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so gifted, that poetry, forensic skill, elegant literature, and all the highest attainments of human genius, were within his reach; but he thought the noblest occupation of a man was to make other men happy and free; and in that straight line he went on for fifty years, without one side-look, without one yielding thought, without one motive in his heart which he might not have laid open to the view of God and man. He is gone!-but there is not a single day of his honest life of which every good Irishman would not be more proud, than of the whole political existence of his countrymen,--the annual deserters and betrayers of their native land.

Arr. III. « An Account of Experiments for determining the

Variation in the Length of the Pendulum vibrating Seconds at the principal Stations of the Trigonometrical Survey of Great Britain. By Captain H. KATER, F. R. S. From Phil. Transactions. London, 1819. Part III.

It is not long since we laid before our readers a detailed ac

count of the experimer ts made by Captain Kater, with a view to determine the length of a pendulum vibrating seconds in the latitude of London. We have now to direct their attention to a more extended investigation of the same careful observer, by which he has ascertained the length of a Seconds Pendulum, at the principal stations of the great survey of this Island.

It may be recollected, that this inquiry originated in a bill submitted to Parliament, for the general regulation of Weights and Measures, and fortunately thrown out in the House of Lords. We say fortunately,--because those who most readily admit the expediency of adopting some uniform system, will naturally be the first to reject a plan so crude and so ill calculated to attain that desirable object. One good, however, resulted from the discussion; an address was presented to the Crown, praying that instructions might be given for determining the length of a Seconds Pendulum in the latitude of London, as compared with the standard made for the House of Commons in 1758, known by the name of Bird's Parliamentary Standardfor ascertaining the variations in the length of the Pendulum at the different stations, and for comparing the standard measures with the ten-millionth part of the quadrant of the meridian, the basis of linear measure in France. In order to carry this purpose into effect, a Committee was appointed by the Royal Society; and Captain Kater, a Member of it, was desired to conduct the inquiry. The choice was amply justified by the success which attended his labours in the first branch of the operations; and still more decisive testimony is borne to the same point, by the satisfactory manner in which he has now brought the task to its close, attended as it was with great difficulty, and demanding the utmost patience which a mind, ardent in the pursuit of its object, could bestow upon the endless details essential to the attainment of perfect accuracy.

If in Captain Kater the inquiry found a most able conductor, in the Government it met with no less efficient supporters. Every aid was given him which the enterprise could possibly require. He had sloops of war at his orders, to convey his attendants and instruments; the use of barracks wherever they were to be found; and all the minor accommodations of waggons, non-commissioned officers, gunners, artillery horses and tents. With an establishment thus liberally provided, he left London on the 24th of June 1818, accompanied by Lieutenant Frank of the Royal Navy, and arrived at Unst, one of the Shetland islands, on the 9th of July. This was the most northern station of the Meridional Arc of the Trigonometrical Survey; and Dunnose, in the Isle of Wight, the southernmost. The intermediate stations were Portsoy, lat. 57° 40'; Leith Fort, lat. 55° 58'; Clifton, lat. 53° 27'; Arbury-bill, lat. 52° 12'; and London, lat. 51° 31'. The latitudes of the extreme points, Unst and Dunnose, were 60° 45', and 50° 37' respectively.

As the operations for determining the length of the pendulum were the same at each station, it will only be necessary to enter into the detail of the experiments made at any one of them; and we shall take for example the experiment made at Unst. But before proceeding to this abstract, we must express our regret that Captain Kater should have departed from the old received method of describing the various parts of his apparatus, by references with letters to the parts of the plates representing it. This is peculiarly requisite towards forming, speedily, a distinct idea of instruments which we are not in the habit of seeing; and it enables us to avoid erroneous notions, which a verbal description is apt to create. This defect is no doubt remedied in some degree by the plates annexed to Captain Kater's former paper in the Phil. Trans. for 1818: but they are useful only as a general reference; they present a handsome perspective of the apparatus, while the reader would prefer a more ordinary drawing, with specifick references to the several

parts

described in the text. It may be remembered that the former experiments fo the

latitude of London, were founded upon a very ingenious application of the well known property of oscillating bodies, namely, that the centres of oscillation and suspension are reciprocal. From hence it follows, that the time of oscillation is the same, whether the centre of suspension or of oscillation be taken; and, conversely, if any two points of suspension can be found in a pendulum, such, that the time of vibration is the same in both cases,-then one is the centre of oscillation, when the other is the centre of suspension; and thus, from the distance between the two, we ascertain the true length of the pendulum. In Captain K.'s convertible pendulum, one point of suspension being fixed, the other is placed as near as possible to the calculated centre of oscillation: any inequality in the vibration when it is suspended from different points, is regulated by shifting a moveable weight made to slide between the two centres; and as soon as the oscillations in the two opposite positions are accurately adjusted to one another, the weight is fixed in its place, and the pendulum is complete.

