Beschreibung seiner neu erfundenen Rechenmaschine, nach ihrer Gesalt, ihrem Gebrauch und Nutzen. Herausgegeben und mit einer Vorrede begleitet von Ph. E. Klipstein by MUELLER, Johann Helfrich von

One large folding engraved plate. xii, 50 pp. 8vo, cont. half-calf & marbled boards (bound with six other works, see below), flat spine gilt, red morocco lettering-piece on spine (lettered "Tracts Technical"). Frankfurt am Main: Varrentrapp Sohn & Wenner, 1786. First edition of one of the greatest rarities in the literature concerning the history of computers; this work describes the first difference engine, invented well before the time of Charles Babbage, who conceived it nearly 40 years later. WorldCat locates no copy in North America. This is a wonderful association copy and comes from the library of James Watt (1713-1819), engineer, scientist, and developer of the steam engine. Mueller (1746-1830), studied mathematics, engineering, and physics at the University of Giessen. Following his service in the Artillery Corps, he devoted his energies to engineering, architecture, and mechanical inventions. During the years 1776-90, he was the state architect of Giessen. In the beginning of the 1780s Mueller designed a greatly improved calculating machine based on the machine devised by Philipp Hahn; it was capable of addition, subtraction, multiplication, and division. That machine is described in the main part of the present work. By 1784, Mueller began to conceive the difference engine, which he writes about in his Appendix entitled "Further Inventions of Superior Calculating Machines and an Arithmetical Printing Machine" (in trans.), on pages 48-50. "A difference engine is simply a machine which is capable of both storing a series of numbers and performing additions with these numbers. The numbers will represent the function value, its first difference, second difference, third difference, etc. By performing a series of additions on these numbers, the engine is capable of generating successive values of the function... "At Frankfurt in 1786 a Mr. E. Klipstein published a small book whose title translates as: 'Description of a Newly Invented Calculation Machine'...This book describes the operation of a mechanical calculator invented by J.H. Müller who was a Captain of Engineers in the Hessian Army. The book contains an appendix in which Müller describes a much more ambitious calculating machine which he could construct if only someone would provide the finances. This calculator was to be a difference engine operating from a constant third difference. The device was designed to print out its results on a piece of paper. Müller figures that his device would be capable of one addition per second and that a table of the cubes of the integers from 1 to 100,000 could be produced by 'a common labourer' in about 10.5 days. Although it appears that his plea for financial aid was never answered, it is certainly the case that he deserves recognition as the one who first published the basic idea of a difference engine."-M.R. Williams, 'The Difference Engines,' in The Computer Journal, Vol. 19 (1976), p. 82. Babbage, who had a collection of books on all aspects of calculation, was unaware of the existence of Mueller's book until his friend John Herschel brought him a copy that he had found on a trip to the Continent. The large plate (ca. 34 x 19 cm.) depicts five different sections of Mueller's calculator, which is still preserved in the Grossherz Hessischen Museum at Darmstadt. Fine copy from the library of James Watt (his sale, Sotheby's London, 20 March 2003, lot 115). As mentioned above, the Mueller is bound with six other quite interesting works, and on the free front-endpaper Watt has provided a list of the works in the volume: 1. COURREJOLLES, François-Gabriel. [Drop-title]: Corrections des Moulins à Sucre. N.p.: [Imprimerie du Docteur Caullet Deveaumorel], 1790. One folding engraved plate. 39, [1] pp. 2. FOURCROY, A.F., VAUQUELIN, L.N., & SÉGUIN, Armand. [Drop-title]: Mémoire sur la combustion du gaz hydrogène dans les vaisseaux clos lu à l'Académie royale des Sciences, le 21 Mai 1790. N.p.: 1790. 99 pp. Presentation inscription from Séguin to Watt. 3. SÉGUIN, Armand. [Drop-title]: Abrégé des principaux phénomènes qui dependent de l'action du calorique. N.p.: 1790. 31 pp. With a presentation inscription from the author to Watt. Manuscript errata. 4. SÉGUIN, Armand. [Drop-title]: Observations générales sur les sensations, et particulièrement sur celles que nous nommons chaleur et froid. N.p.: 1790. 28 pp. Presentation inscription from the author to Watt (cropped). 5. [SCHWEDIAUER, Franz Xavier]. [Drop-title]: Mémoire remis aux comités des monnoies et des finances de l'Assemblée nationale. [Paris: de l'Imprimerie de la Feuille du jour, 1790]. 14 pp. 6. PRÉVOST, Pierre. Recherches physico-mécaniques sur la chaleur. Geneva: Printed for the author by Barde, Manget & Compagnie, 1792. Folding engraved plate. xvi, 232 pp. First edition of an important work in which the author propounds the theory of the equilibrium of radiant heat by continual exchanges. His "theory of exchanges" is a forerunner of the "wave theory of heat." ❧ Hook & Norman, Origins of Cyberspace, p. 65-"P. Klipstein publishes a small book on a new calculating machine invented by Johann-Helfrich Müller...In an appendix to this work, Müller describes his plans for a difference engine that would be capable of one addition per second and would print its results on paper. This is the first description of the idea for a difference engine. The machine is never built because funding cannot be obtained." Science Museum, Calculating Machines and Instruments. Catalogue of the Collections in the Science Museum (comp. D. Baxandall), 1975, p. 2 & item 38.