128. Let us now suppose that the observer has gone from the Equator e towards the North Pole _n_, and that he stops at _i_, from which place he then sees the Hemisphere _MElNL_; his Horizon _MCL_ having shifted as many [27]Degrees from the Celestial poles _N_ and _S_ as he has travelled from under the Equinoctial _E_. And as the Heavens seem constantly to turn round the line _NCS_ as an Axis, all those Stars which are as far from the North Pole _N_ as the observer is from under, the Equinoctial, namely the Stars north of the dotted parallel _DL_, never set below the Horizon; and those which are south of the dotted parallel _MO_ never rise above it. Hence, the former of these two parallel Circles is called _the Circle of perpetual Apparition_, and the latter _the Circle of perpetual Occultation_: but all the Stars between these two Circles rise and set every day. Let us imagine many Circles to be drawn between these two, and parallel to them; those which are on the north side of the Equinoctial will be unequally cut by the Horizon _MCL_, having larger portions above the Horizon than below it; and the more so, as they are nearer to the Circle of perpetual Apparition; but the reverse happens to those on the south side of the Equinoctial, whilst the Equinoctial is divided in two equal parts by the Horizon. Hence, by the apparent turning of the Heavens, the northern Stars describe greater Arcs or Portions of Circles above the Horizon than below it; and the greater as they are farther from the Equinoctial towards the Circle of perpetual Apparition; whilst the contrary happens to all Stars south of the Equinoctial: but those upon it describe equal Arcs both above and below the Horizon, and therefore they are just as long above as below it. [Sidenote: PLATE II.] 129. An observer on the Equator has no Circle of perpetual Apparition or Occultation, because all the Stars, together with the Sun and Moon, rise and set to him every day. But, as a bare view of the Figure is sufficient to shew that these two Circles _DL_ and _MO_ are just as far from the Poles _N_ and _S_ as the observer at _i_ (or one opposite to him at _o_) is from the Equator _ECQ_; it is plain, that if an observer begins to travel from the Equator towards either Pole, his Circle of perpetual Apparition rises from that Pole as from a Point, and his Circle of perpetual Occultation from the other. As the observer advances toward the nearer Pole, these two Circles enlarge their diameters, and come nearer one another, until he comes to the Pole; and then they meet and coincide in the Equator. On different sides of the Equator, to observers at equal distances from it, the Circle of perpetual Apparition to one is the Circle of perpetual Occultation to the other. [Sidenote: Why the Stars always describe the same parallel of motion, and the Sun a different.]