him, though in the prime of life, of the discussions through which he had been dragged. We have referred to Warren Hastings's impeachment, but there is a more recent parallel. The marquis of Dalhousie did almost as much to complete the territorial area and civilized administration of British India in his eight years' term of office as Lord Clive to found the empire in a similar period. As Clive's accusers sought a new weapon in the great famine of 1770, for which he was in no sense responsible, so there were critics who accused Dalhousie of having caused that mutiny which, in truth, he would have prevented had the British Government listened to his counsel not to reduce the small English army in the country. Clive tells us his own feelings in a passage of first importance when we seek to form an opinion on the fatal act by which he ended his life. In the greatest of his speeches, in reply to Lord North, he said,-"My sitnation, sir, has not been an easy one for these twelve months past, and though my conscience could never accuse me, yet I felt for my friends who were involved in the same censure as myself. . . . I have been examined by the select committee more like a sheep-stealer than a member of this House." Fully accepting that statement, and believing him to have been purer than his accusers in spite of temptations unknown to them, we see in Clive's end the result merely of physical suffering, of chronic disease which opium failed to abate, while the worry and chagrin caused by his enemies gave it full scope. This great man, who fell short only of the highest form of moral greatness on one supreme occasion, but who did more for his country than any soldier till Wellington, and more for the people and princes of India than any statesman in history, ceased to exist on the 22d November, 1774, in his fiftieth year.

The portrait of Clive, by Dance, in the Council Chamber of Government House, Calcutta, faithfully represents him. He was slightly above middle-size, with a countenance rendered heavy and almost sad by a natural fulness above the eyes. Reserved to the many, he was beloved by his own family and friends. His encouragement of scientific undertakings like Major Rennell's surveys, and of philological researches like Mr. Gladwin's, was marked by the two honorary distinctions of F.R.S. and LL.D.

The best authorities for his life, which has yet to be worthily written, are-article "Clive," in the second or Kippis's edition of the Biographia Britannica, from materials supplied by his brother, Archdeacon Clive, by Henry Beaufoy, M.P.; Broome's History of the Bengal Army; Aitchison's Treaties, second edition, 1876; Orme's History; and Malcolm's Life. (G. SM.)

CLOCKS. The origin of clock work is involved in great obscurity. Notwithstanding the statements by many writers that clocks, horologia, were in use so early as the 9th century, and that they were then invented by an archdeacon of Verona, named Pacificus, there appears to be no clear evidence that they were machines at all resembling those which have been in use for the last five or six centuries. But it may be inferred from various allusions to horologia, and to their striking spontaneously, in the 12th century, that genuine clocks existed then, though there is no surviving description of any one until the 13th century, when it appears that a horologium was sent by the sultan of Egypt in 1232 to the Emperor Frederick II. "It resembled a celestial globe, in which the sun, moon, and planets moved, being impelled by weights and wheels, so that they pointed out the hour, day, and night with certainty." A clock was put up in a former clock tower at Westminster with some great bells in 1288, out of a fine imposed on a corrupt chief-justice, and the motto Discite justitiam, moniti, inscribed upon it. The bells were sold or rather, it is said, gambled away, by Henry VIII. In 1292 one is mentioned in Canterbury Cathedral as costing £30. And another at St. Albans, by R. Wallingford the abbot in 1326, is said to have been such as there was not in all Europe, showing various astronomical phenomena. A description of one in Dover Castle with the date 1348 on it was published by the late Admiral Smyth, P.R.A.S., in 1851, and the clock itself was exhibited going, in the Scientific Exhibition of 1876. In the early editions of this Encyclopædia there was a picture of a very similar one, made by De Vick for the French king Charles V. about the same time, much like our common clocks of the last century, except that it had a vibrating balance, but no spring, instead of a pendulum, for pendulums were not invented till three centuries after that.

