Ambroise Paré, in treating of medicinal weights (1582) said:
Every weight arises from some beginning and element. For as our bodies arise from the four first simple or elementary bodies, so all weights arise from the grain, which is _tanquam_ the beginning and the end of the remainder. We understand a grain of barley, neither dried nor mouldy, but well made and of medium fatness. From 10 grains of this sort comes the obolus, from 2 oboli or 20 grains the scruple ... &c.
This is medieval rubbish. As John Greaves, Professor of Astronomy at Oxford, in his ‘Discourse of the Roman foot’ (1647) wisely said:
I cannot but approve the counsel of Villapandus who adviseth such as will examine measures and weights to begin with the greater and not the lesser.... The most curious man alive with the exactest scale that the most skilful artisan can invent, shall never be able, out of the standard of one grain, to produce a weight equal to the weight of ten thousand grains.
While the subdivision of linear measures and of weights usually stopped at some familiar quantity named after a seed, yet efforts were sometimes made to get at an ultimate atom as the term of the series. The Hindus who began, or ended, a series of weights with one of the motes or fine particles of dust visible in a sunbeam, were imitated by the English moneyers who continued the 20-dwt. and 24-grain series by dividing the grains into 20 Mites, each of 24 Droits, each of 20 Periots, each of 24 Blanks, the blank being 1/230400 of a grain.
So our mint expressed the weight of a Stuart silver penny, not as 7-23/31 grains (all the silver coins having then a fraction of 31sts); that would have been too simple—but as 7 grains, 14 mites, 20 droits, 2 periots, 12 blanks. Even then the statement was not exact; one or two more infinitesimal units would have had to be added to the series.
It may be noted that 7-23/31 grains is simpler than the modern decimal equivalent 7·74193548, &c.
The origin of these mint-terms is obscure; the ‘N.E.D.’ casts no light on it. I consider their source to be—
Droit—a corruption of the Dutch _duit_, Sc. ‘doit,’ a fraction of a farthing. It was more properly written ‘dwit’; perhaps the _r_ was inserted to avoid confusion with ‘dwt.’