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during the short administration of Lord Derby, and it led to no result. The time was unfortunate; a great political contest was impending, and before there was a lull in politics, so that the voice of Science could be heard, Lord Derby’s government was at an end.”

      〈MR. BABBAGE’S LETTER TO THE EARL OF DERBY.〉

      The following letter was then drawn up, and placed in Lord Derby’s hands by Lord Rosse:—

      June 8, 1852. MY LORD,

      I TAKE the liberty of drawing your Lordship’s attention to the subject of the construction of a Difference Engine, for {101} calculating and printing Astronomical and Nautical Tables, which was brought under the notice of the Government so far back as the year 1823, and upon which the Government of that day desired the opinion of the Royal Society.

      I annex a copy of the correspondence which took place at that time, and which your Lordship will observe was laid before Parliament.

      The Committee of the Royal Society, to which the subject was referred, reported generally that the invention was one “fully adequate to the attainment of the objects proposed by the inventor, and that they considered Mr. Babbage as highly deserving of public encouragement in the prosecution of his arduous undertaking.”—Report of Royal Society, 1 st May, 1823. Parliamentary Paper, 370, 22 nd May, 1823.

      And in a subsequent and more detailed Report, which I annex also, they state:—

      “The Committee have no intention of entering into any consideration of the abstract math­e­mat­i­cal principle on which the practicability of such a machine as Mr. Babbage’s relies, nor of its public utility when completed. They consider the former as not only sufficiently clear in itself, but as already admitted and acted on by the Council in their former proceedings. The latter they regard as obvious to every one who considers the immense advantage of accurate numerical Tables in all matters of calculation, especially in those which relate to Astronomy and Navigation, and the great variety and extent of those which it is the object and within the compass of Mr. Babbage’s Engine to calculate and print with perfect accuracy.”—Report of Committee of Royal Society, 12th Feb., 1829.

      Upon the first of these Reports, the Government determined to construct the machine, under my personal {102} superintendence and direction. The Engine was accordingly commenced and partially completed. Tables of figures were calculated, limited in extent only by the number of wheels put together.

      Delays, from various causes arose in the progress of the work, and great expenses were incurred. The machine was altogether new in design and construction, and required the utmost mechanical skill which could be obtained for its execution. “It involved,” to quote again from the Report of the Committee of the Royal Society, “the necessity of constructing, and in many instances inventing, tools and machinery of great expense and complexity (and in many instances of ingenious contrivances 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 true explanation both of the slow progress and of the cost of the work is clearly stated in this passage; and I may remark in passing, that the tools which were invented for the construction of the machine were afterwards found of utility, and that this anticipation of the Committee has been realized, as some of our most eminent mechanical engineers will readily testify.

      Similar circumstances will, I apprehend, always attend and prolong the period of bringing to perfection inventions which have no parallel in the previous history of mechanical {103} construction. The necessary science and skill specially acquired in executing such works must also, as experience is gained, suggest deviations from, and improvements in, the original plan of those works; and the adoption or rejection of such changes, especially under circumstances similar to those in which I was placed, often involves questions of the greatest difficulty and anxiety.

      From whatever cause, however, the delays and expenses arose, the result was that the Government was discouraged, and declined to proceed further with the work.

      Mr. Goulburn’s letter, intimating this decision to me, in 1842, will be found in the accompanying printed Statement. And that the impediments to the completion of the engine, described by the Royal Society, were those which influenced the Government in the determination they came to, I infer from the reason assigned by Mr. Goulburn for its discontinuance, viz., “the expense which would be necessary in order to render it either sat­is­fac­tory to yourself or generally useful.” I readily admit that the work could not have been rendered sat­is­fac­tory to myself unless I was free to introduce every improvement which experience and thought could suggest. But that even with this additional source of expense its general usefulness would have been impaired, I cannot assent to, for I believe, in the words of the Report I have already quoted, the “immense advantage of accurate Numerical Tables in all matters of calculation, especially in those which relate to Astronomy and Navigation, cannot, within any reasonable limits, be over-estimated.” As to the expense actually incurred upon the first Difference Engine, that of the Government was about 17,000 l. On my own part, and out of my own private resources, I have sacrificed upon this and other works of science upwards of 20,000 l. {104}

      From the date of Mr. Goulburn’s letter, nothing has been done towards the further completion of the Difference Engine by the Government or myself. So much of it as was completed was deposited in the Museum of King’s College, where it now remains.

      Three consequences have, however, resulted from my subsequent labours, to which I attach great importance.

      First, I have been led to conceive the most important elements of another Engine upon a new principle (the details of which are reduced accurately to paper), the power of which over the most complicated analytical operations appears nearly unlimited; but no portion of which is yet commenced. I have called this engine, in contradistinction to the other, the Analytical Engine.

      Secondly, I have invented and brought to maturity a system of signs for the explanation of machinery, which I have called Mechanical Notation, by means of which the drawings, the times of action, and the trains for the transmission of force, are expressed in a language at once simple and concise. Without the aid of this language I could not have invented the Analytical Engine; nor do I believe that any machinery of equal complexity can ever be contrived without the assistance of that or of some other equivalent language. The Difference Engine No. 2, to which I shall presently refer, is entirely described by its aid.

      Thirdly, in labouring to perfect this Analytical Machine of greater power and wider range of computation, I have discovered the means of simplifying and expediting the mechanical processes of the first or Difference Engine.

      After what has passed, I cannot expect the Government to undertake the construction of the Analytical Engine, and I do not offer it for that purpose. It is not so matured as to {105} enable any other person, without long previous training and application, even to attempt its execution; and on my own part, to superintend its construction would demand an amount of labour, anxiety, and time which could not, after the treatment I have received, be expected from me. I therefore make no such offer.

      But that I may fulfil to the utmost of my power the original expectation that I should be able to complete, for the Government, an Engine capable of calculating astronomical and nautical Tables with perfect accuracy, such as that which is described in the Reports of the Royal Society, I am willing to place at the disposal of Government (if they will undertake to execute a new Difference Engine) all those improvements which I have invented and have applied to the Analytical Engine. These comprise a complete series of drawings and explanatory notations, finished in 1849, of the Difference Engine No. 2—an instrument of greater power as well as of greater simplicity than that formerly commenced, and now in the possession of the Government.

      I have sacrificed time,

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