eccentric-rods ought to be long; the longer they are in proportion to the eccentricity the more symmetrical will the travel of the valve be on both sides of the centre of motion. 3. The link ought to be short. Each of its points describes a curve in a vertical plane, whose ordinates grow larger the farther the considered point is from the centre of the link; and as the horizontal motion only is transmitted to the valve, vertical oscillation will cause irregularities. 4. The link-hanger ought to be long. The longer it is the nearer will be the arc in which the link swings to a straight line, and thus the less its vertical oscillation. If the link is suspended in its centre, the curves that are described by points equidistant on both sides from the centre are not alike, and hence results the variation between the forward and backward gear. If the link is suspended at its lower end, its lower half will have less vertical oscillation and the upper half more. 5. The centre from which the link-hanger swings changes its position as the link is lowered or raised, and also causes irregularities. To reduce them to the smallest amount the arm of the lifting-shaft should be made as long as the eccentric-rod, and the centre of the lifting-shaft should be placed at the height corresponding to the central position of the centre on which the link-hanger swings." All these conditions can never be fulfilled in practice, and the variations in the lead and the period of admission can be somewhat regulated in an artificial way, but for one gear only. This is accomplished by giving different lead to the two eccentrics, which difference will be smaller the longer the eccentric-rods are and the shorter the link, and by suspending the link not exactly on its centre line but at a certain distance from it, giving what is called "the offset." For application of the Zeuner diagram to link-motion, see Holmes on the Steam-engine, p. 290. See also Clark's Railway Machinery (1855), Clark's Steam-engine, Zeuner's and Auchincloss's Treatises on Slide-valve Gears, and Halsey's Locomotive Link Motion. (See page 859a.) The following rules are given by the American Machinist for laying out a link for an upright slide-valve engine. By the term radius of link is meant the radius of the link-arc ab, Fig. 150, drawn through the centre of the slot; this radius is generally made equal to the distance from the centre of shaft to centre of the link-block pin P when the latter stands midway of its travel. The distance between the centres of the eccentric-rod pins e, e, should not be less than 21⁄2 times, and, when space will permit, three times the throw of the eccentric. By the throw we mean twice the eccentricity of the eccentric. The slot link is generally suspended from the end next to the forward eccentric at a point in the link-arc prolonged. This will give comparatively a small amount of slip to the link-block when the link is in forward gear; but this slip will be increased when the link is in backward gear. This increase of slip is, however, considered of little importance, because marine engines, as a rule, work but very little in the backward gear. When it is necessary that the motion shall be as efficient in backward gear as in forward gear, then the link should be suspended from a point midway between the two eccentric-rod pins; in marine engine practice this point is generally located on the link-arc; for equal cut-offs it is better to move the point of suspen. sion a small amount towards the eccentrics. For obtaining the dimensions of the link in inches: Let L denote the length of the valve, B the breadth, p the absolute steam-pressure per sq. in., and R a factor of computation used as below; then R= .01 √ L × B × p. Breadth of the link.... Thickness T of the bar............................. Length of sliding-block.. ............... Diameter of eccentric-rod pins. Diameter of suspension-rod pin when overhung.. = RX 1.6 = RX 2.5 Diameter of block-pin when secured at both ends = (R × ́.8) + 1⁄4 The length of the link, that is, the distance from a to b, measured on a straight line joining the ends of the link-arc in the slot, should be such as to allow the centre of the link-block pin P to be placed in a line with the eccentric-rod pins, leaving sufficient room for the slip of the block. Another type of link frequently used in marine engines is the double-bar link, and this type is again divided into two classes: one class embraces those links which have the eccentric-rod ends as well as the valve-spindle end between the bars, as shown at B (with these links the travel of the valve is less than the throw of the eccentric); the other class embraces those links, shown at C, for which the eccentric-rods are made with fork-ends, so as to connect to studs on the outside of the bars, allowing the block to slide to the end of the link, so that the centres of the eccentric-rod ends and the block-pin are in line when in full gear, making the travel of the valve equal to the throw of the eccentric. The dimensions of these links when the distance between the eccentric-rod pins is 21⁄2 to 234 times the throw of eccentrics can be found as follows: When the distance between the eccentric-rod pins is equal to 3 or 4 times