13

The general construction of the going part of all clocks, except large or turret clocks, which we shall treat sep arately, is substantially the same, and fig. 1 is a section of any ordinary house clock. B is the barrel with the rope 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 prolonged pillars p, p, which (4 or 5 in number) connect the plates or frame of the clock together, though the dial is commonly, but for no good reason, set on to the front 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 action of which is shown more fully in fig. 14. The intermediate wheel r in this drawing is for a purpose which will be described hereafter, and for the 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 e which

is called the centre pinion, on the arbor of the centre whee C, which goes through to the dial, and carries the long, or minute-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 åre usually called), C will have 64 teeth and D 60, in a clock of which the scape-wheel 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 pivot turns in a cock OFQ screwed on to the back plate. From the pallet arbor at F descends the crutch Ff, ending in the 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 close to the end of that arbor as possible a point too frequently neglected.

We may now go to the front (or left hand) of the clock, and describe the dial or "motion-work." The minute-hand fits on to a squared end of a 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 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 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 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 pipe carrying the hour hand, and riding on the former socket, or rather (in order to relieve the centre arbor of that extra weight) on an intermediate socket fixed to the 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 catgut line passing through a pulley attached to the weight, the other end of the cord being tied to some convenient place in the clock frame or seat-board, to which it is fixed by screws through the lower pillars. It has usually been the practice to make the case of house clocks and astronomical clocks not less than 6 feet high; but that is a very unnecessary waste of space and materials; for by either diminishing the size of the barrel, or the number of its turns, by increasing the size of the great wheel by one-half, or hanging the weights by a treble instead of a double line, a case just long enough for the pendulum will also be long enough for the fall of the weights in 7 or 8 days. Of course the weights have to be increased in the same ratio, and indeed rather more, to overcome the increased friction; but that is of no consequence.

PENDULUM.

The claim to the invention of the pendulum, like the claim to most inventions, is disputed; and we have no intention of trying to settle it. It was, like many other discoveries and inventions, probably made by various persons independently, and almost simultaneously, when the state of science had become ripe for it. The discovery of that peculiarly valuable property of the pendulum called isochronism, or the disposition to vibrate different arcs in very nearly the same time (provided the arcs are none of them large), is commonly attributed to Galileo, in the well-known story of his being struck with the isochronism of a chandelier hung by a long chain from the roof of the church at Florence. And Galileo's son appears as a rival of Avicenna, Huyghens, Dr. Hooke, and a London clockmaker named Harris, for the honor of having first applied the pendulum to regulate the motion of a clock train, all in the early part of the 17th century. Be this as it may, there seems little doubt that Huyghens was the first who mathematically investigated, and therefore really knew, the true nature of those properties of the pendulum which may now be found explained in any mathematical book on mechanics. He discovered that if a simple pendulum (i.e., a weight or bob consisting of a single point, and hung by a rod or string of no weight) can be made to describe, not a circle, but a cycloid of which the string would be the radius of curvature at the lowest point, all its vibrations, however large, will be performed in the same time. For a little distance near the bottom, the circle very nearly coincides with the cycloid; and hence it is that, for small arcs, a pendulum vibrating as usual in a circle is nearly enough isochronous for the purposes of horology; more especially when contrivances are introduced either to compensate for the variations of the arc, or, better still, to destroy them altogether, by making the force on the pendulum so constant that its arc may never sensibly

vary.

The difference between the time of any small are of the circle and any arc of the cycloid varies nearly as the square of the circular are; and again, the difference between the times of any two small and nearly equal circular arcs of the same pendulum, varies nearly as the arc itself. If a, the arc, is increased by a small amount da, the pendulum will lose 10800ada seconds a day, which is rather more than 1 second, if a is 2° (from zero) and da is 10', since the numerical value of 2° is 035. If the increase of arc is considerable, it will not do to reckon thus by differentials, but we must take the difference of

time for the day as 5400 (a,2-a2), which will be just 8 seconds if a = 2° and a,- 3°. For many years it was thought of great importance to obtain cycloidal vibrations of clock pendulums, and it was done by making the suspension string or spring vibrate between cycloidal cheeks, as they were called. But it there is and can be no such thing in reality as a simple penduwas in time discovered that all this is a delusion,-first, because lum, and cycloidal cheeks will only make a simple pendulum vibrate isochronously; secondly, because a very slight error in the form of the cheeks (as Huyghens himself discovered) would do more harm than the circular error uncorrected, even for an arc of 10°, which is much larger than the common pendulum arc; thirdly, because there was always some friction or adhesion between the cheeks and the string; and fourthly (a reason which applies equally to all the isochronous contrivances since invented), because a common clock escapement itself generally tends to produce an error exactly opposite to the circular error, or to make the pendulum vibrate quicker the farther it swings; and therefore the circular error is actually useful for the purpose of helping to counteract the error due to the escapement, and the clock goes better than it would with a simple pendulum, describing the most perfect cycloid. At the same time, the thin spring by which pendulums are always suspended, except in some French clocks where a silk string is used (a very inferior plan), causes the pendulum to deviate a little from circular and to approximate to cycloidal motion, because the bend does not take place at one point, but is spread over some length of the spring.

