But if these machines were ingenious, what shall we think of the calculating machine of Mr. Babbage?  What shall we think of an engine of wood and metal which can not only compute astronomical and navigation tables to any given extent, but render the exactitude of its operations mathematically certain through its power of correcting its possible errors?  What shall we think of a machine which can not only accomplish all this, but actually print off its elaborate results, when obtained, without the slightest intervention of the intellect of man?  It will, perhaps, be said, in reply, that a machine such as we have described is altogether above comparison with the Chess-Player of Maelzel.  By no means—­it is altogether beneath it—­that is to say provided we assume (what should never for a moment be assumed) that the Chess-Player is a pure machine, and performs its operations without any immediate human agency.  Arithmetical or algebraical calculations are, from their very nature, fixed and determinate.  Certain data being given, certain results necessarily and inevitably follow.  These results have dependence upon nothing, and are influenced by nothing but the data originally given.  And the question to be solved proceeds, or should proceed, to its final determination, by a succession of unerring steps liable to no change, and subject to no modification.  This being the case, we can without difficulty conceive the possibility of so arranging a piece of mechanism, that upon starting In accordance with the data of the question to be solved, it should continue its movements regularly, progressively, and undeviatingly towards the required solution, since these movements, however complex, are never imagined to be otherwise than finite and determinate.  But the case is widely different with the Chess-Player.  With him there is no determinate progression.  No one move in chess necessarily follows upon any one other.  From no particular disposition of the men at one period of a game can we predicate their disposition at a different period.  Let us place the first move in a game of chess, in juxta-position with the data of an algebraical question, and their great difference will be immediately perceived.  From the latter—­from the data—­the second step of the question, dependent thereupon, inevitably follows.  It is modelled by the data. It must be thus and not otherwise.  But from the first move in the game of chess no especial second move follows of necessity.  In the algebraical question, as it proceeds towards solution, the certainty of its operations remains altogether unimpaired.  The second step having been a consequence of the data, the third step is equally a consequence of the second, the fourth of the third, the fifth of the fourth, and so on, and not possibly otherwise, to the end.  But in proportion to the progress made in a game of chess, is the uncertainty of