Page:Passages from the Life of a Philosopher.djvu/77

Rh {| align="center"
 * 2648
 * 4564
 * align="center" | Stages&emsp;
 * align="center" rowspan="2" | 1
 * rowspan="2"|
 * 6102
 * Add each digit to the digit above.
 * 111
 * Record the carriages.
 * align="center" | 2
 * 7212
 * Add the above carriages.
 * }
 * rowspan="2"|
 * 6102
 * Add each digit to the digit above.
 * 111
 * Record the carriages.
 * align="center" | 2
 * 7212
 * Add the above carriages.
 * }
 * align="center" | 2
 * 7212
 * Add the above 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, 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:—