The accurate performance of a clock depends so essentially on the pendulum, that we shall go somewhat into detail respecting it. First then, the time of vibration depends entirely on the length of the pendulum, the effect of the spring being too small for consideration until we come to differences of a higher order. But the time does not vary as the length, but only as the square root of the length; i.e., a pendulum to vibrate two seconds must be four times as long as a seconds pendulum. The relation between the time of vibration and the length of a pendulum is expressed thus:

t, where t is the time in seconds, the well-known symbol for 3.14159, the ratio of the circumference of a circle to its diameter, the length of the pendulum, and g the force of letter g, in the latitude of London, is the symbol for 32.2 feet, gravity at the latitude where it is intended to vibrate. This that being the velocity (or number of feet per second) at which a body is found by experiment to be moving at the end of the first second of its fall, being necessarily equal to twice the actual number of feet it has fallen in that second. Consequently, the length of a pendulum to beat seconds in London is 39.14 inches. But the same pendulum carried to the equator where the force of gravity is less, would lose 2 minutes a day The seconds we are here speaking of are the seconds of a common clock indicating mean solar time. But as clocks aro also required for sidereal time, it may be as well to mention the proportions between a mean and a sidereal pendulum. A sidereal day is the interval between two successive transits over the meridian of a place by that imaginary point in the heavens called Y, the first point of Aries, at the intersection of the equator and the ecliptic; and there is one more sidereal day than there are solar days in a year, since the earth has to turn more than once round in space before the sun can come a second time to the meridian, on account of the earth's own motion in its orbit during the day. A sidereal day or hour is shorter than a mean solar one in the ratio of 99727, and consequently a sidereal pendulum must be shorter than a mean time pendulum in the square of that ratio, or in the latitude of London the sidereal seconds pendulum is 38.87 inches. As we have mentioned what is 0 or 24 o'clock by sidereal time, we may as well add, that the mean day is also reckoned in astronomy by 24 hours, and not from midnight as in civil reckoning, but from the following noon; thus, what we call 11 A.M. May 1 in common life is 23 h. April 30 with astronomers.

It must be remembered that the pendulums whose lengths we have been speaking of are simple pendulums; and as that is a thing which can only exist in theory, the reader may ask how the length of a real pendulum to vibrate in any required time is ascertained. In every pendulum, that is to say, in every body hung so as to be capable of vibrating freely, there is a certain point, always somewhere below the centre of gravity, which possesses these remarkable properties-that if the pendulum were turned upside down, and set vibrating about this point, it would vibrate in the same time as before, and moreover, that the distance of this point from the point of suspension is exactly the length of that imaginary simple pendulum which would vibrate in the same time. This point is therefore called the centre of oscillation. The rules for finding it by calculation are too complicated for ordinary use, except in bodies of certain simple and regular forms; but they are fortunately not requisite in practice, because in all clock pendulums the centre of oscillation is only a short distance below the centre of gravity of the whole pendulum, and generally so near to

the centre of gravity of the bob-in fact a little above it-that there is no difficulty in making a pendulum for any given time of vibration near enough to the proper length at once, and then adjusting it by screwing the 'bob up or down until it is found to vibrate in the proper time.

Revolving or Conical Pendulum.

