locomotives will stop and start the loads given at any point on the grade4 ,the results of a series of experiments reported by ,mr4 ,a4 ,c4 ,dennis in his paper1 ,virtual ,grades for ,freight ,trains1 previously referred to1 indicate a utilization of somewhat more than #bc1 decreasing with the speed4 ,all this indicates that the general failure of locomotives to utilize more than from #af to #ah on long grades1 as shown by ,table #a1 can only be due to the failure of the boilers to supply the necessary steam4 ,while the higher percentage shown for the shorter grades may be ascribed largely to momentum present when the foot of the grade is reached1 the energy due to stored heat is responsible for a large portion of it4 ,when a locomotive has been standing still1 or running with the steam consumption materially below the production1 the pressure accumulates until it reaches the point at which the safety valve is set4 ,this means that the entire machine is heated to a temperature sufficient to maintain this pressure in the boiler4 ,when the steam consumption begins to exceed the production1 this temperature is reduced to a point where the consumption and production balance4 ,the heat represented by this difference in temperature has passed into the steam used1 thus adding to the energy supplied by the combustion going on in the furnace4 ,the engines1 therefore1 are able to do considerably more work during the time the pressure is falling than they can do after the fall has ceased4 ,the curve in ,fig4 #a would indicate that the energy derived from the two sources just discussed is practically dissipated at #ae miles1 though the position of the points representing ,items #af1 #ah1 #ai1 #bj1 and #ba would indicate that this takes place more frequently between #aj and #ab miles4 ,from this point onward the performance depends on the efficiency of the steam production1 which does not appear to be able to utilize more than #af of the weight on the drivers4 ,the diagrams presented by ,mr4 ,dennis in his paper on virtual grades1 and by ,john ,a4 ,fulton1 ,m4 ,am4 ,soc4 ,c4 ,e41 in his discussion of that paper1 indicate that similar results would be shown were they extended to include the distance named4 ,from this it would appear that a locomotive is capable of hauling a larger train on grades less than #aj miles in length than on longer grades1 and that1 even when unexpectedly stopped1 it is capable of starting again as soon as the steam pressure is sufficiently built up4 ,conversely1 it should be practicable to use a higher rate of ascent on shorter grades on any given line without decreasing the load which can be hauled over it4 ,in other words1 what is known as the ruling grade is a function1 strictly speaking1 of the length as well as the rate of grade4 ,in any discussions of the practicability of using a higher rate on the short grades1 which the writer has seen1 the most valid objection has appeared to be the danger of stalling and consequent delay4 ,as far as momentum is relied on1 this objection is valid4 ,within the limits of the load which can be handled by the steam1 it has small value1 as it is only a question of waiting a few minutes until the pressure can be built up to the point at which the load can be handled4 ,as this need only be an occasional occurrence1 it is not to be balanced against any material saving in cost of construction4 ,the writer does not know of any experiments which will throw much light on the value of heat storage as separated from momentum1 though the following discussion may prove suggestive3 ,a train moving at a rate of #fj ft4 per sec41 and reaching the foot of a grade1 will have acquired a velocity head of #ef4g ft41 equivalent to stored energy of #ef4g #b1jjj #aac1djj ft-lb4 per ton4 ,on a #j4jjb grade 