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The Difference Engine

There once was a man who said, "Damn!
It is borne in upon me that I am
  An engine that moves
  In determinate grooves,
I'm not even a bus, but a tram." 1

In order to understand the attention Babbage devoted to the invention and construction of the Difference Engine, beginning at the end of 1821, it is important to understand that prior to that time, he had not become committed to any particular vocation or area of scientific research. Since his graduation from Cambridge in 1814, Babbage had been publishing mathematical papers, and he had gained a substantial reputation for this work; but his attention was being drawn increasingly in other directions. As early as May 8, 1818, Edward F. Bromhead, a close friend of Babbage, wrote him, asking his opinion on a plan for reforming the poor laws. Bromhead said:

If you continued in the dignified Situation of a Mathematician. I should feel some Conscience against distracting you thus, but as you are a dissenter from the true faith, and turned naturalist, I am hardened. You are wrong. This is not the way to a great Name in England. You must do something strikingly useful, and then everything you do afterwards will be properly valued. Better to be one of the House of Peers in Analysis (as you are) than be mixed up with the 1010 Geologists etc. etc. Your Genius is mechanical. Try to invent some plan for propelling wagons by the steam engine. This might perhaps be effected by two feat beating the ground at an angle alternatively. Perhaps the cylinder of the Engine might work with pistons at both ends. At all events it will be effected in some manner in a few years, and why should not you do what will get great credit and perhaps profit. 2

By 1820, Babbage's attention was also being directed toward the organization of science. He had been interested in the reform of the Royal Society as early as 1816, and this interest emerged again in 1820, in connection with the struggle over the election of a new President to replace Sir Joseph Banks: 3 Further, Babbage was one of the individuals chiefly responsible for the founding of the Astronomical Society in 1820, although he did not think of himself primarily as an astronomer. 4 Bromhead again chided Babbage for allowing this activity to distract him from his own investigations, saying: "I fear you are so busy managing the machinery of the scientific mill, that you may forget that you are one of the principal husbandmen to supply the corn." 5

Yet the problem was precisely that neither in science itself nor in its organization had Babbage found a problem of sufficient interest and magnitude and of the right character to be made peculiarly his own. As one who liked to commit himself to his activities with almost missionary zeal, Babbage was a man in search of a goal. The goal he was to choose came into being at the end of 1821, with the invention of the Difference Engine.

The genesis of Babbage's interest in the Difference Engine is not reflected in his correspondence or other extant documents exactly contemporaneous with it. However, that the idea first arose at the end of 1821, and the way in which it developed, are fairly clear, for the three major accounts written by Babbage (one less than a year after the event) are in substantial agreement. 6

Babbage's first extensive description of the early development of the Difference Engine was written in November, 1822. He gave the following account of the origin of the invention:

Being engaged in conjunction with my friend Mr. Herschel about the conclusion of the last year in arranging and superintending some calculations of considerable extent which were distributed amongst several computers, the delays and errors which are inseparable from the nature of such undertakings soon became sufficiently sensible. . . .

In the course of our conversation on this subject it was suggested by one of us, in a manner which certainly at the time was not altogether serious, that it would be extremely convenient if a steam-engine could be contrived to execute calculations for us, to which it was replied that such a thing was quite possible, a sentiment in which we both entirely concurred; and here the conversation terminated.

During the next two days the possibility of calculating by machinery (which I should never for a moment have doubted had I ever proposed it to myself as a question) recurred several tires to my imagination; the idea appeared to possess that species of novelty which gives so much pleasure and makes so strong an impression on the mind when for the first time we express in words some principle of or precept to which we have long tacitly assented. When we have clothed it with language, we appear to have given permanent existence to that which was transient, and we admire what was frequently only a step in the process of generalization as the creation of our own intellect.

Finding myself a leisure the next evening, and feeling confident not only that it was possible to contrive such a machine but that it would not be attended with any extraordinary difficulty, I commenced the task. The first point in the inquiry was to be fully aware of the power of the machine I wished to construct. In order to produce printed tables free from error I proposed the engine should be able to calculate any tables whatever and that it should produce a stereotype plate of the computed results, or at least that it should deliver a copper plate from which they could be printed. . . .

In order to satisfy the condition that the calculating part should be capable of computing every species of tables, it was necessary to found it on some great and comprehensive mathematical principle; the method of differences is the only one that possesses this extensive range. 7

Babbage's second major account of the invention of the Difference Engine was written on September 6, 1834, almost 13 years after the event. It reads as follows:

The first idea which I remember of the possibility of calculating tables by machinery occurred either in the year 1820 or 1821; it arose out of the following circumstance. The Astronomical Society had appointed a Committee consisting of Sir J. Herschel and myself to prepare certain tables; we had decided on the proper formulae and had put them into the hands of two computers for the purpose of calculation. We met one evening for the purpose of comparing the calculated results, and finding many discordances, I expressed to my friend the wish, that we could calculate by steam, to which he assented as to a thing within the limits of possibility.

In reflecting upon the nature of the greater part of the operations employed in table-making and on the extreme difficulty as well as on the importance of succeeding in having correct tables, it appeared to me to be exactly the circumstance in which machinery ought to be applied. For although its application to the manufacture of numbers was novel, yet machinery is always valuable wherever extreme accuracy is required, and also wherever the same process is to be repeated in almost endless succession. 8

This account of the occasion of the first idea of Babbage's machine is somewhat more specific than the earlier one. The only discrepancy is that in the second account Babbage asserted that it was he who first suggested the idea of a steam engine to compute tables, whereas in the first account he could not remember which of them brought up the idea. The final account of this occasion was written in November, 1839. It reads as follows:

The earliest thought which I recollect of reducing any part of the science of number of pure mechanism arose on the following occasion.

Mr. Herschel and myself having been appointed by the Astronomical Society on a Committee for the purpose of procuring certain calculations, we first agreed on the proper formulae, and then employing two independent computers to reduce them to numbers, ourselves compared the manuscript results. On the first of these occasions my friend brought with him the calculations of both computers, and we commenced the tedious process of verification. After a time many discrepancies occurred, and at one point these discordances were so numerous that I exclaimed, "I wish to God these calculations had been executed by steam," to which he replied, "It is quite possible."

The idea continually presented itself during the few succeeding days, and soon after, having a leisure evening, I resolved in devoting it to the preliminary enquiry. In a few hours I satisfied myself that it is possible to make machinery compute tables by differences, and even to print them when computed. This however was but a general view, and was very far indeed from the subsequent realization of the conclusion. 9

The exact course by which the design of the Difference Engine developed from the general view to the subsequent realization cannot be traced in detail, and, indeed, one cannot say just when Babbage began to make specific plans, for most of his notes and drawings from the time have not survived. However, a certain amount can be reconstructed from the paper written in November, 1822, referred to above, and another manuscript from the spring of 1822.

In the first stage, evidently in early 1822, Babbage was concerned simply with establishing the theoretical possibility of constructing calculating machinery. He was concerned with three types of machines. One, a machine to calculate tables by the method of differences where some order of difference is constant. Two, a machine to calculate tables by the method of differences where there is no constant order of differences. Three, a machine to multiply two numbers together.

The last of these machines is described in some notes entitled "Of an Engine to Multiply N Figures by M Figures," written in early 1822. 10 This machine has no significance. Babbage said that if one has two wheels connected by a mechanism (not described and evidently not contrived) which will make the second wheel turn through an angle which is an integral multiple from one to nine of the angle through which the first wheel is turned, then one can multiply two digits. If this is repeated with different increments set into the first wheel, corresponding to the digits of the multiplicand, and the whole set of operations is repeated with different ratios between the wheels, corresponding to the digits of the multiplier, and the entire collection of partial products is added together in the appropriate positions, then the machine will multiply. The entire idea is rather preposterous, and Babbage never pursued it.

The machine to construct tables where no order of difference was constant was of considerable theoretical interest to Babbage in the latter part of 1822, but he did not attempt to design an actual mechanism to accomplish this for more than a decade; since its significance lies really in the transition from the Difference Engine to the Analytical Engine, discussion of the subject will be postponed until the following chapter. We need, then, consider here only the machine to calculate tables using a constant difference.

First, a brief explanation of the method of finite differences itself must be provided. This branch of mathematics, analogous to the more familiar calculus of infinitesimals, considers the variation in the value of a function as the independent variable is increased through equal, finite increments. In mathematical terms, for a function u(x) and an increment of w the basic operator of finite differences, Δ, is defined by the relation:

Δu(x) = u(x+w) - u(x)

In other words, given a series of tabular values of a function, we can generate a series of first differences, corresponding to the arithmetic difference between the values of the function.

The series of first differences is of course itself a function of the variable, and it is a series from which we can form another series of differences, namely second differences. Mathematically:

Δ2 u(x) = Δu(x+w) - Δu(∞)

We can further generate a series of third differences, and so on, as long as we please.

As an example, we may take the function u(x) = x2; when we set the increment, w, equal to 1, and apply the above definitions, we find that:

Δ1x2 = (x+l)2 - x2 = 2x + 1
and Δ2x2 = 2(x+1)+1 - 2x+1 = 2

This can be clearly seen when the different values are set out in tabular form as follows:


Here the first difference is the series of odd integers, the second difference is a constant, namely two, and all higher orders of difference are naturally all equal to zero.

It is a happy fact that any algebraic function of order n will have its nth order difference constant. This makes it easy to generate a table of such a function by simple addition. Take the following as an example.

Set: A1=2; B1=2; C1=41.
Then set: C2=C1+B1; B2=B1+A1; A2=A1.
Generally: Cn+l=Cn+Bn; Bn+1=Bn+An; An+l=An.

Then the series of values C1, C2, C3....Cn will give us a table of the function u(x) = x2 + x + 41, a function which Babbage liked to use as an example, since it generates a large quantity of prime numbers. 11

As has been said, any algebraic function will have some order of difference constant, and is thus subject to generation in tabular form by this method without limit. Transcendental functions are another matter, however, for they do not have any order of difference constant. As a rule, they can be handled by selecting an algebraic function which approximates the desired transcendental function to a desired degree over a given domain, then switching to a slightly different algebraic function to tabulate another section of the function, and so on. As suggested above, Babbage also had a quite different method for tabulating transcendental functions without manually altering the differences, but this subject will be discussed in the next chapter.

It is not difficult to imagine how a machine could be constructed to carry out the above mathematical process mechanically. Basically, if a column of wheels is provided to hold the digits of each order of difference, if a mechanism is provided to add each digit to the corresponding digit in the next lower order of difference (naturally carriage of tens must be provided for), and if the machine is so organized that the different operations will take place in the proper order, then the machine can tabulate any function without limit, simply by turning the crank that drives it.

Naturally, the physical design of a difference engine is a vastly more complex problem than its theoretical organization. An account of the elegant form which Babbage's machine eventually took is provided as an Appendix to this thesis. What will be considered here is the early development of the design, in so far as it can be reconstructed.

An mentioned above, Babbage was initially concerned only with establishing the theoretical possibility of building a Difference Engine. It was evident to him from the first that the problem of the design of the entire machine could be reduced to the problem of adding one digit to another, since the machine would consist of this mechanism repeated many times over.

The first approach Babbage proposed was admirable for its indifference to mechanical details or problems. As he described it in November, 1822, the plan was that: "a rod sliding in a groove and divided into ten parts numbered from 0 to 9 might be set so that a fixed mark or pointer should indicate one of the numbers, 5 for instance; and the moving power being set in action might urge on the slider until it was released from it by a stud or pin previously fixed at a point indicated by another set of numbers, and which we will in the present case call three; the slide would now have moved over 3 spaces, and consequently the number under the fixed pointer would be 8." 12

Evidently Babbage developed this notion of a machine based on sliding rods to the point where he was satisfied that a difference engine was possible, and wrote describing his idea to Edward Bromhead, for in a letter to Babbage, Bromhead said: "I have turned your scheme of Rod Tables over and over, and can make nothing of it, scarcely even in the simplest cases; I think I might by a machine like a 74 gun ship construct a table of squares." 13 Unfortunately, because this letter was not dated, it does not indicate when Babbage had reached this stage.

It is not surprising that Bromhead was perplexed by Babbage's "scheme of Rod Tables," for clearly the idea was simply a passing phase in Babbage's thought which satisfied him that a difference engine should be possible, rather than a proposal for an actual design. Babbage said that on considering the grave difficulties that would result in this plan from the discontinuity arising when a digit passed from nine to zero (carriage to the next higher digit being assumed): "I was induced to lay down the following maxim to which I have made but few exceptions in the variety of machinery I have contrived: Always to prefer a circular motion to any other when its immediate object relates to number." 14

Taking the principle that the digits from zero to nine should be represented in the machine by divisions around the circumference of a wheel, Babbage drew up a rough sketch of a possible adding mechanism entitled "Engine for Table of Differences." 15 Again Babbage was concerned only to establish the possibility of adding a single digit from one difference to the next, forming the basic module out of which a complete engine could be constructed; and again, he did not attempt to describe the details of the mechanism that would do the adding or perform the carrys; but the description did begin to bear some resemblance to the Difference Engine as constructed.