Thus far we have been speaking of vibrating pendulums; but the notice of pendulums would be incomplete without some allusion to revolving or conical pendulums, as they are called, because they describe a cone in revolving. Such pendulums are used where a continuous instead of an intermittent motion of the clock train is required, as in the clocks for keeping an equatorial telescope directed to a star, by driving it the opposite way to the motion of the earth, to whose axis the axis on which the telescope turns is made parallel. Clocks with such pendulums may also be used in bedrooms by persons who cannot bear the ticking of a common clock. The pendulum, instead of being hung by a flat spring, is hung by a thin piece of pianoforte wire; and it should be understood that it has no tendency to twist on its own axis, and so to twist off the wire, as may be apprehended; in fact, it would require some extra force to make it twist, if it were wanted to do so. The time of revolution of such a pendulum may be easily ascertained as follows:-Let be its length; a the angle which it makes with the vertical axis of the cone which it describes; the angular velocity; then the centrifugal force = sin. a; and as this is the force which keeps the pendulum away from the vertical, it must balance the force which draws it to the vertical, which is g tan. a: and therefore the angular velocity, or the angle l cos. @ described in a second of time; and the time of complete revo2T l cos. a lution through the angle 360° or 2x is -2x that is to say, the time of revolution of a pendulum of any given length is less than the time of a double oscillation of the same pendulum, in the proportion of the cosine of the angle which it

9

=

makes with the axis of revolution to unity.

A rotary pendulum is kept in motion by the train of the clock ending in a horizontal wheel with a vertical axis, from which projects an arm pressing against a spike at the bottom of the pendulum; and it has this disadvantage that any inequality in the force of the train, arising from variations of friction or any other cause, is immediately transmitted to the pendulum; whereas it will be seen that in several kinds of escapements which can be applied to a vibrating pendulum, the variations of force can be rendered nearly or quite insensible. And it is a mistake to imagine that there is any selfCorrecting power in a conical pendulum analogous to that of the governor of a steam-engine; for that apparatus, though it is a couple of conical pendulums, has also a communication by a system of levers with the valve which supplies the steam. The governor apparatus has itself been applied to telescopedriving clocks, with a lever ending in a spring which acts by friction on some revolving plate in the clock, increasing the friction, and so diminishing the force as the balls of the governor fly out farther under any increase in the force. And with the addition of some connection with the hand of the observer, by which the action can be farther moderated, the motion can be made sufficiently uniform for that purpose.

Various other contrivances have been invented for producing a continuous clock-motion. The great equatorial telescope at Greenwich is kept in motion by a kind of water clock called in books on hydrostatics Barker's Mill, in which two horizontal pipes branching out from a vertical tubular axis have each a hole near their ends on opposite sides, from which water flows, being poured constantly into the tubular axis, which revolves on a pivot. The resistance of the air to the water issuing from the holes drives the mill round, and there are means of regulating it. Another plan is to connect a clock train having a vibrating pendulum with another clock having a conical pendulum by one of the lower wheels in the train, with a spring connection; the telescope is driven by the revolving clock train, and the other pendulum keeps it sufficiently in order, though allowing it to expatiate enough for each beat of the pendulum. The more complicated plan of Wagner of Paris described in Sir E. Beckett's Rudimentary Treatise on Clocks and Watches and Belle does not appear to have ever come into use, and therefore it is now omitted.

Pendulum Suspension.

The suspension of the pendulum on what are called knifeedges, like those of a scale-beam, has often been advocated. But though it may do well enough for short experiments, in which the effects of the elasticity of the spring are wanted to be eliminated, it fails altogether in use, even if the knife-edges and the plates which carry them are made of the hardest stones. The suspension which is now used universally, in all but some inferior foreign clocks, which have strings instead, is a thin and

short spring with one end let into the top of the pendulum, and the other screwed between two chops of metal with a pin through them, which rests firmly in a nick in the cock which carries the pendulum as shown in fig. 2 a little farther on; and the steadiness of this cock, and its firm fixing to a wall, are essential to the accurate performance of the clock. The thinner the spring the better; provided, of course, it is strong enough to carry the pendulum without being bent beyond its elasticity, or bent short; not that there is much risk of that in practice. Pendulum springs are much oftener too thick than too thin; and it is worth notios that, independently of their greater effect on the natural time of vibration of the pendulum, thick and narrow springs are more liable to break than thin and broad ones of the same strength. It is of great importance that the spring should be of uniform thickness throughout its breadth; and the bottom of the chops which carry it should be exactly horizontal; otherwise the pendulum will swing with a twist, as they may be often seen to do in illmade clocks. If the bottom of the chops is left sharp, where they clip the spring, it is very likely to break there; and therefore the sharp edges should be taken off.

