90i 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[July, 



he deduced from the apparently unaltered motion on both gradients, 

 we arrive at the absurdity of giving the resistance two dirt'ercnt 

 values, of which one is between six and seven times as great as 

 the other. 



'J'o exhibit more clearly the very great effect of the inertia of 

 trains in maintaining their velocity, we will calculate the motion 

 on level ground, at a uniform resistance of 20 lb. per ton, when 

 the train is started at a velocity of 80 feet per second (or ratlier 

 more than 5+ miles an liour). I5y the principle of Conservation of 

 Fix Viva— 



J,W (V-' - j)«) = 2Rj-; 

 where R is the uniform resistance, V the initial velocity in feet 

 iier second, v the velocity at a subsequent time when the train has 

 travelled x feet, W the weight, and therefore j', V/ the mass 

 (putting 32 feet for the measure of gravity): or one thirti/secoiid part 

 of the u-eiyitt X ''.V the difference between the squares of the initial and 

 xubsequeyit velocity, is equal to twice the corresponding distance tra- 

 versed X by the uniform resistance. This is a simple arithmetical 

 rule for calculating all cases of the rectUineal motion of a body 

 started with a given initial velocity, and then abandoned to the 

 influence of a constant retarding force. 



To suit the present case, we put V = 80, and the resistance = 



20 pounds per ton, and multiply the weight of tlie train by 2210, 



to express it in pounds ; and the above formula becomes 



pgj,o 7 



(V-' - «=) = 40 x; or, 11,200 «^ = x, 



32 ^ ' ' ' ' 4, 



to find the distance in feet corresponding to any subsequent 

 velocity. Putting v — 0, we find tliat the train mores 2-12 miles 

 before it comes to rest ; and putting v = 70, we find that the train 

 mores 2,9^5 feet, or more than half a mile, before its velocity is reduced 

 from. 80 to 70 feet per second. If, instead of making the resistance 

 uniform, we supposed it to decrease gradually, as it does on rail- 

 way, the distances above calculated would be increased. 



These considerations show the absolute necessity of using long 

 distances in performing experiments on the retardation of trains. 

 IJut though thev throw a doubt on the experiments before us, it 

 would be too much to say that they render them absolutely worth- 

 less. On the contrary, with some exceptions, the conclusions dis- 

 play a certain degree of consistency which adds to their weight. Of 

 course, the testimony inferred from this consistency would be much 

 greater if we were informed that these experiments are all that 

 have been undertaken, and that none other inconsistent with them 

 have been performed. 



Now, of the experiments on the tJ;, gradient, the 2nd, 3rd, 

 and 3th, with an initial velocity of 50 to 52 miles an hour, ex- 

 hibit tolerably uniform velocities. This would indicate that at 

 50 to 52 miles an hour, the resistance is -^ the weight, or 22-4 lb. 

 per ton. Experiments 1, 4, and 7, show retarding velocities, indi- 

 cating that at 54 to 58 miles an hour, the resistance exceeds 22-4 lb. 

 per ton. Again, in the 13th experiment, on a gradient of about J;, 

 the speed is tolerably uniform ; in the 11th, on the same gradient, 

 it is accelerated. In both experiments on a giadient of -[^j, the 

 speed is accelerated. Reasoning as before, we have — on the assump- 

 tion that the above form of "the data is accurate — the following 

 general conclusions, in three pairs, corresponding with the three 



gradients : — 



milea per hour. lb. per ton. 



When velocity is 50 — 2 Resistance equals \ r,, 



54 — 8 exceeds / 



55 equals "1 ,g 

 43 less than j 



36 less than \ jg 



37 less than J 



These results agree very well with those obtained in 1846, by 

 Mr. W. Harding, by the dynamometer, on the South Eastern nar- 

 row-gauge railway, and reported in his paper presented to the 

 Institution of Civil Engineers: — 



miles per hour. lb- per ton. 



Velocity 29 Resistance 16o 



37 18-3 



45 21-7 



46 21-3 



To complete the comparison, we select those of the experiments 

 of the British Association which were made at velocities above 

 30 miles an hour, on inclined planes on narrow-gauge lines :— 



miles per hour. lb. per too. 



Velocity 31 Resistance 23-4 



34 23-4 



37 25 



32 225 



It is to be observed, that these rates of resistance considerably 

 exceed the former. 



