The superiority of detached escapements has been noticed under llonotoor. In those in ordinary use, time and dirt and thickening of the oil not only affect the amount of the impulse, which is compara tively of slight moment, but the continuing action of the teeth on the pallets is also irregular. The space through which the pendulum swings, or arc of vibration, is thus liable to variation, which again pro duces a change in the time in which each oscillation is performed, that is, if the pendulum be supposed to oscillate round a fixed axis. This in equality was more apparent in the early clocks, where the pendulum was light and the arc of vibration very large, than in those of modern construction, where the pendulum is heavy and the arc small. Huyghens's remedy of cycloidal cheeks is noticed under HOaOLOOY. It is said by all later writers on the subject that the remedy is worse than the disease ; and it is possible enough that something like sticking between the flexible top and the cycloidal cheek may take place at the critical point, that is, just when the pendulum has arrived at the end of its swing, and is pausing for its return ; and that there may be a difficulty In making and setting the cheeks so truly as to act on the pendulum in every part of its swing. A second objection is alleged against Huyghens's cheeks—namely, that, as the pendulum cannot be considered to be a heavy point suspended by a rod without weight, the centre of oscillation shifts downwards as the flexible portion of the top wraps on the cheek. This objection might be easily got over by making the cheeks not truly cycloidal, but of such a form that the centre of oscillation of the compound pendulum shall oscillate in a cycloid,which would be easy enough when the form of the pendulum was given. In truth this is a 'natter of mere speculation in astronomical clocks, for there is a munch easier way of producing sensible isochronism in them, which we will describe ; but we suspect that the cycloidal cheeks might still be used advantageously in clocks which resemble Iluyghens'e, as the Dutch clocks which are in common use.
Instead of suspending the pendulum by a perfectly flexible string, or on a knife-edge, when the motion must be in a circle, the top of the rod ends in a flat spring. (See Figs. 20, 21, under HOROLOGY, where the spring is seen in front, like a fine line, at the top of each pendulum.) This produces two effects upon the time of oscillation : first, by re Larding the motion of the pendulum in its rise and accelerating its fall, the spring shortens the time of vibration,and the more the stronger it is ; but as its action at each point is nearly proportional to the degree in which it is bent, that is, as the arc of vibration reckoned from the position of rest, this action will have no tendency to alter the isochronism of unequal arcs. The bending of the spring has how ever a second effect, that of causing the bob of the pendulum to describe a curve which is not circular, but which falls within a circle ; and this, by proportioning the strength of the spring to the weight of the pendulum, may be made to approach to Huyghens's cycloid, or to that modification of it which we have described. It is possible to select a spring of such strength as shall completely satisfy this con dition, at least within the necessary limits, that is, for such variations in the moving power as arise from dirt, thickened oil, and wear in the works.
Frodsham's experiments on suspending springs are also noticed under HOROLOGY. In no case does Mr. Frodsham seem to have found a spring which caused the clock to gain in the larger arcs, which, on the information of other makers, and on theoretical grounds, we consider possible. With a spring stiffer than that which was isochronous, Mr. Frodsham found that using as effective lengths and of an inch, the change of rate produced by using 41b. loz. as the weight, instead, of 21b. 2oz., was to give the clock a losing rate of 3.7', 2.6', and 3.5', respectively. The law is not apparent, and it would seem that, even with this spring, shortening the spring had no sensible effect. Another remark of Mr. Frodsham's, which is very valuable if it be confirmed by extended trials, is, that the spring which produces isochronism is also the spring with which the pendulum, unattached to any clock, will keep up its motion for the longest time. It seems to
us probable that this latter quality will belong to the weakest spring which preserves its full elasticity under the pull of the bob ; for if the elasticity were perfect, the only cause of loss of motion would be the resistance of the air, which is not sensibly altered by the effect of the spring. However this may be, the subject is well worth further con sideration. Notwithstanding the care bestowed by Mr. Frodsham, it is difficult to conduct inquiries of such nicety with an uncompensated pendulum. It will also be necessary, as we shall now point out, to attend to the state of the barometer when the experiments are in pro gress. For when the effect of the air upon the time of oscillation of a pendulum is examined, it will be found that the resistance of the air has no influence except the indirect one of shortening the arc of vibra tion, that is, of tending to make the clock gain, if the bob move in a circular arc. The buoyancy of the air acts more immediately, for it diminishes the weight of the pendulum, and leaves the inertia unaltered, and therefore diminishes the accelerating force. Hence a greater density in the air acts as a diminution in the force of gravity, that is, makes the clock go slower. The effect is greater indeed than was at one time anticipated; for, as was remarked long ago by Du Buat, and subsequently shown by Besse!, the pendulum must be considered to include in its inertia a small wrapper of air which is involved in it or accompanies it in its course. (See a very elaborate and valuable memoir by Mr. Baily, ' On the Correction of a Pendulum for the Reduction to a Vacuum," Phil. Trans.,' 1832, p. 399.) This latter portion of the effect of the air depends on the form of the pendulum, and possibly may even be affected by the polish of its surface. Now the density of the air is proportional directly to the pressure of the atmosphere shown by the barometer, and inversely to the temperature, which is known from the thermometer. The latter portion might be practically included in the general compensation for temperature, but the former requires either a specific and peculiar compensation, or may be determined as a residual quantity, and tabulated for each clock with the mean height of the barometer for the period required. Dr. Robin son's investigation on the effect of atmospheric pressure ou the rate of a transit clock is referred to under HOROLOGY. The compensation for the variation of atmospheric pressure was made by attaching small barometers to the pendulum rod, but we believe this ingenious idea was not attended with any practical benefit. It would perhaps be possible so to balance some of these contending principles as to obtain a performance nearly perfect ; thus an arc of vibration might be selected in which the increased density of the air, by reducing the arc, might accelerate the time of an oscillation as much as the increased buoyancy and inertia would retard it, or so nearly so, that the remaining difference ini4ht be completely annihilated by a proper selection of the pendulum spruig. But even if this should be effected, and we see no obstacle to it except the time and trouble it would require, any change of the moving power, or of the action of the escapement, would alter the arc and derange the equilibrium. As the effect of time is generally to produce a falling off in the arc, a small addition to the clock weight might be made from time to time, so as to bring back the pendulum to its primitive arc, until the clock is cleaned, and its action restored that way. We shall conclude this long disquisition (which we propose for consideration until decisive experiments are made) by a piece of advice which we can warrant. Where the clock is much exposed to variations of temperature, enclose it in a second covering or closet. This will protect it from injury, and moreover will very much regularise the rude transitions of temperature to which clocks are in this climate liable. It is not improbable that the parts of a clock, and of its pen dulum, if much exposed, may take their temperature at different times, and if so, the compensating principle is not brought into action, but must act irregularly.