The Mathematical Principles of Natural Philosophy, Book III: Of the System of the World
Phænomena, or Appearances. Phænomenon I
That the circumjovial planets, by radii drawn to Jupiter’s centre, describe areas proportional to the times of description; and that their periodic times, the fixed stars being at rest, are in the sesquiplicate proportion of their distances from its centre.
This we know from astronomical observations. For the orbits of these planets differ but insensibly from circles concentric to Jupiter; and their motions in those circles are found to be uniform. And all astronomers agree that their periodic times are in the sesquiplicate proportion of the semi-diameters of their orbits; and so it manifestly appears from the following table.
The periodic times of the satellites of Jupiter.
1d. 18h. 27’. 34’’. 3d. 13h. 13’ 42’’. 7d. 3h. 42’ 36’’. 16d. 16h. 32’ 9’’.
The distances of the satellites from Jupiter’s centre.
From the observations of 1 2 3 4
Borelli 14
Townly by the Microm. 5,52 8,78 13,47 24,72
Cassini by the Telescope 5 8 13 23
Cassini by the eclip. of the satel. 9
From the periodic times 5,667 9,017 14,384 25,299
Mr. Pound has determined, by the help of excellent micrometers, the diameters of Jupiter and the elongation of its satellites after the following manner. The greatest heliocentric elongation of the fourth satellite from Jupiter’s centre was taken with a micrometer in a 15 feet telescope, and at the mean distance of Jupiter from the earth was found about 8’ 16’’. The elongation of the third satellite was taken with a micrometer in a telescope of 123 feet, and at the same distance of Jupiter from the earth was found 4’ 42’’. The greatest elongations of the other satellites, at the same distance of Jupiter from the earth, are found from the periodic times to be 2’ 56’’ 47’’’, and 1’ 51’’ 6’’’.
The diameter of Jupiter taken with the micrometer in a 123 feet telescope several times, and reduced to Jupiter’s mean distance from the earth, proved always less than 40’’, never less than 38’’, generally 39’’. This diameter in shorter telescopes is 40’’, or 41’’; for Jupiter’s light is a little dilated by the unequal refrangibility of the rays, and this dilatation bears a less ratio to the diameter of Jupiter in the longer and more perfect telescopes than in those which are shorter and less perfect. The times in which two satellites, the first and the third, passed over Jupiter’s body, were observed, from the beginning of the ingress to the beginning of the egress, and from the complete ingress to the complete egress, with the long telescope. And from the transit of the first satellite, the diameter of Jupiter at its mean distance from the earth came forth, and from the transit of the third. There was observed also the time in which the shadow of the first satellite passed over Jupiter’s body, and thence the diameter of Jupiter at its mean distance from the earth came out about 37’’. Let us suppose its diameter to be very nearly, and then the greatest elongations of the first, second, third, and fourth satellite will be respectively equal to 5,965, 9,494, 15,141, and 26,63 semi-diameters of Jupiter.