having gone over the Earth obliquely southward, as its center described the line _AOm_: whereas in the latter case the Penumbra touches the Earth at _n_, south of the Equator _ÆQ_, and describing the line _nEq_ (similar to the former line _AOm_ in open space) goes obliquely northward over the Earth, and leaves it at _q_, north of the Equator. In all these circumstances, the Moon has been supposed to change at noon in her descending Node: had she changed in her ascending Node, the Phenomena would have been as various the contrary way, with respect to the Penumbra’s going northward or southward over the Earth. But because the Moon changes at all hours, as often in one Node as the other, and at all distances from them both at different times as it happens, the variety of the Phases of Eclipses are almost innumerable, even at the same places, considering also how variously the same places are situated on the enlightened Disc of the Earth, with respect to the Penumbra’s motion, at the different hours that Eclipses happen. [Sidenote: How much of the Penumbra falls on the Earth at different distances from the Nodes.] 341. When the Moon changes 17 degrees short of her descending Node, the Penumbra _P_ 18 just touches the northern part of the Earth’s Disc, near the North Pole _N_; and, as seen from that place the Moon appears to touch the Sun, but hides no part of him from sight. Had the Change been as far short of the ascending Node, the Penumbra would have touched the southern part of the Disc near the South Pole _S_. When the Moon changes 12 degrees short of the descending Node, more than a third part of the Penumbra _P 12_ falls on the northern parts of the Earth at the middle of the general Eclipse: had she changed as far past the same Node, as much of the other side of the Penumbra about _P_ would have fallen on the southern part of the Earth; all the rest in the _expansum_, or open space. When the Moon changes 6 degrees from the Node, almost the whole Penumbra _P6_ falls on the Earth at the middle of the general Eclipse. And lastly, when the Moon changes in the Node, the Penumbra _PN_ takes the longest course possible on the Earth’s Disc; its center falling on the middle thereof, at the middle of the general Eclipse. The farther the Moon changes from either Node within 17 degrees of it, the shorter is the Penumbra’s continuance on the Earth, because it goes over a less portion of the Disc, as is evident by the Figure. [Sidenote: The Earth’s diurnal motion lengthens the duration of solar Eclipses, which fall without the polar Circles.]