Section 6 of Passages from the Life of a Philosopher This is a LibriVox recording, or LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org. Passages from the Life of a Philosopher by Charles Babbage. Section 6. Difference Engine number 1. Part 2. Triangular Numbers. Perhaps my young friend may now ask me, what is the use of such tables? Until he has advanced further in his arithmetical studies, he must take for granted that they are of some use. The very table about which he has been reasoning possesses a special name. It is called a Table of Triangular Numbers. Almost every general collection of tables hitherto published contains portions of it of more or less extent. Above a century ago a volume in small quarto containing the first twenty thousand triangular numbers was published at the Hague by E. de Youngcourt, A.M., and Professor of Philosophy. I cannot resist quoting the author's enthusiastic expression of the happiness he enjoyed in composing his celebrated work. Quote, The trigonals, here to be found, and nowhere else, are exactly elaborate. Let the candid reader make the best of these numbers, and feel, if possible, in perusing my work the pleasures I had in composing it. A sweet joy may arise from such contemplations cannot be denied. Numbers and lines have many charms, unseen by vulgar eyes, and only discovered to the unwearyed and respectful sons of art, in features the serpentine line, who starts not at the name, produces beauty and love, and in numbers high powers and humble roots give soft delight. Low the raptured arithmetician, easily satisfied, he asks no Brussels lace, nor a coach in six. To calculate, contents his liveliest desires, and obedient numbers are within his reach. Unquote, Square numbers, I hope my young friend is acquainted with the fact that the product of any number multiplied by itself is called the square of that number. Thus, thirty-six is the product of six multiplied by six, and thirty-six is called the square of six. I would now recommend him to examine the series of square numbers one, four, nine, sixteen, twenty-five, thirty-six, forty-nine, sixty-four, et cetera, and to make for his own instruction the series of their first and second differences, and then to apply to it the same reasoning which has been already applied to the table of triangular numbers. Canon balls. When he feels that he has mastered that table, I shall be happy to accompany mamas darling to Woolwich or to Portsmouth where he will find some practical illustrations of the use of his newly acquired numbers. He will find, scattered about in the arsenal, various heaps of cannon balls, some of them triangular, others square, or oblong pyramids. Looking on the simplest form, the triangular pyramid, he will observe that it exactly represents his own heaps of marbles, placed each successively, one above another, until the top of the pyramid contains only a single ball. The new series thus formed by the addition of his own triangular numbers is, represented in a table where the first row contains the number one, the table one, the first difference of three, the second difference of three, and the third difference of one. In the second row the number is two, the table is four, the first difference is six, the second difference is four, the third difference is one. In the third row the number is three, the table is ten, the first difference is ten, the second difference is five, the third difference is one. In the fourth row the number is four, the table is twenty, the first difference is fifteen, the second difference is six. In the fifth row the number is five, the table is thirty-five, the first difference is twenty-one, in the sixth row the table is fifty-six. He will at once perceive that this table of the number of cannonballs contained in a triangular pyramid can be carried to any extent by simply adding successive differences, the third of which is constant. The next step will naturally be to inquire how any number in this table can be calculated by itself. A little consideration will lead him to a fair guess. A little industry will enable him to confirm his conjecture. Number in each pile. It will be observed at page forty-nine that in order to find independently any number of the table of the price of butcher's meat, the following rule was observed. Take the number whose tabular number is required, multiply it by the first difference. The product is equal to the required tabular number. Again at page fifty-three the rule for finding any triangular number was take the number of the group, five, add one to this number and become six, multiply these two numbers together, thirty, divide the product by two, fifteen. This is the number of marbles in the fifth group. Now let us make a bold conjecture. Respecting the table of cannonballs and try this rule. Take the number whose tabular number is required, say five, add one to that number, six, add one more to that number, seven, multiply all three numbers together, two hundred and ten, divide by two, one oh five. The real number in the fifth pyramid is thirty-five. But the number one oh five at which we have arrived is exactly three times as great. If therefore instead of dividing by two we had divided by two and also by three we should have arrived at a true result in this instance. The amended rule is therefore take the number whose tabular number is required, say n, add one to it, n plus one, add one to this, n plus two, multiply these three numbers together, n times n plus one times n plus two, divide by one, by two, divide by three. The result is n times n plus one times n plus two divided by six. This rule will upon trial be found to give correctly every tabular number. By similar reasoning we might arrive at the knowledge of the number of cannonballs in square and rectangular pyramids. But it is presumed that enough has been stated to enable the reader to form some general notion of the method of calculating arithmetical tables by differences which are constant. Astronomical Tables It may now be stated that mathematicians have discovered that all the tables most important for practical purposes, such as those relating to astronomy and navigation, can, although they may not possess any constant differences, still be calculated in detached portions by that method. Hence the importance of having machinery to calculate by differences, which if well made cannot air, and which if carelessly set presents in the last term a calculates the power of verification of every antecedent term. Of the mechanical arrangements necessary for computing tables by the method of differences. From the preceding explanation, it appears that all tables may be calculated to a greater or less extent by the method of differences. That method requires, for its successful execution, little beyond the mechanical means of performing the arithmetical operation of addition. Subtraction can, by the aid of a well-known artifice, be converted into addition. Addition The process of addition includes two distinct parts. First, the first consists of the addition of any one digit to another digit. Second, the second consists in carrying the tens to the next digit above. Let us take the case of the addition of the two following numbers in which no carriages occur. 6023 plus 19070 equals 7993. It will be observed that in making this addition the mind acts by successive steps. The person adding says to himself, zero and three makes three, seven and two make nine, nine and zero make nine, one and six make seven. Carriage In the following addition there are several carriages. 2648 plus 4564 equals 7212. The person adding says to himself, four plus eight makes twelve. Put down two and carry one. One and six are seven, and four makes eleven. Put down one and carry one. One and five are six, and six make twelve. Put down two and carry one. One and four are five, and two makes seven. Put down seven. Now the length of time required for adding one number to another is mainly dependent upon the number of figures to be added. If we could tell the average time required by the mind, to add two figures together, the time required for adding any given number of figures to another equal number would be found by multiplying that average time by the number of digits in either number. When we attempt to perform such additions by machinery we might follow exactly the usual process of the human mind. In that case we might take a series of wheels. Each having marked on its edges the digits zero, one, two, three, four, five, six, seven, eight, nine. These wheels might be placed above each other upon an axis. The lowest would indicate the unit's figure, the next above the tens, and so on, as in the difference engine at the exhibition, a woodcut of which faces the title page. Several such axes, with their figure wheels, might be placed around a system of central wheels, with which the wheels of any one or more axes might at times be made to gear. Thus the figures of any one axis might, by means of those central wheels, be added to the figure wheels of any other axis. But it may fairly be expected, and it is indeed of great importance. The calculations made by machinery should not merely be exact, but that they should be done in a much shorter time than those performed by the human mind. Suppose there were no tens to carry, as in the first of the two cases, then if we possessed mechanism capable of adding any one digit to any other unit's place of figures, a similar mechanism might be placed above it to add to the tens figures, and so on for as many figures as might be required. But in this case, since there are no carriages, each digit might be added to its corresponding digit at the same time. Thus the time of adding by means of mechanism any two numbers, however many figures they might consist of, would not exceed that of adding a single digit to another digit. If this could be accomplished, it would render additions and subtractions with numbers, having ten, twenty, fifty, or any number of figures, as rapid as those operations are with single figures. SUCCESSIVE CARRIGE Let us now examine the case in which there were several carriages. Its successive stages may be better explained thus. STAGES 2648, plus 4584, equals 2642. 1. Add units. Figure equals 4. 2. Carry 1. 3. Add tens figures, equals 8. 2632. Carry the 1. 2732. Add hundreds figures, equals 5. 2232. Carry the 1. 3232. Add thousands figures, which is 4. 7232. Carry zero. There is no carriage. Now, if as in this case all the carriages were known, it would then be possible to make all the additions of digits at the same time, provided we could also record each carriage as it became due. We might then complete the addition by adding, at the same instant, each carriage in its proper place. The process would then stand thus. STAGES 2648, plus 4564. 6102. Add each digit to the digit above. 111. Record the carriages. 7212. Add the above carriages. Now, whatever mechanism is contrived for adding any one digit to any other must, of course, be able to add the largest digit. 