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186 length; or if any one were told where the lamp was, he could calculate the length. The lamp that casts the shadows of the lunar mountains is of course the Sun; and we can find his position at any date from the Nautical Almanac or a similar book, and then we can calculate the length of shadow if we know how high the mountain is; or, if we measure the length of shadow, we can calculate the height of the mountain. But there is one thing to be very careful about: if the plain on which the shadow falls is not quite flat we may be misled.

We can see that by a little experiment. Here is a rough model of a lunar mountain attached to a flat board, and from the lantern, which represents the Sun, we will cast a shadow on the board. But now the board is made up of two pieces hinged together, and if I slope the outer piece a little, you will see how the shadow alters in length; I can lengthen it or shorten it by a very slight inclination of the hinged piece (Figs. 55 and 56). I can, of course, see that I am sloping the board, and make due allowance; but on the Moon we do not know whether the plain is flat or not, so that when we measure heights in this way, we are liable to some uncertainties. The case is not