If the meeting occur when Mars is in perihelion the planets approach one another within 35,000,000 miles; if in aphelion, only within 61,000,000 miles.

But even this difference in distance does not measure the full extent of the variation in brilliancy. As the brightness of an illuminated body varies inversely as the square of its distance from the source of light, and as the total amount of light it reflects to an observer varies inversely as the square of his distance from it, it makes every difference in the apparent brilliancy of a body how the body is situated, both with regard to the source of light and with regard to the observer. Now it so chances that at the meetings of Mars with the Earth these two factors attain their maximum effects nearly together, and similarly with their minimum. For at the times when we are closest to Mars, Mars is nearly at his closest to the Sun, and reversely when we meet him at the opposite part of his orbit. It thus comes about that at some meetings,--oppositions, they are called, because Mars then is in the opposite part of the sky from the Sun,--the planet appears four and one half times as bright as at others. Here, then, we have the explanation of the planet's great changes in appearance, changes so great as to deceive any one who has not followed its wanderings, into the belief that it is some new and portentous apparition.

Important as is the ellipse in which Mars moves with regard to his visibility by us, it is considerably more important as regards the physical condition of the planet itself. For the Sun being situated at one of the foci of his orbit, the motion of the planet sweeps him now near to, now far from that dispenser of light and warmth; and the amount of both which the planet receives varies just like gravity with his distance from their source. Now the eccentricity of the orbit of Mars is such that when nearest the Sun his distance is 129,500,000 miles, when at his mean distance 141,500,000 miles, and when most remote 154,500,000 miles. The proportion of light and heat he receives respectively is therefore roughly as 16 to 20 to 24; or half as much again at certain times as at others.

So much in our knowledge of Mars is pre-telescopic. Men might have and practically did learn this much without ever seeing the planet other than as a point of light. Its orbit was tolerably accurately known and could have been known still more accurately without telescopic aid; not so, until we become much more nearly omniscient than we at present are, the planet's self.

III. Size and Shape

The relative plan of the solar system can be learned with great accuracy from observations of the motions of its members; not so easily learned is the scale upon which it is constructed. Although the former is intrinsically a very complicated, the latter a very simple problem, two characteristics of the actual system make it possible to solve the former much more nearly than the latter. One of these characteristics is the fact that the distances between the masses which compose the system are very much greater than than dimensions of the masses themselves, of quite a higher order of magnitude. The diameters of the planets are measured by thousands of miles, the distances between them by tens of millions. The second characteristic consists in the approximately spherical shape of the planets themselves, and in the fact that by a mathematical consequence of the actual law of gravitation a sphere acts upon any outside body as if all its mass were concentrated at its centre, a most interesting peculiarity not true under many other supposable laws. These two facts very materially simplify the problem of the motions of celestial mechanics.

But just as the first of these peculiarities helps us to comprehension of the relative dimensions of the solar system, so does it hinder us in determining its actual dimensions. For this determination depends upon a problem in celestial surveying, the finding the distance to a body by measuring the angle it subtends from the two ends of a base-line. Now, as unfortunately we cannot get off the earth for the purpose, our base-line is at most the diameter of the earth itself, and as the distance to the other body immensely exceeds our own size, the angle to be measured becomes so excessively small as to be very difficult