9. To that other digit. Supposing, therefore, one unit of number to be passed over in one second of time, it is evident that any number of pairs of digits may be added together in nine seconds, and that, when all the consequent carriages are known, as in the above case, it will cost one second more to make those carriages. Thus, addition and carriage would be completed in ten seconds, even though the numbers consisted each of a hundred figures. But unfortunately there are multitudes of cases in which the carriages that become due are only known in successive periods of time. As an example, add together the two following numbers, 8473 and 1528. Add all the digits. 9991. Carry on tens and warn the next carriage. 9901. Carry on hundreds and ditto. 9001. Carry on thousands and ditto. 00001. Carry on ten thousands. 1001. In this case, the carriages only become known successively, and the amount to the number of figures to be added. Consequently the mere addition of two numbers, each of fifty places of figures, would require only nine seconds of time whilst the possible carriages would consume fifty seconds. The mechanical means I employed to make these carriages bear some slight analogy to the operation of the faculty of memory, a toothed wheel, had the ten digits marked upon its edge. Between the nine and the zero, a projecting tooth was placed. Whenever any wheel, in receiving addition, passed from nine to zero, the projecting tooth pushed over a certain lever. Thus, as soon as the nine seconds of time required for addition were ended, every carriage, which had become due, was indicated by the altered position of its lever. An arm now went round, which was so contrived that the act of replacing that lever caused the carriage, which its position indicated, to be made to the next figure above. But this figure might be a nine. In which case, in passing to zero, it would put over its lever, and so on. By placing the arms spirally round in axis, these successive carriages were accomplished. Multitudes of contrivances were designed, and almost endless drawings made for the purposes of economizing the time and simplifying the mechanism of carriage. In that portion of the difference engine in the exhibition of 1862, the time of carriage has been reduced to about one-fourth part of what was at first required. Anticipating Carriage At last, having exhausted, during years of labor, the principle of successive carriages. It occurred to me that it might be possible to teach mechanism to accomplish other mental processes, namely to foresee. This idea occurred to me in October of 1834. It cost me much thought. But the principle was arrived at in a short time. As soon as that was attained, the next step was to teach the mechanism which could foresee to act upon that foresight. This was not so difficult. Certain mechanical means were soon devised which, although very far from simple, were yet sufficient to demonstrate the possibility of constructing such machinery. The process of simplifying this form of carriage occupied me at intervals during a long series of years. The demands of the analytical engine for the mechanical execution of arithmetical operations were of the most extensive kind. The multitude of similar parts required by the analytical engine, amounting in some instances to upwards of fifty thousand, rendered any, even the simplest improvement of each part, a matter of the highest importance, more especially as regard to the diminished amount of expenditure for its construction. Description of the existing portion of Difference Engine Number One. That portion of Difference Engine Number One, which during the last twenty years has been in the Museum of King's College at Somerset House, is represented in the woodcut opposite the title page. It consists of three columns, each column containing six cages. Each cage contains one figure wheel. The column on the right hand has its lowest figure wheel covered by a shade, which is never removed, and to which the reader's attention need not be directed. The figure wheel next above may be placed by hand at any one of the ten digits. In the woodcut it stands at zero. The third, fourth, and fifth cages are exactly the same as the second. The sixth cage contains exactly the same as the four just described. It also contains two other figure wheels, with which a similar one above the frame may also be dismissed from the reader's attention. Those wheels are entirely unconnected with the moving part of the engine and are only used for memoranda. It appears therefore that there are in the first column on the right hand five figure wheels, each of which may be set by hand to any of the figures, zero, one, two, three, four, five, six, seven, eight, nine. The lowest of these figure wheels represents the units of any number, the next above the tens figure, and so on. The highest figure wheel will therefore represent tens of thousands. Now, as each of these figure wheels may be set by hand to any digit, it is possible to place on the first column any number up to nine, nine, nine, nine, nine. It is on these wheels that the table to be calculated by the engine is expressed. This column is called the table column, and the axis of the wheels is the table axis. The second, or middle column, has also six cages in each of which a figure wheel is placed. It will be observed that in the lowest cage the figure on the wheel is concealed by a shade. It may therefore be dismissed from the attention. The five other figure wheels are exactly like the figure wheels on the table axis, and can also represent any number up to nine, nine, nine, nine. This column is called the first difference column, and the axis is called the first difference axis. The third column, which is that on the left hand, has also six cages in each of which is a figure wheel capable of being set by hand to any digit. The mechanism is so contrived that whenever maybe the numbers placed respectively on the figure wheels of each of the three columns, the following succession of operations will take place as long as the handle is moved. First, whatever number is found upon the column of first differences will be added to the number found upon the table column. Second, the same first difference remaining upon its own column, the number found upon the column of second differences will be added to that first difference. It appears therefore that with this small portion of the engine any table may be computed by the method of differences, provided neither the table itself nor its first and second differences exceed five places of figures. If the whole engine had been completed it would have had six orders of differences, each of twenty places of figures, whilst the three first columns would each have had half a dozen additional figures. This is the simplest explanation of that portion of the difference engine number one at the exhibition of 1862. There are, however, certain modifications in this fragment which render its exhibition more instructive and which even give a mechanical insight into those higher powers with which I have endowed it in its completed state. As a matter of convenience in exhibiting it there is an arrangement by which the three upper figures of the second difference are transformed into a small engine which counts the natural numbers. By this means it can be set to compute any table whose second difference is constant and less than a thousand, whilst at the same time it thus shows the position in the table of each tabular number. In the existing portion there are three bells. They can be respectively ordered to ring. When the table, its first differences and its second difference pass from positive to negative. Several weeks after the machine had been placed in my drawing room a friend came by appointment to test its power of calculating tables. After the engine had computed several tables I remarked that it was evidently finding the root of a quadratic equation. I therefore set the bells to watch it. After some time the proper bell sounded twice indicating and giving the two positive roots to be twenty-eight and thirty. The table thus calculated related to the barometer and really involved a quadratic equation although its maker had not previously observed it. I afterwards set the engine to tabulate a formula containing impossible roots, and of course the other bell warned me when it had attained those roots. I had never before used these bells simply because I did not think the power had thus possessed to be of any practical utility. Again the lowest cages of the table and of the first difference have been made use of for the purpose of illustrating three important faculties of the finished engine. First, the portion exhibited can calculate any table whose third difference is constant and less than ten. Second, it can be used to show how much more rapidly astronomical tables can be calculated in an engine in which there is no constant difference. Third, it can be employed to illustrate those singular laws which might continue to be produced through ages, and yet after an enormous interval of time change into other different laws. Each again to exist for ages and then to be superseded by new laws. These views were first proposed in the Ninth Bridgewater Treatise. Curious Questions Amongst the various questions which have been asked respecting the difference engine, I will mention a few of the most remarkable. One gentleman addressed to me thus. Pray, Mr. Babbage, can you explain to me in two words what is the principle of this machine? Had the queerest possessed a moderate acquaintance with mathematics, I might in four words have conveyed to him the required information, by answering the method of differences. The question might have indeed been answered with six characters, thus. Delta to the seventh power times u sub x equals zero. But such information would have been unintelligible to such inquirers. On two occasions I have been asked, Pray, Mr. Babbage, if you put into the machine wrong figures will the right answers come out? In one case a member of the upper, and in another a member of the lower house, put this question. I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question. I did however explain the following property, which might in some measure approach towards an answer to it. It is possible to construct the analytical engine in such a manner that after the question is once communicated to the engine it may be stopped at any turn of the handle, and set on again, as often as may be desired, at each stoppage, every figure wheel throughout the engine, which is capable of being moved without braking, may be moved onto any other digit. Yet after each of these apparent falsifications the engine will be found to make the next calculation with perfect truth. The explanation is very simple, and the property itself useless. The whole of the mechanism ought of course to be enclosed in glass, and kept under lock and key, in which case the mechanism necessary to give it the property alluded to would be useless. End of section 6. Section number 7 of passages from the life of a philosopher. This is a LibriVox recording, or LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org, recording by Elaine Conway, England. Passages from the life of a philosopher by Charles Babbage. Section number 7, statement relative to the difference engine, drawn up by the late Sir H. Nicholas from the author's papers, part 1. The following statement was drawn up by the late Sir Harris Nicholas, G, S, M and E, from papers and documents in my possession relating to the difference engine. I believe every paper I possessed at all bearing on the subject was in his hands for several months. For some time, previous to 1822, Mr Babbage had been engaged in contriving machinery for the execution of extensive arrhythmical operations, and in devising a mechanism by which the machine that made the calculations might also print the results. On the 3rd of July 1822, he published a letter to Sir Humphrey Davy, president of the Royal Society, containing a statement of his views on that subject, and more particularly describing an engine for calculating astronomical, nautical and other tables, by means of the method of differences. In that letter, it is stated that a small model consisting of six figures and capable of working two orders of differences had been constructed, and that it performed its work in a satisfactory manner. The concluding paragraph of that letter is as follows. Whether I shall construct a larger engine of this kind, and bring to perfection the others I have described, will in a great measure depend on the nature of the encouragement I may receive, induced by a conviction of the great utility of such engines, to withdraw for some time my attention from a subject on which it has been engaged during several years, and which possesses troms of a higher order. 