Part 6

There is, however, a difference in the unit of angular measurement commonly used for right ascensions in the heavens and longitude on the earth. In astronomical practice, right ascension is very generally expressed by hours, twenty-four of which make a complete circle, corresponding to the apparent revolution of the celestial sphere in twenty-four hours. The reason of this is that astronomers determine right ascension by the time shown by a clock so regulated as to read 0 hrs., 0 min., 0 sec. when the vernal equinox crosses the meridian. The hour hand of this clock makes a revolution through twenty-four hours during the time that the earth makes one revolution on its axis, and thus returns to 0 hrs., 0 min., 0 sec. when the vernal equinox again crosses the meridian. A clock thus regulated is said to show sidereal time. Then the right ascension of any star is equal to the sidereal time at which it crosses the meridian of any point on the earth’s surface. Right ascension thus designated in time may be changed to degrees and minutes by multiplying by 15. Thus, one hour is equal to 15°; one minute of time is equal to 15′ of arc, and one second of time to 1″ of arc.

It may be remarked that in astronomical practice terrestrial longitudes are also expressed in time, the longitude of a place being designated by the number of hours it may be east or west of Greenwich. Thus, Washington is said to be 5h. 8m. 15s. west of Greenwich. This, however, is not important for our present purpose.

The first astronomer who attempted to make a catalogue of all the known stars is supposed to be Hipparchus, who flourished about 150 B.C. There is an unverified tradition to the effect that he undertook this work in consequence of the appearance of a new star in the heavens, and a desire to leave on record, for the use of posterity, such information respecting the heavens in his time that any changes which might take place in them could be detected. This catalogue has not come down to us--at least not in its original form.

Ptolemy, the celebrated author of the ‘Almagest,’ flourished A.D. 150. His great work contains the earliest catalogue of stars which we have. There seems to be a certain probability that this catalogue either may be that of Hipparchus adopted by Ptolemy unchanged, or may be largely derived from Hipparchus. This, however, is little more than a surmise, due to the fact that Ptolemy does not seem to have been a great observer, but based his theories very largely on the observations of his predecessors. The actual number of stars which it contains is 1,030. The positions of these are given in longitude and latitude, and are also described by their places in the figure of the constellation to which each may belong. Not unfrequently the longitude or latitude is a degree or more in error, showing that the instruments with which the position was determined were of rather rough construction.

So far as the writer is aware, no attempt to make a new catalogue of the stars is found until the tenth century. Then arose the Persian astronomer, Abd-Al-Rahman Al-Sufi, commonly known as Al-Sufi, who was born A.D. 903 and lived until 986. Nothing is known of his life except that he was a man celebrated for his learning, especially in astronomy. His only work on the latter subject which has come down to us is a description of the fixed stars, which was translated from the Arabic by Schjellerup and published in 1874 by the St. Petersburg Academy of Science. This work is based mainly on the catalogue of Ptolemy, all the stars of which he claimed to have carefully examined. But he did not add any new stars to Ptolemy’s list, nor, it would seem, did he attempt to redetermine their positions. He simply used the longitudes and latitudes of Ptolemy, the former being increased by 12° 42′ on account of the precession during the interval between his time and that to which Ptolemy’s catalogue was reduced. The translator says of his work that it gives a description of the starry heavens at the time of the author and is worthy of the highest confidence. The main body of the work consists of a detailed description of each constellation, mentioning the positions and appearances of the stars which it contains. Here we find the Arabic names of the stars, which were not, however, used as proper names, but seem rather to have been Arabic words representing some real or supposed peculiarity of the separate stars, or arbitrarily applied to them.

Four centuries later arose the celebrated Ulugh Beigh, grandson of Tamerlane, who reigned at Samarcand in the middle of the fifteenth century. Bailey says of him: “Ulugh Beigh was not only a warlike and powerful monarch, but also an eminent promoter of the sciences and of learned men. During his father’s lifetime he had attracted to his capital all the most celebrated astronomers from different parts of the world; he erected there an immense college and observatory, in which above a hundred persons were constantly occupied in the pursuits of science, and caused instruments to be constructed of a better form and greater dimensions than any that had hitherto been used for making astronomical observations.”

