"On the Theoretical Principles of Machinery for Calculating Tables. In a Letter from Charles Babbage, Esq., F.R.S., Lond. & Edin. To Dr. Brewster," in the Edinburgh Philosophical Journal.

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BABBAGE, Charles. "On the Theoretical Principles of Machinery for Calculating Tables. In a Letter from Charles Babbage, Esq, FRS, Lond. & Edin. To Dr. Brewster," in the Edinburgh Philosophical Journal, vol 8, 1823, pp 122-128 in the full volume of iv,iv,428pp, with 7 engraved plates. Beautifully and recently rebound in calf-backed marbled boards. It was in this year that Babbage was presented with the (new) Royal Astronomical Society's first gold medal "for his invention of an engine for calculating mathematical and astronomical tables." VG copy. [++] This is a very early description (his second, following his famous "open letter" to Humphry Davy (1) dated 3 July 1822 in which Babbage first describes the difference engine and his earlier paper in the Edin Jnl (2)) of a modified difference engine with feedback and the full potential of a machine such as this to correctly calculate mathematical tables. The correctness of these tables was of mountainous importance as those calculated by hand were often plagued by errors in calculation and transcription (and printing) which in the long run could have fatal results to those depending upon the accuracy of the tables. [++] "As a founding member of the Royal Astronomical Society, Babbage had seen a clear need to design and build a mechanical device that could automate long, tedious astronomical calculations. He began by writing a letter in 1822 to Sir Humphry Davy, president of the Royal Society, about the possibility of automating the construction of mathematical tables specifically, logarithm tables for use in navigation. He then wrote a paper, On the Theoretical Principles of the Machinery for Calculating Tables, [the paper offered here] which he read to the society later that year. (It won the Royal Society s first Gold Medal in 1823.) Tables then in use often contained errors, which could be a life-and-death matter for sailors at sea, and Babbage argued that, by automating the production of the tables, he could assure their accuracy. Having gained support in the society for his Difference Engine, as he called it, Babbage next turned to the British government to fund development, obtaining one of the world s first government grants for research and technological development. Nevertheless, the Difference Engine performed only one operation. The operator would set up all of its data registers with the original data, and then the single operation would be repeatedly applied to all of the registers, ultimately producing a solution. Still, in complexity and audacity of design, it dwarfed any calculating device then in existence. "--Encyclopedia Britannica. [++] ALSO: at the end of this paper Babbage states that the progress of science will be impeded unless machines better than his are invented in the future, which I find to be remarkable: "If the absence of all encouragement to proceed with the mechanism I have contrived, shall prove that I have anticipated too far the period at which it shall become necessary, I will yet venture to predict, that a time will arrive, when the accumulating labour which arises from the arithmetical applications of mathematical formulae, acting as a constantly retarding force, shall ultimately impede the useful progress of the science, unless this or some equivalent method is devised for relieving it from the overwhelming incumbrance of numerical detail."--(Babbage's closing paragraph of this paper.) [+++] "NOTES: (1) A letter to Sir Humphry Davy, Bart. on the Application of Machinery to the Purpose of Calculating and Printing Mathematical Tables, July 3, 1822. (2) "On Machinery for Calculating and Printing Mathematical Tables," that appeared in vol 7 of the Edin Phil Journal in 1822, which was one the Babbage's earliest writing on the difference engines and largely based on his Davy letter publication. N° de ref. del artículo ABE-1635184994965

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