investigations lie outside the field of astronomy, but his formula connecting the time of oscillation of a pendulum with its length and the intensity of gravity (or, in other words, the rate of falling of a heavy body) afforded a practical means of measuring gravity, of far greater accuracy than any direct experiments on falling bodies; and his study of circular motion, leading to the result that a body moving in a circle must be acted on by some force towards the centre, the magnitude of which depended in a definite way on the speed of the body and the size of the circle, is of fundamental importance in accounting for the planetary motions by gravitation.
159. During the 17th century also the first measurements of the earth were made which were a definite advance on those of the Greeks and Arabs (chapter ii., §§ 36, 45, and chapter iii., § 57). Willebrord Snell (1591–1626), best known by his discovery of the law of refraction of light, made a series of measurements in Holland in 1617, from which the length of a degree of a meridian appeared to be about 67 miles, an estimate subsequently altered to about 69 miles by one of his pupils, who corrected some errors in the calculations, the result being then within a few hundred feet of the value now accepted. Next, Richard Norwood (1590?–1675) measured the distance from London to York, and hence obtained (1636) the length of the degree with an error of less than half a mile. Lastly, Picard in 1671 executed some measurements near Paris leading to a result only a few yards wrong. The length of a degree being known, the circumference and radius of the earth can at once be deduced.
160. Auzout and Picard were two members of a group of observational astronomers working at Paris, of whom the best known, though probably not really the greatest, was Giovanni Domenico Cassini (1625–1712). Born in the north of Italy, he acquired a great reputation, partly by some rather fantastic schemes for the construction of gigantic instruments, partly by the discovery of the rotation
- In modern notation: time of oscillation = .
- I.e. he obtained the familiar formula , and several equivalent forms for centrifugal force.