Preface   Chapter 1   Chapter 2   Chapter 3   Chapter 4   Chapter 5  



His great engines never cranked out answers, for ingenuity can transcend but it cannot ignore its context. Yet Charles Babbage's monument is not the dusty controversy of the books, nor priority in a mushrooming branch of science, nor the few wheels in the museum. His monument, not wholly beautiful, but very grand, is the kind of coupled research and development that is epitomized today, as it was foreshadowed in his time, by the big digital computers. 1

Having given, in the previous chapters, an account of the invention, development and fate of the Difference and Analytical Engines in fairly narrow, chronological terms, an attempt will be made here to examine the character of Babbage's work in a much broader perspective.

It was the opinion of most of Babbage's contemporaries that he was a kind of eccentric dreamer, obsessed with a slightly mad vision; even those who tried to understand that vision would generally concede only that it was an interesting theoretical possibility. From the perspective of the computer age, with Babbage's vision as it has been realized in hardware not only understood, but reshaping the world, Babbage appears rather differently. He is seen as am unheralded prophet of the modern era, an impractical genius who could not reconcile the grandeur of his vision with the technological capabilities of his own age, and who therefore wasted most of his talents. He was, it is said, a hundred years ahead of his time.

Both of these views of Babbage point to two principal facts about his work on calculating machines: his invention of the Analytical Engine was a truly remarkable phenomenon, and his attempts to bring his machines into being were almost complete failures. Yet neither view attempts any explanation of these facts. It must then be asked: what difference between Babbage and his contemporaries gave his work its special character? Casting the question in another way, what was the divergence of Babbage's work from the mainstream of technological development that made his inventions both so brilliant and such failures?

On the surface, the statement that Babbage was a hundred years ahead of his time suggests that he happened to invent a machine which, while sound in theory, could not be built until engineering capabilities had advanced one hundred years. Yet this is not adequate. On the one hand, it is clear that in some sense the idea itself, not just its constructability, was out of keeping with Babbage's time. On the other hand, it is doubtful that the machine was so impracticable. While the attempted construction of the Difference Engine during the 1820s was pushing at the technical capabilities of the day, and thus became an expensive and protracted failure, the Difference engine almost certainly could have been constructed at much lower cost during the 1850s, as is shown by the successful construction of the two Scheutz machines. And while it would be virtually impossible to prove, it seems that the construction of the Analytical Engine in the 1860s would have been less of a strain on the available technology than that of the first Difference Engine had been in the 1820s. Conversely, the existence of adequate technical capabilities does not assure the construction of machines such as the Analytical Engine; this is illustrated by the fact that all the components necessary for the construction of Howard Aiken's computer, Mark I, were available for many years before it was built, or even conceived.

Thus the prophetic character of Babbage's work, and his failure to complete it, cannot be explained simply by the inadequacy of the machining techniques of the times; two additional factors must be brought into the account. On the one hand, there was little support for the construction of the Analytical Engine because there was no widely felt need for it; not only did few people understand the machine, but the age did not require the manipulation of large amounts of data or the frequent execution of complex calculations. On the other hand, many of Babbage's difficulties seem to have arisen from his own temperament; in relation to his efforts to construct his machines, Babbage was too much of a perfectionist; he was unable to recognize when his plans were good enough, and stop improving them.

Yet although these factors may explain why the Analytical Engine was not constructed, they do not explain why it was invented, and they do not help in understanding Babbage's character, for they require the assertion that Babbage was an impractical man, and was not in touch with the needs of his own age. That this is true in a certain special sense will be granted below, but certainly it was not true in general. Babbage was a practical man both in the sense that he was (and was recognized to be) extremely knowledgeable about the practical affairs of his time, and in the sense that he was able to get things done in cooperation with other people, as his successful and important role in founding several mayor scientific societies illustrates. Some deeper understanding must be sought.


Babbage's work appears peculiar, and his failure remarkable, only when he is considered as an inventor and engineer in the usual sense, and this is a complete misunderstanding of his motives and methods. To make this clear, let us consider what is meant by a "technologist" of the successful, conventional sort, and how Babbage diverged from this model.

The prime characteristic of the conventional technologist is that he is motivated by the desire for profit and success in a clear-cut goal. This generally means two things. First, the goal that he selects must be either to do something that cannot yet be done, but for which there is some demand, or else to do something that already can be done, but faster, cheaper, or in some other way better. Second, given a range of problems he might attack, the technologist will tend to choose the one that he thinks will be easiest to solve; he must at least be confident that the problem is soluble. These two facts have the effect of assuring that in most cases technology will advance by small gradual steps; generally the problems solved are those where the technologist knows in advance that the solution will be both practical and profitable.

Further, such a solution of a technical problem generally consists of the combination in a slightly new way of components or techniques which are already known and available, or in relatively minor modifications or additions to them. For unless such elements are already being combined in more or less the proper way, and in an application somewhat similar to the one to be solved, it is quite possible that no one will notice the possible connection between the parts and the problem. This can, for example, explain why machines such as Mark I are not built whenever the necessary components become available.

It is clear that Babbage does not fit this picture of the conventional technologist. Certainly he did not invent his calculating machines for profit, or to solve same practical problem; rather he found the process of inventing them to be its own reward, as a purely intellectual exercise. To be sure, it was the unsatisfactory character of manually calculating and checking mathematical tables that first directed his attention to the desirability of machines to do the job; but once he began considering them, their perfection became an end in itself, and the tables from which he had begun were no longer important. Of course, the Difference Engine was interesting only because it could actually calculate tables, but this was more a theoretical than a practical point. And clearly the Analytical Engine was not invented because of the need for a table which the Difference Engine could not handle.

Thus it is vitally important in understanding Babbage's character that he was not a technologist who happened to have a scientific background, but rather a scientist and intellectual who happened to be working on technical problems. It was crucial in the development of Babbage's interests that before 1822 he had not found any area of scientific research that was wholly satisfying to him. After he begin considering calculating machines for practical reasons, he found that working on them was a kind of problem-solving activity that was highly enjoyable and well suited to his own talents as an end in itself. In this sense, Babbage's work on calculating machines was more similar to his interest in cyphers, word squares, and a tic-tae-toe machine than it was to the construction of the Scheutz Difference Engine. This characterization of Babbage's motives may explain his being "a hundred years ahead of his time." Since he was dealing with gears and pinions as if they were primarily theoretical entities, he was not especially concerned if they could not, at the time, be made with sufficient precision for the resulting machine to be practicable. Likewise, although he sometimes wished to justify his work to the rest of the world by arguing for its usefulness, practical applications of the Analytical Engine were by no weans the crucial factor in his own mind. Rather he was constructing an elegant theoretical structure more comparable to an abstract mathematical theory than to the productions of a conventional engineer.