The bob of the pendulum used to be generally made in the shape of a lens, with a view to its passing through the air with the least resistance. But after the importance of making the bob heavy was discovered, it became almost necessary to adopt a form of more solid content in proportion to its surface. A sphere has been occasionally used, but it is not a good shape, because a slight error in the place of the hole for the rod may make a serious difference in the amount of weight on each side, and give the pendulum a tendency to twist in motion. The mercurial jar pendulum suggested the cylindrical form, which is now generally adopted for astronomical clocks, and in the best turret clocks, with a round top to prevent any bits of mortar or dirt falling and resting upon it, which would alter the time; it also looks better than a flat-topped cylinder. There is no rule to be given for the weight of pendulums. It will be shown hereafter that, whatever escapement may be used, the errors due to any variation of force are expressed in fractions which invariably have the weight and the length of the pendulum in the denominator, though some kind of escapements require a heavy pendulum to correct their errors much less than others. And as a heavy pendulum requires very little more force to keep it in motion than a light one, being less affected by the resistance of the air, we may almost say that the heavier and longer a pendulum can be made the better; at any rate, the only limit is one of convenience; for instance, it would obviously be inconvenient to put a large pendulum of 100 b weight in the case of an astronomical or common house clock. It may perhaps be laid down as a rule, that no astronomical clock or regulator (as they are also called) will go as well as is now expected of such clocks with a pendulum of less than 28 b weight, and no turret clock heavier bobs than short ones; and such a clock as that of the with less than 1 cwt. Long pendulums are generally made with Houses of Parliament, with a two-seconds pendulum of 6 cwt., ought to go 44 times as well as a small turret clock with a onesecond pendulum of 60 b. Pendulums longer than 14 feet (2 seconds) are inconvenient, liable to be disturbed by wind, and expensive to compensate, and they are now quite disused, and most or all of the old ones removed, with their clocks, for bet

ter ones.

Pendulum Regulation.

The regulation of pendulums, or their exact adjustment to the proper length, is primarily effected by a nut on the end of the rod, by which the bob can be screwed up or down. In the best clocks the rim of this nut is divided, with an index over it; so the exact quantity of rise or fall, or the exact acceleration or retardation, may be known, the amount due to one turn of the nut being previously ascertained. By the calculation used below for compensation of pendulums, it may be seen that if the length of the pendulum rod is 1, and the breadth of one thread of the screw is called dl, then one turn of the nut will alter the di seconds a day; which would be rate of the clock by 43200 just 30 seconds, if the pendulum rod is 45 inches long, and the

screw has 32 threads in the inch. To accelerate the clock the nut has always to be turned to the right, as it is called, and 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 fixing a collar, as shown in fig. 2, capable of having very small weights laid upon it, half-way down the pendulum, this being the place where the addition of any small weight produces the greatest effect, and where, it may duces the least effect. If M is the weight of the pendulum and be added, any moving of that weight up or down on the rod prol its length (down to the centre of oscillation), and m a small weight added at the distance d below the centre of suspension tion, and -dt the acceleration due to adding ; then or above the c.o. (since they are reciprocal), t the time of vibra

celeration

3

M

7200

to

from which it is eviden. that if d, then-d T the daily ac10800 m ; or if m is the 10800th of the weight of M the pendulum it will accelerate the clock a second day, or 10 grains will do that on a pendulum of 15 lb. weight (7000 gr. being 1 lb.), or an ounce on a pendulum of 6 cwt. In like manner if d= from either top or bottom, m must accelerate the clock a second a day. The higher up the collar is the less risk there is of disturbing the pendulum in putting on or taking off the regulating weights. The weights should be made in a series, and marked 1,, 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.

Compensation of Pendulums.

