S73 



PENDULUM. 



PENDULUM. 



374 



coated over, so as to be impervious to moisture, it will be liable to 

 small errors arising from that cause. A range of 50 will not alter the 

 rate of a clock with a white deal pendulum more than 5" a day, if 

 Capt. Hater's value of the expansion of deal be correct. 



In a well-made clock, the error arising from expansion from tempe- 

 rature is the most considerable, and is that which must be guarded 

 against. Mr. Baily's contrivance with a leaden weight is given under 

 HOROLOGY. We may add that a lenticular form may be given to the 

 weight, provided the proper length be preserved, and this will be an 

 improvement, as it diminishes the resistance of the air, and the error 

 which arises from the inertia of the air carried by the pendulum. 



It is stated in the article just referred to, that in Harrison's pen- 

 dulum foreign artists use zinc rods instead of brass. Zinc is objection- 

 able as being a weak metal, and it is said by some persons to expand 

 by jumps, which seems not very probable unless much exposed. The 

 great objection to the gridiron pendulum is that the astronomer, if he 

 be no workman, must rely upon the artist for perfect compensation 

 (and this is perhaps never achieved) ; and again, if from rust or bad 

 fitting the slipping parts should bind, the action will necessarily be by 

 bounds and irregular. After the clock-maker has done his best, a 

 experience will point out the error in the compensation, which 

 can easily be remedied, if the fault be over-compensation, by cutting 

 the zinc rods shorter. All the fixed parts should then be secured as 

 firmly as possible by steady pins, as any attempt to reserve a power of 

 further adjustment would be too dearly purchased by a ricketty frame. 

 The bands attached to rods 1 and 5 for the purpose of keeping the 

 zinc rods in their places should not squeeze the zinc, and but just 

 press against them with the spring of the metal. Harrison is said, by 

 Short (' Phil. Trans.,' vol. 47, p. 517), to have invented his pendulum 

 about 17-!.'. 



The construction of Graham's pendulum allows the astronomer to 

 alter and finally perfect the compensation. This quality, and the 

 absence of any nice fitting or slipping parts, give Graham's construc- 

 tion a very decided superiority over Harrison's, especially for a clock 

 which is not to be moved from place to place. These mercurial pen- 

 dulums are generally constructed in a more expensive manner than is 

 necessary. The vertical rods may all be made of stout steel wire, and 

 the base and top of the stirrup of brass. Mr. Baily, in his valuable 

 memoir (' Astron. Soc.,' vol. i.), justly recommends that the thread of 

 the regulating screw should be deeper and coarser than it is usually 

 made, and be tapped on a stouter cylinder. Graham's pendulum is 

 described by himself. (' Phil. Trans./ vol. xxxiv. p. 40.) It was in- 

 vented in 1722. There are many ways of compensating a pendulum 

 for the effects of temperature, some of which are very ingenious, and 

 others very simple. Those described under HOROLOGY will suffice for 

 an explanation of the principle ; they are the moat usual, the most 

 easy of execution, and most exact in their operation. 



The superiority of detached escapements hag been noticed under 

 HOROLOGY. 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 ore of ribralion, 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 wan 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 U heavy and the are small. 

 Huyghens's remedy of cycloidal cheeks is noticed under HOROLOGY. 

 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 Huyghenss 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 dovmeardt 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 matter of mere speculation in astronomical clocks, for 

 there is a much 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 Huyghens's, 

 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 Pig$. 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- 

 tarding 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 0'97, O'Gfl.and 0'50 

 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 37', 

 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 tbe 

 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 uucompen.sited 

 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 Bessel, 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 knowni 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 on 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 

 might be completely annihilated by a proper selection of the pendulum 

 spring. But even if this should be effected, and we see no obstacle to 

 it except the tune 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 uiuch 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. 



It has already been said that a clock, to go steadily, should be securely 

 fixed. The common mode is to fasten the case by strong bolts, under 

 the rising board and again about as low as the pendulum bob, to a 



