122 



KNOWLEDGE, 



[June, 1902. 



horizontally in tliat plane, -while the attachment of the 

 spiral s]iring, L, to a point near the outer end of the 

 eccentric iirm, K, places all the steel rods in a state of 

 loni,'itudinid coiU]iression ; so tliiit-. if the wci<,dit is dis- 

 jiliUiMl ill ;i vertical direction, its return is resisted hy the 

 thrust of the rods. The resultant force tending' to restore 

 the \veifj;ht to its former position depends, therefore, on the 

 difference between the force exerted hy the sprint,' and the 

 vertical comjionents of the thrusts of the rods. By 

 adjusting the jwint of contact of the si>ring and the arm 

 K, this resultant force, and consequently the period of 

 oscillation of the plate, can be varied at pleasure. It was 

 found by trial that a period of abo\it four-fifths of a 

 second was lon^' enoun;h compared with the period of the 

 vibrations to be measured, while a much lons^cr period 

 rendered the instrument too sensitive to changes of 

 temperature. 



The movements of the plate A with respect to the frame 

 were registered photogra]}hieally, in order to avoid the 

 friction introduced by a mechanical recorder. For this 

 purpose, a microscopic objective, M, one-si.vtli of an inch 

 in focal length, was fixed to the plate with its axis hori- 

 zontal. In its focus was placed a horizontal quartz fibre 

 mounted on a stage, S, attached to the frame (see Fig. 2, 

 the stage being omitted from Fig. 1 to simplify the 

 diagram). Close to, but just short of, the conjugate focus 

 of the objective, a vertical cylindrical lens, N,is fixed, and, 

 the field of view being illuminated by a lamp at L, there 

 aj)pears in the focus of this lens a moderately bright 



Vertical line on which the image of the quartz fibre is cast 

 as two black dots on either side of a very briglit dot. The 

 photographic plate, P, on which this image is received, 

 was made to travel at the rate of about three-quarters of 

 an inch a second ; and the records on the negative, when 

 developed, showed a dark line bordered by two narrow 

 bands of nearly clear glass. The sensitiveness of the 

 instrument may be judged from the fact that records are 

 clearly given of every footfall of a horse when distant 

 more than a hundred yards. 



The vibrations in the ground are due to the passage of 

 a heavy load over an uneven surface. If the wheels were 

 absolutely circular and the rails perfectly straight and 

 yielding uniformly throughout, there would be nothing to 

 cause vibration. 



In the Central London Railway none of these conditions 

 is fulfilled. The rails are bridge rails in continuous contact 

 with the sleepers, which are laid longitudinally and are 

 bedded on concrete. This, however, varies in depth, being 

 least over the flanges of the sections of the tube. In the 

 intervals between the flanges, the yielding under a heavy 

 load would therefore be greater than in the parts imme- 

 diately above them, and this may in time cause a per- 

 manent unevenness of the rails. 



But a far more serious cause of vibration lies in the 

 fact that the rails, when first laid, are not straight. As 

 they leave the rolls the rails are curved, and they are then 

 bent under a press at intervals of two or three feet until 

 they api'car straight to the eye of the trained workman 

 superintending the operation. This process naturally 

 results in a slight waviuess of surface, the average de])tli 



of the hollows being, as Mr. Mallock ascertained, about 

 /„th of an inch, and the average distance from crest to 

 crest between H and 2^ feet, though deeper hollows and 

 longer waves are of frequent occurrence. 



Again, the wheels, thougli nearly circular at first, wear 

 irregularly owing to the action of the brakes, the slipping 

 which takes ])lace in travelling round curves, and jiossibly 

 to variability in their material. A pair of wheels that 

 had been in use for more than a year on the Central 

 Tjondon Railway were found to be worn so that they were 

 no longer concentric with the axles, and were also furrowed 

 by minor waves. 



There must thus be a continual variation of pressure 

 between the wheels and the rails, and it is to this that the 

 objectionable vibration is due. It is important to notice 

 that the variation of pressure is not proportional to the 

 total load on the wheels, but to that part of it which is not 

 supported by springs. Tlie part of the load which is 

 spring-borne moves practically in a horizontal line 

 without following the inequalities of the rails, so that 

 there is no change of any consequence in the pressure 

 corresponding to it. 



The diagrams obtained by Mr. Mallock show that the 

 vibrations of the ground caused by the passing trains are 

 of many different periods. When, however, they are large 

 and well-marked, the principal vibrations are found to be 

 nearly constant in period, whatever be the speed of the 

 train and however greatly the inequalities in the rails may 

 vary in length. The reason of this is that the irregular 

 impulses given by the uneven rail-surfaces set uja an 

 oscillation of the rails and the road-bed, which may be 

 regarded as an elastic support loaded with that part of 

 the mass which is not carried by springs. 



Mr. Mallock remarks that a somewhat similar case is 

 that of a ship rolling at sea. Whatever be the period of 

 the waves, the period of rolling is very nearly that of the 

 ship when it rolls in still water. It is only when there is 

 a long succession of equal waves that the period of the 

 rolling approaches that of the waves. 



A few of the diagrams obtained by Mr. Mallock are 

 given in Figs 3 and 4. Those in Fig. 3 represent the 

 vibration caused Iw an ordinary locomotive and train in 

 No. 19, Hyde Park Terrace, the upper curve, a, showing the 

 vibration in the basement, and the lower, 6, that on the 

 first floor. The vibrations caused by the train have 

 a period of about y'j of a second, and are, in both cases, 

 superposed on longer waves due to the swinging of the 

 heavy plate of the vibration apparatus. These diagrams 

 show very clearly how much greater is the vibration on 

 the first floor than in the basement of the building. 



The series of curves in Fig. 4 were obtained on the 

 ground floor of No. 13, Hyde Park Terrace. The first 



Fia. 3. 



three diagrams, a, h, c, represent the vibration caused 

 resjiectivcly by an ordinary locomotive and train, a geared 

 locomotive and train, and a multiple unit train. The last 

 curve, d, shows the vibration of the same floor caused by a 

 single light stamp of the foot. The effects of the differt ut 

 kinds of trains will be referred to afterwards. For the 

 present it is worth noticing how much the vibration 

 caused by stam])ing exceeds that due to any one of tin? 

 trnins. 



