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 be regarded as only a reversed repetition of the preceding. But now, carrying on the reverse motion, the moving images of star and asteroid separate from their respective fixed images, the moving image of the star drawing near to the fixed image of the asteroid and eventually coinciding with it. Here we have a third measure of the distance, which is independent of the two former. Reversing the motion, and carrying the moving images to coincidence with the fixed images, we have a fourth measure, which is simply the third reversed. These four measures will give a