14. The earth's equatorial protuberance, being acted on by the attraction of the sun and moon, must disturb its axis of rotation in a calculated manner; and thus is produced the precession of the equinoxes. [The attraction of the planets on the same protuberance causes a smaller and rather different kind of precession.]
15. The waters of the ocean are attracted towards the sun and moon on one side, and whirled a little further away than the solid earth on the other side: hence Newton explained all the main phenomena of the tides.
16. The sun's mass being known, he calculated the height of the solar tide.
17. From the observed heights of spring and neap tides he determined the lunar tide, and thence made an estimate of the mass of the moon.
Reference Table of Numerical Data.
| Masses in Solar System. | Height dropped by a stone in first second. | Length of Day or time of rotation. | |
| Mercury | ·065 | 7·0 feet | 24 hours |
| Venus | ·885 | 15·8 " | 23½ " |
| Earth | 1·000 | 16·1 " | 24 " |
| Mars | ·108 | 6·2 " | 24½ " |
| Jupiter | 300·8 | 45·0 " | 10 " |
| Saturn | 89·7 | 18·4 " | 10½ " |
| The Sun | 316000· | 436·0 " | 608 " |
| The Moon | about ·012 | 3·7 " | 702 " |
The mass of the earth, taken above as unity, is 6,000 trillion tons.
Observatories.—Uraniburg flourished from 1576 to 1597; the Observatory of Paris was founded in 1667; Greenwich Observatory in 1675.
Astronomers-Royal.—Flamsteed, Halley, Bradley, Bliss, Maskelyne, Pond, Airy, Christie.