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. The model alluded has been shown to a large number of Mr Babbage's acquaintances, and to many other persons, and copies of his letter have been given to several of his friends. It is probable that one of the copies was sent to the Treasury. On the 1st of April, 1823, the Lords of the Treasury referred that letter to the Royal Society requesting the opinion of the Royal Society on the merits and utility of this invention. On the 1st of May, the Royal Society reported to the Treasury that Mr Babbage has displayed great talent 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 they consider Mr Babbage as highly deserving of public encouragement in the prosecution of his arduous undertaking. On the 21st of May, these papers were ordered to be printed by the House of Commons. In July 1823, Mr Babbage had an interview with the Chancellor of the Exchequer, Mr Robinson, to ascertain if it was the wish of the government that he should construct a large engine of the kind which would also print the results it calculated. For the conversation which took place on that occasion, Mr Babbage apprehended that such was the wish of the government. The Chancellor of the Exchequer remarked that the government were in general unwilling to make grants of money for any inventions. However meritorious, because if they really possessed the merit claimed for them, the sale of the article produced would be the best, as well as largest reward of the inventor, but that the present case was an exception. It had been apparent that the construction of such a machine could not be undertaken with a view to profit from the sale of its produce, and that as mathematical tables were peculiarly valuable for nautical purposes, it was deemed a fit object of encouragement by the government. The Chancellor of the Exchequer mentioned two modes of advancing money for the construction, either through the recommendation of a committee of the House of Commons, or by taking a sum from the Civil Contingences, and he observed that as the session of Parliament was near its termination, the latter calls might perhaps be the most convenient. Mr Babbage thinks the Chancellor of the Exchequer also made some observation, indicating that the amount of money taken from the Civil Contingences would be smaller than that which might be had by means of a committee of the House of Commons, and he then proposed to take £1,000 as a commencement from the Civil Contingences Fund. To this, Mr Babbage replied in words which he distinctly remembers, would it be too much in the first instance to take £1,500? The Chancellor of the Exchequer immediately answered that £1,500 should be advanced. Mr Babbage's opinion at that time was that the engine would be completed in two, or at the most in three years, and that by having £1,500 in the first instance he would be enabled to advance from his own private funds, the residue of the £3,000 or even £5,000, which he then imagined the engine might possibly cost, so that he would not again have occasion to apply to government until it was completed. Some observations were made by the Chancellor of the Exchequer about the mode of accounting for the money received, as well as about its expenditure, but it seemed to be admitted that it was not possible to prescribe any very definite system and that much must be left to Mr Babbage's own judgment. Very unfortunately no minute to that conversation was made at the time, nor was any sufficiently distinct understanding between the parties arrived at. Mr Babbage's conviction was that whatever might be the labour and difficulty of the undertaking, the engine itself would, of course, become the property of the government, which had paid for its construction. Soon after this interview with the Chancellor of the Exchequer, a letter was sent from the Treasury to the Royal Society, informing that body that the Lord's the Treasury had directed the issue of £1,500 to Mr Babbage to enable him to bring his invention to perfection in the manner recommended. These latter words in the manner recommended can only refer to the previous recommendations of the Royal Society, but it does not appear from the report of the Royal Society that any plan, terms or conditions had been pointed at by that body. Towards the end of July 1823 Mr Babbage took measures for the construction of the present difference engine, and it was regularly proceeded with for four years. Note it will be convenient to distinguish between the small model of the original or difference engine, to the difference engine itself belonging to the government, a part only of which had been put together, three the designs for another engine, which in this statement is called the analytical engine. In October 1827 the expense incurred had amounted to £3,475, and Mr Babbage having suffered severe domestic affliction and being in a very ill state of health was recommended by his medical advisors to travel on the continent. He left however sufficient drawings to enable the work to be continued, and gave an order to his own banker to advance £1,000 during his absence. He also received from time to time drawings and inquiries relating to the mechanism, and returned instructions to the engineer who was constructing it, as it now appeared probable that the expense would much exceed what Mr Babbage had originally anticipated. He thought it desirable to inform the government of that fact, and to procure a further grant as a preliminary step. He wrote from Italy to his brother-in-law, Mr Woolwright Whitmore, to request that he could see Lord Godrich upon the subject of the interview in July 1823, but it is possible that he did not sufficiently inform Mr Whitmore of all the circumstances of the case. Mr Whitmore, having had some conversation with Lord Godrich of the subject, addressed a letter dated on the 29th of February 1828 to Mr Babbage, who was then at Rome stating that that interview was unsatisfactory, that Lord Godrich did not like to admit that there was any understanding, at the time the £1,500 was advanced, that more would be given by government. On Mr Babbage's return to England towards the end of 1828, he waited in person upon Lord Godrich, who admitted that the understanding of 1823 was not very definite. He then addressed a statement to the Duke of Wellington as the head of the government, explaining the previous steps in the affair, stating the reasons for his inferences from what took place at the interview with the Chancellor of the Exchequer in July 1823, and referring his grace for further information to Lord Godrich, to whom also he sent a copy of that statement. The Duke of Wellington, in consequence of this application, requested the Royal Society to inquire whether the progress of the machine confirms them in their former opinion that it will ultimately prove adequate, give to the important object it was intended to attain. The Royal Society reported in February 1829 that they had not the slightest hesitation in pronouncing their decided opinion in the affirmative. The Royal Society also expressed their hope that whilst Mr Babbage's mind is intensely occupied in 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. On the 28th of April 1829, a treasury minute directed a further payment to Mr Babbage of £1,500 to enable him to complete the machine by which such important benefit to science might be expected. At that time the sum expended on the engine amounted to £6,697, 12 shillings of which £3,000 had been received from the treasury, so that Mr Babbage had provided £3,697, 12 shillings from his own private funds. And the circumstances by the advisor of Mr Walwright, Whitmore, a meeting of Mr Babbage's personal friends was held on the 12th of May 1829. It consisted of the Duke of Somerset, Lord Ashley, Sir John Franklin, Mr Walrich, Whitmore, Dr Fitton, Mr Francis Bailey, Mr Nasa John, Herschel. Being satisfied upon inquiry of the following facts, they came to the next resolutions. First, that Mr Babbage was originally induced to take up the work on its present extensive scale, by an understanding on his part that it was the wish of the government that he should do so, and by an advance of £1,500 at the outset, with a full impression on his mind that such further advances would be made as the work might require. Second, that Mr Babbage's expenditure had amounted to nearly £7,000, while the whole sum advanced by government was £3,000. Third, that Mr Babbage had devoted the most assiduous and anxious attention to the progress of the engine, to the injury of his health, and the neglect and refusal of other profitable occupations. Fourth, that a very large expense remained to be incurred, and that his private fortune was not such as would justify his completing the engine, without further and effectual assistance from government. Fifth, that a personal application upon the subject should be made to the Duke of Wellington. Sixth, that if such application should be unsuccessful in procuring a factual and adequate assistance, they must regard Mr Babbage, considering the great pecuniary and personal sacrifices he will then have made, the entire expenditure of all he had received from the public on the subject of its destination, and the moral certainty of completing it, to which it was, by his exertions reduced, as no longer could hold on to proceed with an undertaking which might destroy his health and injure if not ruin his fortune. Seventh, that Mr Woolrich Whitmore and Mr Herschel should request