the throw of the eccentrics, then Depth of bars... Thickness of bars............. ................... = (RX 1.25" .5) + 1⁄44′′ All the other dimensions may be found by the first table. These are empirical rules, and the results may have to be slightly changed to suit given conditions. In marine engines the eccentric-rod ends for all classes of links have adjustable brasses. In locomotives the slot-link is usually employed, and in these the pin-holes have case-hardened bushes driven into the pinholes, and have no adjustable brasses in the ends of the eccentric-rods. The link in B is generally suspended by one of the eccentric-rod pins; and the link in C is suspended by one of the pins in the end of the link, or by one of the eccentric-rod pins. (See note on Locomotive Link Motion in Appendix. p. 1077.) Other Forms of Valve-Gear, as the Joy, Marshall, Hackworth, Bremme, Walschaert, Corliss, etc., are described in Clark's Steam-engine, vol. ii. The design of the Reynolds-Corliss valve-gear is discussed by A. H. Eldridge in Power, Sep. 1893. See also Henthorn on the Corliss engine. Rules for laying down the centre lines of the Joy valve-gear are given ia American Machinist, Nov. 13, 1890. For Joy's "Fluid-pressure Reversingvalve," see Eng'g, May 25, 1894. GOVERNORS. Pendulum or Fly-ball Governor.-The inclination of the arms of a revolving pendulum to a vertical axis is such that the height of the point of suspension h above the horizontal plane in which the centre of gravity of the balls revolve (assuming the weight of the rods to be small compared with the weight of the balls) bears to the radius r of the circle described by the centres of the balls the ratio which ratio is independent of the weight of the balls, v being the velocity of the centres of the balls in feet per second. If T number of revolutions of the balls in 1 second, v = 2′′rT = ar, in which a = the angular velocity, or 2πT, and g being taken at 32.16. If N = number of revs. per minute, h = inches. 35190 N2 For revolutions per minute..... ... 40 45 50 60 75 21.99 17.38 14.08 9.775 6.256 | Number of turns per minute required to cause the arms to take a given angle with the vertical axis: Let = length of the arm in inches from the centre of suspension to the centre of gyration, and a the required angle; then The simple governor is not isochronous; that is, it does not revolve at a uniform speed in all positions, the speed changing as the angle of the arms changes. To remedy this defect loaded governors, such as Porter's, are used. From the balls of a common governor whose collective weight is 4 let there be hung by a pair of links of lengths equal to the pendulum arms a load B capable of sliding on the spindle, having its centre of gravity in the axis of rotation. Then the centrifugal force is that due to A alone, and the effect of gravity is that due to A+2B; consequently the altitude for a given speed is increased in the ratio (A + 2B): A, as compared with that of a simple revolving pendulum, and a given absolute variation in altitude produces a smaller proportionate variation in speed than in the common governor. (Rankine, S. E., p. 551.) For the weighted governor let = the length of the arm from the point of suspension to the centre of gravity of the ball, and let the length of the suspending-link, l, the length of the portion of the arm from the point of suspension of the arm to the point of attachment of the link; G = the weight of one ball, Q = half the weight of the sliding weight, h the height of the governor from the point of snspension to the plane of revolution of the balls, a = the angular velocity=2πT, Tbeing the number of revolutions per second; then a = √32,16 (1+4); h = 32.16 (1+2; 2) in feet, or h a2 in inches, N being the number of revolutions per For various forms of governor see App. Cycl. Mech., vol. ii. 61, and Clark's Steam-engine, vol. ii. p. 65. To Change the Speed of an Engine Having a Fly-ball Governor.-A slight difference in the speed of a governor changes the position of its weights from that required for full load to that required for no load. It is evident therefore that, whatever the speed of the engine, the normal speed of the governor must be that for which the governor was designed; i.e., the speed of the governor must be kept the same. To change the speed of the engine the problem is to so adjust the pulleys which drive the governor that the engine at its new speed shall drive it just as fast as it was driven at its original speed. In order to increase the engine-speed we must decrease the pulley upon the shaft of the engine, i.e., the driver, or increase that on the governor, i.e., the driven, in the proportion that the speed of the engine is to be increased. Fly-wheel or Shaft Governors.