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THE CIVIL ENGINEER AND ARCIIITIilC TS JOURNAL. 



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repose. The amount of Ibis inelinatiori had lieen made t!ie suliject of inueli 

 <Usi)ute ; I)ut it iiail lieen geneially assumeil to be 1 in 250, or at tlic rate of 

 alioiit twenty feet in the mile. Any incUjiation greater tlian tliis would 

 cause tlic train to move down spontaneoubly; and it bad l)een assumed in 

 railway investigations before committees of jiarlianient, tbat tbc train, under 

 such circumstances, would {loul)le its velocity every second of time. The 

 inevitable conehiMon to be drawn from this was, that if they liad a steep in- 

 clined plane of sutticient length, the consequence would be an indetiuite in- 

 crease of speed till they actually acquired a velocity of 100(1 miles au hour. 

 Now, they wouhl after this hardly crcilit the lesults which actual experiment 

 gave. iSotbing could be easier than tlie jn'oblem to determine the actual 

 resistance from the luoliou of trains ou railways, because it was a uiattcr of 

 easy mathematical calculation to predict whiit the velocity .icquired at the 

 end of the first miiiute would lie, and, ,'iccording to the rule laid down, tbat 

 it would be twice as great at tlie eml of the second minute, and so on. I!y 

 comparing this with the velocity tlie train actually acquired, the comparison 

 would furnish tliem with an easy clue. \J\mu this principle, Dr. Lardner 

 luid jiroceeded in a series of experiments made on the Winston Plane, whicli 

 has a fall of 1 in 90. They had four coaches, the gross weight of which 

 was 15! tons, and these coaches were propelled along the siunmit level to 

 tlie brink of the plane, until a velocity of about 29 miles au hour was given 

 to them, and then the engine was detacbed, leaving them to move down. 

 By means of stakes placed on the side of the line, they were enabled to re- 

 gister the length of time it took to descend every successive 110 yards. 

 They commenced their descent from the summit of the plane at a \clocily of 

 nearly thirty uules an h:)ur, which, in a very short space of time, increased 

 fo 31:J miles an hour, and then the\' fouiul that gravity could do no more for 

 them. Instead of going at the frightfid velocity anticipated by parliament, 

 they found they got into the most uiuform rate of motion at the third or 

 fom-tli stake, after which there was no increase of velocity whatsoever ; and 

 at this uniform motion they coulinucd to descend tdl they reached the end 

 of the plane. They subndtted this experimetit to all possible tests, by in- 

 creasing the weight of the carriages to 18 tons, but it only gave them an 

 increased velocity at starting of 33} miles, the train descending at a uniform 

 speed the remainder of the distance. 



Upon these experiments Dr. Lardner proceeded to remark — " There is an 

 important thing connected with this which I will briefly explain to you. 

 The force that moves the train down an inclined plane is, as you will see, the 

 gravitation of the weight of the train down the plane. This gravitation 

 woidd, until altogether balanced by some resisting force, acquire an accele- 

 rated motion. So long as the resistance to the descending train is less than 

 the gravitation down the plane, so long will the excess of gravitating force 

 down the |ilane produce an acceleration of velocity, he it more or less. But 

 as soon as the resistance becomes equal to the gravitating force, then there 

 will no longer be any acceleration; the train will no longer acquire an in- 

 creasing speed. On the other hand, it will not lose speed ; if it did, then 

 the inference would be, that the retarding force exceeded the gravitation; 

 out they acquire an equilibrium, and as soon as the resisting force increases 

 to that point that it is exactly equal to the gravitation, then the motion is 

 uniform. The inference we deduced, therefore, was this: — that at 3\-p^ 

 miles an ho'ir, the gravitation of this train down the plane of 1 in 96 was 

 equal to the resistance ; in other words, that the resistance to that speed 

 was Jj part of the weight. And you will see that a necessary consccincnce 

 of this is, that a train of equal weight, placed ou a level, and drawn along a 

 level at the same speed of 31} miles au hour, the resistance which it would 

 oppose to the moving power would be tjV part of the whole load. This alone 

 will show you the extent of the error which these experiments exposed ; for 

 the common notion before was, that the resistance in all cases was ttjtt I'art 

 of the load, or somewhere about 9 fts. per ton ; whereas it appeared that it 

 was in this case Jj part of the load, or about 23 fts. per ton ; so that the 

 engineer's estimate woidd be in error to the inconceivable extent of mistaking 

 resistance of 23 lbs. for a resistance of 9tbs. per ton." 