7as in ,item #ae of ,table #a7 the resistance would be1 gravity #d lb4 train #d4g lb4 #h4g lb41 against which the energy above given would carry the train through #aac1djj #h4g #ac1jcd ft41 say1 #b4e miles1 leaving #e miles to be provided for by the steam production4 ,examining the items in the table having grades in excess of #aj miles1 it will be noted that #af is about all the weight on drivers which can be utilized by the current supply of steam4 ,in ,item #ae the energy derived from all sources is equivalent to #bd4c2 hence the stored heat may be considered as responsible for an equivalent of #bd4c - #af #h4c for a distance of #e miles4 ,,table #a4 ,item ,no4 ,length of grade1 in miles4 ,rate of grade4 ,maximum curvature4 ,compensation4 ,gross weight of load1 in tons4 ,weight of tender1 in tons4 ,weight of locomotive1 in tons4 ,weight on drivers1 in tons4 ,percentage of weight on drivers utilized in draft4 ,class4 ---------------------------------------- ------------------------- #a #j4jfj4jff #aae #cg4e #bi #j4ceh #h-bh-a_/c ,c #b #j4ccj4jbjcbebj' #bdbbe #ce #bc #j4bhe #h-bh ,c #c #a4j #j4jf #af #j4je #aibbb #eg4e #ej #j4cajaj-cf ,e #d #a4c #j4jabg #fjjaf #dj #cb4ej4cjj,mogul4 #e #a4d #j4jabh #cab' #gejae #ea #dd #j4bgjaj-cd ,e #f #b4j #j4ja #a1jjjae #ea #dd #j4biaaj-cd ,e #g #b4b #j4jac #c #gbeae #ea #dd #j4bdeaj-cd ,e #h #b4e #j4jadd #f #djjbg #db #cb #j4bcgaj-cb ,e #i #b4e #j4jjd #b1gjjgj #if4g #he4hj4bjg ,h #f - ,a #aj #c4e #j4jcc #ad #ajjbe #ce #ce #j4afj #aa #c4f #j4jce #aj #j4je #bcfbb #eg4e #ej #j4bdeaj-cf ,e #ab #d4j #j4jjhe #d #a1jbjcj #ea #dd #j4befaj-cd ,e #ac #f4j #j4jade #cjhbe #ch #bh #j4bjgaj-bh ,d #ad #f4j #j4jbj #aj #j4je #dfjcb #eg4e #ej #j4bdbaj-cd ,e #ae #g4e #j4jjb ,c #f1aebhfacd4eaji4ej4bdc,mallet4 #af #i4gej4jah #bjjah #bi #bi #j4agj #agaj4j #j4jjf ,c #f1agchfbii #bfe #j4bjc,mallet4 #ahab4j #j4jah #aj #bhjcj #ea #dd #j4afjaj-cd ,e #aiab4j #j4jbb #hejgdage #aef #j4aff;,d-,d #af #bjac4j #j4jbb #hjjgdagg #aeh #j4aec;,d-,d #a #baac4j #j4jbb #ad #daeej #ia #hc #j4aed;,consol4 #bbaf4j #j4jjdd #iejcj #ea #dd #j4afdaj-cd ,e #bcbj4j #j4jbb #ejjfb #ig4e #ij #j4agj;,f #h1 ,consol4 #bdbj4j #j4jbb #hjjgdagg #aeh #j4aei,l-#a1 ,mallet4 ,maker4 ,railroad4 ,reporting ,officer4 ,year4 ---------------------------------------- -------------------------------- #a;,baldwin4,morgan's ,louisiana ,texas ,newell ,tilton1 ,asst4 ,supt4 #ahhj #b ,long ,island ,s4 ,spencer1 ,gen4 ,supt4 #ahgh #c ,atchison1 ,topeka ,santa ,fe ,j4 ,d4 ,burr1 ,asst4 ,engr4 #ahgi #d ,chillan ,talcahuana ,j4 ,e4 ,martin1 ,local ,supt4 #ahgi #e ,chicago1 ,burlington ,quincy,h4 ,b4 ,stone #ahhj #f ,chicago1 ,burlington ,quincy #ahhj #g ,chicago1 ,burlington ,quincy #ahhj #h ,st4 ,louis ,san ,francisco ,c4 ,w4 ,rogers1 ,gen4 ,mgr4 #ahgi #i,pa4 ,r4,r ,cumberland ,valley4 #aiaj #aj #aiaj #aa;,baldwin4,atchison1 ,topeka ,santa ,fe ,j4 ,d4 ,burr1 ,asst4 ,engr4 #ahgi #ab ,missouri ,pacific ,john ,hewitt1 ,supt4 ,m4 ,p4 #ahhj #ac ,western ,maryland ,d4 ,holtz1 ,m4 of ,mach'y4 #ahgh #ad ,atchison1 ,topeka ,santa ,fe ,j4 ,d4 ,burr1 ,asst4 ,engr4 #ahgi #ae ,virginian ,ry4 #aiaj #af ,pennsylvania #aiaj #ag;,baldwin4,virginian ,ry4 #aiaj #ah ,lehigh ,valley1 ,wyoming ,div4 ,a4 ,mitchell1 ,div4 ,supt4 #ahga #ai ,great ,northern ,grafton ,greenough4 #aijh #bj ,great ,northern ,grafton ,greenough4 #aijh #ba ,baltimore ,ohio ,f4 ,e4 ,blaser1 ,div4 ,supt4 #aiaj #bb ,central of ,n4 ,j4 ,w4 ,w4 ,stearns1 ,asst4,gen4,supt4#ahhj #bc ,great ,northern ,grafton ,greenough4 #aijh #bd ,great ,northern ,grafton ,greenough4 #aijf ,source of ,data4 ,remarks4 ---------------------------------------- ------------------------------------ #a;,baldwin ,catalogue1 #ahha1 p4 #acd #b #ahha1 #gb #aj miles per hour4 #c #ahha1 #aae #h ,stops and starts on grade4 #d #ahha1 #ajj #e #ahha1 #aaf ,stops