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Originally appearing in Volume V28, Page 477 of the 1911 Encyclopedia Britannica.
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WEIGHING MACHINES. Mechanical devices for determining weights or comparing the masses of bodies may be classified as (a) equal-armed balances, (b) unequal-armed balances, (c) spring balances and (d) automatic machines. Equal-armed balances may be divided into (1) scale-beams or balances in which the scale-pans are below the beam; (2) counter machines and balances on the same principle, in which the scale-pans are above the beam. Unequal-armed balances may be divided into (I) balances consisting of a single steelyard; (2) balances formedby combinations of unequal-armed levers and steelyards, such as platform machines, weighbridges, &c. Equal-armed Balances. Scale-beams are the most accurate balances, and the most generally used. When constructed for purposes of extreme accuracy they will turn with the one-millionth part of the load weighed, though to ensure such a result the knife-edges and their bearings must be extremely hard (either hardened steel or agate) and worked up with great care. The beam must be provided with a small ball of metal which can be screwed up and down a stem on the top of the beam for the purpose of accurately adjusting the position of the centre of gravity, and there should be a small adjustable weight on a fine screw projecting horizon-tally from one end of the beam for the purpose of accurately balancing the arms. The theory of the scale-beam is stated by Weisbach in his Mechanics of Machinery and Engineering, as follows:—In fig. 1 D is the fulcrum of the balance, S the centre of gravity of the beam a'one without the scales, chains or weights; A and B the points of suspension of the chains. If the length of the arms AC=BC=I,CD=a,SD=s, the angle of deviation of the balance from the horizontal =d), the weight of the beam alone =G, the weight on one side = P, that on the other = P+Z, and lastly the weight of each scale with its appurtenances =Q then 'Z l tans)= {2 (P+Q)+Z}a+G s, From this it is inferred that the deviation, and therefore the sensitiveness, of the balance increases with the length of the beam, and de-creases as the distances, a and s, increase; also, that a heavy balance is, ceteris paribus, less sensitive than a light one, and that the sensitiveness decreases continually the greater the weight put upon the scales. In order to increase the sensitiveness of a balance, the line AB joining the points of suspension and the centre of gravity of the balance must be brpught nearer to each other. Finally, if a is made extremely small, so that practically tan di = Zl/Gs, the sensitiveness is independent of the amount weighed by the balance. Weisbach also shows that if Gy2 is the moment of inertia of the beam, the time, t, of a vibration of the balance is t—'r This shows that the time of a vibration increases as P, Q and 1 increase, and as a and s diminish. Therefore with equal weights a balance vibrates more slowly the more sensitive it is, and therefore weighing by a sensitive balance is a slower process than with a less sensitive one. The conditions which must be fulfilled by a scale-beam in proper adjustment are:—(1) The beam must take up a horizontal position when the weights in the two scale-pans are equal, from nothing to the full weighing capacity of the machine. (2) The beam must take up a definite position of equilibrium for a given small difference of weight in the scale-pans. The sensitiveness, i.e. the angle of deviation of the beam from the horizontal after it has come to rest, due to a given small difference of weight in the scale-pans, should be such as is suited to the purposes for which the balance is intended. Bearing in mind that with ordinary trade balances there is always a possibility of the scale-pa.ns and chains getting interchanged, these conditions require; (a) That the beam without the scale-pans and chains must be equally balanced and horizontal; (b) that the two scale-pans with their chains must be of equal weight; (c) that the arms of the beam must be exactly equal in length; i.e. the line joining the end knife edges must be exactly bisected by a line drawn perpendicular to it from the fulcrum knife-edge. By testing the beam with the scale-pans attached and equal weights in the pans, and noting carefully the position which it takes up; and then inter-changing the scale-pans, &c., and again noting the position which the beam takes up, a correct inference can be drawn as to the causes of error; and if after slightly altering or adjusting the knife-edges and scale-pans in the direction indicated by the experiment, the operation is repeated, any required degree of accuracy may be obtained by successive approximations. The chief reason for testing balances with weights in the scale-pans rather than with the scale-pans empty, is that the balance might be unstable with the weights though stable without them. This is not an infrequent occurrence, and arises from the tendency on the part of manufacturers to make balances so extremely sensitive that they are on the verge of in-stability. In fig. 2 let ABCD be the beam of a scale-beam, Z the 1. Balaninus glandium, magnified. 2. The same, natural size. 3. The larva, magnified. 4. The same, natural size. 5. Head and snout of the female, magnified. 6. The same parts of the male, magnified. to show arrangement of antennae. J2 (P+Q) (12+a2)+Gy2 g{2 (P+Q) a+Gs} fulcrum knife-edge, and X, Y the knife-edges on which the scales are hung In order to ensure a high degree of sensitiveness, balances are sometimes constructed so that Z is slightly below the line joining X and Y, and is only slightly above H, the centre of gravity of the beam with the scale-pans and chains attached. The addition of weights in the scales will have the effect of raising the point H till it gets above Z, and the balance, becoming unstable, will turn till it is brought up by a stop of some kind. Fig. 3 represents a precision balance constructed to weigh with great accuracy. The beam is of bronze in a single deep casting, cored out in the middle so as to allow the saddle at the top of the stand to pass through the beam and afford a continuous bearing for the fulcrum knife-edge. The knife-edge and its bearing are both of steel or agate, and the bearing surface is flat. The end knife-edges also are of steel or agate, and have continuous bearing on flat steel or agate surfaces at the upper part of the suspension links. To relieve the knife-edges from wear when the balance is not being used a triangular frame is provided, which is lifted and lowered by a cam action at the bottom, and moves vertically in guides fixed on the stand. By its upward movement the tops of the screw studs near its ends are first received by the projecting studs on each side of the suspension links, and the suspension links are lifted off the'end knife-edges; and next, as the sliding frame continues its upward motion, the horizontal studs at the two ends of the beam are received in the forks at the ends of the sliding frame, and by them the fulcrum of the beam is lifted off its bearing. To keep the beam truly in its place, which is very necessary, as all the bearings_are flat,athe re- From Airy, " On Weighing Machines," Institution of Civil Engineers, 1892. FIG. 3.