Thanks, Grishka; my Google search for the term before I posted here had located many instances of the technique having been required in examination papers, but no explanation of the technique itself.

(What a cracking grammar question follows your cite, btw: 'Parse the following: "Whoever is admitted or sought for in company upon any other account than that of his merit and manners, is never respected there, but only made use of."' You don't come across sentences like that these days!)

After a weekend of reflection, during which my memory has returned if not a clear idea of the technique at least a few hazy recollections, I am prepared to hazard the following illustration. To solve my initial problem, 37 articles at £1.17s 3¾d each, by practice, I write down 37 quids, 37 ten-bobs, 37 two-bobs, 37 thruppences and 37 three-farthings, and add 'em all up.

But I could be wrong. My wife tells me it's happened before.