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The rationale of circulating numbers: with the investigation of all the rules and peculiar processes used in that part of decimal arithmetic. To which are added, several curious mathematical questions; with some useful marks on adfected equations, and the doctrine of fluxions.

Henry Clarke (1743-1818)
London: Printed for Messrs. Ogilvy and Speare, 1794

Rare Books & Manuscripts
Rare Books Collection RB 511.1 C5982r

We thank our donor...

Conservation treatment of The Rationale of Circulating Numbers... was generously funded by Adopt-a-Book donor, Professor Matthew Roughan.  His valued contribution has ensured this important 18th century text will be available for future generations of researchers for many years to come.

Synopsis

Baptised in 1743 at Salford, England, Henry Clarke was educated at Manchester Grammar School.  At age thirteen he became assistant in the Leeds academy of the Quaker Aaron Grimshaw, before partnering with schoolmaster, Robert Pulman, to establish a new school in Leeds.

In the 1760s Clarke travelled to Europe, meeting Italian Professor of Mathematics, Antonio Maria Lorgna, at the Military Academy for Engineers in Castelvecchio.  On his return to Manchester, he married and took a position as a land surveyor.  Mathematics was never far from his mind, though, and by 1765 he had started his own Commercial and Mathematical School in Salford.  He taught pure and applied mathematics and other sciences, and in 1772 introduced adult evening classes.  Although the school was not profitable, it did produce several excellent students, including stenographer and schoolteacher, Thomas Molineux.

In the latter part of the century, Clarke turned his attention to writing, publishing texts such as his Tabula Linguarum (1793), with its tables of declension and conjugation, and his 1779 Dissertation on the Summation of Infinite Converging Series, a translation from Antonio Lorgna.  He also produced The Rationale of Circulating Numbers (1777).

The Library’s copy of The Rationale of Circulating Numbers is the new edition, published in 1794 and dedicated to Thomas Butterworth Bayley of The Royal Society.  Profusely illustrated with fold-out plates of fine engraved diagrams, it covers the theory of calculates; the logarithms of repeating decimals; rules for finding the cubic root of an impossible binomial, as well as the Newtonian Method of approximating to the roots of literal equations.  It also considers the nature of fluxions, and is bound with both Elements of Fluxions (printed for Alex Wilson, 1805) and Rev. B Bridge’s 1811 Compendious and Practical Treatise on the Construction, Properties, and Analogies of the Three Conic Sections, a series of eight lectures dedicated to the nature of curves, such as the parabola, ellipse and hyperbola.

Lightly annotated throughout with pencil calculations, the book is a fine example of early printed decimal arithmetic.

Adapted from Stephen, L., and Wallis, R.  ‘Clarke, Henry’, Oxford Dictionary of National Biography, 23 Sep 2004, accessed online 8 Feb 2021.

Original Condition

Severe acid decay to spine and joint leather, prompting lateral splitting of the binding into four sections.  Both boards detached.  Front board previously repaired and attached incorrectly, such that discolouration from tape adhesive appears along the inside and outside foredge rather than the joint.  Back board similarly discoloured at the inner hinge and outer joint. Grain layer largely missing from spine leather, resulting in loss of original tooling.  Head and tail cap leather missing, with further loss at all board corners exposing the weakened millboard.  Minor soiling and finger marks throughout the text, and localised water staining to early sections.  Creasing to some page corners.  Tie-downs for the hand-sewn headbands (located in several sections of the textblock), to be returned to correct location when spine leather is replaced.

Restored Condition

Covering leather cleaned with a soft brush to remove surface dirt.  Fibre Cohesion Assessment (FCA) test conducted with results revealing highly degraded spine leather beyond repair.  Spine removed, and degraded areas of board, corner and joint leather treated with Klucel G.  Small sutures attached across spine and into board slots to avoid disturbing original sewing system.  Reversible barrier layer of Japanese repair paper applied with wheat starch paste to spine.  New headbands, embroidered in cream and red cotton and worked around unbleached linen cord, attached to spine lining.  Covering boards reattached, using aerolinen sutures, to spine and beneath board.  Handmade paper then applied to spine to strengthen original sewing and create a flat surface for tight back leather spine rebacking.  Calfskin pared and dyed to sympathetically replace degraded spine leather and corners.  New spine leather decorated with single pallet lines in blind and gold, and red goatskin spine label added to the second panel.  Both inner hinge splits in the endpapers consolidated with matching Japanese repair paper.  Edges of text leaves and fold-out plates cleaned with smoke sponge to reduce dirt.  Paper creases relaxed with humidification, water staining to first few sections reduced using Gellan gum, and Japanese Usumino repair paper applied along textblock splits to prevent future preferential opening.

Full citation:

The rationale of circulating numbers, with the investigation of all the rules and peculiar processes used in that part of decimal arithmetic. To which are added, several curious mathematical questions; with some useful remarks on adfected equations, and the doctrine of fluxions. Henry Clarke. A new edition. Illustrated with many copper-plates. London: Printed for Messrs. Ogilvy and Speare, 1794

Lee Hayes
February 2021