For these reasons, the results of Babbage's work had a character opposite from that of normal technical activity. Babbage found the progress through small steps of the conventional technologist to be uninteresting, since it was not intellectually challenging, although he recognized its importance to society more than most of his contemporaries. What Babbage strove for was the kind of great leap forward which the technologist avoided, pushing ideas to their limits to see what would happen to them, and synthesizing elements between which there had been no obvious relationships.

Thus Babbage's being "a hundred years ahead of his time" is related not as much to the mechanical practicability of the Analytical Engine as it is to the fact that the invention of the Engine required too large a mental jump to mesh with the main thrust of the technological progress of the time. The machine's character was too strange for engineers to imagine building it. More important, the scientists who might have been interested in using it were accustomed to carrying on their work in ways which were too different from what the Analytical Engine would make possible - and indeed require - for them to comprehend its potential as Babbage had, or to generate pressure for its construction.

It seems that to a large extent Babbage himself understood the abnormal character of his inventive activity. During the main period of his work on the Analytical Engine, he had no intention of constructing it, although potential constructability was always required. Yet he was always confident that the Engine would eventually be built, though perhaps long after his death, and that it would have a large impact on the world when introduced, even if in ways which he could not predict. Babbage's sporadic efforts toward constructing the Analytical Engine toward the end of his life were not so much a change in his attitude, as they were a result of his belief that he had not been adequately rewarded for his work, and of his desire for justification and recognition.

It may also be noted that Babbage understood the character of the Analytical Engine as a general purpose computer well enough to realize that when a computer was eventually built, it would in principle be identical in function to his own machine, even if designed much later and wholly independently.

The idea developed here of the crucial and fundamental difference between practical and intellectual motivation in technological development, and of the difference in the kinds of change that result from each, has implications reaching beyond the case of Babbage. Indeed, many examples of each type could be given from within the history of calculating machines and computers. However, such an undertaking is beyond the scope of this thesis.

In final conclusion, if one were to draw a moral from the history of Charles Babbage and his calculating machines, it would have to be that while there is certainly truth in Countess Teleki's maxim that "The Best is the enemy of the Good," it is also true, as illustrated by Babbage's life and work, that "The Satisfactory is the enemy of the Marvellous."


The Operation of the Babbage
Difference Engine

It will be assumed that the mathematical principles of the method of finite differences is understood from the description given in Chapter Two. The basic features of the operation of the Babbage Difference Engine, as exemplified in the partial section assembled in 1832, will be described here.

The basic organization of the machine is as follows. The core of the machine is three vertical axes; the right axis is the Table Axis, where the results are produced; the middle axis holds the first differences; and the left axis holds the second difference, which here will be assumed to be constant. For each axis, each digit of the number on the axis is held on a Figure Wheel, which turns freely on the axis. The Figure wheels are placed at equal spaces along the axis, with that for the lowest digit at the bottom; it will here be assumed that the lowest digit corresponds to the units place.

The way in which addition is performed can be understood in terms of the method of adding any single digit, since all digits are added alike; we shall consider the way the units digit of the second difference is added to the units place of the first difference.

Each figure wheel is divided into ten sections, corresponding to the digits from zero to nine. The units digit of the second difference - let us suppose it to be five - is set by turning the lowest Figure Wheel on the second difference axis so that "5" faces the front. Immediately above the Figure Wheel on the second difference axis is a mechanism called the Bolt, which is fixed to the axis, and turns with it. Immediately above the bolt is another wheel, the Adding Wheel, which is held by the axis, but turns independently of it. This Adding Wheel in turn gears with the Figure Wheel for the units of the first difference, in the column to its right; thus the Figure Wheel on the first difference column is slightly higher than the corresponding Figure Wheel in the second difference column (similarly the units Figure Wheel on the Table Axis is slightly higher than that on the first difference axis).

Addition takes place as follows. At the beginning of a cycle, the Bolt is activated in such a way that it engages with the Adding Wheel above it. Then the axis is rotated; this turns the Bolt, the Adding Wheel, and thus the Figure Wheel in the next column to the right, in this example the units wheel of the first difference. The axis is given a full turn, but when it has rotated through an amount corresponding to the number on the Figure Wheel (in this case five), the Bolt hits a projection on the Figure Wheel below it which disconnects the Bolt from the Adding Wheel above it; this projection is in the correct position by virtue of the proper Figure Wheel having been set before the operation, in this example to five.

The effect of this action is that after the axis has been rotated through a full turn, the Bolt is back to its original position, and the units digit of the second difference, namely five, has been added to the units Figure Wheel of the first difference. This sequence can be repeated later in the operation as many times as necessary.

The units digit of the first difference can be added to the Figure Wheel of the Table Axis in exactly the same way. However, two things must be noted. First, if the second difference were added to the first difference at the same time that the first difference is added to the Table, the two additions would interfere; therefore the two additions are performed alternately. Second, whereas the units figure of the second difference remains constant, the units figure of the first difference is always changing; this does not matter, however, as it simply means that the projection which disconnects the Bolt is in a different position on successive cycles.

Naturally, the addition of a digit will in many cases make a carry necessary. In order that this not interfere with the basic addition, carries are delayed and sequential, as follows. When a Figure Wheel passes from nine to zero, it cocks a spring and lever above it. When the addition is complete, a separate carriage axis turns, and an arm on it releases the cocked lever and spring, adding one unit to the next higher Figure Wheel. As this carry might itself make necessary a second order carry, the arms on the carriage axis are staggered around the axis so that they release the levers in sequence, one at a time.

Thus the entire cycle consists of four parts. First the second difference digit is added to the first difference; then the necessary carries are performed on the first difference; then the first difference digit is added to the Table; then the carries are performed on the Table. All the digits on any one axis can be handled at the same time and in the same way. The activation of the Bolts at the correct time and the rotation of the various axes in the correct sequence is all controlled by a series of gears on top of the machine; these gears are turned by stroking a long lever back and forth by hand.

