From this description the use of the Comparer will be obvious. The rule and its tongue being divided equally, if, when the tongue was protruded, the divisions of the one coincided exactly with those of the other, the part protrud ed would be indicated precisely; but as this coincidence of the divisions could very seldom happen, the tongue would in general be pushed out a certain number of divisions, plus a fraction, the value of which it was the object to ascertain. For this purpose, the rule was placed upon the Comparer, with its extremity resting upon the heel T. The frame was then moved till the other point T' attached to the extremity b of the lever was brought into contact with the tongue of the rule, and V was at the middle of the scale. The observer then retired till the equable temperature, which had been disturbed by his pre sence, was restored ; after which the vernier was observed, and the tongue drawn back by means of its screw, till the divisions coincided exactly with those of the rule. The temperature having again been allowed to acquire its na tural elevation, the vernier was read off; and the tenth of the space passed over by the long arm of the lever gave the fraction whose value was required. To insure the ut most possible accuracy, the coincidences of the divisions were always observed with very powerful lenses.
After the proper reductions had been made, and the length of the pendulum at each station deduced in the manner already described, it became necessary to make an allowance for the height of the station above the level of the sea; for since the lengths of simple synchronous pen dulums are proportional to the forces by which they are incited, that is, to the force of gravity, which varies with the distance from the centre of the earth, the length of the pendulum is affected by the elevation of the place at which the observation is made. Let R= radius of the earth at the latitude of the station, h= height of the station above the level of the sea, 1= observed length of the pendulum, and r= length at the level of the sea, then 1: : : whence.
(R h)2 2 h .=1 (— I 1+ R rejecting the small fraction- . Therefore, to obtain the length of the synchronous pendulum at the level of the sea, the length measured at any station must be multiplied, 2 h by 1 +— R.
Biot commenced his observations at Leith Fort on the 18th of June ; and they were continued without interrup tion during fourteen days. The clock was by Breguct ; the rod of its pendulum was of fir deal, and so constructed that it could be changed at pleasure from the sexagesimal to the decimal pendulum. The clock had been put in motion several days before the commencement of the ex periments, and its rate carefully determined by compari son with the stars ; a precaution which was taken every day during the whole time of the experiments.
When the experiments at Leith were finished, the whole apparatus, together with the instruments that were to be employed by Captain Colby in fixing the limit of the En glish arc, were embarked on board a brig of war, to be conveyed to Shetland. Blot, attended by Captain Mudge,
was taken on board at Aberdeen. On their arrival in Shetland, they immediately proceeded to Lerwick, where they had originally intended to perform the experiments ; but, on farther consideration, they determined to proceed to the small island of Unst, on account of the advantages it offered, in being about half a degree farther to the north, and also a little to the cast ; and, consequently nearer the meridian of Formentera. At this station, Blot conducted his experiments with greater caution, if possible, than at any of the preceding ; and considering the discouraging circumstances under which he laboured, it is impossible to admire too highly his zeal and perseverance. A few days after their arrival, Captain Mudge was obliged to leave the island on account of ill health ; and Biot, thus left alone, continued his observations, with unremitting
for two
till he had accumulated n'a fewer than thirty-eight series of observations on the pendulum, each of five or six hours ; fourteen hundred observations of latitude, in fifty-five series, taken both to the north and south of the zenith ; and about twelve hundred observations of the absolute heights of the sun and stars, in order to re gulate his clock .See Recited d' Observations Geodesiques, &c. by Blot and Arago, Paris, 1821. • The results of Biot's experiments are given in parts of the metre. The reduction to English inches is made, as has already been stated, by multiplying the lengths expres ed in metres by n9.37076. To obtain the length of the sexagesimal from that of the decimal pendulum, it is neces 1000 „ sary to multiply by the ratio (— 864 Some time previous to the experiments of Biot in Scot land, a bill had been introduced into the British Parliament to establish a uniform system of weights and measures throughout the country. With a view to facilitate the at tainment of this most desirable object, the attention of the scientific men, who promoted the scheme, was turned to the experiments by which the length of the pendulum could be accurately determined, as it had been proposed to assume it as the unit of linear extension ; being one of the very few quantities within the reach of man, which na ture preserves always of the same invariable magnitude. Among those who gave their attention to this subject, Captain Rater particularly distinguished himself by the invention of a method extremely different from that of Bor