be the place of the planet and S' that of the sun, produce D'E to P. Then M'DE will answer to the angle gained by the earth on planet in Art. 101, and Fig. 16, but S'ES — DED' = angle gained, because the deferent is described in the periodic time of the planet. Hence M'D'E S'ES-PES = PES' : therefore D'M' and S'E are parallel, and consequently M'ES' = D'M'E. But if the radius of the epicycle : radius of the deferent SE SN (Fig. 16): distance of earth from sun: distance of planet from sun in true system; the triangle ED'M' will be always equiangular to SEN (Fig. 16). Hence D'M'E, and therefore S'EM' will always shew the true angular distance of the sun from the planet, and so the motions of the superior planets will be rightly represented.

119. There are some circumstances in the Ptolemaic system that ought naturally to have led to the true system. The former determines nothing with respect to the distances of the planets from the earth; it only requires that the proportion of the radii of the deferent and epicycle be such as to represent the motion for each planet. The distances therefore are arbitrary. If we take the radius of the deferent of an inferior planet equal to the radius of the sun's orbit, we immediately have the inferior planets revolving round the sun, while the sun is carried round the earth, according to the reported system of the Egyptians. This simplification of the Ptolemaic system with respect to the inferior planets is so obvious, that we may suppose it soon occurred without any reference to the Egyptian system, and to have been the first advance toward the true system. We know it is mentioned by Martianus Capella, who appears to have lived in the fifth century, and by others long before the time of Copernicus. If we take the radius of the deferent of a superior planet equal to the planet's true distance from the sun, the radius of the epicycle for each planet will be the earth's distance from the sun. This striking circumstance might have led Coperni

cus to simplify the system, by giving a motion to the earth, by which one circle is made to serve the purpose of several equal

ones.

120. Although the Ptolemaic system explains the general appearances with much simplicity; yet when it was applied to explain those appearances which arise from the inclination of the orbits to the ecliptic, from the eccentricities and the unequal motions in those orbits, the introduction of other circles beside the deferent and epicycle being necessary, the system became very complex, and much ingenuity and mathematical sagacity were shewn in adapting it to different circumstances. Had the instruments now in use then existed, a very few observations would have been sufficient to have completely overthrown all those speculations. But the state of instruments and of observations was such in the time of Copernicus, after whom the true system has justly been named, that he could use scarcely any arguments in support of his system but what he derived from its simplicity. It was only a short time before his death, in 1543, at the age of 71, he ventured to propose his system to the world, in his work entitled "De Revolutionibus Orbium," after having meditated upon it above 36 years. It does not seem to have made much impression till above half a century after, when Galileo, aided by his telescope, was enabled to bring most powerful arguments in favour of it. His observation of the gibbosity of Venus was decisive in favour of the motion of Venus about the sun. Had the motion of Venus been according to the Ptolemaic system, it must always have appeared in a telescope as a crescent.

121. The ancients observing that the planets moved faster or slower according to the place of the ecliptic they were in, when in opposition, or near conjunction, named this the first inequality. The retrograde, stationary, and direct appearances they called the second inequality. Copernicus, who conceived

G

that the celestial motions were necessarily performed in circles, was obliged to retain epicycles to explain the first inequality.

122. Although there was nothing in the Ptolemaic system, that could properly lead to the knowledge of the actual distances of the planets from the earth; yet as the system appeared very imperfect without it, astronomers substituted an hypothesis resting on no foundation. They imagined that the convex boundary of the space, within which the epicycle of a planet performed its motion, was the concave boundary of the space belonging to the next; and as they knew, although inaccurately, the distance of the moon, they obtained from it the distance of Mercury; from the distance of Mercury that of Venus, &c. The distances obtained in this way differed extremely, as might be expected, from the truth. Till therefore the Copernican system was established, nothing whatever was known with respect to the actual distances, and consequently the magnitudes, of any of the planets. But the distances of the sun and moon, although very inaccurate, were deduced from just principles.

CHAPTER VIII.

ON THE SECONDARY PLANETS AND MOON-ATMOSPHERES OF PLANETS-RINGS OF SATURN-COMETS.

123. FOUR Small stars, only visible by the help of telescopes, always accompany Jupiter, and are continually changing their positions with respect to each other and Jupiter. They are called satellites and secondary planets. The first satellite is that which elongates itself least from Jupiter, &c. They clearly shew that Jupiter is an opaque body enlightened by the sun; for when they intervene between him and the sun, they project a shadow on his disc. They themselves are also opaque bodies illuminated by the sun; for when the planet intervenes between any of them and the sun, they are eclipsed. The phænomena prove that they revolve about their primary at different distances in orbits nearly circular, while they are carried together with their primary about the sun. Their orbits are inclined to the plane of Jupiter's orbit, as is concluded from the unequal durations of the eclipses of the same satellite. The fourth satellite is sometimes in opposition to the sun, without being eclipsed. This is owing to the inclination of its orbit and great distance from Jupiter. The third and fourth satellites disappear and re-appear on the same side of Jupiter. Only the beginnings or the endings of the eclipses of the first and second satellite are visible.

124. Let S (Fig. 21) be the sun; I Jupiter and its shadow; A and P the earth before and after the opposition of Jupiter;

sp the path of the first satellite in the shadow; At a tangent to Jupiter. When the first satellite enters the shadow, the apparent distance of the satellite from the body of Jupiter is tAs; but at its emersion, the line pA always passes through Jupiter, and therefore the emersion is invisible; but after opposition, the earth being at P, the emersion and not the immersion will be visible. The same things take place with respect to the second satellite. If mn be the path of the third satellite, mA frequently lies without the body of Jupiter, and therefore both the immersion and emersion are visible; and the phænomena are very striking, from the circumstances of the satellite disappearing and re-appearing at a distance from the body of Jupiter on the same side. The same may be observed with respect to the fourth satellite. Before the opposition of Jupiter to the sun, the eclipses happen on the west side of Jupiter; after opposition, on the east. If the telescope invert, the contrary takes place.

125. It has long been suspected, that the satellites of Jupiter revolve on their axes; and lately Dr. Herschel has observed that each of them revolves in the time of its revolution round the primary. Their motions about the primary, and their motions about their axes, are from west to east.

a

126. Their distances in semi-diameters of Jupiter, and their periodic times are nearly as follow:

They must be very magnificent objects to the inhabitants of Jupiter. The first satellite appears to them with a disc four times greater than that of our moon appears to us, and goes through all the changes of our moon in the short space of 42

a Phil. Trans. 1797, page 332.