# Page:Scientific Memoirs, Vol. 3 (1843).djvu/678

668
L. F. MENABREA ON BABBAGE'S ANALYTICAL ENGINE.

ging); each of these numbers may consist of twenty-five figures, ${\displaystyle \scriptstyle {v_{1},v_{2},\ldots \ldots v_{n}}}$ being any numbers whatever, ${\displaystyle \scriptstyle {n}}$ being less than a hundred; if ${\displaystyle \scriptstyle {f(v_{1},v_{2},v_{3},..v_{n})}}$ be any given function which can be formed by addition, subtraction, multiplication, division, extraction of roots, or elevation to powers, the machine will calculate its numerical value; it will afterwards substitute this value in the place of ${\displaystyle \scriptstyle {v}}$, or of any other variable, and will calculate this second function with respect to ${\displaystyle \scriptstyle {v}}$. It will reduce to tables almost all equations of finite differences. Let us suppose that we have observed a thousand values of ${\displaystyle \scriptstyle {a}}$, ${\displaystyle \scriptstyle {b}}$, ${\displaystyle \scriptstyle {c}}$, ${\displaystyle \scriptstyle {d}}$, and that we wish to calculate them by the formula ${\displaystyle \scriptstyle {p={\sqrt {\frac {a+b}{cd}}}}}$, the machine must be set to calculate the formula; the first series of the values of ${\displaystyle \scriptstyle {a}}$, ${\displaystyle \scriptstyle {b}}$, ${\displaystyle \scriptstyle {c}}$, ${\displaystyle \scriptstyle {d}}$ must be adjusted to it; it will then calculate them, print them, and reduce them to zero; lastly, it will ring a bell to give notice that a new set of constants must be inserted. When there exists a relation between any number of successive coefficients of a series, provided it can be expressed as has already been said, the machine will calculate them and make their terms known in succession; and it may afterwards be disposed so as to find the value of the series for all the values of the variable.'

"Mr. Babbage announces, in conclusion, 'that the greatest difficulties of the invention have already been surmounted, and that the plans will be finished in a few months.'"

In the Ninth Bridgewater Treatise, Mr. Babbage has employed several arguments deduced from the Analytical Engine, which afford some idea of its powers. See Ninth Bridgewater Treatise, 8vo, second edition. London, 1834.

Some of the numerous drawings of the Analytical Engine have been engraved on wooden blocks, and from these (by a mode contrived by Mr. Babbage) various stereotype plates have been taken. They comprise—

1. Plan of the figure wheels for one method of adding numbers.

2. Elevation of the wheels and axis of ditto.

3. Elevation of framing only of ditto.

4. Section of adding wheels and framing together.

5. Section of the adding wheels, sign wheels and framing complete.

6. Impression from the original wood block.