-At the Centennial Exhibition in 1876 there were shown a few steam-engines in which the governors were contained in the fly-wheel or band-wheel, the fly-balls or weights revolving around the shaft in a vertical plane with the wheel and shifting the eccentric so as automatically to vary the travel of the valve and the point of cutoff. This form of governor has since come into extensive use, especially for high-speed engines. In its usual form two weights are carried on arms the ends of which are pivoted to two points on the pulley near its circuni ference, 180° apart. Links connect these arms to the eccentric. The eccentric is not rigidly keyed to the shaft but is free to move transversely across it for a certain distance, having an oblong hole which allows of this movement. Centrifugal force causes the weights to fly towards the circumference of the wheel and to pull the eccentric into a position of minimum eccentricity. This force is resisted by a spring attached to each arm which tends to pull the weights towards the shaft and shift the eccentric to the position of maximum eccentricity. The travel of the valve is thus varied, so that it tends to cut off earlier in the stroke as the engine increases its speed. Many modifications of this general form are in use. For discussions of this form of governor see Hartnell, Proc. Inst. M. E., 1882, p. 408: Trans. A. S. M. E., ix. 300; xi. 1081; xiv. 92; xv. 929; Modern Mechanism, p. 399; Whitham's Constructive Steam Engineering; J. Begtrup, Am. Mach., Oct. 19 and Dec. 14, 1893, Jan. 18 and March 1, 1894. Calculation of Springs for Shaft-governors. (Wilson Hartnell, Proc. Inst. M. E., Aug. 1882.)-The springs for shaft-governors may be conveniently calculated as follows, dimensions being in inches: Let W = weight of the balls or weights, in pounds; r1 and the maximum and minimum radial distances of the centre of the balls or of the centre of gravity of the weights; l1 and l the leverages, i.e., the perpendicular distances from the cen tre of the weight-pin to a line in the direction of the centrifugal force drawn through the centre of gravity of the weights or balls at radii r1 and r1; m, and m, the corresponding leverages of the springs; C1 and C2 the centrifugal forces, for 100 revolutions per minute, at radii r1 and r2; P and P2 the corresponding pressures on the spring; (It is convenient to calculate these and note them down for reference.) C3 and C4 = maximum and minimum centrifugal forces; S mean speed (revolutions per minute); S1 and S, the maximum and minimum number of revolutions per minute; P and P the pressures on the spring at the limiting number of revo. lutions (S, and S2); P-PD the difference of the maximum and minimum pressures on the springs; V the percentage of variation from the mean speed, or the sensitive The mean speed and sensitiveness desired are supposed to be given. Then To It is usual to give the spring-maker the values of P, and of v or w. ensure proper space being provided, the dimensions of the spring should be calculated by the formula for strength and extension of springs, and the least length of the spring as compressed be determined. With a straight centripetal line, the governor-power = C4 2 12 For a preliminary determination of the governor-power it may be taken as equal to this in all cases, although it is evident that with a curved centripetal line it will be slightly less. The difference D must be constant for the same spring, however great or little its initial compression. Let the spring be screwed up until its minimum pressure is P's. Then to find the speed P = P+D, The speed at which the governor would be isochronous would be 2 Suppose the pressure on the spring with a speed of 100 revolutions, at the maximum and minimum radii, was 200 lbs. and 100 lbs., respectively, then the pressure of the spring to suit a variation from 95 to 105 revolutions will 90.2 and 200 × =220.5. That is, the increase of resistance from the minimum to the maximum radius must be 220 - 90 = 130 lbs. be 100 × (95)2= 100 、 The extreme speeds due to such a spring, screwed up to different pressures, are shown in the following table: Revolutions per minute, balls shut. Increase of pressure when balls open fully. 80 90 95 100 110 120 64 81 90 100 121 144 130 130 130 130 130 130 194 211 220 230 251 274 98 102 105 107 112 117 10 6 5 3 1 -1 The speed at which the governor would become isochronous is 114. Any spring will give the right variation at some speed; hence in experimenting with a governor the correct spring may be found from any wrong one by a very simple calculation. Thus, if a governor with a spring whose stiffness is 50 lbs. per iuch acts best when the engine runs at 95, 90 being its proper speed, then 50 X 45 lbs. is the stiffness of spring required. 2 To determine the speed at which the governor acts best, the springs may be screwed up until it begins to "hunt and then slackened until the gov ernor is as sensitive as is compatible with steadiness. CONDENSERS, AIR-PUMPS CIRCULATING- The Jet Condenser, (Chiefly abridged from Seaton's Marine Engineering.) The jet condenser is now uncommon in marine practice, being generally supplanted by the surface condenser. It is commonly used where fresh water is available for boiler feed. With the jet condenser a vacuum of 24 in. was considered fairly good, and 25 in, as much as was possible with most condensers; the temperature corresponding to 24 in. vacuum, or 3 lbs. pressure absolute, is 140°. In practice the temperature in the hot-well varies from 110° to 1200, and occasionally as much as 130° is maintained. To find the quantity of injection-water per pound of steam to be condensed: Let ture of steam at the exhaust pressure; To temperature of the cool = |