Polar circle

“ A large brass semicircle intersects this meridian circle at right angles through the north pole, and is attached to the horizon circle at its extremities. The instrument rests upon an artistic and substantial brass support. On the surface of the sphere are engraved the principal celestial circles, including the colures, the equator, the tropics, the polar circles, the ecliptic, and twelve parallels. The stars, of which the largest are distinguished by a bit of inlaid silver, and the several figures of the constellations which are very artistically engraved, are clearly the work of a master. ”

“ The Earth is shewn in eight different positions in this Circle, and in each position Æ is the Equator, T the Tropic of Cancer, the dotted Circle the parallel of London, U the arctic or north polar Circle, and P the north Pole where all the Meridians or hour Circles meet § 198. As the Earth goes round the Sun the north Pole keeps constantly towards one part of the Heavens, as it keeps in the Figure towards the right hand side of the Plate. ”

“ Yes, we are very near the Earth again, and this is far inside the arctic polar circle, where the sun [82] never goes down during summer, but sets for a long night in the winter. I have kept far to the westward to avoid the magnetic pole, which might play havoc with my apparatus. ”

“ At each pole, in turn, there are six months of continual day followed by six months of continual night, and when the sun is at one of the solstices it just touches the horizon on the corresponding polar circle at the hour that marks midnight on the parts of the earth which lie outside the polar circles. ”

“ If you examine the stars of the Great Bear, you will observe that they turn in a circle considerably larger than that of the Polar Star, but they are still visible in the whole extent of the circle, and they turn completely round in it, without descending below the horizon. If you examine the next bright star Capella, which you will find on the globe in the constellation Auriga, you will find it describes a circle also, of which the Pole Star is apparently the centre. It goes very near the horizon when lowest in the north, and almost over our heads when highest in the south. ”

“ If we further attach to the polar axis a graduated circle DD, called the "hour circle," of which the microscope or vernier R reads 0° when the declination axis is horizontal, we can obviously read off the hour angle from the meridian of any star to which the telescope may be directed at the instant of observation. If the local sidereal time of the observation is known, the right ascension of the star becomes known by adding the observed hour angle to the sidereal time if the star is west of the meridian, or subtracting it if east of the meridian. ”

“ If we assume for the moment that the observer is at the north pole, the pole star will be exactly over head, and therefore, supposing the pole star to absolutely represent the pole of the heavens, all the observer has to do is simply to take a reading of the pole star on the arc of his circle—call it 0° O ́ 0 ̋—and then use it as another zero to reckon polar distance from, seeing that every particular star or body we observe has so many degrees, minutes, seconds, or tenths of seconds, from the pole star. ”

“ The two projections most commonly used for polar charts are the modified Lambert conformal and the polar stereographic. When a directional gyro is used as a directional reference, the track of the craft is approximately a great circle. A desirable chart is one on which a great circle is represented as a straight line with a constant scale and with angles correctly represented. These requirements are not met entirely by any single projection, but they are approximated by both the modified Lambert conformal and the polar stereographic. ”

“ Such a star is as much above the pole at its highest passage, as it is below at its lowest, so that the mean must necessarily give the height of the pole itself free from doubt, except as regards incidental errors. The Pole-star is usually selected for the purpose of such observations because it describes the smallest circle, and is thus on the whole least affected by atmospheric refraction. ”

“ So by moving from the equator to the pole (or a quarter of the distance round the earth) the stars have moved from the horizon to the point overhead, or the zenith, that is also a quarter of a circle. So it appears that if an observer moves to such a distance that the stars appear to move over a certain division of a circle with reference to the horizon, he must have moved over an equal division on the earth’s surface. ”

“ The pole-star describes so small a circle that its motion can only with difficulty be detected with the naked eye, stars a little farther off the pole describe larger circles, and so on, until we come to stars half-way between the two poles, which describe the largest circle which can be drawn on the celestial sphere. The circle on which these stars lie and which is described by any one of them daily is called the equator. ”

