POETRY. THE CLOUDLESS. “Sorrow and sighing shall flee away."-ISAL. XXXV. 10. No shadows yonder! All light and song; And say, How long From that dear throng? No weeping sonder ! All fied away ; Each weary day, My long, long stay. No parting yonder! Time and space never Hearts cannot sever; Hands clasp for ever. None wanting yonder! Bought by the Lamb; The evergreen palm ; Ascends the glad psalm.-Q. J. P. CELESTIAL OBJECTS. AUGUST, 1854. Celestial sphere, And heavenward flies, " For the bright firmament Shoots forth no flame, In speaking the Creator's name. Contracts its light We shall discern How man may heavenly knowledge learn." We have had and may again have occasion to remark on the parabolic form of the orbits of Comets. To render such remarks intelligible to those who have not given any attention to the geometry of curved lines, it seems desirable to convey a correct idea of the parabola, and to define the terms connected with it, which must be used if we would avoid circumlocution. A parabola is a plane curve, every point of which is equally distant from a fixed point and an indefinite straight line given in position, the point and line being in the plane of the curve. Thus, if K A L represents the parabola, S the fixed point, and EF the indefinite straight line, all in the same plane, the distance of any point, P, in the curve is equal to the perpendicular distance from E F, that is, the straight line PS is equal to PG. The fixed point S, is called the focus. This is the point occupied by the centre of the Sun when the parabola is the orbit of a Comet. The indefinite straight line EF is called the directrix. The straight line A B drawn through the focus, at right angles to the directrix, and produced indefinitely, is the aris of the parabola. The point A, where the axis meets the curve, is the vertex. This is the point in the curve which is nearest to the focus. In the case of a parabolic orbit it is called the perihelion (Tepi, near, and rjdlos, the sun ;) the straight line A S is then called the perihelion distance. The line PS, drawn from any point to the focus, is called the radius rector at that point: this, as well as the perihelion distance, is expressed numerically by taking the Earth's mean distance from the Sun as unity. The angle A S P is the true anomaly. The straight line, CD, drawn through the focus, perpendicular to the axis and terminated both ways in the curve, is the latus rectum, or right parameter : its length is equal to four times the perihelion distance. By measuring off SH equal to SP, the radius vector at any point, P, the line PH is a tangent to the curve at the point P, and is therefore the direction of the Comet’s motion at that point. PH bisects the angle contained by SP and PG. The velocity of the Comet at any point is found by the following simple rule :Divide 722 by the radius vector at that point, the square root of the quotient is the velocity in English miles per second. Thus, if S P be twice the mean distance of the Earth from the Sun : Divide 722 by 2; the square root of 361, the quotient, is 19, and the velocity is 19 English miles per second. It is manifest from this rule that the velocity is greatest at the perihelion, where the distance from the Sun is least. Let the perihelion distance be half of our mean distance from the Sun: Divide 722 by }, that is, multiply by 2; the square root of 1444, the result, is 38, which is the greatest velocity in miles per second. The parabola extends indefinitely beyond the points K L, and recedes indefinitely from the axis and directrix : from this it will be easily understood that a body moving in a parabola round the Sun can never return. But we must remember that the limits of our paper are not indefinite. MERCURY having crossed below the Sun's disc, reappears this month in the morning to the telescopic observer, gradually waxing from a thin crescent to the form of the Moon three days after the full. The distance from us is more than doubled during the month : it increases to 118 millions of miles, whereas in perigee it was only 56 millions. The apparent diameter diminishes in exactly the same proportion as the distance increases, and will, therefore, at the end of the month, be less than half what it was at the beginning. The apparent motion will be retrograde till the 9th, at 8h. in the afternoon. It rises in declination till the 18th, when it will be 17° 51' north of the equator. It appears to recede from the Sun