—Precision Balance. cesses for the ends of the studs are formed so as to draw the beam without strain into its true position every time that it is thrown out of gear by the sliding frame. The end knife-edges are adjusted and tightly jammed into exact position by means of wedge pieces and set screws, and the beam is furnished with delicate adjusting weights at its top. The position of the beam with respect to.the horizontal is shown by a horizontal pointer (not shown) projecting from one end of it, which plays past a scale, each division of which corresponds to the 1 th or iibth of a grain according to the size and delicacy of the machine. A first-class chemical balance would be made in this manner, but in all places where there are acids and gases the knife-edges and bearings must be made of agate, as the fumes attack and corrode steel. For the weighing of very small quantities with balances of great delicacy, the following method is adopted:—If the balance be in perfect adjustment, and I be the length of each arm, and w a very minute difference of the weights in the two scale-pans, by which the beam is deflected from the horizontal by a very small angle c, it can easily be shown that tan 0, or 4), varies as wXl. Therefore the angle of deflection which would be produced by grain weight hung at the distance 1/to (for example) from the centre is the same as would be produced by j loth of- a grain in the scale-pan at the distance 1. Therefore by graduating the top of the beam and shifting a rider grain weight till the beam is horizontal, it is easy to ascertain the small difference of weight in the scale-pans which caused the deflection to the lath or ninth part of a grain without using a weight smaller than a grain. The fitting of the knife-edges is of great importance. In ordinary trade balances a triangular piece of hard steel, with a finely. ground edge, is driven through a triangular hole in the beam and jammed tight. This forms the knife-edge, and the scale-pans are hung from the two projecting ends of the piece of steel. Similarly the twoprojecting ends of the central piece of steel which forms the fulcrum take bearing on two cheeks of the stand, between which the beam sways. It is clear that errors will arise if the pieces of steel are not truly perpendicular to the plane of the beam, and the adjustment of great accuracy would be very tedious. Therefore for balances of precision the end knife-edges are fixed on the top of the beam so as to present a continuous unbroken knife-edge, and the fulcrum knife-edge is also made continuous, the beans being cored out or cut away to admit of the introduction of the stand bearing. With this arrangement the knife-edges can be easily adjusted and examined, and the system is now rapidly extending to the better class of trade balances. The knife-edges of weighing machines are the parts that wear out soonest, but very little is known about them experimentally, and the knife-edges made by different makers vary extremely in their angles. Those made by some of the best makers for the most delicate machines are formed to an angle of about 80° between the sides, with the finished edge ground to an angle varying from iio° to 120°. The following may be taken as the maximum loads per in, of acting or efficient knife-edge allowed by the best makers: I. For scale-beams of the highest accuracy—From 1lb per in for a machine of z lb capacity, to 25 lb per in. for a machine of 80 lb capacity. 2. For ordinary trade scale-beams, counter machines, and dead-weight machines—From 20 lb per in. for a machine of 7 lb capacity to 600 lb per in. for a machine of 2 ton capacity. 3. For platform machines and weighbridges—From Ito lb per in_ for a machine of 4 cwt. capacity, to i ton per in. for a machine of 25 tons capacity. The sensitiveness of scale-beams depends entirely upon the skill and care used in their construction. With balances of the highest precision it may be as high as ru e-asth of the loaa weighed while with trade balances when new it would be about 2hoth of the load. In Emery's testing machine there are no knife-edges, but their function is performed by thin steel plates, which are forced under a very heavy pressure into slots formed in the parts that are to be connected, so that the parts are united by the plate. In this case there is no friction and no sensible wear, so that very great permanency of condition and constancy of action might be expected But the resistance to bending of the steel plates would render this arrangement unsuitable for scale-beams, in which the movement is large. In some respects it would appear to be very suitable for weighbridges, in which the movement of the lever is very small, but for general convenience of adjustment the knife-edges appear preferable. In the comparison of standard weights, or in any weighing operations where great accuracy is required, it is necessary to use many precautions. The comparison of standard weights has to be con-ducted at the standard temperature, and the room must be brought to that temperature and maintained at it. The balance must be enclosed in a glass case to protect it from draughts of air or from the heat of the body of the operator. And the operations of placing and shifting the weights must be effected by mechanism which will enable this to be done without opening the case or exposing the machine. When the weights which are to be compared are of different metals further complications arise, for the volumes of equal weights of different metals will be different, and therefore the quantity of air displaced by them will be different, and the difference of the weights of air displaced by the two weights must be allowed for. And the weight of air displaced depends upon the density of the air at the time of weighing, and therefore the barometer reading must be taken. For this correction an exact knowledge of the specific gravities of the metals under comparison is required. In this way an exact comparison of the weights in vacuo can be computed, but of course the simplest way of arriving at the result would be by the construction of a strong air-tight case which can be completely exhausted of air by an air-pump, and in which the weighing can then be effected in vacuo. The difficulty about weighing in vacuo is that it is found almost impossible to exhaust the case entirely, or even to maintain a constant degree of exhaustion, by reason of the leakage connected with the weighing operations, and in consequence weighing in vacuo is not much in favour. Whatever method is adopted, very exact weighing is a difficult and troublesome work. Counter machines have an advantage over scale-beams in not being encumbered with suspension chains and the beam above. They are usually made with two beams, each with its three knife-edges, rigidly tied together or cast in one piece and some distance apart, so that the scale-pans being carried on two knife-edges, each is prevented from tipping over sideways. To prevent them from tipping over in the direction of the beams a vertical leg is rigidly fastened to the under side of each pan, the lower end of which is loosely secured by a horizontal stay to a pin in the middle of the frame. In using these machines there is seldom any question of determining the weight to any great nicety, and rapid action is generally of high importance. Hence they are very commonly made unstable, or accelerating," i.e. they are constructed with the fulcrum knife-edges lower than the line joining the end knife-edges, and they are arranged so that the beam is horizontal when the stop of the r'eights-pan is hard down on its bearings. This arrangement a 0 A is well adapted for weighing out parcels of goods of a definite weight, though not for ascertaining the correct weight of a given article. For the latter purpose machines are used of which the beams are made stable, or " vibrating," by constructing them with the fulcrum knife-edges above the line joining the end knife-edges. " Accelerating " machines can be used to the advantage of the vendor in two ways. Firstly, in using them to determine the weight ~f of a given article. For with unstable balances, although the smallest excess of weight in the goods-pan will cause it to descend till it is brought up by its stop, yet being in this position, a