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THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



The next question namely, the effect or value of gradients, is one so 



susceptible of calculation, that it might be supposed to be a point upon which 

 no great diffi-rencc of opinion could exist ; and when the calculations are 

 exactly made, and the simple results clearly stated, no difference will be found 

 to exist. 



In the comparison between gradients of 10 feet per mile and 4 feet per mile 

 (p. 49), in which a diminution of resistance when ascending the latter, as 

 compared with the former, of 17 per cent, is admitted, data arc assumed 

 different from those generally given by the best authorities on the subject, and 

 conditions most essential to an accurate comparison are omitted. Ten lbs. 

 per ton are assumed as the resistance on a level ; eight lbs. have generally 

 been taken as nearer tlic truth, and, upon a railway in good order, with 

 carriages also in good order, may safely be taken as the total resistance of a 

 train. The effect of gravity in inclina'ions of 4 feet and 10 fcetwillbo I.Tibs., 

 and 4. 25lbs., which, with the constant of 8lbs., makes 9.7lbs., and l-2.'2.jlbs. 

 per ton; this, or 1(10 to 12G, gives the ratio of tlie resistance on the two 

 gradients, being already 20 per cent., instead of 17. But if the maximum 

 load that an engine can draw (of course at the regular speed of the trains) up 

 the incline be taken, the weight of the engine and tender must be deducted, in 

 either case, to obtain the effcclive load. In fast trains, s,uch as those running 

 on the Liverpool and Manchester line, the engine and tender will be about 30 

 per cent, of the gross weight, in the three cases cited by the writer at p. 8 and 

 9, the proportion is even (jreater, being two-fifths, or 40 per cent. ; but I will 

 admit even one fourth to be the proportion, which would be allowing a fast 

 passenger- train to weigh nett tiO tons, with an engine and tender, such as 

 those of the Grand Junction, weighing 20 tons. From 100 and 120 is therefore 

 to be deducted one quarter of 100, or 2o, leaving 7J and 101, which are as 

 loo to 134, being an excess of 34 per cent, instead of 17 in the nett load 

 which the same engine will be capable of drawing at the same velocity up the 

 incline of 4 feet over that which it would draw on an incline of 10 feet ; but 

 the writer, after making the calculation, proceeds to sink all comparison by the 

 simple assertion, tlsat " on an inclined plane '' of 1 in 628 (10 feet per mile) 

 all average loads " could be taken." Undoubtedly they can, but at a propor- 

 tionate sacrifice of power or speed, which ought to have been added ; without 

 it the statement is incorrect, and with it I do not understand the object of the 

 observation. The naked result of the above calculation is not altered Ijy the 

 omission, although certainly it may in consequence escape the recollection of 

 the reader. 



In the next paragraph the same thing is asserted in a different shape. It 

 nould have been desirable to have had explained what was meant by a " full 

 average load." It appears to be assumed as a fixed or constant quantity for all 

 railways, and quite independently of the gradients, or even of the power of the 

 engines. I do not understand how any such fixed quantity can exist. Several 

 of the present trains on the Grand Junction railway require two engines; 

 sbould they increase so as to require three, it will probably be necessary to 

 divide them ; the capabilities of the line, or of the engines, will then have 

 influenced the load. In the cases of the three different railways before referred 

 to as quoted in the report, the average nett loads of the trains referred to are, 

 24 tons, 32 tons, and 40 tons respectively ; and the average load in one case 

 is therefore nearly double that in another. 



