Astronomical tables

“ Astronomers claim an accuracy to the twentieth part of a second when such transits are carefully taken, but over a long period, greater exactness is obtained. Really, the time at which any given star passes the meridian is taken, in practical life, from astronomical tables in the Nautical Almanacs. Those tables are the result of the labors of generations of mathematicians, are constantly subject to correction, and cannot be made simple. Remember, the Earth's rotation is the only uniform motion, all the others being subject to variations and even compound variations. ”

“ In a word, then, all the purely arithmetical, trigonometrical, and logarithmic tables already mentioned, are necessary, either immediately or remotely, for this purpose. But in addition to these, a great number of tables, exclusively astronomical, are likewise indispensable. The predictions of the astronomer, with respect to the positions and motions of the bodies of the firmament, are the means, and the only means, which enable the mariner to prosecute his art. ”

“ When we contemplate the ease and expedition with which the seaman determines the position of his vessel, and with what confidence he directs it to the most distant quarter of the globe, we are not perhaps aware of the immense variety of tables which have been formed almost solely for his use: and without the aid of which he dare not venture on the boundless ocean. Not only must the general tables of the sun and moon be first computed, together with the various equations for determining their apparent places ”

“ Their Knowledge of the motion of the Heavens, for which the Arabians and the other Eastern Nations have been so deservedly famous, as their Astronomical Tables of the Longitude and Latitude of the fixed Stars, and of the appulse of the Moon to them, fully evince, is now very mean, and is chiefly studied for the use of Judiciary Astrology. The great Instrument they make use of is an Astrolabe, with which they make very imperfect Observations, having no such thing as a Quadrant or Sextant, much less a Telescope, or any mechanical Engine, to direct and assist them in their Calculation. ”

“ This superiority of the new tables was only indirectly connected with the difference in the principles on which the two sets of tables were based, and was largely due to the facts that Reinhold was a much better computer than the assistants of Alfonso, and that Coppernicus, if not a better mathematician than Ptolemy, at any rate had better mathematical tools at command. Nevertheless the127 tables naturally, had great weight in inducing the astronomical world gradually to recognise the merits of the Coppernican system, at any rate as a basis for calculating the places of the celestial bodies. ”

“ Independent of their very limited extent, the elements from which they were deduced, have been superseded by others more agreable to actual observation; which, together with their exclusion of the solar nutation, and other minute quantities which cannot safely be neglected in the present state of astronomy, renders these tables of doubtful utility to the practical astronomer.
The number of zodical stars (without including the very minute ones) is considerably above a thousand: each of which may, in the course of a revolution of the nodes, suffer an occultation by the moon. ”

“ We must first know by the most exact and refined observations that the astronomer can make exactly how a heavenly body does move. Its position, or, as we cannot directly measure distance, its direction from us, must be determined as precisely as possible from time to time. Its course has been mapped out for it in advance by tables which are published in the "Astronomical Ephemeris," and we may express its position by its deviation from these tables. Then comes in the mathematical problem how it ought to move under the attraction of all other heavenly bodies that can influence its motion. ”

“ Tables necessary to determine the places of the planets are not less necessary than those for the sun, moon, and stars. Some notion of the number and complexity of these tables may be formed, when we state that the positions of the two principal planets, (and these the most necessary for the navigator,) Jupiter and Saturn, require each not less than one hundred and sixteen tables. ”

“ But the telescope and microscope enable us at present to measure celestial arcs much more accurately than was done by the older astronomers. In the best instruments, the measurements extend to a single second of space, or one thirty-six hundredth part of a degree,—a space, on a circle twelve feet in diameter, no greater than one fifty-seven hundredth part of an inch. To divide, or graduate, astronomical instruments, to such a degree of nicety, requires the highest efforts of mechanical skill. ”

“ But the Finder, which is a telescope with a small power, and consequently has a large field of view—when directed to any object, it is easily found, and being brought to the centre of the field, where two cross hairs intersect each other, it will then be seen in the larger telescope. B is the eye-tube for terrestrial objects, containing 4 glasses, and C, one of the astronomical eye-pieces. A socket is represented at g, containing a stained glass, which is screwed to any of the eye-pieces, to protect the eye from the glare of light, when viewing the spots of the sun. ”

“ The only instrument which, as I think, may possibly be called for by the demands of the astronomer or the astronomical public, is a telescope of the largest size, for the observation of faint nebulae and minute double stars. Whether the addition of such an instrument to our apparatus would be an advantage, is, in my opinion, not free from doubt. The line of conduct for the Observatory is sufficiently well traced; there can be no doubt that our primary objects ought to be the accurate determination of places of the fundamental Stars, the Sun, the Planets, and, above all, the Moon. ”

“ If equal portions of space really held equal numbers of stars, it is obvious that the number of stars visible in any particular direction would be strictly proportional to the range of the system in that direction, apparent accumulation being produced by real extent. The process of "gauging the heavens," accordingly, consisted in counting the stars in successive telescopic fields, and calculating thence the depths of space necessary to contain them. The result of 3,400 such operations was the plan of the Galaxy familiar to every reader of an astronomical text-book. ”

“ I have fitted up several instruments of the above description with specula of 16, 27, 35, and 49 inches focal distance. One of these having a speculum of 27 inches focal length, and an astronomical eye-piece, producing a magnifying power of about 90 times, serves as a good astronomical telescope. By this instrument the belts and satellites of Jupiter, the ring of Saturn, and the mountains and cavities of the moon, may be contemplated with great ease and distinctness. With a magnifying power of 35 or 40 times, terrestrial objects appear remarkably bright and well-defined. ”