very much greater weight than the difference which brought it there will be required in the weights-pan to enable it to mount again. If W be the weight in each pan when the goods-pan commenced to sink, 1 the length of each arm, m the distance of the fulcrum below the line joining the end knife-edges, and l3 the angle at the fulcrum which defines the range of sway of the beam, it can easily be shown that w, the additional weight required in the weights-pan to enable the goods-pan to rise from its stop, is given by the equation w =W 2m tan l3/L—m tan $. So that if, for example, a fishmonger uses such a machine to ascertain the weight of a piece of fish which he places in the goods-pan, and thereby depresses it down upon its stop, and then places weights in the weights-pan till the goods-pan rises, the customer is charged for more than the real weight of the fish. Secondly, in using them out of level, with the goods end of the machine lower than the weights end. If B be the angle of tilt of the machine, and the other symbols be as before, it may be shown that the additional weight, w which is needed in the weights-pan to enable the goods-pan to rise off its stop, is given by the equation w= W 2m tan ()3 —B)/L—m tan (3—0. When 8 is negative, as it is when the goods end of the machine is lower than the weights end, the value of w may be very appreciable. With " vibrating " machines the value of m is in general so extremely small that w is of no practical importance in either of the above cases. If a counter machine be made with a large flat goods-pan, as in fig. 4, an error may be caused by placing the goods eccentricallyon the pan, as at D or E. Using the symbols of the diagram, . it can be shown that the effect of placing the weight W at E instead of F is to cause the end of the beam to descend, as if under the action of an additional weight, w, at F such that w=Wa(ml'1 Stan 0)/h. The condition that must exist in order that the balance may weigh correctly for all positions of the weight W is w = o, or tan B = —ml-i; that is, the stay KG must be adjusted parallel to the line joining the points A and C. From the equation for w, it is seen that the larger h is the smaller w will be. Therefore for the larger counter machines, where it is not convenient to have the scale-pans raised high above the counter, and for " dead-weight " machines on the same principle, where it is not convenient to have the scale-pans raised high above the floor, there is an advantage in adopting the " inverted counter machine " arrangement (fig. 5), because the vertical leg can be produced upwards as high as is required. This arrangement is very common. As will be readily understood from the construction of the machines, there is more friction in counter machines than in scale-beams. The "sensitiveness " error allowed by the Board of Trade for counter machines is five times as great as that allowed for scale-beams. The torsion balance made by the United States Torsion Balance and Scale Company of New York is a counter machine made with-out knife-edges, and is very sensitive. It is constructed with two similar beams, one above the other, which are coupled together at the ends to form a parallel motion for carrying the pans up-right. The coupling is effected by firmly clamping the ends of the beams upon the top and bottom respectively of a loop of watch-spring, which is tightly stretched round the casting carrying the pan, as is shown in the end view in fig. 6. At their middles the beams are similarly clamped upon the top and bottom of a loop of watch-spring which is tightly stretched round a casting which is bolted upon the bed-plate. When the case which holds the machine is adjusted horizontally by means of its foot-screws, and the weights in the pans are equal, the beams remain perfectly horizontal; but with the slightest difference of weight in the pans the beams are tilted, and the elastic resistance of the springs to torsion allows the beams to take up a definite position of equilibrium. The lower beam carries on a saddle a scale which is raised FIG. 6. nearly to the top of the glass case in which the machine is enclosed, and as the beams sway this scale plays past a scratch on the glass, which is so placed that when the zero point on the scale coincides with the scratch the beams are horizontal. With proper care this machine should be very permanent in its action. Unequal-armed Balances. Steelyards are simple, trustworthy and durable, but unless special contrivances are introduced for ascertaining the position of the travelling poise with very great accuracy, there will be a little uncertainty as to the reading, and therefore steelyards are not in general so accurate as scale-beams. When carefully nicked they are well-adapted for weighing out definite quantities of goods, such as r lb, 2 lb, &c., as in such cases there is no question of estimation. The ordinary way of using a steelyard is to bring it into a horizontal position by means of movable weights, and to infer the amount of the load from the positions of these. But it is sometimes convenient to use a fixed weight on the long arm, and to infer the amount of the load from the position of the steelyard. The rule for graduation is very simple. The simplest form is that which has a single travelling poise. The more elaborate ones are made either with a heavy travelling poise to measure the bulk of the load with a light travelling poise for the remainder, or else with a knife-edge at the end of the steel-yard, on which loose weights are hung to measure the bulk of the load, the remainder being measured with a light travelling poise. The advantage of the first arrangement is that the weights on the steelyard are always the same, and inconsistencies of indication are avoided, while in the second arrangement the loose weights are lighter and handier, though they must be very accurate and consistent among themselves, or the error will be considerable, by reason of the great leverage they exert. Steelyards, like other weighing machines, will be "accelerating," or " vibrating " according to the arrangement of the knife-edges. + w In fig. 7 let Z be the fulcrum knife-edge, X the knife-edge on which the load R is hung, and H the centre of gravity of the weights to the right of Z, viz. the weight, W, of the steelyard acting at its centre of gravity ; G, the travelling poise ; P, acting at M ; and the weights, Q, hung on the knife-edge at Y. Then if Z be below the line joining X and H, the steelyard will be " accelerating " ; i.e. with the smallest excess of moment on the left-hand side of the fulcrum, the end C of the steelyard will rise with accelerating velocity till it is brought up by a stop of some sort; and with the smallest excess of moment on the right-hand side of the fulcrum, the end C of the steelyard will drop, and will descend with accelerating velocity till it is brought up by a similar stop. If Z be above the line XH, the steelyard is " vibrating "; i.e. it will sway or vibrate up and down, ultimately coming to rest in its position of equilibrium. Steelyards, again, are frequently arranged as counter machines, having a scoop or pan resting on a pair of knife-edges at the short end, which is prevented . M C ZZ : W P Q from tipping over by a stay arrangement similar to that of other counter machines. Steelyards are largely used in machines for the automatic weighing out of granular substances. The principle is as follows: The weighing is effected by a steelyard with a sliding poise which is set to weigh a definite weight of the material, say i lb. A pan is carried on the knife-edges at the short end, and is kept from tipping over by stays. A packet is placed on the pan to receive the material from the shoot of a hopper. A rod, connected at its lower end with the steelyard, carries at its upper end