and starts at any point on grade4 #f #ahha1 #aaf #g #ahha1 #aaf #h #ahha1 #hg #i #aj,trautwine's ,pocket ,book1 ,ed4 #ahhb1 p4 #dab;,empty cars2 many curves and reversions4 #aa;,baldwin ,catalogue1 #ahha1 p4 #aad #ab #ahha1 #aab #ac #ahha1 #hf #ab miles per hour4 #ad #ahha1 #aad #h #ae;,engineering ,news1 ,jan4 #ac1 #aiaj4 #af,trautwine's ,pocket ,book1 ,ed4 #ahhb1 p4 #dab #ag;,engineering ,news1 ,jan4 #ac1 #aiaj4 ,road locomotive and helper4 #ah;,baldwin ,catalogue1 #ahha1 p4 #aab #ai;,baldwin ,loco4 ,wks4 ,record1 ,no4 #fe1 p4 #bi #bj;,baldwin ,loco4 ,wks4 ,record1 ,no4 #fe1 p4 #bi #ba ,very crooked line4 ,uncompensated4 #bb;,baldwin ,catalogue1 #ahha1 p4 #aac #bc;,baldwin ,loco4 ,wks4 ,record1 ,no4 #fe1 p4 #bi #bd;,baldwin ,loco4 ,wks4 ,record1 ,no4 #fe1 p4 #bi ,in proportioning grade resistance for any line1 therefore1 a locomotive may be counted on to utilize #bd4c of the weight on the drivers for a distance of #e miles on a #j4jjb grade without any assistance from momentum1 and1 in the event of an unexpected stop1 should be able1 as soon as a full head of steam is built up1 to start the train and carry it over the grade4 ,this is probably a maximum1 considering the condition of the equipment of this ,virginian ,railway1 as previously mentioned4 ,treating ,item #ad in the same way1 a distance of #b1caj ft4 is accounted for by momentum1 leaving1 say1 #e4e miles for the steam1 or the length of a #j4jb grade on which a locomotive may be loaded on a basis of tractive power equal to #bd4b of the weight on the drivers4 ,from these figures it may be concluded that on lines having grades from #ab to #ae or more miles in length1 grades of #c to #e miles in length may be inserted having rates #ej in excess of that of the long grades1 without decreasing the capacity of the line4 ,this statement1 of course1 is general in its bearings1 each case being subject to its especial limitations1 and subject to detailed calculations4 ,it may be noted that the velocity of #fj ft4 per sec41 assumed at the foot of the grade1 is probably higher than should be expected in practice2 it insures1 on the other hand1 that quite enough has been allowed for momentum1 and that the results are conservative4 ,arguments like the foregoing are always more or less treacherous2 being based on statistics1 they are naturally subject to material modifications in the presence of a larger array of data1 therefore1 material assistance in reaching practical conclusions can be given by the presentation of additional data4 ,,discussion ,c4 ,d4 ,,purdon1 ,m4 ,,am4 ,,soc4 ,c4 ,e4 7by letter74--,some years ago the writer1 in making studies for grade revision1 found that the tractive power of a locomotive up grade becomes less as the length of the grade increases1 and in some unknown proportion4 ,this was a practical confirmation of the saying of locomotive engineers1 that the engine got tired on long grades4 ,on a well-known ,western railroad1 with which the writer is familiar1 experiments were made for the purpose of rating its locomotives4 ,the locomotives were first divided into classes according to their tractive power1 this being calculated by the usual rule1 with factors of size of cylinders1 boiler pressure1 and diameter of drivers1 also by taking one-fourth of the weight on the drivers1 and using the lesser of the two results as the tractive power4 ,locomotives of different classes1 and hauling known loads1 were run over a freight division1 the cars being weighed for the purpose2 thus the maximum load which could be handled over a division1 or different parts of a division1 was ascertained1 and this proportion of tonnage to tractive power was used in rating all classes4 ,of course1 this method was not mathematically accurate1 as the condition of track1 the weather1 and