earth and sun, sometimes far from it, when she is on the outside of the earth. Now if it be true that the power which moves the earth and the moon round the sun remains of the same efficacy, and if it be true that the same moveable, acted on by the same force, passes over similar arcs of circles in a time which is least when the circle is smallest, we are forced to the conclusion that at new moon, when in conjunction with the sun, the moon passes over greater arcs of the orbit round the sun, than when in opposition at full moon; and this inequality of the moon will be shared by the earth also. So that exactly the same thing happens as in the balance of the clocks; for the moon here represents the leaden weight, which at one time is fixed at a greater distance from the centre to make the vibrations slower, and at another time nearer to accelerate them." Wallis adopted and improved this theory in a paper which he inserted in the Philosophical Transactions for 1666, in which he declares, that the circular motion round the sun should be considered as taking place at a point which is the centre of gravity of the earth and moon. "To the first objection, that it appears not how two bodies that have no tie can have one common centre of gravity, I shall only answer, that it is harder to show how they have it, than that they have it."[113] As Wallis was perfectly competent from the time at which he lived, and his knowledge of the farthest advances of science in his time, to appreciate the value of Galileo's writings, we shall conclude this chapter with the judgment that he has passed upon them in the same paper. "Since Galileo, and after him Torricelli and others have applied mechanical principles to the solving of philosophical difficulties, natural philosophy is well known to have been rendered more intelligible, and to have made a much greater progress in less than a hundred years than before for many ages." FOOTNOTES: [93] See page 56. [94] Playfair's Dissertation, Supp. Encyc. Brit. [95] Astronomia Nova. Pragæ. 1609. [96] The new Planet no Planet, or the Earth no wandering Star, except in the wandering heads of Galileans. London, 1646. [97] Aristarchi Samii de Mundi Systemate. Parisiis 1644. [98] See page 12. [99] De Cœlo, lib. iv. cap. 3. [100] Reflexiones Physico-Mathematicæ, Parisiis, 1647. [101] Venturi. [102] Riccioli. [103] The notions commonly entertained of 'up' and 'down,' as connected with the observer's own situation, had long been a stumbling-block in the way of the new doctrines. When Columbus held out the certainty of arriving in India by sailing to the westward on account of the earth's roundness, it was gravely objected, that it might be well enough to sail down to India, but that the chief difficulty would consist in climbing up back again. [104] See page 50. [105] Riccioli Almag. Nov. [106] Plutarch, De placit. Philos. lib. iii. c. 17. [107] συμπαθεως τῃ σεληνη. Geographiæ, lib. iii.