a horizontal dividing knife, which cuts off the flow from the shoot when the steelyard kicks. When the filled packet is removed, the steelyard resumes its original position, and the filling goes on automatically. The automatic personal weighing machine found at most railway stations operates by means of a steelyard carrying a fixed weight on its long arm, the load on the platform being inferred from the position of the steelyard. In fig. 8 the weight on the platform is transferred by levers to the vertical steel band, A, which is wrapped round an arbor on the axle of the disk-wheel, B, to which is rigidly attached the toothed segment, C. The weight, D, is rigidly attached to the axle of the wheel, B, and the counter-balance, E, is hung from the wheel, B, by means of a cord wrapped round it. When the pull of the band, A, comes upon the wheel, B, it revolves through a certain angle in the direc- tion of the arrow until the three forces, viz. the pull of A, the weight, D, and the counterbalance, E, are in equilibrium. The toothed segment, C, actuates the pinion, F, which carries the finger, G, and this finger remains fixed in position so long as the person is standing on the platform. If now a small weight, as a penny, be passed through the slot, H, it falls into the small box, I, and causes the lever, J, to turn; the lever, J, which turns in friction wheels at K, and is counterbalanced at 0, carries a toothed segment, L, which actuates a small pinion on the same axle as F, and is free to turn on that axle by a sleeve. This small pinion carries a finger, M, which is arranged to catch against the finger, G, when moved up to it. Consequently as the lever, j, turns, the finger, M, revolves, and is stopped when it reaches G. The sleeve of the pinion which carries M also carries the dial finger, and if the dial is properly graduated its finger will indicate the weight. The box, I, has a hinged bottom with a projecting click finger which, as the box de- scends, plays idly over the staves of a ladder arc. When the weight is removed from the platform, the counterbalance, E, causes the finger, G, to run back to its zero position, carrying with it the finger M, and causing the click finger of the box, I, to trip open the bottom of the box and let the penny fall out. The lever, J, regains its zero position, and all is ready for another weighing. Since so small a weight as a penny has to move the lever, J, together with the dial finger, &c., it is evident that the workmanship must be good and the friction kept very low by means of friction wheels. Some of the largest and most accurate steelyards are those made for testing machines for tearing and crushing samples of metals and other materials. They are sometimes made with a sliding poise weighing i ton, which has a run of 200 in., and the steelyard can exert a pull of too tons. Balances are frequently used as counting machines, when the articles to be counted are all of the same weight or nearly so, and this method is both quick and accurate. They are also used as trade computing machines, as in the case of the machine made by the Computing Scale Company, Dayton, Ohio, U.S.A. In this machine the goods to be priced are placed on the platform of a small platform machine whose steelyard is adjusted to balance exactly the weight of the platform, levers and connexions. The rod which transmits the pull of the long body lever of the platform machine to the knife-edge at the end of the short arm of the steelyard is continued up-wards, and by a simple mechanical arrangement transmits to an upper steelyard any additional pull of the long body lever due to the weight of goods placed on the platform. This upper steelyard is arranged as in fig 9, where A is the point where the pull of the long body lever due to the weight of the goods on the platform comes upon the steelyard; C is the fulcrum of the steelyard, which with the steelyard can be slid to and fro on the frame of the machine; and Q i 3 4! 6 7 Q Q /C ze Q 7 e A 4 3 4 FIG. 9. is a poise which can be slid along the upper bar of the steelyard. The steelyard is exactly in balance when there is no weight on the platform and Q is at the zero end of its run, at O. Suppose that the weight of the goods on the platform is (p) lb, and that nth of this weight is transmitted by the long body lever to the point A, so that n lb is the pull at A." Let the lower bar of the steel- yard be graduated in equal divisions of length, d, each of which represents one penny, so that the distance CA=qXd represents q pence. Then the number pXq represents the total value of the goods on the platform. If Q lb be the weight of the poise Q, the position of Q when the steelyard is exactly in balance is given by the equation nXq.d=QXOQ, or OQ=pXgXnQ If therefore the upper bar be graduated in divisions, each of which is nQ, the indication of the poise Q, viz. pXq graduations, gives correctly the value of the goods. Thus to ascertain the value of goods on the platform of unknown weight at a given price per lb, it is only necessary to slide the steelyard till the weight acts at the division which represents the price per lb, and then to move the poise Q till the steelyard is in balance; the number of the division which defines the position of the poise Q will indicate the sum to be paid for the goods. When the load on the platform is large, so that the value of the goods may be considerable, it is convenient to measure the larger part of the value by loose weights which, when hung at the end of the steelyard, represent each a certain money value, and the balance of the value is determined by the sliding poise Q. In the machines commonly used to weigh loads exceeding 2 cwt. the power is applied at the end of the long arm of the steelyard and multiplied by levers from too to 500 times, so that the weights used are small and handy. The load is received upon four knife-edges, so that on the average each knife-edge receives only one-fourth of the load, and, as will be seen, it is immaterial whether the load is received equally by the four knife-edges or not, which is essential to the useful application of these machines. In fig. to AB is the steelyard. The platform and the load upon it are carried on four knife-edges, two of which, xi and x2, are shown, and the load is transferred to the steelyard by the two levers shown, the upper one CD being known as the " long body," and the lower one EF as the " short body." If =z2xs, and zit=z2y2, then the leverage of any portion of the load applied at x2 will be the same as the leverage of any part of the load applied at xi, and the pressure produced at yl will be the same for equal portions of the load, whether. they were originally applied at xi or x2. Platform machines, like steelyards, may be arranged either on the " accelerating " principle or on the " vibrating " principle. If in fig. 1 o gi be the centre of M C =~ gravity of the long body CD, and h1 be the centre of gravity of the three vertical forces acting downwards at the points t and g1, considered as weights collected at those points; then if h1 be above the line it can be shown that this arrangement of the knife-edges of CD favours the " acceleration " principle, and is suited to act with and assist an " accelerating " steelyard, and similarly if the point h2 be above the line z2y2 in the case of the short body EF. If the knife-edges be placed so that h1 and h2 are below the lines xly1 and x2y2 respectively, the arrangement will favour the " vibration " principle, and is suited to act with and assist a " vibrating " steelyard. It is very important that platform machines should be truly level. W'ith accelerating machines a small amount of tilt in any direction considerably affects the accuracy of the weighing, and when the amount of tilt is considerable the action may be changed, so that a