Quadrant of Altitude.
The fiducial edge thereof representing the Vertical Circles, and the Degrees upon it, describing the Parallels of Altitude. This thin plate is called the Quadrant of Altitude.
The center of the horizon being the place of observation, it is evident that this circle, and all the others belonging to it, are continually changed, which way soever we move; wherefore we may suppose the horizon, with its secundaries and parallels, to invest the globe like a rete or net; and to be moveable every way round it. This is very naturally illustrated by the globes; if we move directly North, or directly South, the change made in the horizon, is represented by moving the brass meridian (keeping the globe from turning about its axis) in the notches made in the wooden horizon, just so much as we travelled. If our course should be due East, or due West, the alterations made thereby are represented by turning the globe accordingly about its axis, the brass meridian being kept fixed; and if we steer betwixt the meridian and the East or West points, then we are to turn the brass meridian, and also the globe about its axis accordingly; the sum of which is, let the spectator be at what point soever of the Earth’s surface, he’ll there gravitate, or tend exactly towards its center, and imagine himself to be on the highest part thereof, (the unevenness of the ground not being here considered) wherefore if we turn the globe in such a manner as to bring the several progressive steps of a traveller successively to the Zenith, we shall then have the successive alterations made in the horizon, in every part of his journey. This explication being well considered, will be of help to young beginners, to conceive how the Earth is every where habitable; and how passengers can travel quite round it; for since every thing tends toward the center of the Earth, we are to conceive that point as being the lowest, and not to carry our idea of downwards any farther. Those that are diametrically opposite to us being as much upon the upper part of the Earth as we are, there being no such thing in nature as one place being higher than another, but as it is at a greater distance from the center of the Earth, let it be in what country soever.
We have now done with all the circles of the sphere, and it may be observed, that the Equinoctial, the Ecliptic, and the Horizon, with their Secundaries and parallels, are all alike; and altering their position, may be made to serve for one another. Thus, if the Poles of the World be brought into the Zenith and Nadir, the Equinoctial will coincide with the Horizon, the Meridians will be the same with the Vertical Circles, and the parallels of Declination will be the parallels of Altitude. After the same manner, if shifting the position, we bring the Ecliptic to coincide with the Horizon, the circles of Longitude will be the Vertical Circles, and the parallels of Latitude and Altitude will coincide.
The horizon and the equator may be either parallel, perpendicular, or oblique to each other.
Parallel Sphere.
15. A Parallel Sphere is that position where the equator coincides with the horizon, and consequently the poles of the world are in the Zenith and Nadir: The inhabitants of this sphere (if there be any) are those who live under the poles of the world.
Right Sphere.
16. A Right or Direct Sphere is that position where the equator is perpendicular to the horizon, the inhabitants whereof are those who live under the equinoctial.