A more complete Difference Engine, using more orders of difference, would not require a longer cycle, as all the even numbered differences could be added together, followed by all the odd numbered differences together. Similarly, each column could include as many digits as desired, without lengthening the time of operation.

The assembled Difference Engine section incorporated a few other special features. It was arranged so that a single digit third difference (actually stored at the bottom of the first difference axis) could be added to the lowest Figure Wheel of the second difference. Three Figure Wheels at the top of the second difference axis could be disconnected from the rest of the axis and made to serve as a cycle counter. Each axis had a bell which could be set to ring when any Figure Wheel or combination of Figure Wheels on that column reached zero; this might be used to indicate when it was necessary to manually alter a difference in some operations; it could also be used to located maxima and minima of a function.

Finally, there was a special provision whereby any one digit on the Table Axis could be added repeatedly to any one Figure Wheel on the second difference axis; this was to demonstrate Babbage's method of handling transcendental functions, discussed at the beginning of Chapter Three.


As the body of this thesis is a documentary history of the calculating machines of Charles Babbage, drawing predominantly on the manuscript collections, the main text must serve as the principal guide to the sources.

The purpose of this bibliography, therefore, is not to be exhaustive, but to discuss the three main manuscript collections on their own, and then to discuss the most important published sources.

Manuscript Collections

There are three main collections of Babbage manuscripts. Most of his papers were left to his son Henry P. Babbage; the voluminous correspondence was deposited in the British Museum, while the technical papers, including all notebooks and drawings on the calculating machines, were given to the Science Museum in South Kensington. In addition, some years before his death, Charles Babbage had given to his friend H. Wilmot Buxton a collection of privately printed and manuscript papers concerning the machines, including most of the explanatory essays Babbage had undertaken (but never completed or published) describing the two Engines. It was Babbage's intention that Buxton should compose an account of his life and scientific work; this he did, but it was never published. The Buxton biography and the collection of papers Babbage had given him are deposited in the Museum of the History of Science at Oxford University.

British Museum.

The material at the British Museum is much the most straightforward and best organized, and will be dealt with first. It is part of the collection of Additional Manuscripts, bearing the catalogue numbers Add.MS. 37,182-37,201. Thus the catalogue number for any of the twenty volumes may be found by adding 37,181 to the number of the volume. As each volume contains on the order of 500 folios, the entire collection makes up about 10,000 folios.

The letters are arranged chronologically in Volumes I to XVIII, with Volumes XIX and XX containing letters that cannot be dated. When possible, letters without dates are placed approximately in sequence, as suggested by the context; inevitably, some of the placements are questionable and some are definitely wrong, but on the whole the cataloging is quite competent. Since almost any important letter will have at least some clues as to the date, the material in the last two volumes is generally very uninteresting.

Since Babbage made one or more drafts of all important letters, and of most minor ones, the collection has letters from him as well as to him, although not the copy actually sent. It is clear that there are some items missing from both categories, but on the whole the correspondence seems fairly complete.

The printed catalogue relating to the material (Catalogue of Additions to the Manuscripts in the British Museum in the Years 1900-1905, London, 1907) does not have an inventory of individual letters, but many of them are indexed by correspondent at the end of the catalogue.

For this study, the entire collection was examined, and some 2000 folios were selected for closer study. Only a fraction of these are actually cited in this thesis.

In addition to the letters, the British Museum holds, as Add. MSS. 37,202-37,205, a collection of manuscripts and privately printed papers concerning Babbage's interests in mathematics, astronomy, geology, lighthouses, cyphers and mathematical games.

Science Museum.

The collection of Babbage manuscripts at the Science Museum in South Kensington is much more diverse and confused, and it is not catalogued. At the beginning of World War II it was packed up in several crates and deposited in a warehouse away from London, for its own protection. It remained there, largely untouched, until the summer of 1967, when it was very kindly brought back to London for examination by the author. It has subsequently been placed in the Library of the Science Museum, and hopefully it will soon be arranged and catalogued.

Although the collection is not catalogued, there are two guides to it. One is a section of Babbage's Calculating Machines (pp. 271-94) prepared before Charles' death, including a list of Notations and Drawings of the Analytical Engine and a rather confused list of Scribbling Books, this material now being in the Science Museum. The other guide is a much more complete and careful inventory of the Museum collection prepared by G.H. Dennis in 1927.

This inventory consists of almost 100 large typewritten pages, and there would be no point in trying to duplicate it here. Rather a brief and hopefully less confusing guide will be provided to the most important material.

Bound Volumes.

The most important items are the Scribbling Books, in which Babbage made most of his day to day notes. The descriptions here will standardize the names and numbers as much as possible, although even Babbage's own terminology for them was often confused; for example, he intended to change the name of the volumes to Sketch Books beginning with Volume III, but later went back to calling them Scribbling Books. They are all bound volumes, most running between 200 and 600 pages.

The first important volume is not actually a Scribbling Book proper, but it came to be called the Great Scribbling Book. It was originally intended to record share appropriations for the Protector Life Assurance Society, and the pages are divided accordingly and marked with line numbers, but Babbage used it as a general notebook. Much of the material in it is undated (and often uninteresting), but the dates given range from 1829 to 1847. The volume is important because between about lines 1231 and 2301 it contains material, mostly very rough sketches, from the summer and fall of 1834, the crucial period when Babbage was developing the Difference Engine into the Analytical Engine, as discussed in Chapter Three.

The first volume of the regular Scribbling Books was at some point given the number XIII by mistake (see B.C.E., p. 294), and this number is still on it, but it was originally marked "Vol. I, " and this is its proper number. Its main working dates were from February 1, 1835 to October 30, 1835, but there was some material from 1836 at the end.

Scribbling Book Volume II ran from November 6, 1835 to February 8, 1837, that is, through the adoption of punched cards and the first full development of the Analytical Engine. Volume III was begun February 9, 1837, and continued through August, 1838; after this there was miscellaneous material with dates through 1841, much of it copied from Volume IV; additional material was entered upside down from the back of Volume III, with pages numbered from the back, and confused dates from 1838 through 1841. Volume IV was similarly confused; its main working dates were from February, 1839, through May, 1841, but there were some earlier notes, and some as late as 1846.

