Passages from the Life of a Philosopher

by Charles Babbage

Let us now examine the case in which there were several carriages. Its successive stages may be better explained, thus—

Stages.
	2648
	4584
1 Add units’ figure = 4	2642
2 Carry	1
	2652
3 Add tens’ figure = 8	8
	2632
4 Carry	1
	2732
5 Add hundreds’ figure = 5	5
	2232
6 Carry	1
	3232
7 Add thousands’ figure = 4	4
	7232
8 Carry 0. There is no carr.

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:— {61}

Stages
	2648
	4564
1	6102	Add each digit to the digit above.
	111	Record the carriages.
2	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, nine, 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:—

Stages
	8473
	1528
1 Add all the digits	9991
2 Carry on tens and warn next car.	1
	9901
3 Carry on hundreds, and ditto	1
	9001
4 Carry on thousands, and ditto	1
	00001
5 Carry on ten thousands	1
	10001

{62}

In this case the carriages only become known successively, and they 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 bears 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 an axis, these successive carriages were accomplished.