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751 ASTRONOMY Stars. Periods. motions. The former is proportional to the sine of the 63 Less than 50 days angular distance of the star from the apex divided by its 6 50 to 100 ,. 9 distance from the earth. It follows from the approach to 100 ,, 150 ,, 18 150 ,, 200 ,, uniformity in the ratio that the peculiar motions of the 29 200 „ 250 „ stars are also, in the general mean, inversely proportional 40 250 „ 300 „ to their distance from us. Consequently, the actual mean 44 300 ,, 350 „ 44 linear velocity of the motion may be taken as the same 350 ,, 400 ,, 18 400,, 450 „ for stars of various distances,' so that the apparent motion 6 450 „ 500 „ will be inversely as the distance. Of course this equality 1 500 ,, 550 ,, in the general mean by no means implies any approxima1 550 ,, 600 „ 1 tion to equality in the case of individual stars; yet there 600 ,, 650 ,, is some reason to believe that it is only in exceptional The most suggestive feature of this table is the wellcases that the linear velocity of motion of the stars exceeds marked limitation of the period. From the maximum of a certain limit which it is difficult to fix with precision, but which may be estimated at 40 or 50 kilometres per about 350 days, the number of periods having a given second. To such a limit there are two remarkable excep- length continually falls off until we reach 610 days. This tions, one of which has been known for some time, while is the longest yet known. It follows that there is somethe other is of recent discovery. Although the proper thing in the constitution of these bodies, or in the cause motion of the star 1830 Groombridge, is, with one excep- on which their variation depends, which limits the period. tion, the greatest of any known, measures of its parallax It was formerly supposed that the eleven-years period in show that it is by no means among the nearer stars. The the magnitude and frequency of spots on the sun made combination of the parallax already given with the observed the sun a variable star; in fact, that the periodicity of the motion indicates a component of linear velocity perpen- stars might be due to the same cause as that of the solar dicular to the line of sight amounting to about 240 spots. But the great length of the sun-spot period, taken kilometres per second. The recent measures of Elkin on in connexion with this limitation, seems to disprove the the parallax of Arcturus indicate that its linear velocity is analogy. Passing up towards the other end of the table probably nearly as great as and possibly much greater than we are struck by the rapid falling off towards the limit of that of the Groombridge star. The parallax found by 50 days and the great number less than 50 days. It Elkin was 0■016,,; but in view of the fact that other might seem that we have here a sharp line of distinction measures, though far less trustworthy, have given a larger between the two classes—those of long and those o| short value in the table, 0'03" has been assigned as the most period. But an examination of the periods in detail does probable parallax. This gives a linear velocity of some not show any such line. Eight periods are less than 1 day, and about 40 between 1 and 10 days, and from this 350 kilometres per second. One of the most interesting questions growing out of point up to 100 days they are scattered with a fair the proper motions of the stars is whether there is any approach to uniformity. The law of change of a periodic star may. be represented general law among them which indicates that Law of tpgy m0ve in definite orbits and that the graphically by a curve. A straight horizontal line or axis of abscissae is taken to represent the time, and on it motfon universe as a whole forms a stable system. Up equal spaces represent equal times. At each point upon m ° to the present time nothing in the way of a general law has been discovered. In a few cases, some of it an ordinate is erected proportional to the amount of which are mentioned in the original article in the ninth light emitted by the star at the corresponding moment. edition of the Ency. Brit., stars in the same region are A curve through the ends of these ordinates is the light found to have a common proper motion, indicating that curve of the variable star. It will be readily seen that, they may form a system among themselves, but these in the case of a star of constant brightness, the ordinates cases are so exceptional as to prove nothing: the general will all be equal, and the curve will be a straight horirule seems to be that the proper motion of a star has no zontal line. Whatever the law, if the star be a periodic connexion with its location in space or its relation to the one, the ordinate will return to the same value at the end universe in general. On no probable hypothesis that ue of a period, and the continuance of the curve through periods will be repetitions of the curve correcan make respecting the mass of the stars could the successive sponding to the first period. It is therefore only necessary attraction of all the known bodies of the universe hold to continue the curve through a single period. either Arcturus or 1830 Groombridge in an orbit. A classification of variable stars has been facilitated by the discovery of the cause of variation in certain classes of Variable Stars. the stars of shorter periods. The most distinctive class of The study of variable stars has in recent times, in such stars are those which remain constant during the connexion with measures of motions in the line of. sight, greater part of the period, and then temporarily lose a opened up a new and interesting branch of Sidereal portion of their light, soon to recover it again. The Astronomy, and the number of these objects which have brightest and longest-known of this class being Algol or been made the subject of accurate observation is now. so /3 Persei, stars which vary in this way are said to be of great that a classification according to the law and period the “ Algol type.” The curve of such a type is a straight of the variations *is possible. The . statistical basis on line with a depression at the end of each period. This which such a classification must begin is found in Chandler s feature strongly distinguishes the type from those in catalogues, of which the third was .published m the which the variation, whatever its law, is continuous, for Astronomical Journal, vol. xvi. Omitting from our con- in those cases, which include a great majority of variable sideration 7] Argus and other irregularly variable stars, as stars, the curve is nowhere a straight line. The great development of the subject in our times well as the so-called new stars, we find in that catalogue 280 began with the discovery of the cause of the change in periodic stars, properly so called ; that is, such as go through the case of stars of the Algol type. Ever since type all their changes in a definite period. Classifying the the variability of Algol was observed, it was periods according to the length, we find them to be as suspected to be due to a partial eclipse of the star by the follows :—