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CLOCK . The measurement of See also:time has always been based on the revolution of the See also:celestial bodies, and the See also:period of the apparent revolution of the See also:sun, i.e. the See also:interval between two consecutive crossings of a See also:meridian, has been the usual See also:standard for a See also:day. By the Egyptians the day was divided into 24 See also:hours of equal length. The Greeks adopted a different See also:system, dividing the day, i.e. the period from sunrise to sunset, into 12 hours, and also the See also:night. Whence it followed that it was only at two periods in the See also:year that the length of the hours during the day and night were See also:uniform (see See also:CALENDAR). In consequence, those who adopted the See also:Greek system were obliged to furnish their See also:water-clocks (see See also:CLEPSYDRA) with a compensating See also:device so that the equal hours measured by those clocks should be rendered unequal, according to the exigencies of the See also:season. The hours were divided into minutes and seconds, a system derived from the sexagesimal notation which prevailed before the decimal system was finally adopted. Our mode of computing time, and our angular measure, are the only See also:relics of this obsolete system. The simplest measure of time is the revolution of the See also:earth See also:round its -See also:axis, which so far as we know is uniform, perfectly See also:regular, and has not varied in See also:speed during any period of human observation. The time of such a revolution is called a sidereal day, and is divided into hours, minutes and seconds. The period of rotation of the earth is practially measured by observations of the fixed stars (see TIME), the period between two successive transits of the same See also:star across a meridian constituting the sidereal day. But as the axis of the earth slowly revolves round in a See also:cone, whereby the phenomenon known as the precession of the equinoxes is produced, it follows that the astronomical sidereal day is not the true period of the earth's rotation on its axis, but varies from it by less than a twenty millionth See also:part, a fraction so small as to be inappreciable. But the See also:civil day depends not on the revolution of the earth with regard to the stars, but on its revolution as compared with the position of the sun. Therefore each civil day is on the See also:average longer than a sidereal one by nearly four minutes, or, to be exact, each sidereal day is to an average civil day as •99727 to 1, and the sidereal See also:hour, See also:minute and second are also shorter in like proportion. Hence a sidereal clock has a shorter, quicker-moving pendulum than an See also:ordinary clock. Ordinary civil time thus depends on the apparent revolution of the sun round the earth. As, however, this is not uniform, it is needful for See also:practical convenience to give it an artificial uniformity. For this purpose an imaginary sun, moving round the earth with the average velocity of the real sun, and called the " mean " sun, is taken as the measure of civil time. The day is divided into 24 hours, each hour into 6o minutes, and each minute into 6o seconds. After that the sexagesimal See also:division system is abandoned, and fractions of seconds are estimated in decimals. A clock consists of a See also:train of wheels, actuated by a See also:spring or See also:weight, and provided with a governing device which so regulates the speed as to render it uniform. It also has a mechanism by which it strikes the hours on a See also:bell or See also:gong (cp. Fr. clothe, Ger. Glocke, a bell; Dutch klok, bell, clock), whereas, strictly, a timepiece does not strike, but simply shows the time. The earliest clocks seem to have come into use in See also:Europe during the 13th See also:century. For although there is See also:evidence that they may have been invented some centuries sooner, yet until that date they were probably only curiosities. The first See also:form they took was that of the See also:balance clock, the invention of which .is ascribed, but on very insufficient grounds, to See also:Pope See also:Silvester II. in A.D. 996. A clock was put up in a former clock See also:tower at See also:Westminster with some See also:great bells in 1288, out of a See also:fine imposed on a See also:chief-See also:justice who had offended the See also:government, and the See also:motto Discite justitiam, moniti, inscribed upon it. The bells were sold,
or rather, it is said, gambled away, by See also: The See also:works of one of these old clocks still exist in a going See also:condition at the See also:Victoria and See also:Albert Museum. It came from See also:Wells cathedral, having previously been at See also:Glastonbury See also:abbey. These old clocks had what is called a See also:verge escapement, and a balance. The train of wheels ended with a See also:crown See also:wheel, that is, a wheel serrated with See also:teeth like those of a saw, placed parallel with its axis (fig. 1), These teeth, D, engaged with pallets CB, CA, mounted on a verge or See also:staff placed parallel to the See also:face of the crown wheel. As the crown wheel was turned round the teeth pushed the pallets alternately until one or the other slid past a tooth, and thus let the crown wheel rotate. When one pallet had slipped over a tooth, the other pallet caught a corre- sponding tooth on the opposite See also:side of the wheel. The verge was terminated by a balance See also:rod placed at right angles to it with a See also:ball at each end. It is evident that when the force of any tooth on the crown wheel began to See also:act on a pallet, it communicated See also:motion to the balance and thus caused it to rotate. This motion would of course be accelerated, not uniformly, but according to some See also:law dependent on the shape of the teeth and pallets. When the motion had reached its maximum, the tooth slipped past the pallet. The other pallet now engaged another tooth on the op- posite side of the wheel. The motion of the balls, however, went on and they continued to See also:swing round, but the pressure of the tooth. For a time they overcame that pressure, and drove the tooth back, causing a recoil. As, however, every motion if subjected to an adverse See also:acceleration (i.e. a retardation) must come to See also:rest, the balls stopped, and then the tooth, which had been forced to recoil, advanced in its turn, and the swing was repeated. The arrangement was thus very like a huge See also:watch balance wheel in which the See also:driving weight acted in a very irregular manner, not only as a driving force, but also as a regulating spring. The going of such clocks was influenced greatly by See also:friction and by the oil on the parts, and never could be satisfactory, for the time varied with every variation in the swing of the balls, and this again with every variation of the effective driving force. The first great step in the improvement of the balance clock was a very See also:simple one. In the 17th century Galileo had discovered the isochronism of the pendulum, but he made no practical use of it, except by the invention of a little See also:instrument for enabling doctors to See also:count their patients' See also:pulse-beats. His son, however, is supposed to have applied the pendulum to clocks. There is at the Victoria and Albert Museum a copy of an See also:early clock, said to be Galileo's, in which the pins on a rotating wheel kick a pendulum outwards, remaining locked after having done so till the pendulum returns and unlocks the next See also:pin, which then administers another kick to the pendulum (fig. 2). The See also:interest of the specimen is that it contains the germ of the chronometer escapement and See also:free pendulum, which is possibly destined to be the escapement of the future. The essential component parts of a clock are: 1. The pendulum or time-governing device; 2. The escapement, whereby the pendulum controls the speed of going; 3. The train of wheels, urged round by the weight or See also:main-spring, together with the recording parts, i.e. the See also:dial, hands and hour motion wheels; 4. The striking mechanism. The See also:general construction of the going part of all clocks, except large or See also:turret clocks, is substantially the same, and fig. 3 is a See also:section of any or- dinary See also:house clock. B is the See also:barrel with the See also:cord coiled round it, generally 16 times for the 8 days; the barrel is fixed to its arbor K, which is prolonged into the winding square coming up to the face or dial of the clock; the dial is here shown as fixed either by small screws x, or by a socket and pin z, to the See also:pro-longed pillars p, p, which (4 or 5 in number) connect the plates or See also:frame of the clock together, though the dial is commonly set on to the front See also:plate by another set of pillars of its own. The great wheel G rides on the arbor, and is connected with the barrel by the ratchet R, the See also:action of which is shown more fully in fig. 25. The FIG. 3.—Section of House Clock. intermediate wheel r in this See also:drawing is for a purpose which will be described hereafter, and for the See also:present it may be considered as omitted, and the click of the ratchet R as fixed to the great wheel. The great wheel drives the pinion c which is called the centre pinion, on the arbor of the centre wheel C, which goes through to the dial, and carries the See also:long, or minute-See also:hand; this wheel always turns in an hour, and the great wheel generally in 12 hours, by having 12 times as many teeth as the centre pinion. The centre wheel drives the " second wheel " D by its pinion d, and that again drives the scape-wheel E by its pinion e. If the pinions d and e have each 8 teeth or leaves (as the teeth of pinions are usually called), C will have 64 teeth and D 6o, in a clock of which the scapewheel turns in a minute, so that the seconds hand may be set on its arbor prolonged to the dial* A represents the pallets of the escapement, which will be described presently, and their arbor a goes through a large hole in the back plate near F, and its back See also:pivot turns in a See also:cock OFQ screwed on to the back plate. From. the pallet arbor at F descends the crutch Ff, ending in the See also:fork f, which embraces the pendulum P, so that as the pendulum vibrates, the crutch and the pallets necessarily vibrate with it. The pendulum is hung by a thin spring S from the cock Q, so that the bending point of the spring may be just opposite the end of the pallet arbor, and the edge of the spring as See also:close to the end of that arbor as possible. We may now go to the front (or See also:left hand) of the clock, and Escapement. describe the dial or " motion-See also:work." The minute hand fits on to a squared end of a See also:brass socket, which is fixed to the wheel M, and fits close, but not tight, on the prolonged arbor of the centre wheel. Behind this wheel is a See also:bent spring which is (or ought to be) set on the same arbor with a square hole (not a round one as it sometimes is) in the See also:middle, so that it must turn with the arbor; the wheel is pressed up against this spring, and kept there, by a cap and a small pin through the end of the arbor. The consequence is, that there is friction enough between the spring and the wheel to carry the hand round, but not enough to resist a moderate push with the See also:finger for the purpose of altering the time indicated. This wheel M, which is sometimes called the minute-wheel, but is better called the hour-wheel as it turns in an hour, drives another wheel N, of the same number of teeth, which has a pinion attached to it; and that pinion drives the twelve-hour wheel H, which is also attached to a large socket or See also:pipe carrying the hour hand, and See also:riding on the former socket, or rather (in See also:order to relieve the centre arbor of that extra weight) on an intermediate socket fixed to the See also:bridge L, which is screwed to the front plate over the hour-wheel M. The weight W, which drives the train and gives the impulse to the pendulum through the escapement, is generally hung by a See also:catgut See also:line passing through a palley attached to the weight, the other end of the cord being tied to some convenient See also:place in the clock frame or seat-See also:board, to which it is fixed by screws through the See also:lower pillars. Pendulum.