The proper motions of nearly a hundred stars have now been ascertained to be more than one second of arc annually, while a large number have less than this, and the majority have no perceptible motion, presumably due to their enormous distance from us. It is therefore not difficult in most cases to find one or two motionless stars sufficiently close to a star having a large proper motion (anything more than one-tenth of a second is so called) to serve as fixed points of measurement. All that is then required is, to measure with extreme accuracy the angular distance of the moving from the fixed stars at intervals of six months. The measurements can be made, however, on every fine night, each one being compared with one at nearly an interval of six months from it. In this way a hundred or more measurements of the same star may be made in a year, and the mean of the whole, allowance being made for proper motion in the interval, will give a much more accurate result than any single measurement. This kind of measurement can be made with extreme accuracy when the two stars can be seen together in the field of the telescope; either by the use of a micrometer, or by means of an instrument called a heliometer, now often constructed for the purpose. This is an astronomical telescope of rather large size, the object glass of which is cut in two straight across the centre, and the two halves made to slide upon each other by means of an exceedingly fine and accurate screw-motion, so adjusted and tested as to measure the angular distance of two objects with extreme accuracy. This is done by the number of turns of the screw required to bring the two stars into contact with each other, the image of each one being formed by one of the halves of the object glass.
But the greatest advantage of this method of determining parallax is, as Sir John Herschell points out, that it gets rid of all the sources of error which render the older methods so uncertain and inaccurate. No corrections are required for precession, nutation, or aberration, since these affect both stars alike, as is the case also with refraction; while alterations of level of the instrument have no prejudicial effect, since the measures of angular distance taken by this method are quite independent of such movements. A test of the accuracy of the determination of parallax by this instrument is the very close agreement of different observers, and also their agreement with the new and perhaps even superior method by photography. This method was first adopted by Professor Pritchard of the Oxford Observatory, with a fine reflector of thirteen inches aperture. Its great advantage is, that all the small stars in the vicinity of the star whose parallax is sought are shown in their exact positions upon the plate, and the distances of all of them from it can be very accurately measured, and by comparing plates taken at six months' intervals, each of these stars gives a determination of parallax, so that the mean of the whole will lead to a very accurate result. Should, however, the result from any one of these stars differ considerably from that derived from the rest, it will be due in all probability to that star having a proper motion of its own, and it may therefore be rejected. To illustrate the amount of labour bestowed by astronomers on this difficult problem, it may be mentioned that for the photographic measurement of the star 61 Cygni, 330 separate plates were taken in 1886-7, and on these 30,000 measurements of distances of the pairs of star-images were made. The result agreed closely with the best previous determination by Sir Robert Ball, using the micrometer, and the method was at once admitted by astronomers as being of the greatest value.
Although, as a rule, stars having large proper motions are found to be comparatively near us, there is no regular proportion between these quantities, indicating that the rapidity of the motion of the stars varies greatly. Among fifty stars whose distances have been fairly well determined, the rate of actual motion varies from one or two up to more than a hundred miles per second. Among six stars with less than a tenth of a second of annual proper motion there is one with a parallax of nearly half a second, and another of one-ninth of a second, so that they are nearer to us than many stars which move several seconds a year. This may be due to actual slowness of motion, but is almost certainly caused in part by their motion being either towards us or away from us, and therefore only measurable by the spectroscope; and this had not been done when the lists of parallaxes and proper motions from which these facts are taken were published. It is evident that the actual direction and rate of motion of a star cannot be known till this radial movement, as it is termed—that is, towards or away from us—has been measured; but as this element always tends to increase the visually observed rate of motion, we cannot, through its absence, exaggerate the actual motions of the stars.