an interview with the Duke of Wellington, to state to his Grace these opinions on the subject. Mr Whitmore and Mr Herschel accordingly had an interview with the Duke of Wellington, and some time after they were informed by the Chancellor of the Exchequer, doing they had applied for his Grace's answer, that the Duke of Wellington intended to see the portion of the engine should be then made. In November 1829, the Duke of Wellington accompanied by the Chancellor of the Exchequer, Mr Gulburn and Lord Ashley saw the model of the engine, the drawings and the parts in progress. On the 23rd of that month, Mr Babbage received a note from Mr Gulburn, dated on the 20th, informing him that the Duke of Wellington and himself had recommended the Treasury to make a further payment towards the completion of the machine, and that their Lordships had in consequence directed a payment of £3,000 to be made to him. This letter also contained a suggestion about separating the calculating from the printing part of the machine, which was repeated in the letter from the Treasury of the 3rd of December, 1829, communicating officially the information contained in Mr Gulburn's private note, and stating that directions had been given to pay it to you, the further sum of £3,000 to enable you to complete the machine which you have invented for the calculation of various tables. But I have to intimate to you that in making this additional payment, my Lords think it extremely desirable that the machine should be constructed, that if any failure should take place in the attempt to print by it, the calculating part of the machine may nevertheless be perfect, and available for that object. Mr Babbage informed from this further grant that Government had adopted his view of the arrangement entered into with the Chancellor of the Exchequer in July 1823, but to prevent the recurrence of difficulty from any remaining indistinctness, he wrote to Mr Gulburn, stating that before he received the £3,000, he wished to propose some general arrangements for expediting the completion of the engine, further notes of which he would shortly submit to him. On the 25th of November, 1829, he addressed a letter to Lord Ashley to be communicated to the Chancellor of the Exchequer, stating the grants on which he thought the following arrangements desirable. First, that the engine should be considered as a property of Government. Second, that professional engineers should be appointed by Government to examine the charges made for the work already executed, as well as for its future progress, and that such charges should be defrayed by Government. Third, that under this arrangement, himself should continue to direct construction of the engine, as he had hitherto done. Mr Babbage also stated that he had been obliged to suspend the work for nearly nine months, and that such delay risked the final completion of the engine. In reply to these suggestions, Mr Gulburn wrote to Lord Ashley, stating that we, the Government, could not adopt the course which Mr Babbage had pointed out. Consistently, with the principle on which we have rendered him assistance in the construction of his engine, and without considerable inconvenience, 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, be down to his honour, and be a great public advantage. 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 three thousand pounds, and in the letter in which I informed him of that grant. Mr Gulburn's letter was enclosed by Lord Ashley to Mr Babbage, with a note, in which his Lordship observed, with reference to Mr Gulburn's his opinion that it was a wrong view of the position in which Mr Babbage was placed, after his conference with Lord Godrich, which must be explained to him, Mr Gulburn. The original intention of the Government is here stated to have been communicated to Mr Babbage, both in the letter from the Treasury of the 3rd of December, 1829, granting the three thousand pounds, and also in Mr Gulburn's his private letter of the 20th of November, 1829. These letters have just been given, and it certainly does not appear from either of them, that the original intention was then in a degree more apparent than it was at the commencement of the undertaking in July 1823. On the 16th of December, 1829, Mr Babbage wrote to Lord Ashley, observing that Mr Gulburn seemed to think that he, Mr Babbage, had commenced the machine on his own account, and that pursuing it zealously, he had expended more than was prudent, and had then applied to Government for aid. He remarked that a reference to papers and dates would confirm his own positive declaration, that this was never for one moment in his apprehension, the ground on which the matter rested, and that the following facts would prove that it was absolutely impossible, it could have been so. Firstly, Mr Babbage referred to the passage, already quoted in his letter to Sir Humphrey Davy, in which he had expressed his opinion as decidedly adverse to the plan of making a larger machine on his own account. Secondly, Mr Babbage stated that the small model of the machine seen by the Duke of Wellington and Mr Gulburn was completed before his interview with Lord Goderich in July 1823, which was alluded to in the report of the Royal Society on 1 May 1823. Thirdly, that the interview with Lord Goderich, having taken place in July 1823, the present machine, i.e. the difference engine, was commenced in consequence of that interview, and after Mr Babbage had received the first grant of £1,500 on 7 August 1823. Having thus shown that the light in which Mr Gulburn viewed these transactions was founded on a misconception, Mr Babbage requested Lord Ashley to enquire whether the facts to which he had called Mr Gulburn's attention might not induce him to reconsider the subject, and in case Mr Gulburn should decline revising his opinion, then he wished Lord Ashley to ascertain the opinion of government upon the contingent questions which he enclosed. This, supposing Mr Babbage received a £3,000 now directed to be issued, which are the claims which government will have on the engine, or on himself. Would Mr Babbage owe the £6,000 or any part of that sum to the government? If this question be answered in the negative, is the portion of the engine now made as completely Mr Babbage's property as if it had been entirely paid for with his own money? Is it expected by government that Mr Babbage should continue to construct the engine at his own private expense, and if so, to what extent in money? 5. Supposing Mr Babbage should decline resuming the construction of the engine, to whom do the drawings and parts already made belong? The following statement was also enclosed. Expenses up to 9th May 1829 when the work ceased £6,628 £2,000 of £1,500 each mounting to £3,000 by Treasury minute November 1829 but not yet received. £3,000 In January 1830 Mr Babbage wrote to Lord Godrich stating that the Chancellor of the Exchequer Mr Goulburn would probably apply to his lordship respecting the interview in July 1823. He therefore records some of the circumstances attending it to Lord Godrich and concluded thus the matter was as you have justly observed on another occasion left in a certain measure indefinite and I have never condended that any promise was made to me. My subsequent conduct was founded upon the impression left on my mind by that interview. I always considered that whatever difficulties I might encounter it would never happen that I should ultimately suffer any pecuniary loss. I understand that Mr Goulburn wishes to ascertain on your lordship whether from the nature of that interview it was reasonable that I should have such expectation. In the meantime Mr Babbage had encountered difficulties of another kind. The engineer who had been constructing the engine and in Mr Babbage's direction had delivered his bills in such a state as it was impossible to judge how far the charges were just and reasonable and although Mr Babbage had paid several thousand pounds yet there remained a considerable balance which he was quite prepared and willing to pay as soon as the accounts should be examined and the charges approved of by professional engineers. The delay in deciding where the engine was the property of the government added greatly to this embarrassment. Mr Babbage therefore wrote to Lord Ashley on the 8th of February to mention these difficulties and to point out the serious inconvenience which would arise in the future progress of the engine from any dispute between the engineer and himself relative to payments. On the 24th of February 1830 Mr Babbage called on Lord Ashley to request he would represent to the Duke of Wellington the facts of the case and to point out to his grace the importance of a decision. In the afternoon of the same day he again saw Lord Ashley be communicated to him the decision of the government to the following effect. First, although the government would not pledge himself to complete the machine they were willing to declare it their property. Second, that professional engineer should be appointed to examine the bills. Third, that the government were willing to advance £3,000 more than the sum £6,000 already granted. Fourth, that when the machine was completed the government would be willing to attend to any claim of Mr Babbage to remuneration either by bringing it before the treasury or the House of Commons. First, after considerable discussion the doubts arising from the indefiniteness of the understanding with the Chancellor of the Exchequer in July 1823 were at length removed. Mr Babbage's impression of the original arrangement entered into between Lord Godrich and himself was thus formally adopted in the first three propositions and the government voluntarily added the expression of the disposition to attend to any claim of his full remuneration when the engine should be completed. When the arrangements consequent upon this decision were made the work of the engine was resumed and continued to advance. After some time the increasing amount of costly drawings and of parts of the engine already executed remaining exposed to destruction from fire and from other casualties became a source of some anxiety. These facts have been represented to Lord Allthorpe then Chancellor of the Exchequer an experienced surveyor was directed to find a site adapted for a building for the reception of the engine in the neighbourhood of Mr Babbage's residence. On the 19th of January the surveyor's reports were forwarded to Lord Allthorpe the Chancellor of the Exchequer who referred the case to a committee of practical engineers for their opinion. This committee reported strongly in favour of the removal on the grounds of security and of economy in completing the engine and also recommended the site which had been previously selected by the surveyor the Royal Society also to whom Lord Allthorpe had applied examined the question and likewise reported strongly to the same effect. A lease of some property adjacent to Mr Babbage's residence was therefore subsequently granted by him to the government at a fireproof building capable of containing the engine with its drawings and workshops necessary