His fate was one which so enlightened a promoter of learning little deserved; he was assassinated by the order of his own son, who desired to succeed him on his throne; and in order to make his position the more secure, also put his only brother to death. A catalogue of the stars bears the name of this monarch; he is supposed to have made many or most of the observations on which it is founded. Posterity will be likely to suppose that a sovereign used the eyes of others more than his own in making the observations. However this may be, his catalogue seems to have been the first in which the positions of the stars given by Ptolemy were carefully revised. He found that there were twenty-seven of Ptolemy’s stars too far south to be visible at Samarcand, and that eight others, although diligently looked after, could not be discovered. It is curious that, like Al-Sufi, he does not seem to have added any new stars to Ptolemy’s list.

Next in the order of time comes the work of Bayer, whose method of naming the stars has already been described. The main feature of this work consists of maps of all the constellations. Previous to his time, celestial globes, made especially for the use of the navigator, took the place of maps of the stars. The first edition of this book was published in 1603, and is distinguished by the fact that a list of stars in each constellation is printed on the backs of the maps. Bayer did not confine himself to the northern hemisphere, but extended his list over the whole celestial sphere, from the north to the south pole.

The catalogue of the celebrated Tycho Brahe, prepared toward the end of the sixteenth century, though of great historic value, is of no special interest to the general reader at the present time. A supplement to it, continuing its list of stars to the south pole, was published by Halley, who made the necessary observations during a journey to St. Helena in 1677.

The catalogue of Hevelius, published in 1690, offers no feature of special interest, except the addition of several new constellations which he placed between those already known. Having the aid of the telescope, he was able to include in his catalogue stars which had been invisible to his predecessors.

Modern catalogues of the stars may be divided into two classes: Those which include only stars of a special class, or stars of which the observer sought to determine the position or magnitude with all attainable precision; and catalogues intended to include all the stars in any given region of the heavens, down to some fixed order of magnitude. It may appear remarkable that no attempt of the latter sort was seriously made until more than two centuries after the telescope had been pointed at the heavens by Galileo. A reason for the absence of such an attempt will be seen in the vast number of stars shown by the telescope, the difficulty of stopping at any given point, and the seeming impossibility of assigning positions to hundreds of thousands of stars. The latter difficulty was overcome by the improved methods of observation devised in modern times.

About the middle of the present century the celebrated Argelander commenced the work of actually cataloguing all the stars of the northern celestial hemisphere to magnitude 9½. This work was termed a _Durchmusterung_ of the northern heavens, a term which has been introduced into astronomy generally to designate a catalogue in which all the stars down to a certain magnitude are supposed to be mustered, as if a census of them were taken. The work fills three quarto volumes and contains more than 310,000 stars, of each of which the magnitude and the right ascension and declination are given. This work was extended by Schönfeld, Argelander’s assistant and successor, to 22° of south declination.

In the latitudes in which most of the great observatories of the world are situated, that part of the celestial sphere within 40° or 50° of the south pole always remains below the horizon. Around this invisible region a belt of somewhat indefinite breadth, 10° or more, can be only imperfectly observed, owing to the nearness of the stars to the horizon, and the brevity of the period between their rising and setting. Up to the middle of the nineteenth century, the few observatories situated in the southern hemisphere were too ill-endowed to permit of their undertaking a complete census of this invisible region.

The first considerable work emanating from the Cordoba Observatory, under Gould, was a catalogue of all the stars from the south pole to 10° of north declination which could be seen with the naked eye. Another work, which was not issued until after Dr. Gould’s death, was devoted to photographs of southern clusters of stars.

The work of the Cordoba Observatory, with which we are more especially concerned in the present connection, consists of a ‘Durchmusterung’ of the southern heavens, commencing at 22° of south declination, where Schönfeld’s work ended, and continued to the south pole. This work is still incomplete, but two volumes have been published by Thome, extending to 41° of south declination. It is expected that the third is approaching completion. This catalogue is, in one point at least, more complete than that of Argelander and Schönfeld, as it contains all the stars down to the tenth magnitude. The two volumes give the positions and magnitudes of no less than 340,000 stars, and therefore more than the catalogue of Argelander gives for the entire northern hemisphere. If the remaining part of the heavens, from 42° to the south pole, is equally rich, it will contain nearly half a million stars, and the entire work will comprise more than 800,000 stars.