the personal equation of the locomotive engineers all had an effect1 but1 later1 when correcting the rating by tests with dynamometers1 it was found that the results were fairly practical4 ,there were three hills where the rate of grade was the same as the rest of the division1 but where the length was much in excess of other grades of the same rate4 ,designating these hills as ,a1 ,b1 and ,c1 the lengths are1 respectively1 #b4dd1 #c4eg1 and #d4da miles4 ,there were no other grades of the same rate exceeding #a mile4 ,in one class of freight engines1 #aj-wheel ,brooks1 the weight of the engine was #aig1ijj lb42 tender1 #acb1hjj lb42 weight on drivers1 #adb1fjj lb42 boiler pressure1 #bjj lb42 and tractive power of cylinders1 #cc1cjj lb4 ,on ,hill ,a these engines are rated at #hfe tons1 as compared with #ide on other parts of the division4 ,as the engine weighs #afe tons and the caboose #ae tons1 #ahj tons should be added1 making the figures1 #a1jde and #a1abe tons4 ,thus the length of the grade1 #b4dd miles1 makes the tractive power on it #ib of that on shorter grades4 ,on ,hill ,b1 the rating1 adding #ahj tons as above1 is #a1afj and #a1bcj tons1 respectively1 giving #id for #c4eg miles4 ,on ,hill ,c1 the rating1 with #ahj tons added1 is #a1acj and #a1bcj tons1 making #ib for #d4da miles4 ,taking the same basis as the author1 namely1 #d4g lb4 per ton1 rate of grade #bj1 and weight on drivers1 gives3 ,hill ,a1 #ah4jgh1 remainder of division1 #ai4dfb ,hill ,b1 #bj4jfh1 #ba4bgi ,hill ,c1 #ai4edi1 #ba4bgi ,it will be noted that the author uses the weight on the drivers as the criterion1 but the tractive power is not directly as the weight on the drivers1 some engines being over-cylindered1 or under-cylindered2 in the class of engines above mentioned the tractive power is #bc4ce of the weight on the drivers4 ,the writer made a study of several dynamometer tests on ,hill ,c4 ,there is a grade of the same rate1 about #a mile long1 near this hill1 and a station near its foot1 but there is sufficient level grade between this station and the foot of the hill to get a good start4 ,all the engines of the above class1 loaded for ,hill ,c1 gained speed on the #a-mile grade1 but began to fall below the theoretical speed at a point about #b-a_/d miles from the foot of the hill4 ,this condition occurred when the trains stopped at the station and also when they passed it at a rate of some #af or #ah miles per hour1 the speed becoming less and less as the top of the hill was approached4 ,the writer concludes that the author might stretch his opinion as to using heavier rates of grade on shorter hills than #aj miles1 and indeed his diagram seems to intimate as much1 and that1 for economical operation1 the maximum rate of grade should be reduced after a length of about #b miles has been reached1 and more and more in proportion to the length of the hill1 in order that the same rating could be applied all over a division4 ,this conclusion might be modified by local conditions1 such as an important town where cars might be added to or taken from the train4 ,while it does not seem practicable to the writer to calculate what the reduction of rate of grade should be1 a consensus of results of operation on different lengths of grade might give sufficient data to reach some conclusion on the matter4 ,the ,american ,railway ,engineering and ,maintenance of ,way ,association has a ,committee on ,railway ,economics1 which is studying such matters1 but so far as the writer knows it has not given this question any consideration4 ,the writer hopes that the author will follow up this subject1 and that other members will join1 as a full discussion will no doubt bring some results on a question which seems to be highly important4 ,,john ,c4 ,,trautwine1 ,,jr41 ,,assoc4 ,,am4 ,,soc4 ,c4 ,e4 7by letter74--,in his collection of data1 ,mr4 ,randolph includes two ancient cases taken from the earliest editions 7#ahgb-ahhc7 of ,trautwine's ,civil ,engineer's ,pocket-,book1 referring to performances on the ,mahanoy and ,broad ,mountain ,railroad 7now the ,frackville ,branch of the ,reading7 and on the ,pennsylvania ,railroad1 respectively4 ,in the private notes of ,john ,c4 ,trautwine1 ,sr41 these two cases are recorded as follows3 ,on the ,mahanoy ,broad ,mtn4 ,r4 ,r41 tank ,engines of #ce tons1 all on #h drivers1 draw #dj empty coal cars weighing #ajj tons1 up a continuous grade of #age ft4 per mile for #c-a_/b miles2 around curves of #dej1 #ejj1 #fjj ft4 c4 rad41 at #h miles an hour4 7#ahfd7 ,this is equal to #gg-ad_/ajj tons for a #bg-ton engine4 7,vol4 ,,iii1 p4 #agf47 ,on the ,penn ,central #ie ft4 grades for #i-c_/d miles1 a #bi-ton engine all on #h drivers takes #abe tons of freight and #aab tons of engine1 tender1 cars1 in all #bcg tons1,c and a passenger engine takes up #c cars at #bd miles an hour 7large #h wheels74 ,when more than #c1 an auxiliary engine4 ,it will be seen that ,mr4 ,randolph is well within bounds in ascribing to the ,mahanoy and ,broad ,mountain case 7his ,no4 #aj7 a date certainly prior to #ahhb1 the date being given1 in the notes1 as #ahfd2 while another entry just below it1 for the ,pennsylvania ,railroad case1 is dated #ahfj4 ,it also seems1 as stated by ,mr4 ,randolph1 quite probable that the frictional resistance 7#f lb4 per #b1jjj lb47 assumed by him in the calculation is far below the actual for this ,case #aj4 ,the small1 empty1 four-wheel cars weighed only #d1djj lb4 each4 ,furthermore1 the tons1 in the ,trautwine reports of these experiments1 were tons of #b1bdj lb4 ,on the other hand1 the maximum curvature was #ab #de' 7not #ad1 as given by the author71 and the engine was a tank locomotive1 whereas the author has credited it with a #be-ton tender4 ,after making all corrections1 it will be found that1 in order to bring the point1 for this ,case #aj1 up to the author's curve1 instead of his #f lb4 per #b1jjj lb41 a frictional resistance of #ff lb4 per #b1jjj lb4 would be required1 a resistance just equal to the gravity resistance on the #c4c grade1 making a total resistance of #acb lb4 per #b1jjj lb4 ,while this #ff lb4 per ton is very high1 it is perhaps not too high for the known conditions1 as above described4 ,for modern rolling stock1 ,mr4 ,a4 ,k4 ,shurtleff gives the formula3,d ,frictional resistance1 on tangent1 in pounds per #b1jjj pounds #a #ij ,c1 where ,c weight of car and load1 in tons of #b1jjj lb4 ,this would give1 for #d1djj-lb4 7#b4b-ton7 cars1 a frictional resistance of #db lb4 per #b1jjj lb42 and1 on the usual assumption of #j4h lb4 per #b1jjj lb4 for each degree of curvature1 the #ab4ge curves of this line would give #aj lb4 per ton additional1 making a total of #eb lb4 per #b1jjj lb4 over and above grade resistance1 under modern conditions4 ,in the #ith to #agth editions of ,trautwine 7#ahhe-aijj71 these early accounts were superseded by numerous later instances1 including some of those quoted by the author4 ,in the #ahth and #aith editions 7#aijb-aiji7 are given data respecting performances on the ,catawissa ,branch of the ,reading 7,shamokin ,division7 in #ahih-aija4 ,these give the maximum and minimum loads hauled up a nearly continuous grade of #ca4dg ft4 per mile 7#j4ei7 from ,catawissa to ,lofty 7#cd4jc miles7 by engines of different classes1 with different helpers and without helpers4 ,table #b 7in which the writer follows the author in assuming frictional resistance at #d4g lb4 per #b1jjj lb47 shows the cases giving the maximum and minimum values of the quantity represented by the ordinates in the author's diagram1 namely1 ,traction1 in percentage