Volume V ran fairly coherently from May, 1841, to December, 1844. Volume VI picked up in December, 1844, and ran rather quickly to October, 1846, at which point there began to be obscure notes on the "New Difference Engine;" these notes continued through 1848; in March and April, 1849, there were again some notes on the Analytical Engine, as wall as a statement that accounts had been settled with Jarvis, Babbage's assistant. Then there was an abrupt jump to June, 1857, when the Analytical Engine was again taken up; notes on it continued in Volume VI through early 1859, but with little after January, 1858.

Volume VII ran from March, 1858, to June, 1859, with Volume VIII continuing this material, almost all on the Analytical Engine, from June, 1859, to December, 1864. Volume IX went from December, 1864, through November, 1866, with a few notes from 1867 and 1868 at the end. Volume X ran from December, 1866 to October, 1868, with Volume XI starting then and going to August, 1870. A Volume called XIA was mostly blank, but had some scattered interesting material from 1868 and 1869. Volume XII, the last of the regular Scribbling books, ran from August, 1870, to Babbage's death, with a few notes after this by Henry P. Babbage.

Apart from the Scribbling Books, there are several miscellaneous notebooks. One which is now called Volume XIIA has only about fifty pages used, mostly containing obscure material on the first Difference Engines; the few dates given are from 1830. Another, which has gotten the name Volume XIV, was originally called the Travelling Scribbling Book; it has dates from 1845 to 1863, but little on calculating machines; the most interesting material, irregularly from p. 8 to p. 85, with a few later pages, is a very rough development by Babbage of a highly mathematical theory of supply and demand in economics; this deserves further study.

A volume with the number XV, but no original title, is mostly blank, but has some obscure mathematical figuring connected with the Analytical Engine; the only date mentioned is August, 1860; there are also some long calculations concerning the ways in which spherical and ellipsoidal molecules might be close-packed, and some other interesting material not connected with the Engines.

Another volume, without number, but saying on the flyleaf "Analytical Engine 4 Feb. 1859," is almost entirely blank; it contains an index listing parts of the Analytical Engine, with corresponding headings on the appropriate pages, and was clearly intended for recording progress on the Engine at that time; but it was never filled in.

A volume called "Tool Book Vol. 1" is sometimes confused with Scribbling Book, Volume I (which was mistakenly given the number XIII, as mentioned above); the Tool Book has material from 1841 and 1842, with some inserts dated April, 1844, but it is almost entirely obscure small sketches; there is, however, on pp. 132-35, a description of a universal planing machine. The final bound volume contains mostly similar obscure sketches, with dates from 1842 to 1860; it has neither a volume number nor a title, but is in any case uninteresting.



The Science Museum collection also contains nearly 300 large, carefully executed Drawings, mostly of the Analytical Engine, each measuring approximately two by three feet. No full listing of these will be given here, as lists may be found in Babbage's Calculating Engines, pp. 288-93, and in the Science Museum inventory. However, a few obscure points about their character and order must be cleared up.

The Drawings are contained in three Mahogany Cases, numbered l, 2 and 3. These cases are very handsome and ingenious, and apparently were especially designed by and built for Babbage. They are solid enough to protect the Drawings and allow them to be easily carried about; when opened, special fittings can be drawn up to provide a convenient stand on which to hang and view individual Drawings; the Drawings are also held within the Cases in a way which allows any single Drawing to be removed from and returned to any part of the sequence without disturbing the order of the other Drawings.

Mahogany Case Number 2 contains Drawings numbered from 1 to 116. Drawings 1 to 106 are general plans and details of the Analytical Engine, with dates from 1834 to 1842. Drawings 107 to 116 are plans for a large planing machine. At the back of the Case are general plans of the Difference Engine No. 1, which for some reason have the numbers 197 and 198.

Mahogany Case Number 2 begins quite straightforwardly, Drawings 117 to 144 are plans for the Analytical Engine, with dates between 1842 and November, 1846. Drawings 145 to 158 are plans for the Difference Engine No. 2, made during 1846 and 1847. At this point, however, confusion sets in, for the same number will often refer to more than one Drawing, of different dates and of different machines. Drawings of the Analytical Engine have numbers running from 159 to 207, with dates from July, 1857, to August, 1870; in cases where there are Drawings of the Difference Engine No. 2 with the same numbers (this occurs through number 181) the Analytical Engine Drawing is marked with an asterisk, as 159*. In some additional instances there will be two Analytical Engine Drawings with the same number; one will be marked with an asterisk.

The Difference Engine No. 2 Drawings are more confusing. There are twenty six Drawings of the Difference Engine with numbers between 159 and 177 which also form a distinct sequence of Drawings with numbers from 1 to 20 (there are four Drawings each for numbers 6 and 8), although the order of the two sets of numbers is quite different. The Drawings in this special set are not dated, but they probably correspond to the set of twenty four referred to on p. 180 of Babbage's The Exposition of 1851 (London, 1851).

At the end of Mahogany Case 2 there are also some miscellaneous Drawings, some unnumbered, some copies of Drawings earlier in the Case.

Mahogany Case Number 1 contains a separate set of Drawings of the Analytical Engine with numbers from 1 to 47, and dates from June, 1857 to March, 1859. Apparently this was an attempt to form a complete set of Drawings of the machine when Babbage began work on it at this time, for there is only one Drawing from this period in the main sequence of numbers in Case 3; but for some reason Babbage shifted back to the old series of numbers early in 1859. Also in Case 1 is a series of Drawings with numbers from T.1 to T.19 (plus one that is unnumbered), and dates from 1857 to 1861, showing a series of Tools Babbage was apparently planning for use in the construction of the Analytical Engine.


The Notations are contained in loose-leaf form in seven portfolio volumes. They are numbered from 1 to 388 (some numbers arc duplicated, but not in a confusing way), and dated from 1835 to 1848; a few at the end refer to the Difference Engine No. 2, the rest being of the Analytical Engine. The order of the Notations is quite straightforward, and as there is a full annotated list of them in the Science Museum inventory, and both a list and a "Classed Catalogue" in Babbage's Calculating Engines, pp. 273-87, no further guide to them need be given here.



The Science Museum collection also contains a large quantity of additional miscellaneous papers, drawings and notations, often in fairly random order. Most of this material is not important, and it is too confused to make easy reference possible; therefore no general description will be attempted here. Hopefully this confusion will be alleviated when the Science Museum Library has catalogued the material; in the meantime, their inventory list will have to serve as the only guide, although the material is no longer in the order in which it was listed.