In this same paper, Babbage provided the first notes on a printing mechanism for the machine. As his orientation was almost entirely toward building a machine to calculate accurate, mathematical and astronomical tables, he naturally considered it very important that the possibility of the introduction of errors in typesetting and proofreading be eliminated. In this paper, Babbage considered only the problem of printing single digits, since he again assumed that by repeating the same mechanism, multiple digits could be printed. He proposed that connected with the wheel whose number was to be printed there be a series of dies for the different digits. When printing was to be done, a hammer would fall and strike the die in the appropriate position, thus stamping the corresponding digit in a sheet of pewter or "music-plate-composition metal," from which "the figures could be printed in the same manner as music." 16 He also suggested that the digits might be stamped deeper into some other material from which stereotype plates could be cast.

The point reached when Babbage had written up the first rough notes on the Difference Engine may be described as the first stage of its development. In this stage, Babbage had satisfied himself that a Difference Engine was constructible in principle, and formed a vague idea of how the individual digits ought to be added.

In the second stage of development. he considered how the individual sections for adding single digits could be organized together to form a coherent difference machine. . Exactly when this second stage was reached is not clear. In his November, 1822 paper, where it is described, Babbage said that it occurred while he "was visiting Mr. Herschel in the country." 17 In the Babbage correspondence, there is a letter to him from Bromhead, addressed in care of Sir William Herschel at Slough, and dated January 12, 1822. 18 Quite possibly this was the visit to which Babbage referred, but it could also have been a separate visit, up to a few months later.

Babbage described the progress made during this visit as follows. 19 Taking the "rough outlines of the first idea" he had already sketched out, he "proceeded to enquire into the duties of the several parts, to curtail those which were unnecessary and to unite those which were similar." The progress made was most gratifying. "Wheel after wheel gradually disappeared, and the axes on which they were supported becoming unnecessary, individuals became substitutes for classes, actions intended to operate simultaneously were effected by the same agent, and the connections of the several parts with the moving power becoming apparent, gave to the design a unity in which it had appeared deficient." The simplification was such that a machine for constant second differences which in the original arrangement would have required 96 wheels and 24 axes, would in the new design require only 18 wheels and 3 axes. The details of this new design are nowhere described, but presumably the organization was fairly close to that of the section of the Difference Engine that was eventually constructed.

On his return to London from this visit to Herschel, Babbage again turned his attention to the design of a printing mechanism. Inspection of a variety of printing presses driven by steam engines suggested to him a method of automatic inking which would allow the machine to print single copies of its results directly, when this was all that was needed. But he was still primarily concerned with the problem of preparing tables for publication.

Experiments with stamping the machine's results in metal to form stereotype plates were not satisfactory. Babbage decided to explore the possibility of having the machine set conventional type, and he was encouraged in this by hearing, from "an American gentlemen, Mr. Church," of a machine he had invented for setting type which was controlled "by means of keys similar to those of a piano."

Babbage was concerned with two possible sources of error that could arise if the machine were to set movable type. First, the machine would have to select the pieces of type from hoppers corresponding to the ten digits; Babbage wished to assure that the type would never get into the wrong hopper. Second, pieces of type could fall or be drawn out of the frame either before or during printing, and then be wrongly replaced; Babbage wished to guard against this danger.

Babbage said that he remembered hearing a few years earlier from Sir William Herschel of a technique tried out at a printing concern in Glasgow, whereby a hole would be drilled through the center of each pica of type, and after composition was complete, a wire would be placed through the holes in each line of type, assuring that no letter could fall out. In the Glasgow experiments, it was decided that the expense of drilling was too great to justify the technique.

Babbage decided to modify this method in two ways. First, instead of drilling a hole through the center of each piece of type, he decided to plane a semicircular groove in one edge of the type, as this would be cheaper and easier than drilling; then, when two lines of type were placed together, they could be secured by a single wire placed through the single hole formed by the two semi-circular grooves. Second, in addition to this groove common to all pieces of type, he decided to add a second special groove whose position was peculiar to each different digit separately. Then when the type was divided among the ten hoppers, each one could be checked for wrong type by passing a wire down this special groove.

However, design of a printing mechanism did not progress any further. In the spring of 1822, Babbage assembled a small working model of the Difference Engine, but it did not include any printing mechanism; 20 indeed, Babbage never did assemble a printing mechanism the whole time he was working on the Difference Engine. In July, 1822, Babbage was still thinking in terms of a machine to set movable type, 21 but by November, he was again considering the idea of stamping the results in a matrix from which stereotype plates could be cast. 22 In July, 1823, Babbage was still undecided between these two methods of printing, 23 but by the spring of 1824, Babbage had decided in favor of stereotype plates. 24

Little can be said about the working model of the Difference Engine referred to above. In a letter dated June 2, 1822, Babbage spoke of this model as being "just finished," and as having two orders of differences. 25 At the beginning of July, Babbage described having tabulated thirty values from the formula x2 + x + 41 in two and one half minutes, the net speed being thirty three digits per minute. The number of figures that could be handled by the model is not clear; writing in 1864, Babbage said that the model "consisted of from six to eight figures"; 27 this could mean the number of figures in the result column, but more probably it also included the difference columns. It is plausible that the machine had three figures for the result, two for the first difference, and one for the second difference (six in all), for this would allow tabulation of exactly the thirty values of x2 + x + 41 referred to above; but this is by no means conclusive. In any case, the model constructed at this early date is nowhere described, and evidently has not survived. It is not possible to say exactly how similar in design it was to the larger section later put together for the government.

Having considered the early development of the Babbage Difference Engine on paper and in metal, we must now consider the process by which the government came to decide that it should provide support for the construction of a full scale machine.

Evidently Babbage did not feel ready to make public his invention of the Difference Engine until after he completed the working model, near the end of May, 1822. But in June, Babbage sent to the Astronomical Society a "Note on the Application of Machinery to the Computation of Astronomical and Mathematical Tables." This brief paper, dated June 2, 1822, and read to the Society on June 14, simply announced that he had completed a working model of the calculating mechanism, and was engaged in designing the printing mechanism. 28

Francis Baily, in a letter to Babbage dated June 8, 1822, remarked: "I trust you are making rapid progress with your new machine: I long to see some practical results. " 29 Again on June 29, Baily wrote: "I trust you are getting along with your expose of the valuable properties of your machine; and I sincerely wish you success through every stage of your progress." 30

The "expose" refereed to was that which emerged as Babbage's "Letter to Sir Humphrey Davy, Bart., President of the Royal Society," dated July 3, 1822, bearing also the, title: "On the Application of Machinery to the Purpose of Calculating and Printing Mathematical Tables." 31 In this letter, Babbage reviewed the success of the working model of the Difference Engine and the possibility of having the machine set type. He described at some length the methods used and the difficulties and expense involved in calculating complicated mathematical tables by hand, and suggested how a difference engine would alleviate the problems. Babbage concluded this letter with the following observations:

Whether I shall construct a larger engine of this kind . . . will in a great measure depend on the nature of the encouragement I may receive. . . . I , have now arrived at a point where success is no longer doubtful. It must, however, be attained at a very considerable expense, which would not probably be replaced, by the works it might produce, for a long period of time, and which is an undertaking I should feel unwilling to commence, as altogether foreign to my habits and pursuits. 32

This "Letter to Sir Humphrey Davy" Babbage had privately printed and distributed to his friends and others whom he thought might be interested, and their reactions began to come in. Writing to Babbage on July 16, 1822, Olinthus Gregory thanked Babbage for a copy of the letter, and remarked:

The application of machinery to the purposes of computation, in the way you have so happily struck out, is highly interesting, and cannot fail, I should think, to be exceedingly beneficial. I trust that our valued friend Mr. D [avies] Gilbert, and some other friends to science who possess influence in high quarters, will exert it cordially on this occasion, and obtain an adequate grant from the Government to complete and render extensively effectual the whole of your curious invention. 33

Edward Bromhead, writing to Babbage on August 20, 1822, said that he had distributed "where I thought the effect would be greatest" the copies of the letter which Babbage had sent him. He continued:

It is my impression that you are much to blame if you put yourself to any trouble or expense in forming one of the larger Engines; it ought to be done at the charge of the Literary World, and I need not say how anxious I am that something of the kind be set on foot. A Memoir in the Phil[osophical] Trans[actions] containing the particulars of your method will give all the fame you can procure by it. Napier and Newton did not increase their Glory by making Rods and Reflectors. 34

It is not clear whether at this time Babbage agreed with Gregory's suggestion that he should seek financial support for constructing a full scale machine, or with Bromhead's belief that he should not himself construct it, but rather make the plans available to any group that wished to. It is clear that at this point Babbage ceased working on the practical problems of building a Difference Engine.

This can be seen in a letter to David Brewster, dated November 6, 1822, in which Babbage said that he had, "during the last two or three months, laid aside the further construction of machinery for calculating tables." 35 This letter, together with a paper read to the Astronomical Society on December 13, 1822, 36 developed at some length the idea Babbage had first formed much earlier in the year, suggesting that the mathematical powers of the Difference Engine could be greatly extended if it could automatically alter the highest order difference depending on its own results. This subject will be discussed in the next chapter.

The closing passage of the letter to Brewster, however, must be quoted here, for It provides insight into Babbage's deep conviction in the ultimate significance of the work he was doing; indeed, it seems almost prophetic. Babbage said:

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. 37

A more poetic side to this version of the importance of the calculating machine was expressed in a letter to Babbage from W.W. Lamb, dated December 29, 1822, saying: "I hope your new machine is growing strong and active like a new giant. I suppose it must begin to feel its powers about this time and to think about moving the whole solar system." 38

Babbage's "Letter to Sir Humphrey Davy," discussed above, had been distributed to him not only among fellow scientists, but also among those who might have influence in winning financial support for construction of a full scale Difference Engine. By the spring of 1823, interest in the machine on the part of people in various sections of the government was beginning to emerge.

On March 21, 1823, John Croker, secretary of the Admiralty, wrote to Sir Robert Peel, secretary of the House of Commons (and later Prime Minister). This letter read as follows:

Mr. Babbage's invention is at first sight incredible, but if you will recollect those little numerical locks which one has seen in France in which a series of numbers are written on a succession of wheels, you will have some idea of the first principle of the Machine, which is very curious and ingenious and which not only will calculate all regular series but also arranges the types for printing all the figures. At present indeed it is more a matter of curiosity than use, and I believe some good judges doubt whether it ever can be of any. But when I consider what has been already done by what are called Napiers bones and Gunters Scale and the infinite and undiscovered variety of what may be called the mechanical powers of numbers, I cannot but admit the possibility, may be probability, that important consequences may be ultimately derived from Mr. Babbage's principle. As to Mr. Gilbert's proposition of having a new machine constructed, I am rather inclined (with deference to his very superior judgment in such matters) to doubt whether that would be the most useful application of further money towards the object at present.

I apprehend that Mr. Babbage's machine, which however I have not seen, answers the purposes which it is intended for sufficiently well, and I rather think that a sum of money given to Mr. B. to reward his ingenuity, encourage his zeal and repay his expenses would tend eventually to the perfection of his machine. It was proposed at the Board of Longitude to give him £500 out of the sum placed at our disposal for the reward of inventions tending to facilitate the ascertaining the Longitude, but the Board doubted that the invention was likely to be practically useful to a degree to justify a grant of this nature.

I think you can have no difficulty in referring the matter to the Committee of the Royal Society (of which although unworthy I have the honor to be one), which by the assistance of its scientific members will give you the best opinion as to the value of the invention; and when that is obtained it may be considered whether another machine should be made at the public expense, or whether Mr. Babbage should receive a reward either from Parliament or the Board of Longitude. 39

Exactly what the "proposition" of Davies Gilbert referred to here was, and to whom it was made, is not clear. But as early as July, 1822, he had been suggested by Olinthus Gregory as the obvious person to plead Babbage's cause with the government. 40

On April 1, 1823, George Harrison of the Treasury wrote to Sir Humphrey Davy, as President of the Royal Society; he enclosed a copy of Babbage's "Letter to Sir Humphrey Davy," saying that it had been sent to the Treasury by Babbage, and stating that the Lords Commissioners of the Treasury "request to be favored with the opinion of the Royal Society on the merits and utility of this invention." 41

In response to this enquiry, the Royal Society formed a committee to consider the matter; it consisted of the President, Treasurer, and the two Secretaries of the Society, and eight other distinguished men. On May 1, 1823 William Thomas Brande, Secretary of the Society, wrote to Harrison, reporting their opinion. They had concluded: "That it appears that Mr. Babbage has displayed great talents and ingenuity in the construction of his machine for computation, which the Committee think fully adequate to the attainment of the objects proposed by the inventor, and that they consider Mr. Babbage as highly deserving of public encouragement in the prosecution of his arduous undertaking." 42 This correspondence between the Royal Society and the Treasury was mentioned in the House of Commons on May 6 and May 22, 1823, and was directed to be printed in the Parliamentary Papers; but no formal action was taken, and the question was turned back to the Treasury. 43

Advice and information continued to flow in to Babbage from his various friends. Edward Bromhead wrote him, saying:

I have always objected to your undertaking your machine yourself; it would have been more just, and would have had a better effect, that you should have thrown out the Principle, and a Committee of scientific Men taken it up. You should have two courses in view on the Parliamentary inquiry; 1st, a remunerative Grant, such as was granted to Dr. Jenner and many others, 2ndly an annual Grant of 5 or 10 thousand a year to the Board of Longitude, for scientific purposes. Either of these would be carried, but you will find it hard to Persuade Parliament to address the Crown for the manufacture of a Machine. The addresses for printing the National Records and Chronicles are almost the only cases in point. I shall mention the Business among my friends who may be in Parliament. 44

On May 26, 1823, Francis Baily wrote Babbage, suggesting that he would be better prepared to answer such questions as might be raised if he would look into the earlier history of calculating machines. In a postscript he added this: "A celebrated mathematician, who has seen your machine, says that it would take as much time to make calculations [as] with the pen!!! You see how difficult it is to lead the public." 45

On May 28, 1823, Davies Gilbert wrote Babbage, saying:

I have some very unpleasant news to communicate. To my great astonishment . . . the Administration have . . . declared an extreme unwillingness to consent to encourage or assist any invention whatsoever, partly arising I believe by the large demands of London Bridge.

