The "Lorentz" force law of electromagnetic theory has a complicated and unclear history; muddled versions of it were in circulation for most of the Nineteenth Century. One of these -- accurate so far as it goes -- stated that a current-bearing wire placed between the poles of a horse-shoe magnet experiences a force that is perpendicular to both the currrent-direction and the line joining the magnetic poles. This law was known by the 1820s and was the basis of one of the first electric motors: "Barlow's wheel".
In this device, wires join one end of a battery to a pool of liquid mercury and the other to the axle of a metal wheel (for some reason usually a toothed gear, although a round disc behave the same way and seems more elegant). When the wheel is lowered into the quicksilver, current flows through the circuit. If a horse-shoe magnet be then placed with its poles on opposite sides of the wheel-mercury contact, the force law predicts that the wheel will experience a tangential acceleration and rotate.
An essay on Magnetic Attractions, and on the laws of Terrestrial and Electro Magnetism : comprising a popular course of curious and interesting experiments on the latter subject, and an easy experimental method of correcting the local attraction of vessels on the compass in all parts of the world : with an appendix, containing the results of experiments made on ship board from latitude 61° S. to latitude 80° N.
by PETER BARLOW, F.R.S., of the Royal Military Academy; Honorary Member of the Philosophical Societies of Cambridge and Newcastle, and Associate in the Society of Civil Engineers. [London: Mawman, 1824] p 279-282.
Barlow's words are in bold
To show the effect of a horse-shoe magnet on a freely suspended galvanic wire.
¶281 . Let Zz (fig. 18) denote a part of the galvanic wire, freely suspended by the chain connection at o, proceeding from the zinc end of a battery, its lower extremity being amalgamated and slightly immersed in a reservoir of pure mercury, having a connection at C with the other extremity of the battery. N S is a horse-shoe magnet, posited as shown in the figure.
The contact being now made at C and Z, the hanging part of the wire o z will be thrown out of the mercury into the position o z′ ; the contact being thus broken, it falls by its own gravity into the mercury, by which means the contact being renewed it is again projected, and so on with an extraordinary rapidity ; and if the position of the magnet be reversed, or the contact be changed, the direction of the motion will be changed also, but the effect will be the same.
This singular motion may be still explained by the hypothesis that has been advanced ; for the wire having a tendency to pass round the north end of the magnet to the right hand, and round the south end to the left hand, is urged by equal forces directly in a line with the open space of the magnet, the equality of the two forces preventing the rotatory motion about either, but both conspiring to give to the wire the rectilineal motion which has been described.
This experiment is also due to Mr. J. Marsh. This young man, to whose ingenuity and industry I am much indebted for the success of my experiments, is at present employed in an inferior situation in the laboratory of the Royal Arsenal ; but his dexterity as a workman, his practical chemical knowledge, and his regular conduct, are qualifications which render him deserving of a more respectable and profitable occupation.
To exhibit a wheel and axle rotation by means of a horse-shoe magnet.
¶282. The machine by which this motion is produced is represented in (fig. 19), where A B is a rectangular piece of hard wood, C D an upright wooden pillar, D E a piece of stout brass or copper wire, and a b a somewhat smaller wire, soldered upon it at E, on the lower side of which the wheel W, of thin copper, turns freely ; h f is a small reservoir for mercury, sunk in the wood, and g i a narrow channel running into it : H H is a strong horse-shoe magnet. Mercury being now poured into the reservoir f g, till the tips of the wheel are slightly immersed in it, and the surface covered with weak dilute nitric acid, let the connection with the battery be made at i and D, and the wheel W will immediately begin to rotate with a great velocity. If the contact be changed, or if the magnet be inverted, the motion of the wheel will be reversed ; but in general, the best effect is produced when the wheel revolves inwards. The suspension of the wheel, which I find to answer the best, is shown in (fig. 20) [perhaps the unlabelled figure between figs. 18 and 19, although I don't quite understand what it shows; the next illustration in the text is labelled "Fig. 21".]. This is a necessary consequence of the motion described in the last experiment, by which it was suggested, and is explained on the same principles.
In the Nineteenth Century, Barlow's Wheel was a popular demonstration experiment in physics classes. There are videos on YouTube showing fairly exact replicas of the original experiment, e.g. this one by "Roobert33" [5 min]:
Although the laboratory techniques used in the video are quite typical of the 1800s, one can hardly avoid thinking that Roobert33 is taking authenticity a bit too far in his complete disregard of all safety procedures for handling mercury; spraying blobs of it across the lab bench doesn't really seem like a good idea. Any reader tempted to build their own Barlow's Wheel should follow the lead of "Pdebye" in the next video [2 minutes] and use a non-toxic conducting liquid such as Galinstan (or simply an electroyte solution):
Some people use the term "Barlow's Wheel" more loosely for any homopolar motor with a big disc in it, like this one: