Mars over ten, whence we observe that Venus is our nearest neighbor, and her distance from the sun two and a half times ours from her.
As round numbers are given only for simplicity, and as we could in fact draw such a map, with the actual elliptic orbits, in which no error would exist which a microscope could detect, it may be asked, "What more can be wanted?"
But there is a most important want unsupplied: our map has no scale, and we do not know how much an inch on it represents in actual distance. Our case, then, is like that of a person with an accurate chart of his country before him, from which he wants to find his distance from the capital. If it have no scale attached, or an erroneous one (and the latter is our own case), he cannot measure a single distance upon it.
If, however, he can ascertain the actual number of miles between any two points of the map, he will plainly know what an inch on it stands for, and thus be able to construct the lacking scale; and so we, if we can measure the distance between any two primary planets, or between any one of them (such as the earth) and the sun, have got at the same time the means of determining all the dimensions of the solar system.
A determination of the distance of any remote object, which we can see but cannot reach, whether celestial or terrestrial, the sun or a mountain-top, requires that we should know either its size and the angle it fills to the eye, or else how much the direction in which we see it changes, as we change our own position by a known amount. Thus, in the latter case, a surveyor, who wishes to determine his distance from an inaccessible object of unknown size, sends an assistant to hold up a staff at the end of a line measured on the ground by a chain. First he notes, with an instrument for the purpose, the direction in which the object is seen as compared with that of the staff, and then, the assistant and observer changing places, the latter notes again the direction from the second point of view, and this will enable him to calculate the distance desired. That first found by direct measurement with the chain is called the "base-line," and it ought to be considerable when the object is far away, since in that case its direction will not, evidently, be much altered, without a corresponding alteration in the observer's position. This difference of direction, caused by a changed point of view, is called by astronomers parallax; nearly the only professional term with which the reader need be troubled, but one which should be clearly understood.
The principle involved in the method is probably familiar to him already, but it is here recalled, to point out how its application must be modified in finding the distance of the sun. As the earth sweeps round that far-distant controller of her path, we can send no messenger in advance along our orbit to distinguish the place we shall move