One item from this group must be mentioned, however. It is called "History," and is a series of seventeen sheets, each corresponding to a year between 1834 and 1850. Each sheet is divided into rows corresponding to the different months, and columns corresponding to different aspects of the Analytical Engine. In the spaces are entered references to Scribbling Books, Drawings and Notations which Babbage felt were significant in the development of the machine. Seemingly Babbage was intending to write a history of the Analytical Engine, and began to prepare this guide to the original material; possibly he filled it in as the work progressed. In any case, the references are rather incomplete, and the material referred to is often quite cryptic, so the usefulness of the outline is diminished; however, it does frequently indicate what steps Babbage thought to be important. The sheets for the last few years are mostly blank, but there are some references to material on the Difference Engine No. 2.



In addition to manuscript material, the Science Museum collections contain the section of the first Difference Engine put together in 1832, the second Scheutz Difference Engine, and two sections of the Analytical Engine, one put together and one redesigned by Henry P. Babbage, as discussed in Chapter Four. Also in the collection are various loose wheels, axes and other parts front the Analytical Engine, together with some moulds for casting them. These items are described in: Catalogue of the Collections in the Science Museum, South Kensington; Mathematics: I. Calculating Machines and Instruments, compiled by D. Baxandall (London, 1926), pp. 30-35.


As mentioned above, the Babbage material at the Museum of the History of Science at Oxford University came from Babbage's friend H. Wilmot Buxton. Quite a lot of this material is not interesting, being such things as proof sheets from some of Babbage's publications; some, however, is very important, and it will be described.

The most extensive Babbage manuscript (MSS. Buxton, Vol. 13) is a volume entitled "The History of the Origin and Progress of the Calculus of Functions during the years 1809, 1810 . . . 1817." It is a 289 page account of the mathematical work in which Babbage was involved during this period, centering around the Analytical Society. It would be extremely important to anyone working on this phase of Babbage's life, but was not used in or relevant to this thesis.

MSS.Buxton, Volume 9 contains the following manuscript papers of special interest. First, "Engine for table of differences" (11 pp. with some small sketches); Babbage added a note at the beginning, dated August, 1840, saying: "This is the first idea and earliest sketch of the Cal. Engine probably in 1820;" in fact, the paper was doubtless from early 1822. Second, a paper called "Of an Engine to multiply n figures by m figures" (3 pp. with sketches); this paper has no explicit indication of date, but was written about the same time as the first. Third, introductory pages to a paper to be called "The Science of Number reduced to Mechanism" (4 pp.); this paper is not dated, but elsewhere in the Buxton manuscripts there is an outline of a paper with the same name, dated November 26, 1839; it was to be a long paper, mostly on the Analytical Engine, but clearly all Babbage wrote was the first few pages, on the early stages of the Difference Engine. All three of these Babbage manuscripts are discussed early in Chapter Two of this thesis.

In MSS.Buxton, Volume 7 there are the following Babbage manuscript papers on the Difference Engine. First, an untitled paper on the early development of the Difference Engine (26 pp.), dated November, 1822. Second, an introductory fragment of a paper to be called "History of the invention of the Calculating Engine" (3 pp.), dated September 6, 1834. Third, "Sketch of the Principles of the Analytical Engine" (2 pp.), dated September, 1841; this is actually an introductory fragment on the Difference Engine, but is not very interesting. Fourth, an untitled paper, (3 pp.), dated October 3, 1843; this is a very vague introductory fragment from a paper apparently intended to justify Babbage's position in relation to the government and their large expenditures on the Difference Engine.

There are also two privately printed items concerning the Difference Engine in Volume 7. One is Babbage's letter to Lord Derby, Prime Minister, dated June 8, 1852, recounting the history of the Difference Engine No. 1, and offering the government the plans for the Difference Engine No. 2 (this was reprinted in P.L.P., pp. 100-107). The other such item is a forty three page pamphlet entitled "Statement of the Circumstances Respecting Mr. Babbage's Calculating Engines," and is dated August, 1843; it was originally printed anonymously, but when reprinted as Chapter VI of Passages from the Life of a Philosopher, it was stated to have been drawn up by Sir Harry Nicolas from papers Babbage made available to him. This last item must be distinguished from the similarly titled paper "Statement of the circumstances attending the Invention and Construction of Mr. Babbage's Calculating Engines," written by Babbage, and appearing in Babbage's Calculating Engines, pp. 1-4, reprinted from the Philosophical Magazine for September, 1843. Babbage himself apparently confused the two titles in the list of his publications appended to Passages from the Life of a Philosopher.

MSS.Buxton, Volume 7 also contains the following papers on the Analytical Engine. First, "Of the Mathematical powers of the Calculating Engine" (53 pp.), dated December 26, 1837; this was Babbage's most complete description of the operation of the Analytical Engine, and has been quoted extensively in Chapter Three of this thesis. Second, "Of the Analytical Engine" (28 pp.), dated October, 1841; this is another interesting paper, but it has many quite confusing changes and additions. Third, an untitled paper on the Analytical Engine (13 pp.), dated September, 1842, and/or September, 1844; this is partly on the operation of the Analytical Engine and partly on Babbage's ideas about the psychology of invention. Fourth, "Of the Analytical Engine" (9 pp.), an incomplete paper dated July 19, 1869. Fifth, an incomplete and untitled paper on the Analytical Engine (14 pp.), dated October 7, 1869. Sixth, "The Analytical Engine" (30 pp., sparsely filled), apparently dated November 6, 1869. The last three of these papers are quite elementary introductions to the Analytical Engine, and are generally not nearly as interesting as the earlier papers; the last one does, however, give a simplified account of the transition from the Difference Engine to the Analytical Engine. There are also a few additional miscellaneous sheets in this volume of the manuscripts, but most of then are not very important.

MSS.Buxton Volumes 3 and 8 contain fair copies of the Babbage manuscripts in Volumes 7 and 9, made by either Buxton or an amanuensis. There is no new material, but the fair copies are usually much easier to read than the originals, and they occasionally supply words or portions of the papers which are missing from or no longer legible in the original autograph copies. The one minor problem is that the most important paper on the Analytical Engine, "Of the mathematical powers of the Calculating Engine," dated December 26, 1837, is quite incomplete in the fair copy; as the missing section is, in the case of the original in Volume 7, out of order and separated from the rest, it is likely that it was similarly misplaced at the time it was being copied; it therefore can only be read in full in the original version.

