result which is expressed by the formula for the time 

 of swing of the ideal simple pendulum. He also 

 used a pendulum to measure lapse of time, and he 

 designed a pendulum clock. Galileo's experimental 

 results are important historically, but have required 

 correction in the light of subsequent measurements 

 of greater precision. 



Mersenne in 1644 made the first determination of 

 the length of the seconds pendulum, 3 that is. the length 

 of a simple pendulum that beats seconds (half- 

 period in the sense of physics). Subsequently, lie 

 proposed the problem to determine the length of 

 the simple pendulum equivalent in period to a given 

 compound pendulum. This problem was solved 

 by Huygens, who in his famous work Horologium 

 oscillatorium . . . (1673) set forth the theory of the 

 compound pendulum. 4 



Huygens derived a theorem which has provided 

 the basis for the employment of the reversible com- 

 pound pendulum for the absolute determination ol 

 the intensity of gravity. The theorem is that a given 

 compound pendulum possesses conjugate points on 

 opposite sides of tin' tenter of gravity; about these 

 points, the periods of oscillation are the same I 01 

 each of these points as center of suspension the other 

 point is the (tnter of oscillation, and the distance 

 between them is the length of the equivalent simple 

 pendulum. Earlier, in 1657, Huygens independently 

 had invented and patented the pendulum clock, 

 which rapidly came into use for the measurement 

 of time. Huygens also created the theory of centrip- 

 etal force which mule it possible to calculate the 

 effect of the rotation of the earth upon the observed 

 value of gra\ it\ . 



The theory of the gravity field of the earth was 

 founded upon the laws of motion and the law of 

 gravitation by Isaac Newton in his famous Princijna 

 (1687). It follows from the Newtonian theory 

 of gravitation that the acceleration of gravity as 

 determined on the surface of the earth is the 

 resultant of two factors: the principal factor is the 

 gravitational attraction of the earth upon bodies, 

 and the subsidiary factor is the effect of the rotation 

 of the earth. A body at rest on the surface of the 

 earth requires some of the gravitational attraction 



Glossary oi Gravity Iermino 



absoliii (.R.wii'i : the value of the acceleration of gravity, 

 alsi ■ expressed 1>\ the length of die sei onds pendulum. 



RELATTVi gravity: the value of the acceleration of gravity 

 relative t" the valui i idard point. 



siMii i pendulum: see theoretical pendulum. 



[-HEORETII \i pendulum: a h'\i\ j bob (point-mass) at the 

 end of a weightless rod. 



seconds pendi 1 1 m : .1 1 1 in, on. ,il oi simple pendulum of such 

 length thai its time oi swing (half-period) is one 

 1 htis length is about one meter.) 



gravity pendulum: .1 precisely made pendulum u ■ 

 the measurement of gravity. 



COMPOUND PI NDl 1 1 Ml .1 pendulum in which the Supporting 

 rod is not weightless; in other words, any actual pendulum. 



convertible pendulum: a compound pendulum having 

 knife edges at different distances from jra> it % . 



Huygens demonstrated (1673) that il such a pendulum 

 were to swing with equal periods from either knife edge, 



the distance between those knife edges would be equal to 

 the length of a theoretii al or simple pendulum of the same 

 period. 



reversible pendulum: a convertible pendulum which is 

 also symmetrical in 1 1. 



invariable pendulum a compound pendulum with only 

 one knife edge, used foi relative measurement ol gravity. 



1 P. \l akin Mersenne, Cogitate, physua — malhtmatka (Paris, 

 1644), p. 44. 



' CiiRisriAAN IIcvcens, Horolcgium oscillatorium, site de molu 

 penduhrum ad horologia adaplalo demonstrations geomelricae (Paris, 

 1673), proposition 20. 



for the centripetal acceleration of the body as it is 

 carried in a circle with O eed by the rotation 



of the earth about its axis. If the rotating earth is 

 used as a frame of n ference, the effect ol the rotation 



is expressed as a Centrifugal force which acts to 



diminish the observed intensity of gravity. 



From Newton's laws of motion and the hypothesis 

 that weight is proportional to mass, the formula for 

 the half-period of a simple pendulum is given by 

 T=Tyl g. If a simple pendulum beats seconds, 

 l = 7r^\g, where X is the length of the seconds 

 pendulum. From T Xijl/g and 1 iryA/J, it follows 

 that X— / 7~ J . Then g tt j \. Thus, the intensity of 

 gravity can be expressed in terms of the length of 

 the seconds pendulum, as well as by the acceleration 

 of a freely falling body. During the 19th century, 

 gravity usually was expressed in terms of the length 

 of the seconds pendulum, but present practice is to 

 express gravity in terms of g, for which the unit is 

 the gal, or one centimeter per second per second. 



PAPER 44: DEVELOPMENT OF GRAVITY PENDULUMS IN THE I'll I CENT! RY 



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