I believe it would be in my power to persuade them to reimburse any actual expense incurred since the matter has been in actual agitation; but this for the present I have declined doing.

I have mentioned the affair to the Solicitor General, who has promised to look at your machine tomorrow. 46

Shortly after this, Babbage received his first formal public honor for the invention of the Difference Engine, in the form of the Gold Medal of the Astronomical Society. Communication of this award was sent to Babbage on June 13, 1823, by John Millington, Secretary to the Society (Babbage had resigned from this same position a short time earlier). The resolution passed by the Council stated that the Medal was being presented to Babbage by the Society "as a token of the high estimation in which it holds his Invention of an engine for calculating and printing Mathematical and Astronomical Tables." 47

The actual award of the Medal took place on July 13, 1823, and its presentation was accompanied by a speech by Henry Thomas Colebrooke, President of the Astronomical Society. In this speech, Colebrooke stressed the importance of the machine to astronomy; not only would it alleviate "the most irksome portion of the astronomer's task," but he hoped it would make applicable by the astronomer mathematical equations "which involve operations too tedious and intricate for use, and which must remain without efficacy, unless some mode be devised of abridging the labour or facilitating the means" of their application. 48

There is no evidence that this award had any effect on the Government's decision, but this did follow shortly after. At some point in July, Babbage had an interview with F.J. Robinson (afterward Lord Goderich, later Earl of Ripon), Chancellor of the Exchequer. 49 At this interview, Babbage was told of the government's intention to support the Difference Engine, but unfortunately there was no written record of any details of what was agreed upon; as we shall see, this lack became rather important later on. Apparently the interview took place about July 11, for on that day there was a Treasury Minute authorizing the first payment to Babbage. 50

The Committee of the Royal Society which had reported to the Treasury on the merits of Babbage's machine was informed of the government's decision in a letter from the Treasury to Davies Gilbert, dated July 21, 1823. The letter stated that the Lords Commissioners of the Treasury had "directed a Warrent to be prepared for the issuing the sum of one Thousand Five hundred Pounds to Mr. Babbage to enable him to bring his invention to perfection in the manner recommended." 51

Unfortunately, there was no indication of what "the manner recommended" meant; the Royal Society committee had recommended nothing about how the Difference Engine should be built. Further, the letter did not make clear whether the Treasury expected that £1500 would be enough to complete the machine, or what they would do if it was not. It is even possible that they intended the money simply as a reward for Babbage's invention, with the expectation that this would encourage him to construct it, rather than as direct support for construction. As we shall see, all these ambiguities were to cause considerable trouble in later years.

Babbage started work on construction of the Difference Engine shortly after this grant of £1500 was announced, and he hired Joseph Clement (1779-1844) as his chief engineer and draftsman. Clement, who was largely self-taught in machining and drawing, had come to London in 1813 to become a professional mechanic. He had worked in the shops of two of the foremost engineers of the time, Joseph Brahmah and Henry Maudslay, and himself later employed Joseph Whitworth, the leading machine-tool maker.of the 19th century. Clement was himself responsible for several important improvements in lathes and other tools. 52

Due to the lack of the appropriate documents, it is unfortunately not possible to reconstruct a detailed account of the progress of the Difference Engine during the early years of its development. The first surviving Babbage letter with any substantial comment on the work was written on November 21, 1826, to Christopher Wordsworth, Master of Trinity College and Vice Chancellor of Cambridge University. Babbage had applied for the post of Lucasian Professor at Cambridge, and in this letter he argued that the requirement, generally not enforced, that the Lucasian Professor reside at the University not be applied in his case, if he were elected. In regard to the Difference Engine, Babbage said:

During the last four years I have been occupied in the construction of an engine for calculating and printing mathematical tables. I am executing this work at the desire of the government, and although in my first interview with the Chancellor of the Exchequer I did not pledge myself to devote my whole time exclusively to this object, yet I feel that the liberal and very handsome manner in which I was received at the Treasury would be but ill returned if I were to allow any other agreements to impede its progress. I have hitherto given up everything for this object, situations far more lucrative although not at all more honorable have been sacrificed, and I should not wish to change these sentiments now that it is approaching, I hope, to a successful termination.

The thought and time which this has cost me will never be known. Severe illness in my Draftsman has delayed me much beyond my original expectation, but my machinery and arrangements are now arrived at such a point as to admit of occasional absences of some duration without detriment to the progress of the work. 53

However, this determination to proceed rapidly to the completion of the Difference Engine was not to last, despite the fact Babbage was not elected to the Lucasian chair. Early in 1827, Babbage's father died, leaving to Charles a fortune of about £100,000. Whether it was due to grief over his father's death, the time required to look after his affairs and care for his mother, or other matters, Babbage was soon led to suspend work on the Difference Engine temporarily.

About the end of March,1827, Babbage wrote to Thomas W. Hill, in response to a complaint from Hill that Babbage had not sent him any news of progress on the machine. Babbage's response was simply: "As the machine is out of order and condemned to the lumber room I did not think it worth while troubling you about it." 54 Hill replied, on April 10, 1827, suggesting to Babbage the same feelings that had been advanced by Edward Bromhead several years earlier:

For your sake I rejoice that your machine cannot at present be brought from its retirement. Your justly high reputation, like many other things good in prospect, must by this time, like a chain of Gold, have hung heavy upon you and impeded your escape from many an impertinent hunter after some new thing, who might stare at your Promethean machine without the ability to see its excellence or at all appreciate its value or its uses.

Time like yours ought not to be thus preyed upon, and until the period shall arrive when the engine can work in other hands than your own, I wish it may rest in peace. 55

No doubt Babbage's remark had arisen from the press of other affairs and momentary annoyance at the slow progress of the work, for it was clearly not his intention to abandon it for good. However, there was soon another set-back, for in October, Babbage's wife died; 56 this loss, added on to the deaths of Babbage's father and two of his children, caused something approaching a nervous breakdown. It was decided that for the sake of his health, Babbage should go on an extended tour of the Continent. Even in these circumstances, however, Babbage considered himself to be under an obligation to work on the Difference Engine; he thus applied to the government for permission to leave the country; this permission was granted on October 24, 1827. 57

During his European tour, Babbage paid little direct attention to the continuation of the construction of his machine. He had, however, left behind drawings from which the work could be continued, as well as £1000 of his own money to advance toward the expenses. By this time, the money expended or owing from the project amounted to some £3500. 58 Babbage thus naturally became concerned with the status of his understanding with the government about the support of its construction.

Early in 1828, Babbage wrote to his brother-in-law, Wolryche W. Whitmore, M.P., asking him to obtain from F.J. Robinson, now Lord Goderich (who had been Prime Minister for the last few months of 1827), acknowledgement that at his interview with Babbage in July, 1823, he had promised that the government would reimburse Babbage for all expenses incurred in constructing the Difference Engine. Whitmore obtained an interview with Lord Goderich, and on February 29, 1828, he wrote the following pessimistic account of the results:

It was under disadvantageous circumstances that I entered upon this subject with him, as I was ignorant of the precise nature of the promise to you at the time, and all I could do was to take it for granted and argue accordingly. I did not find him very candid about it; he did not like to admit that there was any understanding at the time the 1500 was advanced that more would be given by government, and all I could prevail upon him to do was to state if referred to by the Treasury that the subject had been mentioned to him and that he had sanctioned an advance of money to begin it. . . .

Economy is now so much the order of the day that I should despair of obtaining any pecuniary aid from Government at present. But I should hope that when money is more plentiful and the machine is completed, we might be more successfu1. 59

Apparently Babbage decided that no clarification of the mutual obligations between himself and the government could be reached in his absence; the matter was not pursued until he returned to England near the end of 1828. At this time he talked directly to Lord Goderich; seemingly what they agreed was that no definite arrangements had been settled on in 1823. 60

In January, 1828, the Duke of Wellington had replaced Lord Goderich as Prime Minister, and Babbage decided that the matter could be resolved only by direct appeal to him. Consequently, on December 6, 1828, he addressed to the Duke a lengthy statement of the circumstances surrounding the construction of the Difference Engine. With respect to the crucial interview with Robinson, as Chancellor of the Exchequer, in July, 1823, Babbage said that he had gone to this interview:

with the view of ascertaining whether it was the wish of the government whether he should construct a larger machine, and one which could also print the results it calculated. Mr. Babbage apprehended that such was their wish, and in the course of the interview with which he was honored, the Right Honorable the Chancellor of the Exchequer stated this principle:

That the government were unwilling to make grants of money to inventions however meritorious, because if they really possessed the merit claimed for them, the sale of the article produced would always be the best reward to the inventor.

That the present case was an exception, and that it was apparent that the construction of such a machine could not be undertaken with a view to pecuniary profit arising from the sale of its produce, and that as the tables it was intended to produce were peculiarly valuable for nautical purposes, it was deemed a fit object of encouragement by the Government.

It was proposed in the present instance to make a grant to Mr. Babbage of £1500, which was taken from a certain fund in the Civil List.

The impression which remained in Mr. Babbage's mind from this interview was that whatever might be the labor and difficulties of his undertaking, he should not suffer any pecuniary loss from it, and it was on the firm conviction of this that he has relied during the many difficulties he has encountered. 61

This statement went on to say that much progress had been made toward the completion of the machine, although it had taken longer and cost more than had been anticipated. Babbage said that about £6000 had been spent, all but £1500 having come from Babbage's own resources, and that he would find it difficult to advance any more money; further, if the uncertainty as to his position continued, "the additional anxiety thus created would be highly unfavorable to that state of mind most fitted for the performance of this and his other scientific duties." 62

In response to this statement by Babbage to the Duke of Wellington, the Treasury wrote to the Royal Society, in December, 1828, asking them "whether the progress made by Mr. Babbage in the construction of his Machine confirms them in their former opinion, that it will ultimately prove adequate to the important objects which it was intended to attain." The response of the Royal Society, predictably, was to appoint a committee to consider the question; it consisted of ten distinguished scientists and engineers, with Babbage's good friend John Herschel serving as chairman. 63

The committee decided to consider neither the mathematical principles of Babbage's engine, nor its usefulness when complete, for these matters had been settled in the Royal Society report of 1823. They confined themselves rather to the actual progress in execution of the machine. They submitted their report to the Council of the Royal Society in early February, 1829. The key findings of this report were as follows:

In the actual execution of the work they find that Mr. Babbage has made a progress, which, considering the very great difficulties to be overcome in an undertaking so novel, they regard as fully equaling any expectations that could reasonably have been formed; and that although several years have now elapsed since the first commencement, yet that when the necessity of constructing plans, sections, elevations, and working drawings of every part; that of constructing, and in many cases inventing, tools and machinery of great expense and complexity (and in many instances of ingenious contrivances, and likely to prove useful for other purposes hereafter), for forming with the requisite precision parts of the apparatus dissimilar to any used in ordinary mechanical works; that of making many previous trials to ascertain the validity of proposed movements; and that of altering, improving, and simplifying those already contrived and reduced to drawings; your Committee are so far from being surprised at the time it has occupied to bring it to its present state, that they feel more disposed to wonder it has been possible to accomplish so much. . . .

The actual work of the calculating part is in great measure constructed, although not put together, a portion only having been temporarily fitted up for the inspection of the Committee; and from its admirable workmanship they have been able to form a confident opinion that it will execute the work expected from it. At the same time, the Committee cannot but observe that, had inferior workmanship been resorted to, such is the number and complexity of the parts, and such the manner in which they are fitted together, the success of the undertaking would have been hazarded; and they regard as extremely judicious, although, of course, very expensive, Mr. Babbage's determination to admit of nothing but the very best and most finished work in every part; a contrary course would have been false economy, and might have led to the loss of the whole capital expended on it. . . .

