410 THE MATHEMATICAL PRINCIPLES [BOOK III. gravity, and in the latitude of Paris, the length of a pendulum vibrating seconds is 3 Paris feet, and S£ lines, or rather because of the weight of the air, 8f lines, the length of a pendulum vibrating in the same time arider the equator will be shorter by 1,087 lines. And by a like calculus the following table is made. Latitude of the place. Length ol the pendulum iMeasure of one degree in the meridian. Deg. Feet Lines. Toises. 0 3 . 7,468 56637 5 3 . 7,482 56642 10 3 . 7,526 56659 15 3 . 7,596 56687 20 3 . 7,692 56724 25 3 . 7,812 56769 30 3 . 7,948 56823 35 3 . 8,099 56882 40 3 . 8,261 56945 1 3 . 8.294 5695? 2 3 . 8,327 5697 1 3 3 . 8,361 56984 4 3 . 8;394 56997 45 3 . 8.428 57010 6 3 . 8,461 57022 7 3 . 8,494 57035 8 3 . 8,528 57048 9 3 . 8,561 57061 50 3 . 8,594 57074 55 3 . 8.756 57137 60 3 . 8^907 57196 65 3 . 9,044 57250 70 3 . 9,162 57295 75 3 . 9,258 57332 80 3 . 9,329 57360 85 3 . 9,372 57377 90 3 . 9,387 57382 By this table, therefore, it appears that the inequality of degrees is sc small, that the figure of the earth, in geographical matters, may be con sidered as spherical ; especially if the earth be a little denser towards the plane of the equator than towards the poles. Now several astronomers, sent into remote countries to make astronomical observations, have found that pendulum clocks do accordingly move slower near the equator than in our climates. And, first of all, in the year I 72, M. Richer took notice of it in the island of Cayenne ; for when, in the month of August, he was observing the transits of the fixed stars over the meridian, he found his clock to go slower than it ought in respect of the mean motion of the sun at the rate of 2' 29" a day. Therefore, fitting up a simple pendulum to vibrate in seconds, which were measured by an ex cellent clock, he observed the length of that simple pendulum ; and this he did over and over every week for ten months together. And upon his re turn to France, comparing the length of that pendulum with the length