machine which was intended to act as an accelerating machine acts like a vibrating one. Vibrating machines are only slightly affected by being out of level in comparison with accelerating machines, and in this matter they have a distinct advantage. When a platform machine is in true adjustment, and the loose weights which are intended to be hung at the end of the steelyard are correct and consistent among themselves, a good and new machine, whose capacity is 4 cwt., should not show a greater error than 4 oz. when fully loaded. Platform machines are slightly affected by changes of temperature. In some cases they are made " self-recording " by the following arrangement: The steelyard is provided with a large and a small travelling poise. Each of these poises carries a horizontal strip of metal, which is graduated and marked with raised figures corresponding to those on the steelyard itself. These strips pass under a strong punching lever arranged on the frame of the machine. A card prepared for the purpose is introduced through a slit in the frame between the punch and the strips. When the poises have been adjusted to weigh a load on the platform the punch is operated by a strong pull, and the impression of the raised figures is left on the card. Thus the weight is recorded without reading the positions of the poises. In another arrangement the self-recording parts are entirely enclosed in the travelling poise itself. Fig. II shows the ordinary arrangement of the parts of a plat-form machine, but there are many types which differ greatly in detail though not in principle. When the goods to be weighed are very heavy, portable weigh-bridges or platform machines are inapplicable and it is necessary to erect the weighbridge on a solid foundation. Some weigh-bridges are arranged in a manner similar to that of the platform machines already described, but having the long body lever turned askew, so that the end of it projects considerably beyond the side of the weighbridge casing, and the pillar and steelyard which receive its pull are clear of the wagon on the platform. In another arrangement two similar triangular levers take bearing on opposite sides of an intermediate lever which communicates their pressures to the steelyard; this is a very sound and simple arrangement for ordinary long weighbridges. Lastly, when the weighbridge is very long—and they are sometimes made 40 ft. long, and are arranged to weigh up to too tons or more—it is practically composed of two platform machines end to end, each having its four knife-edges to receive the load, and the two long bodies take bearing on the opposite sides of an intermediate horizontal lever, the end of which is connected with the steelyard. When skilfully made they are very accurate and durable. A useful application of weighbridges is to ascertain the exact weights on the separate wheels of locomotive engines, so that they may be properly adjusted. For this purpose a number of separate weighbridges of simple construction are erected, one for each wheel of the engine, with their running surfaces in exactly the same horizontal plane. The engine is moved on to them, and the pressures of all the wheels are taken simultaneously, each by its own weighbridge. There are many kinds of weighing machines depending for their action on combinations of levers, and arranged to meet special requirements. Such are coal platform machines for weighing outcoal in sacks, the levers of which are arranged as in the ordinary platform machines, but for the sake of compactness the steelyard is returned back over the long body, and when loaded with the proper weight indicates the correct weight of the coal in the sack by its end Elevation. Plan with cover removed. Section on AB. Section on Section on CD. EF. kicking up. Crane machines are used to weigh goods as they are hoisted by a crane; the lever arrangement is shown in fig. 12. A crane machine of peculiar construction, well adapted for weighing heavy loads, and extremely simple and compact, which does not properly come under any of the heads under which the machines have been classified, is the hydrostatic weighing machine. This machine is constructed with an open top cylinder, a stirrup strap being provided by which it may be suspended from a crane. The cylinder, which is filled with oil or other liquid, is fitted with a piston having a piston-rod passing downwards and terminating in an attachment for the goods to be weighed. As the goods are lifted by the crane the whole of their weight is taken by the liquid in the cylinder, and the pressure on the liquid, as indicated by a pressure gauge, gives the weight. The gauge has a plain dial, marked off to indications given by the application of standard tons and cwts. ; it could probably be read to about 1°/e of the load weighed. Spring Balances. For many purposes spring balances are the most convenient of all weighing machines. They are rapid in action, the indication is in general clear, and there is no need of loose weights except for testing the machine occasionally. Their action depends upon the extension of one or more spiral springs, and as the extension is proportionate to the weight which causes it the graduation is very simple. The accuracy of spring machines depends upon the accuracy of the springs and the workmanship of the machines. The springs in general are very accurate and uniform in their extension, and are very permanent when fairly well used; but their indications are apt to vary from fatigue of the springs if they are kept extended by a weight for a long time. Their indications also vary with the temperature, so that for good work it is advisable that spring balances should be frequently checked with standard weights. For the sake of compactness and convenience of reading the extension of the springs, and consequently the load, is frequently indicated on a dial, by means of a small rack and pinion, which give motion to a finger on the dial-plate, but the regularity and correctness of the indications of the finger will depend upon the condition of the rackwork and upon the friction, and these will vary with the wear of the machine. For the above reasons spring balances are nbt in general so accurate as knife-edge machines. It is found that when a spiral spring is extended by a weight it has a tendency to turn a little round its axis. Therefore an index pointer attached to the bottom of the spring, and moving past a scale would rub slightly against the case. To correct this tendency the spring is usually made half with right-hand spiral and half with left-hand spiral. The extension of a spiral spring is given by the formula:- Extension=W4nR3/Er4, in which W = weight causing extension, in lbs; n= number of coils; R = radius of spring, from centre of coil to centre of wire, in inches; r=radius of wire of which the spring is made, in inches; E =coefficient of elasticity of wire, in Ibs per square inch. The value of E depends upon the tempering of the wire and will vary accordingly: for the springs of trade balances E will usually be about 10,5oo,000. For the application of the above formula it is necessary to measure (R) and (r) very accurately, by reason of the high powers involved, but when this has been carefully done the formula may be relied upon. Thus in the case of a spring for which the values of the quantities were W = 7 lb, n =51, R = .30 in., r = •038 in., E=lo,500,000, the formula gives extension =1.764 in., while airect experiment gave extension =1.75 in. And with a very long and weak spring for which the values of the quantities were W =1 oz., n =233, R= •35 in., r=.0085 in., E =10,500,000, the formula gives extension =22.78 in., while direct experiment with the spring gave 23.5 in. Automatic Weighing Machines. During the last few years great efforts have been made to expedite the operation