Page:Passages from the Life of a Philosopher.djvu/404

388 most complicated kind, to which they contributed. I observed that the Tables thus formed were of so artificial and abstract a nature, that I could not foresee the time when they would be of any use.

This remark additionally excited their curiosity, and they requested me to set the machine at work to compute such a table.

Having taken a simple case of this kind, I set the Engine to do its work, and then told them—

That it was now prepared to count the natural numbers; but that it would obey this law only as far as the millionth term.

That after that term it would commence a series, following a different, but known law, for a very long period.

That after this new law had been fulfilled for another long period, it would then suddenly abandon it, and calculate the terms of a series following another new law, and so on throughout all time.

Of course it was impossible to verify these assertions by making the machine actually go through the calculations; but, after having made the Engine count the natural numbers for some time, I proceeded to point out the fact, that it was impossible, by its very structure, that the machine could record any but the natural numbers before it reached the number 999,990. This I made evident to my friends, by showing them the actual structure of the Engine. Having demonstrated this to their entire satisfaction, I put the machine on to the number 999,990, and continued to work the Engine, when the result I had predicted soon arrived. After the millionth term a new law was taken up, and my friends were convinced that it must, from the very structure of the machine, continue for a very long time, and then