asG 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[October, 



It is evident tluit no effcot whatever was ])rodiiced Ijy the Ijeali, and, con- 

 seqnenliv, tlie flat cud of tlic coacli produced none of tliat resistance which 

 Mr. lirnnel aserilicd to it. Tlic same experiment was now rei)eated nilli a 

 train of eight coaciies, down tlie series of inclined jdanes at Madeley. Tlic 

 heali lieiiig jilaced ujion tlie first eoacli, tlie train was started from the sum- 

 mit of the Madeley plane, falling yt^' ^"'1 't ^^"'' dismissed down the series 

 of planes already described, the circumstances of its motion being carefully 

 observed. It was then brought back to the top of the Madeley plane, and 

 the licak removed, and was once more dismissed, the circumstances being 

 again observed. The particulars of this experiment is exbiliilcd in T.ible V[. 



It appears, therefore, that the distance run witliout the sharp end ditlVrcd 

 only eighty yards in a distance of ,ibout eight miles; and the other dif- 

 fereticcs exhibited in the table, are evidently such only as would take place 

 with the same ex])eriment twice re])eated with the same carriages. 



With a view to ascertain how far mere magnitude of frontage, independent 

 of the general magnitude of the train, is jiroductive of resistance, the front 

 of a coach was enlarged by side boards, extending on either side about 20 

 inches, adding about 24 square feet to the front surface, forming a sort of 

 wings in front of the carriage, but no corresponding width being given to 

 any other part of the carriage. The coach, thus prepared, was ])laced at the 

 snniinit of the Sutton plane, and allowed to descend from a state of rest. It 

 was then brought once more to the summit, and the sides removed, and it 

 was allowed to descend with its proper front. The result of these two ex- 

 ]>erimeiits is exhibited in Talde V. 



Table \. 



From which it was inferred, that mere width of frontage, apart from the 

 general increase of magnitude, was not productive of any considerable prac- 

 tical eft'cit in increasing the resistance. 



A strong imjiression existed in the minds of some engineers and scientific 

 men, to whom Dr. Lardner comnninicated the results of these experiments 

 while they were in progress, tliat the shape of the hinder part of the train 

 might have an etfeet upon the resistance. It was supposed that in very 

 rapid motion a tendency to a vacuum would be produced behind the train, 

 and that a corresponding atmospheric resistance, due to this partial vacuum, 

 would be produced in front ; that, consequently, if the sipiare sliajie was 

 removed from the hinder part, less resistance would be found. Although Dr. 

 Lardner did not attach any weight to this objection, he was willing, never- 

 theless, to submit it to trial, and with tliat view he prepared a train of three 

 cai-riages, which he first placed at the summit of the Sutton i)lane, falling 

 .g\j, and allowed them to descend by gravity in tlieir ordinaiT state. He 

 next allowed them to descend, having the pointed end behind ; they next 

 descended with the pointed enil before, ; and, lastly, they were once more 

 allowed to descend without the pointed end. The residt of these four ex- 

 periments is given ill Table VII. 



In the third column is expressed the entire distance run, in yards; in the 

 fourth cohimu is the time of going that distance; in the fiftli column is the 

 speed acquired in descending the Sutton plane ; in the sixth colnnin tlie 

 time of descending that plane; in the seventh column the time of moving a 

 di-staiicc of 2^ miles from the time of starting; and, in the last column, the 

 time of moving from the twelfth to the twenty-eighth stake, throughout 

 which, the motion being tolerably rapid, the effect of the air might be ex- 

 pected to be greatest. It will be evident, from this table, that the jiointed 

 eml. whether before or behind, was not attended v\ith any apjireciable effect, 

 the discrepancies being only siu-b as woidd occur in the same ex])eriinent 

 twice rejieated. 



It had been suggested tliat the resistance ojiposed by the air might be 

 more or less produced by the sjiaccs between the successive carriages of the 

 train, the end of each successive carriage being more or less exposed to 

 pressure against the air. In order to ascertain what weight this suggestion 

 was entitled to, a train of eight carriages was ])reparcd, having tenter hooks 

 attached round the corners of their ends. Canvass was prepared, which, 

 being hooked on these, might be stretched from carriage to cari'iage, so as 

 entirely to enclose the space between the successive carriages, and to convert 

 tlie whole train into one unbroken )irisin. The train being thus prepared 

 ^^itll the canvass, was brought to the summit of the Madeley plane, and al- 

 lowed to descend towards Crewe, the circumstances of the motion being 

 obsened as in the former exiieriments. It was then ag.iin removed to the 

 summit, and, the canvass being taken off, thefrain was allowed to descend 

 in its ordinal) state, the spaces between the carriages being left open. The 

 reiult of these two experiments is exhibited in table VIII; and it will be 



seen that the differences are nothing more than what would arise from 

 casual causes affecting the same experiment twice repeated. 



