I propose in the Engine I am constructing to have places for only a thousand constants, because I think it will be more than sufficient. But if it were required to have ten, or even a hundred times that number, it would be quite possible to make it, such is the simplicity of its structure of that portion of the Engine.
(_c_). The next stage in the arithmetic is the number of times { 127} the four processes of addition, subtraction, multiplication, and division can be repeated. It is obvious that four different cards thus punched
+ − × ÷ ┌───────┐ ┌───────┐ ┌───────┐ ┌───────┐ │◊ ◊ ◊ │ │◊ ◊ ◊│ │◊ ◊ ◊│ │ ◊ ◊ ◊│ └───────┘ └───────┘ └───────┘ └───────┘
would give the orders for the four rules of arithmetic.
Now there is no limit to the number of such cards which may be strung together according to the nature of the operations required. Consequently the condition (_c_) is fulfilled.
(_d_). The fourth arithmetical condition (_d_), that the order of succession in which these operations can be varied, is itself _unlimited_, follows as a matter of course.
The four remaining conditions which must be fulfilled, in order to render the Analytical Engine as general as the science of which it is the powerful executive, relate to algebraic quantities with which it operates.
The thousand columns, each capable of holding any number of less than fifty-one places of figures, may each represent a constant or a variable quantity. These quantities I have called by the comprehensive title of variables, and have denoted them by V_{ _n_}, with an index below. In the machine I have designed, _n_ may vary from 0 to 999. But after any one or more columns have been used for variables, if those variables are not required afterwards, they may be printed upon paper, and the columns themselves again used for other variables. In such cases the variables must have a new index; thus, ^{ _m_}V^{ _n_}. I propose to make _n_ vary from 0 to 99. If more variables are required, these may be supplied by Variable Cards, which may follow each other in unlimited succession. Each card will cause its symbol to be printed with its proper indices. { 128}
For the sake of uniformity, I have used V with as many indices as may be required throughout the Engine. This, however, does not prevent the printed result of a development from being represented by any letters which may be thought to be more convenient. In that part in which the results are printed, type of any form may be used, according to the taste of the proposer of the question.