Finally, taking into consideration all that has already been said, and relying not less on the talent and skill displayed by Mr. Babbage as a mechanician, in the prosecution of this arduous undertaking, for what remains, -- than on the matured and digested plan and admirable execution of what is accomplished -- your Committee have no hesitation in giving it as their opinion, that "in the present state of Mr. Babbage's engine, they do regard it as likely to fulfill the expectations entertained of it by its inventor." 64

The Council of the Royal Society considered this report on February 12, 1829, and resolved to report to the Treasury their conclusion that Babbage's machine indeed would "ultimately prove adequate to the important objects which it was intended to attain." They further expressed "a hope that while Mr. Babbage's mind is intently occupied on an undertaking likely to do so much honour to his country, he may be relieved, as much as possible, from all other sources of anxiety." 65

Babbage's own state of mind and health at this time, and the degree of his recovery from his wife's death, can be judged from the following passage in a letter to the Reverend Edward Smedley, dated March 1, 1829:

I have suffered so severely in health that however much I desire to be active, all my friends, and more especially my medical ones, urge me to lay aside my pursuits and to set my mind at rest or asleep. The alternative in case of refusal seems to be the long sleep. The intensive occupation I have used as a remedy has had its effect. I have lived through two years and I may live two or twenty more, but the medicine has produced a disorder, and if I am to finish the machine I must cure the new complaint. I have therefore decided on giving up everything but that. 66

Babbage had been reassured by the response from the Treasury to his statement to the Duke of Wellington, and also by the report of the special committee of the Royal Society. Although by early April, the Treasury had not responded to this report, Babbage thought that his relations with the government were on their way to being put on a proper footing, since it seemed that they were going to accept his view that he had undertaken construction of the Difference Engine on their behalf and at their request.

This led Babbage to turn his attention to another area, namely his relations with Joseph Clement. He believed that if the government was to pay Clement's bills, they ought to get appropriate assurance that the amounts of the bills were reasonable. Therefore, on April 11, 1829, Babbage wrote to Bryan Donkin and George Rennie, both distinguished civil engineers who had served on the special committee of the Royal Society to consider Babbage's progress, asking them to undertake an examination of Clement's bills for work done to date. 67

There were also certain more general matters that Babbage wanted to have settled, and he asked Donkin and Rennie to discuss them with Clement. These included the questions of ownership of the drawings and special tools made for the calculating machine, liability for damage to them or to parts of the machine itself, and procedures for examining future bills. Babbage also desired assurance from Clement that he would not make further copies of the Difference Engine without written permission from Babbage; he gave the following reason:

The machine when completed may perhaps have cost 12,000 and many years of my own labor. When it is completed it would be possible in twelve months to make another such at an expense of perhaps two thousand pounds. It would be manifestly a great injustice for the contriver of such a machine at whose sole risk it was made that any other should be made by the same workman with the same tools. 68

The character of Babbage's request to Donkin and Rennie, especially in light of the open break between Babbage and Clement that was about to erupt, might give the impression that Babbage already felt some apprehensions about Clement's work, and wished to have Clement's bills examined to prevent him from cheating Babbage and the government. But this seems not to have been the case; Babbage simply wanted to have matters put on as business-like a basis as possible, in order to guard against later problems. Indeed, in Babbage's letter to Donkin, he said: "I believe you are perfectly aware of my feelings toward Mr. Clement; he is a most excellent workman and draftsman, and ought to be well paid." 69

On April 22, 1829, Donkin wrote Babbage, reporting the results of the interview he and Rennie had conducted with Clement. Clement had maintained that the tools belonged to him, as they had been made at his own expense; the patterns, drawings and machinery belonged to Babbage, and should be insured against damage by him. Clement would not promise to refrain from making a copy of the machine without written permission. As to Clement's bill, Donkin said that Clement was preparing a detailed itemization of it for examination. 70

In the meantime, the Treasury was slowly acting on the report to it from the Royal Society. On April 16, 1829, Edward Walpole wrote Babbage from the Treasury, saying that Henry Goulburn, Chancellor of the Exchequer, had agreed to another grant of £1500 from the Civil Contingencies funds. 71 On April 28, 1829, there was a formal Treasury minute: it reviewed the reports submitted to it, and concluded that the Treasury was "fully justified in directing a further payment of £1500 to Mr. Babbage to enable him to complete the machine by which such important benefit to science may be expected to result." 72

On the surface, things appeared to be going fairly smoothly at this point, but difficulties and misunderstandings in two different directions very shortly brought work on the Difference Engine to a halt -- one that was to last more than a year. The initial problem involved disputes with Clement over payment of his bills; the second and longer lasting involved the lack of any clear-cut understanding with the government. Although these problems were inter-related, their course will here be traced separately.

As mentioned above, Rennie and Donkin had thought that Clement's bill was not sufficiently detailed for a thorough examination, but Clement had agreed to supply the particulars of the charges. At this point, both parties seemed to have confidence in the good faith of the other; but near the end of April, something occurred between Babbage and Clement which caused them to become suspicious of one another's motives. The first indication of this is in a letter from Richard Penn to Babbage, dated May 5, 1829. Penn wrote:

I am truly sorry to hear of the annoyances to which you are exposed by the conduct of Mr. Clement. . . . I feel scarcely qualified to advise on such a subject, but it appears to me at first sight that (as Mr. Clement has chosen by his offensive conduct to forfeit all claim to that liberality on your part which disposed you at first not to question the amount of his charges, but merely to require the particulars of them) your best course would now be to force the matter to a more hostile Arbitration. I cannot but think that if you should do so, Mr. Clement's low cunning will be defeated, because I conceive that under such an Arbitration he would not be allowed to charge both for his own time and also a Tradesman's profit on the articles; and I am sure that an investigation made in this spirit would greatly reduce the amount of his charges, and show that you have purchased and paid for everything which is now done. A conclusive settlement made now seems to be absolutely necessary for your future Comfort in the business. 73

Exactly what had occurred is not clarified by the other correspondence at this time, but the basis of the trouble was monetary. The financial transactions surrounding the the machine can be seen from a summary financial statement prepared by Babbage on May 13, 1829; 74 the amounts are somewhat rounded off here:

Clement's total bills through Jan. 1, 1829:£4775
Other expenses paid by Babbage:1120
Estimate of Clement's bill, Jan. to May, 1829:800
Paid to Clement by Babbage, through May, 1829:3260
Owing to Clement by Babbage, May, 1829:2315
Total paid by or due from Babbage:6695
Paid to Babbage by the Treasury:3000
Expenses not Covered by the Treasury:3695

The bill with which Rennie and Donkin had been dissatisfied was the one for the period through January 1, 1829. The work had continued after that, but on May 9, it was halted, for reasons that are complex and obscure, and will emerge as this account proceeds. On May 25, 1829, Babbage wrote Clement a note of very frosty tone, requesting that Clement inform him of the amount of his bill through the time when the work stopped. This Clement did on May 29, 1829. The amount of the new bill was about £680; for some reason, his figure for the previous bill was lower than that given by Babbage (above), amounting to only £4630. Thus in Clement's reckoning, Babbage owed him a balance of just over £2050. 75

Although some further contact between Babbage and Clement was carried on through intermediaries, including the leading engineer Mark Isambard Brunel, 76 there was apparently no more direct correspondence between the two until November 18. On this date, Clement wrote Babbage, saying:

It is now upwards of Six months since you informed me that you should be prepared to settle my account in about ten days or fortnight; Since that time I have scarce had the pleasure of seeing you.

You now impose on me the unpleasant task of demanding the money on you. I therefore request that you will not exceed Ten days . . . in settling my account with you. 77

On the back of this letter, Babbage wrote his own account of the course of events:

The true state was this. Clement asked for payment about 6 months since. I said that I must submit the bill to Mess. Rennie and Donkin previous to payment. Mess. Rennie and Donkin said the bill was not properly made out and ought to be more detailed. They communicated this to Clement, who promised to give it in detail, and he told me (this day 18 November, 1829) that he had begun it at that time.

After about 2 months I wrote to request to know the expense incurred from 1 January 1829 to the time the work ceased. Clement in about 2 weeks called on me and said he had discontinued to make out detailed bills because he thought from my letter that I did not want it. I told him that my letter implied nothing of the kind and I desired him to continue it and communicate with Mess. Rennie and Donkin.

The day after the letter of 18 November, 1829, I saw him, and he then for the first time told me he declined making such bill because it is not the custom of engineers to do so. I requested him to communicate this to me through Mess. Rennie and Donkin. 78

Despite Clement's demand for prompt action, matters proceeded very slowly. The next letter preserved from Babbage to Clement was dated December 18, 1829, and simply stated that "all communications between us relative to accounts" would take place through Rennie and Donkin, and not directly. Babbage said that Rennie would see Clement at his convenience to discuss the general situation. 79

Apparently this discussion, if it took place, was not fruitful, for on January 23, 1830, Babbage wrote a letter to Clement including the following passage:

Your refusal to furnish me with any of the particulars of your bill renders it necessary that I should adopt some mode of satisfying myself of its correctness. Arbitration or a suit in one of the courts seems to be the only means of deciding the question. Having myself little reason for preferring one more than the other of those courses, I request you will choose that which you think most advantageous to yourself. 80

In response to this letter, J.B. DeMole wrote to Babbage on February 16, 1830, on behalf of Clement. He said that Clement accepted the proposal of arbitration of the bill, and wished the matter "to be referred in the usual way . . . to 3 Engineers of eminence, one to be chosen by each party, and the third by the two so first chosen." As his own representative, Clement chose Henry Maudsley, another eminent engineer. 81

Babbage chose Brian Donkin as his representative; evidently Donkin and Maudsley did not find it necessary to select a third party to settle disputes. They examined the bills in April, 1830, and found them to be correct and reasonable; on May 6, 1830, the account was settled by a new payment from Babbage to Clement which brought the total of payments through that date to just under £5420. 82

We must now return to early May, 1829, to the point where the Treasury had granted Babbage £1500, the first money he had received from them since 1823, and trace through this same period his interactions with the government with respect to the machine.

No doubt Babbage was relieved that the government was willing to grant him more money, but he was rather disturbed that they saw fit to limit the payment to £1500, since they had been informed in the report from the Committee of the Royal Society that expenses had already amounted to £6000. Further, there was still no progress toward an understanding as to the mutual obligations between Babbage and the government.

This anxiety led to two actions. First, as mentioned above, work on the engine was halted on May 9. The difficulties with Clement discussed above undoubtedly contributed to this stoppage, but it seems clear that the principal cause was Babbage's anxiety about the government's intentions. On the one hand, Babbage was reluctant to continue laying out funds at the rate of about forty pounds per week with no assurance of being reimbursed; on the other hand, he felt that he could use the halt in construction as a lever with which to pry some attention out of the government.

This attention was to be gained through the second action taken, apparently at the suggestion of Wolryche Whitmore. This consisted of a report and appeal to the government drawn up on May 12, 1829, by seven distinguished personal friends of Babbage, namely Lord Ashley, the Duke of Somerset, Sir John Franklin, Wolryche Whitmore, Henry Fitton, Francis Baily and John Herschel. This report advanced the following main points: that Babbage had begun construction of a full scale Difference Engine at the desire of the government; that it had been understood that the government would pay for the work as it progressed; that although Babbage "had devoted the most assiduous and anxious attention to the progress of the Engine," he was not being reimbursed, and could not afford to go on making large advances from his personal funds; and that if the government did not respond appropriately, Babbage would be under no obligation to continue the work. 83

These conclusions were presented by Whitmore and Herschel in an interview with the Duke of Wellington, the Prime Minister. For once the government did not respond by asking for the opinion of the Royal Society; presumably the opinion expressed four months earlier still held. Rather the government did not respond at all. After some weeks, Whitmore inquired of the Chancellor of the Exchequer as to what had happened; he was informed that the Duke of Wellington wished to personally inspect the progress made on the machine. 84

This clearly pleased Babbage, for he felt that the Engine was finally getting the attention it deserved from the only man who could really decide the government's policy toward it. The Duke of Somerset considered it necessary to warn Babbage against excessive optimism; writing to him on June 8, 1829, the Duke said:

I am very glad that the Duke of Wellington will see the machine. If he should understand it, he must be a much greater Mechanician than I imagine him to be, and if he should comprehend its uses, he must have much more science than what usually falls to the lot either of a soldier or a statesman. So that I apprehend he must take a great deal upon trust, or else your end will not be answered. You seem to think your wishes very moderate, when you wish for nothing more than that it may be completely understood. Now I consider this as altogether hopeless. 85

As it turned out, it was optimistic even to expect a prompt visit from the Prime Minister. After more than two months of waiting, Babbage wrote again to the Duke of Wellington on August 13, 1829. He once again reviewed the circumstances of the construction of the Difference Engine, and urged that a rapid resolution of the problems surrounding it was important, because, among other reasons, as long as the work was halted, Clement would be free to sell the tools made especially for the Engine, since they were legally his property. 86

Once again, there was no response. On October 7, 1829, almost another two months later, Babbage wrote to Edward Drummond, secretary to the Duke of Wellington, complaining that he had received no reply to his letter of August 13, and saying that he had been waiting in London since June in daily expectation of a visit from the Duke. Babbage stated that he had some business away from London, and needed to know if the visit would occur within three weeks, so that he should delay his departure. 87 On October 13, Babbage wrote again to Drummond, saying that since he had received no reply to his last letter, he was leaving for Worcester, but would return at once if they wrote him there. 88

Babbage returned to London on November 16, and wrote to Drummond again, informing him that he awaited a visit at the Duke's convenience. 89 Finally, after nearly six months of silence, he received a reply, setting up an appointment a few days later. 90 The Prime Minister and Henry Goulburn, Chancellor of the Exchequer, were shown the model of the difference engine that was built in 1822 and the drawings and parts that had been completed since then.

