Meridian circle

“ It has been shown that meridians are, necessarily, straight lines; and that it is impossible to travel round the Earth in a north or south direction: from which it follows that, in the general acceptation of the word “degree,”—the 360th part of a circle—meridians have no degrees: for no one knows anything of a meridian circle or semicircle, to be thus divided. But astronomers speak of degrees of latitude in the same sense as those of longitude. ”

“ The earliest spheres were doubtless made to revolve just as the globes of today, around their polar axes which turn within sockets firmly attached to the meridian circle. This meridian circle of brass or wood was usually graduated from one to ninety degrees, that is, from the equator to the poles, and being adjustable relative to the horizon circle, a globe could be set with a polar elevation for any desired latitude. Those who have had occasion to refer to the construction and the uses of the globe more or less in detail, make mention of what they call its threefold position. ”

“ The sun, moving along the ecliptic, always moves in a great circle, while the point of the meridian which is to overtake the sun moves in a diurnal circle, which is sometimes a great circle and sometimes a small circle. When the sun is at the equinoxes, the point of the meridian which is to overtake it moves in a great circle. As the sun passes from the equinoxes to the solstices, the point of the meridian which is to overtake it moves on a smaller and smaller circle: hence, as we pass away from the celestial equator, the points of the meridian move slower and slower. ”

“ But with the telescope of the meridian circle the watch-dial would be visible even at the distance of a mile. The meridian circle is indeed capable of such precision as a sighting instrument that it could be pointed separately to each of two stars which subtend at the eye an angle no greater than that subtended by an adjoining pair of the sixty minute dots around the circumference of a watch-dial a mile distant from the observer. ”

“ Each elliptical meridian has for one axis the central meridian, and for the other the intercepted portion of the equally divided equator. It follows that the meridians 90° east and west of the central meridian form a circle. It is easy to show that to preserve the property of equal areas the distance of any parallel from the equator must be √2 sin δ where π sin φ = 2δ + sin 2δ, φ being the latitude of the parallel. The length of the central meridian from pole to pole = 2 √2, where the radius of the sphere is unity. The length of the equator = 4 √2. ”

“ These globes have a diameter of about 1 m. and still retain the greater part of their original mounting, which, in each, consists of a meridian circle (this in the terrestrial globe is modern) not graduated, within which they are adjusted to revolve on their equatorial polar axes, of a horizon band, likewise not graduated, being circular on the inner edge, but octagonal on the outer, the whole being supported by four turned legs joined by crossbars at their lower extremities. ”

“ But, supposing we do not trust to them; supposing we make use of the Transit Instrument, and the Mural Circle. By the former we observe how long the sun is passing the meridian after a star; we find it is later and later every day; that every time the sun comes to the meridian, he has travelled (with respect to the stars) towards the left or towards the east, in such a manner, that, in the apparent diurnal motion, or passage, he is later and later, with respect to the stars, every day. Suppose that with the Mural Circle we observe the altitude of the sun every day when he passes the meridian ”

“ The true meridian may also be ascertained, or rather the equinoctial line, which cuts the meridian at right angles, by observing the points where the sun rises and sets, and by observing how much they are distant from the equinoctial either to the north or to the south. For this purpose an astrolabe is formed with the globe; that is, a circle is made representing the earth’s circumference, divided into 360 deg. ”

“ This circle represents the plane of the meridian; its centre the actual point of east or west, i.e., the common intersection of the horizon and æquator; all those lines æquidistant from the æquator denote the parallels of the sun and stars; the fiducial line of the rule or alhidade represents the horizon; and its parts signify the degrees of the horizon, beginning from the point of setting or of rising. {176}
Therefore if the fiducial line of the rule be applied to the given latitude of the place reckoned from either end of that diameter which represents the axis of the world ”

“ If the latitude is known, the declination of any body can be determined by observing a meridian altitude. It is usually best to make a number of observations shortly before and after transit, plot the values on graph paper, letting the ordinate (vertical scale) represent altitude, and the abscissa (horizontal scale) the time. The altitude is found by fairing a curve or drawing an arc of a circle through the points, and taking the highest value. A meridian altitude problem is then solved in reverse. ”

“ The shell thus formed is then cut along the line of the intended equator into two hemispheres, they are then again glued together and made to revolve round an axis the ends of which passed through the poles and entered a metal meridian circle. The sphere is then coated with plaster or whiting, and when it has been smoothed on a lathe and dried, the lines representing meridians and parallels are drawn upon it. Finally the globe is covered with the paper gores upon which the map is drawn. The adaption of these gores to the curvature of the sphere calls for great care. ”

“ Correspondingly the two meridian planes, which are determined by one perradial axis and the spineless axis, may be called the two primary or perradial meridian planes.
The globe is divided by the equatorial plane into two equal halves, the northern and the southern hemisphere. In each hemisphere there are disposed quite symmetrically eight radial spines, the distal ends of which fall in two parallel circles, a larger tropical circle (nearer to the equator) and a smaller polar circle (nearer to the pole of the spineless axis) . ”

“ A transverse or inverse meridian is a great circle perpendicular to a transverse equator. An oblique meridian is a great circle perpendicular to an oblique equator. Any meridian used as a reference for reckoning time is called a time meridian. The meridian used for reckoning standard zone, daylight saving, or war time is called standard, zone, daylight saving, or war meridian respectively. The meridian through any particular place or observer, serving as the reference for local time, is called local meridian, in contrast with the Greenwich meridian, the reference for Greenwich time. ”

