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 of the pendulum at Paris (which was 3 Paris feet and 8$3/5$ lines), he found it shorter by 1¼ line.

Afterwards, our friend Dr. Halley, about the year 1677, arriving at the island of St. Helena, found his pendulum clock to go slower there than at London without marking the difference. But he shortened the rod of his clock by more than the $1/8$ of an inch, or 1½ line; and to effect this, be cause the length of the screw at the lower end of the rod was not sufficient, he interposed a wooden ring betwixt the nut and the ball.

Then, in the year 1682, M. Varin and M. des Hayes found the length of a simple pendulum vibrating in seconds at the Royal Observatory of Paris to be 3 feet and 8$5/9$ lines. And by the same method in the island of Goree, they found the length of an isochronal pendulum to be 3 feet and 6$5/9$ lines, differing from the former by two lines. And in the same year, going to the islands of Guadaloupe and Martinico, they found that the length of an isochronal pendulum in those islands was 3 feet and 6½ lines.

After this, M. Couplet, the son, in the month of July 1697, at the Royal Observatory of Paris, so fitted his pendulum clock to the mean motion of the sun, that for a considerable time together the clock agreed with the motion of the sun. In November following, upon his arrival at Lisbon, he found his clock to go slower than before at the rate of 2′ 13″ in 24 hours. And next March coming to Paraiba, he found his clock to go slower than at Paris, and at the rate 4′ 12″ in 24 hours; and he affirms, that the pendulum vibrating in seconds was shorter at Lisbon by 2½ lines, and at Paraiba, by 3⅔ lines, than at Paris. He had done better to have reckoned those differences 1⅓ and 2$5/9$: for these differences correspond to the differences of the times 2′ 13″ and 4′ 12″. But this gentleman's observations are so gross, that we cannot confide in them.

In the following years, 1699, and 1700, M. des Hayes, making another voyage to America, determined that in the island of Cayenne and Granada the length of the pendulum vibrating in seconds was a small matter less than 3 feet and 6½ lines; that in the island of St. Christophers it was 3 feet and 6¾ lines; and in the island of St. Domingo 3 feet and 7 lines.

And in the year 1704, P. Feuillé, at Puerto Bello in America, found that the length of the pendulum vibrating in seconds was 3 Paris feet, and only 5$7/12$ lines, that is, almost 3 lines shorter than at Paris; but the observation was faulty. For afterward, going to the island of Martinico, he found the length of the isochronal pendulum there 3 Paris feet and 5$10/12$ lines.

Now the latitude of Paraiba is 6° 38′ south; that of Puerto Bello 9° 33′ north; and the latitudes of the islands Cayenne, Goree, Gaudaloupe, Martinico, Granada, St. Christophers, and St. Domingo, are respectively 4° 55′, 14° 40″, 15° 00′, 14° 44′, 12° 06′, 17° 19′, and 19° 48′, north. And