The results of this interview were expressed in a letter from Goulburn dated November 20. He said that he and Wellington had, as a result of their visit, recommended to the Treasury that it give Babbage another 3000 pounds, as "a further payment towards the completion of the Machine." He also expressed their belief that since the printing mechanism would have to be quite complicated, "the Machine should be so arranged that in the event of any failure in the printing department of it the calculating part should be nevertheless perfect and available." 91 Babbage replied to Goulburn on November 24, describing at length the relation and relative independence of the calculating and printing sections of the Engine, although no detailed plans for the printing mechanism had been made at this point. 92

The fact that the government was now ready to pay Babbage another £3000, though gratifying, did not really reassure him. This emerges very clearly in a letter from Babbage to Lord Ashley, dated November 25, 1829, in which Babbage expressed his anxieties about his relations with both Clement and the government in great detai1. 93 With respect to Clement, Babbage said that he was quite satisfied with the work he had done, and that it was "clearly of the greatest advantage to the progress of the machine that he should continue under my direction to execute it." However, Babbage continued, he was "much displeased" with Clement's conduct with respect to his bills. Babbage considered it most important that the need for discussion between him and Clement of financial arrangements, being a source of considerable irritation, should be removed.

With respect to the government, Babbage admitted that the difficulties he had had, arose in part "from my own fault in not requesting at the outset [July, 1823] from the then Chancellor of the Exchequer [F.J. Robinson, later Lord Goderich] some more distinct understanding and some written document which would place me in a similar relation to his successor." Despite the additional grants the government had made or proposed, there was still no definite commitment or understanding.

Babbage called these two sources of anxiety "the moral difficulties of the machine," and said that they were "difficulties which perhaps the very constitution of my mind rendered me as incompetent to contend with as it seems to have rendered it fatally susceptible of them as a source of disgust."

Babbage proposed that these moral difficulties could be removed if the government would agree to consider the Difference Engine to be their own property, and if they would pay Clement directly, appointing some engineers to examine the propriety of his bills. This course, he said, "would relieve my mind from all causes calculated to distract its attention, and I should be enabled to devote all my energies to complete the machine." Babbage requested that Lord Ashley propose this arrangement to the government, along with the reasons for it.

On December 3, 1829, Babbage received a minute from the Treasury confirming their intention to grant him a further £3000 to enable him "to complete the Machine." It repeated the suggestion about the printing mechanism earlier made by Goulburn, but proposed no basis for a future understanding. 94

On December 13, 1829, Goulburn wrote to Lord Ashley in response to the proposals he had forwarded on behalf of Babbage. Goulburn said that accepting the suggested arrangements would be inconsistent with the principle on which the earlier support had been granted:

The view of the Government was to assist an able and ingenious man of science whose zeal had induced him to exceed the limits of prudence in the construction of a work which would if successful redound to his honor and be of great public advantage. It was no part of our intention to divest Mr. Babbage of the machine or by transferring the property in it to Government to place him in the situation of a Government Agent acting under the instructions of the Treasury. 95

Goulburn claimed that such a course would be to nobody's advantage, and would set an unfortunate precedent. "We feel ourselves, therefore, under the necessity of adhering to our original intention, as expressed in the minute of the Treasury, which granted Mr. Babbage the last £3000, and in the letter in which I informed him of that grant." Unfortunately for the cogency of Goulburn's reply, nothing concerning the government's "original intention" had been expressed in either of those documents.

Babbage found Goulburn's letter, forwarded to him by Lord Ashley, rather astonishing. As he said in a letter to Lord Ashley on December 16, 1829, Goulburn seemed to feel "that I commenced the machine on my own account, that pursuing it zealously I expended more than was prudent, and then applied to government for aid." Babbage flatly contradicted Goulburn's view. He pointed out that the small model of the Difference Engine had been completed long before he had had any contact with the government, and that in his letter to Sir Humphrey Davy he had expressed his disinclination to undertake a full scale machine, which, indeed, he had started on only after he had received the first £1500 from the government. 96

A thought that Babbage expressed in some private notes on Goulburn's letter to Ashley, but did not include in his own letter to Ashley, was as follows: "Having already suffered so much from the want of a sufficiently clear understanding, I hope I shall be excused in not advancing further until I perfectly understand the nature of the position in which I am placed." 97 In the letter to Ashley, Babbage put the matter in terms of a list of questions he wanted to have Ashley put to the government. Among them were the followings

Supposing I receive the £3000 last given. What are the claims which Government have in the machine, or on myself?

Does Mr. Babbage owe the £6000 or any part of that sum to Government? . . . Is it expected by government that Mr. Babbage should continue to construct the machine at his own expense, and if so, to what extent in money?

Suppose Mr. Babbage should decline resuming the machine, to whom do the drawings and parts already made belong? 98

The pessimistic view Babbage had of the future of the project at this point, and some further insight on his relations with Clement, is revealed in a letter he wrote to Rennie three days later, on December 19. He said:

I have had since I saw you some discussion with government which it appears to me will not be speedily terminated, and I am inclined to believe that the result must be my giving up the machine.

However, Mr. Clement has worked well, and notwithstanding that I am dissatisfied with some parts of the engine, he ought to be paid liberally. I have not yet accepted the sum last proposed, and shall probably him from my own means. 99

Exactly what happened in the following few weeks is not clear, but evidently Lord Ashley had some fruitful discussions with Goulburn, for on January 10, 1830, Babbage mote to Lord Goderich, who (as F.J. Robinson) had been Chancellor of the Exchequer in 1823, and said: "The communications I have had with the Government relative to the calculating machine are I hope about to be terminated in a way which will enable me to continue its construction." 100

Babbage went on to say that Goulburn would probably ask Goderich for his account of the 1823 interview, and consequently Babbage wished to refresh his memory as to what had been said. Babbage's version was summarized in the following passage:

The matter was, as you have justly observed on another occasion, left in a certain measure indefinite, and I have never contended that any promise was made to me. My subsequent conduct was founded in the impression left in my mind by that interview. I always considered that whatever difficulties I might encounter, it could never happen that I should ultimately suffer any pecuniary loss. 101

This series of negotiations was finally terminated at an interview between Lord Ashley and Goulburn on February 24, 1830. Babbage made the following notes on the government's decision, as described to him by Lord Ashley:

Government would not pledge themselves to complete the machine.

Government were willing to declare the machine their property.

Government were willing to advance 3000 more than that already granted [apparently this refers to the £3000 authorized on December 3, 1829].

At the end when it is completed they were most willing to attend to my claim for remuneration. 102

Although this understanding was still somewhat vague, it was enough to satisfy Babbage, and he forgot his thoughts of abandoning the project. One point of considerable concern to him which had not been resolved, was his desire not to be involved in the payment of Clement's bills. Although Babbage could not get the government to pay Clement directly, he did manage to bring about another aspect of his plan, namely that the bills would be examined on behalf of the government by engineers whom they appointed. In a letter to Goulburn dated March 19, 1830, Babbage suggested that the government name Bryan Donkin and Henry Maudsley to do this; he did not mention that these were the two men whom he and Clement had already agreed upon to arbitrate their disputes. On March 29, Babbage was informed that Goulburn had agreed to this. 103

That Babbage was not quite optimistic about the prospects of finishing his machine is revealed in a letter to Nathaniel Bowditch, dated March 20, 1830. Babbage first referred to his finally "inducing the government to place my Calculating machine on a proper footing." He then said. "The construction of a large machine is now going on under my direction for the government and will probably be completed in three years." 104

Exactly when Clement resumed work on the machine is not clear; the statement last quoted implies he had done so by March 20; but there is also a note from Babbage to Clement, dated July 5, 1830, which reads: "I request you will continue to execute the drawings and machinery for the Calculating machine under my supervision." 105 But it is possible that this note was meant not to get Clement to start the work again, but rather to give him formal assurance that he was still responsible directly to Babbage, rather than to the government. In any case, work on the machine began again on the order of one year after it had been halted.

It is to be noted and marveled at that although both Babbage and the government felt that the project had been put on a satisfactory basis, there was once again no written statement describing their agreement; indeed, this agreement had been arrived at through an interview with a third party.

With construction under way again, and with his earlier disputes with Clement and with the government out of the way, Babbage turned his attention to the acquisition of a site where the Difference Engine could be assembled and operated. On July 13, 1830, Babbage sent a report on this matter to the Chancellor of the Exchequer. In it, Babbage stated that nothing could "render doubtful the full success" of the machine, provided that both he and Clement lived a few more years. The time was nearly at hand when the parts of the machine which had been made would have to be assembled, and this could not be done in Clement's workshop. Since after its completion Babbage would need to superintend the operation of the engine, he argued that new workshops and space for assembly should be acquired near his own house (Clement's shop was about four miles away). He also argued that such a course would tend to preserve Clement's rather frail health. 106 On August 6, 1830, Edward Walpole wrote Babbage from the Treasury, saying that Goulburn did not accept Babbage's proposal. 107

The matter rested until December 21, 1830. On this date, Babbage wrote Lord Althorp, who had replaced Goulburn as Chancellor of the Exchequer, pointing out that at the last settlement of accounts there had still been £600 owing to Babbage, and that since then an additional £600 had become due to Clement. Clement had told Babbage that he was running short of funds, and would have to lay off some of the workmen if he was not paid soon. In this letter, Babbage also repeated his suggestion that work on the Difference Engine should be carried on near his house. 108

In reply, James Stewart wrote Babbage from the Treasury on December 24, 1830, saying that the Treasury would pay Babbage an additional £600 if he would declare the machine to be the property of the government. 109 Evidently the government simply wanted a written statement to this effect from Babbage, for the same day Stewart also wrote to the Royal Society, informing them "that the machine is the property of Government and consequently my Lords [ Commissioners of the Treasury ] propose to defray the further expense necessary to its completion." 110 Stewart also told them that Babbage was to be paid an additional £600, and requested the Royal Society to report again on the progress on the Difference Engine and estimate the additional money it would cost.

In Babbage's reply to Stewart's letter to him, he stated that it had been understood at the interview between Lord Ashley and Lord Goulburn in February, 1830, that the machine belonged to the government, and that they would pay all expenses incurred in its construction, this being in remarkable agreement with the points made in Stewart's letter to the Royal Society. 111 Stewart replied again on December 31, informing Babbage that the payment of another 600 pounds had been authorized. 112

Babbage, meanwhile, had continued to explore the possibility of new workshops on his own. In December, 1830, he had Charles Jearrad, surveyor, inspect several possible sites near Babbage's house; in early January, 1831, they decided that the only one suitable was some space in Babbage's own garden. 113 On January 19, Babbage wrote Lord Althorp (Chancellor of the Exchequer) arguing again the desirability of the move, reporting his findings, and estimating the cost of construction and. other expenses at £2250. 114

Early in February new difficulties arose involving Clement, this time involving a quarrel between him and a drafting assistant, C.G. Jarvis. Jarvis (who Babbage later hired as his chief assistant on the Analytical Engine) wrote Babbage in early February, 1831, saying:

It should be borne in mind that the inventor of a machine and the maker of it have two distinct ends to attain. The object of the first is to make the machine as complete as possible. The object of the second - and we have no right to expect he will be influenced by any other feeling - is profit; to gain as much as possible by making the machine; and it is his interest to make it as complicated as he is permitted to make it. I am fully aware how far these observations may do me injury. But they are made, Sir, whether well or ill judged, for your good. 115

Jarvis had resigned from Clement's employment by February 19, but in a letter to Babbage on that day, he stated that the only major cause was a disagreement over his salary; a compromise salary was proposed for Babbage's approval. In another letter a short time later, Jarvis stated that the fault in the salary dispute lay with Donkin and Field (the latter had become co-inspector of Clement's bills upon Maudsley's death earlier in the month), since they had refused to let Clement pay a salary higher than that for an ordinary draftsman. Eventually Jarvis was rehired. 116

On March 26, 1831, the Royal Society issued the new report on the progress of the Difference Engine that had been requested by Stewart on December 24, 1830; the Council of the Society had again appointed a special Committee. They stated that "the various parts of the Machine appear to them to have been executed with the greatest possible degree of perfection as to workmanship," and that the bills had been carefully checked. In regard to the question of building a new workshop for the engine, they considered the reasons advanced for the move by Babbage to be valid, and the plans he had suggested to be sound. As to the probable future expense of the Difference Engine, they forwarded an estimate by Brunel, who said that the new arrangements would cost about £2000 initially, and then about £2000 to 2500 per year; £8000 total additional funds would probably be ample, but the government should allow for as much as £12,000. 117

For the next two years, work on the Difference Engine proceeded fairly routinely. Babbage received another £1000 to pay clement in July, 1831, 118 and almost £2000 in September, 1831. 119 In August, 1831, Babbage urged that the new workshops be in a large permanent building, as space would be needed for the staff necessary to produce such things as the Nautical Almanac. 120 In March, 1832, Jarvis wrote Babbage criticising Clement's plan for a glass case for the machine from which the printing mechanism would stick out, since this would result in an appearance "as grotesque as that of a stuffed tiger, the body of which was encased in glass, and the tail left dangling outside through a hole made for that purpose." 121

As the new fire-proof building to hold the workshops progressed, Babbage began to plan its use. It was intended that Clement and his family actually live on the premises. On July 6, 1832, Clement, responding to a request from Babbage, sent him an estimate of what it would cost him to move. He wanted £350 for moving his tools to the new workshop and back when the work was finished, £130 for furniture, and an extra £660 per year "as compensation for having a divided business, keeping up an extra Establishment," and extra travel expenses. Clement also wanted some alterations made in the living quarters of the new building. 122

Babbage forwarded Clement's memorandum to the Treasury. On September 14, James Stewart replied, saying that Clement's demands were "unreasonable and inadmissible." 123 The Treasury would pay the actual expenses of moving the engine and tools; as for the other items, perhaps it would be cheaper to have Clement live at his own house; in this case the government would pay him two pounds per week for extra travel expenses; the other items were disallowed. Babbage forwarded a copy of this letter to Clement, who replied on October 12, suggesting that the matter be arbitrated by Donkin and Field. 124

Exactly what happened between October, 1832, and March, 1833, is difficult to reconstruct from the partial and somewhat conflicting accounts given by the various parties, but the following seems to be true.

