Nov. 15, 1883] 



NA TURE 



65 



MOVEMENTS OF THE EARTh^ 

 11. 

 Measurement of Time 

 I T has been shown how, by the application of geometrical and 

 optical ])rinciples, the measurement of angular space has 

 been carried down to the i/iocth of a second of arc, such 

 a quantity being 1/ 129, 600,000th part of an entire circum- 

 ference, and when such an accuracy as this has been attained, 

 and the altitude or the azimuth of the sun, or moon, or any 

 other heavenly body can be correctly stated with this exactitude, 

 it will be seen how much better off in the way of defining posi- 

 tions is the modern astronomer than was Hipparchus with his 

 l/3rd, and Tycho Brahe with his i/4th of a degree. To do 

 this, however, is not enough. It is not only necessary accurately 

 to define the po,-ition of a heavenly body, it is necessary al?o to 

 know at what particular lime it occupied that position. The 

 next tiling to be d^ne, then, is to ;ee how far we moderns 

 have got in another kind of measurement, no longer the measure- 

 ment of arc — the measurement of angular distance — but the 

 measurement of time. 



The measurement of time, however, is not quite so simple a 

 matter as was the mea>urement of space. A certain angular 

 measurement of s])ace, or the angular distance between two 

 bodies, whether that distance be a degree, or a minute, or a 

 second, is a very definite thing, having a beginning and an end ; 

 but time, s > fir as we can conceive, has neither beginning nor 

 end ; so that the problem of the meaiurement of time has to 

 be a'tacked rather in a different way. Here again it will be as 

 well that the matter shuuld be studied historically. 



5 



Fig. iS. — Ancient Ctcck Escapement. 



What more natural than that manhavinggot theideaof the flow 

 of time, should have begun to measure it by the ?iOV! of water, 

 or the flaw of sand? The earliest time measurers were really 

 made in this way ; water or sand being allowed to drop from 

 one receptacle to another. There were difficulties, however, in 

 thus determining the flow of tiaie. In the first place the thing 

 was always wanting to be wound up, so to speak, something was 

 wanted to continue the action, and to prolong it ; and the first 

 appeal to mechanical principles was made with that view. 



The first real clock put up in England was put up in Old 

 Palace Yard, in the year 1288, by the Lord Chief Justice of 

 that time, who had t> pay the expense of it as a fine for 

 some fault he had committed. Its construction was somewhat 

 after this wise. One method of dealing with the flow of time 

 was to call in the aid of wheelwork ; but, as is well known, if a 

 weight acts upon a train of wheels the velocity increases as 

 the rotati ->n goes on. Therefore the science of mechanics was 

 called in to supply some principle which could be applied to 

 prevent this unequal velocity cf a train of wheels. Consider 

 the arrangement shown in Fig. 18. 



The wheelwork train is capable of being driven by a falling 

 weight. On the same axis as the smallest wheel, and therefore the 

 one w hich turns most rapidly, w ill be seen another wheel provided 

 with saw -like teeth. Then at the top is a weighted cross-bar, from 

 the centre of which a perpendicular rod, provided with pallets, 

 comes down to engage the teeth of the pallet-wheel. Now sup- 

 pose the clock to be started. The weight is allowed to fall, and 

 ' Continued from vol. xxviii. p. 604. 



the whetls, including the pallet wheel, begin to revolve; then 

 begins a reciprocating action betw een the swinging bar and the 

 wheel with which it acts, because the pallets which act on the 

 bar as they are on either side of the centre of motion rtally drive 

 the bar first in one direction and then in the other. The teeth of 

 the pallet wheel are continually coming into contact with the 

 pallets of the sw ingiiig bar. First suppose that one of the teeth 

 has encountertd the upper pallet ; it pushes this aside, and swings 

 tlie bar in one direction. No sooner, however, has this been 

 dor.e than another tooth in the wheel at the bottom of the bar 

 encounters the pallet and swings it in the opposite direction. In 

 this way it is obvious that the bar is continually meeting and 

 being met by the teeth of the rotating wheel, swinging first in 

 one direction, and then in the other, the result of this reciprocal 

 action being to prevent the increase in the velocity of the wheels 

 which would otherv\i-e take place. 



It is in ttis way, then, by the performance at constant definite 

 intervals of an equally constant definite amount of work, that 

 the regularity of action of the clock is produced. The greater 

 the distance of the weights on the cross-bar from its centre of 

 motion, the longer will the bar take in swinging, the slower will 

 be the action of the clock ; so that the clock may be regulated 

 by altering the position of these weight--, bringing them nearer to, 

 or removing them further from the centre of motion of the bar, ac- 

 cording as it is desired to hasten or retard the action of the clock's 

 mechanism. Yet at whatever distance from the centre of motion 

 the two weights be placed, assuming always that they are both at 

 the same distance from it, there is still this con-tantly-recurring 

 performance, at equal intervals, of an equal amount of work 

 which produces the regular action of the clock. This was the 

 kind of clock then which was put up in Old Palace Yard. 

 But that did not go well enough, giving such inaccurate results 

 that Tycho Brahe had to discontinue its use. Fortunately some 

 few years later two most eminent men, Galileo and Huyghens, 

 had their attention drawn to this very proljlem. The first of 

 these, Galileo, was at that time studying medicine. He hap- 

 pened one day to be in the Cathedral at Pisa, where, it will be 

 remembered, they have a most beautiful lamp which sv\ings 

 from a great height in the cathedral. Galileo was at this 

 time working at that branch of his medical studies which deals with 

 the pul-e, and he looked at this lamp and found that its swinging 

 was perfectly regular. To day perhaps it may seem very natural 

 that this should be so, but Galileo had the advantage of being 

 before u-, and that is why it did not seem quite so natural to 

 him. There was at that time no known reason why it should 

 swing in perfect regular rhythm. He found that the lamp when 

 sw inging, no matter with w hat amplitude, took practically the 

 same time for each swing, timing it by his pulse. His idea was 

 that this would be an admirable method of determining the rate 

 of a man's pulse, and the first clock on this principle was con- 

 structed fro.n that medical pjint of view, being called a 

 Pulsilogium. Some years afterwards, however, the extreme 

 importance of such an arrangement from an astronomical stand- 

 point became obvious, and very much attention was given to 

 it. It is unnecessary to add that this swinging body is nowadays 

 called a pendulum. The most perfect pendulum made in those 

 early days is represented in Fig. 19. 



1 he fundamental difference between that and the modern 

 pendulum is that part of the pendulum between s and A 

 was elastic. It was made elastic for the rea- on that although 

 Galileo could not find any difference between the times of 

 the oscillations of the lamp in Pisa Cathedral, according as 

 its amplitude of swing was large or small, yet such a differ- 

 ence did exist, although it was only a slight c- ne ; and the only 

 method of getting a perfect pendulum which should make its 

 swing in exactly equal times, independent of its arc of oscilla- 

 tion, was to construct this so called cycloidal pendulum. It 

 was so named because in its swing its elastic portion w as held 

 by the curved guides seen in the figure, and made to bend in 

 that particular curve. By thii means the pendulum in lead of 

 swinging through the arc, K u R, was made to oscillate through 

 D u L. But when the pendulum was at the points D and L, 

 it was practically a shoiter pendulum than when at rest. In 

 other words, whilst the pendulum was swinging from u to D 

 and from u to L, its curvature, and con equently its vibrating 

 length was continually changing. In that way, by continually 

 varying the length of the swinging part, it was found possible to 

 make a pendulum which, independent of the length of its arc of 

 oscillation, would make its swing in times which for all practical 

 purposes were absolutely equal in length. That was the most 



