attracts as if its mass were concentrated at
its centre. For any other figure, such as an oblate spheroid, this is
not exactly true. A hollow concentric spherical shell exerts no force on
small bodies inside it.

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| Height dropped by a | Length of Day or|
| | System. |stone in first second.|time of rotation.|
+---------+---------------+----------------------+-----------------+
|Mercury | .065 | 7.0 feet | 24 hours |
|Venus | .885 | 15.8 " | 23-1/2 " |
|Earth | 1.000 | 16.1 " | 24 " |
|Mars | .108 | 6.2 " | 24-1/2 " |
|Jupiter | 300.8 | 45.0 " | 10 " |
|Saturn | 89.7 | 18.4 " | 10-1/2 " |
|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.

LECTURE IX

NEWTON'S "PRINCIPIA"

The law of gravitation, above enunciated, in conjunction with the laws
of motion rehearsed at the end of the preliminary notes of Lecture VII.,
now supersedes the laws of Kepler and includes them