William Gilbert Considers the Internal Structure of the Terrella

William Gilbert's De Magnete, Book Two, part 3

This post is part of a series of posts about William Gilbert’s De Magnete (On the Magnet¹), which is composed of six books. This is the third post on Book Two. Here are the previous posts related to De Magnete.

• On Little Earths and Little Suns

• De Magnete, Nothing Less than the First Ever Work of Experimental Physics

• Book One, part 1: William Gilbert Writes about the Loadstone

• Book One, part 2: William Gilbert Examines Iron, Calls Aristotle's Earth Element Dead

• Book Two, part 1: William Gilbert Compares Electric Bodies to Magnetic Bodies

• Book Two, part 2: William Gilbert Discusses Magnetic Bodies

As I wrote in a previous post, De Magnete is considered to be the first work of experimental physics. For this to be possible, Gilbert had to develop a theoretical framework under which the experiments were to be taken. More specifically, he had to speculate about the internal structure of the terrella. His key idea was that all of the material in a terrella participates in coition with magnetic bodies. In this post, I will present four diagrams from De Magnete, together with Gilbert’s explanations therefore, along with my own comments. Here is his overall summary:

Loadstone does not attract iron with equal force at every point; in other words, the magnetic body does not tend with the same force to every point of the loadstone; for the loadstone has points (i.e., true poles) at which its rare energy is most conspicuous. And the regions nearest the poles are the stronger, those remotest are the weaker; yet in all the energy is in some sense equal. [p.115, my emphasis]

The first diagram shows a terrella with poles at A and B, with equator defined by the line CD. The point here is to compare the attraction at points along the equator, at F, and at E. Right at the equator, the attraction towards A and the attraction towards B cancel each other out. However, if a magnetic body is moved slightly north, say to F, then it will be drawn towards the pole A. And the attraction increases as the body approaches the pole.

But the directive force at the equator is strong. C and D are at equal distances from both poles; hence a piece of iron on the line CD, being pulled in contrary directions, does not cling steadily, but it stays and adheres to the stone only when it falls to either side of the line. At E the attractive force is greater that at F, for E is nigher the pole. And this is not for the reason that there is more energy resident at the pole, but because all the parts, being united in the whole, direct their forces to the pole. [p.116]

The second diagram shows a terrella with poles at H and I, with the curved lines corresponding to meridians, i.e., north-south lines on the surface of the terrella. The attraction at point A will be along the meridian towards B, at B towards C, and so on towards the pole I. Gilbert is stating that the contribution to the magnetic energy of points from A to B is as important as that of points from C to D or D to E.

From A the energy is transmitted to B, from AB to C, from ABC to D, and from them to E, and likewise from G to H; and so on as long as the whole mass is one body. But if the piece AB be cut out, though it be near the equator, nevertheless the effect will be as great on the magnetic action as if CD or DE, equal quantities, had been taken away. For no part has any supereminent value in the whole; whatever it be, that it is because of the parts adjoining, whereby an absolute and perfect whole is produced. [pp.118-119]

The third diagram is of the cross-section (a cut through the middle) of a terrella with pole E, equatorial plane HMQ, and center M. The line EM is part of the polar axis. According to Gilbert, for every point on the equatorial line, the magnetic energy moves towards the surface of the terrella, but only towards points between the pole and the point directly “above” it, following a line parallel to the axis to the surface from the original point. For example, for point A, the energy moves towards all of the points on the surface of the terrella between C and E, including F and N.

Let HEQ be a terrella, E a pole, M the centre, HMQ the plane of the equinoctial circle. From every point of the equinoctial plane the energy reaches out to the periphery, but differently from each: for from A the formal energy goes toward CFNE and to every point betwixt C and E (the pole), and not toward B; neither from G toward C. The attractive force in the region FGH is not strengthened by the force residing in the region GMFE; but FGH increases the energy in the rising curve FE. Thus energy never proceeds from the lines parallel to the axis to points above those parallels, but always internally from the parallels to the pole. From every point of the plane of the equator the energy goes to the pole E; the point F derives its forces only from GH, and the point N from OH; but the pole E is strengthened by the whole plane HO. Therefore this mighty power has here its chief excellency; here is its throne, so to speak. But in the intervals at F, for example, there resides so much attractional energy as can be given by the section HG of the plane. [p.120]

The fourth diagram focuses on the attractive power towards magnetic bodies at different points on the surface of the terrella with poles a and b, and point c on the equator. The bars outside of the terrella are magnetic bodies such as iron bars. When an iron bar is placed near the equator of the terrella, such as at point e, the iron bar fixes itself at a slight angle from the tangent to the terrella at that point; as a result, the iron bar is pointed slightly into the terrella, and the resulting chord (a straight line from one point of the surface to another point on the surface) is relatively short. As the iron bar is moved closer to the pole, the angle between the iron’s orientation and the tangent increases, and as a result, the resulting chord becomes longer, as we can see at points f and g. At the pole a, the chord is in fact the diameter. According to Gilbert, the attractive power at a point is a result of the length of the chord at that point, because that length is a measure of how much of the terrella is participating in the attraction.

Let ab be the poles. An iron bar or the other magnetic body c is attracted at e; yet the end that is pulled does not tend toward the centre of the loadstone, but obliquely toward the pole, and a chord drawn from that end obliquely in the direction in which the body is attracted is a short one; the strength of the coition therefore is less, and so too the attracted object turns at a less angle to the terrella. But as from a body at f a longer chord proceeds, so the action there is stronger. At g the chord is still longer. At a (the pole) it is longer of all (for the diameter is the longest line), and thither do all the parts send their forces: there stands, as it were, the citadel, the judgment-seat, of the whole region, — not that the pole holds this eminence in its own right, but because it is the depository of forces contributed to it by all the other parts; it is like the soldiers bringing reinforcement to their commander. [pp.130-131]

As we can see above, Gilbert’s understanding of the internal structure of the terrella is consistent with his idea that the magnetic property of the terrella comes from the quantity of that primordial terrene material that makes up the core of the earth.

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1. William Gilbert. De Magnete. Dover, New York, 1958. Translation by P. Fleury Mottelay of De Magnete, first published in 1600.