Soon after pendulums began to be generally used in clocks, it was discovered that they contained within themselves a source of error independent of the action of the clock upon them, and that they lost time in the hot weather and gained in cold, in consequence of all the substances of which they could be made expanding as the temperature increases. If is the length of a pendulum, and dl the small increase of it from increased heat, # time of the pendulum l, and t + dt that of the pendulum l+dl; then + di Nl + di

since

t

=1+

di 21'

the daily loss of the clock will be 43200 seconds. The foldl lowing is a table of the values of for 1000° Fahr. of heat in different substances, and also the weight of a cubic inch of each:

Ib

⚫036

•116

•28

•26

⚫30

....016

•41

..017

⚫25

-49

Mercury (in bulk, not in length)........... 100 Thus a common pendulum with an iron wire rod would lose 43200-00007 · 3 seconds a day for 10° of heat; and if adjusted for the winter temperature it would lose about a minute a week in summer, unless something in the clock happened to produce counteracting effect, as we shall see may be the case when we come to escapements. We want therefore some contrivance which will always keep that point of the pendulum on which its time depends, viz., the centre of oscillation, at the same distance from the point of suspension. A vast number of such contrivances have been made, but there are only three which can be said to be at all in common use: and the old gridiron pendulum, made of 9 alternate bars of brass and steel is not one of them, having been superseded by one of zinc and iron, exactly on the same principle, but requiring much fewer bars on account of the greater expansion of zinc than brass. The centre of oscillation so nearly coincides in most clock pendulums with the centre of the bob that we may practically say that the object of compensation is to keep the bob always at the same height. For this purpose we must hang the bob from the top of a column of some metal which has so much more expansion than the rod that its expansion upwards will neutralize that of the rod, and of the wires or tube by which the bob is hung, downwards. The complete calculation, taking into account the weight of all rods and tubes, is too long and complicated to be worth going through, especially as it must always be finally adjusted by trial either of that very pendulum or of one exactly similar. For practical purposes it is found sufficient to treat the expansion of zinc as being 016 to steel 0064, instead of 017 as it is really; and for large pendulums with very heavy tubes even the 016 is a little too much. Moreover the c.o. is higher above the c.g. of the bob in such large pendulums than in small ones with light rods and tubes.

But neglecting these minutia for the first approximation, and supposing the bob either to be of iron, in which case it may be Bonsidered fixed anywhere to the iron tube which hangs from the top of the zine tube, or a lead bob attached at its own centre, which obviates the slowness of the transmission of a change of temperature through it, the following calculation will hold. Let be the length of the steel rod and spring, a that of the sine tube, half the height of the bob; the length of the iron

tube down the centre of the bob is - b. If the iron tube is of steel for simplicity of calculation, we must evidently have 064 (r+x-b) — 16z. .'. s —— (r-b). It is practically found that for a seconds pendulum with a lead cylindrical bob 9 in. X3 hung by its middle r has to be about 44 inches, and s nearly 27. At any rate it is safest to make it 27 at first, especially if the second tube is iron, which expands a little more than steel; and the tube can be shortened after trial but not

lengthened.

回

C

The rod of the standard sidereal pendulum at

Greenwich (down to the bottom of the bob, which is such as has been described and weighs 261b), is 43 and z is 26 inches, the descending wires being steel. A solar time pendulum is about inch longer, as stated above. If the bob were fixed at its bottom to the steel tube the zino would have to be 4.88 longer. Fig. 2 is a section of the great Westminster pendulum. The iron rod which runs from top to bottom ends in a screw, with a nut N, for adjusting the length of the pendulum after it was made by calculation as near the right length as possible. On this nut rests a collar M, which can slide up the rod a little, but is prevented from turning by a pin through the rod. On a groove or annular channel in the top of this collar stands a zinc tube 10 feet 6 inches long, and nearly half an inch thick, made of three tubes all drawn together, so as to become like one (for it should be observed that cast zine cannot be depended on; it must be drawn). On the top of this tube or hollow column fits another collar with an annular groove much like the bottom one M. The object of these grooves is to keep the zine column in its place, not touching the rod within it, as contact might produce friction, which would interfere with their relative motion under expansion and contraction. Round the collar C is screwed a large iron tube, also not touching the zino, and its lower end fits loosely on the collar M; and round its outside it has another collar D of its own fixed to it, on which the bob rests. The iron tube has a number of large holes in it down each side, to let the air get to the zinc tube; before that was done, it was found that the compensation lagged a day or two behind the changes of temperature, in consequence of the iron rod and tube being exposed, while the zinc tube was enclosed without touching the iron. The bottom of the bob is 14 feet 11 inches from the top of the spring A, and the bob itself is 18 inches FIG. 2.-Section of high, with a dome-shaped top, and twelve Great Westmin- inches in diameter. As it is a 2-seconds ster pendulum. pendulum, its centre of oscillation is 13 feet from the top A, which is higher than usual above the centre of gravity of the bob, on account of the great weight of the compensation tubes. The whole weighs very nearly 700mb, and is probably the heaviest pendulum in the world.

