*THE POPULAR SCIENCE MONTHLY.*

serving its displacement in the sky as seen from remote points on the earth. The *relative* distances of the planets are easily found in several different ways,^{[1]} and are known with very great accuracy—the possible error hardly reaching the ten-thousandth in even the most unfavorable cases. In other words, we are able to draw for any moment an exceedingly accurate map of the solar system—the only question being as to the scale. Of course, the determination of any line in the map will fix this scale; and for this purpose one line is as good as another, so that the measurement of the distance from the earth to the planet Mars, for instance, will settle all the dimensions of the system.

The figure illustrates the method of observation. Suppose two observers, situated one near the north pole of the earth, the other near the south. Looking at the planet, the northern observer will see it at *N* (in the upper figure), while the other will see it at *S,* farther north in the sky. If the northern observer sees it as at *A* (in the lower part of the figure), the southern will at the same time see it as at *B;* and, by measuring carefully at each station the apparent distance of the planet from several of the little stars (*a, b, c*) which appear in the field of view, the amount of the displacement can be accurately ascertained. The figure is drawn to scale. The circle *E* being taken to represent the size of the earth as seen from Mars when nearest us, the black disk represents the apparent size of the planet on the same scale, and the distance between the points *N* and *S,* in either figure *A* or *B,* represents, on the same scale also, the displacement which would

- ↑ One method of determining the relative distances of a planet and the sun from each other and from the earth is the following, known since the days of Hipparchus: First, observe the date when the planet comes to its opposition—i. e., when sun, earth, and planet, are in line, as in the figure, where the planet and earth are represented by
*M*and*E*Next, after a known number of days, say one hundred, when the planet has advanced