+---------+---------------+----------------------+-----------------+ | |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 as special cases. The more comprehensive law enables us to criticize Kepler's laws from a higher standpoint, to see how far they are exact and how far they are only approximations. They are, in fact, not precisely accurate, but the reason for every discrepancy now becomes abundantly clear, and can be worked out by the theory of gravitation. We may treat Kepler's laws either as immediate consequences of the law of gravitation, or as the known facts upon which that law was founded. Historically, the latter is the more natural plan, and it is thus that they are treated in the first three statements of the above notes; but each proposition may be worked inversely, and we might state them thus:-- 1. The fact that the force acting on each planet is directed to the sun, necessitates the equable description of areas. 2. The fact that the force varies as the inverse square of the distance, necessitates motion in an ellipse, or some other conic section, with the sun in one focus. 3. The fact that one attracting body acts on all the planets with an inverse square law, causes the cubes of their mean distances to be proportional to the squares of their periodic times.