The changes of the moon, commonly called her _phases_, arise from different portions of her illuminated side being turned towards the earth at different times. When the moon is first seen after the setting sun, her form is that of a bright crescent, on the side of the disk next to the sun, while the other portions of the disk shine with a feeble light, reflected to the moon from the earth. Every night, we observe the moon to be further and further eastward of the sun, until, when she has reached an elongation from the sun of ninety degrees, half her visible disk is enlightened, and she is said to be in her _first quarter_. The terminator, or line which separates the illuminated from the dark part of the moon, is convex towards the sun from the new to the first quarter, and the moon is said to be _horned_. The extremities of the crescent are called _cusps_. At the first quarter, the terminator becomes a straight line, coinciding with the diameter of the disk; but after passing this point, the terminator becomes concave towards the sun, bounding that side of the moon by an elliptical curve, when the moon is said to be _gibbous_. When the moon arrives at the distance of one hundred and eighty degrees from the sun, the entire circle is illuminated, and the moon is _full_. She is then _in opposition_ to the sun, rising about the time the sun sets. For a week after the full, the moon appears gibbous again, until, having arrived within ninety degrees of the sun, she resumes the same form as at the first quarter, being then at her _third quarter_. From this time until new moon, she exhibits again the form of a crescent before the rising sun, until, approaching her _conjunction_ with the sun, her narrow thread of light is lost in the solar blaze; and finally, at the moment of passing the sun, the dark side is wholly turned towards us, and for some time we lose sight of the moon. By inspecting Fig. 38, (where T represents the earth, A, B, C, &c., the moon in her orbit, and _a_, _b_, _c_, &c., her phases, as seen in the heavens,) we shall easily see how all these changes occur. [Illustration Fig. 38.]