—Suppose that we hive a See also:body P (fig. 4) at rest, and that it is material, that is to say, has " See also:mass." And for simplicity let us consider it a ball of some heavy See also:matter. Let it be free P to move horizontally, but attached A pendulum is isochronous for similar reasons. If the bob be See also:drawn aside from D to C (fig. 5), then the restitutional force tending to bring it back to rest is approximately the force which See also:gravitation would exert along the tangent CA, i.e. ACW= BC displacement BC g See also:cos g OC = glength of pendulum' Since g is See also:constant, and the length of the pendulum does not vary, it follows that when a pendulum is drawn aside through a small arc the force tending to bring it back to rest is proportional to the displacement (approximately). Thus the pendulum bob under the See also:influence of gravity, if the arc of swing is small, acts as though instead of being acted on by gravity it was acted on by a spring tending to See also:drag. it towards D, and therefore is isochronous. The qualification " If the arc of swing is small " is introduced because, as was discovered by Christiaan See also:Huygens, the arc of vibration of a truly isochronous pendulum should not be a circle with centre 0, but a See also:cycloid DM, generated by the See also:rolling of a circle with See also:diameter DQ=OD, upon a straight line QM. However, for a See also:short distance near the bottom, the circle so nearly coincides with the cycloid that a pendulum swinging in the usual circular path is, for small arcs, isochronous for practical purposes. The See also:formula representing the time of oscillation of a pendulum, in a circular arc, is thus found:—Let OB (fig. 6) be the pendulum, B be the position from which the bob is let go, and P be its position at A some period during its swing. Put FC =h, and MC=x, and OB=I. Now when a C body is allowed to move under the force FIG. 6. of gravity in any path from a height h, the velocity it attains is the same as a body would attain falling freely vertically through the distance h. Whence if v be the velocity of the bob at P, v='I 2gFM = s/ 2g(h—x). Let Pp=ds, and the See also:vertical distance of p below P=dx, then Pp=velocity at PXdt; that is, dt=ds/v. Also dx=MP=x(21—x)' whence dl =— = s ldx sl x(2l—x) ',12g(h—x) =IA . l de 1 2 g x(p—x) ,/ i—x/2l Expanding the second part we have dt=2,~g . fi x . (1+41~-...) . If this is integrated between the limits of o and h, we have t=Ir/Vg (1+81+...) where 6 is the time of swing from B to A. The terms after the second may be neglected. The first See also:term, x sl l/g, is the time of swing in a cycloid. The second part represents the addition necessary if the swing is circular and not eycloidal, and therefore expresses the " circular See also:error." Now- h = BC2/l =27f2021/36o2, where 0 is See also:half the See also:angle of swing expressed in degrees; hence h/81=82/52520, and the formula becomes t =,rV - (1+ 52520) . . Hence the ratio of the time of swing of an ordinary pendulum of any length, with a semiarc of swing =8 degrees is to the time of swing of a corresponding cycloidal pendulum as 1+82/52520:1. Also the difference of time of swing caused by a small increase 0' in the semiarc of swing=288'/52520 second per second, or 3.388' seconds per day. Hence in the See also:case of a seconds pendulum whose semiarc of swing is 2° an increase of .10 in this semiarc of 20 would cause the clock to lose 3.3 X2 Xo• 1= •66 second a day. Huygens proposed to apply his See also:discovery to clocks, and since the evolute of a cycloid is an equal cycloid, he suggested the use of a flexible pendulum swinging between cycloidal cheeks. But this was only an example of theory pushed too far, because the friction on the cycloidal cheeks involves more error than they correct, and other disturbances of a higher degree of importance are left uncorrected. In fact the application of pendulums to clocks, though governed in the abstract by theory, has to be modified by experiment. Neglecting the circular error, if L be the length of a pendulum and g the acceleration of gravity at the place where the pendulum is, then T, the time of a single vibration = 7r\i (L/g). From this formula it follows that the times of vibration of pendulums are directly 'proportional to the square See also:root of their lengths, and inversely proportional to the square root of the acceleration of gravity at the place where the pendulum is swinging. The value of g for See also:London is 32.2 ft. per second per second, whence it results that the length of a pendulum for London to See also:beat seconds of mean See also:solar time=39.14 in. nearly, the length of an astronomical pendulum to beat seconds of sidereal time being 38.87 in. This length is calculated on the supposition that the arc of swing is cycloidal and that the whole mass of the pendulum is concentrated at a point whose distance, called the See also:radius of oscillation, from the point of suspension of the pendulum is 39.14 in. From this it might be imagined that if a See also:sphere, say of See also:iron, were suspended from a See also:light rod, so that its centre were 39.14 in. below its point of support, it would vibrate once per second. This, however, is not the case. For as the pendulum swings, the ball also tends to turn in space to and fro round a See also:horizontal axis perpendicular to the direction of its motion. Hence the force stored up in the pendulum is expended, not only in making it swing, but also in causing the ball to oscillate to and fro through a small angle about a horizontal axis. We have therefore to consider not merely the vibrations of the rod, but the oscillations of the bob. The moment of the momentum of the system round the point of suspension, called its moment of inertia, is composed of the sum of the mass of each particle multiplied into the square of its distance from the axis of rotation. Hence the moment of inertia of the body I=E(ma2). If k be defined by the relation E(ma2) = (m) X k2, then k is called the radius of gyration. If k be the radius of gyration of a bob round a horizontal axis through its centre of gravity, h the distance of its centre of gravity below its point of suspension, and k' the radius of gyration of the bob round the centre of suspension, then k'2=h2+k2. If I be the length of a simple pendulum that oscillates in the same time, then lh=k'2=112+k2. Now k can be calculated if we know the form of the bob, and 1 is the length of the simple pendulum =39.14 in.; hence h, the distance of the centre of gravity of the bob below the point of suspension, can be found. In an ordinary pendulum, with a thin rod and a bob, this distance h is not very different from the theoretical length, 1=39.14 in., of a simple theoretical pendulum in which the rod has no weight and the bob is only a single heavy point. For the effect of the weight of the rod is to throw the centre of oscillation a little above the centre of gravity of the bob, while the effect of the See also:size of the bob is to throw the centre of oscillation a little down. In ordinary practice it is usual to make the pendulum so that the centre of gravity is about 39 in. below the upper free end of the suspension spring and leave the exact length to be determined by trial. Since T =ref E]g, we have, by differentiating, dL/L = 2dT/T, that is, any small percentage of increase in L. will correspond to See also:double the percentage of increase in T. Therefore with a seconds See also:pen- dulum, in order to make a second's difference in 2 a day, See also:equivalent to 1/86,400 of the pendulum's See also:rate of vibration, since there are 86,400 seconds in 24 hours, we must have a difference of length amounting to 2/86,400 =143,200 of the length of the rod. This is 39.138/43,200=•000906 in. Hence if under the pendulum bob be put a See also:nut working a See also:screw of 32 threads to the See also:inch and having its See also:head divided into 30 parts, a turn of this nut through one division will alter the length of the pendulum by .0009 in. and See also:change the rate of the clock by about a second a day. To accelerate the clock the nut has always to be turned to the right, or as you would drive in a corkscrew and See also:vice versa. But in astronomical and in large turret clocks, it is desirable to avoid stopping or in any way disturbing the pendulum; and for the finer adjustments other methods of regulation are adopted. The best is that of fixing a See also:collar, as shown in fig. 7 at C, about midway down the rod, capable of having very small weights laid upon it, this being the place where the addition of any small weight produces the greatest effect, and where, it may be added, any moving of that weight up or down on the rod produces the least effect. If M is the weight of the pendulum and 1 its length (down to the centre of oscillation), and m a small weight added at the distance n below the centre of suspension or above the c.o. (since they are reciprocal), t the time of vibration, and -dt the acceleration due to adding m; then -dt m n n2l of Westminster Clock Pendulum. from which it is evident that if n=l/2, then =dt/t=m/8M. But as there are 86400 seconds in a day, —dT, the daily acceleration, =86400 dt, or io800 m/M, or if m is the io800th of the weight of the pendulum it will accelerate the clock a second a day, or 10 grains will do that on a pendulum of 15 lb weight (700o gr. being =1 lb.), or an See also:ounce on a pendulum of 6 cwt. In like manner if n=1/3 from either See also:top or bottom, m must =M/7200 to accelerate the clock a second a day. The higher up the collar the less is the See also:risk of disturbing the pendulum in putting on or taking off the regulating weights, but the bigger the weight required to produce the effect. The weights should be made in a See also:series, and marked 4, 4, 1, 2, according to the number of seconds a day by which they will accelerate; and the pendulum adjusted at first to lose a little, perhaps a second a day, when there are no weights on the collar, so that it may always have some weight on, which can be diminished or increased from time to time with certainty, as the rate may vary. The length of pendulum rods is also affected by temperature and also, if they are made of See also:wood, by See also:damp. Hence, to ensure See also:good gym_ time-keeping qualities in a clock, it is necessary (I) to make pensatlan. the rods of materials that are as little affected by such
influences as possible, and (2) to provide means of See also:compensation by which the effective length of the rod is kept constant in spite of expansion or contraction in the material of which it is composed. Fairly good pendulums for ordinary use may be made out of very well dried wood, soaked in a thin See also:solution of shellac in See also:spirits of See also:wine, or in melted See also:paraffin See also:wax; but wood shrinks inso uncertain a manner that such pendulums are not admissible for clocks of high exactitude. See also:Steel is an excellent material for pendulum rods, for the See also:metal is strong, is not stretched by the weight of the bob, and does not suffer great changes in molecular structure in the course of time. But a steel rod expands on the average lineally by •o000064 of its length for each degree F. by which its temperature rises; hence an expansion of .00009 in. on a pendulum rod of 39.14 in., that is .000023 of its length, will be caused by an increase of temperature of about 4° F., and that is sufficient to make the clock lose a second a day. Since the summer and See also:winter temperatures of a See also:room may differ by as much as 5o° F., the going of a clock may thus be affected by an error of 12 seconds a day. With a pendulum rod of brass, which has a coefficient of expansion of •0000i, a clock might gain one-third of a minute daily in winter as compared with its rate in summer. The coefficients of linear expansion per degree F. of some other materials used in making pendulums are as follows: See also: The glass having a small coefficient of expansion, the lateral expansion of the mercury will be checked by it, and this will help to raise the See also:column. For the linear coefficient of expansion of glass is •0000048 per degree F., whence the sectional See also:area of a glass vessel increases by •0000096 per degree F., and therefore the coefficient of vertical expansion of a column of mercury whose volumetric expansion coefficient is •000i per degree F. is (000i —.0000096) = •0000904. Let x be the height of the vessel necessary to compensate a steel rod upon the bottom of which it rests. Then, the coefficient of expansion of steel being •000oo66 per degree F., we have -(•0000904—•0000066)=•0000066X39.14, whence x=64 in. It must, however, be remembered that the glass See also:jar has some weight and that it does not rise by anything like the amount of the mercury. This tends to keep the centre of gravity down. So that the height of mercury of 64 in. will not be sufficient to effect the compensation, and about 61 to 7 in. will be required. Some authors specify 7 in.; this is when the diameter of the jar is small. A certain amount of negative compensation must also be deducted to allow for the changes of temperature in the See also:air, as will presently be seen; this amounts in the case of mercury to about § in. In consequence of the complication of all these calculations it is usual to allow about 64 to 7 in. of mercury in the glass vessel and to adjust the exact amount of mercury by trial. Another very good form of mercurial pendulum was proposed by E. J. Dent; it consists of a See also:cast-iron jar into the top of which the steel pendulum rod is screwed, having its end plunged into the mercury contained in the jar. By this means the mercury, jar and rod rapidly acquire the same temperature. This pendulum is less likely to break than the form just described. The See also:depth of mercury required in an iron jar is stated by See also:Lord See also:Grimthorpe to be 84 to 9 in. The See also:reason why it is greater than it is when a glass jar is employed is that iron has a larger coefficient of expansion than glass, and that it is also heavier,. In all cases, however, of mercury pendulums experiment seems to be the only ultimate test of the quantity of mercury required, for the results are so complicated by the behaviour of the oil and the barometric errors that at its best the regulation of a clock can only be ultimately a matter of scientifically guided See also:compromise. A small amount of compensation of a purely experimental See also:character is also allowed to compensate the changes which temperature effects on the suspension spring. This is sometimes made as much as 4 of the length correction.
