iant. Of his scientific achievements those now
reckoned most weighty, are the discovery of the Laws of Motion, and the
laying of the foundations of Mechanics.

_Particulars of Jupiter's Satellites,
Illustrating their obedience to Kepler's third law._

--------------------------------------------------------------------------
| | | Distance| | | T^2
| | Time of | from | | | ----
Satellite.|Diameter revolution | Jupiter, | T^2 | d^3 | d^3
| miles.| in hours. |in Jovian | | | which is
| miles | (T) | radii. | | |practically
| | | (d) | | | constant.
----------|-------|------------|----------|---------|---------|-----------
No. 1. | 2437 | 42.47 | 6.049 | 1803.7 | 221.44 | 8.149
No. 2. | 2188 | 85.23 | 9.623 | 7264.1 | 891.11 | 8.152
No. 3. | 3575 | 177.72 | 15.350 | 29488. | 3916.8 | 8.153
No. 4. | 3059 | 400.53 | 26.998 |160426. |19679. | 8.152
--------------------------------------------------------------------------

The diameter of Jupiter is 85,823 miles.

_Falling Bodies._

Since all bodies fall at the same rate, except for the disturbing effect
of the resistance of the air, a statement of their rates of fall is of
interest. In one second a freely falling body near the earth is found to
drop 16 feet. In two seconds it drops 64 feet altogether, viz. 16 feet
in the first, and 48 feet in the next second; because at the beginning
of every second after the first it has the accumulated velocity of
preceding seconds. The height fallen by a dropped body is not
proportional to the time simply, but to what is rather absurdly called
the square of the time, _i.e._ the time multiplied by itself.

For instance, in 3 seconds it drops 9 x 16 = 144 feet; in 4 seconds 16 x
16, or 256 feet, and so on. The distances travelled in 1, 2, 3, 4, &c.,
seconds by a body dropped from rest and not appreciably resisted by the
air, are 1, 4, 9, 16, 25, &c., respectively, each multiplied by the
constant 16 feet.

Another way of stating the law is to say that the heights travelled in
successive seconds proceed in the proportion 1, 3, 5, 7, 9, &c.; again
multiplied by 16 feet in each case.

[Illustration: FIG. 35.--Curve described by a projectile, showing how it
drops from the l