till noon of the same day: its western elongation will then be 18° 31'. In respect to its heliocentric positions :-on the morning of the 2d, it would appear, from the Sun, at the greatest angular distance from the ecliptic, 7° south; on the evening of the 21st, it will be in the ecliptic; and at 6h. on the morning of the 26th, it will be in perihelion ; distance, 29,326,600 miles. The heavens, seen from Mercury, must present a rapidly varying aspect. Uranus will be in opposition on the morning of the 21st, Saturn un the morning of the 25th, and Venus on the morning of the 28th. On the morning of the 24th, Mars will be in conjunction. The angular distance of the Earth, westward of the Sun, is diminishing: on the 18th, it will be 90°, which is Jupiter's angular distance on the 17th : therefore at this period these two bodies will appear very close together. VENUS recedes from us sixteen millions of miles during the month. She is now approaching the Sun; the angular distance on the 16th will be about 30° west. At noon of the 1st she will begin to descend, after having attained her greatest northern declination, 22° 24'. At half-past five on the morning of the 20th, she will be in ascending node. At 2h. on the morning of the 21st, she will be near the Moon. Referred to this planet as a centre, Mars will be in conjunction on the afternoon of the 5th; Saturn in opposition on the afternoon of the 15th. Mercury will be at his greatest western elongation, 29°, on the 13th or 14th. Up to this time he will appear gibbous, subsequently falcate. The Earth and Jupiter appear very close together. The former, on the 16th, will be at an angular distance of 44o east from the Sun; that of the latter, 41°. MARS recedes from us at almost precisely the same rate as Venus. The Sun appears to be daily gaining on him. His eastern elongation on the 16th is 60°. As he sets on the 1st two hours, and on the 31st an hour and a half, after the Sun, he will be barely perceived with the naked eye, low in the west, after dusk. At two o'clock on the morning of the 15th, he will be within 1° 49' of the bright star Spica in Virgo. At 10h. on the morning of the 28th, he will be near the Moon. To a dweller on this planet, Venus would be in superior conjunction on the afternoon of the 5th ; Saturn close to the Sun on the western side, and approaching conjunction; Uranus on the western side, receding ; Mercury in superior conjunction on the 24th; the Earth, his morning star, at an angular distance from the Sun of 35° on the 16th,-form that of the Moon five days after the full; Jupiter on the same side, elongation 106o. JUPITER is now a fine object in the southern heavens. About the middle of the month he sets as Venus rises. On the evening of the 6th he will be near the Moon. In the absence of these two bodies, he is by far the most conspicuous celestial object. His apparent magnitude on the 16th is that of a ball an inch and a half in diameter, at a distance of two hundred yards. SATURN has again presented himself, with his extraordinary appendages, for inspection. The elliptic outline of the ring will be broadest, in proportion to the length, on the 29th, when the outer axes of the outer ring will be forty-one and eighteen seconds, the diameter of the sphere sixteen seconds. At that time we view the a planet from an elevation of 26° 27' above the plane of the ring on the southern side. The planet is now approaching the Milky Way. URANUS will move eastward among the fixed stars till the 22d, after which his apparent motion will be retrograde. The distance from the Earth is diminishing. He is now favourably situate for telescopic examination. Seen from this planet, the Earth is now nearly at its greatest elongation from the Sun, 3o eastward; and the apparent magnitude of “this huge ball on which we tread" is that of a grain of sand three-hundredths of an inch in diameter placed at a distance of two hundred yards. RISING AND SETTING OF THE SUN, FOR THE PARALLELS OF THE BRITISH ISLANDS. Rises. Sets. Rises. Sets. Rises. Sets. Rises. Sets. Rises. Sets. h. m. h. mh, m. h.m. n. m. h. m. h. m. h. m. h. m. h. m Aug. 14 28 7 43 4 20 7 51 4 12 7 59 4 2 8 93 51 8 19 11 4 42 7 27 4 36 7 33 4 29 7 40 4 21 7 47 4 13 7 56 21 4 57 7 84 52 7 12 4 47 7 18 4 41 7 24 4 35 7 30 31 5 12 6 47 5 9 6 51 5 5 6 54 5 1 6 58 4 56 7 3 SUN AND PLANETS AT GREENWICH. Sun. MERCURY. VENUS. Mars. JUPITER. SATURN. URANUS. H. 1. & J. Roche, Printers, 25, Hoxton-square, London. |