Upon this, Professor MacCullagh naturally asked why, if the machine could tell whether the logarithm was the right one, it should have asked the attendant at all? I told him that the means employed were so ridiculously simple that I would not at that moment explain them; but that if he would come again in the course of a few days, I should be ready to explain it. Three or four days after, Bessel and Jacobi, who had just arrived in England, were sitting with me, inquiring about the Analytical Engine, when fortunately my friend MacCullagh was announced. The meeting was equally agreeable to us all, and we continued our conversation. After some time Bessel put to me the very same question which MacCullagh had previously asked. On this Jacobi remarked that he, too, was about to make the same inquiry when Bessel had asked the question. I then explained to them the following very simple means by which that verification was accomplished.
〈KNOWS WHAT IT WANTS.〉
Besides the sets of cards which direct the nature of the operations to be performed, and the variables or constants {121} which are to be operated upon, there is another class of cards called number cards. These are much less general in their uses than the others, although they are necessarily of much larger size.
Any number which the Analytical Engine is capable of using or of producing can, if required, be expressed by a card with certain holes in it; thus—
| NUMBER. | TABLE. | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 3 | 0 | 3 | 3 | 6 | 2 | 2 | 9 | 3 | 9 | |
| • | • | ◊ | • | • | • | • | • | • | • | • | |
| • | • | ◊ | • | • | • | • | • | • | • | • | |
| ◊ | • | ◊ | • | • | • | ◊ | ◊ | • | • | • | |
| ◊ | ◊ | ◊ | ◊ | ◊ | • | ◊ | ◊ | • | ◊ | • | |
| ◊ | ◊ | ◊ | ◊ | ◊ | • | ◊ | ◊ | • | ◊ | • | |
| ◊ | ◊ | ◊ | ◊ | ◊ | • | ◊ | ◊ | • | ◊ | • | |
| ◊ | ◊ | ◊ | ◊ | ◊ | ◊ | ◊ | ◊ | • | ◊ | • | |
| ◊ | ◊ | ◊ | ◊ | ◊ | ◊ | ◊ | ◊ | • | ◊ | • | |
| ◊ | ◊ | ◊ | ◊ | ◊ | ◊ | ◊ | ◊ | • | ◊ | • | |
The above card contains eleven vertical rows for holes, each row having nine or any less number of holes. In this example the tabular number is 3 6 2 2 9 3 9, whilst its number in the order of the table is 2 3 0 3. In fact, the former number is the logarithm of the latter.
The Analytical Engine will contain,
- 1st. Apparatus for printing on paper, one, or, if required, two copies of its results.
- 2nd. Means for producing a stereotype mould of the tables or results it computes.
- 3rd. Mechanism for punching on blank pasteboard cards or metal plates the numerical results of any of its computations.
〈STOPS AND RINGS A BELL.〉
Of course the Engine will compute all the Tables which {122} it may itself be required to use. These cards will therefore be entirely free from error. Now when the Engine requires a tabular number, it will stop, ring a bell, and ask for such number. In the case we have assumed, it asks for the logarithm of 2 3 0 3.