MSS.Buxton. Volumes 16 and 17 are Harry Wilmot Buxton's manuscript biography of Babbage, called "Memoir of the life and labours of the late Charles Babbage, Esq., . . . Comprising a descriptive and historical account of his Analytical and Difference engines, derived principally from his posthumous M.S.S. and papers" (no date). Although this biography gathers together more material on the calculating machines than any other single source, it does not add new information. It is made up largely of extensive extracts from the Babbage manuscripts in the Buxton collection, together with quotations or paraphrases from published material. Unfortunately, the biography is rather poorly organized, and evidently Buxton did not understand Babbage's machines sufficiently to form his extracts into a very clear or coherent account of their development, purpose or operation.

Published Sources

The published material is described below in two categories; the first contains material of a general biographical character, while the second contains material specifically related to the calculating machines. The important published sources were few in number, although many minor extracts from these have been published; no attempt has been made here to be exhaustive.

General Life.

There are two extensive general books on Babbage's life. On is Babbage's own memoirs, Passages from the Life of a Philosopher (London, 1864; reprinted London, 1968); although quite selective, and, having been written in old age, not always wholly accurate, it is a fascinating and delightful book. The other major biographical work is Maboth Moseley's Irascible Genius: A Life of Charles Babbage, Inventor (London, 1964); this is more a personal than a scientific biography, and some of its drawbacks have been discussed earlier in this thesis, but it is still useful.

One other book that serves as a general source on Babbage's life is Charles Babbage and his Calculating Engines, edited and with an introduction by Philip and Emily Morrison (New York, 1961). This book is made up almost entirely of selections reprinted from Passages from the Life of a Philosopher and from Babbage's Calculating Engines, but it also contains a nice biographical sketch as an introduction; this introduction is based in part on an earlier article by the same authors: "The Strange Life of Charles Babbage," Scientific American, Vol. 197, No. 4 (April, 1952), pp. 66-73.

There are a number of briefer sketches of Babbage's life. The best of these are his obituaries, most notably the following: Nature, Vol. V (1871-72), pp. 28-29; Monthly Notices of the Royal Astronomical Society, Vol. XXXII, No. 4 (February, 1872), pp. 101-9; and the memorial remarks by William Farr in his Presidential Address to the Statistical Society of London (later the Royal Statistical Society) on November 21, 1871, printed in the Journal of the Statistical Society, Vol. XXXIV (1871), pp. 411-417. The last item emphasizes Babbage's contributions to statistics and life insurance, and discusses the English Life Table.

Two later biographical sketches which are valuable are the Babbage article, written by Agnes Mary Clerke, in Dictionary of National Biography (Oxford, 1917 and later), Vol. I, pp. 776-78; also Faster than Thought, edited and with an introduction by B.V. Bowden (New York, 1953), pp. 6-31; Bowden also reprints the Menabrea-Lovelace paper on the Analytical Engine in an Appendix.

There are a number of other brief biographies of Babbage which are entirely secondary or tertiary, and are of little value; examples are: John Fyvie, Some Literary Eccentrics (London, 1906), pp. 179-209; Alexander Macfarlane, Ten British Physicists of the 19th Century (New York, 1919), pp. 71-83 and passim; Royce W. Van Norman, "Charles Babbage (1792-1871)," in The Journal of Industrial Engineering, Vol, XVI, No. 1 (January-February, 1965), pp. 3-71 Jeremy Bernstein, The Analytical Engine: Computers - Past. Present and Future (New York, 1966), pp. 30-46; and Paul L. Garwig, "Charles Babbage (1792-1871)," in American Documentation, October, 1969, pp, 320-24.

A number of sources written by Babbage's contemporaries give accounts of his character or particular incidents in his life. Charles' son Henry Prevost Babbage's Memoirs and Correspondence of Major-General H.P. Babbage (London, 1910) is mostly about Henry's life in India, but there is some information about Charles' family life (see esp. pp. 10-11, 80-95, and 181-82); there are also brief appendices on Henry's involvement late in life with some of Charles' work.

Other such personal accounts may be found in the following works: Harriet Martineau's Autobiography, edited by Maria Weston Chapman (Boston, 1877), Vol. I, pp. 265-68; Mary Lloyd, Sunny Memories (London, 1880), pp. 47-69; The Hon. and Mrs. Lionel A. Tollemache, Safe Studies (London, 1884), pp. 148-58; Samuel Smiles, Life and Labor (New York, 1888), pp. 166 and 271; The Diaries of William Charles Macready (1833-1851), edited by William Toynbee (New York, 1912), Vol. I, pp. 157 and 409-10, and passim; finally the Inaugural Address by Lord Moulton in the Napier Tercentenary Memorial Volume, edited by Cargill Gilston Knott (London, 1915), pp. 19-20.

Babbage's own published works will not be discussed here exhaustively, though those concerning the calculating machines will be covered in the next section, and some of the major ones will be mentioned below. But a fairly complete list of his papers can be found in Passages from the Life of a Philosopher, pp. 493-96; it was reprinted in the Morrisons' Charles Babbage and his Calculating Engines, pp. 372-77, and in slightly revised form as an appendix to Babbage's Calculating Engines.

Babbage published some seventeen papers on mathematics before he became interested in the Difference Engine; this early work is treated in J.M. Dubbey, "The Mathematical Work of Charles Babbage" (unpublished Ph.D, thesis, the University of London, 1968).

Babbage gained a vital role in the struggle over the reform of the Royal Society which eventually led to the founding of the British Association for the Advancement of Science through two publications: "Account of the great Congress of Philosophers at Berlin, on 18 September, 1828," Edinburgh Journal of Science, Vol. X (1829), p. 225; and Reflections on the Decline of Science in England, and on some of its Causes (London, 1830). Babbage's book stirred up a great deal of controversy, and provoked favorable responses, such as the review of it by David Brewster in The Quarterly Review, Vol. XLIII (1830), pp. 305-342, and unfavorable responses, such as Gerard Moll, On the Alleged Decline of Science in England (London, 1831). The circumstances surrounding Babbage's break with the British Association in 1839 are dealt with in his pamphlet "Letter from Mr. Babbage to the Members of the British Association for the Promotion of Science" (privately printed, London, 1839).

