Secular In illustration of the great accuracy with which calculations and ob servations may be compared at the present time may be mentioned what is known as the secular acceleration. Observation shows that at the end of each century the average time of revolution of the moon round the earth is 2 seconds less than it was at the beginning. Newton's law shows that a slight change in the shape of the earth's orbit (that is in the shape of the rail above) due to the attractions of the planets will account for M of this amount; the other M are still unexplained. This means that astronomers are searching for the cause of a monthly change of less than 1/1000 of a second in the length of the month.
phases of the moon arise from the combined motion of the earth and moon. To resume our mechanical model, imagine the tube to be.transparent and the ball an electric light. When the bead is furthest from the ball, the side of the bead facing the carriage is illu minated and this corresponds to full moon. As the bead moves round the tube a spectator on the carriage sees less and less of the illuminated half ; the bead then passes through its third and last quarters until it is at its nearest to the ball and almost invisible. Still progressing, its illu minated half begins to be visible from the other side (new moon) and passing on to its first and second quarters its illuminated half is again fully seen.
An eclipse of the moon takes place whenever the earth gets between the moon and the sun, cutting off the light of the latter from the moon, an eclipse of the sun when the moon gets between the earth and the sun. (See ECLIPSE). It so happens that the apparent size of the moon as seen from the earth is very nearly equal to that of the sun. Owing to the varying distance of the moon and sun from the earth, sometimes the moon, as seen from a place on the earth, will completely cover the sun for a time which may be as long as eight minutes, and we have a total eclipse; at other times it fails to cover it and we get a partial eclipse or, if its centre passes across the sun's centre, an annular eclipse. A total or annular eclipse is seen over only a narrow band of the earth's surface. From our mechanical illustra tion it is evident that an eclipse of the moon can occur only at full moon, and one of the sun just before new moon. If the plane of the
tube were horizontal there would be eclipses of both moon and sun every revolution of the bead, that is, once a month; actually, it is only when the bead is very near the horizontal plane (or near the line of nodes) at the time when it is nearest or furthest from the ball, that the event can take place. A complete cycle of eclipses will evidently occur each time the line of nodes completes a circuit —once in about 18 years. This is known as a lunar cycle and during that period there will be on the average 41 eclipses of the sun and 29 of the moon.
Besides the indirect effect of the moon as a light-giver on the earth the most important influence it exerts is that which causes the tides. (See TIDES). These have in their turn a slight reactionary effect on the motion of the moon as we shall see presently. Some slight traces of lunar effect are also ob servable in the variations of the earth's mag netism. But the most widespread idea with re gard to lunar influence is its supposed connec tion with the changes in the weather. Many an old saying exists, handed down the ages, giving a rule for prophesying the weather by its con dition at certain phases of the moon. Since the time when careful daily records have been kept of the temperature, height of the barometer, rainfall, etc., science has been employed in ex amining whether any kind of period can be traced in them and especially periods connected with the moon's changes. Little positive suc cess has attended these efforts, but there is plenty of negative evidence. Every attempt to connect a periodical change in the weather with one in the moon's motion has resulted in fail ure. Undoubtedly some slight connection of a tidal nature must exist, hut it is very small and is entirely masked by variations of the weather due to unknown causes. A reason for the pop ular error is not far to seek. The weather changes, especially in countries lying within the temperate zone, follow one another at short and seemingly irregular intervals; the changes of the moon's phases occur also at short but regular intervals. Coincidences between the two must frequently occur, but humanity is apt to notice these and to forget the failures of co incidence which are just as numerous if not more so.