267. The Moon’s absolute motion from her Change to her first Quarter, or from _a_ to _b_, is so much slower than the Earth’s, that she falls 240 thousand miles (equal to the Semidiameter of her Orbit) behind the Earth at her first Quarter in _b_, when the Earth is in _B_; that is, she falls back a space equal to her distance from the Earth. From that time her motion is gradually accelerated to her Opposition or Full at _c_, and then she is come up as far as the Earth, having regained what she lost in her first Quarter from _a_ to _b_. From the Full to the last Quarter at _d_ her motion continues accelerated, so as to be just as far before the Earth at _D_, as she was behind it at her first Quarter in _b_. But, from _d_ to _e_ her motion is retarded so, that she loses as much with respect to the Earth as is equal to her distance from it, or to the Semidiameter of her Orbit; and by that means she comes to _e_, and is then in conjunction with the Sun as seen from the Earth at _E_. Hence we find, that the Moon’s absolute motion is slower than the Earth’s from her third Quarter to her first; and swifter than the Earth’s from her first Quarter to her third: her path being less curved than the Earth’s in the former case, and more in the latter. Yet it is still bent the same way towards the Sun; for if we imagine the concavity of the Earth’s Orbit to be measured by the length of a perpendicular line _Cg_, let down from the Earth’s place upon the straight line _bgd_ at the Full of the Moon, and connecting the places of the Earth at the end of the Moon’s first and third Quarters, that length will be about 640 thousand miles; and the Moon when New only approaching nearer to the Sun by 240 thousand miles than the Earth is, the length of the perpendicular let down from her place at that time upon the same straight line, and which shews the concavity of that part of her path, will be about 400 thousand miles. [Sidenote: A difficulty removed. PL. VII.]