668 LL. F. MENABREA ON BABBAGE’S ANALYTICAL ENGINE. | 
ging) ; each of these numbers may consist of twenty-five figures, 
Vy9 Voy «+++ ¥, being any numbers whatever, n being less than a 
hundred; if f (v,, V5 V3,» + Un) be any given function which can 
be formed by addition, subtraction, multiplication, division, ex- 
traction of roots, or elevation to powers, the machine will 
calculate its numerical value; it will afterwards substitute this. 
value in the place of v, or of any other variable, and will caleu- 
late this second function with respect to v. It will reduce to 
tables almost all equations of finite differences. Let us suppose 
that we have observed a thousand values of a, 6, c, d, and that 
we wish to calculate them by the formula p = a/ : ne the 
c 
machine must be set to calculate the formula; the first series of 
the values of a, 5, c, d must be adjusted to it; it will then calcu- 
late 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 dif- 
ficulties 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. 