After Clement's letter of October 12, Babbage several times tried to get Clement to make some alternate proposal on moving himself and the Engine to the East Street building, but Clement did not respond. 125 Early in 1833, Clement drew up his bill for work done between July 1 and December 31, 1832. On February 8, 1833, Donkin and Field examined the relevant parts of the machine in Clement's shop, and then proceeded with Clement to Babbage's house, where they examined a section of the Engine which had been assembled and could be operated (doubtless corresponding to the extant section); they found the material to be satisfactory. 126

On February 26, Donkin and Field approved Clement's bill, and on February 27, he submitted it to Babbage. According to Clement, Babbage said that "he would not present my account to Government unless I would give him some other proposition for my removal to East Street; I told him the very great inconvenience that I should be put to made me decline going there altogether." 127

According to Babbage, Clement not only did. not give such a definite answer on the question of removal, but "ultimately he had refused even to write a letter to me to state that he declines giving me any answer." 128

Babbage evidently once again found that he "moral difficulties" of the project were an onerous burden, and that disagreements over financial transactions with Clement interfered with his supervision of its actual construction, and he returned to his earlier conviction that satisfactory progress would be made only if the government paid Clement directly, Accordingly, when Clement again demanded payment on March 20, Babbage told him that he would forward the latest bill to the Treasury, and that as soon as he received payment, he would transfer it to Clement, but that he would no longer make advances from his own money. 129

Clement replied, quite correctly, that he had had no dealings with the Treasury, and that as Babbage had given him all instructions and orders, he was personally responsible for paying the bill. Clement declared that he could not proceed with the machine unless someone took responsibility. Accordingly, the following day. Clement laid off the workmen employed in his shop and halted all construction. 130

Babbage must have expected this result. Apparently he had decided that he could no longer serve as a financial middle man between Clement and the government, and decided that the government would agree to other arrangements if it was necessary in order for the work to continue. This is exactly what happened. Donkin, acting as intermediary, soon got Clement and the government to agree in principle that the latter would take direct responsibility for the cost of the machine, and the former would proceed with its construction. 131 In practice, the matter was not worked out so swiftly. Not until May 29 did the Treasury make an explicit commitment to pay Clement's old bill and give him direct authorization to proceed, as soon as the finished parts of the machine were deposited in the new building. 132 Clement on the other hand responded to this proposal by insisting that he be paid in full before any parts of the engine were moved. 133

The matter rested without progress for some time, 134 but on July 22, 1833, Clement wrote a long letter to the Treasury, giving his own version of everything that had happened to date, and proposing what future course should be followed. He argued that his bill for the period ending December 31, 1832 had been approved and due several months earlier, and should be paid right away; further, it would be more convenient for the engineers to examine the work done between January 1, 1833, and March, when the work stopped, before it was moved to the new building; after the bill for that period was approved, the finished parts and unnecessary drawings could be moved, and then the Treasury could pay the bill. Clement also said that he would proceed with construction of the Difference Engine under Babbage's direction if the Treasury instructed him to, but he stressed the need for new procedures that would assure the prompt payment of his bills. 135

The Treasury responded on August 13 with a minute directing that the £l782/11/4 due to Clement for work done up to December 31, 1832, should be paid to him forthwith, and that when the completed parts and drawings not needed in Clement's shop were deposited in East Street, they would pay his bill for January through March, 1833, the implication being that the work would be inspected after it was moved. 136

On August 25, C.G. Jarvis, who had formerly worked on the Difference Engine as an assistant to Clement, wrote Babbage, suggesting that. if the machine was to be finished within any reasonable time it would be necessary to adopt a new procedure whereby the plans and working drawings would be executed in the new workshop under Babbage's immediate supervision, and then manufacture of the various parts could be contracted out to a variety of people, so that work on various sections could proceed simultaneously. Jarvis then continued with the following passage, highly revealing of his feelings toward Clement:

I am aware there will be great opposition to any such plan as this, and that every thing will be said and every thing will be done by more than one person to prevent its adoptions this I do not wonder at. To a man who although inactive and unenterprising loves money, it must be very agreeable to construct a newly invented machine, the cost of the parts of which cannot be taxed; and still more agreeable to be able to charge for time expended upon arranging the parts of that machine without the possibility of the useful employment of that time being disputed, and to doze over the construction year after year for the purpose of making one thing after another, and thus without any inconvenient exertion to gain the profit upon all; but it is not to the interest of the inventor that this should be suffered. His credit requires his invention to be completed with as small an outlay of time and money as possible; and his interest is any thing but promoted when his invention is placed at the disposal of persons who do not even know the names or purposes of the several parts without appealing to better heads than their own. 137

Exactly how Babbage responded to this proposal is not clear, but it is clear that he valued Jarvis' abilities, and tried to persuade him to return to working on the Difference Engine under Clement when construction was continued. In a letter to Babbage on September 11, Jarvis expressed his disinclination to do so, despite his gratitude to and respect for Babbage, in even stronger terms:

Now let me consider what my situation would be if I returned. I must devote all my attention and care to this machine because, if any thing was made to a drawing which did not answer its purpose, I should incur the principal share of the blame as being necessarily most familiar with the details, whereas all the praise which perfection would secure would attach to Mr. Clement, who would come over now and then an sanction my plan only when he could not substitute any of his own, either better or worse; and I should have the indescribable satisfaction of knowing that I was labouring to increase the credit of a man who was envious of my talents and jealous of my influence, whose interest and inclination it would be to use every method in his power, however mean and mortifying, to guard against the suspicion of my possessing ability, and who would be paid about four times as much as myself for generously condescending to reap the fruits of my exertions. No! Whatever situation circumstances may force me into I will bear as best I may; but I will never, if I know it, become a party to my own degradation. 138

In the meantime, the process of moving the appropriate material to East Street proceeded with incredible slowness, for reasons that cannot be determined. On December 4, 1833, Babbage wrote Clement, saying that he understood that preparations for the move were nearly complete, and asking that a day be agreed upon for the move itself. 139 On January 10, 1834, Clement wrote to James Stewart, at the Treasury, to say that preparations for the move were complete, but that it would be much more convenient for the engineers to make their examination before the parts were packed up. 140 This information was forwarded by Stewart to Babbage, who wrote Donkin and Field on February 4, requesting that they make the examination. 141

What happened during the next six months is not clear, but on July 6, 1834, Babbage wrote to Donkin, saying that the parts and drawings were now in the new building, but that they needed to be examined before he could officially take charge of them. 142

Finally, on July 16, 1834, Babbage wrote Stewart to inform the Treasury that the material had been examined and delivered into his charge the day before; he pointed out that no progress had been made since March, 1833, and asked for further instructions. In a private cover note to Stewart, Babbage said "The drawings and parts of the Engine are at length in a place of safety. I am almost worn out with annoyance and disgust at the whole affair. 143

Before turning to the final phase of the Difference Engine project, we must consider two other matters from earlier in the year which shed some light on the public view of the Difference Engine.

In an undated letter evidently written in the later part of 1833, Dionysius Lardner (the immensely prolific popularizer of science) informed Babbage that he wished to consult him "respecting some steps to get up an contrivance for explaining the Machine at popular lectures." 144 In about December, 1833, Babbage wrote to Alexander von Humbolt in Berlin, saying that he and Lardner had been cooperating on preparing lectures on the Difference Engine and the mechanical notation which Lardner was to deliver in Manchester, Leeds, "and several other large manufacturing towns" through Easter; but after that Lardner could deliver them in Berlin, if Humbolt cared to invite him. 145

On February 16, 1834, Lardner reported to Babbage from Manchester that the first lecture had been a great success, but that he feared he could not complete the exposition in three lectures. 146 At the end of March, Lardner wrote Babbage that more than 5000 people had thus far heard the lectures, and that he would present them again at the Royal Institution in London in April and May. 147 By this time, it had also been arranged for Lardner to write an article on the Difference Engine for the Edinburgh Review, but he complained that he had had no time to work on it. In April and May, Lardner and Babbage corresponded about the article, and Babbage took a large hand in preparing it. 148 The article finally appeared in the July, 1834, issue of the Edinburgh Review, 149 and it formed much the most competent and extensive description of both the background and the actual operation of the Difference Engine published up to the present day.

As far as one can tell, Lardner took no direct part in mediating between Babbage, Clement and the government, although he was highly interested in seeing the Difference Engine completed. But in this regard, there is a most interesting passage at the end of his Edinburgh Review article, one which clearly was not submitted for Babbage's approval, and, indeed, was directed more toward Babbage himself than toward other readers. Lardner mentioned that construction had been halted for a considerable period and showed no signs of being soon resumed. He said that Babbage ought to have suggested to the government exactly what arrangements would be most conducive to the completion of the machine, but he had not done so:

On the contrary, it is said that he has of late almost withdrawn from all interference on the subject, either with the Government or the engineer. Does not Mr. Babbage perceive the inference which the world will draw from this course of conduct? Does he not see that they will impute to it a distrust of his own power, or even to a consciousness of his own inability to complete what he has begun? We feel assured that such is not the case; and we are anxious, equally for the sake of science, and for Mr. Babbage's own reputation, that the mystery - for such it must be regarded - should be cleared up; and that all obstructions to the progress of the undertaking should immediately be removed. Does this supineness and apparent indifference, so incompatible with the known character of Mr. Babbage, arise from any feeling of dissatisfaction at the existing arrangements between himself and the Government? If such be the actual cause of the delay (and we believe that, in some degree, it is so), we cannot remain from expressing our surprise that he does not adopt the candid and straightforward course of declaring the grounds of his discontent, and explaining the arrangement which he desire to be adopted. 150

Some further interesting light is shed on the Difference Engine and its reputation by a letter to Babbage from Richard Wright, dated June 18, 1834. Wright had formerly worked on the machine under Clement, and he wrote to tell Babbage that he had subsequently gotten a job in a Manchester factory through Joseph Whitworth; Whitworth, later Sir Joseph Whitworth, had himself worked in Clement's shop during 1831 to 1833, 151 and had subsequently become a partner in the Manchester firm where Wright was employed. Wright said that the fact that he had worked on the Difference Engine had been a great help to him, since there "is much talk about the Machine here, so much so that a Man who has worked at it has a greater chance of the best work, and I am proud to say I am getting more wages than any other workman in the factory." 152

Another interesting fact revealed in this letter is that Babbage had. been considering hiring someone to replace Clement in charge of construction, one candidate being Wright. Wright said that he was confident that he could finish the machine "with workmanship equal to that which is done, and I think.I shall not exaggerate in saying with one half the trouble to yourself, one third the time, and one fourth-the Expense." 153

Returning to the fate of the construction of the Difference Engine itself, as stated above, Babbage reported on July 16, 1834, that the finished parts were back in his possession, and asked the Treasury for instructions; one reason he felt the need for new authorization was that in July, a new government was formed, although it lasted only until December, and Babbage felt the need for a new sanction to proceed.

On August 16, James Stewart replied, telling Babbage that the payment of an additional £1200 to Clement had been authorized, to bring the accounts up to date, and giving Babbage authority to proceed with construction. 154

This did not happen. The reasons were many and complicated, and no fully accurate explanation can be reconstructed, but some of the reasons can be given here.

Babbage no longer felt it possible to work effectively with Clement, yet he was reluctant to try and teach a new man what was wanted. Babbage had already spent many more years on the project than he had originally intended, and he had had to forego many other activities, some directed toward science and some toward profit. He was fed up with having to deal from a position of weakness with a series of governments which often seemed to have neither understanding nor enthusiasm for the. project. Despite the fact that Babbage had lost money because of the Difference Engine, he was thought by many people to have been paid for his work. Further, despite all of these sacrifices and annoyances, Babbage had received neither reward nor honor for his time and energy, indeed not even an expression of gratitude.

However, all of these factors had been present to a greater or lesser degree in previous years, and the crucial factor was a new development which undermined Babbage's deep interest in the Difference Engine, an interest which previously had brought him to overcome such obstacles; this development was the invention of the Analytical Engine. The way in which the Analytical Engine. (which was not in fact called this until many years later) emerged out of Babbage's work on the Difference Engine and then developed on its own is the subject of the next chapter. What is crucial at this point is that in September, 1834, Babbage began working in a new direction, though without yet knowing just where he was going, and his interest in the Difference Engine steadily waned.

