In considering of the means by which the length of the pendulum could be best determined, it occurred to Captain Rater that advantage might he taken of a well known pro perty of an oscillating body, which had been demonstrated by Huygens; namely, that the centres of suspension and of oscillation arc convertible with one another ; in other words, if in any pendulum the centre of oscillation he made the centre of suspension, the times of oscillation will be equal in both cases. Hence it is evident, that if the same pendulum with two points of suspension, can be brought to oscillwe in the same time, the one of these points will be the centre of suspension, while the other is the centre of oscillation; and consequently their distance will be the true length of the pendulum, On this principle Captain Rater constructed his conver tible pendulum, of which a detailed account is published in the Transactions of the Royal Society of London for 1318. It was formed of a bar of plate brass, (Fig. 8 ) one inch and a half wide, and one-eighth of an inch thick ; which dimensions were chosen, that it might be readily affected by any change of temperature. Through this bar two triangular holes were made, to admit the knife-edges, n n', which, after a number of experiments, had been selected as the least exceptionable mode of suspension. " Four strong knees of hammered brass, A A, of the same width as the bar, six inches long, and three-fourths of an inch thick, are firmly screwed by pairs to each end of the bar, in such a manner that, when the knife-edges are passed through the triangular apertures, their backs may bear steadily against the perfectly plane surfaces of the brass knees, which are formed as nearly as possible at right angles to the bar. The knife-edges had previously been tapped half way through, near the extremities, to receive two sercars, which, being passed through the knee pieces, drew the knife-edges into close contact with them, the surfaces of both having been previously ground together, to guard against any Strain
might injure their figure. The bar is cut of such a ten. th ;hat its ends may be short of the extremities of the knee pieces about two inches. Two slips of deal, B B. 11 inclies long, and of the same thickness as the bar, are hise”ted in the spaces thus left between the knee pieces, and ,• c, i ,-ay secured there by means of pins and screw 1 se of deal are only half the width of the bar ;
cv . r ta;ned black, and in the extremity of each a sited win
viini is inserted, to indicate- the extent of the
" A cylindrical weight of brass, t • re: inches and a half in diameter, and abw• tv.n pounds seven ounces, has a rectangular opvl.ing it, the direction of a diameter, to admit the knee pieces of one end of the pen dulum. This weight being pssed on the pendulum, is so firmly screwed in its place, as to render any change of po sition impossible. A second weight, D, of about 71 ounces, is made to slide on the bar near the knife-edge at the op posite end, and this weight may he fixed at any distance on the bar, by two screws with whi h it is furnished. A third w eight or slider, E, of only four ounces, is move able along the bar, and is capable of nice adjustment, by means of a screw and damp, which clamp is included in the weight. It is intended to move near the centre of the
bar, through which may be seen divisions of twentieths of an Men." By means of this moveable weight, the oscillations of the pendulum in its opposite positions were adjusted to one another, and rendered of equal duration. When this had been effected, it was secured immoveably in its place.
The prisms or knife-edges, which were employed as the axes of motion, were made of the steel prepared in India, and known by the name of wootz. As the accuracy of the experiment depended materially on the uniformity and fineness of their edges, every precaution was taken to render them straight ; Ind the hardest temper was given to the steel, to secure them as much as possible against any change during the operations. The angle of inclina tion of the two planes, which formed the edge of each prism, was about 120 degrees.
Fig. 9. represents the support of the pendulum, "It consists of a piece of bell metal, six inches long, three inches wide, and three-eighths of an inch thick. An opening is made longitudinally through half the length of the piece, to admit the pendulum, and the bell metal is cast with a rectangular elevation, on each side of the open ing, extending through the whole length of the piece. Two plates of agate were cemented to this elevated piece, beds having been made to receive them, in order that their surfaces might be in the same plane with the bell metal. The whole was then ground perfectly flat. A frame of brass, represented, Fig. 10. is attached by two opposite screws, which serve as centres to the elevated part of the support ; and one end of this frame being raised or de pressed by means of the screw A, the pendulum, when placed with its knife-edges resting in Ys at the other end of the frame, could be elevated entirely above the surface of the agate, or be gently lowered till the knife-edges rest ed_wholly upon it ; and thus the knife-edge was sure to bear always precisely on the same part of the agate plane, by elevating the Vs above its surface, placing the knife edge in them, and then letting down the whole gently by means of the screw, till the Ys were completely clear of the knife-edge. The support was firmly screwed to a solid plank of mahogany." With this apparatus Captain hater commenced his ex periments in the house of H. Brown, Esq. in Portland Place. The oscillations of the pendulum were compared with those of a cluck of excellent construction, by Arnold, and the coincidences were observed exactly in the same manner as had been done by Birda. After the number of oscillations in a given time had been observed with suffi cient care, Captain Katcr proceeded to reverse his pendu lum, and by means of the sliding weight E, (Fig. 8.) to bring the oscillations to an equality in the two opposite positions.
This was accomplished with such precision, that in twelve sets of experiments, each consisting of a great number of individual trials, the number of oscillations in twenty-four hours, with the one end of the pendulum up permost, was 86058.71; and with the other end uppermost, the number in the same time was 86053.72, differing from the former only by the hundredth part of an oscillation. When this equality was obtained, the sliding weight was firmly fixed in its place ; and it only remained to ascertain the distance between the knife-edges.