103. THE MOON'S ATMOSPHERE.--Upon the earth the sun casts no shadows so sharp and black as those of Fig. 60, because his rays are here scattered and reflected in all directions by the dust and vapors of the atmosphere (§ 51), so that the place from which direct sunlight is cut off is at least partially illumined by this reflected light. The shadows of Fig. 60 show that upon the moon it must be otherwise, and suggest that if the moon has any atmosphere whatever, its density must be utterly insignificant in comparison with that of the earth. In its motion around the earth the moon frequently eclipses stars (_occults_ is the technical word), and if the moon had an atmosphere such as is shown in Fig. 61, the light from the star _A_ must shine through this atmosphere just before the moon's advancing body cuts it off, and it must be refracted by the atmosphere so that the star would appear in a slightly different direction (nearer to _B_) than before. The earth's atmosphere refracts the starlight under such circumstances by more than a degree, but no one has been able to find in the case of the moon any effect of this kind amounting to even a fraction of a second of arc. While this hardly justifies the statement sometimes made that the moon has no atmosphere, we shall be entirely safe in saying that if it has one at all its density is less than a thousandth part of that of the earth's atmosphere. Quite in keeping with this absence of an atmosphere is the fact that clouds never float over the surface of the moon. Its features always stand out hard and clear, without any of that haze and softness of outline which our atmosphere introduces into all terrestrial landscapes. [Illustration: FIG. 60.--Archimedes and Apennines. NASMYTH and CARPENTER.] 104. HEIGHT OF THE LUNAR MOUNTAINS.--Attention has already been called to the detached mountain peaks, which in Fig. 55 prolong the range of Apennines into the lunar night. These are the beginnings of the Caucasus mountains, and from the photograph we may measure as follows the height to which they rise above the surrounding level of the moon: Fig. 62 represents a part of the lunar surface along the boundary line between night and day, the horizontal line at the top of the figure representing a level ray of sunlight which just touches the moon at _T_ and barely illuminates the top of the mountain, _M_, whose height, _h_, is to be determined. If we let _R_ stand for the radius of the moon and _s_ for the distance, _T M_, we shall have in the right-angled triangle _M T C_, R^{2} + s^{2} = (R + h)^{2}, and we need only to measure _s_--that is, the distance from the terminator to the detached mountain peak--to make this equation determine _h_, since _R_ is already known, being half the diameter of the moon--1,081 miles. Practically it is more convenient to use instead of this equation another form, which the student who is expert in algebra may show to be very nearly equivalent to it: