LIFTS 575 of the cage and the ram is balanced by counterpoises on chains fastened to the top of the cage and passing over a pulley overhead, while the water pressure is used to overcome only the friction, and the additional load of passengers or goods. In this case again, owing to the passage of the chains over the pulleys, the balance is disturbed in a rise of 60 feet, by about th the weight of the cage and the ram, while the upward water pressure on the ram is in the same rise diminished by Jin. The former disturbance of balance is a decrease of the load resting on the base of the ram, while the latter is a decrease of the supporting pressure on the same base. If these were made equal, the cage and load would be perfectly balanced in every position. To make them equal, it would be necessary simply to adjust the ratio of the part ot the load borne by the counter poise to the part borne by the water. Let the former part be W l and the latter AV,, the total load being AVj + AV r Then for a water pressure of 200 Ib" per square inch, it would be necessary to have f = W, , or AVj =|AV a = A( Wi + AV 2 ). For a pressure of 400 ft per square inch, the equation would be For 100 ft per square inch it would be This adjustment would necessitate a large unnecessary consump tion of water, because the weight of cage and ram always bears a much greater ratio to the extra weight of passengers or goods than any of the above fractions ^, , or even -|. The adjustment being attainable by other means, this waste can in no case be desirable. If a second cylinder stand beside the lift- well and be connected by a pipe to the cylinder directly underneath the cage, so that there is a continually open passage between the two cylinders, then the supporting rod underneath the cage, together with the column of water leading from its base through the pipes to the second cylinder, is the exact counterpart in compression of the overhead ropes in tension in the other class of machine ; and, as counterweights are hung upon these ropes, a balancing weight may be laid on the surface of the water in the second cylin der. The balance weight, equal ling that of cage and ram, rests on a plunger or piston fitting this cylinder, and the rod is extended upwards into a third smaller cylinder, on the plunger of which is admitted, by means of the valve worked from the cage or landing-platforms, an extra amount of water pressure suf- Fi Fig. 2. ficient to elevate the extra load of passengers or goods. This is the arrangement in Tomassi s hydraulic balanced lift The column of water which takes the place of the rope in. the over head arrangement passes from one cylinder to the other, nd vice versa, in the same way as the rope passes from the cage side to the counterweight side of the overhead pulley. Tim.* the balance, which may be made correct for one position of the lift, becomes dis turbed for other positions by a similar amount to that already investigated. A perfect balance of the constant part of the total load, namely, that of the cage and ram, is, however, obtained for all positions of the cage by the arrangement shown in figs. 1 and 2. This is the design of Mr Edward Ellington, described by him in a paper read before the Institution of Mechanical Engineers in January 1882. The whole load is borne by the rod a underneath the cage, which enters as a ram into the vertical cylinder A. This rod is made solid in order to reduce the .size of the cylinder as much as possible, and, therefore, also the size of the well that has to be bored in tire ground to contain this cylinder. This class of lifts is especially expensive on account of this boring, and the objection to them on the score of expense is lessened by making the well small. The rod is made only just strong enough to safely bear the load on it. Its section should be designed with reference to the height of lift, because the longer the free length of the supporting pillar the greater is its tendency to buckle under a given load. If k be the stress per square inch calculated to be admissible on its section , and if W be the weight of cage and ram together and AV that of passengers or goods to be raised, the section is made equal to - . Since rC this same load has to be supported by the water pressure on the lower end of this rod, that water pressure is made also equal to k. This cylinder A is kept always in open communication with the lower end of the cylinder B. In this moves a piston I fastened to the top of the thick piston rod d. This passes downwards into the third cylinder C, and to its lower extremity is fastened the large piston c. These pistons have a common stroke, which is much shorter than the lift of the cage. The cylinders are correspondingly shorter than A, and they stand above ground. The ratio of the strokes may range from 5 to 8, and is the same as the ratio of the annular area of the under side of the piston b to that of the rod a. If b and d be the areas of the piston and piston rod, and a that of the rod supporting the cage, the ratio of the strokes is b - d : <*. Suppose the piston b to be at the top of its stroke and the cage to be consequently at the bottom of the lift-well, then, if in this position the piston b be at a height above the lower end of a equal to h inches, and if ? be the weight of a cubic inch of water, then, the pressure per square inch on a being k, that on the loicer side of piston b is k - hu The whole upward pressure on this piston is therefore (k - hw)(b - d) ; and a downward pressure equal to or rather more than this must be exerted on this piston in older to lift the cage. This is supplied by admitting the water from the main, or from thehydraulic accumulator if force-pumps are employed to provide water-pressure, into the upper ends of the cylinders B and C. The lower end of C is always kept in open communication with the atmosphere. The water is continually admitted to B, and the water pressure on the top surface of piston b is designed to balance the constant load of cage and ram when this piston is at the top of its stroke. During the ascent of the cage, the water is admitted into C by a valve moved from the cage or platforms by means of the rope t, and the water pressure on the annular top surface of piston c, when that piston is at its highest position, is designed to balance the extra load of passengers or goods. During the descent, the cage being empty, the connexion between C and the accumulator is shut by the valve actuated from the cage, and the water is allowed to escape freely to the drains, so that the pressure on c becomes equal to atmospheric pressure. If p be the pressure per square inch of the working water at the level of the piston b at its highest position, and c be the area of the cross-section of cylinder C, and if h be the length of plunger d, then in this position the whole downward force that is borne by the water underneath the piston b, and distributed over its area (b - d), is pb + (p + h ic)(c - d), when the pressure is on piston c, and simply pb when this pressure is cut off from C. (To this should be added the weight of b, d, and c, but for our present purpose of explanation only this may be left out of account.) The former quantity has to equal (k - hiv)(b - d), and the latter should equal These two equations serve to determine two of the quantities in volved in terms of the others. AVhen the water pressure is admitted to the upper side of b alone, the intensity of pressure on the under side of b is evidently as many times greater than the intensity on its upper side as the area of its upper side is greater than that of its lower surface. Thus any increase of intensity on the upper surface will cause a correspond ingly greater increase of intensity on the lower. Now if the pres sure on the under side of b were to remain the same while the cage ascended, the pressure on the lower end of a would decrease by an amount proportional to the change in their difference of level. If, for example, the rati} of the strokes 6 -d: a is 6:1, then, as the cage rises 6 inches, b will fall 1 inch, and h, the difference of lcvl
