Page:Passages from the Life of a Philosopher.djvu/59
ADDITION AND CARRIAGE. 43
operationB of arithmetic^ would be oomparatiyely of little valae, 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.
On the other hand, the method of differences supplied a general principle by which oC Tables might be computed through limited intervals, by one uniform process* Again, the method of differences reqaired the use of mechanism for Addition only. In order, however, to insure accuracy in the printed Tables, it was necessary that the machine which com- puted 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