Being impressed with the idea that the amount of resistance might be 

 more or less de])endcnt on the general volume of air dis]>laced by the train 

 as it moves, rather than by the mere magnitude of frontage, an exiietiment 

 was made which was attended with a result sufficiently remarkable. A train 

 of five VA'aggons was prepared, weighing exactly 30 tons, and loaded with 

 iron rails : sides and ends were constructed, which, being put ii|i, these 

 waggons received the form of coaches, but which, being moveable, could be 

 ]mt up or laid flat upon the ^vaggons at pleasure, This train of waggons was 

 brought to the summit of the Madeley plane, and allowed to descend, by 

 gravity, towards Crewe, the circmnstances of its motion being obser\ed, as 

 before. It was then brought back to the summit of the same plane, and the 

 sides were taken down and laid flat upon the waggons, and it was then 

 moved down the ]dane. The particulars of these two experiments are ex- 

 hibited in Table IX. 



The eft'ect of the form of the waggons upon the resistance is here snfl!i- 

 ciently manifest, and the concuiTent circumstances upon the several gra- 

 dients plainly show the increased resistance produced by the increased mag- 

 nitude of the train. From this and the former experiments, if may therefore 

 be inferred that the mere form, whether of the front or hinder part, or the 

 mere magnitude of frontage, produces no practical effects upon resistance ; 

 but that, by increasing not the frontage only, but the ir/iole rahinie of the 

 train, a material effect is produced. 



It had been found, contrary to what was at first expected, that by in- 

 creasing the number of carriages in the train, that portion of the resistance 

 which must be ascribed to the afmosiiherc was increased. It ajipeared, at 

 first view, that the chief, if not the only source of atmospheric resistance 

 was to be found in the frontage or maxiinum transverse section. The expe- 

 riments, however, are entirely inconipatible vrith any such supposition. Had 

 such been the case, the trains of six and eight carriages ought to have ac- 

 quired a considerably greater velocity in descending the inclined planes, than 

 the trains of four carriages, which was not the case. This is in some degree 

 accounted for by the result of the last experiment indicating the connexion 

 between the volume of air displaced and the resistance, and not between the 

 mere frontage and the resistance. But, in addition to this, there is another 

 circumstance, which was pointed out by Dr. I.ardncr long since. The wheels 

 of the several carriages produce a v ortex of air around them, and play in 

 some measure the ])art of fanners or blowers. .\ considerable force must he 

 absorbed by so great a number of these wheels moving at such a velocity. 

 In a train of eight carriages we have thirty-two three-feet wheels, playing 

 these parts of blowers, and revolving from four to five times in a second. 

 How much force must be expended in maintaining such a motion, it is need- 

 less to say. But, besides this, another circumstance v*as observed. In these 

 experiments, as well as in general railway practice, it is found that an ex- 

 tensive current of air moves beside a train, flic current diminishing in ve- 

 locity as the distance from the train increases. Immediately coufiguons to 

 the side of the coaches, the air moves with little less velocity than the 

 coaches themselves. Outside that is another current, moving at a less rate, 

 and beyond that another at a fm-fher diminished rate. There is, thus, a 

 succession of currents, one outside another, extending to a considerable dis- 

 tance at each side of the train. .\11 the resistance produced by the motion 

 of this mass of air through the atmosphere, forms part of the resistance op- 

 posed to the moving power. 



In all the exiieriments which were made on the series of planes between 

 Madeley and Crewe, it was found that in moving over those jiarts of the 

 line which were curved, the uniform velocity was precisely the same as on 

 those parts which were straight. There was no discoverable dift'erence in 

 the rate of motion, from whence it follows tliaf curves like these, having a 

 radius of a mile, inoduce no observable effect upon the resistance. The ex- 

 periments were so numerous, and performed under such a variety of circum- 

 stances, that, unexpected as these results were, there can be no doubt of 

 their truth. 



It has been stated confidently in print and at public meetings, by men re- 

 puted to possess information in jiracfical science, that the atmospheric 

 resistance has been long kiio\^ii, not ]ierlia]is with perfect accuracy, but that 

 fables, giving a near a[)proxiiiiation, have been published by different em- 

 inent men, and arc to be found in most elementary works ; that calcula- 

 tions founded on these fables, of the resistance of the atmosphere may be 

 made, and that such calculations would give more correct results than such 

 experiments as have now been described. As such .statements are calcu- 

 lated to mislead. Dr. Lardner had no hesitation in declaring that they are 

 utterly unfounded. No details exist, nor have any experiments ever been 

 made by which the resistance of the air to a train of railway carriages could 

 be obtained by any calculation whatever ; nor was the aiiiounf of such re- 

 sistance ever sus])ccted, even by the persons who have ventured to utter 

 such statements, as have been here proved to exist. 



Having been s.ifisfied of the large amount of the resistance of railway 

 trains at the usual speed of passenger trains, the next inquiry was one of a 

 still more difficult kind, namely, to obtain, by reducing the results of the 

 experiments to mathematical analysis, an estimate of the quantity of this 

 resistance which was due to friction and to the atmosphere respectively. 

 Fart of the details of this investigation may be seen by reference to the 

 vohiiue of the Transactions of the British Association, lateh imblished, 

 and the remainder will appear in Dr. Larilner's second Report. In the 



