In order to be certain that the longitudinal wire shall pass through the centre of the moon, it is best to take the moon when its disc is in the form of a crescent, and to place the longitudinal wire against the points, or _cusps_, of the crescent, as shown in Fig. 103. [Illustration: Fig. 104.] 89. _The Real Size of the Moon._--The real diameter of the moon is a little over one-fourth of that of the earth, or a little more than two thousand miles. The comparative sizes of the earth and moon are shown in Fig. 104. [Illustration: Fig. 105.] The distance and apparent size of the moon being known, her real diameter is found by means of a triangle formed as shown in Fig. 105. _C_ represents the centre of the moon, _CB_ the distance of the moon from the earth, and _CA_ the radius of the moon. _BAC_ is a triangle, right-angled at _A_. The angle _ABC_ is half the apparent diameter of the moon. With the angles _A_ and _B_, and the side _CB_ known, it is easy to find the length of _AC_ by trigonometrical computation. Twice _AC_ will be the diameter of the moon. The volume of the moon is about one-fiftieth of that of the earth. 90. _Apparent Size of the Moon on the Horizon and in the Zenith._.--The moon is nearly four thousand miles farther from the observer when she is on the horizon than when she is in the zenith. This is evident from Fig. 106. _C_ is the centre of the earth, _M_ the moon on the horizon, _M'_ the moon in the zenith, and _O_ the point of observation. _OM_ is the distance of the moon when she is on the horizon, and _OM'_ the distance of the moon from the observer when she is in the zenith. _CM_ is equal to _CM'_, and _OM_ is about the length of _CM_; but _OM'_ is about four thousand miles shorter than _CM'_: hence _OM'_ is about four thousand miles shorter than _OM_. [Illustration: Fig. 106.] Notwithstanding the moon is much nearer when at the zenith than at the horizon, it seems to us much larger at the horizon. This is a pure illusion, as we become convinced when we measure the disc with accurate instruments, so as to make the result independent of our ordinary way of judging. When the moon is near the horizon, it seems placed beyond all the objects on the surface of the earth in that direction, and therefore farther off than at the zenith, where no intervening objects enable us to judge of its distance. In any case, an object which keeps the same apparent magnitude seems to us, through the instinctive habits of the eye, the larger in proportion as we judge it to be more distant.