“ It will be seen from Fig. 13, that if the distance of a star from the elevated pole does not exceed the elevation of the pole, or the latitude of the place, its diurnal circle will be wholly above the horizon. As the observer approaches the equator, the elevation of the pole becomes less and less, and the belt of circumpolar stars becomes narrower and narrower: at the equator it disappears entirely. As the observer approaches the pole, the elevation of the pole increases, and the belt of circumpolar stars becomes broader and broader, until at the pole it includes half of the heavens. ”

“ The third adjustment is to place the pivots east and west. Note by the clock the time of transit of a circumpolar star, when above the pole, over the central wire, and then half a day later when below it, and again when above it; if the times from upper to lower transit, and from lower to upper are equal, then the line of collimation swings so as to bisect the circle of the star round the pole, and therefore it passes through the pole, and further it describes a meridian which passes through the zenith by reason of the second adjustment. ”

“ By a report of the Astronomer-royal to the Board of Visitors, who have lately made their annual inspection of the Greenwich Observatory, we are informed, of a singular fact, that observations of the pole-star shew that its position varies some three or four seconds on repeating the observations at intervals of a few months, and this notwithstanding the extreme accuracy of the transit circle. The only explanation which can as yet be given for this phenomenon is, that the earth, solid as it appears, is liable to slight occasional movements or oscillations. ”

“ Next (Prop. 2) it is shown that, if a lesser sphere be illuminated by a greater, the illuminated portion of the former will be greater than a hemisphere. Prop. 3 proves that the circle in the moon which divides the dark and the bright portions (we will in future, for short, call this “the dividing circle”) is least when the cone which touches the sun and the moon has its vertex at our eye. In Prop. 4 it is shown that the dividing circle is not perceptibly different from a great circle in the moon. ”

“ Those which are nearest the pole describe the smallest 11circle, and those upon the Arctic circle the largest. The latter appears to graze the horizon.
“The stars to the south of this circle all rise and set, on account of their circles being partly above and partly below the earth. The segments above the earth are large and the segments below the earth are small in proportion as they approach the Arctic circle, because the motion of the stars nearest the circle above the earth is made in the longest time, and of those below the earth in the shortest. ”

“ As conceived by astronomers the æquinoctial circle is equidistant from both poles, cutting the world in the middle, measures the motions of their primum mobile or tenth sphere, and is named the zone of the primum mobile. It is called æquinoctial, because when the sun stands in it (which must happen twice in the year) the days are equal to the nights. That circle is also spoken of as æquidialis, wherefore it is called by the Greeks ἰσημερινός. In like manner it is also properly called Æquator, because it divides the whole frame of the earth between the poles into equal parts. ”

“ Still I confess I do not follow you in your circle theory."
"To begin with," returned Heliobas, "the Universe is a circle. Everything is circular, from the motion of planets down to the human eye, or the cup of a flower, or a drop of dew. MY 'circle theory,' as you call it, applied to human electric force, is very simple; but I have proved it to be mathematically correct. Every human being is provided INTERNALLY and EXTERNALLY with a certain amount of electricity, which is as necessary to existence as the life-blood to the heart or fresh air to the lungs. ”

“ Why should not the circle represent other things than the sun? In modern astronomy the full moon is represented by the plain circle, while the sun, at least in heraldry, is always represented as a circle with rays. It is believed that the “cross or four wheel-like spokes” in the Chaldean emblem of the sun will be found to be rays rather than cross or spokes. A cast is in the U. S. National Museum (Cat. No. 154766) of an original specimen from Niffer, now in the Royal Museum, Berlin, of Shamash, the Assyrian god of the sun. ”

“ Although it is agreed on all hands that 500 greater accuracy may be obtained by a repeating circle, than by any other having the same radius, yet there are some objections to its use which do not apply to the altitude and azimuth circle. The following are the principal objections, as stated in Vol. I., of the ‘Memoirs of the Astronomical Society of London.’ 1. The origin of the repeating circle is due to bad dividing, which ought not to be tolerated in any instrument in the present state of the art. 2. ”