ON BABBAGE’S ANALYTICAL ENGINE. 697 
idea of applying the cards had occurred; and the Analytical Engine 
does not occupy common ground with mere “ calculating machines.” 
_ It holds a position wholly its own; and the considerations it suggests 
ate most interesting in their nature. In enabling mechanism to com- 
_ bine together general symbols, in successions of unlimited variety and 
extent, a uniting link is established between the operations of matter 
and the abstract mental processes of the most abstract branch of mathe- 
“matical science. A new, a vast, and a powerful language is developed 
for the future use of analysis, in which to wield its truths so that these 
_ may become of more speedy and accurate practical application for the 
_ purposes of mankind than the means hitherto in our possession have 
_ rendered possible. Thus not only the mental and the material, but the 
_ theoretical and the practical in the mathematical world, are brought 
_ into more intimate and effective connexion with each other. We are 
_ not aware of its being on record that anything partaking in the nature 
of what is so well designated the Analytical Engine has been hitherto 
_ proposed, or even thought of, as a practical possibility, any more than 
_ the idea of a thinking or of a reasoning machine. 
We will touch on another point which constitutes an important 
distinction in the modes of operating of the Difference and Analy- 
tical Engines. In order to enable the former to do its business, it is 
“necessary to put into its columns the series of numbers constituting the 
_ first terms of the several orders of differences for whatever is the par- 
ticular table under consideration. The machine then works upon 
these as its data. But these data must themselves have been already 
_ computed through a series of calculations by ahuman head. Therefore 
that engine can only produce results depending on data which have 
been arrived at by the explicit and actual working out of processes 
_ that are in their nature different from any that come within the sphere 
of its own powers. In other words, an analysing process must have been 
gone through bya human mind in order to obtain the data upon which 
_ the engine then synthetically builds its results. The Difference Engine 
_is in its character exclusively synthetical, while the Analytical Engine 
s equally capable of analysis or of synthesis. 
It is true that the Difference Engine can calculate toa much greater 
extent with these few preliminary data, than the data themselves re- 
quired for their own determination. The table of squares, for instance, 
tan be calculated to any extent whatever, when the numbers one and 
two are furnished ; and a very few differences computed at any part of 
a table of logarithms would enable the engine to calculate many hun- 
_ dreds or even thousands of logarithms. Still the circumstance of its 
_ requiring, as a previous condition, that, any function whatever shall 
have been numerically worked out, makes it very inferior in its nature 
and advantages to an engine which, like the Analytical Engine, requires 
merely that we should know the succession and distribution of the ope- 
rations to be performed ; without there being any occasion*, in order 
to obtain data on which it can work, for our ever having gone through 
either the same particular operations which it is itself to effect, or any 
ers. Numerical data must of course be given it, but they are mere 
arbitrary ones ; not data that could only be arrived at through a syste- 
matie and necessary series of previous numerical calculations, which 
is quite a different thing. 
* This subject is further noticed in Note F, 