We do not bring into the comparison the experiments of the 

 Gauge Commission, in which the resistance is derived from the con- 

 sumption of water by such an arbitrary and dangerous i)rocess, tliat 

 we feel justified in rejecting that evidence entirely. Neither can 

 Mr. Wyndham Harding's experiments on tlie Croydon Atmo- 

 spheric Railway, by the difference of barometric pressures, be ad- 

 mitted into the comparison. His case for the rapid increase of re- 

 sistance with increase of speed, rests almost entirely on thete experi- 

 ments, and therefore, as we tliink, on an insufficient foundation. 

 These experiments are as follows : — 



miles per hour. lb. per ton. 



Velocity 01 Resistance 52-6 



53 41-7 



55 36 



50 32-9 



47 33-7 



In the first place, the results obtained by the barometer are in- 

 consistent with themselves : the resistance at 55 miles an hour is 

 fifteen per cent, more than at a less velocity of 53 miles. The only 

 experiment at upwards of 60 miles an hour, shows an increase of 

 resistance so disproportionate, as naturally to induce suspicion ; — 

 at all events, a single result, so inconsistent with all previous ob- 

 servation, ought not of itself to be sufficient evidence of a 

 general law. Moreover, this very experiment was conducted 

 under circumstances most unfavourable to a general conclusion. 

 The distance traversed was 3-5 miles, the time of transit four 

 minutes and a half, and the recorded velocity fluctuated from 32 to 

 61 miles. And yet this single trial is the mainstay of the theory 

 of high resistances at high velocities ! We have already shown 

 the great effect of the inertia of trains at high velocities, and the 

 extreme uncertainty of any conclusions from the apparent uni- 

 formity of motion ; — that the uniformity is apparent only and 

 not absolutely certain, the brief duration of the experiment and 

 its great fluctuations are sufficient testimony. 



It is important to observe, in confirmation of this view of the 

 subject, that the barometric method of calculating resistances, 

 always gives results which, as far as they can be compared, ex- 

 ceed those obtained by any other method. 



On the whole, we are inclined to an opinion, from the insuffi- 

 cient evidence before us, that the resistanee does not increase so 

 much with the velocity as has sometimes been contended ; and 

 that the resistances per ton, do not differ widely on the broad and 

 narrow gauge. The advantage, if any, belongs to the former ; 

 principally, we imagine, on account of the comparative smoothness 

 of motion over longitudinal sleepers. There can be no reasonable 

 doubt, that comparing the longitudinal and transverse sleepers, 

 when both are in perfect order, the former, by giving more perfect 

 support to the rails, render them less liable to vibration and con.» 

 cussion. It may be laid down, as a general rule, that whatever 

 increases the regularity of motion, diminishes the resistance. One 

 of the consequences of this rule is, that the resistance of trains is 

 diminished by diminishing their lateral oscillation. On this sub- 

 ject we have not space to speak at length; it is sufficient to 

 observe, that the tendency to oscillate depends on what is known 

 in mathematics as the radius of gyration, and is therefore di- 

 minished by diminishing the weight projecting beyond the wheels 

 outside, and by reducing the proportion of the height of the 

 centre of gravity to the distance between the points of support. 



[Abbreviated from the " Morning Herald,"'] 

 We return to the consideration of this interesting and important practical 

 railway investigation. As we have previously stated, the question of the 

 " resistances to railway trains at certain velocities," is not a mere scientific 

 question, but one in which the convenience and accommodation of the 

 public are very materially involved. The establishment of the truth of the 

 "formula" which makes the resistance, at 00 miles per hour, some 40 lb. 

 per ton, or 50 per cent, higher than we shall presently show it to he, would 

 present a strong economical argument either against express travellinc;, or 

 for the restriction of the accommodation of quick transit to first-chiss 

 passengers at high faros. 



In the ohservations made by us a few days since, in reference to the 

 extraordinary differences of opinion existing on the subject between practical 

 engineers, we noticed the singidar fact that while a uniform velocity of not 

 more than 36 miles per hour has ever been maintained with narrow-gauge 

 trains, by the force of gravity, down an incline of 1 in 100, a uniform velo- 

 city of upwards of 53 miles per hour had been maintained with hroad-gauge 

 trains by gravity down an equal incline. We then stated that we had our- 

 selves gone done the Box Tunnel incline (1 in 100) at a greater uniform 

 velocitv than 53 miles per hour. We have since made a series of experi- 

 ments down the Wootton Uassett incline, stated to be 1 in 100, hut some 

 nortiim of which is 1 in 110 only; and down other inclines on the Bristol 

 1 and Exeter Railway; and from the details given below, it will he seen that a 



