Passages from the Life of a Philosopher. Charles Babbage

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      CHAPTER V. DIFFERENCE ENGINE NO. 1.

       Table of Contents

      “Oh no! we never mention it,

      Its name is never heard.”

      Difference Engine No. 1—First Idea at Cambridge, 1812—Plan for Dividing Astronomical Instruments—Idea of a Machine to calculate Tables by Differences—Illustrations by Piles of Cannon-balls.

      CALCULATING MACHINES comprise various pieces of mechanism for assisting the human mind in executing the operations of arithmetic. Some few of these perform the whole operation without any mental attention when once the given numbers have been put into the machine.

      Others require a moderate portion of mental attention: these latter are generally of much simpler construction than the former, and it may also be added, are less useful.

      The simplest way of deciding to which of these two classes any calculating machine belongs is to ask its maker—Whether, when the numbers on which it is to operate are placed in the instrument, it is capable of arriving at its result by the mere motion of a spring, a descending weight, or any other constant force? If the answer be in the affirmative, the machine is really automatic; if otherwise, it is not self-acting.

      Of the various machines I have had occasion to examine, many of those for Addition and Subtraction have been found {42} to be automatic. Of machines for Multiplication and Division, which have fully come under my examination, I cannot at present recall one to my memory as absolutely fulfilling this condition.

      〈ORIGIN OF DIFFERENCE ENGINE.〉

      The earliest idea that I can trace in my own mind of calculating arithmetical Tables by machinery arose in this manner:—

      One evening I was sitting in the rooms of the Analytical Society, at Cambridge, my head leaning forward on the Table in a kind of dreamy mood, with a Table of logarithms lying open before me. Another member, coming into the room, and seeing me half asleep, called out, “Well, Babbage, what are you dreaming about?” to which I replied, “I am thinking that all these Tables (pointing to the logarithms) might be calculated by machinery.”

      I am indebted to my friend, the Rev. Dr. Robinson, the Master of the Temple, for this anecdote. The event must have happened either in 1812 or 1813.

      About 1819 I was occupied with devising means for accurately dividing astronomical instruments, and had arrived at a plan which I thought was likely to succeed perfectly. I had also at that time been speculating about making machinery to compute arithmetical Tables.

      One morning I called upon the late Dr. Wollaston, to consult him about my plan for dividing instruments. On talking over the matter, it turned out that my system was exactly that which had been described by the Duke de Chaulnes, in the Memoirs of the French Academy of Sciences, about fifty or sixty years before. I then mentioned my other idea of computing Tables by machinery, which Dr. Wollaston thought a more promising subject.

      I considered that a machine to execute the mere isolated {43} operations of arithmetic, would be comparatively of little value, unless it were very easily set to do its work, and unless it executed not only accurately, but with great rapidity, whatever it was required to do.

      〈ADDITION AND CARRIAGE.〉

      On the other hand, the method of differences supplied a general principle by which all Tables might be computed through limited intervals, by one uniform process. Again, the method of differences required the use of mechanism for Addition only. In order, however, to insure accuracy in the printed Tables, it was necessary that the machine which computed Tables should also set them up in type, or else supply a mould in which stereotype plates of those Tables could be cast.

      I now began to sketch out arrangements for accomplishing the several partial processes which were required. The arithmetical part must consist of two distinct processes—the power of adding one digit to another, and also of carrying the tens to the next digit, if it should be necessary.

      The first idea was, naturally, to add each digit successively. This, however, would occupy much time if the numbers added together consisted of many places of figures.

      The next step was to add all the digits of the two numbers each to each at the same instant, but reserving a certain mechanical memorandum, wherever a carriage became due. These carriages were then to be executed successively.

      Having made various drawings, I now began to make models of some portions of the machine, to see how they would act. Each number was to be expressed upon wheels placed upon an axis; there being one wheel for each figure in the number operated upon.

      Having arrived at a certain point in my progress, it became necessary to have teeth of a peculiar form cut upon these {44} wheels. As my own lathe was not fit for this job, I took the wheels to a wheel-cutter СКАЧАТЬ