As an alternative to the mercurial pendulum other systems have been employed. The " gridiron " pendulum consists of a See also:group of alternate rods of steel and brass, so arranged that the expansion of the brass acts upwards and counteracts that of the steel downwards. It was invented in 1726 by See also: Of the 4 brass rods the 2 outside ones are 26.87 in.; and the two inside ones 22.25 in.; total 49.12 in. Thus the expansion of 88a in. of steel is counteracted by the expansion of 494 in. of brass. Everything depends, however, on the expansion coefficient of the steel and brass employed; the requirement in every case being that of total lengths of the brass and iron should be in proportion to the linear coefficients of expansion of those metals. The above figures Regsda- tbn. are for a very soft brass and steel. Thos. See also:Reid, with more ordinary steel and brass, prescribed a ratio of 112 to 71, Lord Grimthorpe a ratio of Too to 61: It is absolutely necessary to put the actual rods to be used for making the pendulum in a hot water See also:bath, and measure their expansions with a See also:microscope. John See also:Smeaton, taking advantage of a far greater expansion co-efficient of zinc as compared with brass, proposed to use a steel rod with a collar at the bottom, on which rested a hard drawn zinc rod. From this rod hung a steel See also:tube to which the bob was attached. The total length of the steel rod and of the steel tube down to the centre of the bob was made to the total length of the zinc tube, in the ratio of 5 to 2 (being the ratio of the expansions of zinc and steel) ; for a 39.14 in.pendulum we should therefore want a zinc tube equal in length to 1 (39.14) =264 in. In practice the zinc tube is made about 27 in. long, and then gradually cut down by trial. In fact the weight of a heavy pendulum squeezes the zinc, and it is impossible by See also:mere theory to determine what will be its behaviour. The zinc tube must be of rolled zinc, hard drawn through a See also:die, and must not be cast. Ventilating holes must be made in suitable places in the steel tube and the collar on which it rests, to ensure that changes of temperature are rapidly communicated throughout the system. A pendulum with a rod of dry varnished deal is tolerably compensated by a bob of lead or of zinc See also:lot to 13 in. in height, resting on a nut at the bottom of the rod. The old methods of pendulum compensation for See also:heat may now be considered as superseded by the invention of " See also:invar," a comlnvar. bination of See also:nickel and steel, due to Charles E. See also:Guillaume, of the See also:International See also:Office of Weights and See also:Measures at Sevres near See also:Paris. This alloy has a linear coefficient of expansion on the average of •00000i per degree centigrade, that is to say, only about ; i that of ordinary steel. Hence it can be easily compensated by means of brass, lead or any other suitable metal. Brass is usually employed. In the invar pendulum introduced into Great See also:Britain by Mr Agar Baugh a departure is made from the previous practice of merely calculating the length of the compensator, fastening it to the lower part of the pendulum, and attaching it to the centre of the bob. In the case of these pendulums, accurate cornputations are made of the moments of inertia of every See also:separate individual part. Thus, for instance, since an addition of See also:volume due to the effect of heat to the upper part of the bob has a different effect upon the moment of inertia from that of an equal quantity added to the lower part of the bob, the bob is suspended not from its centre, but from a point about ii.o in. below it, the distance varying according to the shape of the bob, so that the heat expansion of the bob may cause its centre of gravity to rise and compensate the effect of its increased moment of inertia. Again the suspension spring is measured for isochronism, and an alloy of steel prepared for it which does not alter its See also:elasticity with change of temperature. Moreover, since rods of invar steel subjected to See also:strain do not acquire their final coefficients of expansion and elasticity for some time, the invar is artificially " aged " by exposure to strain and heat. These considerations serve as a See also:guide in arranging for the compensation of the expansion of the rod and bob due to change of temperature. But they are not the only ones required; we See also:ave also to deal with changes due to the See also:density of the air in which the pendulum is moving. A body suspended in a fluid loses in weight by an amount equal to the weight of the fluid displaced, whence it follows that a pendulum suspended in air has not the weight which ought truly to correspond to its mass. M remains constant while Mg is less than in a vacuum. If the density of the air remained constant, this loss of weight, being constant, could be allowed for and would make no difference to the time-keeping. The period of swing would only be a little increased over what it would be in vacua. But the weight of a given volume of air varies both with the barometric pressure and also with temperature. If the bob be of type metal it weighs less in air than in a vacuum by about .000103 part, and for each 1 ° F. rise in temperature (the See also:barometer remaining constant and therefore the pressure remaining the same), the variation of density causes the bob to gain .00000024 of its weight. This, of course, makes the pendulum go quicker. Since the time of vibration varies as the inverse square root of g, it follows that a small increment of weight, the mass remaining constant, produces a diminution of one half that increment in time of swing. Hence, then, a rise of temperature of 1 ° F. will produce a diminution in the time of swing of -00000012th part or .c104 second in a day. But in making this calculation it has been assumed that the mass moved remains unaltered by the temperature. This is not so. A pendulum when swinging sets in motion a volume of air dependent on the size of the bob, but in a 10 lb bob nearly equal to its own volume. Hence while the rise of 1° of temperature increases the weight by. .00000012th part, it also decreases the mass by about the same proportion, and therefore the increase of period due to a rise of temperature of 1° F. will, instead of being •0104 second a day, be about •02 second. This must be compensated negatively by lengthening the pendulum by about 10020 in. for each degree of rise of temperature, which will require a piece of brass about 2 in. long. It follows, therefore, that with an invar rod having a linear expansion coefficient of -0000002 per degree F., which requires a piece of brass about •8 in. long to compensate it, the compensation which is to regulate both the expansion of the rod and also that of the air must be •8 in.-2 in., or -1.2 in.; so that the bob must be hung downwards from a piece of brass nearly xi in. in length. If the co-efficient of expansion of the invar were .00000053 per degree F., then the two corrections, one for the expansion of the rod and the other for the expansion of the air, would lust neutralize one another, and the pendulum rod would require no compensator at all. There are a number of other refinements which might be added, but which are too long for insertion here. By taking in all the See also:sources of error of higher orders, it has been possible to calculate a pendulum so accurately that, when the clock is loaded with the weight sufficient to give the pendulum the arc of swing for which it is designed, a rate of error has been produced of only half a minute in a year. These refinements, however, are only required for clocks of precision; for ordinary clocks an invar pendulum with a lead bob and brass compensator is quite sufficient. Invar pendulum rods are often made of steel with coefficients of expansion of about •00000l2 linear per C.; such a bob as this would require about 6.7 cm. of brass to compensate it, and, deducting 5 cm. of brass for the air compensation, this leaves about 1.7 cm. of See also:positive compensation for the pendulum. But as has been said, the exact See also:deduction depends on the shape and size of the bob, and the metal of which it is made. The diameters of the rods are 8 mm. for a 15 lb bob, 5 mm. for a 4 lb bob, and 12 to 15 mm. for a 6o lb bob. The bob is either a single See also:cylinder or two cylinders with the rod between them. Lenticular and spherical bobs are not used. The great See also:object is to allow the air ready See also:access to all parts of the rod and compensator, so that they are all heated or cooled simultaneously. The bobs are usually made of a See also:compound of lead,-See also:antimony, and See also:tin, which forms a hard metal, free from bubbles and with a specific gravity of about to. The usual weight of the bobs of the best pendulums for an ordinary astronomical clock is about 15 lb. A greater weight than this is found liable to make the support of the pendulum See also:rock and to put an undue strain on the parts, without any corresponding advantage. The rods used are all artificially aged, and have their heat expansion measured. No adjusting screw at the bottom is provided, the regulation being done by the addition of weights half way up the rod. An adjusting screw at the bottom has the disadvantage that it is impossible to know on which of the threads the rod is really resting; hence extra compensation may be introduced when not required. It is considered better that the supports of the bob should be rigid and invariable. The effect of changes in the pressure of the air as shown by a barometer is too important to be omitted in the See also:design of a good clock. But we do not propose to give more than a mere Baroindication of the principles which govern compensation metrical for this effect, since the full discussion of the problem error. would be too protracted. We have seen that the action of the air in affecting the time of oscillation of a pendulum depends chiefly on the fact that its buoyancy makes the pendulum lighter, so that while the mass of the bob which has to be moved remains the same or nearly the 'same, the acceleration of gravity on it has less effect. A volume of air at ordinary temperature and pressure has, as has been said, •000103 the weight of an equal volume of type metal, whence it follows that the acceleration of gravity on a type metal bob in air is .999897 of the acceleration of gravity on the bob in vacuo. If, therefore, we diminish the value of g in the formula T =as/ig by .000103, we shall have the difference of time of vibration of a type metal bob in air, as compared with its time in vacuo, and this, by virtue of the principle used when discussing the increase of time of oscillation due to increased pendulum lengths, is (•000lo3) second in one second, or about 41 seconds in a day of 86,400 seconds. It follows that a barometric pressure of 3o in. causes a loss of 41 seconds in the day, equivalent to .15 second per day for each inch of difference of the barometer. But, as has already been explained, the effect of the mass of the air transported with the pendulum must also be taken into See also:account and therefore the above figures must be doubled or nearly doubled. A difference of 3o in. of barometric pressure would thus make a difference of 9 seconds per day in the rate of the pendulum, and the clock would lose about s of a second a day for each inch of rise of the barometer, the result being of the same magnitude as would be produced by a fall of temperature of 15° F. in the air. Either of these effects would require a shortening of the pendulum of 1-01,1-0 in. This estimate is not far from the truth, for observations taken at various See also:European observatories on various clocks, and collected by See also:Jakob Hilfiker, give a mean of .15 second of retardation per day per centimetre of barometric pressure, or •37 second per day for each inch rise of the barometer. In order to counteract See also:variations in going which must thus obviously be produced by variations of barometrical pressure, attempts have been made purposely to disturb the isochronism of the pendulum, by making the arcs of vibration abnormally large. Again, the bob has been fitted with a piece of iron, which is subjected to the attraction of a piece of magnetized steel floating on the mercury in the open end of a barometer tube, so that when the barometer falls the attraction is increased and the pendulum retarded. Again, mercury barometers have been attached to pendulums. A simple method is to See also:fix an aneroid barometer with about seven compart-, ments on the pendulum about 5 to 6 in. below the suspension spring, and to attach to the top of it a suitable weight which is lowered according to the friction of the wheels, while every change in temperature causes a difference in the thickness of the oil. It is therefore desirable, if possible, to secure uniformity of impulse —say, by causing the train of wheels to lift up a certain specified weight, and let it drop on the pendulum at regular intervals, or by some equivalent method. The two requirements above stated have given rise respectively to what are known as detached escapements, and remontoires, which will be described presently. In the first place, however, it is desirable to describe the See also:principal forms of escapement in ordinary use. as the barometric pressure increases. One of the best methods of neutralizing the effects of variations of barometric pressure is to enclose the whole clock in an air-tight case, which may either be a large glass cylinder or a square case with a stout plate-glass front. This renders it See also:independent of outside variations, whether of temperature or pressure, and keeps the density of the air inside the case uniform. If the case could be completely, or almost completely, exhausted of air, and kept so exhausted, of course the pendulum would experience the minimum of resistance and would have to be lengthened a little. But in practice it is impossible to secure the See also:maintenance of a good vacuum without sealing up the case in such a way as to render See also:repairs very difficult, and this See also:plan is therefore rarely resorted to. What is usually done is to put the clock in a metal case covered with a thick See also:sheet of plate glass bedded in See also:india-See also:rubber strips, and held down by an iron flanged lid or frame firmly fixed by means of small bolts. An air-See also:pump is attached to the case, a turn-off tap being inserted, and by a few strokes the pressure of the air inside the case can be lowered to (say) 29 in., or a little below the usual barometric height at the place where the clock is. The difference of pressure being small, the tendency of air from outside to leak in is also small, and if the workmanship is good the inside pressure will remain unaltered for many days. In any case the difference produced by leakage will he small, and will not greatly affect the going of the clock. With care, and a daily or weekly See also:touch of the pump, the pressure inside can be kept practically constant, and hence the atmospheric error will be eliminated. The See also:cover has also incidentally the effect of keeping damp and fumes from the clock and thus preserving it from See also:rust, especially if a vessel with quicklime or some hygroscopic material be put in the case. Cases have considerable effect on the air, which moves with a pendulum and is flung off from it at each vibration; the going rate of a chronometer can be altered by removing the case. It is therefore desirable that cases enclosing pendulums should be roomy. Many See also:people prefer to omit the air-tight case, and to keep a See also:record of barometric, thermometric and hygrometric changes, applying corrections based on these to the times shown by the clock. It was formerly usual to suspend pendulums by means of a single spring about a in. wide riveted with chops of metal. The upper chop Suapen- had a pin driven through it, which rested in grooves See also:sion of so as to allow the pendulum to hang vertically. The pendulums. best See also:modern pendulums are now made with two parallel springs put a little less than an inch apart. The edges of the chops where the springs enter are slightly rounded so as to avoid too See also:sharp bending of the springs. Suspension of pendulums on See also:knife edges was tried by B. L. Vulliamy and others, but did not prove a success. It was once thought that lenticular pendulum bobs resisted the air less than those of other shapes, but it was forgotten that their large See also:surface offered more " skin friction." They are now no longer used, nor are See also:spheres on account of difficulty of construction. A cylinder is the best form of bob; it is sometimes rounded at the top and bottom. Escapements.—The term escapement is applied to any arrangement by which, as the wheels rotate, periodic impulses are given to the pendulum, while at the same time the motion of the wheels is arrested until the vibration of the pendulum has been completed. It thus serves as a mechanism for both counting and impelling. Since the vibrations of a pendulum through small arcs are performed in times independent of the length of the arc, it follows that if a pendulum See also:hanging at rest receive an impulse it will swing out and in again, and the time of its excursion outwards and of its return will remain the same whatever (within limits) be the arc of the swing, and whatever be the impulse given to it. If the impulse is big, it starts with a high velocity, but makes a larger excursion outwards, and the distance it has to travel counteracts its increase of speed, so that its time remains the same. Hence a pendulum, if free to swing outwards and in again, without impediment, will adapt the length of its swing to the impulse it has received, and any interference with it, as by the locking or unlocking of the escapement, will be far less deleterious to its isochronim when such interference occurs at the middle of its path rather than at the ends. It follows that the best escapement will be one which gives an impulse to the pendulum for a short period at the lowest point of its path, and then leaves it quite free to move as it chooses until the time comes for the next impulse. But a pendulum is not quite truly isochronous, and has its time slightly affected by an increase of its arc; it is therefore desirable that the impulses given to it shall always be equal. If the escapement forms the termination of a clock-train impelled by a weight, the driving force of the escapement is See also:apt to vary The balance escapement, which has been already mentioned, was in use before the days of pendulums. It was to a balance escapement that Huygens applied the pendulum, Balance by removing the weight from one See also:arm and increasing the See also:escape-length of the other arm. ment. Very shortly afterwards R. See also:Hooke invented the See also:anchor or recoil escapement. This is represented in fig. 8, where a tooth of the escape- wheel is just escaping from the right pallet, and another Anchor tooth at the same time falls upon the left-hand pallet at escape. some distance from its point. As the pendulum moves on ment. in the same direction, the tooth slides farther up the pallet, thus producing a recoil, as in the crown-wheel escapement. The acting faces of the pallets should be See also:convex. For when they are See also:flat, and of course still more when they are See also:concave, the points of the teeth always See also:wear a hole in the pallets at the extremity of their usual swing, and the motion is obviously easier and therefore better when the pallets are made convex; in fact, they then approach more nearly to the " dead " escapement, which will be de-scribed presently. The effect of some escapements is not only to counteract the circular error, or the natural increase of the time of a pendulum as the arc increases, but to over-balance it by an error of the contrary See also:kind. The recoil escapement does so; for it is almost invariably found that whatever may be the shape of these pallets, the clock loses as the arc of the pendulum falls off, and vice versa. It is unfortunately impossible so to arrange the pallets that the circular error may be thus exactly neutralized, because the escapement error depends, in a manner reducible to no law, upon variations in friction of the pallets themselves and of the clock train, which produce different effects; and the result is that it is impossible to obtain very accurate time-keeping from any clock of this construction. The point in which the anchor escapement was See also:superior to all that had gone before, was that it would work well with a small arc of swing of the pendulum. The balance escapement, even when adapted to a pendulum, necessitated a swing of some 20°,G and hence the circular error, that is to say, the deviation of the path from a true cycloid, was considerable. But with an anchor escapement the pendulum swing need be only 3° or 4°. On the other hand, it violates the conditions above laid down for a perfect escapement, inasmuch as the pendulum is never free, but at the end of its swing is still operated on by the escapement, which it causes to recoil. To get rid of this defect the dead escapement, or, as the French See also:call it, l'echappement a repos, was invented by G. Graham. It is Dead represented in fig. 9. It will be observed that the teeth escape• of the shape-wheel have their points set the opposite way meats. to those of the recoil escapement. The tooth B is here represented in the act of dropping on to the right-hand pallet as the tooth A escapes from the left pallet. But instead of the pallet having a continuous face as in the recoil escapement, it is divided into two, of which BE on the right pallet, and FA on the left, are called the impulse faces, and BD, FG, the dead faces. The dead faces are portions of circles (not necessarily of the same circle), having the axis of the pallets C for their centre; and the consequence evidently is, that as the pendulum goes on, carrying the pallet still nearer to the wheel than the position in which a tooth falls on to the corner A or B of the impulse and the dead faces, the tooth still rests on the dead faces without any recoil, until the pendulum returns and lets the tooth slide down the impulse face, giving the impulse to the pendulum as it goes. In order to diminish the friction and the See also:necessity for using oil as far as possible, the best clocks are made with jewels (sapphires are the best for the purpose) let into the pallets.
