William Gilbert Explains How Magnetic Bodies Acquire Direction
William Gilbert's De Magnete, Book Three, part 1
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 post is the first on Book Three. Here are the previous posts related to De Magnete.
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
Book Two, part 3: William Gilbert Considers the Internal Structure of the Terrella
Book Two, part 4: William Gilbert States that the Moon Causes the Tides
Book Two, part 5: William Gilbert Aligns Several Loadstones
Book Three focuses on how magnetic bodies acquire and manifest direction, turning towards the poles, at a theoretical level. The exact verticity of magnetic bodies, at different points of the earth, is the topic of Book Four:
But it is to be understood at the threshold of their argument, before we proceed farther, that these directions of loadstone or of iron are not ever and always toward the world’s true poles, that they do not always seek those fixed and definite points, nor rest on the line of the true meridian, but that at places, more or less far apart, they commonly vary either to the east or to the west; sometimes, too, in certain regions of land or sea, they point to the true poles. This discrepance is known as the variation of the needle and of the loadstone; and as it is produced by other causes and is, as it were, a sort of perturbation and depravation of the true direction, we propose to treat here only of the true direction of the compass and the magnetic needle, which would all over the earth be the same, toward the true poles and in the true meridian, were not hindrances and disturbing causes present to prevent: in the book next following we will treat of its variation and of the cause of perturbation. [p.178, emphasis mine]
In this post, I will focus on how exactly a magnetic body acquires its direction, and how manipulations of the body can change this direction.
Recall from previous blog posts that the opposite poles of two magnetic bodies attract each other, and the same poles of two magnetic bodies repel each other. Keeping this mind, Gilbert claims it is possible to understand how bodies acquire direction. In the diagram below, the earth is pictured, with north pole G and south pole H. He distinguishes between three different cases:
CD is a mass of iron, for example, a compass needle, in the air: C is the south pole and D is the north pole of CD;
AB is a loadstone mine: were it to be extracted from the earth, B would be the south pole and A the north pole of AB, and so AB would not change verticity;
EF is an integral part of the core of the earth: were it to be extracted from the earth, E would be the north pole and F the south pole of EF, and so EF would spin around with F pointing north and E pointing south.
Let AB be a loadstone mine, and between it and the uniform earthen globe suppose there are various earths and mixtures that in a manner separate the mine from the true globe of the earth. It is therefore informated [sic] by the earth’s forces just as CD, a mass of iron, is in air; hence the extremity B of the mine or of any part thereof moves toward the north pole G, just as does C, the extremity of the mass of iron, but not A nor D. But with the part EF, which comes into existence continuous with the whole and which is not separated from it by any mixed earthy matter, the case is different. For if the part EF, being taken out, were to be floated, it is not E that would turn to the north pole, but F. Thus, in those bodies which acquire verticity in the air, C is the south extremity and is attracted by the north pole G. In those which come into existence in the detrital outermost part of the earth, B is south, and so goes to the north pole. But these parts which, deep below, are of even birth with the earth, have their verticity regulated differently. For here F turns to the north parts of the earth, being a south part; and E to the south parts of the earth, being a north part. So the end C of the magnetic body CD, situate near the earth, turns to the north pole; the end B of the agnate body EF to the north; the end E of the inborn body EF to the south pole…. [pp.184-185]
The difference that Gilbert makes between CD and EF is important, and needs some careful thought. He makes the case that CD is demonstrated through experience; prior to presenting this diagram, he explains that actual loadstones pulled from mines act exactly as he states:
We once had chiselled and dug out of its vein a loadstone 20 pounds in weight, having first noted and marked its extremities; then, after it had been taken out of the earth, we placed it on a float in water so it could freely turn about; straight-way that extremity of it which in the mine looked north turned to the north in water and after a while there abode; for the extremity that in the mine looks north is austral and is attracted by the north parts of earth, just as in the case of iron, which takes verticity from the earth. [p.184]
As for the case of EF, Gilbert develops another experiment, illustrated with this next diagram. Here, a terrella with poles AB has a part EF cut out, and dangled from a string inside a hollowed-out cavity in the terrella. Then EF would spin around so that E points towards B and F towards A.
Describe a terrella with poles A, B; from its mass separate the small part EF, and suspend that by a fine thread in a cavity or pit in the terrella. E then does not seek the pole A but the pole B, and F turns to A, behaving quite differently from the iron bar CD; for, there, C, touching a north part of the terrella, becomes magnetized and turns to A, not to B. But here it is to be remarked that if pole A of the terrella were to be turned toward the southern part of the earth, still the end E of the solitary part cut out of the terrella and not brought near the rest of the stone would turn to the south; but the end C of the iron bar would, if placed outside the magnetic field, turn to the north. Suppose that in the unbroken terrella the part EF gave the same direction as the whole; now break it off and suspend it by a thread, and E will turn to B and F to A.
So what happens if we chop off a part of a terrella, more or less in a north-south line? This is what is illustrated in the third diagram. A cut has been made from point E to point F, and the cut-off part is dangled from a string. If that part is taken away from the terrella, then point E will be drawn to A and F to B. However, if the cut-off part is joined back with the terrella, then the two parts will hold as if they had never been separated.