At first, Babbage simply wished to inform the government of the invention of the new machine so that they could decide whether they wished him to continue building the old one. Babbage wrote twice in September and again in October, 1834, to Lord Melbourne, the Prime Minister, requesting an interview and suggesting that Melbourne ought to personally inspect the machine. Melbourne showed some interest, but his government was thrown into crisis, and he was out of office by December with no interview having taken place. 155

The Whig government of Melbourne was replaced by the Tory government of Sir Robert Peel, who also served as his own Chancellor of the Exchequer. The Duke of Wellington served as Foreign Secretary, and on December 17, 1834, Babbage wrote to him, saying:

Sir Robert Peel's known opinions upon science render me unwilling to apply to him in the first instance, and my object in applying to your Grace is to entreat you to procure for me a decision; after the delay and neglect I have experienced, the nature of that decision is of comparatively minor importance. 156

On December 18, Wellington replied, asking Babbage just what it was he wished him to do. Babbage responded by preparing an important paper dated December 23, entitled "Statement addressed to the Duke of Wellington respecting the Calculating Engine. 157

Babbage began by summarizing the first ten years of the project, and the personal and financial sacrifices he had had to make. He then stated that the successful operation of the section of the machine assembled in 1832 had shown the soundness of his plans and of the work done. Whereas it would have been reasonable to expect that the government would recognize and honor this "first conversion of mental into mechanical processes," they chose instead to ignore it.

Babbage then laid out the four different courses that could be followed. First, the government could request that Babbage continue to supervise Clement in the construction of the machine; Babbage said that this would be virtually impossible, implying that present relations with Clement make it so. Second, the government might suggest that Clement be replaced by another engineer; Babbage commented that this would be much more successful, but that it would call for sacrifices from him which he was not willing to make; he hinted, however, that he might agree to this plan if the government would in some way reward him. Third, the government might find someone other than Babbage to supervise construction; Babbage said that this would be a course of "doubtful expediency," but that if they wished to follow it, he would fully cooperate. Finally, it might be decided to abandon the project; Babbage predicted that if this were done there would probably be a Parliamentary inquiry which would end up unjustly blaming Babbage for squandering large sums of public moneys but, Babbage said, "I have experienced the injustice of my countrymen, and if need be I shall not quail before a greater exercise of it."

Babbage then announced his recent invention of "a totally new engine possessing much more extensive powers, and capable of calculations of a nature far more complicated." But, he hastened to add, although much more powerful than the old machine, "it is not intended to supersede it, on the contrary, it will greatly extend its range and usefulness." He declared his intention to complete the design of the new machine so that it could be constructed from the drawings "at any future period."

Babbage expressed doubt that he could ever afford to build the new machine himself, and clearly he did not expect that the English government would support it. Curiously, however, he warned that some foreign government might decide to sponsor the construction of the new machine in their own country, and that foreign workmen would learn about the best of English machining tools and techniques the result would be "that a school of mechanical engineers might arise whose influence would give a lasting impulse to the whole of the manufactures of that country, and that the secondary consequences of the acquisition of that Calculating Engine might become more valuable than the primary object for which it was sought."

Despite this suggestion that the construction of the Analytical Engine might easily pay for itself in the value of its technological spin-off alone, Babbage did not in fact request or even suggest that the English government should underwrite it. Indeed, the thrust of the whole Statement to Wellington is rather perplexing; although Babbage requested as rapid a decision on the Difference Engine as possible, the effect of the letter was to argue that any of the decisions he enumerated would be wrong.

Evidently Wellington also found Babbage's statement perplexing, for there was no response. On April 7, 1835, Babbage sent to Sir Robert Peel, Prime Minister, a copy of the statement to Wellington, again appealing for a prompt decision; 158 but Peel's government soon fell, and Viscount Melbourne (William Lamb) returned to head a new one. Babbage sent him another copy of his statement with the same appeal on May 4, 1835. 159

On May 15, 1835 there was a Parliamentary debate on the Civil Contingencies funds, out of which Babbage had been paid. It was charged that a number of projects that had been supported had constituted "unprincipled waste and squandering public money," and Babbage's machine was mentioned among these. In reply, Spring Rice, the new Chancellor of the Exchequer, said that the Difference Engine was "a most distinguished scientific discovery," and stated that the money had been used only to pay the expenses of construction, not "a single farthing" going to Babbage himself. In response, another Member (Mr. Warburton) expressed his apprehensions "lest the Gentleman, who had produced the invention, greatly desirous to bring his machine to as great a degree of accuracy as possible, and successive improvements occurring to himself, should go on, step by step, and be led on to greater expense than would be proper." He suggested that the Treasury call for a report on the present state of the machine. 160

On April 20, Spring Rice wrote to Babbage, inquiring whether he wanted his statement to the Duke of Wellington to be made a public document. Rice also mentioned the questions on the machine in the House of Commons, and suggested that in order to answer them the government could refer again to the Royal Society for the report on progress. 161 In his reply, dated May 22, and in an interview on May 26, Babbage argued that nothing would be gained by referring the question to the Royal Society. Babbage said that the most progress on construction would be made if the work were done in the new East Street workshop under the control of Jarvis, and under an agreement which gave incentive to the workmen to finish the machine rapidly. 162

Apparently Jarvis had been working for Babbage on the drawings of the new engine since the fall of 1834; in November, 1835, Jarvis was offered another job at higher pages which would have required him to move abroad; the result was a new one year renewable contract between Jarvis and Babbage, wages being paid by Babbage personally at the rate of £l/l/8 per day. 163

On January 14,1836, after more than a year's delay, Babbage finally received from Spring Rice a letter responding to Babbage's statement to the Duke of Wellington. In this letter Rice said the following:

The conclusion to be drawn from the statement alluded to is that you have invented a machine of much more extensive powers and capable of calculations of a nature far more complicated than those to be performed by the machine at present in progress; and you request to be informed whether Government would undertake to defray the expense of this new machine. 164

At this point Babbage wrote in the margin of the letter: "I never did make this request nor ever thought of doing so."

Rice further stated that the government would not feel justified in considering support for the construction of the new machine until the old one was finished. Rice anticipated that there would be further questions raised in Parliament, and again suggested that in order to be able to answer them the government should ask for a report from the Royal Society.

Babbage replied on February 2, 1836. He said that the state of the new engine at the time he had written to Wellington had been such that it would have increased the usefulness of a Difference Engine, but that subsequently the new machine had progressed to a point where it not only can do many things that the old machine couldn't, but "it also performs all those calculations which were peculiar to the old engine both in less time and to a greater extent," and, in fact, "it completely supersedes the old Engine." Further, Babbage said, the new machine had become so mechanically simple that if it were desired only to have a machine with the powers of the Difference Engine, still "it would be more economical to construct such an engine on the new principles than to finish the one already partly constructed." Babbage pointed out that it was fairly common for machines to become obsolete very rapidly, sometimes even before they were completed. Babbage concluded his letter by saying that his report was merely for the information of the government, and that "I wish distinctly to state that I do not entertain the slightest doubt of the success of the first Engine, nor do I intend it as an application to finish the one or to construct the other." 165

From Rice's letter to Babbage of January 14, it had appeared that the government fully intended to support the completion of the Difference Engine, despite the delays and difficulties which had beset it. But Babbage's reply seems, understandably, to have thrown them into some confusion, and they neither replied to Babbage nor asked the Royal Society for a report. The next move came, after a long delay, from Babbage, who wrote to Lord Melbourne, still the Prime Minister, on July 26, 1838. Babbage appealed "for the last time to ask for no favor, but to ask for that which it is an injustice to withhold from me: a decision." He said that he had been asking for a definite decision for five years, and "if the question has now become more difficult because I have invented superior mechanism which supersedes that already partly erected, this consequence has arisen from that very delay against which I have repeatedly remonstrated." 166

An assistant to Lord Melbourne (whose name cannot be deciphered) replied to Babbage on August 16, 1838, saying that the government did not understand what Babbage wanted them to decide. Did he wish to finish the old machine or to start the new one? What did he think either of these courses would cost? 167

Babbage replied on October 21, 1838 (he had not received the August 16 letter until he returned "from a tour of the Highlands"). He said that he had never applied for support for the new engine; not being a Professional engineer, he declined to estimate the cost of either machine. The only question he wished to have decided was: "whether the government require me to superintend the completion" of the Difference Engine "or whether they intend to discontinue it altogether." 168

For unknown reasons, the government made no further response, and Babbage apparently gave up hope of extracting from them the decision that he wanted. He made no further advances for well over three years, until Sir Robert Peel had again become Prime Minister. Then, on January 22, 1842, Babbage wrote to Peel and asked if the understanding implied by his early relationship with the government (that he would work on the machine until it was finished) could be considered as ended. 169

On January 29, 1842, Sir George Clerk replied to Babbage from the Treasury, saying that Peel was at the time too busy to make any decision in the matter, but that he would attend to it as soon as he could. As expressed by Clerk, the choice was between completing the Difference Engine on the old principles or building a new difference machine on the new simpler principles. He said that the Treasury understood that the cost would be about £8000, and suggested once again that the matter be referred to the Royal Society. 170

Babbage responded on February 4, 1842, writing to Clerk that he had "never either asked or offered to make any other Machine for the Government" than the original Difference Engine; all that was to be decided was whether it should be abandoned. Further, the estimate of £8000 was probably much too low. There was no reply to this letter; Babbage tried again to get some response from Peel on July 9, August 12, and October 8, but with no success. 171

Although not yet responding to Babbage's letters, the government had by this point begun to consider the matter. On September 15 Henry Goulburn, who was once again Chancellor of the Exchequer, asked the opinion of Sir George Airy, the Astronomer Royal, as to the probable utility of the Difference Engine, and the propriety of spending more money on it; Airy's reply was "that it was worthless." 172 Curiously, in 1822, while an undergraduate at Cambridge, Airy had heard of Babbage's recent invention of the Difference Engine, and had himself sketched out some ideas for calculating machines. 173 However, by 1837, Airy's opinion of the Difference Engine was that "the thing is a humbug," 174

Finally on November 3, Goulburn wrote to Babbage, saying that he and Peel felt that they could not justify the additional estimated expense to complete the Difference Engine, although they greatly regretted abandoning a machine "on which so much scientific ingenuity and labour has been bestowed." But they hoped "that by withdrawing all claim on the part of the Government to the machine as at present constructed and by placing it at your entire disposal, we may to a degree assist your future exertions in the cause of science." 175

On November 6, Babbage replied to Goulburn, refusing the offer of the government to give him the parts of the Difference Engine. 176 The same day he wrote also to Peel; he said that he inferred that the government might be more interested in supporting the construction of the Analytical Engine, and that they might be prepared to consider Babbage's claim for remuneration. He requested an interview with Peel to discuss these matters. 177

This interview took place on November 11. The only record of it is several pages of "Recollections" recorded shortly afterwards by Babbage. 178 It appears that Babbage focused on the statement reported to him by Lord Ashley on the basis of his interview with Goulburn when he was Chancellor of the Exchequer in February, 1830, to the effect that "at the end when it is completed they were most willing to attend to my claim for remuneration." 179 Babbage had written to Lord Ashley on January 17, 1842, asking him to confirm that this had been said; in the same letter he remarked that the proposal had been totally unexpected by him. 180

From the meager record of the 1830 understanding, it is not possible to determine if the government was undertaking to simply repay the expenses of the Difference Engine when it was finished, or whether they were agreeing to reward Babbage himself for the work he had done.

Clearly, in 1842, Babbage thought both these things were implied.

Thus it seems that his intentions in the interview with Peel in November were to determine if the government intended to reward him, since, as he saw it, the Difference Engine had been abandoned as the result of the government's decision, and through no fault of his own. He was then going to make some proposal for building either the Analytical Engine or a new type of Difference Engine. 181

In fact, although Babbage summarized at length the many sacrifices he had made, and described how many other men of science had been rewarded with either money or honor, Peel denied that Babbage had any claim to such reward himself. At this, Babbage "merely remarked that I considered myself to have been treated with great injustice, but that as he was of a different opinion, I could not help myself, on which I got up and wished him good morning." Babbage made no proposal for future arrangements. 182

Thus ended the construction of the Difference Engine finally and officially. Babbage refused to accept the completed section from the government as a gift; he recommended instead "that the finished part of the original Difference Engine and all the drawings in as complete a state as possible ought to be carefully preserved for the history of science; and that the partially manufactured materials are of comparatively insignificant value." 183

The assembled portion was placed in the Museum of King's College, London, along with the drawings. The unassembled parts were sold to Babbage for their value as scrap metal; he also bought one tool and several drawing boards. The extent of the parts of the engine which were completed but not assembled is difficult to judge, as there is nowhere any detailed description of them. However, in November, 1834, Babbage had stated that there were "above ten thousand pieces of the Engine" stored in the new workshop. 184 This number seems implausibly high, even though it doubtless included every screw. But the indirect evidence suggests that it comprised all or nearly all of the parts of the calculating section of the full scale engine, some ten times the magnitude of the section actually assembled, but included nothing from the printing mechanism. 185 The great majority of these pieces were eventually cut up or melted down as scrap. 186

No doubt Babbage felt considerable relief at finally having the matter settled, although also considerable distress at the ingratitude of the government and the failure of his many years of work to bear tangible fruit. The ambivalence felt by Babbage and his friends found expression in the judgment rendered on the entire Difference Engine project in a letter to Babbage from his brother-in-law and supporter, Wolryche Whitmore, dated November 21, 1842, one which could equally well have been a judgment of most of Babbage's life:

Had I not long been convinced that the decision the Government have come to, e.g. abandoning the old machine, was the only one to which, under the circumstances, they could come, I should have been sadly disappointed by your letter. That you should have occupied so much time and expended so large an amount of talent and ingenuity on a machine now superseded and rendered comparatively of smaller moment is much to be lamented but you are your own rival, and exercise too much ingenuity for the age in which you live and your own pecuniary or temporary interests. That posterity will render justice to your talents I do not doubt, but unfortunately such considerations do not add either to ones wealth or consideration in the present age. I scarcely know what to say on this perplexing subject; that you should continue all your life to expend so much talent and money on an undertaking which however ingenious is never in your lifetime likely to be brought practically to a conclusion seems unfortunate, but you are and must be as well the best as in truth the only judge in the matter. 187


#1 Limerick by Maurice Evan Hare, quoted in The Modern Dictionary of Quotations. ed. Robin Hyman, London, 1962, p.128.

