it comes to us from the sun, we know the sun’s distance.
The first of the methods which I here describe as new methods must next be considered. It is one which Leverrier regards as the method of the future. In fact, so highly does he esteem it, that, on its account, he may almost be said to have refused to sanction in any way the French expeditions for observing the transit of Venus in 1874.
The members of the sun’s family perturb each other’s motions in a degree corresponding with their relative mass, compared with each other and with the sun. Now, it can be shown (the proof would be unsuitable to these pages,10 but I have given it in my treatise on “The Sun”) that no change in our estimate of the sun’s distance affects our estimate of his mean density as compared with the earth’s. His substance has a mean density equal to one-fourth of the earth’s, whether he be 90 millions or 95 millions of miles from us, or indeed whether he were ten millions or a million million miles from us (supposing for a moment our measures did not indicate his real distance more closely). We should still deduce from calculation the same unvarying estimate of his mean density. It follows that the nearer any estimate of his distance places him, and therefore the smaller it makes his estimated volume, the smaller also it makes his estimated mass, and in precisely the same degree. The same is true of the planets also. We determine Jupiter’s mass, for example (at least, this is the simplest way), by noting how he swerves his moons at their respective (estimated) distances. If we diminish our estimate of their distances, we diminish at the same time our estimate of Jupiter’s attractive power, and in such degree, it may be shown (see note), as precisely to correspond with our changed estimate of his size, leaving our estimate of his mean density unaltered. And the same is true for all methods of determining Jupiter’s mass. Suppose, then, that, adopting a certain estimate of the scale of the solar system, we find that the resulting estimate of the masses of the planets and of the sun, as compared with the earth’s mass, from their observed attractive influences on bodies circling around them or passing near them, accords with their estimated perturbing action as compared with the earth’s,—then we should infer that our estimate of the sun’s distance or of the scale of the solar system was correct. But suppose it appeared, on the contrary, that the earth took a larger or a smaller part in perturbing the planetary system than, according to our estimate of her relative mass, she should do,—then we should infer that the masses of the other members of the system had been overrated or underrated; or, in other words, that the scale of the solar system had been overrated or underrated respectively. Thus we should be able to introduce a correction into our estimate of the sun’s distance.
Such is the principle of the method by which Leverrier showed that in the astronomy of the future the scale of the solar system may be very exactly determined. Of course, the problem is a most delicate one. The earth plays, in truth, but a small part in perturbing the planetary system, and her influence can only be distinguished satisfactorily (at present, at any rate) in the case of the nearer members of the solar family. Yet the method is one which, unlike others, will have an accumulative accuracy, the discrepancies which are to test the result growing larger as time proceeds. The method has already been to some extent successful. It was, in fact, by observing that the motions of Mercury are not such as can be satisfactorily explained by the perturbations of the earth and Venus according to the estimate of relative masses deducible from the lately discarded value of the sun’s distance, that Leverrier first set astronomers on the track of the error affecting that value. He was certainly justified in entertaining a strong hope that hereafter this method will be exceedingly effective.
We come next to a method which promises to be more quickly if not more effectively available.
Venus and Mars approach the orbit of our earth more closely than any other planets, Venus being our nearest neighbour on the one side, and Mars on the other. Looking beyond Venus, we find only Mercury (and the mythical Vulcan), and Mercury can give no useful information respecting the sun’s distance. He could scarcely do so even if we could measure his position among the stars when he is at his nearest, as we can that of Mars; but as he can only then be fairly seen when he transits the sun’s face, and as the sun is nearly as much displaced as Mercury by change in the observer’s station, the difference between the two displacements is utterly insufficient for accurate measurement. But, when we look beyond the orbit of Mars, we find certain bodies which are well worth considering in connection with the problem of determining the sun’s distance. I refer to the asteroids, the ring of small planets travelling between the paths of Mars and Jupiter, but nearer (on the whole11) to the path of Mars than to that of Jupiter.
The asteroids present several important advantages over even Mars and Venus.
Of course, none of the asteroids approach so near to the earth as Mars at his nearest. His least distance from the sun being about 127 million miles, and the earth’s mean distance about 92 millions, with a range of about a million and a half on either side, owing to the eccentricity of her orbit, it follows that he may be as near as some 35 million miles (rather less in reality) from the earth when the sun, earth, and Mars are nearly in a straight line and in that order. The least distance of any asteroid from the sun amounts to about 167 million miles, so that their least distance from the earth cannot at any time be less than about 73,500,000 miles, even if the earth’s greatest distance from the sun corresponded with the least distance of one of these closely approaching asteroids. This, by the way, is not very far from being the case with the asteroid Ariadne, which comes within about 169 million miles of the sun at her nearest, her place of nearest approach being almost exactly in the same direction from the sun as the earth’s place of greatest recession, reached about the end of June. So that, whenever it so chances that Ariadne comes into opposition in June, or that the sun, earth, and Ariadne are thus placed—
Sun________Earth________Ariadne,
Ariadne will be but about 75,500,000 miles from the earth. Probably no asteroid will ever be discovered which approaches the earth much more nearly than this; and this approach, be it noticed, is not one which can occur in the case of Ariadne except at very long intervals.
But though we may consider 80 millions of miles as a fair average distance at which a few of the most closely approaching asteroids may be observed, and though this distance seems very great by comparison with Mars’s occasional opposition distance of 35 million miles, yet there are two points in which asteroids have the advantage over Mars. First, they are many, and several among them can be observed under favourable circumstances; and in the multitude of observations there is safety. In the second place, which is the great and characteristic good quality of this method of determining the sun’s distance, they do not present a disc, like the planet Mars, but a small star-like point. When we consider the qualities of the heliometric method of measuring the apparent distance between celestial objects, the advantage of points of light over discs will be obvious. If we are measuring the apparent distance between Mars and a star, we must, by shifting the movable object-glass, bring the star’s image into apparent contact with the disc-image of Mars, first on one side and then on the other, taking the mean for the distance between the centres. Whereas, when we determine the distance between a star and an asteroid, we have to bring two star-like points (one a star, the other the asteroid) into apparent coincidence. We can do this in two ways, making the result so much the more accurate. For consider what we have in the field of view when the two halves of the object-glass coincide. There is the asteroid and close by there is the star whose distance we seek to determine in order to ascertain the position of the asteroid on the celestial sphere. When the movable half is shifted, the two images of star and asteroid separate; and by an adjustment they can be made to separate along the line connecting them. Suppose, then, we first make the movable image of the asteroid travel away from the fixed image (meaning by movable and fixed images, respectively, those given by the movable and fixed halves of the object-glass), towards the fixed image of the star—the two points, like images, being brought into coincidence, we have the measure of the distance between star and asteroid. Now reverse the movement, carrying back the movable images of the asteroid and star till they coincide again with their fixed images. This movement gives us a second measure of the distance, which, however, may