The pallets are generally made to embrace about one-third of the circumference of the wheel, and it is not at all desirable that they should embrace more; for the longer they are, the longer is the run of the teeth upon them, and the greater the friction. In some clocks the seconds hand moves very slowly and rests a very short time; this shows that the impulse is long in proportion to the arc of swing. In others the contrary is the case. A not uncommon proportion is that out of a total arc of swing of 3°, 2°, or about one degree on each side of the vertical, are occupied in receiving the impulse. In other words, the points F and A should subtend an angle of 2° at the centre C. It is not to be forgotten that the scape-wheel tooth does not overtake the face of the pallet immediately, on account of the moment of inertia of the wheel. The wheels of astronomical clocks, and indeed of all See also:English house clocks, are generally made too heavy, especially the scape-wheel, which, by increasing the moment of inertia, causes a part of the work to be lost in giving blows, instead of being all used up in See also:gentle pushes.
A very useful form of the dead escapement, which is adopted in many of the best turret clocks, is called the " pin-wheel escapement." Fig. 10 will sufficiently explain its action and construction. Its advantages are—that it does not require so much accuracy as the other; if a pin gets broken it is easily replaced, whereas in the other the wheel is ruined if the point of a tooth is injured; a wheel of given size will work with more pins than teeth, and therefore a train of less velocity will do, and that sometimes amounts to a saving of one wheel in- the train, and a good deal of friction; and the See also:blow on both pallets being down-
See also: Thus the pendulum is subject to a constant retardation by friction. Curiously enough, this friction, which at first sight might appear a defect, is an advantage, and to a large extent accounts for the excellence of the escapement. For if the driving force of the clock is increased so that the impulse on the pallets is greater, the velocity of the pendulum is increased. But this very increase of the driving force causes a greater pressure of the teeth of the scape-wheel on the rest-faces of the pallets, and hence counteracts the increased drive of the pendulum by an in-creased frictional retardation. If the clock weight be enormously increased, the frictional retardation becomes increased relatively in a greater proportion than the drive, so that as the weight of the clock is increased the pendulum's time of vibration is first diminished, until at last a neutral point is reached and finally the increased loading of the clock weight begins to make the time of vibration increase again. It is the neutral point which it is desirable to arrange for, and only trial and experience can so See also:fit the shape and size of the pallets, scape-wheel and clock weight to one another, as to secure that a moderate variation of the driving See also:power neither accelerates nor retards the motion of the pendulum, while at the same time such an arc of vibration is secured as shall be least subject to barometric error, and not have too great a circular error. The celebrated clockmaker B. L. Vulliamy (1780–1854) greatly improved Graham's escapement by careful experiment, and other makers introduced further improvements into the shape of the scape-wheel and pallets, so that the best form of the deadbeat escapement is now fairly well determined and is given in books upon horology. For small clocks a little slope is given to the rest-faces so as todiminish the friction retardation. This is known as the half-dead escapement. The pin-wheel escapement, if properly constructed, is also " dead," that is to say, the outward swing of the pendulum is unfettered except by the slight friction of the teeth against the dead faces of the. pallets. In order to diminish the effect of the impact of the scape-wheel on the pallets, and of the crutch on the pendulum rod, the plan has been tried of making the crutch into an elastic spring. In theory this of course would not destroy the isochronism of the pendulum, for it would only be to apply upon the pendulum a force at right angles to the rod, and varying as the displacement. Hence any acceleration given by such a spring would, like the action of gravity, be See also:harmonic, and it is an See also:analytical principle that harmonic motions superposed on one another still remain harmonic. Hence, then, the action of a spring superadded upon the action of gravity on a pendulum still leaves the motion harmonic. But changes of temperature would affect the spring considerably. In the case of such a spring the repose faces of Graham's escapement might be minimized and the escapement checked each side by a stop, so as to prevent the pallets from rubbing on the points of the scape-wheel. Graham's escapement can, if well made, be arranged so as not to vary more than an average of -Ay of a second from its mean daily rate, and this is so good a result that many people doubt whether further effort in the direction of inventing new escapements will result in any better form. Two adaptations of Graham's escapement have been made, one by Clemens Riefler of Nesselwang, and the other by L. Strasser of Glashutte, See also:Saxony, which give good results in practice. Riefler's See also:scheme is to See also:mount the upper See also:block, into which the suspension spring is fastened, upon knife edges, and rock it to and fro by the action of a modified Graham's escapement, thus giving impulses to the pendulum. Fig. II shows the arrangement. PP are the agates upon which the knife edges CC rest. A is the anchor, RH the scape-wheels, and S the pallets. Strasser's clock is arranged on the same See also:idea as that of Riefler, only that the rocking motion is given, not to the springs that carry the pendulum, but to a second pair of springs placed outside of them and parallel to them. The weight of the pendulum is therefore carried by an upper stationary block, but above that a second block is subjected to the rocking motion of the anchor. The general design is shown in fig. 12. The pallets are each formed of two stones, so contrived as to minimize the banging of the teeth of the scape-wheel. Both Riefler's and Strasser's clocks aim at having a virtually free pendulum; in fact, they are in reality adaptations of the principle of the spring-clutch to Graham's escapement. The weak point in both is the tampering with the suspension. The dead escapement is not, however, truly free. In order to make a free escapement it would be necessary to provide that as soon as the pendulum approached its centre position, some pin or projecting point upon it should free the escapement wheel, a tooth of which should thus be enabled to leap upon the back of the pendulum, give it a short push, and then be locked until the pendulum had returned and again swung forward. An arrangement of this kind is shown in fig. 13. Let A be a block of metal fixed on the lower end of a pendulum rod. On the block let a small See also:pall B be fastened, free to move round a Detached escapement. centre C and resting against a stop D. Let E be a 4-leaved scapewheel, the teeth of which as they come round rest against the bent pall GFL at G. The pall is prevented from flying too far back by a pin H, and kept up to position by a very delicate spring K. As soon as the pendulum rod, moving from left to right, has arrived at the position shown in the figure, the pall B will engage the arm FL, force It forwards, and by raising G will liberate the scape-wheel, a tooth of which, M, will thus close upon the See also:heel N of the block A, and urge it forward. As soon, however, as N has arrived at G the tooth M will slip off the block A and rest on the pall G, and the impulse will cease. The pendulum is now perfectly free or " detached," and can swing on unimpeded as far as it chooses. On its return from right to left, the pall B slips over the pall L without disturbing it, and the pendulum is still free to make an excursion towards the left. On its return See also:journey from left to right the See also:process is again repeated. Such an escapement operates once every 2 seconds. One made on a some-what similar plan was applied to a clock by See also:Robert-Houdin, about 183o, and afterwards by Mr Haswell, and another by See also:Sir George See also:Airy. (old form). But the principlewas already an old one, as maybe seen from fig. 14, which was the work of an See also:anonymous maker in the 18th century. A See also:consideration of this escapement will show that it is only the application of the detached chronometer escapement to a clock. Even detached escapements, however, are not perfect. In order that an escapement should be perfect, the impulse given to the pendulum should be always exactly the same. It may be asked why, if the time of oscillation of the pendulum be independent of the See also:amplitude of the arc of vibration, and hence of the impulse. it is necessary that the impulse should be uniform. The anwser is that the arc of vibration not being a true cycloid, as it should be if true isochronism is to be secured, but being the arc of a circle, any change of amplitude of vibration produces a change of time in the swing given by the formula g(a2—b2)= loss in seconds per day, where a and b are the semi-arcs of vibration estimated in degrees. Thus 1o' in-crease of arc in a swing of 40, that is to say, •I in. increase of arc in a total arc of 21 in., produces an error of about a second a day. Now See also:cold See also:weather, by making the oil thick and thus clogging the wheels, will easily produce such a change of arc; dust will also make a change even though the clock weight, acted on by gravity, still exerts a uniform pull. Besides, if the clock has work to do of a varying amount—as when the hands of a turret clock are acted on by a heavy See also:wind pressure tending sometimes to retard them, sometimes to drive them on—then it is clear that the impulses given by the scape-wheel to the pendulum may be very unequal, and that the arc of vibration of the pendulum may thus be seriously affected and its isochronism disturbed. To abolish errors arising from the changes in the force driving the escapement, what is known as the "remontoire " system was Remon. adopted. It first came into use for watches, which was take. perhaps natural, seeing that the driving force of a watch
is not a uniform weight like that of a clock, but depends on springs, which are far less trustworthy. The idea of a remontoireis to disconnect the escapement from the clock train, and to give the escapement a driving power of its own, acting as directly as possible on the pallets without the intervention of a clock-train containing many wheels. The escapement is thus as it were made into a separate clock, which of course needs repeated winding, and this winding is effected by the clock-train. From this it results that variations in the force transmitted by the clock-train merely affect the speed at which the " rewinding " of the escapement is effected, but do not affect the force exerted by the driving power of the escapement.