 Dr. Lardner stated that he liad tried similar experiments on the plane of 

 the Grand Junction Railway, which descends from Madeley towards Crewe, 

 at the rate of 1 in 177 for three miles; afterwards descending at the rate of 

 1 in 2G5, followed by another descent of 1 in 330. The coaches loaded at 

 IH tons were moved down this plane in exactly the same way, the wind being 

 fair, and they got a velocity of 21:1 niiles an hour, and with this velocity they 

 continued to descend the tliree planes. Ou making inquiries of the engine- 

 man, he found that the steam was never cut ott" in descending these planes, 

 so that, instead of accelerating the engines at a dangerous speed, as was an- 

 ticipated by the parliamentary committee, they were actually insufficient to 

 propel them at a sufficient speed for the work of the road. The result of all 

 the experiments he made on the Madeley plane was, that he never met with 

 an instance of propelling trains down, with a fair wind, at a specil of more 

 than 23 miles au hour. From a comparison of the experiments made at the 

 Madeley and Whiston ])lanes, Ur. Lardner said, " I made a calculation, from 

 which it appears tbat in the first experiment of the two trains, tbat portion 

 of the resistance which is due to friction amounted to 9fl lbs. only, while that 

 which is due to the atmosphere amounted to 268 tks. In the second experi- 

 ment, with eighteen tons, the portion of resistance due to mechanical causes 

 amounts to 100 lbs., while that which arises from the atmosphere amounts 

 to 321 lbs., at only 33 miles au hour'. One of the objections was, that the 

 train was too light, and that un fail- inference coidd be drawni from four car- 

 riages. We, therefore, tried trains of six and eight carriages. Several ex- 



periments were made down very steep planes — that of Whiston being 1 in 

 96, and that of Sutton 1 in 89. In the first cxpciimeut of six carriages, (be 

 wind was against us. Duv.n the plane of 1 in 89, we could not get more 

 speed than 32^ miles an hour. At this speed the resistance was equal to 

 the gravitation. But w ith the w ind favourable dow n the same plane, we got 

 37. \ miles au hour, and a mean of these two would be about 35 miles an 

 hour. On the \\ liislon |ilane, 1 in 96, with the wind adverse to us, we only 

 got 27~, or nearly 28 miles an hour, but with the wind favourable, we got 

 31 miles an hour, the mean of these being about 31. In both these cases, 

 both on the Sutton and Whistou ]>lanes, you see the evident efl'ects of the 

 wind. The mean of the two, in these cases, gives, on a less steep jilane, a 

 less velocity than on a steeper plane the mean did in the other cases. It is 

 remarkable, ami very satisfactory in coulirmation of the former experiment, 

 that we had six carriages in a calm descending the Sutton ])lane, and what 

 was our uniform sjicfd ? 35^ miles an hour, the atmosphere being calm. In 

 two other cases down the same phme, with adverse wind, we got a speed of 

 32J nnles au hour; with favourable wind, 37.\ miles, the mean of which is 

 3Ji miles ; so tbat in a calm we got a nicaii between the speed with a fa- 

 vourable and that with an adverse wind. .Ml these harmonies in the results 

 are so many corroborations of the principle which they develop." 



Lecture III. 



In this lecture the Doctor cxidained a variety of experiments made on 

 railways, in order to ascertain the source of resistance. He found tliat an 

 enlarged temjiorary frontage constructed with boards, of probably double the 

 magnitude of tbc ordinary "front of the train, caused an increase of resisfauce 

 so trifling and insiguifiennt as to be entirely uuwortliy of account in practice. 

