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§§ 155—158] of Philips von Lansberg (1561–1632), which Horrocks had verified for the purpose. It was not, however, till long afterwards that Halley pointed out the importance, of the transit of Venus as a means of ascertaining the distance of the sun from the earth (chapter, § 202). It is also worth noticing that Horrocks suggested the possibility of the irregularities of the moon's motion being due to the disturbing action of the sun, and that he also had some idea of certain irregularities in the motion of Jupiter and Saturn, now known to be due to their mutual attraction (chapter, § 204; chapter , § 243).

157. Another of Huygens's discoveries revolutionised the art of exact astronomical observation. This was the invention of the pendulum-clock (made 1656, patented in 1657). It has been already mentioned how the same discovery was made by Bürgi, but virtually lost (see chapter, § 98); and how Galilei again introduced the pendulum as a time-measurer (chapter , § 114). Galilei's pendulum, however, could only be used for measuring very short times, as there was no mechanism to keep it in motion, and the motion soon died away. Huygens attached a pendulum to a clock driven by weights, so that the clock kept the pendulum going and the pendulum regulated the clock. Henceforward it was possible to take reasonably accurate time-observations, and, by noticing the interval between the passage of two stars across the meridian, to deduce, from the known rate of motion of the celestial sphere, their angular distance east and west of one another, thus helping to fix the position of one with respect to the other. It was again Picard (§ 155) who first recognised the astronomical importance of this discovery, and introduced regular time-observations at the new Observatory of Paris.

158. Huygens was not content with this practical use of the pendulum, but worked out in his treatise called Oscillatorium Horologium or The Pendulum Clock (1673) a number of important results in the theory of the pendulum, and in the allied problems connected with the motion of a body in a circle or other curve. The greater part of these