D D

M

The second kind of compensation pendulum in use is still more simple, but not so effective or certain in its action; and that is merely a wooden rod with a long lead bob resting on a nut at the bottom. According to the above table, it would appear that this bob ought to be 14 inches high in a 1-second pendulum; but the expansion of wood is so uncertain that this proportion is not found capable of being depended on, and a somewhat shorter bob is said to be generally more correct in point of compensation. All persons who have tried wooden pendulums severely have come to the same conclusion, that they are capricious in their action, and consequently unfit for the highest class of clocks.

The best of all the compensations was long thought to be the mercurial, which was invented by Graham, a London clockmaker, above a century ago, who also invented the well-known dead escapement for clocks, which will be hereafter explained, and the horizontal or cylinder escapement for watches. And the best form of the mercurial pendulum is that which was introduced by the late E. J. Dent, in which the mercury is enclosed in a cast iron jar or cylinder, into the top of which the steel rod is screwed, with its end plunged into the mercury itself. For by this means the mercury, the rod, and the jar all acquire the new temperature at any change more simultaneously than when the mercury is in a glass jar hung by a stirrup (as it is called) at the bottom of the rod; and moreover the pendulum is safe to carry about, and the jar can be made perfectly cylindrical by turning, and also air-tight, so as to protect the mercury from oxidation; and, if necessary, it can be heated in

the jar so as to drive off any moisture, without the risk of breaking. The height of mercury required in a cast-iron jar, 2 inches in diameter, is about 6.8 inches; for it must be rememtered, in calculating the rise of the mercury, that the jar itself expands laterally, and that expansion has to be deducted from that of the mercury in bulk.

The success of the Westminster clock pendulum, however, and of smaller zine and steel pendulums at Greenwich and elsewhere, has established the conclusion that it is unnecessary to incur the expense of a heavy mercurial pendulum, which has become more serious from the great rise in the price of mercury and the admitted necessity for much heavier bobs than were once thought sufficient for astronomical clocks. The complete calculation for a compensated pendulum in which the rods and tubes form any considerable proportion of the whole weight, as they must in a zinc pendulum, is too complicated to be worth undertaking generally, especially as it is always necessary to adjust them finally by trial, and for that purpose the tubes should be made at first a little longer than they ought to be by calculation, except where one is exactly copying pendulums previously tried.

BAROMETRICAL ERROR.

It has long been known that pendulums are affected by variations of density of the air as well as of temperature, though in a much less degree,-in fact, so little as to be immaterial, except in the best clocks, where all the other errors are reduced to a minimum. An increase of density of the air is equivalent to a diminution of the specific gravity of the pendulum, and that is equivalent to diminution of the force of gravity while the inertia remains the same. And as the velocity of the pendulum varies directly as the force of gravity and inversely as the inertia, an increase of density must diminish the velocity or increase the time. The late Francis Baily, P.R.A.S., also found from some elaborate experiments (see Phil. Trans. of 1832) that swinging pendulums carry so much air with them as to affect their specific gravity much beyond that due to the mere difference of stationary weight, and that this also varies with their shape, a rod with a flat elliptical section dragging more air with it than a thicker round one (which is not what one would expect), though a lens-shaped bob was less affected than a spherical one of the same diameter, which of course is much heavier. The frictional effect of the air is necessarily greater with its increased density, and that diminishes the arc. In the R.A.S. Memoirs of 1853 Mr. Bloxam remarked also that the current produced in the descent of the pendulum goes along with it in ascending, and therefore does not retard the ascent as much as it did the descent, and therefore the two effects do not counteract each other, as Baily assumed that they did. He also found the circular error always less than its theoretical value, and considered that this was due to the resistance of the air. The conclusions which were arrived at by several eminent clockmakers as to the effect of the pendulum spring on the circular error about 40 years ago were evidently erroneous, and the effect due to other causes.

