Behind the Notes of Ada Lovelace - Note A

Ada Lovelace transcribed and adapted the lecture given by Charles Babbage to English in 1942 as was previously discussed in the post entitled "The First Programmer". The notes were written about Babbage's first invention, "The Difference Engine" and the "Analytical Engine". These machines unfortunately did not manifest due to funding issues among others. Lets look more deeply into some of the notes that were gathered as part of her set of 7 (A-G).

Note A
This set of notes were in relation to the Difference Engine. The particular function that the machine was constructed for is to tabulate the following:

The special purpose of the engine was the computation of nautical and astronomical tables. This included the integral of the expression above, which leads to:

uz = a+bx+cx2+dx3+ex4+fx5+gx6,

The constants, a,b,c, and d etc above, are represented on the discs in seven columns in the engine. This allows accurate and unlimited tabulation of all series whose general form may be expressed in the above formula. It could also tabulate approximate values between other intervals, which may be obtained by the Method of Differences.

The Analytical Engine however could not only tabulate the results of one particular function, but could develop and tabulate any function. The engine could be thought of as the material expression of any possible indefinite function of any complexity. This allowed functions like the following to be tabulated: 

F(x, y, z, log x, sin y, x ^p, &c.),

The engine was said to be in a state of neutral when it was ready to receive data, by means of cards. The cards actually self contained the law of development of the particular function that the machine may be evaluating. The would have to be inputted to the machine in a specific order for the machine to comply. [1] 

An original model of part of the Analytica Engine [2] 

This is a highly complex function that the early machine could carry out. It is quite incredible to think that an engine of such an early time could be capable of such mathematical tabulations.

By Sophie Wicks 

References 

[1] http://www.fourmilab.ch/babbage/sketch.html

[2] http://mentalfloss.com/article/53131/ada-lovelace-first-computer-programmer