The Royal Observatory of the Cape of Good Hope, under the able and energetic direction of Dr. David Gill, has undertaken a work of the same kind, which is remarkable for being based on photography. The history of this work is of great interest. In 1882 Gill secured the aid of photographers at the Cape of Good Hope to take pictures of the brilliant comet of that year, with a large camera. On developing the pictures the remarkable discovery was made that not only all the stars visible to the naked eye, but telescopic stars down to the ninth or tenth magnitude were also found on the negatives. This remarkable result suggested to Gill that here was a new and simple method of cataloguing the stars. It was only necessary to photograph the heavens and then measure the positions of the stars on the glass negatives, which could be done with much greater ease and certainty than measures could be made on the positions of the actual stars, which were in constant apparent motion.

As soon as the necessary arrangements could be made and the apparatus put into successful operation, Gill proceeded to the work of photographing the entire southern heavens from 18° of south declination to the celestial pole. The results of this work are found in the ‘Cape Photographic Durchmusterung,’ a work in three quarto volumes, in which the astronomers of all future time will find a permanent record of the southern heavens towards the end of the nineteenth century. The actual work of taking the photographs extended from 1887 to 1891. This, however, was far from being the most difficult part of the enterprise. The most arduous task of measuring the positions of a half-million of stars on the negatives, including the determining of the magnitude of each, was undertaken by Professor J. C. Kapetyn, of the University of Groningen, Holland, and brought to a successful completion in the year 1899.

What the work gives is, in the first place, the magnitude and approximate position of every star photographed. The determining of the magnitude of a star is an important and delicate question. There is no difficulty in determining, from the diameter of the image of the star as seen in the microscope, what its photographic magnitude was at the time of the exposure, as compared with other stars on the same plate. But can we rely upon similar photographic magnitudes on a plate corresponding to similar brightnesses of the stars? In the opinion of Gill and Kapetyn we cannot. The transparency of the air varies from night to night, and on a very clear night the same star will give a stronger image than it will when the air is thick. Besides, slightly different instruments were used in the course of the work. For these reasons a scale of magnitude was determined on each plate by comparing the photographic intensity of the images of a number of stars with the magnitudes as observed with the eye by various observers. Thus on each plate the magnitude was reduced to a visual scale.

It does not follow from this that the magnitudes are visual, and not photographic. It is still true that a blue star will give a much stronger photographic image than a red star of equal visual brightness. In a general way, it may be said that the catalogue includes all the stars to very nearly the tenth magnitude, and on most of the plates stars of 10.5 were included. In fact, now and then is found a star of the eleventh magnitude.

A feature of the work which adds greatly to its value is a careful and exhaustive comparison of its results with previous catalogues of the stars. When a star is found in any other catalogue the latter is indicated. Most interesting is a complete list of catalogued stars which ought to be on the photographic negatives, but were not found there. Every such case was inexhaustibly investigated. Sometimes the star was variable, sometimes it was so red in color that it failed to impress itself on the plate, sometimes there were errors in the catalogue.

The great enterprise of making a photographic map of the heavens now being carried on as an international enterprise, having its headquarters at Paris, is yet wider in its scope than the works we have just described. One point of difference is that it is intended to include all the stars, however faint, that admit of being photographed with the instruments in use. The latter are constructed on a uniform plan, the aperture of each being 34 centimetres, or 13.4 inches, and the focal length 343 cm. Two sets of plates are taken, one to include all the stars that the instrument will photograph near poles, and the other only to take in those to the eleventh magnitude. Of the latter it is intended to prepare a catalogue. Some portions of the German and English catalogues have already been published, and their results will be made use of in the course of the present work.

NUMBERING THE STARS.

Closely connected with the work of cataloguing the stars is that of enumerating them. In view of what may possibly be associated with any one star--planets with intellectual beings inhabiting them--the question how many stars there are in the heavens is one of perennial interest. But beyond the general statement we have already made, this question does not admit of even an approximate answer. The question which we should be able to answer is this: How many stars are there of each easily visible magnitude? How many of the first magnitude, of the second, of the third, and so on to the smallest that have been measured? Even in this form we cannot answer the question in a way which is at the same time precise and satisfactory. One magnitude merges into another by insensible gradations, so that no two observers will agree as to where the line should be drawn between them. The difficulty is enhanced by the modern system--very necessary, it is true--of regarding magnitude as a continuously varying quantity and estimating it with all possible precision. In adjusting the new system to the old one, it may be assumed that an average star of any given magnitude on the old system would be designated by the corresponding number on the new system. For example, an average star of the fourth magnitude would be called 4.0; one of the fifth, 5.0, etc. Then the brightest stars, which formerly were called of the fourth magnitude, would now be, if the estimate were carried to hundredths, 3.50, while the faintest would be 4.50. What were formerly called stars of the fifth magnitude would range from 4.50 to 5.50, and so on. But we have meet with a difficulty when we come to the sixth magnitude. On the modern system, magnitude 6.0 represents the faintest star visible to the naked eye; but the stars formerly included in this class would, on the average, be somewhat brighter than this, because none could be catalogued except those so visible.