for its completion were erected. With respect to the expenses of constructing the engine the following planners agreed upon and carried out. The great bulk of the work was executed by the engineer and to the direction of Mr Babbage. When the bills were sent in they were immediately forwarded by him to two eminent engineers Messers Donkin and Field who at the request of government had undertaken to examine their accuracy. On these gentlemen said to find those bills to be correct Mr Babbage transmitted them to the treasury and out of the usual forms and warrant was issued directing the payment of the respective sums to Mr Babbage. This course however required considerable time and the engineer having represented that he was unable to pay his workmen without more immediate advances Mr Babbage to prevent delay in completing the engine did himself from time to time advance from his own funds several sums of money so that he was in fact usually in advance from £500 to £1000 though sums were of course repaid when the treasury was issued. Early in the year 1833 an event of great importance in the history of the engine occurred. Mr Babbage had directed a portion of it consisting of 16 figures to be put together which was capable of calculating tables having two or three orders of differences and to some extent of forming other tables. The action of this portion completely justified the expectations raised and gave the most satisfactory assurance of its final success. The fireproof building and workshops having been completed arrangements were made for the removal of the engine. Mr Babbage finding it no longer convenient to make payments in advance informed the engineer that he should in future not pay him until the money received was received on the treasury. Upon receiving this intimation the engineer immediately discontinued the construction of the engine and dismissed the workmen employed on it which fact Mr Babbage immediately communicated to the treasury. In a state of affairs it appeared both to the treasury and Mr Babbage that it would be better to complete the removal of the drawings and all the parts of the engine to the fireproof building and then make such arrangements between the treasury and the engineer respecting the future payments as might prevent further discussion on that subject. Of too much delay and difficulty to the whole of the drawings and parts of the engine were at length removed to the fireproof building in East Street Manchester Square. Mr Babbage wrote on the 16th July 1834 to the treasury informing their lordships the fact adding that no advance would be made in its construction or above a year and a quarter and requesting further instructions on the subject. Mr Babbage received a letter from the treasury expressing their lordships his satisfaction at learning that the drawings and parts of the calculating engine were removed to the fireproof building and stating that as soon as Mr Clements' account should be received and examined they would take into consideration what further proceedings may be requisite with a view to its completion A few weeks afterwards Mr Babbage received a letter from the treasury conveying their lordships' authority to proceed with the construction of the engine. During the time which had elapsed since the engineer had ceased to proceed with the construction of the engine Mr Babbage had been deprived of the use of his own drawings having in the meanwhile naturally speculated upon the general principles on which machinery or calculation might be constructed a principle of an entirely new kind to go to him the power of which over the most complicated arrhythmical operations seemed nearly unbounded on re-examining his drawings when returned to him by the engineer the new principle appeared to be limited only by the extent of the mechanism it might require the invention of simpler mechanical means for executing the elementary operations of the engine now derived of all greater importance than it had hitherto possessed ensured such simplifications be discovered it seemed difficult to anticipate or even to overestimate the vast results which might be attained in the engine for calculating by differences such simplifications affected only about 120 similar parts whilst in the new or analytical engine they would affect a great many thousand the difference engine might be constructed with more or less advantage by employing various mechanical modes for the operation of addition the analytical engine could not exist without inventing for it a method of mechanical addition possessed of the utmost simplicity in fact it was not until upwards of 20 different mechanical modes before performing the operation of addition had been designed and drawn that the necessary degree of simplicity required the analytical engine was ultimately attained hence therefore the powerful motive for simplification these new views required additional importance from their bearings upon the engine already partly executed for the government for if such simplifications should be discovered it might happen that the analytical engine would execute more rapidly the calculations for which the difference engine was intended all that the difference engine would itself be superseded by a far simpler mode of construction though these views might perhaps such that period of appeared visionary both have subsequently been completely realised to withhold those new views from the government and under such circumstances to have allowed the construction of the engine to be resumed would have been improper yet the state of uncertainty in which those views were then necessarily involved rendered any written communication respecting their probable bearing on the difference engine a matter of very great difficulty it appeared to Mr Babbage that's the most straightforward cause was to ask for an interview on the subject the head of the government and communicate to him the exact state of the case had that interview taken place the first lord of the treasury might have ascertained from his inquiries in a manner quite impracticable by any written communications the degree of importance which Mr Babbage attached to his new inventions and his own opinion of their probable effect in superseding the whole or any part of the original or different engine the first lord of the treasury would then have been in a position to decide either on the immediate to continuation and completion of the original design or on its temporary suspension until the character of the new view should be more fully developed by further drawings and examination there was another although a far less material point on which also it was desirable to obtain the opinion of the government the serious impediments to the progress of the engine arising from the engineer's conduct as well as the consequent great expense had induced Mr Babbage to consider whether it might not be possible to employ some other person as his agent for constructing it his mind had gradually become convinced of the practicability of that measure but he was also aware that however advantageous it might prove to the government from its greater economy yet that it would add greatly to his own personal labour responsibility and anxiety on the 26th of September 1834 Mr Babbage therefore requested an interview with Lord Marlborn for the purpose of placing before him these views Lord Marlborn acceded to the proposed interview but it was then postponed and soon after the administration of which his lordship was the head and head of office without the interview having taken place for the same purpose Mr Babbage applied in December 1834 for an interview with the Duke of Wellington who in reply expressed his wish to receive a written communication on the subject he accordingly addressed a statement to his grace pointing out the only plans which in his opinion could be pursued for terminating the questions relative to the difference engine namely first the government might desire Mr Babbage to continue the construction of the engine in the hands of the person who has hitherto been employed in making it secondly the government might wish to know whether any other person could be substituted for the engineer at present employed to continue the construction a cause which was possible thirdly the government might although he did not presume that they would substitute some person to superintend the completion of the engine instead of Mr Babbage himself fourthly the government might be disposed to give up the undertaking entirely he also stated to the Duke of Wellington the circumstances which had led him to the invention of a new engine of far more extensive powers of calculation which he then observed did not supersede the former one but added greatly to its utility after this period the impediments relating to the difference engine had been partially and temporarily removed the chief difficulty would have been either the formation of new arrangements with the engineer or the appointment of some other person to supply his place this latter alternative which was of great importance for economy as well as for its speedy completion Mr Babbage had carefully examined and was then prepared to point out means for its accomplishment the duration of the Duke of Wellington's administration was short as no decision on the subject of the difference engine was obtained on the 15th of May the difference engine was alluded to in the House of Commons when the Chancellor of the Exchequer did Mr Babbage the justice to state distinctly that the whole of the money voted had been expended in paying the workmen on for the materials employed in constructing it and that's not one shilling of it had ever gone into his own pocket about this time several communications took place between the Chancellor of the Exchequer and Mr Babbage respecting a reference to the Royal Society for an opinion on the subject of the engine a new and serious impediment to the possibility of executing one of the plans which had been suggested to the Duke of Wellington for completing the difference engine arose from these delays the jasmin whom Mr Babbage had at his own expense employed both on the difference and on the analytical ending received an offer of a very liberal salary if he would enter into an engagement abroad which would occupy many years his assistance was indispensable and his services were retained only by Mr Babbage considerably increasing his salary on the 14th of January 1836 Mr Babbage received a communication from the Chancellor of the Exchequer Mr Spring Rice expressing his desire to come to some definite result on the subject of the calculating engine in which he remarked that the conclusion should be drawn from Mr Babbage's statement to the Duke of Wellington was that he, Mr Babbage having invented a new machine a far greater power than the former one wished to be informed if the government would undertake to defray the expense of this new engine the Chancellor of the Exchequer then pointed out reasons why he could feel himself bound to look to the completion of the first engine before he could have proposed to Parliament to enter on the