In 1671 l'imrt was sent to determine the position of Tycho Brali6's observatory at Uranibourg. Ile took this opportunity of swinging the pendulum, and found the length of the seconds pendulum 3 ft. 0 in. 861.
Paris measure, exactly the same as lie had previously found it to be at Paris, and subsequently at Cette, on the south coast of France.
Roemer obtained the same result at London, and these erroneous measures of Picart, the first astronomical observer of his day, were for a long timo cited as objections to the theory of gravitation.
In 1672 Richer was sent to Cayenne (about 4' 56' N. let.) to make a course of observations, and among the rest to observe the length of the seconds pendulum. Ilia words are : "L'une des plus conaiderables observations quo j'ay faites, est celle tie la longueur du pendule it seconder de temps, laquelle dest trouvae plus courte en CaIenno qu'h Paris : qtr In memos mesure qui avoit est6 marqu6e en cc lieu-lb sur une verge de for, suivant la longueur qui s'estoit trour6e necessaire pour fair un pendule h secondes de temps, avant eattS apportee en France, et comparde avec cello de Paris, leur difference a est6 trouv6e d'une ligne et un quart, dont cello de Calcium eat moindro que cello do Paris, Immelle cat de 3 pieds 82 lignea. Cott() observation a Mai reiter6e pendant dix moil entiers, oh id ne s'est point pass6 do somaine qu'elle n'ait est6 faite plusieurs lois aveo beaucoup de soil. Les vibrations du pendule simple dont on so servoit, estoient fort petites et duroient fort sensibles jusqucs h cinquantosleux minutes do temps, et out est6 compardes it cellos dune besiege tree excellente, dont lea vibrations marquoient les secondes de temps." (' liecuell des Obser vations faites en plu.sieurs Voyages par ordre de sa 3Iajest,4,* p. 66, Paris, 1693.) We have cited this passage textually, not only on account of its importance, but because it is generally merely stated that Ricber's clock, which was regulated on Paris time, lost more than two minutes at Cayenne. This misrepresents the cridcnce of the experiment, and moreover leaves room to suppose that Richer made a chance dis covery, whereas the determination of the length of the pendulum was one of the special objects of his mission (see p. 2). Neither Picart nor Richer gives any details of his modus operandi.
In 1673 Huyghens published his' Horologium Oscillatorium; perhaps the most remarkable matheinatico-mechanical work which preceded Newton's Principia! He therein explains the isochronism of oscil lations in a cycloid, and the mechanical means of making the pendulum swing in a cycloid. He gives theorems for finding the centre of oscil lation of several figures, and thence the length of the simple pendulum, corresponding to a compound pendulum of certain forms ; and in pro positions 19 and 20 (p. 124-5) proves that when the body is the same, the distances of the axes of suspension from the centre of gravity are reciprocally as the distances of the centre of gravity from the respec tive centres of oscillation, and that the point of suspension and centre of oscillation are convertible. His proposition 25 (p. 151) is on the mode of fixing a universal and perpetual measure, which he proposes should be the third part of a seconds pendulum, and names a /torary foot.
Newton, in his 'Principia; lib. i., a. 10, investigates the oscillations
of a body in a cycloid, or in any other curve; lib. ii., a. 6, ho considers the effects of a resisting medium on a pendulous body ; and lib. prop. 19, he determines the figure of the earth, supposing it to be fluid and of uniform density, to be a spheroid of which the equatorial and polar diameters are as 220 : 229. In prop. 20 he computes the lengths of the seconds pendulum and of the degrees of the meridian, which are required on the foregoing suppositions ; and he remarks, " Quod inequalitaa diametrorum term facilius et certius per experimenta pen duloruin deprehendi possit quam per emus geographice tnensuratos in meridiano." In the following pages is an analysis of the lengths of the pendulum which had come to his knowledge.
We have not been able to find any account by Graham himself of two very capital improvements which he seems to have introduced into pendulum experiments. The first is a clock, in which " he carefully contrived that its pendulum might at pleasure be reduced to the same length whenever there should be occasion to remove the clock from one place and set it up in another." (Bradley's Account of the going of a Clock by Graham, in London, and at Black River, Jamaica," Phil. Trans.,' vol. xxxviii, p. 302.) Probably this was done by drawing the spring through a clip to a given mark ; for in another description of a similar clock it is said the suspending spring was broken. We do not, however, see need for any adjustment in this respect, if the spring be pinned into the rod and into its upper axis. The pendulum was not compensated, but a thermometer was enclosed in the clock, and as the rate in different temperatures at the same place had been determined, the reduction to a normal temperature was easy. Clocks of this kind were supplied to the French expeditions for measuring arcs of the meridian in Lapland and Peru. For this latter expedition Graham supplied Godin with a detached pendulum, which Godin thus describes : —" Ce pendule est composd en general d'un fil de cuivre, dune boulo de memo matitire it un de sea bouts, et d'uue piece (racier Lillie° en coutcau it rautre bent, qui est cclui de suspension : cc couteau poste our deux mutants d'acier en deux points qui designeut l'axo du mouvement du pendule." (` Acad. Roy. des Sciences,' 1735, p. 507.) He says its motion was sensible for eighteen hours. It seems that this pendulum, the vibrations of which were to be counted by a clock, was also intended to measure the actual length of the pendulum. Messrs. Bouguer and La Condamine both had detached pendulums made after Graham's idea. Bouguer (same volume, p. 526) describes this pendulum as an invention of his own; La Condamine (` Journal du Voyage,' p. 143) is more open, and says he took the idea from a copy which Hugo made after Graham's. This is almost exactly Kater's invariable pendulum. Mairan's measurement of the length of the seconds pendulum (' Acad. Roy. des Sciences,' 1735, p. 153) is a good specimen of the old method of measuring the length of the pendulum : and the measures of Godin, Bouguer, and La Condamine, in the same volume, are worthy of notice. For references to various pendulum experiments, see Lalande, Astronomie,' 3rd edit., s. 2710, et seq.