October, 1906.] 



KNOWLEDGE & SCIENTIFIC NEWS. 



559 



Pendulums Used in 

 Gravitation Research. 



By W. H. Sharp 



The laws of falling or moving bodies were investigated 

 in ages long before Galileo's time (about 1600), and 

 probably vi'ith much greater success than is at present 

 commonly supposed. His experiments with bodies fall- 

 ing from the top of the Tower of Pisa were connected 

 with the opening of a new chapter in gravitation re- 

 search. 



Newton, in lyio, made similar experiments in London 

 with bodies falling freely directly downwards to the 

 earth from a great height, and based his celebrated 

 theory of gravitation upon the results attained thereby, 

 and by means of his own famous experiments with 

 vertical pendulums, eleven feet long, suspended from 

 the ceiling of a room. 



Two centuries ago the pendulum had become recog- 

 nised as specially suitable for gravitation re.search, 

 because it was possible by its means to substitute the 

 gliding motion of a pendulum bob in a smooth curved 

 path or long arc of a circle, for its fall down a short 

 straight path representing the versed sine of that arc, 

 or in other words the vertical depth from top to bottom 

 of that smooth curved path. 



Fciididums — and 1 must I>e understood to refer par- 

 ticularly to such as are u.sed for astronomical purposes 

 — may be regarded as belonging to one or other of three 

 classes, according as the plane in which they a'e 

 designed to oscillate is : — (A) Vertical, (B) Horizontal, 

 or (C) Inclined, with reference to the horizon at the place 

 where they are used. 



When the pendulum is constructed by hanging a 

 weight at the lower end of a cord, wire, fibre, or other 

 material from one point above, so that the weight m.'iy 

 oscillate to and fro, its suspension is said to be unifilar. 

 Newton's was of this kind (sec Fig. i). But, if by 

 hanging a weight by two equal cords, w'ires, or other 

 inateii:ils, from two points above, its suspension is said 

 to be bifilar (see Fig. 3). The unifilar vertical pendu- 

 lum is like an ordinary plumb-line, and one great ob- 

 jection to it is, that being free to move not only to and 

 fro, but also sideways, it does not continue oscillating 

 in one direction — in one plane — to and fro, but tends 

 to change its direction all the time it continues swing- 

 ing. 



The bililar suspension imposes a hmit upon that ten- 

 dency to change, and tends to lea\e the pendulum Irre 

 to oscillate to and fro in one plane only. 



Gauss and Weber used a bifilar suspension, and also 

 the well-known mirror reflecting a ray of light, about 

 1836, in their pendulum experiments. 



(.\) Vertical, pendulums, or plumb-lines have been us<'d 

 in four different ways in gravitation research. 



(i) To compare forces acting upon them, by count- 

 ing the number of oscillations produced in equal times 

 under similar conditions by different forces (Fig. i). 



(2) To compare forces acting lalerallv upon tlu-ni, 

 when hung as plumb-lines at rest, for inst;nuH' near 

 the side of a mountain, by measuring; tin' distances 

 through which thev were drawn out of the vertical. 

 Bouguer (1738) and Maskeleyn (1772) used that 

 method, with long plumb-lines near mountain sides, 



■ AU Riglils R,sciUi-cl. 



and (jruithuisen (181 7) used a ten-foot thread pendu- 

 lum — his " clkysmometer " — to indicate variations of 

 lunar attraction (Fig. i). 



(3) To demonstrate the rotation of the earth by 

 measuring the rate of angular deviation of the plane of 

 oscillation of a unifilar pendulum. This w'as done by 

 Foucault in 1851, who proved that the rate of deviation 

 depends upon the latitude of the place in which the ex- 

 periment is made (see Fig. 2). 



(4) To measure, if possible, the " Lunar variation 

 of gravity " by using a vertical bifilar suspended pendu- 

 lum, as suggested by Lord Kelvin in 1878, with a Gauss 

 mirror attachment, and as used by or for the British 

 Association Committee in the abortive experiments re- 

 ported for them by G. H. Darwin, in 1881. (Vide 

 British Association Reports, 1881-2.) 



Among other notable experiments on gravitation by 

 means of vertical pendulums are those of Du Buat 

 (1786), Carlini (at Mont Cenis), Bessel (1826), Hors- 

 ford's " with a 220 feet pendulum in a tower, and .Airy's 

 in a coal mine 1260 feet deep. 



In every instance where a vertical pendulum has been 

 used for gravitation research, a weight has had to be 

 lifted against the vertical downward force of the earth's 

 gravitation, and in order to avoid the necessity of so 

 doing, the vertical pendulum w-as abandoned about the 

 end of the eighteenth century by leading men in the 

 scientific world, who adopted the horizontal pendulum 

 as a more promising instrument of research. 



(B) Horizontal pendulums — most properly so termed — 

 consist of a rod having a ball at each end, and supported 

 horizontally, after the manner of an ordinary compass 

 needle, upon a point at the middle of the rod. The 

 earth's downward pull upon the ball at one end is 

 exactly balanced by its downward pull upon the ball at 

 the other end of the rod, and there is therefore no need 

 in practice to consider the vertical downward force of 

 gravity so far as such a pendulum is concerned. There 

 is also no reason why such a pendulum under ordinary 

 conditions should tend to' rest in any one particular hori- 

 zontal direction rather than in any other. In fact it is 

 not known as having any definite directive tendency. 



It is an immense advantage to be able to work upon 

 delicate gravitation research without interference by the 

 earth's downward attraction, but immediately one be- 

 gins to avail of that advantage, the need of a definite 

 directive tendency is obvious. A magnetic needle has 

 a tendency to set in one definite direction, and we may 

 use various means to cause it to depart therefrom, and 

 measure the angles or distances through which it is 

 moved thereby, for the purpose of comparing the forces 

 involved. So also the plumb-line or vertical pendulum 

 had a definite directive tendency to adopt the nearest 

 position to the earth's centre, and in a straight line 

 directed thereto. 



Coulomb overciune this difficulty by suspending the 

 horizontal rod — with the balls at its ends as aforesaid 

 — by attaching a wire at the middle (or centre of 

 gravity) of the rod and fastening the other end of the 

 wire to a point above. This was instead of using a 

 pointed support, as in the mariner's comp;iss, and with 

 such a wire suspension the rod always had a definite 

 tendency to take up and maintain a certain direction 

 which was determined by the molecular arrangement of 

 the particles of the wire suspension, etc. (see Fig. 4). 



He called his horizontal pendulum, so suspended, a 

 torsion balance, and the horizontal pendulums after- 



• VUU Proc. .\m .\ssoo. for .\dvancement of Science, 1S52. 