of weighing machines by the introduction of machinery, more or less complicated, which renders the machines to a great extent self-acting. The object aimed at varies very much with different machines. Sometimes the object is to weigh out parcels of goods in great numbers of the same definite weight. Sometimes the object is to weigh out parcels of goods, of unknown weight, as in ordinary retail dealing, and to give the exact value of each parcel at different rates per lb. Sometimes the object is to weigh many loads in succession, the loads being of varying weight, and to present the total weight at the end of a day's work; this is the case with machines for weighing coal and other minerals. Of course the introduction of automatic mechanism introduces friction and other complications, and it is difficult to construct automatic machines that shall be as accurate in their weighing as the simpler weighing machines, but in many weighing operations a moderate degree of accuracy will suffice, and speed is of great importance. It is to meet such cases that the greater number of automatic weighing machines have been invented. Some examples of these machines will now be given. Automatic Computing Spring Weighing Machine for Retail Purposes (fig. 13).-A light and carefully balanced drum with its axis horizontal is enclosed within a cylindrical casing, and rotates freely in bearings formed in the ends of the casing. The casing is fixed in supports on the top of a strong frame, which also carries a small platform machine of ordinary construction on which the goods to be weighed are placed. The pull of the load is transmitted to a hook which hangs freely from the middle of a horizontal bar below the drum casing. At each end of the drum casing is attached a vertical spiral spring, and by the extension of these springs the weighing of the goods is effected. There are also two vertical racks, one at each end of the casing, in connexion with - the two springs, and these actuate pinions on the axle of the drum and cause it to revolve as the springs extend. The horizontal bar which receives the pull of the load is connected at its ends with the two spiral springs and pulls vertically upon them. Above the horizontal bar, and parallel with it, is a rod which is connected at its ends with the lower ends of the vertical racks, and at its middle with the horizontal bar. The connexion with the horizontal bar is through the medium of an adjustable cam. This cam can be turned lZy hand in a vertical plane by means of a worm and wheel movement, and by turning the worm the vertical distance between the bar which is attached to the springs and the rod which is attached to the racks can be increased or diminished, and thus the racks can be moved relatively to the springs. By this means the zero of the scale on the drum can be adjusted to the fixed index on the casing when there are no goods on the platform. There is also a compensation arrange- ment for effecting automatically the same adjustment for changes of temperature. To deaden the vibration of the springs after a load has been placed on the platform, and thus to enable the weights and values of the goods to be read rapidly, the piston of a glycerin cylinder is attached to the end of the lever which pulls upon the hook of the horizontal bar and is worked by it in the glycerin. From the Notice issued by the Standards Department of the Board of Trade, by permission of the Controller of H.M. Stationery Office. On the outer surface of the drum are printed the weight of the goods in lb and oz., and the money value of the goods corresponding to the different rates per lb. The side of the casing which is next to the seller is pierced centrally by two slots, one a vertical slot through which the weight is read on the drum, and the other a horizontal slot, half of it on each side of the vertical slot, through which the money values of the goods, corresponding to the different rates per lb, are read. The weight of the goods is recorded by means of an index pointer fixed to the casing on one side of the vertical slot, and the money values are opposite the figures defining the rates per lb, which are marked on the edge of the casing below the hori-values are indicated on the cha. by the toothed edge of the index arm. On the customer's side of the machine the weight of the goods is indicated on a pair of arcs by a separate index arm precisely in the same manner as on the seller's side. In weighing, the goods are placed in the pan of an ordinary lever machine (see fig. 14), and the end of the lever rests on the stirrup end of a short vertical rod. The upper end of this rod is formed into a loop, and this loop pulls upon a knife-edge which is fixed to a short lateral arm rigidly attached to a vertical disk, and this disk turns in bearings formed in the frame of the machine. The same disk carries the index arm, which is rigidly fixed to it and indicates the weight and value of the goods, and also carries the pendulum, which is rigidly attached to it, and regulates the position of the index arm according to the position which it takes up and the leverage which it exerts when swayed out of the vertical position by the action of the lever of the lever machine. This lever is so counterbalanced that when there is no weight in the pan the pendulum is vertical, and the index arm should then stand at zero. The zero adjustment is effected by means of levelling screws in the base of the frame. In order to deaden the vibrations of the index arm when weighing goods a vertical rod is attached to the lever from the lever machine near its left-hand end, and this rod carries on its lower end a plunger which works in a closed cylindrical dash-pot containing oil or glycerin. Automatic Computing Weighing Machine (even balance and pendulum) for Retail Purposes (fig. 15).-This is an equal-armed inverted counter machine (see fig. 5) arranged to weigh up to 14 lb with great accuracy. Up to 2 lb the weight of the load is registered automatically on the chart in much the same manner as in the case of the automatic computing weighing machine already described. When the load exceeds 2 lb one or more 2-lb weights are placed in the weights-pan, and the value of the portion of the goods corresponding to these 2-lb weights is computed, at the rate per lb, in the ordinary manner; and the value of the balance of the weight of the goods is read off the chart, and the two are added together. The advantage of this is that a very open scale is obtained for reading the value of the balance of the load. Thus, for weighing up to the full load of 14 lb, six 2-lb weights are required and no others. The manner in which the balance of the load is weighed is as follows: Near the bottom of the vertical leg from the goods-pan, a projecting piece is rigidly attached to it, and as the pan descends with the balance of the load this piece pulls by a hook on a thin band of steel, which From the Notice issued by the Standards Department of the Board of Trade, by permission of the Controller of II. M. Stationery Office. zontal slot. On the side of the casing which is next to the buyer there is a vertical slot through which the weight of the goods can be read on the drum. Automatic Computing Weighing Machine for Retail Purposes (fig. 14).