consideration of the second but he proposed to refer to the Royal Society for their opinion authorising them if they thought to fit to employ any practical mechanist or engineer to assist them in their inquiries the Chancellor of the Exchequer included with expressing his readiness to communicate with Mr Babbage respecting the best mode of attaining that result on these statements it is evident that Mr Babbage had failed in making his own views distinctly understood by the Chancellor of the Exchequer his first anxiety when applying to Lord Milbourne had been respecting the question whether the discoveries with which he was then advancing might not ultimately supersede the work already executed his second object had been to point out a possible arrangement by which great expense might be saved in the mechanical construction of the difference engine so far was Mr Babbage from having proposed to the government to defray the expenses of the new or analytical engine that though he expressly pointed out in the statement to the Duke of Wellington for courses which it was possible for the government to take yet no one of them was the construction of the new engine alluded to those views have improved machinery for making calculations which had appeared in but faint perspective in 1834 as likely to lead to important consequences had by this time assumed a form of distinctness which fully justified the anticipations then made by patient inquiry aided by extensive drawings and notations the projected analytical engine had acquired such powers that it became necessary for its further advancement to simplify the elements of which it was composed in the progress of this enquiry Mr Babbage had gradually arrived at simpler mechanical modes of performing those arithmetical operations on which the action of the difference engines depended and he found it necessary to communicate these new circumstances as well as their consequences to the Chancellor of the Ex-Jacker on the 20th of January 1836 Mr Babbage wrote in answer to the communication from the Chancellor of the Ex-Jacker that he did not on re-examining the statement addressed to the Duke of Wellington perceive that it contained any application to take up the new or analytical engine and he accompanied this reply by statement relative to the progress of the analytical engine and its bearing upon the difference engine belonging to the government the former it was said is not only capable of accomplishing all those other complicated calculations which I had intended but it also performs all calculations which were peculiar to the difference engine both in less time and to a great extent in fact it completely supersedes the difference engine the reply then referred to the statement laid before the Duke of Wellington in July 1834 in which it was said all the elements of the analytical were essentially different from those of the difference engine and that the mechanical simplicity to which its elements had now been reduced was such that it would probably cost more to finish the old difference engine on its original plan than to construct a new difference engine with the simplified elements devised for the analytical engine it then proceeded to state that the fact of the new superseding and the old engine in a very few years is one of constant currents in our manufacturers at instances might be pointed out in which the advance of invention has been so rapid and the demand for machinery so great that half finished machines have been thrown aside as the use has before their completion it is now nearly 14 years since I undertook for the government to superintend the making of the difference engine during nearly four years its construction has been absolutely stopped and instead of being employed in overcoming the fiscal impediments I have been harassed by what may be called the moral difficulties of the question it is painful to reflect that in the time so employed the first difference engine might under more favorable circumstances have been completed in making this report I wish distinctly to state that I do not entertain the slightest doubt of the success of the difference engine nor do I intend it as any application to finish the one or to construct the other but I make it from a conviction that the information it contains ought to be communicated to those who must decide the question relative to the difference engine the reference to the Royal Society proposed to the Chancellor of the Exchequer in his letter of the 14th January 1836 did not take place and during more than a year and a half no further measures appeared to have been adopted by the government respecting the engine it is obviously of the greatest importance to Mr Babbage that a final decision should to be made by the government when he and took to a superintendent the construction of the difference engine for the government it was of course understood that he would not leave it unfinished he had now been engaged 14 years upon an object which he had anticipated would not require more than two or three and there seemed no limit the time his engagement with the government might thus be supposed to endure unless some steps were taken to terminate it without such a decision Mr Babbage felt that he should be impeded in any plans he might form and liable to the most serious interruption if he should venture to enter upon the execution of them he therefore most earnestly pressed both by his personal applications and by those of his friends with a settlement or the question Mr Wall Wright Whitmore in particular repeatedly urged upon the chancellor of the Exchequer personally as well as by letter the injustice of keeping Mr Babbage so very long in a state of suspense time however passed on and during nearly two years the question remained in the same state Mr Babbage wearied with his delay determined upon making a last effort to retain a decision he wrote to the First Lord of the Treasury Lord Melbourne on the 26th of July 1838 recalling to his lordship's attention the frequency of his applications on this subject and urging the necessity of a final decision upon it he observed that if the question had become more difficult because he had invented superior mechanism which had superseded that which was already partly executed this consequence had arisen from the very delay against which he had so repeatedly remonstrated he then asked for the last time not for any favour but for that which it was an injustice to withhold a decision on the 16th of August Mr Spring Rice the chancellor of the Exchequer addressed a note to Mr Babbage in reference to his application to Lord Melbourne after recapitulating his former statement of the subject which had been shown to be founded on a dis-apprehension fears that Mr Babbage had made an application to the government to construct for them the analytical engine the chancellor of the Exchequer inquired whether he was solicitous that steps should be taken for the completion of the old or for the commencement of a new machine and what he considered would be the cause to the one proceeding and of the other being absent on a distant journey Mr Babbage could not reply to this note until the 21st of October he then reminded the chancellor of the Exchequer of his previous communications of the 20th of January 1836 in which it was explicitly stated that he did not intend to make any application to construct a new machine but that the communication to the Duke of Wellington and the one to himself were made simply because he thought it would be unfair to conceal such important facts from those who were called upon to decide on the continuance or discontinuance of the construction of the difference machine with respect to the expense of either of the courses pointed out by the chancellor of the Exchequer Mr Babbage observed that not being a professional engineer and his past experience having taught him not to rely upon his own judgments on matters of that nature he should be very reluctant to offer any opinion upon the subject in conclusion Mr Babbage stated that the question he wished to have settled was whether the government required him to superintend the completion of the difference engine which had been suspended during the last five years or according to the original plan and principles or whether they intended to discontinue it altogether in November 1841 Mr Babbage on his return from the continent finding that Sir Robert Peale had become first Lord of the Treasury determined upon renewing his application for a decision of the question with this view the previous pages of this statement were drawn up and a copy of it was forwarded to him accompanied by a letter from Mr Babbage in which he observed Of course when I undertook to give the invention of the calculating engine to the government and to superintend its construction there must have been an implied understanding that I should carry it on to its termination I entered upon that understanding believing that to or at the utmost that three years would complete it the better part of my life has now been spent on that machine and no progress whatever having been made since 1834 that understanding may possibly be considered by the government as still subsisting I am therefore naturally very anxious that this state of uncertainty should be put an end to as soon as possible Mr Babbage in reply received a note from Sir George Clark secretary to the treasury stating that Sir Robert Peale feared that it would not be in his power to turn his attention to the subject for some days but that he hoped as soon as the great pressure of business previous to the opening of the session of parliament was over he might be able to determine on the best cause to the pursued the session of the parliament closed in August and Mr Babbage had received no further communication on the subject having availed himself of several private channels for recalling the question to Sir Robert Peale's attention with that effect Mr Babbage on the 8th of October 1842 again wrote to him requesting an early decision on the 4th of November 1842 a note from Sir Robert Peale explained to Mr Babbage that some delay had arisen on his wish to communicate personally with the Chancellor of the Exchequer who would shortly announce to him their joint conclusion on the subject on the same day Mr Babbage received a letter from Mr Gulburn the Chancellor of the Exchequer who stated that he had communicated with Sir Robert Peale and that they both regretted the necessity of abandoning the completion of the machine on which so much scientific labour had been bestowed he observed that the expense necessary for rendering it either satisfactory to Mr Babbage or generally useful appeared on the lowest calculation so far to exceed what they should be justified in incurring that they considered themselves so having no other alternative Mr Gulburn concluded by expressing their hope that by the government withdrawing all claims the machine has already constructed and placing it entirely at Mr Babbage's disposal there might in some degree assist him in his future exertions in the cause of science on the 6th of November 