There are several modes of carrying out this plan. The first of them is simply to provide the scape-wheel with a weight or spring
of its own, which spring is See also:wound up by the clock-train Vain
as often as it runs down. Contrivances of this kind are remon-
called train recnontoires. In arranging such a remontoire Zires. it is obvious that the clock-train must be provided with
a stop to prevent it from overwinding the scape-wheel weight or spring, and further, that there must be on the scape-wheel some sort of See also:stud or other contrivance to See also:release the clock-train as soon as the scape-wheel weight or spring has run down and needs rewinding. We believe the first maker of a large clock with a train remontoire was See also: Whenever, then, the scapewheel completes a half-turn, one spike is let go, and the third wheel is able to move, and with it the whole clock-train and the hands, until the next spike of the other set is stopped by the scape-wheel arbor; at the same time the pinion on that arbor is turned half round, winding up the remontoire weight, but without taking its pressure off the scape-wheel. Reid says that, so long as this apparatus was kept in good order, the clock went better than it did alter it was removed in consequence of its getting out of order from the constant banging of the spikes against the arbor. A clock at the Royal See also:Exchange, London, was made in 1844 on the same principle, except that, instead of the endless chain, an See also:internal wheel was used, with the spikes set on it externally, which is one of the modes by which an occasional secondary motion may be given to a wheel without disturbing its See also:primary and regular motion. The following is a more simple arrangement of a gravity train remontoire, much more frequently used in principle. Let E in fig. 15 be the scape-wheel turning in a minute, and e its pinion, which is driven by the wheel D having a pinion d driven by the wheel C, which we may suppose to turn in an hour. The arbors of the scape-wheel and hour-wheel are distinct, their pivots See also:meeting in a See also:bush fixed some-where between the wheels. The pivots of the wheel D are set in the frame AP, which rides on the arbors of the hour-wheel and See also:scope- wheel, or on another short arbor between them. The hour-wheel also drives another wheel G, which again drives the pinion f on the arbor which carries the two arms f A, f B ; and on the same arbor is set a See also:fly with a ratchet, like a common striking fly, and the See also:numbers of the teeth are so arranged that the fly will turn once for each turn of the scape-wheel. The ends of the remontoire arms f A, f B are capable of alternately passing the notches cut half through the arbor of the scape-wheel, as those notches successively come into the proper position at the end of every half-minute; as soon as that happens the hour-wheel raises the movable wheel D and its frame through a small angle; but, nevertheless, that wheel keeps pressing on the scape-wheel as if it were not moving, the point of contact of the wheel C and the pinion d being the fulcrum or centre of motion of the See also:lever A d P. It will be observed that the remontoire arms f A, f B have springs set on them to diminish the blow on the scape-wheel arbor, as it is desirable not to have the fly so large as to make the motion of the train, and consequently of the hands, too slow, to be d'stinct. Another kind of remontoire is on the principle of one bevelled wheel lying between two others at right angles to it. The first of the bevelled wheels is driven by the train, and the third is fixed to the arbor of the scape-wheel; and the intermediate bevelled wheel, of any size, rides on its arbor at right angles to the other two arbors which are in the same line. The scape-wheel will evidently turn with the same average velocity as the first bevelled wheel, though the intermediate one may move up and down at intervals. The transverse arbor which carries it is let off and lifted a little at half-minute intervals, as in the remontoire just now described; and it gradually works down as the scape-wheel turns under its pressure, until it is freed again and lifted by the clock-train. In all these gravity remontoires, however, only the friction of the heavy parts of the train and the dial-work is got rid of, and the scapewheel is still subject to the friction of the remontoire wheels, which, though much less than the other, is still something considerable. Accordingly, attempts have frequently been made to drive the scapewheel by a See also:spiral spring, like the mainspring of a watch. One of these was described in the 7th edition of this See also:encyclopaedia; and Sir G. Airy invented another on the same principle, of which one specimen is still going well. One of the best forms of such a remontoire is shown in fig. i6, in which A, B, D, E, e, f are the same things as in fig. 15. But e, the scapewheel pinion, is no longer fixed to the arbor, nor does it ride on the arbor, as had been the case in all the previous spring remontoires, thereby producing probably more friction than was saved in other respects; but it rides on a stud k, which is set in the clock frame. On the face of the pinion is a plate, of which the only use is to carry a pin h (and consequently its shape is immaterial), and in front of the plate is set a bush b, with a hole through it, of which half is occupied by the end of the stud k, to which the bush is fixed by a small pin, and the other half is the pivot-hole for the scapewheel arbor. On the arbor is set the remontoire spring s (a Moderate-sized musical-See also:box spring is generally used), of which the See also:outer end is bent into a See also:loop to take hold of the pin h. In fact, there are two pins at h, one a little behind the other, to keep the coils of the spring from B touching each other. Now, it is evident that the spring may be wound up half or a See also:quarter of a turn at the proper intervals without taking the force off the scapewheel, and also without affecting it by any friction whatever. When the scape-wheel turns in a minute, the letting-off would be done as before described, by a couple of notches in the scape-wheel arbor, through which the spikes A, B, as in fig. 15, would pass alternately. During the half-minute that the spring is See also:running down the impulse on the pendulum constantly diminishes; but this error is small if the spring be properly shaped, and besides, being periodic, does not affect the average time-keeping of the clock. It would be inadmissible in astronomical clocks where each particular second has always to be true. In clocks with only three wheels in the train it is best to make the scape-wheel turn in two minutes. In that case four notches and four remontoire arms are required, and the fly makes only a quarter of a turn. Lord Grimthorpe made the following See also:provision for diminishing the friction of the Ietting-off work. The fly pinion f has only half the number of teeth of the scape-wheel pinion, being a See also:lantern pinion of 7 or 8, while the other is a leaved pinion of 14 or 16, and therefore the same wheel D will properly drive both, as will be seen hereafter. The scape-wheel arbor ends in a cylinder about a in. in diameter, with two notches at right angles cut in its face, one of them narrow and deep, and the other broad and shallow, so that a long and thin pin B can pass only through one, and a broad and short pin A through the other. Consequently, at each quarter of a turn of the scape-wheel, the remontoire fly, on which the pins A, B are set on springs, as in fig. 15, can turn half round. It is set on its arbor f by a square ratchet and click, which enables the spring to be adjusted to the requisite tension to obtain the proper vibration of the pendulum. A better construction, afterwards introduced, is to make the fly separate from the letting-off arms, whereby the blow on the cylinder is diminished, the fly being allowed to go on as in the gravity escapement. It should be observed, however, that even a spring remontoire requires a largerweight than the same clock without one; but as none of that additional force reaches the pendulum, that is of no consequence. The variation of force of the remontoire spring from temperature, as it only affects the pendulum through the See also:medium of the dead escapement, is far too small to produce any appreciable effect ; and it is found that clocks of this kind, with a compensated pendulum 8 ft. long, and weighing about 2 cwt., will not vary above a second a See also:month, if the pallets are kept clean and well oiled. No turret clock without either a train remontoire or a gravity escapement will approach that degree of accuracy. The introduction of this remontoire led to another very important alteration in the construction of large clocks. Hitherto it had always been considered necessary, with a view to diminish the friction as far as possible,. to make the wheels of brass or See also:gun-metal, with the teeth cut in an See also:engine. The French clockmakers had begun to use cast iron striking parts, and cast iron wheels had been occasionally used in the going part of inferior clocks for the See also:sake of cheapness; but they had never been used in any clock making pretensions to accuracy. But in consequence of the success of a clock shown in the 1851 Exhibition, it was determined by Sir G. Airy and Lord Grimthorpe (then E. See also:Denison),who were jointly consulted by the Board of Works about the great Westminster clock in 1852, to alter the See also:original requisition for gun-metal wheels there to cast iron. But cast iron wheels must drive cast iron pinions, for they will wear out steel.
The next kind of remontoire still leaves the scape-wheel linked up with the clock-train, but makes it wind up the pallets which are held raised up till their action is wanted, when they are allowed to drop gently on the crutch or the pendulum rod. In this case the two arms of the anchor are usually divided and mounted on separate shafts so as to act independently. This idea was first started by Thomas Mudge (1717–1794) and See also: This, however, appears entirely a matter of construction. The really weak point is that while the impulses on the pendulum due to the gravitational fall of the arms are uniform, the force which has to be exercised by the pendulum in unlocking them from the scape-wheel varies with the pressure of the clock-train. Hence we See also:miss the compensation which is so beautiful a result of Graham's escapement. To avoid this, J. M. Bloxam, a See also:barrister, proposed about the middle of the 19th century his legged gravity escapement (fig. I8). By this arrangement the parts of the scape-wheel which lifted the gravity arms were brought as near to the axis of the scapewheel as possible, while the locking arms were brought as far from the axis as possible so that the oressure should be light. The pallet arbors were cranked, to embrace the pendulum-spring, so that their centres of motion might coincide with that of the pendulum as nearly as possible—perhaps an unnecessary refinement; at least the three-legged and four-legged gravity escapements See also:answer very well with the pallet arbors set on each side of the top of the spring. The size of the wheel determines the length of the pallets, as they must be at such an angle to each other that the radii of the wheel when in See also:con-tact with each stop may be at right angles to the pallet arm ; and therefore, for a wheel of this size, the depth of locking can only be very small. The pinion in Bloxam's clock only raises the pallet through 40' at each beat; i.e. the angle which we call y, viz. the amplitude of the pendulum when it begins to lift the pallet, is only 20'; and probably, if it were increased to anything like a/ ./ 2, where a is the semiarc of swing, the escapement would trip immediately. The two broad pins marked E, F, are the fork-pins, and A and B are the stops. The clock which Bloxam had went very well; hilt it had an extremely fine train, with pinions of 18; and nobody else appears to have been able to make one to answer. Bloxam's escapement was modified in form by Lord Grimthorpe, his chief improvement being the addition of a fly See also:vane, which, how-ever, had previously been used for remontoires to steady the motion. He tried various modifications of construction, but finally adopted the " four-legged " and " double-three-legged " forms as being the most satisfactory, the former for regulators and the latter for large clocks. Fig. 19 is a back view of the escapement part of an astronomical clock with the four-legged wheel; seen from the front the Escapement. Escapement. wheel would turn the other way. The long locking teeth are made about 2 in. long from the centre, and the lifting pins, of which four point forwards while four other intermediate ones point backwards, are at not more than 3l„ of the distance between the centres EC, of the scape-wheel and pallets; or rather C is the top of the pendulum spring to which the pallets Cs, Cs' converge, though the resultant of their action is a little below C. It is not See also:worth while to See also:crank them as Bloxam did, in order to make them coincide exactly with the top of the pendulum, as the friction of the beat pins on the pendulum is insignificant, and even then would not be quite destroyed. The pallets are not in the same See also:plane, but one is behind and the other in front of the wheel, with one stop pointing backwards and the other forwards to receive the teeth alternately—it does not matter which; in this figure the stop s is behind and the stop s' forward. The pendulum is now going to the right, and just beginning to lift the right pallet and free the stop s'; then the wheel will begin to turn and lift the other pallet by one of the pins which is now lowest, and which moves through 45° across the line of centres, and therefore lifts with very little friction. It goes on till the tooth now below s reaches s and is stopped there. Meanwhile the pallet Cs' goes on with the pendulum as far as it may go, to the end of the arc which we have called a, starting from y; but it falls with the pendulum again, not only to -y but to –y on the other side of o, so that the impulse is due to the weight of each pallet alternately falling through 27; and the magnitude of the impulse also depends on the obliqueness of the pallet on the whole, i.e. on the distance of its centre of gravity from the vertical through C. The fly KK' is set on with a friction spring like the common striking-part fly, and should be as long as there is room for, length being much more effective than width.
The double three-legged gravity escapement, which was first used in the Westminster clock, is shown in fig. 20. The principle of it is the same as of the four-legs; but instead of the pallets being one behind and the other in front of the wheel, with two sets of lifting
vI. I8pins, there are two wheels See also:ABC, abc, with the three lifting pins and the two pallets between them like a lantern pinion. One stop B points forward and the other A backward. The two wheels have their teeth set intermediately or 6o° apart, though that is not essential, and the angle of 120 may be divided between them in any other proportions, as 70° and 50°, and in that way the pallets may be still more oblique than 30° from the vertical, which, however, is found enough to prevent tripping even if the fly gets loose, which is more likely to happen from carelessness in large clocks than in astronomical ones.
Of course the fly for those escapements in large clocks, with weights heavy enough to drive the hands in all weather, must be much larger than in small ones. For average See also: Lord Grimthorpe considered that these escapements act better, especially in regulators, if the pallets do not fall quite on the lifting pins, but on a banking, or stop at any convenient place, so as to leave the wheel free at the moment of starting; just as the striking of a common house clock will sometimes fail to start unless the wheel with the pins has a little run before a pin begins to lift the See also:hammer. The best way to See also:manage the banking is to make the beat-pins long enough to reach a little way behind the pendulum, and let the banking be a thin plate of any metal screwed adjustably to the back of the case. This plate cannot well be shown in the drawings together with the pendulum, which, it may be added, should take up one pallet just when it leaves the other. In chronometer spring remontoires the pendulum, as it goes by, flips a delicate spring and releases a small weight or spring which has been wound up in readiness by the action of the scapewheel and which by leaping on to the pendulum gives it Ghrono- a push. One on this principle made about the middle See also:meter re-of the 19th century by Robert Houdin is to he seen at mspranontoigre. the See also:Conservatoire See also:des Arts et Metiers. It is very com- plicated. The following is more simple. In fig. 21 a scape-wheel AB has 30 pins and 36o teeth. It is engaged with a fly vane EP mounted on a pinion of 12 teeth. Each pin as it passes raises an impulse arm CD which is hooked upon a detent K. A pall NM then engages the fly vane and prevents the scape-wheel from moving farther. The impulse arm being now set, as the plate F attached to the lower end of the pendulum flies past from left to right a pall A G knocks aside the detent K, and allows a pin 0 projecting from the end of the impulse arm to fall upon an inclined pallet h, which is thus urged forward. As soon as the pallet has left the pin, the impulse arm in its further fall strikes N, which disengages the pall at P and allows the scape-wheel to move on and again wind up the impulse arm CD, which is then again locked by the detent K. On the return journey of the pendulum the light pall G, which acts the part of a chronometer spring, flips over the detent. The pallet is double sided, h and h', so that if by See also:chance the clock runs down while the pendulum swings from left to right the impulse arm will be simply raised and not smashed. It has a flat See also:apex, on which the pin falls before descending. The impulse given depends on the weight of the impulse arm and may be varied at See also:pleasure. The work done in unlocking the detent is invariable, as it depends on the pressure of the fly vane at P and is independent of the clock-train. The duration of the impulse is very short—only about Sb of the arc of swing. It is given exactly at the centre of the swing, and when not under impulse the pendulum is detached. Clock Wheels.