Much more quickly, therefore, must the versorium rotate than its centre advances, in order that by rotating it may face straight toward the point F. Wherefore the motion of this rotation is rapid in the first degrees from the æquator, namely, from A to L; but more tardy in the later degrees from L to B, when facing from the æquator at F to C. But if the declination were equal to the latitude (_i.e._, always just as many degrees from the horizon, as the centre of the versorium has receded from the æquator), then the magnetick needle would be following some potency and peculiar virtue of the centre, as if it {198} were a point operating by itself. But it pays regard to the whole, both its mass, and its outer limits; the forces of both uniting, as well of the magnetick versorium as of the earth. * * * * * * CHAP. VII. Explanation of the diagram of the rotation of _a magnetick needle_. [Illustration] Suppose A C D L to be the body of the earth or of a terrella, its centre M, Æquator A D, Axis C L, A B the Horizon, which changes according to the place. From the point F on a Horizon distant from the æquator A by the length of C M, the semi-diameter of the earth or terrella, an arc is described to H as the limit of the quadrants of declination; for {199} all the quadrants of declination serving the parts from A to C begin from that arc, and terminate at M, the centre of the earth. The semi-diameter of this arc is a chord drawn from the æquator A to the pole C; and a line produced along the horizon from A to B, equal to that chord, gives the beginning of the arc of the limits of arcs of rotation and revolution, which is continued as far as G. For just as a quadrant of a circle about the centre of the earth (whose beginning is on the horizon, at a distance from the æquator equal to the earth's semi-diameter) is the limit of all quadrants of declination drawn from each several horizon to the centre; so a circle about the centre from B, the beginning of the first arc of rotation, to G is the limit of the arcs of rotation. The arcs of rotation and revolution of the magnetick needle are intermediate between the arcs of rotation B L and G L. The centre of the arc is the region itself or place in which the observation is being made; the beginning of the arc is taken from the circle which is the limit of rotations, and it stops at the opposite pole; as, for example, from O to L, in a latitude of 45 degrees. Let any arc of rotation be divided into 90 equal parts from the limit of the arcs of rotation toward the pole; for whatever is the degree of latitude of the place, the part of the arc of rotation which the magnetick pole on or near the terrella or the earth faces in its rotation is to be numbered similarly to this. The straight lines in the following larger diagram show this. The magnetick rotation at the middle point in a latitude of 45 degrees is