Whatever may be the results on other railways, we know from experience 

 on the Great Western, that our best engines, which are considered so 

 unnecessarily powerful, have been barely sufficient to take the loads which, 

 under certain arrangements of trains, we were obliged to carry, and that inter- 

 mediate or half-hour trains became necessary. That many such inconvenient 

 arrangements would have been required if the loads had practically been 

 increased 34 per cent., with gradients of 10 feet per mile, I need not tell you 

 who are familiar with the details of our traffic. I regret the necessity of 

 devoting so much space to an attempt to render more clear that which appears 

 to me to be self-evident, — namely, that a load of 134 tons cannst be carried at 

 the same speed and with the same power as one of 100 tons, or, in other 

 words, that the addition of a useless load of 10 or l.j tons to one of our ordinary 

 trains would not be unimportant ; but the paragraph I have referred to implies 

 this, and there being no argument advanced in support of it which could be 

 examined, it becomes the more necessary to take notice of it. 



The particular arrangement of the gradients on tlie Great Western railway 

 and their effect upon the Irafiic are then gone into, and at the end of the para- 

 graph, page 49, the adv.antage of 17 per cent., before alluded to, is reduced one 

 half, or Si, per cent. Uow this is done I have not been able to perceive, as I 

 find neither argument nor calculation to justify it. It is true it is very fairly 

 given as an opiiiioii ; but, as there are iniiny figures and quantities given in the 

 course of the preceding paragraphs, the word " therefore," at the conclusion 

 of the paragraph, would lead a cursory reader to suppose it was proved by 

 some preceding calculation or reasoning. As some allusion is made to a 

 supposed saving of the power in one direction which is expended in the other, 

 and as 8j is half of 17, it is barely possible that it is arrived at by a system of 

 averaging the power required in the two directions ; but, in the first place, no 

 such average can be taken, the maximum power that is required in any one 

 part of the line must be provided, and must be carried at all times, even if no 

 power at all be required on other parts of the line; ind, secondly, if the 

 expenditure of power is to be aver.iged, then the increas e of gradients makes 

 no cii/flniicr in the average power, as the decrease of p> wer in descending is 

 said to be equal to the increase in ascending, and therd'orc balances it. Tlie 

 fact is, that there is no ground whatever for halving the 17 per cent, (which I 

 have shown to be 34 per cent.) as it nieiuMfc of tin: rjl'aiivc poit-cr nf llu- same 

 rnijines under Ike two cinumstuiices, and consequently none whatever for fixing 

 it at 82 percent. 



After this, the 8i per cent, is reduced to 2,8 per cent., in so far as relates 



to the value, in money, of such reduction in locomotive power ; and the asser- 

 tion is made, preceded again by the word *' therefore," that a company would 

 do wrong to increase the original capital more than 2.8 per cent., to effect a 

 saving of 2'8 per cent, in the annual expenditure. Can it possibly be meant 

 that if the capital be a certain sum, say 1000/., and the annual expenditure 

 150/., leaving 1 jO/. of nett profit, that a company would do wrong to add 2^ 

 percent., or 25/., to their original outlay, unless this secures t!i per cent, 

 saving, or 31. l.js. on the annual expenditure, or 15 per cent, for the money ? 

 This is evidently a great mistake, arising from the total confusion of the capital 

 with the annual expenses, as if they were the same sum, and the apparent 

 accuracy and proof are produced only by the repetition of the same figures in 

 the two cases, although, in fact, there is no such identity. The way in which 

 a man of business should proceed, would be to capitalize the annual sum likely 

 to be saved at some given rate of interest, which in his opinion would cover all 

 risk, and leave a profit, perhaps of t>, 8, or 10 per cent., according lo circum- 

 stances, but having no reference to the particular per centage which the 

 annual expenditure might bear to the capital ; and this amount a wise man 

 would expend, not only to increase his future profits, but also to secure perma- 

 nent advantages to tlie concern. 