The most complete enumeration of the lucid stars by magnitudes has been made by Pickering (‘Annals of the Harvard Observatory,’ Vol. XIV). The stars were classified by half magnitudes, calling

M. M. Mag. 2.0 all from 1.75 to 2.25 2.5 all from 2.25 to 2.75 etc., etc.

For the northern stars Pickering used the Harvard Photometry; for the southern, Gould’s ‘Uranometria Argentina.’ A zone from the equator to 30° south declination is common to both; for this zone I use Gould. The number of each class in the entire sky, north and south of the celestial equator, is as follows:

Northern Southern Hemisphere. Hemisphere. Pickering. Gould. Total.

1± 9 14 23 2.0 17 15 32 2.5 17 24 41 3.0 37 41 78 3.5 61 74 135 4.0 114 126 240 4.5 228 234 462 5.0 450 426 876 5.5 787 681 1,468 6.0 789 1,189 1,978 ----- ----- ----- Sum. 2,509 2,824 5,333

It would seem from this that the number of lucid stars in the southern celestial hemisphere is 315 greater than in the northern. But this arises wholly from a seemingly greater number of stars of magnitude 6. In the zone 0° to 30° S., Pickering has 214 stars of this class fewer than Gould. Hence it is not likely that there is any really greater richness of the southern sky.

The total number of lucid stars is thus found to be 5,333. But it is not likely that stars of magnitudes 6.1 and 6.2 should be included in this class, though this is done in the above table. From a careful study and comparison of the same data from Pickering and Gould, Schiaparelli enumerated the stars to magnitude 6.0. He found:

North pole to 30° S. 3,113 stars. 30° S. to south pole 1,190 stars. ----- Total lucid stars 4,303

For most purposes a classification by entire magnitudes is more instructive than one by half magnitudes. From the third magnitude downward we may assume that 40 per cent. of the stars of each half magnitude belong to the magnitude next above, and 60 per cent. to that next below. We thus find that of

Total. Mag. 0 and 1 there are 21 stars 21 Mag. 2 there are 52 stars 73 Mag. 3 there are 157 stars 230 Mag. 4 there are 506 stars 736 Mag. 5 there are 1,740 stars 2,476 Mag. 6 there are 5,171 stars 7,647

Here it is to be remarked that under magnitude 6 are included many other than the lucid stars, namely, all down to magnitude 6.4. The last column gives the entire number of stars down to each order of magnitude.

It will be remarked that the number of stars of each order is rather more than three times that of the order next higher. How far does this law extend? Argelander’s ‘Durchmusterung,’ which is supposed to include all stars to magnitude 9.5, gives 315,039 stars for the northern hemisphere, from which it would be inferred that the whole sky contains 630,000 stars to the ninth magnitude. Comparing this with the number 7,647 of stars to the magnitude 6.5, we see that it is forty-fold, so that it would require a ratio of about 3.5 from each magnitude to the next lower. But it is now found that Argelander’s list contains, in the greater part of the heavens, all the stars to the tenth magnitude.

On the other hand, Thome’s Cordoba ‘Durchmusterung’ gives 340,380 stars between the parallels -22° and -42°. This is 0.14725 of the whole sky, so that, on Thome’s scale of magnitude, there are about 2,311,000 stars to the tenth magnitude in the sky. This is more than three times the Argelander number to the ninth magnitude.

It would, therefore, seem that the ratio of number for each magnitude must exceed 3, even up to the tenth. If a ratio of only 3 extends four steps farther, the whole number of stars in the sky down to magnitude 14.5 inclusive must approach 200 millions. Until the international photographic chart of the sky is subjected to a detailed examination, it is impossible to make an estimation with any approach to certainty.

COLONIES AND THE MOTHER COUNTRY (III).

BY JAMES COLLIER.