It appears from further investigation of the subject in several papers in the R.A.S. Notices of 1872 and 1873, that the barometrical error also varies with the nature of the escapement, and (as Baily had before concluded from calculation) with the are of the pendulum, so that it can hardly be determined for any particular clock a priori, except by inference from a similar one. The barometrical error of an ordinary astronomical clock with a dead escapement was said to be a loss of nearly a second a day for an inch rise of barometer, but with a gravity escapement and a very heavy pendulum not more than 3 second. Dr. Robinson of Armagh (see R.A.S. Mem., vol. v.) suggested the addition of a pair of barometer tubes to the sides of the pendulum, with a bulb at the bottom, and such a diameter of tube as would allow a sufficient quantity of mercury to be transposed to the top by the expansion under heat, to balance the direct effect of the heat upon the pendulum. But it is not necessary to have two tubes. In a paper in the R.A.S. Notices of January, 1873, Mr. Denison (now Sir E. Beckett) gave the calculations requisite for the barometrical compensation of pendulums of various lengths and weights, the principle of which is just the same as that above given for regulating a pendulum by adding small weights near the middle of its length. The formula is also given at p. 69 of the sixth edition of his Rudimentary Treatise on Clocks. A barometrical correction of a different kind has been applied to the standard clock at Greenwich. An independent barometer is made to raise or lower a magnet so as to bring it into more or less action on the pendulum and so to accelerate or retard it. But we do not see why that should be better than the barometer tube attached to the pendulum. The necessity for this correction seems to be obviated altogether by giving the pendulum a sufficient are of vibration. Baily calculated that if the arc (reckoned from 0) is about 2° 45' the barometrical error will be self-corrected. And it is remarkable that the Westminster clock pendulum, to which that large arc was given for other reasons, appears to be free from any barometric error, after trying the results of the daily rate as automatically recorded at Greenwich for the whole of the VOL. VI.-236

year 1872. We shall see presently that all the escapement errors of clocks are represented by fractions which have the square or the cube of the arc in the denominator, and therefore if the arc can be increased and kept constant without any objectionable increase of force and friction, this is an additional reason for preferring a large aro to a small one, though that is contrary to the usual practice in astronomical clocks. ESCAPEMENTS.

motion of the wheels is converted into the vibratory motion of The escapement is that part of the clock in which the rotary the balance or pendulum, which by some contrivance or other is made to let one tooth of the quickest wheel in the train escape at each vibration; and hence that wheel is called the "scape-wheel." Fig. 3 shows the form of the earliest clock escapement, if it is held sideways, so that the arms on which the two balls are set may vibrate on a horizontal plane. In that case the arms and weights form a balance, and the farther out the weights are set, the slower would be the vibrations. If

FIG. 3.-Recoil Escapement.

we now turn it as it stands here, and consider the upper weight left out, it becomes the earliest form of the pendulum clock, with the crownwheel or vertical escapement. CA and CB are two flat pieces of steel, called pallets, projecting from the axis about at right angles to each other, one of them over the front of the wheel as it stands, and the other over the back. The tooth D is just escaping from the front pallet CA, and at the same time the tooth at the back of the wheel falls on the other pallet CB, a little above its edge. But the pendulum which is now moving to the right does not stop immediately, but swings a little further (otherwise the least failure in the force of the train would stop the clock, as the escape would not take place), and in so doing it is evident that the pallet

B will drive the wheel back a little, and produce what is called the recoil; which is visible enough in any common clock with a seconds-hand, either with this escapement or the one which will be next described.

It will be seen, on looking at figure 3, that the pallet B must turn through a considerable angle before the tooth can escape;

FIG. 4.-Anchor Escapement.

in other words, the crown-wheel escapement requires a long vibration of the pendulum. This is objectionable on several aocounts,-first, because it requires a great force in the clock train, and a great pressure, and therefore friction, on the pallets; and besides that, any variation in a large arc, as was ex plained before, produces a much greater variation of time due to the circular error than an equal variation of a small arc. The crown-wheel escapement may indeed be made so as to allow a more moderate are of the pendulum, though not so small