Hence the part FE is not attracted into its pit, but the moment it wanders abroad and is away from it, is attracted by the opposite pole. But if the part FE be again placed in its pit or be brought near without any media interposed, it acquires the original combination, and, being again a united portion of the whole, co-operates with the whole and readily clings in its pristine position, while E remains looking toward A and F toward B, and there they rest unchanging. [pp.186-187]
When a loadstone is cut into two loadstones, the magnetic energy is reorganized in such a way that each loadstone acquires its own north pole, south pole, equator, meridians and parallels. In the fourth diagram, a loadstone with poles AB is sliced in two at the equator, and the two new loadstones are placed next to each other, with two different possible arrangements being shown. Each of the loadstones acquires its own new poles and equator.
In the figure, a spherical stone is divided into two equal parts along the axis AB; hence, whether the surface AB be in one of the two parts supine (as in the first diagram), or prone in both (as in the second), the end A tends to B. But it is also to be understood that the point B does not always tend sure to A, for, after the division, the verticity goes to other points, for example to F, G…. LM, too, is now the axis of the two halves, and AB is no longer the axis; for, once a magnetic body is divided, the several parts are integral and magnetic, and have vertices proportional to their mass, new poles arising at each end on division. [pp.187-188]
A specific case of cutting a loadstone in two is when it is elongated. In the diagram below, at the top we see a loadstone with south pole C pointed to the earth’s north pole B, and north pole D to the earth’s south pole A. The loadstone is cut in two, with the loadstone CE taking on a north pole E and loadstone FD taking on a south pole F. The two loadstones can then be reordered so that the FD one is to the north and the CE one to the south. They can be joined together naturally. If, on the other hand, one of the two parts were to be flipped, then the two would repel each other.
Let CD be an unbroken magnetic body, with C looking toward B, the earth’s north, B and D toward A, the earth’s south. Now cut it in two in the middle, in the equator, and then E will tend to A and F to B. For, as in the whole, so in the divided stone, nature seeks to have these bodies united; hence the end E properly and eagerly comes together again with F, and the two combine, but E is never joined to D nor F to C, for, in that case, C would have to turn, in opposition, to nature, to A, the south, or D to B, the north — which were abnormal and incongruous. Separate the halves of the stone and turn D toward C: they come together nicely and combine. For D tends to the south, as before, and C to the north; E and F, which in the mine were connate parts, are now greatly at variance, for they do not come together on account of material affinity, but take movement and tendence from the form. Hence the ends, whether they be conjoined or separate, tend in the same way, in accordance with magnetic law, toward the earth’s poles in the first figure of the stone, whether unbroken or divided as in the second figure; and FE of the second figure, when the two parts come together and form one body, is as perfect a magnetic mass as was CD when first produced in the mine; and FE, placed on a float, turn to the earth’s poles, and conform thereto in the same way as the unbroken stone. [pp.198-199]
Gilbert makes an intriguing analogy of the above situation with the grafting of two cuttings. In the diagram below, cuttings AC and DB can be successfully grafted together, either as AC-DB or as DB-AC, and then successfully grafted onto a living tree. However, if either of the cuttings is flipped, then any graftings will be unsuccessful. It is unclear to me whether for Gilbert this is just an analogy, or whether he actually believes that magnetic phenomena are also taking place.
This agreement of the magnetic form is seen in the shapes of plants. Let AB be a branch of ozier [willow] or other tree that sprouts readily; and let A be the upper part of the branch and be the part rootward. Divide the branch at CD. Now, the extremity CD, if skilfully grafted again on D, begins to grow, just as B and A, when united, become consolidated and germinate. But if D be grafted in A, or C on B, they are at variance and grow not at all, but one of them dies because of the preposterous and unsuitable apposition, the vegetative force, which tends in a fixed direction, being now forced into a contrary one. [pp.199-200]
Now that we have some idea of the differences between different magnetic bodies, the question remains, how do these bodies acquire their verticity? Gilbert focuses on two different methods.
The first method consists in taking advantage of the earth’s verticity to create iron bars with magnetic properties. This method has two cases. The first, active case takes place in an iron forge, carefully set up so that all of the stretching, hammering, and pulling of a heated iron bar is done with the iron aligned north-south; the iron bar will then acquire verticity. The second, passive case consists of aligning an iron bar in a north-south direction, and waiting; over the years, the iron bar will acquire verticity. In both cases, the north end of the iron bar becomes a south pole and the south end a north pole.
The second method consists of rubbing an iron body with a pole of a loadstone. This is how compass needles are magnetized. Ideally, the loadstone is elongated, with clear poles. The part of a compass needle that is to point north is rubbed with the north pole of the loadstone; as a result, that part becomes the south pole of the needle.
The next post will focus on the direction of compass needles in different geometric situations.
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William Gilbert. De Magnete. Dover, New York, 1958. Translation by P. Fleury Mottelay of De Magnete, first published in 1600.