1842 Mr Babbage wrote to Sir Robert Peale and the Chancellor of the Exchequer acknowledging the receipt of their decision thanking them for the offer of the machine as already constructed but under all the circumstances declined to accept it on the 11th of November Mr Babbage obtained an interview with Sir Robert Peale and stated that having given the original invention to the government having super intended for them its construction having demonstrated the possibility of the undertaking by the completion of an important portion of it and that the non-completion of the design arose neither from his fault nor his desire but was the act of the government itself he felt that he had some claims on their consideration he rested those claims upon the sacrifices he had made both personal and pecuniary in the advancement of the mechanical arts and science on the anxiety and the injury he had experienced for the delay of eight years in the decision of the government on the subject and on the great annoyance he had constantly been exposed to by the prevailing belief in the public mind that he had been amply remunerated by the large grants of public money nothing he observed but some public act of the government could ever fully refute that opinion or repair the injustice with which he had been treated the result of this interview was entirely unsatisfactory Mr Babbage went to it prepared had his statement produced any effect till I've pointed out two courses by either of which it was probable that not only a difference engine but even the analytical engine might in a few years have been completed the state of Sir Robert Peale's is informational the subject and the views he took of Mr Babbage's services and position prevented Mr Babbage from making any allusion to either of those plans thus finally terminated an engagement which had existed upwards of 20 years during no part of the last eight of those years does there appear to have been any reason why the same decision should not have been arrived at by the government as was at last actually pronounced it was during this last period that all the great principles on which the analytical engine rests were discovered and that the mechanical contrivances in which they might be embodied were invented the establishment which Mr Babbage had long maintained in his own house and at his own expense was now directed with increased energy to the new enquiries required for its perfection in this statement the heavy sacrifices both pecuniary and personal which the invention of these machines had entailed upon their offer had been alluded to as slightly as possible few can imagine and none will ever know their full extent some idea of these sacrifices must nevertheless have occurred to everyone who has read this statement during upwards of 20 years Mr Babbage has employed in his own home and at his own expense workmen of various kinds to assist him in making experiments necessary for attaining a knowledge of every art which could possibly turn to the perfection of those engines and with that object he has frequently visited the manufacturers of the continent as well as our own since the discontinuance of the difference engine belonging to the government Mr Babbage has himself maintained an establishment for making drawings and description demonstrating the nature and power of the analytical engine and for its construction at some future period when its value may be appreciated to these remarks it'll only be added that at an early stage of the construction of the difference engine he refused more than one highly desirable and profitable situation in order that he might give his whole time and thoughts to the fulfillment of the engagement which he considered himself to have entered into with the government August 1843 end of section seven section number eight of passages from the life of a philosopher this is a LibriVox recording or LibriVox recordings are in the public domain for more information or to volunteer please visit LibriVox.org recording by Elaine Conway England passages from the life of a philosopher by Charles Babbage section eight difference engine number two difference engine number two the Olaf Ross president of the royal society proposed to the government plan by which the difference engine number two might have been executed it was addressed to the Earl of Derby and rejected by his chancellor of the Exchequer it was not until 1848 when I had mastered the subject of the analytical engine that I resolved on making the complete set of drawings of the difference engine number two in this I proposed to take advantage of all the improvements and simplifications which years of unwearyed study had produced for the analytical engine in 1852 the Earl of Ross who from its commencement had looked forward with the greatest interest to the application of mechanism to purposes of calculation and who was well acquainted with the drawings and notations of the difference engine number two inquired of me whether I was willing to give them to the government provided they would have the engine constructed my feeling was after the sad experience of the past that I ought not to think of sacrificing any further portion of my life upon the subject if however they chose to have the difference engine made I was ready to give them the whole of the drawings and also the notations by which it was demonstrated that such a machine could be constructed and that when made it would necessarily do the work prescribed for it my much-valued friend the late Sir Benjamin Hawes had also been consulted and it was agreed that the draft of a letter to Lord Derby who was then Prime Minister should be prepared in which I should make this offer Lord Ross proposed to place my letter in Lord Derby's hands with his own statement of a plan by which the whole question might be determined Lord Ross's suggestion was that the government should apply to the president of the institution of civil engineers to ascertain first whether it was possible from the drawings and notations to make an estimate of the cost of constructing the machine secondly in case this question was answered in the affirmative then could a mechanical engineer be found who would undertake to construct it and at what expense the institution of civil engineers was undoubtedly the highest authority upon the first question that being decided in the affirmative no other body had equal power to find out those mechanical engineers you might be willing to undertake the contract supposing both these questions or even the latter only answered in the negative the proposition of course fell to the ground but if they were both answered in the affirmative then there would have arisen a further question for the consideration of the government namely whether the object to be obtained was worthy of the expenditure Lord Ross's address to the Royal Society the final result of this eminently practical plan was communicated to the Royal Society by the president in his address at the anniversary on the 30th November 1854 the following is an extract the progress of the work was suspended there was a change of government science was weighed against gold by a new standard and it was resolved to proceed no further no enterprise could have had its beginning and a more auspicious circumstances the government had taken the initiative they had called for advice and the advisor was the highest scientific authority in this country your council guided by such men as Davey Walliston and Herschel by your council the undertaking was inaugurated by your council it was watched over in its progress that's the first great effort to employ the powers of calculated mechanism in aid of the human intellect should have been suffered in this great country to expire fruitless because there was no tangible evidence of immediate profit as a british subject i deeply regret and as a fellow my regret is accompanied with feelings of bitter disappointment where a question has once been disposed of succeeding governments rarely a reopen it and still i thought i should not be doing my duty if i did not take some opportunity of bringing the facts once more before government circumstances had changed mechanical engineering had made much progress the tools required and trained workmen would be found in the workshops of the leading mechanists the founders art was so advanced that casting had been substituted for cutting in making the change wheels even a screw cutting engines and therefore it was very probable that persons would be found willing to undertake to complete the difference engine for a specific sum that finished the question would then have risen how far it was advisable to endeavor for the same means to turn to account the great labor which had been expended under the guidance of inventive powers the most original controlled by mathematics of a very high order and which had been wholly devoted for so many years to the great task of carrying the powers of calculating machinery to its utmost limits before i took any step i wrote to several very eminent men of science inquiring whether in their opinion any great scientific object would be gained if mr babbage's views as explained in menabre's little essay were completely realized the answers i received was strongly in the affirmative as it was necessary the subject should be laid before government in a form as practical as possible i wrote to one of our most eminent mechanical engineers to inquire whether i should be safe in state into government that the expense of the calculating engine had been more than repaid in the improvements in mechanism directly referable to it he replied unquestionably fortified by these opinions i submitted this proposition to government that they should call upon the president of the society of civil engineers to report whether it would be practicable to make a contract for the completion of mr babbage's difference engine and if so for what sum this was in 1852 during the short administration of lord darby and it led to no result the time was unfortunate the great political contest was impending and before there was a lull in politics so that the voice of science could be heard lord darby's government was at an end mr babbage's letter to the earl of darby the following letter was then drawn up and placed in lord darby's hands by lord ross june 8 1852 my lord i take the liberty of drawing your lordship's attention to the subject the construction of a difference engine for 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 rule 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 rule 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 consider mr babbage as highly deserving of public encouragement in the prosecution of his arduous and taking report of rule society first of may 1823 parliamentary paper 370 22nd of 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 everyone 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 rule society 12th of February 1829 upon the first of these reports the government determined to construct the machine under my personal superintendent's 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 