Astronomical Constants. MEAN solar parallax, 8".80. Nutation constant, 9".21. Moon's equatorial horizontal parallax, 57' 2".68. Moon's mean distance from the earth (centre to centre), 238.850 miles. Light travels unit of distance-viz. 92,894,800 miles in 498.566 seconds. Mean Length of the Month-Synodical (from new moon to new moon), 29 days 12 hours 44 minutes 2.8 seconds. Tropical, 27 days 7 hours 43 minutes 4.7 seconds. Sidereal (absolute revolution), 27 days 7 hours 43 minutes 11.5 seconds. Anomalistic (from perigee to perigee), 27 days 13 hours 18 minutes 33.1 seconds. Polar radius, 3949.79 miles. Dimensions of the Earth-Equatorial radius, 3963.23 miles. Eccentricity of the oblate spheroid, 0.0822718. Halley's Comet. Of the great number of comets which have temporarily visited our solar system or have become permanent members of it none has surpassed Halley's in historical associations. It has a record dating back to B. C. 240; its visitations spread alarm and consternation throughout Europe during the Middle Ages: was the first whose return was predicted by an Astronomer Royal of England, and will therefore, for these reasons, be an object of great selentific Interest for all time. For the Information of those who appreciate such matters the following are the elements of its orbit as deduced from the last visitation: Perthellon Passage 1910, April, 19.67. Greenwich Mean Time. Longitude of the ascending node = 57° 16′ 12". The semi-axis major and the perihelion distance are expressed in terms of the earth's mean distance from the sun, taken as unity. See also article on Halley's Comet and on Comets in ALMANACS of 1910 and 1911. The periodic time varies considerably by reason of the attraction of the planets. Its average duration is about 76,5 years.-J. M. 60 The Force of Gravity. (By J. Morrison, M. D., Ph. D.) NOTWITHSTANDING all the researches of man Into the arcans of nature, there are several things which he, with all his boasted powers, cannot define, among which may be mentioned time, space, matter and force. We become cognizant of the existence of the first by reason of the dally and annual motions of the celestial bodies; but given a blank sky and a continuous vertical sun we would have a very imperfect appreciation of it, if any at all, since there would be no means of measuring It is a uniformly flowing quantity, of only one dimension, for as regards simple duration, we can only look back to the past and forward to the future. It may therefore be graphically represented by a straight line extending in opposite directions to infinity. it. Space, we know, has three dimensions, length, breadth, and depth or height, each extending In opposite directions to inanity. In a general way we say that matter is any substance which occuples space, but this is no definition. We know nothing of its intrinsic nature or essence whatever. There are on the earth some 67 or 68 different kinds of matter; we know something of their physical properties, of their combinations and reactions on one another, but beyond that we know nothing about them. Everything in the universe, whether visible or Invisible, is either material or spiritual; if there were no spiritual world, It is certain there would be no material one; matter undoubtedly rests or subsists on a spiritual basis. When a portion of matter-a plece of iron for Instance is unsupported it falls to the ground, and being an inanimate substance, it cannot move itself, hence some invisible power or force moves it. This force is called gravity or gravitation and is due to the attraction of the earth. We cannot define force; we know nothing about its intrinsic nature. In general language we say, it is any agent or cause which changes or tends to change the state or position of matter with respect to rest or motion. Different names are given to forces according to the effects produced. Thus we speak of the force of attraction of the earth which holds ourselves and all movable things on its surface, molecular force which binds the molecules of a body together, repulsive forces, electrical forces, vital forces, etc., but they are all alike in their essential quality. All forces are spiritual in their nature; they are certainly not material. For instance the force which holds the moon in its orbit around the earth, does not consist of material bonds or wires. Since then it is not material, what is it? It must necessarily be of a spiritual nature, although it operates through matter. In the case of a body moving in a circle or of the moon around the earth or of a planet around the sun, we have occasion to speak of centripetal and centrifugal forces about which some erroneous impressions are taught in some works on phystes. As an illustration of these forces, let us consider the case of a railway car running on a smooth, straight, level track, to enter a circular curve. While