-The action of the machine shown in fig. 14 depends upon the displacement of a loaded pendulum. And the machine is arranged to weigh goods up to 8 lb" with the fixed weight only on the pendulum, and up to i6 lb with an additional weight which can be readily slipped on to the pendulum rod. The weights and money values are arranged on a vertical chart, the sides of which converge towards the pivoting centre of an index arm which is actuated by the weighing mechanism. The two outer arcs of the chart are occupied by the scales for the weight of the goods in lb and oz., and the rest of the chart is occupied by a series of 25 concentric arcs which show the money values of the goods for 25 rates per lb. The rates per lb are inscribed on the index arm at points corresponding to the values on the concentric arcs of the chart, and theis led upwards and wraps round the surface of a disk to which it is firmly secured. This disk rotates by rocking on a pair of knife-edges whose bearings are rigidly attached to the frame. The disk carries a weighted brass cylinder rigidly attached to it, which is pulled into an oblique position by the steel band until equilibrium is established. And the disk also carries the index arm which plays past the vertical face of the chart, and indicates the weight and price up to 2-lb weight. The disk also carries a second and corresponding index arm which indicates the weight on the purchaser's side of the machine. At the bottom of the vertical leg from the goods-pan there is also a projecting piece which is attached to the top of a vertical piston rod, the piston of which plays in a dash-pot of glycerin as the beam sways, and deadens the vibrations of the index arm. Automatic Tea Weighing Machine (fig. i6).-This machine is designed to weigh out tea in quantities of 4 lb each, which are done up in separate packets by hand. A large number of movements have to be provided for, and the machinery is complicated, so that a general description of the action of the machine is all that will be here given. The tea is fed into a hopper, which has a large opening at the bottom, and this opening is entirely closed by two cylindrical brushes, which are mounted end to end on a horizontal shaft. As they revolve these brushes engage the tea in the hopper, draw it out by degrees, and drop it into a compartment of a circular drum which hangs on one end of a scale-beam. The brushes have the same diameter, but one is much longer than the other, and they move independently of one another. For the bulk of the filling both brushes are in operation, but when the load is nearly complete the longer brush is stopped and the filling is completed by the shorter brush only. When the load is complete the shorter brush also is stopped while the compartment of the dru,n is emptied. And the action is then renewed. All these operations are effected automatically. The circular drum is divided into four equal compartments by radial diaphragms. And in a pan at the other end of the beam (which is counter-balanced for the weight of the drum) is a ;-lb weight to weigh the tea. As the uppermost compartment fills, the weights end of the beam rises, and by means of a vertical rod successively operates on detents connected with the rotation of the two brushes, and stops them in turn. And when the short brush is stopped a rod from the shaft frees a spring detent which keeps the drum in position and tips it over. The tea is shot out and falls into a receptacle below, and the drum make, a quarter of a revolution, and is again held in position by the detent with an empty compartment at top ready for the next filling. The power is applied by a belt round a pulley, which is mounted on the end of the horizontal shaft which carries the brushes. The brushes are carried by sleeves which run loosely on the shaft, and to each sleeve is rigidly fixed a ratchet wheel. Next the ratchet wheel is a disk which is keyed on to the shaft. The ratchet wheel and the disk are automatically connected by clutch mechanism in order to effect the rotation of the brushes. The.clutch mechanism is freed at the proper time by the action of the vertical rod at the end of the beam, and the brushes thenis placed in the weights-pan of the balance, and is the only loose weight used with the machine. The pair of beams are hung centrally by rods and hooks from knife-edges in the forked end of a strong beam, which is carried at its fulcrum by the top plate of the frame of the machine. This beam is heavily counterbalanced at its further extremity. Underneath the top plate of the machine, and strongly framed to it, is a box, which contains the horizontal rods to the ends of which are attached the slides which regu- late the flow of sugar from the bottom of the hopper. These rods pass through holes in the front and back plates of the box. and are furnished with spiral springs, which (when the rods are forced back by hand) are in compression between the back plate of the box and shoulders on the rods. The rods are held in this position by detents which take hold of the shoulders of the rods, and are acted upon from the front end of the upper beam and the weights-pan end of the lower beam respectively, in order to release the rods at the proper times and reduce or cut off the flow of sugar from the hopper. The upper slide has the shape of a truncated cone, and it reduces the orifice of flow so as to render the flow of the sugar more manage- able. The lower slide is simply a cut-off slide. When it is desired to use the machine, a 4-lb bag is placed under the orifice of the hopper upon the goods-pan of the balance, and the slide rods are thrust back by hand till they are held by their detents, and the sugar flows rapidly into the bag. When the bag is nearly charged to the weight of 4 Ib, the weight of the bag of sugar over- comes the resistance of the counterbalance of the upper beam, and its front end drops a certain distance. In dropping it dislodges the detent of the reducing slide, and the slide springs forward and reduces the flow of the sugar. The dim- inished stream of sugar con- tinues to flow till the 4-lb weight in the weights-pan is lifted (the end of the upper beam being for the time brought up against the frame and unable to descend further), and in lifting it dis- From the Notice issued by the Standards Department of the Board of Trade, by permission of the Controller of H. M. Stationery Office. stand still while the load is discharged. The beam then recovers its original position and the action of the machine is renewed. Automatic Sugar Weighing Machine (fig. i7).—This machine is adapted for weighing out granulated white sugar in parcels of i-lb, 2-lb and 4-lb weight. The sugar is run into a conical hopper and is delivered into the open mouth of a bag which is placed on the goods-pan of a balance. The balance consists of a pair of equal-armed beams rigidly connected together and acting as a single beam. A 4-lb weightlodges the detent of the cut-off slide.' The slide springs forward and cuts off the flow. The filled bag is then removed and replaced by an empty bag and the action is renewed. In order to ensure the correct weight of the bag it is necessary to consider that when the cut-off slide acts, a certain quantity of sugar is in transitu and has not at that moment taken its place in the bag. This is allowed for by means of a rider weight, which is arranged so as automatically to add its weight to that of the sugar in the bag while the 4-lb weight is being lifted. But ai the same instant that the cut-off takes place the rider weight is lifted off the end of the balance by a From the Notice issued by the Standards Department of the Board of Trade, by permission of the Controller of H.M. Stationery Office. Flo. f6.