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 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 remembered, 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 zinc 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 compen sated 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 varia tions 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 ll.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 there fore 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 arc 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 mercuiy 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 Green wich. 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 arc of vibration. Baily calculated that if the arc (reckoned from 0) is about 2 45 the barometrical error will W 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 year 1872. We shall see presently that all the escape ment 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 objectionably increase of force and friction, this is an additional reason for pre ferring a large arc to a small one, though that is contrary to the usual practice in astronomical clocks.
Escapements.
The escapement is that part of the clock in which the rotary motion of the wheels is converted into the vibratory motion of 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 77heel. " 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 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 crown- ivheel 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.
Fig. 3.—Recoil Escapement.
Fig. 4.—Anchor Escapement.
It will be seen, on looking at figure 3, that the pallet B must turn through a considerable angle before the tooth can escape; in other words, the crown-wheel escapement requires a long vibration of the pendulum. This is objectionable on several accounts, 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 explained be fore, 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 in deed be made so as to allow a more moderate arc of the pendulum, though not so small as the 2 usually adopted in the best clocks, by putting the pallet arbor a good deal higher above the scape-wheel, and giving a small number of teeth to the wheel; and that also diminishes the length of the run of the teeth, and consequently the friction, on the pallets, though it makes the recoil very great and sudden; but, oddly enough, it never appears to have been resorted to until long after the escapement had be come superseded by the "anchor" escapement, which we shall now
