to the refractive effects of Saturn's atmosphere, the outline of the shadow is probably fringed with a wide ruddy or copper-coloured penumbra.* The central line of the shadow sweeps uniformly round the rings, the shadow disappearing, at or before sunrise, in the west, in the same manner (at all seasons and in all latitudes) as it had appeared in the east. The changes taking place from the vernal equinox to the summer solstice are repeated in reverse order from the summer solstice to the autumnal equinox.

In his 'Outlines of Astronomy,' Sir John Herschel states that 'the regions beneath the dark side' undergo ‘a solar eclipse fifteen years in duration.' Dr. Lardner appears to have imagined that Herschel supposed the whole hemisphere beneath the dark side of the ring to undergo a total eclipse fifteen years in duration; and, in a paper read before the Astronomical Society in 1853, he endeavoured to show 'that by the apparent motions of the heavens produced by the diurnal rotation of Saturn, the celestial objects, including the sun and the eight satellites, are not carried parallel to the edges of the rings; that they are moved so as to pass alternately from side to side of these edges; that, in general, such objects as pass under the rings are only occulted by them for short intervals before and after their meridional culmination; that although, under some rare and exceptional circumstances and conditions, certain objects, the sun being among the number, are occulted from rising to setting, the continuance of such phenomena is not such as has been supposed, and the places of its occurrence are far more limited.'† It will appear, however, on a more exact examination, that Lardner was in error on nearly every point he imagined he had established.

There are two methods by which astronomers determine the occurrence and nature of a solar eclipse. In one, the apparent paths of the sun and moon on the celestial sphere are examined for short intervals of time before and after the time of new moon; and

* No attempt has been made in Plate XII. to indicate either the form of such penumbras or the twilight-circle bordering the parts of the planet in shadow. The extent of these depends altogether on the unknown extent and refractive powers of Saturn's atmosphere. The true penumbra, or that due to the apparent size of the sun's disc, is too small to be appreciable either in these figures or in the figures of Plate XIII.

† Dr. Lardner's 'Museum of Science and Art,' vol. i. p. 59.

the moments of first and last contact and of central eclipse are thence deduced. In the other, a spectator is supposed to view from the sun the passage of the moon's disc across the larger disc of the earth; the manner in which the given place on the earth's surface would appear to move, if viewed from the sun's centre during the time of passage, is easily determined; and the moments of first and last contact, and of central eclipse, are determined from the simple principle that if the given point on the earth is so situated that it would be invisible from a given point of the sun at any instant, then such point of the sun must also be invisible from the" given point on the earth, or, in other words, is eclipsed.

The application of the first method to the eclipses of Saturn's surface by his ring-system is simplified by the consideration that the rings occupy an invariable situation on the celestial sphere of any given point on Saturn's surface. At the autumnal equinox of either hemisphere the sun has at rising an azimuth of 90° (in other words, the sun rises in the east), and attains a meridian altitude equal to the complement of the latitude. After the autumnal equinox the sun passes to the south of the celestial equator in northern, to the north in southern latitudes; and as his declination increases his meridian altitude and azimuth at rising diminish. At length the sun crosses the horizon at the points (called A in Table XI.) in which the outer edge of the outer ring meets the horizon. From this time the sun is eclipsed after rising and before setting for intervals of gradually increasing length, until he crosses the meridian at the same point (called B in Table XI.) as the outer edge of the outer ring. From this time the sun is eclipsed throughout the day (except, in certain latitudes, for two intervals of a few minutes, during which he is seen between the rings), until at rising and setting he crosses the horizon at the points (called A' in Table XI.) in which the inner edge of the inner ring meets the horizon. From this time the sun is visible (through the dark ring), after rising and before setting for intervals of gradually increasing length, until he crosses the meridian at the same point (called B'.in Table XI.) as the inner edge of the inner ring. From this time he is visible throughout the day (neglecting the partial eclipses probably caused

by the dark ring) until the winter solstice, and for a corresponding interval after the winter solstice. During the quarter of a Saturnian year from the winter to the vernal equinox a similar series of eclipses takes place in reverse order. In latitudes higher than 19° 50′ the sun does not reach the point B'; so that in these latitudes eclipses in the middle of each day continue to the winter solstice. Again, in latitudes higher than 35° 52′ the sun does not reach the point a', so that in these latitudes eclipses lasting throughout the day continue to the winter solstice.

