e
It might be to create a "non-progressive winding". If you wind a toroid in the obvious way, starting your winding at one point on the toroid, and addi ng turns until you get back there, you've got a single turn in the plane of the toroid, and any current you put through the toroid creates an external field.
The simplest way of cancelling this external field is to put a loop of wire around the toroid, back from finish to start, that cancels this single tur n. It doesn't provide perfect cancellation, but it's a lot better than noth ing.
does discuss this problem, and lists a couple of different non-progressive winding schemes that offer more perfect cancellation. At least one - the Ay rton-Perry scheme - dates aback to the 1890's. William Edward Ayrton died i n 1908 though his second wife was first woman member of the Institution of Electrical Engineers, and could be the Ayrton involved, though she was pri marily interested in electric arcs.
was a colleague of both.
There's a scheme for measuring fluid conductivity which involves stacking t wo non-progressively wound toroidal coils, driving one and measuring the fl uid conductivity from the voltage induced in the second by the current flow ing the fluid which acts as a single turn winding threading both cores.
It's an obvious enough idea, when you think about it.