Surface Changes.—The evidence as to changes in the moon's surface since the first careful observations were made— about a cen tury ago—is doubtful. One. crater, Linn& ob served by Beer and Mfidler, is given as having a diameter of about six miles. At various times it seems to have appeared and disappeared again — possibly owing to the different circum stances under which it was seen; at present it is scarcely visible. In the absence of air and water such changes must be very rare, the weathering action which takes place on the earth having little or no effect; possibly the enormous differences of temperature every two weeks may in time cause a breaking up of the rock.
Photographs—The photography of the moon's surface was started by Draper and Bond in America about the middle of the 19th cen tury. The pictures of the latter were shown at the London Exhibition in 1851 and inspired De la Rue in England and others as to its pos sibilities for the accurate investigation of the lunar surface. The magnificent photographs of Rutherfurd made in New York and published in 1873 have only recently been surpassed by those taken at the Lick, Yerkes and Paris ob servatories. It is possible that photographs taken 20 or more years from now may, on com parison with these, enable astronomers to detect changes if such occur. The varying aspects of the moon will make this difficult, but the per sonal element, always present when drawings have to be made, will at any rate be eliminated. At the same time the eye can detect minute de tails which are absent from photographs.
Periods,—The average time occupied by the moon, in movingin its orbit round the earth, is 27d. 7h. 43m., its sidereal period. The synodic period is the •interval between successive new moons and it is a little longer owing to the time, 365% days, occupied by the earth in moving round the sun. The moon performs 1/27% of its orbit and the earth 1/365% each day, and therefore the difference between these 1/27A — 1/365% is the daily fraction of its path which the moon describes with respect to the sun; that is, 29% days (29d. 12h. 44m.) is the synodic period. If the plane of the moon's orbit coincided with that of the earth's equator, the moon -would rise about 50 minutes later each day, but the inclination of these planes to one another varies between 18° and so that this retardation is • quite different at different times. When full moon occurs near the autum nal equinox, it may, in the latitude of New York, he as small as 23.minutes, while further north it may reduce to nothing, so that for sev eral nights the full moon rises about the same time, soon after sunset. The feature is known as the harvest moon and in countries where the autumn weather is very uncertain, it is a vale able help to the farmers, furnishing them with light•to get in their crops after the setting of the sun. The hunter's moon is the next full moon after the harvest moon; the same phe nomenon, less marked, occurs. The anomalistic month, a little over 271/4 days, is the interval between the times when the moon is in its peri gee, that is, when it is nearest to the earth.
Moon's Path.— The shape of the moon's path is approximately an ellipse whose two axes are nearly of equal length, but an ellipse will only represent its orbit for a very short time. In order to give an idea of its complicated motions, a model, on a scale of 1:125,000,000, can be constructed as follows: The first part, to represent the motion of the earth, consists of a rail on raised sup ports (which are movable) in the shape of an ellipse whose semi-axes are respectively 390 feet 10 inches and 390 feet 3 inches long and whose plane we shall for convenience take to be hori zontal. The earth is represented by a carriage moving on this rail and the sun by a ball placed on the longest diameter, distance 6 feet 7 inches from the centre of the ellipse. A straight bar two feet long is attached to the carriage by a ball and socket joint at a point 3 inch from the centre of the bar. The bar forms the long est diameter of an elastic tube in the shape of an ellipse and the tube is so attached to the bar that it may change its size and shape slightly. The plane of the tube is to be in clined about 5° to the horizontal. A bead slid ing freely within the tube represents the moon.
Motion.— Now let the carriage run along the rail not quite uniformly but so that its angular velocity about the ball representing the sun varies inversely as the square of its dis tance from the ball, and it makes it a complete circuit once in 3651/4 days. At the same time
the plane of the tube attached to the carriage is to turn round slowly in the opposite direction, so that the horizontal line in it (that formed by the intersection of the plane of the tube with the horizontal plane and called the line of nodes) will describe a circuit once in 18M years; the inclination of the tube is to oscillate not more than 5' on either side of the mean inclination of 5° 8' to the horizontal. With these motions, the bar carrying the tube is to slowly turn round in its own plane in a forward direction so as to complete a circuit once in about nine years, and the tube is to slightly change its shape and size to and fro as it moves, finally, the bead representing the moon moves according to the same law and in the same direction as the carriage, that is, not quite uni formly, but so that its angular velocity about the joint varies inversely as the square of its distance from the joint; its circuit in the tube is completed once in 27.5546 days — the anom alistic period. These various motions, com plicated as they are, only give a general idea of the way in which the moon moves, but the model is sufficient to explain most of the phenomena connected with the moon's motion. All the parts are in a state of oscillation about their average positions, the periods varying from a few days to many thousand years. Even the plane, size, shape and position of the rail are not quite constant but vary slowly from year to year. The attempt to disentangle even the principal oscillations had become an almost hopeless task until Isaac Newton in the 17th century was able to reduce them all to mani festations of a single law known as the law of gravitation. This law states that every two particles of matter in the solar system at tract one another with a force which is pro portional directly to the product of the masses and inversely to the square of the distance be tween them, that is, if either of the masses be doubled, the force is doubled, but if the dis tance be halved, the force is increased four-fold. From his time mathematicians have been en.' gaged in working out the consequences of this law. If there are only two particles acting, they describe ellipses about one another, but if more than two act, the motion is so complicated that it taxes the mathematician to the utmost to determine it completely. The moon is attracted mainly by the earth, but it is much disturbed from its elliptic motion round the earth (that in the tube) by the pull of the sun (which mainly causes the motions of the tube), and to a small extent by that of the planets. Up to the last quarter of the 19th century this work was undertaken by European mathematicians, among whom may be mentioned Euler, Laplace, de Pontecoulant, Hansen, Delaunay and Adams: the tables of Hansen, published in London in 1857, are still used, with a few corrections, for the places of the moon in the nautical almanacs of the present day. The greatest advance made during the last 30 years was started by Dr. George William Hill, who was for many years on the staff of the 'American Nautical Almanac) at Washington. His two papers published in 1877 opened a new era in the mathematics of astronomy and especially in that of the moon, and they have formed the basis of nearly all the progress which has since been made in all departments of celestial mechanics. His name, though fully known to astronomers all over the world, is less familiar to the public, on account of the highly mathematical nature of his work. In a different part of the subject, the work of Professor Newcomb is not less valuable, com prising as it does, difficult and laborious investi gations into the sufficiency of Newton's law for the explanation of every detail of the moon's motion, and involving researches into ancient records of eclipses of the sun. A new theory of the moon's motion, leading to the formation of new tables, has now been nearly completed by E. W. Brown on the basis of Dr. Hill's work. Brown has shown that Newton's law of gravi tation will account for the motion of the perigee of the moon within of 1 per cent.