of weight on drivers4 ,it will be seen that the maximum percentage 7#af4a7 is practically identical with that found by the author 7#af7 for grade lengths exceeding #ag miles4 ,near the middle of the #cd-mile distance there is a stretch of #a4ea miles1 on which the average grade is only #e4ic ft4 per mile 7#j4aab71 and this stretch divides the remaining distance into two practically continuous grades1 #ai4ci and #ac4ac miles long1 respectively2 but1 as the same loads are hauled over these two portions by the same engines1 the results are virtually identical1 the maxima furnishing two more points closely coinciding with the author's diagram4 ,,table #b4--,,tractive ,,force1 ,,catawissa ,,to ,,lofty4 ,length of grade1 in miles #cd4jc ,grade in feet per mile #ca4dg percentage ,a #j4eig ,resistances1 in pounds per #b1jjj lb41 ,gravity 7#bj ,a7 #aa4id4 ,friction #d4gj ,b #af4fd ,load3 ,cars4 ,locomotive4 ,tender4 ,maximum,e #a1efa #dd4fj #be4be ,c #a1fca ,minimum,f #a1jca #fj4ej #cd4ej ,c #a1abf ,traction 7 ,b ,c #b1jjj 7 ,maximum,e ,d #ac4fj ,minimum,f ,d #i4ch ,weight on ,drivers3 ,locomotive4 ,helper4 ,maximum,e #ba4fj #fc4jj ,e #hd4fj ,minimum,f #dg4jj #gb4jj ,e #aai4jj ,percentage 7 ,d ,e 74 ,maximum ,f #af4a ,minimum ,f #g4i ,,footnotes3 ,footnote ,e3 ,giving maximum values of percentage1 ,f4 ,footnote ,f3 ,giving minimum values of percentage1 ,f4 ,,beverly ,s4 ,,randolph1 ,m4 ,,am4 ,,soc4 ,c4 ,e4 7by letter74--,the percentages given by ,mr4 ,purdon would seem to indicate that the length of the grades did not affect the loads in the cases cited1 but these percentages are so much below those shown in the table1 for similar distances1 as to indicate some special conditions which the writer has been unable to find in the text4 ,the use of the percentage of weight on drivers which is utilized in traction as a measure of the efficiency of the locomotive1 while1 probably1 not applicable to individual machines1 is sound for the purposes of comparison of results to be obtained on various portions of a line as far as affected by conditions of grade and alignment4 ,it has the advantage of disregarding questions of temperature1 condition of track1 character of fuel1 etc41 which1 being the same on all portions of the line1 naturally balance and do not affect the comparison4 ,it is1 of course1 simply a method of expressing the final efficiency of the various parts of the locomotive1 and1 since it depends entirely on actual results already accomplished1 leaves no room for difference of opinion or theoretical error4 ,the writer has always considered an under-cylindered locomotive as a defective machine4 ,all weight is a distinct debit1 in the shape of wear and tear of track and running gear1 resistance due to gravity on grades1 interest on cost1 etc4 ,when this weight fails to earn a credit in the way of tractive efficiency1 it should not be present4 ,the statement relative to the performance of locomotives on ,hill ,c is interesting1 especially in that it appears to have been immaterial whether they made a dead start after stopping at the station or approached the foot of the hill at #af to #ah miles per hour4 ,the momentum would appear to be an insignificant factor4 ,it is gratifying to note that ,mr4 ,trautwine has been able to brace up the weak member of ,table #a so completely with his detailed data2 also that his other results strengthen the conclusions reached in the paper4 ,,footnotes3 ,footnote ,a3 ,the ,economic ,theory of ,railway ,location1 #ahhg edition1 p4 #ejb4 ,footnote ,b3 ,transactions1 ,am4 ,soc4 ,c4 ,e41 ,vol4 ,l1 p4 #a4 ,footnote ,c3 ,nearly #bjj tons exclusive of eng4 ten4 7,vol4 ,,iii1 p4 #agf-a_/aj47 ,footnote ,d3 ,american ,railway ,engineering and ,maintenance of ,way ,association1 ,bulletin #hd1 ,february1 #aijg1 p4 #ii4