These difficulties, as already stated, were known to exist; but there is a long interval between transits of Venus, or rather between every pair of such transits. After those of 1874 and 1882 there will be no more until 2004 and 2012, so that we shall never see another; similarly, before that pair of the last century, there had not been any such occasion since 1761 and 1769, and no one was alive who remembered at first hand the trouble which was known to exist. It was proposed to obviate the anticipated difficulties by careful practice beforehand; models were prepared to resemble as nearly as possible the expected appearances, and the times recorded by different observers were compared with the true time, which could, in this case of a model, be determined. In this way it was hoped that the habit of each observer, his “personal equation” as it is called, could be determined beforehand, and allowed for as a correction when he came to observe the actual transit.Failure. The result, however, was a great disappointment. The actual appearances were found to be totally different in character from those shown by the model; chiefly, perhaps, because it had been impossible to imitate with a model the effect of the atmosphere which surrounds the planet Venus. Observers trained beforehand, using similar instruments, and standing within a few feet of each other, were expected, after making due allowance for personal equation, to give the same instant for contact; but their observations when made were found to differ by nearly a minute of time, and after an exhaustive review of the whole material it was felt that all hope of determining accurately the sun’s distance by this method must be given up. The following table will show how much was learned from the transits of Venus, and how much remained to be settled. They left the result in doubt over a range of about two million miles.
Sun’s Distance, in Millions of Miles, as found by Different Observers
Before the Transits of Venus estimates varied between 96 million miles (Gilliss and Gould, 1856) and 91 million (Winneche, 1863), a range of 5 million miles.
The Transits of 1874 and 1882 gave results lying between 93¼ million (Airy, from British observations of 1874), 92½ million (Stone, from British observations of 1882), and 91½ million (Puiseux, from French observations), a range of 1¾ millions.
Gill’s Heliometer results all lie very near 93 millions. The observations of Mars in 1877 give about 100,000 miles over this figure: but the observations of Victoria, Iris, and Sappho, which are more trustworthy, all agree in giving about 100,000 miles less than the 93 millions.
It became necessary, therefore, to look to other methods; and before the second transit of 1882 was observed, an energetic astronomer, Dr. David Gill, had already put into operation the method which may be now regarded as the standard one.
Modern method for sun’s distance.
We have said that the relative distance of Venus from the sun is accurately known from observations of the exact time of revolution. It is easy to see that these times of revolution can be measured accurately by mere accumulation. We may make an error of a few seconds in noting the time of return; but if the whole interval comprises 10 revolutions, this error is divided by 10, if 100 revolutions by 100, and so on; and by this time a great number of revolutions of all the planets (except those just discovered) have been recorded. Hence we know their relative distances with great precision; and if we can find the distance in miles of any one of them, we can find that of the sun itself, or of any other planet, by a simple rule-of-three sum. By making use of this principle many of the difficulties attending the direct determination of the sun’s distance can be avoided; for instance, since the sun’s light overpowers that of the stars, it is not easy to directly observe the place of the sun among the stars; but this is not so for the planets.Photography. We can photograph a planet and the stars surrounding it on the same plate, and then by careful measurement determine its exact position among the stars; and since this position differs slightly according to the situation of the observer on the earth’s surface, by comparing two photographs taken at stations a known distance apart we can find the distance of the planet from the earth; and hence, as above remarked, the distance of the sun and all the other members of the solar system. Or, instead of taking photographs from two different stations, we can take from the same station two photographs at times separated by a known interval. For in that interval the station will have been carried by the earth’s rotation some thousands of miles away from its former position, and becomes virtually a second station separated from the first by a distance which is known accurately when we know the elapsed time. Again, instead of taking photographs, and from them measuring the position of the planet among the stars, we may make the measurements on the planet and stars in the sky itself;Dr. Gill’s expedition to Ascension. and since in 1878, when Dr. Gill set out on his enterprise of determining the sun’s distance, photography was in its infancy as applied to astronomy, he naturally made his observations on the sky with an instrument known as a heliometer. He made them in the little island of Ascension, which is suitably situated for the purpose; because, being near the earth’s equator, it is carried by the earth’s rotation a longer distance in a given time than places nearer the poles, and in these observations for “parallax,” as they are called, it is important to have the displacement of the station as large as possible. For a similar reason the object selected among the planets must be as near the earth as possible; and hence the planet Mars, which at favourable times comes nearer to us than any other superior planet[1] then known, was selected for observation with the heliometer.
And now it will be seen why the discovery of the little planet Eros was important, for Mars was no longer the known planet capable of coming nearest to us; it had been replaced by this new arrival.
Further, a small planet which is in appearance just like an ordinary star has, irrespective of this great proximity, some distinct advantages over a planet like Mars, which appears as a round disc, and is, moreover, of a somewhat reddish colour. When the distance of an object of this kind from a point of line such as a star is measured with the heliometer it is found that a certain bias, somewhat difficult to allow for with certainty, is introduced into the measures; and our confidence in the final results suffers accordingly.Victoria, Iris, and Sappho. After his observations of Mars in 1878, Dr. David Gill was sufficiently impressed with this source of error to make three new determinations of the sun’s distance, using three of the minor planets instead of Mars, in spite of the fact that they were sensibly farther away; and his choice was justified by finding that the results from these three different sets of observations agreed well among themselves, and differed slightly from that given by the observations of Mars.Eros. Hence it seems conclusively proved that one of these bodies is a better selection than Mars in any case, and the discovery of Eros, which offered the advantage of greater proximity in addition, was hailed as a new opportunity of a most welcome kind. It was seen by a little calculation that in the winter of 1900-1901 the planet would come very near the earth; not the nearest possible (for it was also realised that a still better opportunity had occurred in 1894, though it was lost because the planet had not yet been discovered), but still the nearest approach which would occur for some thirty years; and extensive, though somewhat hasty, preparations were made to use it to the fullest advantage. Photography had now become established as an accurate method of making measurements of the kind required; and all the photographic telescopes which could be spared were pressed into the service, and diligently photographed the planet and surrounding stars every fine night during the favourable period. The work of measuring and reducing these photographs involves an enormous amount of labour, and is even yet far from completed, but we know enough to expect a result of the greatest value. More than this we have not time to say here about this great problem, but it will have been made clear that just when astronomers were beginning to wonder whether it was worth while continuing the monotonous discovery of new minor planets by the handful, the 433rd discovery also turned out to be one of the greatest importance.