Mr. H. P. Babbage said,—The system of describing machinery, of which I am about to give a brief outline, is not new. It was published by Mr. Babbage, in the ‘Philosophical Transactions,’ in the year 1826, where apparently it did not attract the notice of those most likely to find it practically useful. It had been used for some years before this in the construction, for the Government, of the Difference Engine, which is now in the Museum at King's College, London; and it was also used in the contrivance of the Analytical Engine, on which my father was engaged for many years. Indeed, without the aid of the mechanical notation, it would be beyond the power of the human mind to master and retain the details of the complicated machinery which such an engine necessarily requires. Its importance as a tool for the invention of machinery for any purpose is very great; since we can demonstrate the practicability of any contrivance, and the certainty of all its parts working in unison, before a single part of it is actually made. It is also important both as a means of understanding and of explaining to others existing machinery; for it is utterly impossible to make the notation of a machine without comprehending its action in every single part. There are also many other uses, which I shall not now stop to mention. The general principles of the notation are the same now as in 1826; but the practical experience of many years has, of course, suggested several alterations of detail, and led to the adoption of some important principles.