Passages from the Life of a Philosopher. Charles Babbage

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      Description of the existing portion of Difference Engine No. 1.

       Table of Contents

      That portion of Difference Engine, No. 1, 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 contains 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 {64} described. It also contains two other figure-wheels, which with 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 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

      The lowest of these figure-wheels represents the unit’s figure of any number; the next above the ten’s 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 99999. 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 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 99999.

      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 whatever may be the numbers placed respectively on the figure-wheels of each of {65} the three columns, the following succession of operations will take place as long as the handle is moved:—

      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 No. 1, 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 had endowed it in its complete 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 1000, 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 difference {66} 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 28 and 30. 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 it 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.

      〈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 me thus: {67} “Pray, Mr. Babbage, can you explain to me in two words what is the principle of this machine?” Had the querist 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 indeed have been answered with six characters thus—

      Δ⁷ u_x = 0.

      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 the other a member of the Lower, House put this question. I am not able СКАЧАТЬ