—Automatic Tea Weighing Machine. self-acting arrangement, and the sugar in transitu takes its place in the bag. And, if the rider weight has been correctly adjusted, the bag of sugar will be shown to weigh exactly 4 lb by the beam vibrating in equipoise. Automatic Coal Weighing Machine (fig. i8). —This machine weighs the coal de- livered into factories, &c., by charges up to 20 cwt. at a time, and records and sums up the weights of the charges so as to exhibit the total weight delivered. The whole of this work is effected automatically. The coal is dropped into a hopper by a grab. The hopper is carried on two knife-edges, one on each side, and is prevented from tipping over fore and aft by a pair of parallel motion bars on each side. The knife-edges on which the hopper rests are on two horizontal levers, one on each side of the hop- From the Notice issued by the Standards Department Per. These levers are of the Board of Trade, by permission of the Controller carried by knife-edge of H.M. Stationery Office. fulcra in bearings on Machine. chine, and transmit the weight of the hopper by means of an intermediate lever and a vertical rod to the indicator lever. And the long arm of the indicator lever pulls vertically upon the spring of an ordinary spring balance, which registers the load, and with the addition of suitable counting mechanism sums up the weights of any number of successive loads. The charges of coal fall into the hopper with a heavy shock, and in order to save the knife-edges there is a strong pin in each side of the hopper below the knife-edge, which, before the charge of coal is dropped into the hopper, is acted on by a strong horizontal flitch-plate, which heaves the hopper off the knife-edges and relieves them from the shock. The heaving-up of the flitch-plate and hopper is effected by a cam on the end of a horizontal shaft which runs along the back of the machine behind the hopper. The flitch-plate rests at one end on the top of this cam, and at the other end is shackled to the horizontal arm of a bell-crank lever which is pivoted on the frame. When a charge of coal is dropped into the hopper, the bell-crank lever receives a violent jerk from the shackle of the flitch-plate, and this jerk by means of suitable mechanical arrangements throws a pinion on the carp shaft into gear with a wheel on a counter shaft From the Notice issued by the Standards Department of the Board of Trade, by permission of the Controller of H.M. Stationery Office. which is kept constantly running by means of a belt and pulley driven by an engine. The cam shaft and the cam then begin to revolve, and the flitch-plate is gradually lowered till the knife-edge bearings of the hopper are received on the knife-edges of the main measuring levers, and the load is then weighed by the levers and the spring-balance. Shortly after this is done the mechanism at the back of the hopper automatically opens the doors at the bottom of the hopper, and the coal drops out. The rotation of the cam shaft continues till the cam has again heaved up the flitch-plate, when the pinion on the cam shaft is thrown out of gear with the wheel on the counter shaft, and the cam remains steady till another charge of coal is dropped into the hopper and the action is renewed. The coal when dropped out of the hopper runs down a shoot into a receptacle, from whence it is lifted by a Jacob's Ladder and distributed to the boilers, &c., of the factory. Automatic Coal Weighing Machine (fig. 19).—This machine is designed to weigh and total up the weight of materials passed over it during a considerable course of operations. The trucks or other receptacles containing the coal, &c., are drawn upon the platform of the machine, and the pull of the load is transferred by a vertical rod at the left-hand end of the machine to the knife-edge on the short arm of the steelyard, whose fulcrum is carried on bearings in the frame. Behind the pulley at the top of the machine and on the same shaft is a spur wheel, which drives both of the spur wheels shown in the diagram. The small spur wheel is mounted on the steelyard, and this wheel and the one that drives it are so arranged that their line of IhI~IIP Ilulprd!NiNilnii91111~16IiI~IIJPI tr,011111111ld4l!VIVII 1 4iII;;IIIIR 111111Vpp 1. rt nUllllllllillllll°lii~ujiulll~l "I~,I -~ 7-_ ~~s I ~~IIINI I ''"-A T.- „, I~I~III~IIIiIIilll~tl''''II,I~iI~~h~~~iI~~IINhII lll!~4iV1' pressure shall exactly coincide with the line of the fulcrum knife- clutch with a shaft in the same line, on which are keyed a sprocket edge; the object of this is that the pressure may not influence the wheel and a ratchet wheel. The sprocket wheel is connected by a sway of the steelyard, which must depend entirely upon the poise. chain with a similar sprocket wheel which is keyed on the same shaft By means of a pair of mitre wheels the small spur wheel causes a as that of the left-hand pulley. The ratchet wheel is acted upon by screwed shaft, which runs along the middle of the steelyard, to a pawl which is shown on the diagram. When the poise is at the zero end, and there is no load on the platform, the end of the steelyard is down, and has locked the ratchet wheel by means of the pawl; the shaft being thus locked, the sprocket wheels are stopped, the drum-shaft runs free by the friction clutch, and the two pulleys which are connected by the crossed band are running idle. When the load to be weighed comes upon the platform, the end of the steelyard rises and unlocks the ratchet wheel through the pawl; the sprocket gearing is driven by the friction clutch, and drives the axle of the left-hand small pulley. The mitre wheels come into operation and the poise is carried along till the end of the steelyard drops, and locks the ratchet From the Notice issued by the Standards Department of the Board of Trade, by permission of the Controller of wheel, By means of a horizontal rod the H.M. Stationery Office. same drop of the steelyard also locks dial in connexion with the wheel. By the second part of the drop the Automatic Luggage Weighing Machine (fig 2o).—This machine is motion of the poise is reversed and the poise is run back to the zero intended for the weighing of personal luggage at railway stations. It consists of a platform which is carried by levers arranged in the manner of an ordinary platform machine, which are connected with the registration mechanism by a vertical rod. This rod is continued upwards by a pair of thin nickel bands which are led right and left over two horizontal cylinders, round which they partly wrap, and to which they are firmly attached. The diameter of the middle part of the cylinders is greater than that of the ends, and the bands from the vertical rod are led over the middle part. To each cylinder a pair of similar nickel bands are led downwards from the top of a casting which is bolted to the frame. The lower ends of these bands pass round the under side of the end portions of the cylinders, wrapping close round them, and are firmly attached to them. To the bottom of each cylinder is rigidly attached a heavy solid cylinder of lead, and these are the regulators of the position of equilibrium of the cylinders when they rotate under the action of the lead. When the load comes upon the platform the pull of the vertical rod is transmitted by the nickel bands to the cylinders around which they are wrapped, and causes them to revolve. As they rotate they roll themselves up the pairs of bands which are attached to the top of the casting, and at the same time cause the leaden weights attached to the bottoms of the cylinders to take up a lateral position, where they exercise a leverage opposing the motion of the cylinders, and bringing them up in a definite position corresponding to the pull of the vertical red. By the rolling oi the cylinders up the vertical bands from the casting the cylinders are raised vertically through a space defined by the position of the leaden regulators. By means of suitable and simple mechanism this vertical movement of the cylinders works plunger pistons in a pair of cylinders which contain glycerin, and these deaden the vibrations of the machinery while weighing is going on. The same vertical movement also actuates the index finger of a large dial, on which the weight of their luggage can be easily read by passengers standing near while their luggage is being weighed. Engineers, vol. for 189o. (W. AY.)

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