The bases of modern astronomy. Their late formation 18 Instruments and measures used by ancient astronomers 19 Weights and measures sought out by modern astronomers 20 Means employed to discover the density of the earth. Measuring by means of plummets not sufficiently exact 20 Measurements with torsion and chemical balances more accurate 21 Sir George B. Airy's theory, and experiments at the Harton colliery 22 Results of experiments not reliable. Theory contrary to the Law of Attraction 23 Proof by arithmetical calculation of its error 24 Difficulties in comparing beats of pendulums at top and bottom of a mine 26 The theory upheld by text-books without proper examination 27 Of a particle of matter within the shell of a hollow sphere. Not exempt from the law of Attraction 28 A particle so situated confronted with the law of the inverse square ofdistance from an attracting body. Remarks thereon 29 It is not true that the attraction of a spherical shell is "zero" for a particle of matter within it 31 CHAPTER II. The moon cannot have even an imaginary rotation on its axis, but is generally believed to have. Quotations to prove this 33 Proofs that there can be no rotation. The most confused assertion that there is rotation shown to be without foundations 35 A gin horse does not rotate on its axis in its revolution 37 A gin horse, or a substitute, driven instead of being a driver 38 Results of the wooden horse being driven by the mill 38 The same results produced by the revolution of the moon. Centrifugal force sufficient to drive air and water away from our side of the moon 39 That force not sufficient to drive them away from its other side 40 No one seems ever to have thought of centrifugal force in connection with air and water on the moon 41 Near approach made by Hansen to this notion 41 Far-fetched reasons given for the non-appearance of air and water 42 The moon must have both on the far-off hemisphere 44 Proofs of this deduced from its appearance at change 44 Where the evidences of this may be seen if looked for at the right place. The centrifugal force shown to be insufficient to drive off even air, and less water, altogether from the moon 45 The moon must have rotated on its axis at one period