There are other kinds of micrometers which we must also briefly consider. In the heliometer[12] we get the power of measuring distances by doubling the images of the objects we see, by means of dividing the object-glass. The two circles, A and B, Fig. 105, represent the two images of Jupiter formed, as we shall show presently, and touching each other; now, if by any means we can make B travel over A till it has the position C, also just touching A, it will manifestly have travelled over a distance equal to the diameters of A and B, so that if we can measure the distance traversed and divide it by 2, we shall get the diameter of the circle A, or the planet. The same principle applies to double stars, for if we double the stars A and B, Fig. 105, so that the secondary images become A´ and B´, we can move A´ over B, and then only three stars will be visible; we can then move the secondary images back over A and B till B´ comes over A, and the second image of A comes to A´. It is thus manifest that the images A´ and B´ on being moved to A´ and B´ in the second position have passed over double their distance apart. Now all double-image micrometers depend on this principle, and first we will explain how this duplication of images is made in the heliometer. It is clear that we shall not alter the power of an object-glass to bring objects to focus if we cut the object-glass in two, for if we put any dark line across the object-glass, which optically cuts it in two, we shall get an image, say of Jupiter, unaltered. But suppose instead of having the parts of the object-glass in their original position after we have cut the object-glass in two, we make one half of the object-glass travel over the other in the manner represented in Fig. 107. Each of these halves of the object-glass will be competent to give us a different image, and the light forming each image will be half the light we got from the two halves of the object-glass combined; but when one half is moved we shall get two images in two different places in the field of view. We can so alter the position of the images of objects by sliding one half of the object-glass over the other, that we shall, as in the case of the planet Jupiter, get the two images exactly to touch each other, as is represented in Fig. 105; and further still, we can cause one image to travel over to the other side. If we are viewing a double star, then the two halves will give four stars, and we can slide one half, until the central image formed by the object-glasses will consist of two images of two different stars, and on either side there will be an image of each star, so that there would appear to be three stars in the field of view instead of two. We have thus the means of determining absolutely the distance of any two celestial objects from each other, in terms of the separation of the centres of the two halves of the object-glass.