The calculations, erroneous as I think I have shown them to be, do neverthe- 

 less, make out a case in favour of good gradients. But upon turning to a 

 statement given of actual results upon three railways, these very calculations 

 are annihilated. These experiments, if they prove any thing, prove an actual 

 advantage in favour of gradients, not of 4 feet per mile, nor of 10 feet, but of 

 very steep gradients of 30 feet per mile. The naked result gives a less 

 expense of power on two lines, on one of which half the length consist of 

 gradients above 26 feet per mile, and on the other, 8 miles out of 20 consst of 

 gradients upwards of 34 feet per itiile, over a line the maximum gradient of 

 which is 4 feet per mile. No explanation is given. The question here is not 

 one of the comparative perfection of the lines, in other respects, or of the 

 carriages, cr of the probable effects of circumstances not mentioned; it is 

 adduced expressly as a practical measure of the value of gradients, and is left 

 without comment or explanation, to produce its effect on the mind of the 

 reader. As such it does appear to me, and I think must to any impartial man, 

 that the proof is overmuch, and becomes valueless ; that the results cannot he 

 correct, and that there evidently must either be an error in the data, or there must 

 be circumstances quite independent of the gradients which require separation ; 

 otherwise vvc are driven to the conclusion that steep fjrailients arc best, 



I have nothing before me but the results, and therefore I cannot pretend to 

 discover all the sources of error ; but I know that some of the data are such as 

 must introduce error ; for instance, the consumption of coke given as that of 

 the Great Western railway, includes all that had been used in raising and 

 keeping up the steam in the engines, which, in the first working of,a portion of 

 a line, and while the arrangements are not matured, is necessarily great; it 

 includes also the coke expended in ballasting trains and experimental trips. 



In fact, during the four weeks ending September 13th, which .ire referred lo 

 by the writer, I find that there were generally seven engines in use, and of 

 these, two were employed upon the line, (not on the passenger traffic,) and 

 one was kept with the steam up, as a spare engine. How can the results of 

 consumption per ton per mile be correct with such sources of error ? 



I must beg, however, to keep your attention to the 34 per cent, at which I 

 have arrived, as the advantage, in actual elVectivc powers of a gradient of 4 feet 

 over one of 10 feet. 



The gradients must ultimately govern the power of your engines, their 

 speed, (at all events in one direction,) the size of each of your trains, a;id con- 

 sequently their number; and it must always be remembered, that their opera- 

 tion is a. permanent one, which nothing can remove or even alter, and the cH'ect 

 of «hich nothing can diminish. On the contrary, I am prepared to show, 

 that the value of low gradients will, in all probability, be much increased. 



I have assumed 8 lbs. per ton as the resistance of a train ; but as the greatest 

 part of this resistance depends upon the workmanship, the form, and the 

 mechanical construction of the carriages, and other causes, and mav be reduced 

 by various contrivances already known, it would be contrary to all experience 

 to suppose that it will not be materially reduced when there is an object to bo 

 gained by its rednction. 



In many experiments, with all the circumstances favourable, the resistance 

 has been as low as G lbs. 



lu some made by Mr. Hawkshaw, on the Great Western Kailway, the re- 

 sistance of a train, consisting partly of trucks and partly of carriages, only 

 gives 6.22 lbs. 



It may therefore be assumed, that w'e have now within our reach improve- 

 ments by which the resistance may be reduced to 6 lbs. 



With this datum, and making tbc same calculations as before, we obtain 100 

 and 144 as the comparative loads which the same engine would take at the 

 same speed up the two gradients of 4 feet and 10 feet per mile. 



Such an increase in the capabilities of engines must be of immense impor- 

 tance in passenger traffic. But how undeniably important it must be, even 

 accordirg to the principle laid down in the report, in the conveyance of goods ; 

 in this service the maximum power of the engine w brought into operation, 

 and (lues constitute the limit ; and if the engine, in such case, only forms one- 

 eighth of the gross load, the proportion will still be as 100 to 13.:).;'). 



This advantage, large as it is, is a highly probable one, and I venture to 

 predict it as a certain one ; but, confining ourselves to the results which may 

 be obtained with the existing rails and carriages, I will consider what is the 

 practical working of an increased useful effect of 3 4 per cent, by the same 

 engine, or an increased resistance of 26 per cent, with the same load. Ac- 

 cording to the view of the writer, in page &, of there being « fixed standard or 



