Augusta Ada Byron (1815-1852)

“Observations on Mr. Babbage's Analytic Engine&rdquo under the pseudonym of A. A. L. appeared in September 1843 in Taylor's Scientific Memoirs, a series of books with selections from transactions of foreign academic societies. It appeared in the third of the 5 volumes of Scientific Memoirs.

Let us now suppose that we have two expressions whose values have been computed by the engine independently of each other (each having its own group of columns for data and results). Let them be a x n, bpy. They would then stand as follows on the columns:--

We may now desire to combine together these two results, in any manner we please; in which case it would only be necessary to have an additional card or cards, which shoul order the requisite operations to be performed with the numbers on the two result-columns V4 and V8, and the result of these futher operations to appear on a new column, V9. Say we wish to divide a x n by bpy. ...

Picture of Ada Lovelace.
From ei.cs.vt.edu/~history
picture of Ada Lovelace

difference engine Sketch of the difference engine.
From ei.cs.vt.edu/~history

reconstruction of difference engine
A modern reconstruction of the difference engine. From ei.cs.vt.edu/~history

The Bernoulli polynomials satisfy

B'_(k+1)(x) = (k+1) B_k(x) and B_(2k+1)(0)=B_(2k+1)(1)=0 for l>0
so
B_0(x)=1, B_1(x)=x-1/2, B_2(x)=x^2-x+1/6, B_3(x)=x^3-3/2x^2+1/2x, B_4(x)=x^4-2x^3+x^2-1/30, ...
The constant terms B_k=B_k(0) are the Bernoulli numbers: 1, -1/2, 1/6, 0, -1/30, 0, 1/42, ...

Additional information about Ada Lovelace

Philip Morrison and Emily Morrison, eds. Charles Babbage and his Calculating Engines, Selected Writings by Charles Babbage and Others, Dover, NY, 1961.

John Fuegi and Jo Francis, "Lovelace & Babbage and the Creation of the 1843 'Notes'," IEEE Annals of the History of Computing, volume 25, number 4, pages 16-16, Oct-Dec, 2003.


Ryan Stansifer <ryan@cs.fit.edu>
Last modified: Thu Aug 19 14:27:58 EDT 2004