all together 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 rule 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 have 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 construction the necessary science and skills specially acquired in executing such works must also as experiences 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 Gulburn's his 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 and fur from the reason assigned by Mr Gulburn for its discontinuance veers 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 ascend 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 overestimated as to the expense actually incurred upon the first difference engine that of the government was about 17 000 pounds on my own part and out of my own private resources have sacrificed on this and other works of science upward of 20 000 pounds from the date of Mr Gulburn's letter nothing has been done towards the further completion of the difference engine by the government or myself so much of it has was completed was deposited in the Museum of Kings's College where it now remains three consequences have however resulted from my subsequent labours to which I attach great importance first 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 contra distinction 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 some other equivalent language the difference engine number two to which I shall presently refer is entirely described by its aid thirdly in laboring to perfect this analytical machine of greater power and wide a 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 enable any other person without long previous training and application even to attend its execution and on my own part to superintend its construction demand an amount of labor 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 fulfill 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'm willing to place at the disposal of government if they will undertake to execute a new difference engine all those improvements which 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 number two an instrument of greater power as well as of greater simplicity than that formally commenced and now in the possession of the government I have sacrificed time health and fortune in the desire to complete these calculating engines I have also declined several offers of great personal advantage to myself but notwithstanding the sacrifice of these advantages for the purpose of maturing an engine of almost intellectual power and after expending from my own private fortune a larger sum than the government of England has spent on that engine the execution of which it only commenced I have received neither an acknowledgement of my labours nor even the offer of those honors or rewards which are allowed to fall within the reach of men who devote themselves to purely scientific investigations I might perhaps advance some claims to consideration founded on my works and contributions in aid of various departments of industrial and physical science but it is for others to estimate those services I now however simply ask your lordship to do me the honour to consider this statement and the offer I make I prefer no claim to the distinctions or the advantages which it is in the power of the crown or the government to bestow I desire only to discharge whatever imagined obligation may be supposed to rest upon me in connection with the original undertaking of the difference engine though I cannot but feel that whilst the public has already derived advantage from my labours I have myself experienced only loss and neglect if the work upon which I have bestowed so much time and thought were a mere triumph over mechanical difficulties or simply curious or if the execution of such engines were of doubtful practicability or utility some justification might be found for the course which has been taken but I venture to assert that no mathematician who has a reputation to lose will ever publicly express an opinion that such an engine would be useless if made and that no man distinguished as a civil engineer will venture to declare the construction of such machinery impracticable the names appended to the report of the committee of the world's society fully justify my expressing this opinion which I apprehend would not be disputed and at a period where the progress of physical science is obstructed by that exhausting intellectual and manual labour indispensable for its advancement which it is the object of the analytical engine to relieve I think the application of machinery in aid of the most complicated and obstruse calculations can no longer be deemed unworthy of the attention of the country in fact there is no reason why mental as well as bodily labour should not be economised by the aid of machinery with these views I have addressed your lordship as the head of the government and whatever may be my sense of the injustice that has hitherto been done me I feel in laying this representation before your lordship and in making the offer I now make that I have discharged the utmost limit every implied obligation I originally contracted with the country I have the honour to be and see and see and see Chowers Babbage Dorset Street Manchester Square June the 8th 1852 as this question was one of finance and a calculation the subjectious premiere adroitly turned it over to his Chancellor of Eastdecker that official being from his office supposed to be well versed in both subjects the opinion pronounced by the novelist and financier was that Mr Babbage's projects appear to be so indefinitely expensive the ultimate success so problematical and the expenditure certainly so large and so utterly incapable have been calculated that the government would not be justified in taking upon itself any further liability extract from the reply of Earl Darby to the application of the Earl of Ross K.P president of the Royal Society referred to the Chancellor of the Exchequer the answer of Lord Darby to Lord Ross was in substance that he had consulted the Chancellor of the Exchequer who pronounced Mr Babbage's project as one indefinitely expensive two the ultimate success problematical three the expenditure utterly incapable of being calculated one with regard to the indefinite expense Lord Ross had proposed to refer this question to the president of the institution of civil engineers who would have given his opinion after a careful examination of the drawings and notations these had not been seen by the Chancellor of the Exchequer and if seen by him would not have been comprehended the objection that its success was problematical may refer either to its mechanical construction or to its mathematical principles who possessing one grain of common sense could look upon the unrivaled workmanship of the then existing portion of the difference engine number one and doubt whether a simplified form of the same engine could be executed as to any doubt of its mathematical principles this was excusable in the Chancellor of the Exchequer who was himself too practically acquainted with the fallibility of his own figures over which the severe duties of his office had stultified his brilliant imagination far other figures are dear to him those of speech in which it cannot be denied he is indeed preeminent any junior clerk in his office might however have told him that the power of computing tables by differences merely required knowledge of simple addition as to the impossibility of ascertaining the expenditure this merges into the first objection but a poetical brain must be pardoned when it repeats or amplifies I will recall to the ex-chancellor of the Exchequer what Lord Ross really proposed namely that the government should take the opinion of the president of the institution of civil engineers upon the question whether the contract could be made for constructing the difference engine and if so for what some but the very plan proposed by Lord Ross and reviews by Lord Derby for the construction of the English difference engine was adopted some few years after by another administration for the swedish difference engine Messrs Johnkin the eminent engineers made an estimate and a contract was in consequence executed to construct for government a facsimile of the swedish difference engine which is now in use in the department of the registrar general at Somerset House there were far greater mechanical difficulties in the production of that machine than in the one the drawings of which I had offered to the government for my own experience of the cost of executing such works I have no doubt although it was highly creditable to the skill of the able firm who constructed it but that it must have been commercially unprofitable under such circumstances surely it was harsh on the part of the government to refuse Messrs Johnkin permission to exhibit it as a specimen of English workmanship at the exhibition of 1862 his opinion worthless but the machine upon which everybody could calculate had a little chance of her play from the man on who nobody could calculate if the Chancellor of the Exchequer had read my letter to Lord Derby he would have found the opinion of the Committee of the Royal Society expressed in these words they consider the former abstract mathematical principle as not only sufficiently clear in itself that is already admitted and added on by the Council in their former proceedings the latter its public utility they consider as obvious to everyone you consider as the immense advantage of accurate numerical tables in all matters of calculation especially in those which relate to astronomy and navigation reports of the Royal Society 12th of February 1829 first it appears first that the Chancellor of the Exchequer presumed to set up his own idea of the utility of a difference engine in direct opposition to that of the Royal Society second that he refused to take the opinion of the highest mechanical authority in the country on its probable cost and even to be informed whether a contract of its construction at a definite sum might not be attainable he then boldly pronounced the expense to be utterly incapable of being calculated difference engine number two feels for the Chancellor of the Exchequer this much abused difference engine is however like its prior relative the analytical a being of sensibility of impulse and of power it cannot only calculate the millions the ex chancellor of the Exchequer squandered but it can deal with the smallest quantities nay it feels even for zeros it is as conscious as Lord Derby himself is of the presence of a negative quantity and it is not beyond the ken of either of them to foresee the existence of impossible ones yet should any unexpected cause of events ever raise the ex chancellor of the Exchequer to his former dignity I am sure he will be its friend as soon as he is convinced that it can be made useful to him to may possibly enable him to unmoddle even his own financial accounts and to but as I have no wish to crucify him I will leave his name in obscurity the hero stratus of science if he escaped oblivion will be linked with a destroyer of the aphesian temple end of section eight