—Since, as we have seen, any increase in the arc of a pendulum is accompanied by a change in its going rate TI ends of the leaves of the pinon wheel. Thus a See also:cog-wheel is shaped out. Clock wheels are made of hard hammered brass cut out by a wheel cutting See also:machine. This machine consists of a vertical spindle on the top of which the wheel to be cut is fixed on a firmly resisting plate of metal of slightly smaller diameter, so as to allow the wheel to overlap. A cutter with the edges most delicately ground to the exact shape of the See also:gap between two teeth is caused to rotate 3000-4000 times a minute, and brought down upon the edge of the wheel. The shavings that come off are like fine dust, but the cutter is pushed on so as to plunge right through the rim of the wheel in a direction parallel to the axis. In this way one gap is cut. The vertical spindle is now rotated one division, by means of a dividing plate, and another tooth is cut, and so the operation goes on round the wheel. It is not desirable in clocks that the pinion wheels which are driven should have too few teeth, for this throws all the work on a pair of surfaces before the centres and is apt to 'produce a grinding motion. Theoretically the more leaves a pinion has the better. Pinions can be made with leaves of thin steel watch-spring. In this case quite small pillions can have 20 leaves or more. The teeth in the driving wheels then become mere notches for which great accuracy of shape is not necessary. Such wheels are easy to make and run well. Lantern pinions are also excellent and are much used in See also:American clocks. They are easy to make in an ordinary See also:lathe. The cog-wheels must. however, be specially shaped to fit them. They consist of a number of round pins arranged in a circle round the axis of the wheel and parallel to it. The ends are secured in flanges like the wires of a See also:squirrel cage. The teeth of cog-wheels engage them and thus drive the wheel round. They were much used at one time but are now falling out of favour again. It is possible to make toothed wheels that drive with perfect uniformity by using for the See also:curve of the teeth involutes of circles. These involutes are traced out by a point on a See also:string it is very desirable to keep the force which acts on the pendulum uniform. This in fact is the great object of the best escapements. Inasmuch as the impulse on the pendulum, derived from the work done by a falling weight or an unwinding spring, is transmitted through a train of wheels, it is desirable that that transmission should be as free from friction and as regular as possible. This involves care in the shaping of the teeth. The object to be aimed at is that as the wheel turns round the ratio of the power of the See also:driver to that of the driven wheel (" runner " or " follower ") should never vary. That is to say, whether the back part of the tooth of the driver is acting on the tip of the tooth of the follower, or the tip of the driver is acting on the back part of the tooth of the follower, the leverage ratio shall always be uniform. For simplicity of manufacture the pinion wheels are always constructed with. radial leaves, so that the surface of each tooth is a plane passing through the axis of the wheel. The semicircular rounding of the end of the tooth is merely ornamental. The question therefore is, suppose that it is desired by means of a tooth on a wheel to push a plane round an axis, what is the shape that must be given to that tooth in order that the leverage ratio may remain unaltered ? If a curved surface, known as a " See also:cam," See also:press upon a plane one, both being hinged or centred upon pivots A and B respectively (fig. 22), then the line of action and reaction at D, the point where they touch, will be perpendicular to their surfaces at the point of contact—that is perpendicular to BD, and the ratio of leverage will obviously be AE : BD, or AC : CB. Hence to cause the leverage ratio of the cam to the plane always to remain unaltered, the cam must be so shaped that in any position the ratio AC : CB will remain unchanged. In other words the shape of the cam must be such that, as it moves and pushes BD before it, the normal at the point of contact must always pass through the fixed point C. If a circle PMB See also:roll upon another circle SPT (fig. 23) any point M on it will generate an See also:epicycloid MN. The radius of curvature of the curve at M will always be MP, for the part at M is being produced by rotation round the point P. It follows that a line from B to M will always be tangential to the epicycloid. If the epicycloid be a cam moving as a centre round the centre R (not shown in the figure) of the circle SPT, the leverage it will exert upon a plane surface BM moving round a parallel axis at B, will always be as BP to PR, that is, a constant; whence MN is the proper shape of a tooth to act on a pinion with radial arms and centred at B. In designing a pair of wheels to transmit motion, which is to be multiplied say 6 times in the transmission (about the usual ratio for clock wheels), if we take two circles (called the " See also:pitch circles ") touching one another with radii as 1:6, then the circumference of the smaller will roll 6 times round that of the larger. The smaller wheel will have a number of teeth, say 8 to 16, each of them being sectors of the circle (fig. 24). If there are 16 teeth, then on the surface of the driving wheel there will be 96 teeth. Each of these teeth will be shaped as the curve of an epicycloid formed by the rolling on the big circle of a circle whose diameter is the radius of the pitch circle of the pinion. Points of the teeth so formed are cut off, so as to allow of the pinion having a solid core to support it, and gaps are made into the pitch circle to admit the rounded Involute that is gradually unwound from a circle. They are teeth. in fact epicycloids traced by a rolling circle of See also:infinite radius, i.e. a straight line. Involute teeth have the advantage that they roll on one another instead of sliding. When badly made they put considerable strain on the axes or shafts that carry them. Hence they have not been regarded with great favour by clockmakers. By the pitch of a wheel is meant the number of teeth to` the inch of circumference or diameter of the wheel; the former is called the circumferential pitch, the latter the Pitch diametral pitch. Thus if we say that a wheel has 40 diametral pitch we mean that it has 40 teeth to each inch of diameter. The circumferential pitch is of course got by dividing the diametral pitch by r. Wheel-cutters are made for all sizes of pitches. If it were needed to make a pair of wheels the ratio of whose motion was say 6 : I and we determined to use a diametral pitch of 30 to the inch, that is teeth about i16 in. wide at the See also:base, and if the smaller circle were to have 20 teeth, we should need a See also:blank of a diameter of f +io =I in. for the smaller wheel, and one of -1320-9_-+12b =' o in. for the larger wheel which would have 120 teeth to the inch and be 4•o6 in diameter to the tips of the teeth. The smaller toothed wheel would be •73 of an inch in diameter over all. The pitch circles of the wheels would be a and 4 in. respectively. For fine wheel work, where the driver is always much larger than the driven wheel, the epicycloidal tooth appears preferable, as it is generally considered to put less side strain on the pinion wheel. But the relative merits of the two systems have never been properly tested for clock work. Going Barrels.—A clock which is capable of going accurately must have some contrivance to keep it going while it is being wound up. In the old-fashioned house clocks, which were wound up by merely pulling one of the strings, and in which one such winding served for both the going and striking parts, this was done by what is called the endless chain of Huygens, which consists of a string or chain with the ends joined together, and passing over two pulleys on the arbors of the great wheels, Ap :E rP Epkycloldal teeth.
with deep grooves and spikes in them, to prevent the chain from slipping. In one of the two loops or festoons which hang from the upper pulleys is a loose See also:pulley without spikes, carrying the clock-weight, and in the other a small weight only heavy enough to keep the chain close to the upper pulleys. Now, suppose one of those pulleys to be on the arbor of the great wheel of the striking part, with a ratchet and click, and the other pulley fixed to the arbor of the great wheel of the going part; then (whenever the clock is not striking) the weight may be pulled up by pulling down that part of the string which hangs from the other side of the striking part; and yet the weight will be acting on the going part all the time. It would be just the same if the striking part and its pulley were wound up with a See also: When it is lifted a spring-bolt attached to the lever, or its arbor, runs into the teeth of one of the wheels, and the weight ,of the lever keeps the train going until the bolt has run itself out of See also:gear. Clocks are not always driven by weights. When accuracy is not necessary, but portability is desirable, springs are used. The old form of spring became weaker as it was unwound and necessitated the use of a device called a fusee or spiral See also:drum. This apparatus will be found described in the See also:article WATCH. Striking Mechanism.—There are two kinds of striking work used in clocks. The older of them, the locking-plate system, which is still used in most See also:foreign clocks, and in turret clocks in See also:England also, will not allow the striking of any hour to be either omitted or repeated, without making the next hour strike wrong; whereas in the See also:rack system, which is used in all English house clocks, the number of blows to be struck depends merely on the position of a wheel attached to the going part, and therefore the striking of any hour may be omitted or repeated without deranging the following ones. We shall only describe the second of these, which is the more usual in modern timepieces. Fig. 26 is a front view of a common English house clock with the face taken off, showing the repeating or rack striking See also:movement. Here, as in fig. 3, M is the hour-wheel, on the pipe of which the minute-hand is set, N the reversed hour-wheel, and n its pinion, driving the 12-hour wheel H, on whose socket is fixed what is called the See also:snail Y, which belongs to the striking work exclusively. The hammer is raised by the eight pins in the rim of the second wheel in the striking train, in the manner which is obvious. The hammer does not quite touch the bell, as it would jar in striking if it did, and prevent the full See also:sound. The form of the hammer-shank at the arbor where the spring S acts upon it is such that the spring both drives the hammer against the bell when the tail T is raised, and also checks it just before it reaches the bell, the blow on the bell thus being given by the hammer having acquired momentum enough to go a little farther than its place of rest. Sometimes two springs are used, one for impelling the hammer, and the other for checking it. But nothing will check the chattering of a heavy hammer, except making it lean forward so as to act, partially at least, by its weight. The pinion of the striking-wheel generally has eight leaves, the same number as the pins; and as a clock strikes 78 blows in 12 hours, the great wheel will turn in that time if it has 78 teeth instead of 96, which the great wheel of the going part has for a centre pinion of eight. The striking-wheel drives the wheel above it once round for each blow, a.nd that wheel drives a See also:fourth (in which there is a single pin P), six, or any other integral number of turns, for one turn of its own, and that drives a See also:fan-fly to moderate the velocity of the train by the resistance of the air, an expedient at least as old as De Vick's clock in 1379. The wheel N is so adjusted that, within a few minutes of the hour, the pin in it raises the lifting-piece LONF so far that that piece lifts the click C out of the teeth of the rack BKRV, which immediately falls back (helped by a spring near the bottom) as far as its tail V can go by reason of the snail Y, against which it falls; and it is so arranged that the number of teeth which pass the click is proportionate to the depth of the snail; and as there is one step in the snail for each hour, and it goes round with the hour-hand, the rack always drops just as many teeth as the number of the hour to be struck. This drop makes the See also:noise of " giving warning." But the clock is not yet ready to strike till the lifting piece has fallen again; for, as soon as the rack was let off, the tail of the gathering pallet G,on the prolonged arbor of the third wheel, was enabled to pass the pin K of the rack on which it was pressing before, and the striking train began to move; but before the fourth wheel had got half round, its pin P was caught by the end of the lifting-piece, which is bent back and goes through a hole in the plate, and when raised stands in the way of the pin P, so that the train cannot go on till the lifting-piece drops, which it does exactly at the hour, by the pin N then slipping past it. Then the train is free; the striking wheel begins to lift the hammer, and the gathering pallet gathers up the rack, a tooth for each blow, until it has returned to the place at which the pallet is stopped by the pin K coming under it. In this figure the lifting-piece is prolonged to F, where there is a string hung to it, as this is the proper place for such a string when it is wanted for the purpose of learning the hour in the dark, and not (as it is generally put) on the click C; for if it is put there and the string is held a little too long, the clock will strike too many; and if the string accidentally sticks in the case, it will go on striking till it is run down—neither of which things can happen when the string is put on the lifting-piece. The snail is sometimes set on a separate stud with the apparatus called a star-wheel and jumper. On the left side of the frame we have placed a lever x, with the letters st below it, and si above. If it is pushed up to si, the other end will come against a pin in the rack, and prevent it from falling, and will thus make the clock silent; and this is much more simple than the old-fashioned " strike and silent " apparatus, which we shall therefore not describe, especially as it is seldom used now. If the clock is required to strike quarters, a third "part" or train of wheels is added on the right hand of the going part; and its general construction is the same as the hour-striking part; only there are two more bells, and two hammers so placed that one is raised a little after the other. If there are more quarter-bells than two, the hammers are generally raised by a See also:chime-barrel, which is merely a cylinder set on the arbor of the striking-wheel (in that case generally the third in the train), with short pins See also:stuck into it in the proper places to raise the hammers in the order required for the tune of the chimes. The quarters are usually made to let off the hour, and this connexion may be made in two ways. If the chimes are different in tune for each quarter, and not merely the same tune repeated two, three and four times, the repetition movement must not be used for them, as it would throw the tunes into confusion, but the old locking-plate movement, as in turret clocks; and therefore, if we conceive the hour lifting-piece connected with the quarter locking-plate, as it is with the wheel N, in fig. 26, it is evident that the pin will See also:discharge the hour striking part as the fourth quarter finishes. But where the repetition movement is required for the quarters, the matter is not quite so simple. The principle of it may shortly be described thus. The quarters themselves have a rack and snail, &c., just like the hours, except that the snail is fixed on one of the hour-wheels M or N, instead of on the twelve-hour wheel, and has only four steps in it. Now suppose the quarter-rack to be so placed that when it falls for the fourth quarter (its greatest drop), it falls against the hour lifting-piece somewhere between 0 and N, so as to raise it and the click C. Then the pin Q will be caught by the click Qq, and so the lifting-piece will remain up until all the teeth of the quarter-rack are gathered up; and as that is done, it may be made to disengage the click Qq, and so See also:complete the letting off the hour striking part. This click Qq has no existence except where there are quarters. The method in which an alarum is struck may be understood by reference to either of the recoil escapements (See also:figs. r and 7). If a short hammer instead of a long pendulum be attached to the axis of the pallets, and the wheel be driven with sufficient force, it will evidently swing the hammer rapidly backwards and forwards; and the position and length of the hammer-head may be so adjusted as to strike a bell inside, first on one side and then on the other. As to the mode of letting off the alarumat the time required: if it was always to be let off at the same time all that would be necessary would be to set a pin in the twelve-hour wheel at the proper place to raise the lifting-piece which lets off the alarum at that time. But as the time must be capable of alteration, this discharging pin Must be set in another wheel (without teeth), which rides with a friction-spring on the socket of the twelve-hour wheel, with a small movable dial attached to it, having figures so arranged with reference to the pin that whatever figure is made to come to a small pointer set as a tail to the hour hand, the alarum shall be let off at that hour. The watchman's or tell-See also:tale clock, used when it is desired to make sure of a watchman being on the spot and awake all the night, is a clock with a set of spikes, generally 48 or 96, sticking out all round the dial, and a handle somewhere in the case, by pulling which one of the spikes which is opposite to it, or to some lever connected with it is pressed in. This wheel of spikes is carried round with the hour-hand, which in these clocks is generally a twenty-four hour one. It is evident that every spike which is seen still sticking out in the See also:morning indicates that at the particular time to which that spike belongs the watchman was not there to push it in—or at any rate, that he did not. At some other part of their See also:circuit, the inner ends of the pins are carried over a See also:roller or an inclined plane which pushes them out again ready for business the next night. The time at which workmen arrive at their work may be recorded by providing each of them with a numbered key with which he stamps his number on a moving tape, on which also the time is marked by a clock. Church and Turret Clocks.—Seeing that a clock—at least the going part of it—is a machine in which the only work to be done is the overcoming of its own friction and the resistance of the air, it is evident that when the friction and resistance are much increased it may become necessary to resort to expedients for neutralizing their effects, which are not required in a smaller machine with less friction. In a turret dock the friction is enormously increased by the great weight of all the parts; and the resistance of the wind, and sometimes See also:snow, to the motion of the hands, further aggravates the difficulty of maintaining a constant force on the pendulum; and besides that, there is the exposure of the clock to the dirt and dust which are always found in towers, and of the oil to a temperature which nearly or quite freezes it all through the usual cold of winter. This last circumstance alone will generally make the arc of the pendulum at least half a degree more in summer than in winter; and inasmuch as the time is materially affected by the force which arrives at the pendulum, as well as the friction on the pallets when it does arrive there, it is evidently impossible for any turret clock of the ordinary construction,"especially with large dials, to keep any constant rate through the various changes of temperature, weather and dirt to which it is exposed. Hence See also:special precautions, such as the use of remontoires and gravity escapements, have' to be observed in the design of large clocks that have any pretensions to accuracy, in order to ensure that the arc of the pendulum is not affected by See also:external circumstances, such as wind-pressure on the hands or dirt in the wheel-train. But such have been the improvements effected in electric clocks, that rather than go to the trouble and expense required by such precautions, it appears far preferable to keep an accurate time-piece in some sheltered position and use it with a, source of See also:electricity to drive the hands of the large dial.
