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DYNAMOMETERS Professor Osborne Reynolds in 1887 patented a water-brake (see made up of two flat bars linked at their ends. Their centres Proc. Inst. C. E. vol. xcix. p. 167), using Fronde’s turbine to Si, s2, are held respectively by the pieces A, B, which together obtain the highly resisting spiral vortices, and arranging passages form a sliding pair. The block A carries the disc D, B carries in the casing for the entry of water at the hub of the wheel and the roller R and counting gear. The pulley E is driven from its exit at the'circumference. Water enters at E (Fig. 5), and an axle of the carriage. In a dynamometer used by Mr F. W. finds its way into the interior of the wheel, A, driving the air in Webb to measure the tractive resistance of trains on the London front of it through the air-passages K, K. Then following into and North-Western Railway, a tractive pull or push comthe pocketed chambers Yx, V2, it is caught into the vortex, and presses two spiral springs by a definite amount, which is finally escapes at the circumference, flowing away at F. The air- recorded to scale by a pencil on a sheet of paper, drawn conways k, k, in the fixed vanes tinuously from a storage drum at the rate of three inches per establish communication between mile, by a roller driven from one of the carriage axles. Thus the the cores of the vortices and the diagram shows the tractive force at any instant. A second pencil atmosphere. From i to 30 H.P. electrically connected to a clock traces a time line on the diagram may be measured at 100 revs, per with a kick at every thirty seconds. A third pencil traces an min. by a brake-wheel of this observation line in which a kick can be made at will by pressing kind 18 inches in diameter. For any one of the electrical pushes placed about the car, and a fourth other speeds the power varies as draws a datum line. The spring of the dynamometer car used by the cube of the speed. The Mr Dean on the Great Western Railway is made up of thirty flat casing is held from turning by plates, 7 ft. 6 in. long, 5 in. x fin. at the centre, spaced by distance weights hanging on an attached pieces nibbed into the plates at the centre and by rollers at the arm. The cocks regulating the ends. The drawbar is connected to the buckle, which is carried water are connected to the casing, on rollers, the ends of the spring resting on plates fixed to the so that any tilting automatically under-frame. The gear operating the paper roll is driven from regulates the flow, and therefore the axle of an independent wheel which is let down into contact the thickness of the film in the with the rail when required. This wheel serves also to measure vortex. In this way the brake the distance travelled. A Morin disc and roller integrator is may be arranged to maintain connected with the apparatus, so that the work done during a a constant torque, notwithstanding variation of the speed. In journey may be read off. Five lines are traced on the diagram. Alden’s brake (see Trans. Amer. Soc. Eng. vol. xi.) the resistance In spring dynamometers designed to measure a transmitted is obtained by turning a cast-iron disc against the frictional resistance of two thin copper plates, which are held in a casing free to turn upon the shaft, and are so arranged that the pressure between the rubbing surfaces is controlled, and the heat developed by friction carried away, by the regulated flow of water through the casing. The torque required to hold the casing still against the action of the disc measures the torque exerted by the shaft to which the disc is keyed. Transmission Dynamometers. — The essential part of many transmission dynamometers is a spring whose deformation indirectly measures the magnitude of the force transmitted through it. For many kinds of spring the change of form is practically proportional to the force, but the relation should always be determined experimentally. Morin (see Notice sur divers apparcils dynamometriques, Paris, 1841), in his classical experiments on traction, arranged his torque, the mechanical problem of ascertaining the change of apparatus so that the form of the spring is complicated by the fact that the spring change in form of the and the whole apparatus are rotating together. In the Ayrton spring was continuand Perry transmission dynamometer or spring coupling of this ously recorded on a type, the relative angular displacement is proportional to the sheet of paper drawn radius of the circle described by the end of a light lever operated under a style. For longer experiments he ! (see Proc. Inst. C. E. vol. cxxxii., 1897-98) uses a device shown in used a “Compteur” Fig. 7, by means of which the change in form of the spring is or mechanical inshown on a fixed indicator, which may be placed in any contegrator, suggested venient position. Two equal sprocket wheels Qx, are fastened, by Poncelet, from the one to the spring pulley, the other to the shaft. An endless which the work done band is placed over them to form two loops, which during during a given disrotation remain at the same distance apart, unless relative placement could be angular displacement occurs between Qx and Q2, due to a change read off directly. in form of the spring. The change in the distance d is proThis device consists portional to the change in the torque transmitted from the shaft of a roller of radius r, to the pulley. To measure this, guide pulleys are placed in the pressed into contact loops guided by a geometric slide, the one pulley carrying a scale, with a disc. The two and the other an index. A recording drum or integrating are carried on a apparatus may be arranged on the pulley frames. A quick common frame, so variation, or a periodic variation of the magnitude of the force arranged that a or torque transmitted through the springs, tends to set up change in form of Fig. 7. oscillations, and this tendency increases the nearer the periodic the spring causes a time of the force variation approaches a periodic time of the relative displacement of the disc and roller, the point of spring. Such vibrations may be damped out to a considerable contact moving radially from or towards the centre of the extent by the use of a dash-pot, or may be practically prevented disc. The radial distance x is at any instant proportional by using a relatively stiff spring. to the force acting through the spring. The angular disEvery part of a machine transmitting force suffers elastic placement, 0, of the disc is made proportional to the displace- deformation, and the force may be measured indirectly by ment, s, of the point of application of the force by suitable measuring the deformation. The relation between the two driving gear. If d is the angular displacement of the roller should in all cases be found experimentally. Hirn (see Lcs corresponding to displacements, dO of the disc, and ds of the Pandynamometres, Paris, 1876) employed this principle to measure xd0 point of application of P, a, and C constants, then d=:'-^r = the torque transmitted by a shaft. Signor Rosio used a teles phonic method to effect the same end, and more recently a /* 2 = C. Pa's, and therefore  = C I Pds; that is, the angular dis- mechanical, optical, and telephonic devices have been utilized rby the Rev. F. J. Jervis-Smith. (See Phil. Mag., Feb. 1898.) J Sl When a belt in which the maximum and minimum tensions placement of the roller measures the work done during the displacement from Sx to s2. The shaft carrying the roller is connected to are respectively P and p tt>, drives a pulley, the torque exerted a counter so that cp may be observed. The angular velocity of is [P-p)r lb ft., r being the radius of the pulley plus half the shaft is proportional to the rate of working. Morin’s the thickness of the belt. P and p may be measured directly by dynamometer is shown in Fig. 6. The transmitting spring is leading the belt round two freely hanging guide pulleys,
 * by mechanism between the spring-connected parts. Prof. Dalby