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361. Periods of some of the binary stars. During the last twenty years, the interesting subject of double stars has claimed great attention, and they have been extensively observed, particularly by Sir J. South and Sir J. Herschel in England, and by Professors Struve and Mädler in Russia.* The observations on many of them completely establish a physical connection between the individuals of which they are composed. These are found to revolve about each other in elliptical orbits and to conform in their motions to the same dynamical laws that govern the motions of the planets round the sun.
The periods of several of the double stars have been computed, and appear to vary from about 40 to more than 1000 years. These computations are, however, to be regarded only as approximations; the more accurate observations not yet having been continued sufficiently long to give, with much accuracy, the lengths of the periods. According to Prof. Maedler, who has made some of the most recent computations, the period of Castor is about 230 years; y Virginis 158; 3 Cancri 60 years; and 36 years.†
362. Proper motions of some of the stars. A number of the stars, both single and binary, are found slowly to change their local situations in the heavens, having progressive apparent motions called their proper motions, varying in different stars from a small fraction of a second to 4" or 5" a year. From the directions and amounts of these motions, Sir W. Herschel drew the conclusion that they were only apparent motions, and were produced by a real motion of the Solar System towards a point of the heavens situated in the constellation Hercules.
This conclusion has recently been confirmed by Prof. Argelander. He finds the point towards which the motion of our system is directed, to be that which, in 1800, had 260° right ascension and 321° north declination.
* Prof. Struve made most of his observations at Dorpat; he is now Director of the Imperial Observatory at Pulkowa, near St. Petersburg. Prof. Maedler is his successor at Dorpat.
+ Astron. Nachrichten. Nos. 317, 363, and 427.
Astr. Nach. Nos. 363 and 364.
Independent determinations of this point have also been made by Struve, Luhndahl and Galloway, all obtaining nearly the same result. According to the calculations of Struve, the velocity with which the Solar System is moving, is about half as great as that of the earth in its orbit.
363. Annual parallax of the stars. The annual parallax of a star is the angle contained between two straight lines, conceived to be drawn from the star, one to the sun, and the other to the earth, when the earth is in such a part of its orbit that its radius vector is perpendicular to the latter line; or, in other words, it is the greatest angle at the star, that can be subtended by the semidiameter of the earth's orbit.
For each star, however situated, there must, it is evident, be some two opposite points of the earth's orbit, for each of which, the radius vector will be perpendicular to the right line joining the star and sun. The positions of the stars as seen from the earth, when at these points, must, therefore, differ by twice the annual parallax of the star. Hence, as the parallax must affect the right ascension and declination of the star, if these be observed when the earth is near these points, or in other favourable situations in its orbit, the parallax of the star may be determined, unless it is so small as to be within the limits of the probable errors of observation and the necessary corrections. Numerous observations, by several eminent astronomers, have been made for this purpose on some stars, which, from their apparent size and brightness, were supposed to be at a less distance than the generality of the stars. The results of these observations have been, that the parallax in each case was too small to be obtained with certainty by this method.
The apparent largeness or brightness of a star, is not, however, necessarily the most certain indication of its comparative proximity to the earth. A considerable proper motion produced by the motion of the Solar System (362), and, in case of a binary star, large apparent orbits, are probably stronger indications. Professor Bessel of Königsberg, therefore, made two entirely distinct series of observations on the binary star 61 Cygni, which has a large proper motion, amounting to 5" a year, and the components of
which are about 16" distant from each other. Instead of observing right ascensions and declinations, he measured with an excellent heliometer the distances from two contiguous, small, stationary stars, and thereby avoided the small errors to which the corrections for refraction, aberration and nutation are liable. The first series of observations gave, for the annual parallax of 61 Cygni, 0.3136; and the second gave 0".3483, differing only about of a second from the former.
¡ Ursæ Maj.
The parallaxes of several other stars have since been determined, but that of 61 Cygni is considered by far the most reliable. results will be found in the following table, of which the third column contains the distance from the sun in millions of millions of miles; and the fourth, the time the light occupies in passing from the star to the earth.