More general treatment of Babbage's role in the reform of scientific institutions can be found in: Charles F. Mullett, "Charles Babbage: A Scientific Gadfly," The Scientific Monthly, Vol LXVII (1948), pp. 361-71; D.S.L. Cardwell, The Organization of Science in England: A Retrospect (London, 1957), Chapter III; and George Basalla, "Science and Government in England: 1800-1870" (unpublished Ph.D. Thesis, Harvard University, 1963).

Babbage published three main items on economics and industrial development and management: On the Economy of Machinery and Manufactures (London, 1832, with several later editions); An Analysis of the Statistics of the Clearing House during the year 1839 (privately printed, London, 1856); and The Exposition of 1851; or, Views of the Industry, the Science, and the Government, of England (London, 1851); the last item also included material criticising scientific organization, and some discussion of the calculating machines. The significance of this aspect of Babbage's work is discussed at length in Richard S. Rosenbloom, "Men and Machines: Some 19th-Century Analyses of Mechanization," Technology and Culture, Vol. V (1964), pp. 489-511. See also Friederich Klemm, A History of Western Technology (Cambridge, 1964), pp. 287-89. 305.

Babbage's work on insurance was published as A Comparative View of the Various Institutions for the Assurance of Lives (London, 1826); this work and Babbage's calculating machines as useful to insurance companies are discussed in Cornelius Walford, The Insurance Cyclopaedia (London, 1871), especially in the articles "Babbage" and "Calculating Machines."

Although Babbage occasionally published notes on particular ciphers he had decoded, he wrote no general work on deciphering; but he discussed his work on the subject in Chapter XVIII of Passages from the Life of a Philosopher. David Kahn, in The Codebreakers (London, 1967), pp. 204ff., argues that Babbage foresaw the principles of the modern science of cryptoanalysis.

Babbage discussed his Mechanical Notation in Chapter IX of Passages from the Life of a Philosopher. He published a brief description of the fully developed notation as used in the Drawings and Notations of the Analytical Engine, for distribution at the Exposition of 1851, as Laws of Mechanical Notation (privately printed, London, 1851; reprinted in B.C.E., pp, 242-45).

Finally, three other Babbage publications which will simply be listed were: A Table of the Logarithms of the Natural Numbers from 1 to 108,000 (London, 1826); Notes Respecting Lighthouses (privately printed, London, 1852); and The Ninth Bridgewater Treatise (London, 1837). The last item mentioned included some discussion of the Difference Engine in Chapters II, VIII, XIII and XVIII, and in "Note B."

Calculating Machines.

Much the most useful book on Babbage's work on calculating machines is Babbage's Calculating Engines: Being a Collection of Papers Relating to them; their History and Construction, edited by Henry P. Babbage (London, 1889). This volume, on which Charles Babbage had been working before his death, reprinted almost all the important published material on the Babbage Difference andAnalytical Engines, and the Scheutz Difference Engine.

Two other general discussions of Babbage's calculating machines, interesting because they were published shortly after the construction of the first computers, are: Howard H. Aiken, et. al., Annals of the Computation Laboratory of Harvard University, Vol. I (Cambridge, Mass., 1946), Chapter I; and in Vol. XVI of the same Annals (Cambridge, Mass., 1948), "The Work of Charles Babbage," by Richard H. Babbage.

The Babbage Difference Engine.

Babbage published four papers on the Difference Engine during 1822. The first, read to the Astronomical Society on June 14, 1822, was a "Note on the Application of Machinery to the Computation of Astronomical and Mathematical Tables," Memoirs of the Astronomical Society of London, Vol. I, Part II (1825), p. 309 (reprinted in B.C.E., p. 211). The second was Babbage's "Letter to Sir Humphrey Davy," dated July 3, 1822, also called "On the Application of Machinery to the Purpose of Calculating and Printing Mathematical Tables" (privately printed, London, 1822; reprinted in B.C.E., pp. 212-15). The third was "On the Theoretical Principles of the Machinery for Calculating Tables," being a letter to David Brewster, dated November 6, 1822, and printed in the Edinburgh Philosophical Journal, Vol. VIII (1822), pp. 122-28 and reprinted in B.C.E., pp. 216-19). The fourth paper, read December 13, 1822, was "Observations on the Application of Machinery to the Computation of Mathematical Tables," Memoirs of the Astronomical Society of London, Vol. I, Part II (1825), pp. 311-14 (reprinted in B.C.E., pp, 220-22).

Babbage wrote little on the Difference Engine later in life. In September, 1843, he published in the Philosophical Magazine (Vol. XXIII, London, 1843, pp. 235-39) a "Statement of the Circumstances attending the Invention and Construction of Mr. Babbage's Calculating Engines" (reprinted in B.C.E., pp. 1-3). In Passages from the Life of a Philosopher, Chapter V concerned the Difference Engine No. 1, and Chapter VII discussed the Difference Engine No. 2.

Of the brief descriptions of or notices about the Difference Engine published by others shortly after its invention, the following may be mentioned: unsigned items appeared in the Edinburgh Philosophical Journal as "on Machinery for Calculating and Printing Mathematical Tables," Vol. VII (1822), pp. 274-81, and "Mr. Babbage's Calculating Engine," Vol. IX (1823), p. 197. A much more interesting account was Francis Baily's "On Mr. Babbage's New Machine for Calculating and Printing Mathematical and Astronomical Tables," printed in the Philosophical Magazine, Vol. LXIX, May, 1824 (and reprinted in B.C.E., pp. 225-31). But much the best and fullest account of the Difference Engine published to date was Dionysius Lardner's "Babbage's Calculating Engine," in the Edinburgh Review, Vol. LIX (1834), pp. 264-327 (and reprinted in B.C.E., pp. 51-82).

In August, 1843, Babbage privately printed a pamphlet called Statement of the Circumstances Respecting Mr. Babbage's Calculating Engines; it was originally published anonymously, but when reprinted as Chapter VI of Passages from the Life of a Philosopher, it was said to have been drawn up by Sir H. Nicolas. In the same year, Sir David Brewster gave a superficial but highly enthusiastic account of the Difference Engine in his Letters on Natural Magic Addressed to Sir Walter Scott, Bart. (New York, 1843, pp. 263-67).

Another account of Babbage's relations with the government, particularly as mediated by the Royal Society, was given as Chapter XI of C.R. Weld's History of the Royal Society (London, 1848). Babbage had this chapter, together with some notices concerning it from the Athenaeum, reprinted as an appendix to his The Exposition of 1851; Babbage believed that this material established that the abandonment of the Difference Engine was the fault of the government. Another account of the Difference Engine was given by Lord Rosse in an address to the Royal Society in 1855 (Proceedings of the Royal Society of London, Vol. VII, 1854-55, pp. 255-58); Rosse also discussed the offer to the government of the plans for the Difference Engine No. 2.