moving on the straight track there is no force operating to sway It to one side or the other, but when it enters the curve it is constrained to move In the arc of a circle. The flange on the outer wheels presses against the inner edge of the outer rail, and the inner edge of the outer rall presses against the flanges, these pressures are equal, in opposite directions and always at right angles to the direction of motion upon which they have no Influence whatever. The former-the pressure of the flange against the rall-is the centrifugal force-away from the centre, and the latter-the pressure of the rail against the flange-is the centripetal force. When the car leaves the curve and enters a straight track, these forces vanish instantly. The mode or manner in which gravity or gravitation acts on matter, was discovered by Sir Isaac Newton. Its action is continuous and according to a certain law which we shall now explain. In mathematics and physics a law may be defined to be the constant and continuous operation of a cause or agent by which certain effects or phenomena are produced. Thus we have the law of a series which determines the order of succession of the terms; the law of the compressibility of gases; the laws of motion; Kepler's laws of the planets; the law of universal gravitation, etc. As an illustration of some of these laws, let us take the series 1-3+3-5+5-7+7-9+, etc., to infinity. Here the law of formation of the terms is evident. Each term increases but can never exceed unity and the sum of them all is infinity. As another example take the series 1+6+20+56 +144 +, etc. Here the law is not evident, but the subsequent terms are determined by a law as invariable as in the preceding. The law of universal gravitation as originally propounded by Sir Isaac Newton is this: "Every particle of matter in the universe attracts every other particle with a force which varies directly as the mass and Inversely as the square of the distance between them." In accordance with this law it is easy to show mathematically that the attraction of a sphere on a body external to it, is exactly the same as if the entire mass of the sphere were condensed or collected at the very centre. This will be more easily understood from the following Illustration: 1 16 13 36 รั้ว 10 ETC. " म 100 ETC. Let CA represent the radius of the earth and the points 2, 3, 4, etc., two, three, etc., rad!! from the centre C; then whatever may be the attraction at the surface A, one radius from the centre, at 2 It is 1-4; at 3. 1-9; at 4, 1-16 and so on, of what it is at A, that is to say, the force varies inversely as the square of the distance. If the mass of the earth, for instance, were doubled, trebled, etc., the force would be increased in the same ratio. This is what is meant by "directly as the mass.' The mean radius of the earth is about 3,956 miles-say 4,000 for the sake of illustration-and at the surface it has been found by actual experiments that a body will fall from rest. 16 feet and one inchsay 16 feet to avoid fractions-in one second; then according to the above law, at the distance of two rad from the centre or 4,000 miles above the surface, the body would fail only one-fourth of 16 feet or 4 feet in a second; at three radil from the centre it would fall one-ninth of 16 feet; at four radi one-sixteenth of 16 feet or one foot in a second and so on, decreasing as the square of the distance from the centre increases. At sixty radi-the moon's average distance-it would fall only the 1-3,600 of 16 feet or about one-nineteenth of an inch, and this is what the moon actually does fall or depart from the straight line in which it would move if not disturbed by the earth's attraction. This was the first verification made by Sir Isaac Newton, of this wonderful law. Gravitation is universal, it holds the universe together in its tremendous grasp, It prevents the planets, the sun and stars from disintegration, that is to say from being torn in fragments by the centrifugal force generated by the rotation on their axes; its suspension would wreck the universe. I gravity were suspended on the earth only, our atmosphere would instantly vanish into space; our oceans and lakes would leave their beds and be thrown off like spray; our continents and mountains. now so solid under our feet, would be torn from their foundations and hurled in countless millions of fragments into the limitable regions of space. This, however, is a catastrophe which can never occur. But to return to a consideration of the effect of gravity on the earth's surface, in which every one is more or less interested, we first remark that it confers weight on bodies. Weight, however, is not an essential property of matter like porosity, elasticity, etc. The weight of a body is the measure of the attractive force of gravity on it and is not the same in all places. A pound of |