In extending the observations made in London to the other stations, very little alteration was made upon the apparatus described in the former paper, and in our thirtieth volume. The pendulum was of the same construction, and the other parts of the machinery were similar, excepting the frame to which the pendulum, with its support, was attached. This, in all the latter cases, was made of cast-iron, and furnished with a back pierced to receive very large screws, by which it might be firmly fixed to the wall of a building. For further security against any lateral motion, there were brackets below, so formed as to spread at the bottom to a distance of three feet. Every precaution was thus t:ken to render the point of suspension perfectly immoveable. The clock with which the pendulum was compared, was made by Arnold, and had a gridiron pendulum for the compensation of temperature. The other instruments with which Captain Kater was provided, were a box chronometer by Arnold, a transit by Dolland three feet and a half in length, and a repeating circle, of one foot diameter, by Troughton.

On his arrival at Unst, Captain Kater was received by Mr Edmonstone with an hospitality which supplied every thing that might be wanting in so remote a spot. The place which he chose for his experiments was the shell of a cottage adjoining to Mr Edmonstone's house: one wall of it being ancient, and upwards of three feet in thickness, seemed to have all the stability requisite for his purpose. It was the same, 100, in which M. Biot had, the summer before, made his observations on the pendulum. Into this thick wall, strong oak wedges, ilbove a foot in length, were driven; to these the projecting frame of cast-iron was fixed by the long screws mentioned above. Underneath this frame were fastened to the wall by long nails, two deal planks, two inches and a half in- thickness, to which the clock-case was screwed, at such a distance below the frame, as to allow the end of the brass pendulum to reach a little below the clock pendulum. The bell-metal support was next put in its place on the frame; and, being properly levelled, the pendulum was carefully lowered until the knife edges rested on the agate planes. The stand for the telescope was then fixed to the floor at about eight feet and a half from the front of the clock, and the telescope so adjusted, that the centre of the object glass might be in the line joining the white disk and the extremity of the pendulum. The diaphragm was finally brought to correspond with the edges of the pendulum; and the divided arc for indicating the extent of the vibrations, was placed so, that its zero coincided with the extremity of the pendulum.

The Transit instrument was placed on a large stone laid in a box nearly filled with sand, and adjusted so as to be nearly in the meridian, this being sufficient in finding the intervals of time between the transits of the same star. The weather was unfavourable for observations during the first part of Captain Kater's stay in Unst; and it was not till the 22d of July that he began to observe the transits of a few stars. In observing the time of the transits, the chronometer was used, and found to be very convenient from beating half seconds. A comparison of this with the clock (applying a correction for the gain or loss of the clock during the interval between the observation and the comparison) gave the time shown by the clock at the instant of the transit. From observations of the transits of the sun and of six fixed stars, the rates of the clock for several intervals were obtained, by dividing the difference between the times of the transits of each star by the interval in days; and subtracting this from 3' 55".91 (the acceleration of the fixed stars in 24 hours.) This gives the rate of the clock for a sidereal day; while to obtain the rate for a solar day, the gain of the clock in four minutes, namely, 0".14 must be added.

On the 23d of July, Captain Kater began to observe the coincidences of the two pendulums; and he found, between the 22d and 28th, from two series of experiments, each of ten intervals, taken on each day, that the mean number of vibrations in 24 hours amounted to 86090.74, the temperature being corrected for 62°, while the clock made in the same time 86450.63, vibrations. The number of vibrations for each day of the intervals, was deduced from the rate of the clock, gaining 50".69

during the observed interval ; consequently, for any other less-
er interval and rate, the mean of the vibrations during such in-
terval is taken, and to this is added the difference between the
corresponding rate and 50".63, which corrected is positive or
negative, according as the rate of the clock has diminished or
increased. Proceeding in this way, results were obtained for
seven different intervals, the greatest of which was from the
22d to the 28th of July—the least from the 26th to the 28th.
In four of these intervals, the rate of the clock was deduced
from observations upon stars; and in the other three, from ob-
'servations

upon
the sun.

But before employing those seven results to obtain a mean, it is necessary to attend to the errors which are likely to accompany each. In observations on the stars, the chief source of error will arise from the position of the transit instrument with respect to the meridian mark, a flat board fixed in the ground at a distance from the transit, and so adjusted, that when the middle wire of the transit bisected it, the instrument was nearly in the meridian. This board was erected for the convenience of more readily placing the transit in the same position previously to every observation; and so much depended on the accuracy of the position, and on the levelling of the instrument's axis, that a deviation only equal to the diameter of the silk-worm's thread in the focus of the eyeglass, was found to occasion an error, in the time of transit, amounting to three-tenths of a second. The greater the number of days between the two transits, the less will this error atfect the daily rate of the clock; because the whole amount of the crror is divided by the number of days which compose the in terval between the two transits. The accuracy also in a great measure depends on the number of stars observed. It thus appears, that a correct mean will be obtained by multiplying the result for each interval by the product of the number of stars into the interval, and then dividing the sum of the final products by the sum of the factors. In this way the ultimate mean obtained was 86090.77 vibrations in 24 hours, by observations of the stars; and in like manner, by observations of the sun, considering the transits of both limbs as equal to the transits of two stars, we find the vibrations amount to 86090.79. Now in the case of the stars, the sum of the multipliers is 50; in that of the sun, 16; and as the accuracy of the results is in the ratio of those sums, that is, as 8 to 1 nearly, we are entitled to take the final mean equal to 86090.77 vibrations in a mean solar day.

The next correction to be applied, is the allowance for the height of the station above the level of the sea.

This is readily

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