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Papers regarding payments for work done on behalf of the Board.

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Various algebraic equations by Israel Lyons on finding roots of equations.

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Various undated algebraic notes dealing with the clearing of surds from algebraic equations and a brief resumé of the work of Leonard of Pisa. The volume was compiled by Israel Lyons.

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An analysis by Israel Lyons of the problems in the 'Scholium Generale of Cotes Harmonia Mensurum'.

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An analysis by Israel Lyons of the construction in Roger Cotes' 'Scholium Generale', with an index to fourteen problems.

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A book on central forces by Israel Lyons, including articles on resistance to bodies moving under central forces. The volume includes an answer to Mr Murdoch on the centre of gravity, October 1758, and extracts and analysis of propositions from Newton's 'Principia'.

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A booklet by Israel Lyons on central forces, with diagrams and equations.

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A booklet on mechanics, with diagrams and equations of falling bodies and projectiles, autographed 'I L' (Israel Lyons).

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An undated booklet by Israel Lyons on mechanics and mechanical problems and on the mathematics of falling bodies.

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An undated booklet by Israel Lyons containing sections on mechanical powers, primary planets, moments of bodies and capillary tubes.

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An undated booklet by Israel Lyons on Newton's 'Principia', Book 1, Proposition 91, Corollary 2, dealing with Newton's differential method concerning the logarithmic spiral.

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'To clear the distance of the Moon from a star from the effects of refraction and parallax', February 1766. The envelope includes copies of reports made to the Board of Longitude by John Howe, undated, and M. Raper of Thorley Hall, 9 July 1765, on the method of Israel Lyons and George Witchell for correcting observed distances. There are also a number of tables on the Sun's parallax.

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Letter dated 22 August 1774, regarding a problem to find instrumental errors using the known right ascensions of stars, and errors in a pendulum at altitudes. An unconnected note, dated 22 August to 28 September 1774, concerning theodolite measurements for the Schiehallion Experiment has been included with the letter.

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Letter containing calculations for the occultations of stars.

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A treatise by Israel Lyons, including pieces to resolve an infinite product into an infinite series, to express fluents by infinite products and of interpoling series by infinite products. There are numerous examples of finding the value of a product.

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Differential method by Israel Lyons for the solution to algebraic equations using difference tables, with a loose price list for French science books of 1760-1787.

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Differential method by Israel Lyons, with various algebraic equations and difference tables.

Scope and Contents The original manuscript of Israel Lyons' 'Treatise of Fluxions', divided into twelve sections.1. The direct method of fluxions: i. Definitions; ii. Fluxions of the sum and differences of quantities; iii. Fluxions of rectangles and powers; iv. To find the relation of the fluxion from the relation of the fluents; v. Of 2nd, 3rd and 4th fluxions.2. The inverse method of fluxions: i. Of the fluents of simple quantities; ii. Newton's binomial theorem demonstrated; iii. Demoivre's...