The intervals during which eclipses of each kind are continued can be roughly determined by construction in the method indicated at page 164. The last section of Table XI. contains the more trustworthy results of calculation. From this table it will be seen that, even at the equator, the sun is totally or partially eclipsed for several days; but that the periods of eclipse increase rapidly with the latitude. Thus, in latitude 40°, the eclipses begin when nearly three years have elapsed from the time of the autumnal equinox. The morning and evening eclipses continue for more than a year, gradually extending until the sun is eclipsed during the whole day. As the sun does not reach the point a' in these latitudes, these total eclipses continue to the winter solstice and for a corresponding period after the winter solstice; in all for 6 years 236'4 days, or 5543′0 Saturnian days. This period is followed by an interval of more than a year of morning and evening eclipses. The total period during which eclipses of one kind or another take place is no less than 8 years 292.8 days. In a similar manner the eclipses for other latitudes are determined from Table XI. If we remember that latitude 40° on Saturn corresponds with the latitude of Madrid on our earth, it will be seen how largely the rings must influence the conditions of habitability of Saturn's globe, considered with reference to the wants of beings constituted like the inhabitants of our earth.

The second method of determining the extent and duration of solar eclipses-called the method of projecting eclipses-is less exact than the former, but better adapted for illustration. The figures of Plate XIII. represent Saturn as he would appear if viewed from the sun at the vernal equinox of the northern hemi

sphere (fig. 1); at the summer solstice of the same hemisphere (fig. 8); and at six intermediate periods.* These epochs correspond with those of the figures of Plate XII., and, like them, are separated by equal intervals of 384 days. The arctic circles are represented by the lines a a'a" and a a'a", the tropics by the lines t t't" and t t't", the equator by the line e e'e", and the north pole by the point p, in each figure (see Chapter IV. pp. 95-99); the rings are supposed to be removed, and their shadows on the planet's disc thus rendered visible. † These shadows pass to the southern hemisphere at the autumnal equinox of that hemisphere, travelling rapidly southward at first, but more slowly as their width increases; and about two years before the winter solstice the lower edge of the black shadow passes beyond the lower edge of the disc. The five dotted parallels of latitude in each figure (except fig. 1) represent :-The parallel just reached by the lower edge of the black shadow; a parallel passed over by this edge; a parallel just within the upper edge of the black shadow; a parallel just clear of this edge; and a parallel just clear of the dusky shadow of the dark ring. Now, owing to the rotation of Saturn on his axis, any point on his surface would appear to an observer in the sun to travel along a latitude-parallel, appearing on the left edge of the disc (the moment of sunrise at the place), and disappearing on the right (the moment of sunset at the place). Hence, a place between the lowest pair of dotted parallels in any figure (that is, at the epoch represented by such figure) would be in shadow in the morning and evening, dipping below the shadow in the middle of the day; a place between the second and third dotted parallels (counting upwards) would be in shadow throughout the day; a place between the third and fourth would not be in the black shadow in the morning and evening, but would dip within it in the middle of the day; and, lastly, a place within the two upper dotted parallels would not be in the dusky shadow in the morning and evening, but would dip within it in the middle of the day. These results correspond with those already * Fig. 1 corresponds to Saturn's position on the 18th of May, 1862; fig. 8, to his position in March, 1870.

† To avoid confusion the line of light corresponding to the division between the rings is omitted in the figures of Plate XIII.

obtained, and the figures of Plate XIII. sufficiently indicate the vast extent attained by the shadow near the time of the winter solstice, and the consequent long duration of eclipses, in latitudes not very near the equator. The shadow of the ring passes through the same changes of form in inverse order between the winter solstice and the vernal equinox of the southern hemisphere; but the pole of the planet passes to the left, so that at the latter period fig. 1 inverted represents the disc of the planet. The other figures inverted indicate the manner in which the shadow sweeps across the northern hemisphere, to the winter solstice of that hemisphere. The shadow, in returning, passes through the same changes, but in inverse order, and sloped towards the left instead of towards the right. Thus, at the end of the Saturnian year the appearance of the disc is again as in fig. 1.

All objects whose declinations are variable, such as the planets and the outer satellite, undergo a similar series of eclipses. The extent and duration of such eclipses for any celestial object will vary with the range of the object's changes of declination. Thus the outer satellite, whose declination never exceeds 15° north or south of Saturn's celestial equinoctial-line, may be totally eclipsed during the whole time it is above the horizon only in latitudes lower than 25° north or south; since the point в of the ring is more than 15° from the equinoctial in higher latitudes.

Since the seven interior satellites move very nearly in the plane of the rings, it is clear that in places very near Saturn's equator these satellites can only become visible when they reach their greatest departure from the plane of the rings. In all other parts of Saturn's surface these satellites can never be eclipsed by the rings. Their orbits being (approximately) circles concentric with the rings, would, like the edges of the rings, appear as ellipses to the Saturnians, and would lie altogether clear of the rings-just as the outer edge of a ring lies altogether clear of the inner edge. The apparent magnitudes of the satellites vary with the point of Saturn's surface from which they are viewed, and with their own motions. The following table will serve to give an idea of the relations among the satellites in the latter respect; the satellites are supposed to be viewed from a place near Saturn's