364. Distances of the stars. When the annual parallax of a star has been determined, its distance becomes at once known; it being, in terms of the earth's distance from the sun, equal to the quotient of 206264′′.8 (App. 51), divided by the annual parallax. Thus, taking 0.3483 for the annual parallax of 61 Cygni, its distance is found to be about 592,000 times the distance of the earth from the sun. This is a distance so immense, that light, which moves with the amazing velocity of 192,000 miles in a second, would require more than nine years to come from the star to the earth. Yet, inconceivably great as this distance is, there are observable stars, whose distances are probably more than a hundred times as great, and the light of which would require more than a thousand years to traverse the space which separates them from the earth.
365. Catalogues of stars. Some of the most noted catalogues are, Bode's Catalogue and Atlas, containing the positions of 17,000 stars; Professor Bessel's Catalogue of 3222 stars, deduced from
observations made by Bradley, at the Royal Observatory, Greenwich; Piazzi's Catalogue of 7646 stars; and the Catalogue published by the Astronomical Society in their Memoirs, containing 2861 stars. In this last Catalogue, the mean right ascensions and declinations are given for the 1st of January, 1830; and they contain for each star, certain constant logarithms, by means of which, with other logarithms depending on the positions of the sun, moon and moon's node, given in the Nautical Almanac for each day in the year, the true apparent place of any of these stars, may be found, for a given time, with great facility.
Under the direction of the British Association, the Catalogue of the Astronomical Society has been revised and extended, so as to include 8377 stars, with the mean places reduced to the year 1850.
DIFFERENT METHODS OF FINDING THE LONGITUDE OF A PLACE.
366. General remarks. The determination of the difference of longitude between two places, consists in finding the difference between the times reckoned at these places at the same instant of absolute time (63). When this has been done, if the longitude of one of the places is known, that of the other becomes also known. The method of finding the longitude of a place by means of a chronometer, has already been given (65). It is very simple, and is extensively used at sea. But as a chronometer is liable to change. its rate of going during the voyage, especially if it is a long one, it is not safe to depend on this method alone.
367. Lunar method of finding the longitude. The lunar method is that by which the longitude of a place is found, from the measured angular distance of the moon from the sun, a star, or planet, situated nearly to the east or west of her place, at the time of observation. As the moon's motion is about half a degree an hour, she must change her angular distance from a body thus situated, at that rate, or nearly so. Hence, if the moon's true angular distance from the body at any instant, and also the time,
be obtained from observations at any place, and the time at the first meridian, when the moon has this true angular distance from the body, be found, the longitude becomes known. The Sun, Venus, Mars, Jupiter, Saturn, and nine stars situated contiguous to the moon's path, have been selected for observations of this kind. In the Nautical Almanac, the moon's computed true angular distances from several of these bodies, are given for each three hours, Greenwich time, of every day in the year; and also proportional logarithms, by which the distance for any intermediate time, or the time corresponding to an intermediate distance, may easily be obtained.
To apply this method, the distance of the enlightened limb of the moon, from the nearest limb of the sun, or, from one of the other bodies given in the Nautical Almanac, for the day, is measured with a sextant, and the time of observation noted. The altitudes. of the moon and other bodies, at that time, are also observed with a quadrant or sextant by two assistants.* From these observations, the true distance of the moon's centre from that of the body, corrected for refraction, parallax and semidiameter, may be deduced, by methods given in treatises on Navigation. When the true distance has been obtained, and then the time at Greenwich, corresponding to this distance, the difference between this time, and the time of observation, will be the longitude of the place; which will be east or west according as the Greenwich time is earlier or later than the time of observation.
This method of finding the longitude, is of great importance to the mariner, as all others, with the exception of that by the chronometer, require observations that cannot be made at sea.
368. Longitude by moon culminating stars. Certain stars situated contiguous to the moon's path and passing the meridian at short intervals before or after the moon, are called moon culminating stars. The moon's right ascension increases on an average a
* The observations may be made by one person, by first taking the altitudes, then the distance, and afterwards the altitudes again. From the two sets of altitudes, their values at the time of taking the distance may be obtained with sufficient accuracy.
† Dr. Bowditch's Navigation contains several of the best methods.