 Seeing that the source of resistance, so far as the air was concerned, was not 

 to be ascribed to the form or magnitude of the front, it next occurred to him 

 to inquire whether it might not arise from the general magnitude of the train 

 front ends, toj) and all. -An experiment was made to test this ; a train of 

 waggons was prepared with temporary sides and cuds, so as to rcpiesent for 

 all practical puriioscs, a train of carriages, which was moved from the sum- 

 mit of a series of inclined planes, by gravity, till it was brought to rest; it 

 was next moved down with the high sides and ends laid flat on the platform 

 of the wagaons, and the result was very remarkable. The whole frontage of 

 the latteiCinelndiiig the wheels and every thing, a complete transverse sec- 

 tion of the wagons, measured 24 feet square, and with the sides and cuds up, 

 so as to i>resent a cross section, it amounted to nearly -18 square feet. The 

 uniform velocity, attained on a plane of 1 in 177, without the sides up, was 

 nearly 23 miles' an hour; whereas, with the sides up, it was only 17 miles 

 an hour; so that, as the resistance would be in projiorfion to the square of 

 the velocity, other things being the same, there would be a very considerable 

 diflrcreuce,'duc to tbat ditlVreuce of velocity. Then, at the foot of the second 

 plane, while the sides were down, an undiminished velocity remained of 19J 

 miles au hour, whereas, with the sides up, it was reduced to Si miles an 

 lioiu-; so that a very extensive difterence was produced. They would see at 

 once, that this was a very decisive experiment to prove that the great source 

 of resistance was to be found in the bulk, and not the mere section or the 

 form, whether of the front or the back of a train; but simjily in the general 

 bulk of the body carried through the air. It was very likely to arise from 

 the successive displacements of a quantity of the atmosphere equal to the 

 bulk of the body ; or still more proliahly.'from the fact of the extensive sides 

 of the train; aiid indeed there was little doubt that the magnitude of the 

 sides had a very material influence ; for, if they consider what is going on in 

 the body of air' extending from either side of a train of coaches, they would 

 soon see what a mechanical power must be exercised upon it. Thus, when 

 a train is moving rapidly, the moving power bad not only to pull the train 

 on, but it had to drag a succession of columns of air, at ditferent velocities, 

 one outside the other, to a considerable extent outside the train ; and it did 

 more, for it overcame their friction one upon the other; for as these columns 

 of air were at dift'erent velocities, the one would be rubbing against the 

 other ; and all this the moving power had to encounter. This would go far 

 to explain the great magnitude of resistance found, and its entire discordance 

 with any thing iirevionslv suspected. 



Dr. Lardner next proceeded to consider the practical bearings which the 

 experiments he had detailed would have on the construction of railways. 

 From these experiments a two-fold fact was deducible : first, there w as un- 

 questionably a great amount of resistance, and secondly, this resistance had 

 a material dependence on the velocity; it dimiuished in a very rapid pro|)or- 

 tion as the speed was diminished. If, therefore, by slaokening the speed, 

 thev could relieve the engine from any considerable portion of the resistance 

 opposed to it, thev had at once a ground for throwing ovei board all the ob- 

 jections wdiieh hail been raised against sections of railways which had con- 

 siderable gradients. It was asserted that the resistance was a resistance 

 quite independent of the speed, and that its average amount was quite equal 

 to the gravity down a plane with a fall of twenty feet a mile. Both propo- 

 sitions had been proved to be false. The resistance was not constant; it 

 depended on the speed, and its average amount was equal to a great deal 

 more than twenty feet a mile. The gradient that represented the average 

 resistance, instead of being twenty feet a mile, was probably fifty feet ; and 

 instead of liavinc no power of limiting the speed, they hail a power to which 

 there was scarcely a practical limit. The lecturer stated that he bad been 

 ridiculed for the opinion he bad advanced before the committee of the House 