Another description of the Difference Engine No. 1 was given in John Timbs' Stories of Inventors and Discoverers (London, 1863), pp. 139-44. Timbs also discussed the Scheutz machine, and gave biographical sketches of many of Babbage's contemporaries, such as John Rennie and M.I. and I.K. Brunel. A more detailed description of the operation of the Difference Engine, written by B. Herschel Babbage, one of Charles' sons, was Babbage's Calculating Machine; or Difference Engine (London, 1872), a pamphlet to be sold in connection with the display of the assembled section in the Science Collections of the Victoria and Albert Museum (later these collections became the separate Science Museum).

Finally, a skillful description of the operation of the Difference Engine was given in a paper called "Charles Babbage and his Difference Engine," read at the Science Museum on December 13, 1933, by L.H. Dudley Buxton, grandson of Babbage's friend and biographer H. Wilmot Buxton; it was printed in the Transactions of the Newcomen Society, Vol. XIV (London, 1835), pp. 43-65. This paper also included a general biographical introduction.

The only biography of Joseph Clement of real value is Samuel Smiles, Industrial Biography: Iron Workers and Tool Makers (Boston, 1864), pp. 289-313; the same book gives biographies of other major mechanics and engineers connected with the Difference Engine. Descriptions of tools invented or built by Clement will be found in the Transactions of the Society of Arts, Manufactures and Commerce; Vol. XXXVI (1818), pp. 133-77; Vol. XLIII (1825), pp. 138-42; Vol. XLVI (1828), pp. 67-105; Vol. XLVII (1829), pp. 131-35; and Vol. XLIX (1832), 157-85.

A paper by Babbage "On the Principles of Tools for Turning and Planing Metals" was printed in Charles Holtzapffel, Turning and Mechanical Manipulation (London, 1846), Vol. II, pp. 984-87; see also Holtzapffel's notes on this paper (pp. 983-84 and 987-91), and a number of references to Clement throughout the work. The progress in and reduced cost of machining in the period between the first and second Difference Engines was discussed by Joseph Whitworth in a Presidential Address to the Institution of Mechanical Engineers in 1856 (Proc. Inst. of Mech. Eng. for 1856, pp. 125-33).

The Scheutz Difference Engine.

Many varying accounts of the Scheutz Difference Engine were published, but only the significant ones will be mentioned here.

The most important source on the development of the Scheutz Difference Engine was given in the Preface to Specimen Tables Calculated and Stereomoulded by the Swedish Calculating Machine (London, 1857). An excellent account of the mathematical theory underlying the Scheutz machine was given in the "Report of the Committee Appointed by the Council [of the Royal Society] to examine the Calculating Machine of M. Scheutz," Printed in the Proceedings of The Royal Society of London, Vol, VII (1854-55). pp. 499-509 (reprinted in B.C.E., pp. 264-69). A nice description of the operation of the machine was given in the Annals of the Dudley Observatory, Vol. I (Albany, N.Y., 1866). pp. 116-26.

Henry P. Babbage wrote a paper on the Scheutz machine, illustrated with several large diagrams in Babbage's mechanical notation (the diagrams are now in the Science Museum, South Kensington), which he delivered on several occasions. The most extensive report on this talk, drawn up by Charles Manby, Secretary of the Institution of Civil Engineers, was given as "Scheutz' Difference Engine and Babbage's Mechanical Notation," in the Minutes of Proceedings of Civil Engineers for May, 1856 (and reprinted in B.C.E., pp. 248-57).

Accounts of the use of the Scheutz machine at the General Registry Office can be found in the English Life Table (London, 1864), pp. xiii and cxxxix-cxlv, and Companion to the Almanac for 1866 (London, 1866), pp. 6-15.

Babbage's fullest account of his high regard for the Scheutz machine were given in a paper called Observations Addressed, at the last Anniversary, to the President end Fellows of the Royal Society, After the Delivery of the Medals (London, 1856, reprinted in B.C.E., pp. 260-21).


The Analytical Engine.

There were relatively few publications specifically on the Analytical Engine. The most important was L.F. Menabrea's "Sketch of the Analytical Engine invented by Charles Babbage, Esq.," translated and with notes by Ada Augusta, Countess of Lovelace; this appeared, with some introductory material by Richard Taylor, in Taylor's Scientific Memoirs, Vol. III (1843), pp, 666-731, Menabrea's paper had originally appeared in the Bibliotèque Universelle de Genève, Vol. XLI, New Series (1842), pp. 352-76. The translation and notes were reprinted in Babbage's Calculating Engines, pp. 6-50. Babbage himself discussed the Analytical Engine in Chapter VIII of Passages from the Life of a Philosopher.

The "Report of the Committee . . . appointed [by the British Association] to consider the advisability and to estimate the expense of constructing Mr. Babbage's Analytical Machine, and of printing Tables by its means," was published in the Report of the Forty-Eighth Meeting of the British Association for the Advancement of Science (London, 1879), pp. 92-102; it was abstracted in Nature, Vol. XVII, August 22, 1878, pp. 438-40, and reprinted in Babbage's Calculating Engines, pp. 323-30.

Henry P. Babbage's paper "The Analytical Engine," in part a reply to the above item, was read to the meeting of the British Association at Bath in September, 1888; it was abstracted in the Report of the Fifty-Eighth Meeting of the B.A.A.S. (London, 1889), pp, 616-17. and printed in full in Babbage's Calculating Engines, pp. 331-38.

Only two more recent treatments of the Analytical Engine (apart from those in works cited earlier) will be mentioned here. One, interesting as an indication of continuing knowledge of the Analytical Engine in the early 20th century, was some brief discussion of the machine in Modern Instruments and Methods of Calculation: a Handbook of the Napier Tercentenary Exhibition, edited by E.H. Horsburgh (London, 1914), pp. 75, 124-27. The other, interesting as a description of the Analytical Engine in the light of modern computers, was Douglas Hartree, Calculating Instruments and Machines (Urbana, Illinois, 1949), pp. 69-73.


#1 Charles Babbage and his Calculating Engines, edited and with an introduction by Philip and Emily Morrison (New York, 1961), p. xxxii.

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