See also:Electrical Clocks.—One of the first attempts to apply electricity to clocks was made by Alexander See also:Bain in 184o-185o. About the same time Sir C. See also:Wheatstone, R. L. See also: Electricity is applied to clocks in three main ways:—(1) in actuating timepieces which measure their own time and must therefore be provided with pendulums or balance wheels; (2) in reproducing on one or more dials the movements of the hands of a See also:master. clock, by the aid of electric impulses sent at regular intervals, say of a minute or a half-minute; and (3) in synchronizing ordinary clocks by occasional impulses sent from some accurate regulator at a distance. Electrically driven timepieces may be divided under two heads:—(a) those in which the electric current drives either the pendulum or some lever which operates upon it, which lever or pendulum in turn drives the clock hands; and (b) those time-pieces which are driven by a weight or spring which is periodically wound up by electricity—in fact electrical remontoires. The simplest clock of the first Fio. 27.-Turret Clock for See also:Hidalgo, See also:Mexico, driving four 8 ft. dials. character that could be imagined would be constructed by fastening an electromagnet with a soft iron core to the bottom of a pendulum, and causing it to be attracted as the pendulum swings by another electromagnet fixed vertically under it (fig. 29). As the pendulum approached the vertical and was say half an inch from its lowest point, the current would be switched on, and switched off as soon as the pendulum got to its lowest point. A very small attraction with this arrangement, probably about a See also:grain weight, acting through the 1 in. would drive a heavy pendulum. A switch would have to be worked in connexion with the pendulum. A See also:strip of ebonite with a small face of metal on the end of one side, such as a b (fig. 29) might be pivoted at one end on the pendulum with a weak spring to keep it where free along the rod. As the pendulum swung by this would be swept on its journey from left to right against a fixed pin P. This would complete the electric circuit down through the pendulum rod, round the coil on the bottom of the pendulum, through the switch into the pin P, thence through the fixed electromagnet, and so back to the See also:battery. On the return journey no contact would be made because only the ebonite face of the switch would touch P. The pendulum would thus receive an impulse every other vibration. We have de-scribed this switch, not to See also:advocate it, but to warn against its use. For the contact would be quite insufficient. In order that the switch might not unduly retard the pendulum it must be light, but this would make the pressure on P too light to be trustworthy. Moreover, the strength of the impulse would vary with the strength of the battery, and hence the arc would be repeatedly uneven. In contrast with this, let us consider a clock that is now giving excellent results at the See also:Observatory of See also:Neuchatel in See also:Switzerland on Hipp's system (La Pendule electrique de precision, Neuchatel, 1884 and 1891). The pendulum (fig. 30) consists of two rods of steel joined by four See also:bridges, one just below the suspension spring, the next about 12 in. lower, the next about half way down, and the last supporting a glass vessel of mercury which forms the bob. On the third of them is placed an iron See also:armature, references in the Appendix to Tobler's Die electrischen Uhren (See also:Leipzig, 1883), and a list of books given by F. See also:Hope Jones, Proc. Inst. Elec. Eng., 'goo, vol. 29. The history of electrical clocks is a long and complicated matter, for there are some 600 or 700 See also:patents for these clocks in Europe and See also:America, some containing the germs of valuable ideas but most pure rubbish. All that can be done is to select one or two prominent types of each class and give a brief description of their general construction. It is in the apparently simple matter of making and keeping the electrical contact that most of the systems of electrical time- keeping have failed, for want of See also:attention to the essential conditions of the problem. In practice every metal is covered with a thin film of non-conducting See also:oxide over which is another film of moisture, oil, dirt or air. Hence what is wanted is a good vigorous push of a blunted point or edge preferably obliquely upon a more or less yielding surface so as to get a rubbing action. Thus if the stiff spring a b (fig. 28) were stabbed down on the oblique surface C D a good contact would invariably result, provided that the metals employed were See also:gold, See also:platinum or some not easily oxidizable metal. Or again, if a mercury surface be simply touched with a pin, the slight sparking that is produced on making the current will soon form a little See also:pile of dirty oxide at the point of entry, and the contact will frequently fail. If it be necessary to have a mercury contact, the pin must be well driven in below the surface of the mercury or else swept through it as an See also:oar is swept through the water. Another form of electrical contact that acts well is a knife edge brought into contact with a series of fine elastic strips of metal laid parallel to one another like the fingers of a hand. The best metal for contacts, if they are to See also:bear hard usage, is either See also:silver or gold or a mixture of 40% See also:iridium with 6o% of platinum. A pressure of some 15 grammes, at least, is needful to secure a good contact. As to the source of current for driving electrical clocks, if Leclanche cells be used they should preferably be kept in the open air under cover so as not to dry up. If See also:direct electric current is available from electric light mains or the accumulators used for lighting a private house, so much the better. Of course the pressure of 5o or See also:loo volts used for lighting would be far too great for clock-driving, where only the pressure of a few volts is required. But it is easy by the insertion of suitable resistances, as for instance one or more incandescent lamps, to weaken down (faulty design). which works between the poles of an electromagnet fixed to the case, and by which the pendulum is actuated. The circuit is closed and broken by a flipper, which is swayed to and fro by a block fixed to the pendulum at the second bridge. As long as the flipper is merely swayed, no contact takes place, but when the arc of vibration of the pendulum is diminished the flipper does not clear the block but is caught by a nick in it, and forced downwards. In this way the circuit is closed. Fig. 31 is a dia- See also:gram of the apparatus. When the block g attached to the pendulum catches and presses down the flipper s, the lever 11 is rocked over, so that a contact is made at k, and the current which enters the lever 1 through the knife edge m, runs through the second lever n n, down through the knife edge o to the battery, and through the electromagnet b which causes the armature a to be attracted. As the block g goes on and releases s, the lever 1 again falls upon the rest p, the lever n follows it a part of the way till it is stopped by the contact q; this shortcircuits the electromagnet and prevents to a large extent the formation of an induced current. It is claimed that sparking is by this method almost entirely avoided. It is only when s is caught in the notch of the block g that s is pressed down, so that the electric attraction only takes place every few vibrations. This ingenious arrangement makes the working of the clock nearly independent of the strength of the battery, for if the battery is strong the impulses are fewer and the average arc remains the same. The clock is enclosed in an airtight glass case so as to avoid barometric error. It was tested in 1905 at the Neuchatel observatory. In winter in a room of a mean temperature of 350 F. it was 4 sec. too slow, in summer when the temperature was 7o°, it was a sec. too fast. In the succeeding winter it became .53 sec. too slow again, thus gain- See also:ing a little in summer and losing in winter. Its average variation from its daily rate was, however, only •o33 sec. In another system originated by G. Froment, a small weight is raised by electricity and allowed to fall upon an arm sticking out at right angles to the pendulum in the plane of its motion, so as to urge it onwards. The weight is only allowed to rest on the arm during the downward swing of the pendulum. The method is not theoretically good, as the impulse is given at the end of the vibration of the pendulum instead of at its middle positron. In the clock invented by C. Fery (chef des travaux pratiques at the Ecole de Physique et Chimie, Paris), an electric impulse is given at every vibration, not by a battery but by means of the uniform movement of an armature which is alternately pulled away from and pushed towards a permanent horseshoe magnet. Currents are thus induced in a bobbin of fine See also:wire placed between the poles of the horseshoe maa.nat. The movements of thearmature are produced by another horseshoe magnet actuated by the primary current from a battery which is turned on and off by the swinging of the pendulum. The See also:energy of the induced current that drives the clock depends solely on the total movement of the armature, and is independent of whether that movement be executed slowly or rapidly, and therefore of the strength of the battery. Electrical remontoires possess great advantages if they can be made to operate with certainty. For they can be made to wind up a scape-wheel just as is done in the case of the arrangement shown in fig. 16 so as to constitute a spring remontoire, or better still they can be made to raise a weight as in the case of the gravity train remontoire (fig. 15) but without the complications of wheel-work shown in that contrivance. Of this type one of the best known is that of H. Chesters See also:Pond. A mainspring fixed on the arbor of the hour wheel is wound up every hour by means of another toothed wheel riding loose on the same arbor and driven by a small See also:dynamo, to which the other end of the mainspring is attached. As soon as the hour wheel has made one revolution (driven round by the spring), a contact switch is closed whereupon the dynamo winds up the spring again exactly as the train and fly wind up the spring in fig. 15. These clocks require a good deal of power, and not being always trustworthy seem to have gone out of use. A contrivance of this kind now in use is that patented by F. Hope Jones and G. B. See also:Bowen, and is represented in fig. 32. A pendulum is driven by the scape-wheel A, and pallets B B in the usual way. The scape-wheel is driven by another wheel C which, in turn, is driven by the weighted lever D supported by click E engaging the ratchet wheel F. This lever is centred at G and has an See also:extension H at right angles to it. J is an armature of soft iron pivoted at K and worked by the electromagnet M. D gradually falls in the act of driving the clock by turning the wheels C and A until the contact plate on the arm H meets with the contact screw L at the end of the armature J, thus completing the electrical circuit from terminal T to terminal T' through the electromagnet M, and through any number of step-by-step dial movements which may be included in the same series circuit. The armature is then drawn towards the magnet with rapid acceleration, carrying the lever D with it. The armature is suddenly arrested by the poles of the magnet, but the momentum of the lever D carries it farther, and the click E engages another tooth of the ratchet F. A See also:quick break of the circuit is thus secured, and the contact at L is a good one, first because the whole of the energy required to keep the clock going, or in other words the energy required to raise the lever D is ment of Hipp Clock. mechanically transmitted through its surfaces at each operation, and secondly, owing to the arrangement of the fulcrums at G and K which secure a rubbing contact. The duration of the con-tact is just that necessary to accomplish the work which has to be done, and it is remarkable that when used to operate large circuits of electrically propelled dials the duration accommodates itself to their exact requirements and the varying conditions of battery and self-See also:induction. The ratchet wheel F is usually mounted loosely upon its arbor and is connected to the wheel C by means of a spiral spring, which in See also:conjunction with the back-stop click P maintains the turning force on the wheelwork at the instant when the lever D is being raised. Electrically driven dials usually consist of a ratchet wheel driven by an electrically moved pall. Care has to be taken that the pushes of the pall do not cause the ratchet wheel to be impelled too far. The anchor escapement of a common See also:grand-See also:father's clock can be made to drive the works by means of an electromagnet, the pendulum being removed. With a common anchor escapement the scape-wheel can be driven round by wagging the anchor to and fro. All then that is necessary is to fix a piece of iron on the anchor so that its weight pulls the anchor over one way, while an electromagnet pulls the iron the other. Impulses sent through the electromagnet will then drive the clock. If the clock is wound up in the ordinary way the motion will be so much helped that the electric current has very little to do, and thus may be very feeble. Fig. 33 shows the dial-driving de-vice of Hope Jones's clock. Each time that a current is sent by the master-clock, the electromagnet B attracts the pivoted armature C, and when the current ceases the lever D with the projecting arm E is driven back to its old position by the spring F, thus driving the wheel A forward one division. G is a back-stop click, and H, I, fixed stops. It seems doubtful whether in large towns a number of dials could be electrically driven from a distance because of the large amount of power that would have to be transmitted. But for large buildings, such as hotels, they are excellent. One master-clock in the cellar will drive a See also:hundred or so placed over the See also:building. The master-clock may itself be driven by electricity, but it will require the services from time to time of some one to correct the time. Even this labour may be avoided if the master-clock is synchronized, and as synchronization requires but a small See also:expenditure of force, it can be done over large areas. Hence the future of the clock seems to be a series of master-clocks, electrically driven, and synchronized one with another, in various parts of a See also:city, from each of which a number of dials in the vicinity are driven. Electrical synchronization was worked out by Louis Breguet and others, and a successful system was perfected in England by J. A. See also:Lund. The leading principle of the best systems is at each hour to cause a pair of fingers or some equivalent device to close upon the minute hand and put it exactly to the hour. Other systems are designed to retard or to accelerate the pendulum, but the former appears the more practical method. There is probably a future before synchronization which will enable the services of a clockmaker to be largely dispensed with and relegate his work merely to keeping the See also:instruments in repair. See also:Miscellaneous Clocks.