#2 B.M., Vol. I, ff. 95-96.

#3 See B.M., Vol. I, ff. 52-53. 270-271.

#4 On Babbage's role in founding the Astronomical Society, see B.M., Vol. I, ff. 217. 227-28. 237-38, 241-42.

#5 B.M., Vol. I, ff. 241-42.

#6 The account given in P.L.P., p. 42, the only one ever published, may be regarded as apocryphal, having been written over forty years after the fact, and presented as second hand. Yet it may simply have been set ten years too early, and in the wrong Society. In any case, the event described was not the invention of a calculating machine, but the recognition that one might be invented.

#7 Buxton, Vol. VII.

#8 Buxton, Vol, VII. This passage is from the introduction to a paper Babbage intended to write, entitled "History of the Invention of the Calculating Engine," but he never continued it.

#9 Buxton, Vol. IX. This is from the introduction to an unwritten paper to be called "The science of Number reduced to Mechanism." The existing introductory section is not dated, but elsewhere in the Buxton papers there is a loose sheet, dated November 26, 1839, outlining a paper of the same name; it is clear that the two belong together.

#10 Buxton, Vol. IX.

#11 See B.C.E., p. 211.

#12 Buxton, Vol. VII.

#13 B.M., Vol. I, ff. 415-416.

#14 Again, from the November, 1822 paper; Buxton, Vol. III.

#15 Buxton, Vol. VIII. In a note added to the first page of this manuscript sketch, and dated 1840, Babbage referred to it as "the first idea and earliest sketch of the Calculating Engine." The original paper is not dated.

#16 Ibid.

#17 Buxton, Vol. III.

#18 B.M., Vol. I, ff. 398-99.

#19 The next six paragraphs are all based on the November, 1822. manuscript: Buxton, Vol. III.

#20 See below.

#21 B.C.E., pp. 212-13.

#22 Buxton, Vol. III.

#23 B.C.E., p. 224.

#24 B.C.E., p. 225.

#25 H.C.E., p. 211.

#26 B.C.E., p. 213.

#27 P.L.P., p. 47.

#28 The "Note" was published in the Memoirs of the Astronomical Society, of London, Vol. I, Pt. II (1825), p. 309, and reprinted in B.C.E., p. 211.

#29 B.M., Vol. I, ff. 419-20.

#30 B.M., Vol. I, f. 423.

#31 Reprinted in B.C.E., pp. 212-15.

#32 Ibid.

#33 B.M., Vol. I, f. 425.

#34 B.M., Vol. I, ff. 431-432.

#35 The letter was reprinted in B.C.E., pp. 216-19.

#36 "Observations on the Application of Machinery to the Computation of Mathematical Tables," Memoirs of the Astronomical Society of London, Vol. I, Pt. II (1825), pp. 311-14; reprinted in B.C.E., p. 220-22.

#37 B.C.E., pp. 218-19.

#38 B.M., Vol. II, f. 144. The year is not given in the date on this letter, and the cataloguer of the correspondence has placed it in 1824. This may be correct, but the postmark looks more like 1822, and it is so dated here.

#39 B.M., Vol. II, ff. 8-9. Babbage marked his copy of the original letter; "given me by J.O. Martin."

#40 See above; B.M., Vol. I, f. 425. Gilbert was both Treasurer of the Royal Society and a Member of Commons.

#41 Parliamentry Papers, 1823 (370) VX, 9.

#42 Ibid.

#43 Ibid.

#44 B.M., Vol. I, ff. 433-34. The letter is not dated; the cataloguer has marked it as possibly written about August 20, 1822, but the reference to the "Parliamentary inquiry" make it more plausible that it is from about May, 1823.

#45 B.M., Vol. II, ff. 30-31.

#46 B.M.. Vol. II, f. 32.

#47 B.M., Vol. II, f. 39.

#48 Memoirs of the Astronomical Society of London, Vol. I, Pt. II (1825), pp. 509-12; reprinted in B.C.E., pp. 223-24.

#49 Statement of..the Circumstances Respecting Mr. Babbage's Calculating Machine, privately printed pamphlet, 1843, p. 5; a copy of the pamphlet is in the Buxton material. The "Statement" was reprinted in P.L.P. as Chapter VI; It was there said to have been "drawn up by-the late Sir. H. Nicolas" from Babbage's papers (p. 68).

#50 B.M., Vol. III, f. 285.

#51 B.M., Vol. II, f. 55; Davies Gilbert sent Babbage this copy of the letter.

#52 On Clement, see Samuel Smiles, Industrial Biography: Iron Workers and Tool-Makers, Boston, 1864, pp. 289-313. See also Chapter Four of this thesis.

#53 B.M., Vol. II, ff. 371-72.

#54 B.M., Vol. II, ff. 444-45. The draft of Babbage's letter is not dated, but internal evidence and its relation to other letters place it in late March or early April, 1827.

#55 B.M., Vol. III, f. 3.

#56 Memoirs and Correspondence of Major-General H.P. Babbage, London, 1910, p. 1. Maboth Moseley, in Irascible Genus (London, 1964), p. 83. has evidently misread H.P. Babbage's remarks on his mother's death, and places it in September.

#57 B.M., Vol. III, ff. 92-93.

#58 P.L.P., p. 72.

#59 B.M., Vol. III, ff. 114-15.

#60 P.L.P., p. 73.

#61 B.M., Vol. III, ff. 156-57, 163-65.

#62 Ibid.

#63 . B. C. S., p. 232.

#64 Taken from the full report, reprinted in B.C.E., pp. 233-35.

#65 B.C.E., p. 232.

#66 B.M., Vol. III, ff. 233-34.

#67 B.M., Vol. III, ff. 252-53.

#68 B.M., Vol. III, ff. 254-55.

#69 B.M., Vol. III, ff. 252-53.

#70 B.M., Vol. III, ff. 266-67.

#71 B.M., Vol. III, ff. 264-65.

#72 B.M.. Vol. III, f. 285.

#73 B.M., Vol. III, ff. 281-82.

#74 B.M., Vol. III, f. 310.

#75 These notes are: B.M., Vol. III, ff. 291-92, 310.

#76 B.M. , Vol. III, ff. 337-38.

#77 B.M., Vol. III, f: 419.

#78 Ibid.

#79 B.M., Vol. III, f. 463

#80 B.M., Vol. IV, f. 21.

#81 B.M., Vol. IV, ff. 57-58.

#82 B.M., Vol. V, ff. 25-26.

#83 B.M.,Vol. III, ff. 301-5; P.L.P., pp. 73-74.

#84 P.L.P., pp. 74-75.

#85 B.M., Vol. III, ff. 337-38.

#86 B.M., Vol. III, ff. 369-72.

#87 B.M., Vol. III. f. 404.

#88 B.M., Vol. III, f. 405.

#89 B.M., Vol. III, f. 413.

#90 B.M., Vol. III, f. 412.

#91 B.M., Vol. III, ff. 421-22.

#92 B.M., Vol. III, ff. 426-29.

#93 B.M., Vol. III, ff. 432-35.

#94 B.M., Vol. III, f. 445.

#95 B.M., Vol. III, ff. 451-52.

#96 B.M., Vol. III, ff. 459-60.

#97 B.M., Vol. III, ff. 455-56.

#98 B.M., Vol. III. ff. 459-60.

#99 B.M., Vol. III. f. 464.

#100 B.M., Vol. IV, ff. 10-11.

#101 Ibid.

#102 B.M., Vol. IV, ff. 69-70.

#103 B.M., Vol. IV, ff. 96, 105.

#104 B.M., Vol. IV, ff. 98-99.

#105 B.M., Vol. IV, f. 258.

#107 B.M., Vol, IV, f. 286.

#108 B.M., Vol. IV, f. 380.

#109 B.M., Vol. IV, f. 394.

#110 B.M.. Vol. IV. f. 524.

#111 B.M.. Vol. IV, f. 387. The letter is dated December 23, but this must be a mistake for the 24th or 25th.

#112 B.M., Vol, IV, f. 396.

#113 B.M., Vol. IV, ff. 384, 428, 431, 433.

#114 B.M., Vol. IV, ff. 447, 455-48.

#115 B.M., Vol. IV, ff. 419-20. The letter is undated, but its relation to other letters places it in early February,1831.

#116 B.M., Vol. IV, ff. 474-79, Vol. V, ff. 295-96.

#117 B.M., Vol. IV, ff. 513-15.

#118 B.M., Vol. V, ff. 25-266.

#119 B.M., Vol. VI, f. 125.

#120 B.M., Vol. V, ff. 63-65.

#121 B.M., Vol. V, f. 345.

#122 B.M., Vol. VI, ff. 6-8.

#123 B.M., Vol. VI, ff. 134-36.

#124 B.M.. Vol. VI, f. 168.

#125 B.M., Vol. VI, ff. 458-59.

#126 B.M., Vol. VII, ff. 16-17.

#127 Ibid.

#128 B.M., Vol. VI, ff. 458-59.

#129 B.M., Vol. VII, ff. 16-17.

#130 B.M., Vol. VI, f. 453.

#131 B.M., Vol. VI,.ff. 465, 480.

#132 B.M., Vol. VI, f. 549.

#133 B.M., Vol. VI. f. 557.

#134 According to Babbage, this was because Clement would not make any constructive proposals B.M., Vol, VII, f. 22.

#135 B.M., Vol. VII, ff. 16-17.

#136 B.M., Vol. VII, f. 28.

#137 B.M., Vol. VII, ff. 39-40.

#138 B.M., Vol. VII, ff. 58-59.

#139 B.M., Vol. VII, f. 96.

#140 B.M., Vol. VII, f. 186.

#141 B.M.. Vol. VII, f. 191.

#142 B.M., Vol. VII, f. 435. Replying on July 7 (f. 437), Donkin blamed three months of delay on "the obstinacy of Clement."

#143 B.M.. Vol. VII, ff. 449-50.

#144 B.M., Vol. VII, f. 203.

#145 B.M., Vol. VII, ff. 123-124.

#146 B.M., Vol. VII, ff. 208-09.

#147 B.M., Vol. VII, ff. 288-89.

#148 B.M., Vol. VII, ff. 335-36. 350.

#149 No. CXX, The article "Babbage's Calculating Engine," was reprinted in B.C.E., pp. 51-82.

#150 B.C.E., pp. 81-82.

#151 B.M., Vol. XV, ff. 264-65.

#152 B.M., Vol. VII, ff. 390-91.

#153 Ibid.

#154 B.M., Vol. VII, f. 451.

#155 B.M., Vol. VII, ff. 480-81, 484, 488.

#156 B.M., Vol. VII, ff. 520-21.

#157 B.M., Vol. VII, ff. 525-29.

#158 B.M., Vol. VIII, f. 74.

#159 B.M., Vol. VIII, f. 89.

#160 Eansard's Parliament Debates; Third Series, Vol. XXVII, 1154-55.

#161 B.M.. Vol. VIII, f. 100.

#162 B.M., Vol. VIII, ff. 101, 110, 112.

#163 B.M.., Vol. VIII, ff. 203-4.

#164 B.M., Vol. VIII, ff. 273-76.

#165 B.M., Vol. VIII, ff. 292-93.

#166 B.M., Vol. IX, f. 496.

#167 B.M., Vol. IX, ff. 518-19.

#168 B.M., Vol. X, f. 14.

#169 B.M., Vol. XI, f. 19.

#170 B.M., Vol. XI, ff. 29-30.

#171 B.M., Vol. XI, ff. 37, 128, 147.

#172 Autobiography of Sir George Biddell Airy, ed. Wilfrid Airy, Cambridge, England, 1896, p.152.

#173 Ibid., p. 37.

#174 The Diaries of William Charles Macready, ed. William Toynbee, New York, 1912, p. 410

#175 B.M., Vol. XI, ff. 172-73.

#176 B.M., Vol. XI, f. 178.

#177 B.M., Vol. XI, ff. 176-77.

#178 B.M., Vol. XI, ff. 189-94.

#179 B.M., Vol. IV, ff. 69-70.

#180 B.M., Vol. XI. f. 13.

#181 B.M.. Vol. XI, ff. 180-84.

#182 B.M., Vol. XI, ff. 189-94.

#183 B.M., Vol. XI, ff. 224-26.

#184 B.M., Vol. VII, f. 514.

#185 See, e.g. B.M., Vol. VII, ff. 39-40.

#186 Memoirs and Correspondence of Major-General H.P. Babbage, London, 1910, pp 224-25.

#187 B.M., Vol. VII, ff. 506-7. The year is not supplied on the letter, but is clear from the context, although the cataloguer has placed it in a much earlier volume.

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