constant, although in very rare cases gearing is designed to work with a variable velocity ratio as part of some special machines. For the principles governing the shape of the teeth to fulfil the condition that the velocity ratio between the wheels shall be constant, see MEcHAN1cs, § A pplied. The size of the teeth is determined by the torque the gearing is required to transmit.
Pitch chains are closely allied to gearing; a familiar example is in the driving chain of a bicycle. Pitch chains are used to a limited extent as a substitute for belts, and the teeth of the chains and the teeth of the wheels with which they work are shaped on the same principles as those governing the design of the teeth of wheels.
If a pair of wheels is required to transmit a certain maximum horse power, the angular velocity of the shaft being w, the pressure P which the teeth must be designed to sustain at the pitch circle is 550 H.P./wR, where R is the radius of the pitch circle of the wheel, whose angular velocity is w.
§ 10. Velocity Ratio.-In the case of transmission either by belts, ropes, shafts or gearing, the operating principle is that the rate of working is constant, assuming that the efnciency of the transmission is unity, and that the product Tw is therefore constant, whether the shafts are connected by ropes or gearing. Considering therefore two shafts, T1w1=T2<, .>2; that is wi, /w2=T2/Tl; i.e. the angular velocity ratio is inversely as the torque ratio. Hence the higher the speed at which a shaft runs, the smaller the torque for the transmission of a given horse power, and the smaller the tension on the belts or ropes for the transmission of a given horse power. § rr. Long Distance Transmission of Power.~C. F. Hirn originated the transmission of power by means of wire ropes at Colmar in Alsace in 18 50. Such a telodynamic transmission consists of a series of wire ropes running on wheels or pulleys supported on piers at spans varying from goo to 500 ft. between the prime mover and the place where the power is utilized. The slack of the ropes is supported in some cases on guide pulleys distributed between the main piers. In this way goo h.p. was transmitted over a distance of 6500 ft. at Freiberg by means of a series of wire ropes running at 62 ft. per second on pulleys 177 in. diameter. The individual ropes of the series, each transmitting 300 h.p., were each I'O8 in. diameter and contained ro strands of 9 wires per strand, the wires being each 0'O72 in. diameter. Similar installations existed at Schaffhausen, Oberursal, Bellegarde, Tortona and Zürich. For particulars of these transmissions with full details see W. C. Unwin's Howard Lectures on the “ Development and Transmission of Power from Central Stations ” (Journ. S oc. Arts, 189 3, published in book form 1894). The system of telodynamic transmission would no doubt have developed to a much greater extent than it has done but for the advent of electrical transmission, which made practicable the transmission of power to distances utterly beyond the possibilities of any mechanical system. See W. ]'. M. Rankine, Treatise on Machinery and M illwork; and W. C. Unwin, Elements of Machine Design; and for telodynamic transmission see F. Reuleaux, Die Konslrukteur. (W. E. D.) II. HYDRAULIC
The first proposal for a general transmission of hydraulic power was made by Bramah in 1802. In 1846 Lord Armstrong's hydraulic crane was erected at Newcastle, and was worked from the town water mains, but the pressure in such mains was too low and uncertain to secure satisfactory results. The invention of the accumulator in 1850 enabled much higher pressures to be used; since then 700 lb per square inch has been adopted in most private hydraulic power transmission plants. An attempt to give a public supply of hydraulic power was made in 18 59, when a company was formed for laying mains in London along the river Thames between the Tower and Blackfriars, the engineer being Sir George-Bruce; but though an act of parliament was obtained, the works were not carried out. The first public hydraulic supply station was established at Hull in 1877. In 1883 the General Hydraulic Power Works, Messrs Ellington and Woodall being the engineers, were started in London, and they now form the largest system of hydraulic power transmission in existence. Works of a similar character have since been established in several other towns. The general' features of hydraulic power transmissions are: (1) a central station where the hydraulic pressure is created, usually by means of steam pumping engines; (2) a system of distribution mains; (3) machines for utilizing the pressure. In cases of public supplies there is the further important matter of registration. When dealing with any practical problem of hydraulic power transmission it is of the first importance to determine the maximum demand for power, its duration and frequency. If the duration of the maximum demand is limited gfggzi and the frequency restricted-for instance, when a » swing bridge has to be opened and closed only a few times in the course of a day-a small pumping plant and a large accumulator will be desirable. If the maximum demand is more or less continuous, as when hydraulic pressure is used for working a pump in a mine or a hydraulic engine in a workshop, the central station pumping engine must be capable of supplying the maximum demand without the aid of an accumulator, which may or may not, according to circumstances, be provided to serve as a regulator. A hydraulic accumulator (fig. 1) ordinarily consists of a hydraulic cylinder
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and ram, the ram being loaded with sufficient weight to give the pressure required in the hydraulic mains. If a pressure of 700 lb per square inch is wanted, the weight of the ram and its load, neglecting friction, must be 700 lb for each square inch of its area, and if the cylinder is full, i.e. the ram elevated to its full ~extent, the accumulator is a reservoir of power, exactly as if it were a tank at the same cubical extent placed at an elevation of about 1600 ft. above the mains and connected with them. The function of accumulators in hydraulic power distribution is frequently misunderstood, and it has been urged that as in practice the size of the reservoirs of power that can be obtained by their use is small, they are of little value. An accumulator having a ram zo in. diameter by zo ft. stroke loaded to 700 lb is