By rotation theories I mean those which attribute the production of the (axial dipole) field (of the Earth and other celestial bodies) to some phenomenon primarily due to the rotation. I exclude papers, such as those on dynamo theory, which involve also internal differential motion, or in which the rotation is only incidental.

 

The first theories involved the rotation of real negative charge on or inside the Earth's surface; rotating with the Earth this would create a magnetic field, as had been shown by Rowland in 1878 (reported by Helmholtz in 1876) – "rotating charge" theories. (In those days atmospheric electricity was studied alongside geomagnetism, and the production of the observed vertical electric field needed some negative charge on the Earth.) But it was soon pointed out that a sufficiently large charge to explain the axial dipole magnetic field would give a very large external electric field. Also, while a stationary observer would see a dipole field, an observer rotating with the Earth would see a field of different geometry; the radial field observed would be independent of the whether the observer was stationary or rotating with the Earth, but the horizontal field for a rotating observer would involve an extra term. And when the ionosphere was discovered (rotating with the Earth), which would be carrying the opposite charge, again the wrong geometry field would be observed.

 

It was also pointed out quite early that if a real charge was associated with all moving matter, then laboratory sized objects moving with linear motion with respect to the Earth should give a measurable magnetic field. The 1923 experiment of Wilson is usually quoted as showing that this did not happen, but the present author (FJL) is sceptical.

 

To avoid the problem of very large external electric fields, later theories had the Earth (almost) electrically neutral, but with charge distributions of different sign spread over different radii – "separated charge" theories; these could gave very large internal electric fields, but at that time it was not appreciated that hot rock would be significantly conducting. Various mechanisms were proposed for the production of this separated charge.

 

Most later theories involved some unknown fundamental property of rotation, usually interpreted in terms of some effective (not real) charge moving with, or current density associated with, the local material – "fundamental rotation" theories. However several authors tried to produce (a wide variety of!) theoretical justifications for the empirical formulae.

 

Different theories predicted that the surface polar (or equatorial) field would involve various different powers of the sphere radius a and angular velocity w; Swann (1912) discusses which combinations are feasible.

 

After the burst of papers at the end of the 19^th century, there was a lull until the measurement by Hale of the magnetic field of sunspots in 1908, and of the general magnetic field of the Sun in 1912, triggered another burst.

 

There was then only a steady trickle of papers until in 1947 Babcock made the first measurement of the magnetic field of a star, leading to Blackett's 1947 paper. In this paper Blackett resurrected the idea that for all rotating bodies the ratio of the magnetic dipole moment, P, to the angular momentum, U, was given (in cgsemu) by (P/U)=bG^0.5/2c, where b is a non-dimensional number (surprisingly close to unity), G is the gravitational constant, and c the speed of light. (In rationalized mks units, i.e. SI, the expression becomes (P/U)=b(Ge_o)^0.5/2.) For simplicity, in my notes I will refer to the this equation as the Blackett equation, whatever its context. (The factor G^0.5/c (or (Ge_o)^0.5) is probably the only simple combination of fundamental constants having the right dimensions, so it is not surprising that it appears in almost all theories, of whatever origin.)

 

Fairly quickly however it was realized that the dipole field of the Earth, the Sun, and some stars, all reversed, so could not be explained by a simple "fundamental" theory, though a few authors seemed to have ignored this problem!

 

(Perhaps I should point out that a form of Blackett's equation has survived to the present day, in the form of an empirical "Magnetic Bode's Law" for the planets, as a (possible) way of relating the magnitude of their magnetic moment to their size and spin. Dynamo theorists produce various justifications for it.)

 

There have been seven (possibly eight) experimental tests of such "rotation" theories, which I will briefly summarize. (I will not try to summarize the many, diverse, theoretical papers!) There have been three direct tests, looking for the field from a rotating laboratory mass; The magnetometer used by Lébedèw (1912) was far too insensitive (100 nT) for any realistic test of modern theories (he expected 10 000 nT), and while Swann & Longacre (1928) claimed that any magnetic field produced was less than 10% of the field they expected (about 100 nT), it is doubtful if their paper would have passed present-day refereeing! (Note that modern theories predict very much smaller fields, of the order of 10⁻¹² T.) Surdin (1977) made another laboratory measurement, but his theory predicted random rapid reversals of the field of magnitude about10⁻¹² T, and he looked only at the auto-correlation of the magnetometer noise. (A possible further direct experiment was that of Eichenwald (date unknown), referenced by Kuznetsov (1983), but this might have been only a modern version of Rowland's 1876 experiment.)

 

The remaining experimental tests all relied on making some, not unreasonable, interpretation of the theory, usually by associating a particular pseudo-current with each element of the Earth; this then predicts that for rotation theories the horizontal component of the Earth's magnetic field will decrease with depth, at about 20 nT/km at mid latitudes, compared with the (approximately) inverse-cube law increase of about 10 nT/km if the source were entirely in the core. There have been three attempts to measure this vertical gradient: Hales & Gough (1947), Runcorn et al. (1950, 1951) and Esperson et al. (1956). But of these only the Runcorn et al. measurements were likely to have reasonably corrected for the effects of nearby magnetized rocks; their observed gradients agreed in sign with the "core" values, but to magnitude only to within a factor of two. A fourth indirect test was that of Blackett (1952), who claimed that any field due to the static gold cylinder was less than 10% of the predicted value of 10⁻¹² T. Again a, not unreasonable, interpretation was involved. However Surdin (1977) and Sirag (1979) have disputed both the above interpretations, on different grounds!