William Pratt

The difference between the poet and the mathematician is that the poet tries to get his head into the heavens while the mathematician tries to get the heavens into his head.
G. K. Chesterton

A simple calculating device with the fancy name Arithmetical Jewell was designed by William Pratt in the middle 1610s, and described in the book of the same name (The Arithmeticall Jewell: or the use of a small Table Whereby is speedily wrought, as well all Arithmetical workes in whole Numbers, as all fractional operations, without fraction or reduction. Invented by William Pratt. Published by his Maiesties privilege, granted to the inventor, under the Great Seale of England), published in 1617 in London.

William Pratt, in association with John Harpur and Jeremy Drury, received a patent (privilege) on 27 March 1616, for the sole making of a table for casting accounts. The patent was for making a device “by which all questions arithmetical may be resolved without the use of pen or compters [counters]”. On 4 April 1616, the three men obtained a privilege for printing a book explaining an “instrument or table for cyfering and casting of accomptes”. Soon thereafter, the partners fell out, and published competing manuals of instruction: Harpur entered his in the Stationers’ Register on 8 March 1617, and Pratt on 21 June 1617.

The title page of Arithmeticall Jewell of William Pratt from 1617
The title page of Arithmeticall Jewell of William Pratt

The Arithmetical Jewell of Pratt is an instrument with a flat grid of semi-circular, rotating brass wedges, devised to facilitate addition, subtraction, multiplication, division, and the extraction of roots.

William Pratt was a mathematical practitioner and a member of the active circle of London’s mathematical teachers, close to the famous Gresham College, where the logarithms of Napier were popularized at that time.

The drawing of Arithmeticall Jewell of William Pratt from 1617
The drawing of Arithmeticall Jewell of William Pratt from his book

Pratt’s device was nothing more than a rudimentary mechanical reconfiguration of the conventional reckoning technique: a portable, fancier and gentlemanly adaptation of the century-old techniques of calculation like plume (manual calculations) and jetons of the abacus. With the exception here that you did not need paper to inscribe, for instance, the carry-over numbers of an addition; one could instead, using a small metallic stylus, “inscribe” them on the instrument’s appropriate sectors of brass. The reckoning method, nonetheless, was precisely the same as the plume and jetons.

The Arithmetical Jewell comprises two ivory faced wooden tablets, with dimensions 122 mm x 65 mm x 5 mm each, put in tooled leather binding, 5″ x 3″, with brass stylus 5 inches long. The weight of device is only 0.14 kg. One tablet (below in the picture) has 14 columns, each with small brass parallel sectors, made from brass (copper, zinc alloy). The other has seven pairs of columns for laying out astronomical fractions to the base 60. Numbers are put in by moving the flags to reveal dots. Sums are then worked out with a pen and paper.

The Arithmeticall Jewell of William Pratt (© National Museums Scotland)
The Arithmeticall Jewell of William Pratt (© National Museums Scotland)

There is a later account for Arithmeticall Jewell by the English antiquary, natural philosopher and writer John Aubrey (1626–1697):
Dr Pell told me, that one Jeremiah Grinken [a mathematical instrument maker] frequented Mr Gunters Lectures at Gresham College: He used an Instrument called a Mathematicall Jewell, by which he did speedily performe all Operations in Arithmeticke, without writing any figures, by little sectors of brasse [or some semi-circles] that did turn every one of them upon a Center. The Doctor has the booke… he told me, he thought his name is [William] Pratt.

Arithmetical Jewel in Science Museum Group Collection
The Arithmeticall Jewell of William Pratt (© Science Museum Group Collection, https://collection.sciencemuseumgroup.org.uk/)