The proportion of declination to latitude[236], and the cause of it

I have already discussed:

• the making of an instrument for finding declination
• the causes and manner of declination
• the different degrees of rotation in different places
• the inclination of the stone
• an instrument indicating, by the influence of a stone, the degree of declination from any horizon
• needles on the meridian of a stone, and their rotation shown for various latitudes by their rise toward the perpendicular.

What are the causes of the degree of that inclination?

Whilst a loadstone and a magnetick iron wire are moved along a meridian from the aequator toward the pole, they rotate toward a round loadstone, as also toward the earth with a circular movement. On a right horizon (just as also on the æquinoctial of {197}the stone) the axis of the iron, which is its centre line, is a line parallel to the axis of the earth. When that axis reaches the pole, which is the centre of the axis, it stands in the same straight line with the axis of the earth.

The same end of the iron which at the æquator looks south turns to the north. For it is not a motion of centre to centre, but a natural turning of a magnetick body to a magnetick body, and of the axis of the body to the axis; it is not in consequence of the attraction of the pole itself that the iron points to the earth’s polar point. Under the æquator the magnetick needle remains in æquilibrio horizontally; but toward the pole on either side, in every latitude from the beginning of the first degree right up to the ninetieth, it dips.

The magnetick needle does not, however, in proportion to any number of degrees or any arc of latitude fall below the horizon just that number of degrees or a similar arc, but a very different one: because this motion is not really a motion of declination, but is in A magnetick body rotates mor quickly than the centre advances.reality a motion of rotation, and it observes an arc of rotation according to the arc of latitude.

Therefore a magnetick body A, while it is advancing over the earth itself, or a little earth or terrella, from the æquinoctial G toward the pole B, rotates on its own centre, and halfway on the progress of its centre[237] from the æquator to the pole B it is pointing toward the æquator at F, midway between the two poles.

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. 7. Explanation of the diagram of the rotation of a magnetick needle.

Diagram of the rotation of a magnetick needle.

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 directed toward the æquator, in which case also that arc is a quadrant of a circle from the limit to the pole; but previous to this all the arcs of rotation are greater than a quadrant, whilst after it they are smaller; in the former the needle rotates more quickly, but in the succeeding positions gradually more slowly.

For each several region there is a special arc of rotation, in which the limit to which the needle rotates is according to the number of degrees of latitude of the place in question; so that a straight line drawn from the place to the point on that arc marked with the number of degrees of latitude shows the magnetick direction, and indicates the degree of declination at the intersection of the quadrant of declination which serves the given place.

Take away the arc of the quadrant of declination drawn from the centre to the line of direction; that which is left is the arc of declination below the horizon. As, for example, in the rotation of the versorium N, whose line respective proceeds to D, from the quadrant of declination, S M, take away its arc R M; that which is left is the arc of declination: how much, that is, the needle dips in the latitude of 45 degrees.

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