—Some small clocks are made to go for a year. They have a heavy balance wheel of brass weighing about 2 lb and about 22 in. in diameter, suspended from a point above its centre by a fine watch spring about 4 in. long. The crutch engages with the upper part of the spring, and as thebalance wheel swings the pallets are actuated. The whole clock is but a large watch with a suspended balance wheel, oscillating once in about 8 seconds. Unless the suspension spring be compensated for temperature, such clocks gain very much in winter. An ingenious method of driving a clock by water has been proposed. As the pendulum oscillates to one side, an arm on it rises and at last lightly touches a drop of water hanging from a very fine nozzle; this drop is taken off and carried away by the arm, to be subsequently removed by See also:adhesion to an escape See also:funnel placed below the arm. Hence at each double vibration of the pendulum part of the work done by a drop of water falling through a short distance is communicated to the pendulum, which is thus kept in motion as long as the water lasts. At this rate a See also:gallon of water ought to drive the clock for 40 hours. Care of course must be taken to keep the water in the See also:reservoir at a constant level, so that the drops formed shall be uniform. If it were worth while, no doubt the oscillations of a pendulum working in a vacuum could be maintained by the communication and discharge at each oscillation of a slight See also:charge of electricity; or again, heat might at each oscillation be communicated to a thermo-electric junction, and the resulting current used to drive the pendulum. The expansions and contractions of metal rods under the influence of the changes of temperature which take place in the course of each night and day have also been employed to keep a clock wound up, and if there were t.ny need for it no doubt a small See also:windmill rotating at the top of a tower would easily keep a turret clock fully wound, by a simple arrangement which would gear the going barrel of the clock to the wind vane motion, whenever the weight had fallen too See also:low, and release it when the winding up was completed. Even a See also:smoke See also:jack would do the same office for a See also:kitchen clock. The methods of driving astronomical telescopes by means of clockwork will be found in the article See also:TELESCOPE. Measurements of small intervals of time are performed by means of chronographs which in principle depend on the use of isochronous vibrating tuning-forks in place of pendulums. In practice it is needful in most cases that an observer should intervene in time measurements, although perhaps by means of a revolving photographic film a transit of the sun might be timed with extraordinary accuracy. But if the transit of .a star across a wire is to be observed, there is no mode at present in use of doing so except by the use of the human See also:eye, See also:brain and hand. Hence in all such observations there is an See also:element of See also:personal error. Unfortunately we cannot apply a microscope to time as we can to space and make the See also:cycle of events that takes place in a second last say for five minutes so as to time them truly. By personal observations the divisions of a second cannot in general be made more accurately than to 3'-o or - of a second. The most rapid See also:music player does not strike a See also:note more than io or 12 times in a second. It is only in case of recurring phenomena that we can make personal observations more accurate than this by taking the mean of a large number of observations, and allowing for personal error. For the purpose of determining See also:longitude at See also:sea accuracy to 116 of a second of time would find the place to about 20 yards. It seems to follow that the extent to which astronomical clocks can be made accurate, viz. to rally of a second average variation from their mean daily rate, or one two-and-a-half millionth of 24 hours, is a degree of accuracy sufficient for present purposes, and it seems rather doubtful whether See also:mechanical See also:science will in the case of clocks be likely to reach a much higher figure. In the 17th century it was a favourite device to make a clock show sidereal time as well as mean solar time. The length of the sidereal day is to the mean solar day as •99727 to r, and various attempts have been made by trains of wheels to obtain this relation—but all are somewhat complicated. Magical clocks are of several kinds. One that was in See also:vogue about 188o had a See also:bronze figure on the top with outstretched arm holding in its hand the upper part of the spring of a pendulum, Fic. 33.-Hope Jones's Dial-driving Device. about ro in. long. The pendulum had apparently no escapement and the See also:puzzle was how it was maintained in motion. It was impossible to detect the See also:mystery by the aid of the eye alone; the truth, however, was that the whole figure swung to and fro at each oscillation of the pendulum, to an amount of See also:gig of an inch on the outside rim of the base. A movement of -g of an inch per half second of time is imperceptible; it would be equivalent to See also:perception of motion of the minute hand of a clock about 6 in. in diameter, which is almost impossible. The connexion of the figure to the anchor of the escapement was very complicated, but clocks of the kind kept See also:fair time. A See also:straw, poised near the end on a See also:needle and with the short end See also:united by a See also:thread to the bronze figure, makes the motion apparent at once and discloses the See also:trick. Another magical clock consists of two disks of thin sheet glass mounted one close behind the other, one carrying the minute hand and the other the hour hand. The disks rest on rollers which rotate and turn them round. The front and back of the movable disks are covered by other disks of glass surrounded by a frame, so that the whole looks simply like a single sheet of glass mounted in a frame, in the centre of which the hands rotate, without any visible connexion with the works of the clock. Clocks have been made with a sort of balance wheel consisting of a thread with a ball at the end which winds backwards and forwards spirally round a rod. In others a swing or see-saw is attached to the pendulum, or a See also:ship under See also:canvas is made to oscillate in a heavy sea. In others the time is measured by the fall of a ball down an inclined plane, the time of fall being given by the formula t='f (2s/gsina), where s is the length of the incline and a the inclination. But friction so modifies the result as to render experiment the only mode of adjusting such a clock. Sometimes a clock is made to serve as its own weight, as for instance when a clock shaped like a See also:monkey is allowed to slide down a rope wound round the going barrel. Or the clock is made of a cylindrical shape outside and provided with a weighted arm instead of a going barrel; on being put upon an incline, it rolls down, and the fall supplies the See also:motive power. Clocks are frequently provided with chimes moved exactly like musical boxes, except that the pins in the barrel, instead of flipping musical combs, raise hammers which fall upon bells. The driving barrel is let off at suitable intervals. The See also:cuckoo clock is a See also:pretty piece of mechanism. By the push of a wire given to the body of the See also:bird, it is bent forward, the wings and tail are raised and the See also:beak opened. At the same time two weighted See also:bellows measuring about r X2 in. are raised and successively let drop. These are attached to small wooden See also:organ pipes, one tuned a fifth above the other, which produce the notes. Phonographs are also attached to clocks, by which the hours are called instead of See also:rung. Clocks are also constructed with conical pendulums. It is a See also:property of the conical pendulum that if swung round, the time of one complete revolution is the same as that of the double vibration of a pendulum equal in length to the vertical distance of the bob of the conical pendulum below its point of support. It follows that if the driving force of such a pendulum can be kept constant (as it easily can by an electric contact which is made at every revolution during which it falls below a certain point) the clock will keep time; or friction can be introduced so as to reduce the speed whenever the pendulum flies round too fast and hence the bob rises. Or again by suitable arrangements the bob may be made to move in certain curves so as to be isochronous. Plans of this kind are employed rather to drive telescopes, phonographs and other See also:machines requiring uniform and steady movement. Comical and performing clocks were very popular in the r 5th and 16th centuries. One at See also:Basel in Switzerland was arranged so as gradually to protrude a long See also:tongue as the pendulum vibrated. It is still to be seen there in the museum. The famous clock at See also:Strassburg, originally constructed in 1574, remade in 1842, displays a whole series of scenes, including processions of the apostles and other persons, and a cock that crows. A fine clock at See also:Venice has two rather stiff bronze giants that strike the hours. Clocks with complicated movements representing the positions of the heavenly bodies and the days of the See also:week and month, See also:allowance being made for leap year, were once the delight of the curious. Repeating clocks, which sounded the hours when a string was pulled, were once popular. The string simply raised the lifting piece and let the clock strike as the hands would do when they came to the hour. This was of use in the old days when the only mode of striking a light at night was with a flint. and steel, but See also:lucifer matches and the electric light have rendered these clocks obsolete. Testing Clocks.—The average amount by which a clock gains or loses is called its mean or average daily rate. A large daily rate of error is no See also:proof that a clock is a See also:bad one, for it might be completely removed by pendulum See also:adjustment. What is required is that the daily rate shall be uniform, that is, that the clock shall not be gaining (or losing) more on one day than on another, or at one period of the same day than at another. In fig. 34 A B is a curve in which the abscissae represent intervals of time, the ordinates the number of seconds at any time by which the clock is wrong. The curve C D is one in which the ordinates are proportional to the tangents of the angles of inclination of the curve A B to the axis of x, that is dy/dx. Whenever the line A B is horizontal, C D cuts the axis of x. In a clock having no variation in its daily rate the curve A B would become a straight line, though it might be inclined to the axis of x, and C D, also a straight line, would be parallel to the axis of x, though it might not coincide with it. In a clock set to exact time and having no variations of daily rate, both the curves would be straight lines and would coincide with the axis of x. The curve C D, known as the curve of variation of daily rate, will generally be found to follow changes of day and night, and of tem- perature, and the fluctuations of the barometer and See also:hygrometer; it is the curve which reveals the true character of the clock. Hence in testing a clock two things have to be determined: first, the daily rate of error, and second, the average variations from that daily rate, in other words the irregularities of going. To test a clock well six months' or a year's trial is needed, and it is desirable to have it subjected to considerable changes of temperature. The bibliography of horology is very extensive. Among modern works Lord Grimthorpe's Rudimentary Treatise on Clocks, Watches and Bells (8th edition, London, 1903) is perhaps the most convenient. Many references to older literature will be found in Thomas Reid's Treatise on Clock and Watchmaking (1849). (G.; H. H. C.) Decorative Aspects.—In See also:art the clock occupies a position of considerable distinction, and See also:antique examples are prized and collected as much for the decorative qualities of their cases as for the excellence of their time-keeping. French and English See also:cabinet-makers have especially excelled, although in entirely different ways, in the making of clock cases. The one aimed at comely utility, often made actually beautiful by fit proportion and the employment of finely grained See also:woods; the other sought a bold and dazzling splendour in which See also:ornament overlay material. It was not in either See also:country until the latter part of the 17th century that the cabinet-maker's opportunity came. The See also:bracket or chamber clock gave comparatively little scope to the worker in wood—in its earlier period, indeed, it was almost invariably encased in brass or other metal; and it was not until the introduction of the long pendulum swinging in a small space that it became customary to encase clocks in decorative woodwork. ' The long or " grandfather " clock See also:dates from about the fourth quarter of the 17th century—what is, perhaps, the earliest surviving English dated specimen is inscribed with the date 1681. Originally it was a development !!II^^^^^^^^^^^^^^^!^^^ ^^^^\\^^^^^r~.i^^^iii ^!^^S^lol5i^^^^!^^^^^ M^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^!^^^!^^^^^^^^ ^^!^^!!1/^^!Pi!^!^allThE 1^!^^^^1I^WIMO1^!^^.?.**i ! V U^^11^^^^^^^^^^^^^^ ^^^^ ^^'/^^^^!^!^^^^^^^ ^^^^MIKEI ^!^^!^N !^^! a 7 be g8 ~V6 3 0 D of the See also:dome-shaped bracket clock, and in the older examples the characteristic dome or See also:canopy is preserved. The first time-keepers of this type had oaken cases—indeed See also:oak was never entirely abandoned; but when See also:walnut began to come into favour a few years later that beautifully marked wood was almost invariably used for the choicest and most costly specimens. Thus in 1698 the See also:dean and See also:chapter of St Paul's cathedral paid the then very substantial See also:price of X14 for an inlaid walnut long-cased eight-day clock to stand in one of the vestries. The rapidity with which the new See also:style came into use is suggested by the fact that while very few long clocks can be certainly dated before 169o, between that year and the end of the century there are many examples. Throughout the 18th century they were made in myriads all over England, and since they were a prized See also:possession it is not surprising that innumerable examples have survived. Vary as they may in height and girth, in wood and dial, they are all essentially alike. In their earlier years their faces were usually of brass engraved with cherubs' heads or conventional designs, but eventually the less See also:rich white face See also:grew common. There are two varieties—the eight-day and the See also:thirty-hour. The latter is but little esteemed, notwithstanding that it is often as decorative as the more expensive clock. The favourite walnut case of the See also:late 17th and early 18th century gave place in the course of a See also:generation to See also:mahogany, which retained its primacy until the introduction of cheaper clocks brought about the supersession of the long-cased variety. Many of these cases were made in See also:lacquer when that material was in vogue; satinwood and other costly foreign timbers were also used for bandings and inlay. The most elegant of the " grand-father " cases are, however, the narrow-waisted forms of the See also: The "grandfather" case was also made in the Low Countries, of generous height, very swelling and bulbous. See F. J. Britten, Old Clocks and Watches and their Makers (2nd edition, London, 19o4); Mathieu Planchon, L'Horloge, son histoire retrospective, pittoresque et artistique (Paris, 1899). (J. 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