From measurement of the distance the sun-tipped peak seems to stand aloof from the line where the plain itself is touched by the light, the height of it above that plain may be calculated. In this way have been found the heights of the mountains of the moon. Incidentally, brain outstrips brawn. For pinnacles no Lunarian could scale, both for their precipitous inaccessibility and their loftiness, man has measured without so much as setting foot upon their globe. At each lunar sunrise and again at lunar sunset these old crater walls show their crescent coronets tipped the reverse way; and peaks higher than the Himalayas make gigantic gnomons of themselves with hands outstretched to grasp the plains. In this manner a lunar peak of fifteen thousand feet shows its presence to the unaided eye. With so much for starting-point we can calculate how low an elevation could similarly be made out on Mars under a like phase illumination. Now, in spheres of different diameters the distance out from the terminator for a given height is as the square root of the diameter. Mars has about twice the size of the Moon. In consequence, if we saw the planet at the same distance off as the Moon, the height of a peak upon it sufficient to cast an equal shadow or be seen at an equal separation from the terminator need be but two thirds as high. To see it thus equidistant a power of 250 or 300 is necessary, dependent on the opposition. Twice this power may at times be used, and by the same reasoning this would reduce the height sufficient to show by four or to something like 2500 feet. This, then, would be the theoretic limit of the visible, a limit needing to be somewhat increased because of the imperfection of our air. Having found thus what should be visible on Mars we turn now to see what is. At once we find ourselves confronted with a very unlunar state of things. Common upon the face of the Moon, excrescences of the terminator are rare on Mars. The first ever seen was detected by a visitor at the Lick Observatory in 1888. Since then they have been repeatedly noticed both at the Lick and elsewhere. But although observers are now on the watch for them, they are not very frequently chronicled because not of everyday occurrence. Much depends upon the opposition; some approaches of the planet proving more prolific of them than others. How rare they are, however, may be gathered from the fact that the last three oppositions have disclosed but one apiece. An account of the great projection of May 25, 1903, will give an idea of the extent and interest of the phenomenon and will serve to show to what cause we must attribute all such that have been visible on Mars, for the behavior of this one was typical of the class. [Illustration: Projection on terminator.]