The Sun's Movement Through Space
But there is yet another important factor which affects the apparent motions of all the stars—the movement of our sun, which, being a star itself, has a proper motion of its own. This motion was suspected and sought for by Sir William Herschel a century ago, and he actually determined the direction of its motion towards a point in the constellation Hercules, not very far removed from that fixed upon as the average of the best observations since made. The method of determining this motion is very simple, but at the same time very difficult. When we are travelling in a railway carriage near objects pass rapidly out of sight behind us, while those farther from us remain longer in view, and very distant objects appear almost stationary for a considerable time. For the same reason, if our sun is moving in any direction through space, the nearer stars will appear to travel in an opposite direction to our movement, while the more distant will remain quite stationary. This movement of the nearest stars is detected by an examination and comparison of their proper motions, by which it is found that in one part of the heavens there is a preponderance of the proper motions in one direction and a deficiency in the opposite direction, while in the directions at right angles to these the proper motions are not on the average greater in one direction than in the opposite. But the proper motions of the stars being themselves so minute, and also so irregular, it is only by a most elaborate mathematical investigation of the motions of hundreds or even of thousands of stars, that the direction of the solar motion can be determined. Till quite recently astronomers were agreed that the motion was towards a point in Hercules near the outstretched arm in the figure of that constellation. But the latest inquiries into this problem, involving the comparison of the motions of several thousand stars in all parts of the heavens, have led to the conclusion that the most probable direction of the 'solar apex' (as the point towards which the sun is moving is termed), is in the adjacent constellation Lyra, and not far from the brilliant star Vega. This is the position which Professor Newcomb of Washington thinks most probable, though there is still room for further investigation. To determine the rate of the motion is very much more difficult than to fix its direction, because the distances of so few stars have been determined, and very few indeed of these lie in the directions best adapted to give accurate results. The best measurements down to 1890 led to a motion of about 15 miles a second. But more recently the American astronomer, Campbell, has determined by the spectroscope the motion in the line of sight of a considerable number of stars towards and away from the solar apex, and by comparing the average of these motions, he derives a motion for the sun of about 121/2 miles a second, and this is probably as near as we can yet reach towards the true amount.
Some Numerical Results of the Above
Measurements
The measurements of distances and proper motions of a considerable number of the stars, of the motion of our sun in space (its proper motion), together with accurate determinations of the comparative brilliancy of the brightest stars as compared with our sun and with each other, have led to some very remarkable numerical results which serve as indications of the scale of magnitude of the stellar universe.
The parallaxes of about fifty stars have now been repeatedly measured with such consistent results that Professor Newcomb considers them to be fairly trustworthy, and these vary from one-hundredth to three-quarters of a second. Three more, all stars of the first magnitude—Rigel, Canopus, and Alpha Cygni—have no measurable parallax, notwithstanding the long-continued efforts of many astronomers, affording a striking example of the fact that brilliancy alone is no test of proximity. Six more stars have a parallax of only one-fiftieth of a second, and five of these are either of the first or second magnitudes. Of these nine stars having very small parallax or none, six are situated in or near to the Milky Way, another indication of exceeding remoteness, which is further shown by the fact that they all have a very small proper motion or none at all. These facts support the conclusion, which had been already reached by astronomers from a careful study of the distribution of the stars, that the larger portion of the stars of all magnitudes scattered throughout the Milky Way or along its borders really belong to the same great system, and may be said to form a part of it. This is a conclusion of extreme importance because it teaches us that the grandest of the suns, such as Rigel and Betelgeuse in the constellation Orion, Antares in the Scorpion, Deneb in the Swan (Alpha Cygni), and Canopus (Alpha Argus), are in all probability as far removed from us as are the innumerable minute stars which give the nebulous or milky appearance to the Galaxy.
It is well to consider for a moment what these facts mean. Professor S. Newcomb, one of the highest authorities on these problems, tells us that the long series of measurements to discover the parallax of Canopus, the brightest star in the southern hemisphere, would have shown a parallax of one-hundredth of a second, had such existed. Yet the results always seemed to converge to a mean of 0".000! Suppose, then, we assume the parallax of this star to be somewhat less than the hundredth of a second—let us say 1/125 of a second. At the distance this gives, light would take almost exactly 400 years to reach us, so that if we suppose this very brilliant star to be situated a little on this side of the Galaxy, we must give to that great luminous circle of stars a distance of about 500 light years. We shall now perceive the advantage of being able to realise what a million really is. A person who had once seen a wall-space more than 100 feet long and 20 feet high completely covered with quarter-inch spots a quarter of an inch apart; and then tried to imagine every spot to be a mile long and to be placed end to end in one row, would form a very different conception of a million miles than those who almost daily read of millions, but are quite unable to visualise even one of them. Having really seen one million, we can partially realise the velocity of light, which travels over this million miles in a little less than 51/2 seconds; and yet light takes more than 41/3 years at this inconceivable speed to come to us from the very nearest of the stars. To realise this still more impressively, let us take the distance of this nearest star, which is 26 millions of millions of miles. Let us look in imagination at this large and lofty hall covered from floor to ceiling with quarter-inch spots—only one million. Let all these be imagined as miles. Then repeat this number of miles in a straight line, one after the other, as many times as there are spots in this hall; and even then you have reached only one twenty-sixth part of the distance to the nearest fixed star! This million times a million miles has to be repeated twenty-six times to reach the nearest fixed star; and it seems probable that this gives us a good indication of the distance from each other of at least all the stars down to the sixth magnitude, perhaps even of a large number of the telescopic stars. But as we have found that the bright stars of the Milky Way must be at least one hundred times farther from us than these nearest stars, we have found what may be termed a minimum distance for that vast star-ring. It may be immensely farther, but it is hardly possible that it should be anything less.