“ No matter how longitude is calculated, you must necessarily arrive at discontinuity at some point in passing around the great circle of the earth. It seems to me that the most convenient way of counting both longitude and time is that the discontinuity in both shall take place on the same point on the earth. Now, certainly, as was observed at Rome, it will be far less inconvenient if the discontinuity of date takes place on the meridian of 180 degrees from Greenwich. ”

“ It is as though two men were to keep moving round a circle in the same direction, with the same speed, and at diametrically opposite points; it must be an arbitrary decision which would pronounce that either was in advance, or in arrear, of the other.
Regarding, then, the meridian of 180° as the neutral point, the most rational system, so far as British settlements are concerned, is to reckon longitude both ways, from 0° to 180°, east and west from Greenwich; and to regard all west longitude as in arrear of British time, and all east longitude as in advance of it. ”

“ Founded in 1874; meridian circle by Repsold of 4%-in. ap., and meteorological, magnetical, and tide-registering instruments. AUsTR1A-HUNGARY
Vienna, imperial and royal obs. On the univ. building an obs. was founded in 1756, lat. + 48° 12' 35-5", long. 1 h. 5 m. 31-7s. E. Owing to the unsuitable locality and the want of instruments, very few obs. of value were taken until the obs. was rebuilt in 1826, when some better instruments were procured, especially a meridian circle of 4-in. ap., and a 6-in. refr. by Fraunhofer (mounted in 1832) , used for obs. of planets and comets. ”

“ The meridians are generators of the cone and every parallel such as HH′ is a circle, concentric with the selected parallel Pp and distant from it the true rectified length of the meridian arc between them.
This projection has no merits as compared with the group just described. The errors of scale along the parallels increase rapidly as the selected parallel is departed from, the parallels on paper being always too large. As an example we may take the case of a map of South Africa of the same range as that of the example given in (a) above, viz. ”

“ Having "set up" over the point through which it is proposed to establish the meridian, at a time when the line joining Polaris and Alioth is nearly vertical, level the telescope by means of the attached level, which should be in adjustment, set the vernier of the vertical arc at zero, and take the reading. If the pole star is about making its upper transit, it will rise gradually until reaching the meridian as it moves westward, and then as gradually descend. ”

“ On the contrary, initial meridians for geography need not be fixed with quite such a high degree of accuracy as is required by astronomy; but, in compensation, their operation must be far reaching, and while it is useful to increase as much as possible the number of meridians of observatories, it is necessary to reduce as much as we can the starting points for longitudes in geography.
Further, it may be said that as the position of an observatory should be chosen with reference to astronomical considerations, so an initial meridian in geography should only be fixed for geographical reasons. ”

“ Whatever we may do, the common prime meridian will always be a crown to which there will be a hundred pretenders. Let us place the crown on the brow of science, and all will bow before it.
Commander Sampson, Delegate of the United States, said that he thought that the Delegate of France, Professor Janssen, had explained very fully the advantages of a neutral meridian, but he thought that he had not explained how we are to determine the neutral meridian. ”

“ Because if [Pg 126] you go on reckoning from zero to 360 degrees continuously, you have to make a break at 360 degrees. You do not count on after you have completed one revolution, but have to drop the 360 degrees and start again at zero. But this is attended with great inconvenience, because this break in counting occurs in countries which are thickly inhabited. The longitude would be a little less than 360 degrees on one side of the prime meridian, and on the other side the longitude would be a small angle. ”

“ It is hardly necessary to say that no scientific or practical advantage is to be secured by adopting the meridian of the great pyramid, or by attempting to establish permanent meridian marks over a great length of the selected meridian, for even in the present advanced condition of astronomical and geodetic science it is not practicable to establish two points on the same meridian at a considerable distance from each other with such a degree of accuracy as would warrant the use of them indifferently as the initial point. ”

“ We should prefer to adopt the term mediator, as proposed by M. Bouthillier de Beaumont, it being analogous to the term equator, which is the starting-point in reckoning latitudes.
This matter of a first meridian gives rise to very grave complications. Each nation wants to have its own meridian passing through its capital city, or its principal observatory. Hence result numerous difficulties, errors, even dangers and accidents to ships, in case we are not sure about the meridian employed, or if we are in error in our reckoning of the difference between one meridian and another. ”

“ This distance of the parallels may be expressed in the form r = a (sin φ + 1⁄3 sin3 φ + 1⁄5 sin5 φ + ...) , showing that near the equator r is nearly proportional to the latitude. As a consequence of the similar representation of small parts, a curve drawn on the sphere cutting all meridians at the same angle—the loxodromic curve—is projected into a straight line, and it is this property which renders Mercator’s chart so valuable to seamen. For instance: join by a straight line on the chart Land’s End and Bermuda, and measure the angle of intersection of this line with the meridian. ”

“ But in proceeding in an oblique sphere, from rising or setting to either meridian, the time occupied must be unequal; and in a right sphere, equal, because the entire portions above the earth are, in a right sphere only, equal to those below the earth; whence, for instance, in a right sphere, whatever stars may be together on the meridian must also all rise and set together, until their progress becomes perceptible by the poles of the zodiac; while, on the other hand, in an oblique sphere, whatever stars may be together on the [Pg 146] meridian can neither all rise together nor set together ”