“ The measurements that correspond in astronomy to terrestrial latitude and longitude are called declination and right ascension and are obviously made with reference to the celestial equator, not the ecliptic. For taking these measurements astronomers employ circles on the celestial sphere perpendicular to the plane of the celestial equator and passing through the poles of the heavens. These are called hour circles. The hour circle of any star is the great circle passing through it and perpendicular to the plane of the equator. ”

“ The more numerous, minute, and accurate these predictions can be made, the greater will be the facilities which can be furnished to the mariner. But the computation of those tables, in which the future position of celestial objects are registered, depend themselves upon an infinite variety of other tables which never reach the hands of the mariner. It cannot be said that there is any table whatever, necessary for the astronomer, which is unnecessary for the navigator. ”

“ It is expedient that the astronomical observer should have access 507 to some distant field within a mile of the observatory, on which a meridian mark may be fixed, after his graduated instruments are properly adjusted. The distance at which a meridian mark should be erected will depend in part on the focal length of the telescope generally used for making observations on the Right Ascensions and declinations of the stars. ”

“ A section of the sidereal system along any great circle can be constructed from the data furnished by the gauges in the following way:
The solar system is within the mass of stars. From this point lines are drawn along the different directions in which the gauging telescope was pointed. On these lines are laid off lengths proportional to the cube roots of the number of stars in each gauge. The irregular line joining the terminal points will be approximately the bounding curve of the stellar system in the great circle chosen. Within this line the space is nearly uniformly filled with stars. ”

“ The galactic system is composed of a countless number of stars, spreading out on all sides along a very extended plane. These stars, which are very unevenly distributed, show a decided tendency to cluster together into individual groups of different sizes and forms, separated by comparatively vacant spaces. This layer where the stars congregate in such vast numbers may be conceived as a very irregular flat disk, sending many branches in various directions, and having a diameter eight or ten times its thickness. ”

“ A magnificent volume on the Results of Astronomical Observations made during the years 1834–8 at the Cape of Good Hope appeared in 1847; and a catalogue of all known nebulae and clusters, amounting to 5,079, was presented to the Royal Society in 1864, while a corresponding catalogue of more than 10,000 double and multiple stars was never finished, though the materials collected for it were published posthumously in 1879. ”

“ Such of its members as more specially cultivate practical astronomy in the National Observatories of the capital, are charged to make all Observations which may contribute to the progress of that science, and procure new means for rectifying the tables of the Sun, as well as those which make known the position of the stars, and particularly the tables of the Moon, the improvement of which so essentially concerns the safety of navigation. ”

“ In glancing from side to side of the sun's disk, the eye ranges over a distance of more than 860,000 miles—not a mere ideal distance, or an expanse of empty space, but a distance filled by an actual and, so to speak, tangible body, whose diameter is of that stupendous magnitude. One sees at a glance, then, the enormous scale on which these spots are formed. The earth placed beside them would be but a speck, and yet they are mere pits in the surface of the sun, filled perhaps with partially cooled metallic vapors, which have been cast up from the interior, and are settling back again. ”

“ In the next place, the brass meridian of a common globe is not what is called a small circle, but it divides the globe into two equal parts. For that purpose it is necessary that the telescope CD should be square to its axis AB. The astronomer ascertains whether it be truly square or not, by looking at a distant mark, first with the pivots A,B, of the instrument resting on the piers a,b, and then with the axis turned over, so that the pivots A,B, rest on the piers b,a. ”

“ The telescope is adjusted so that a portion of the sun's limb, usually near a group of active sun-spots, shall be presented before the opened slit of the spectroscope. The light of the chromosphere thus admitted along with some diffused sun-light from the earth's atmosphere, produces a spectrum of intensely bright lines, widely separated, on the fainter background of the strongly dispersed spectrum of sun-light. ”

“ If the Tables could be so constructed as to represent the moon’s real place in the heavens with extreme precision, as it would be seen from a standard observatory, the observation of her apparent place, as seen from any other point of the earth’s surface, would enable the observer to find his longitude from the standard point. ”

“ When we look up into the sky on a clear night the stars and planets appear to be a host of bright dots on the concave surface, unimaginably distant, of a vast hollow sphere at the canter of which we seem to be. Astronomers call this expanse of the heavens with its myriad bright stars the celestial sphere or the star sphere, and have imagined upon its surface various systems of circles. In descriptions of the earth’s relation to the celestial sphere it is customary to disregard altogether the earth’s diameter which is comparatively infinitesimal. ”

“ Although very irregular in form, the general appearance of the galactic belt is that of a regular curve occupying one of the great circles of the celestial sphere. The Milky-way completely encircles the heavens, but, of course, only one-half is visible at any one moment, since our globe prevents the other half from being seen. ”

“ The Sun is an enormous sphere whose diameter is over 108 times the diameter of our globe, or very nearly 860,000 miles. Its radius is nearly double the distance from the Earth to the Moon. If we suppose, for a moment, the Sun to be hollow, and our globe to be placed at the centre of this immense spherical shell, not only could our satellite revolve around us at its mean distance of 238,800 miles, as now, but another satellite, placed 190,000 miles farther than the Moon, could freely revolve likewise, without ever coming in contact with the solar envelope. ”