Atlantic,—­first landfall to the homeward-bound American vessel.  We must, said he, by our last observations and reckoning, be within three or four miles of Cape Race.  A comparison of these two remarks, under the circumstances in which we were placed at the moment, brought my mind to the conclusion, that it is greatly to be wished that the means should be discovered of finding the ship’s place more accurately, or that navigators would give Cape Race a little wider berth.  But I do not remember that one of the steam packets between England and America was ever lost on that formidable point.

It appears to me by no means unlikely that, with the improvement of instrumental power, and of the means of ascertaining the ship’s time with exactness, as great an advance beyond the present state of art and science in finding a ship’s place at sea may take place, as was effected by the invention of the reflecting quadrant, the calculation of lunar tables, and the improved construction of chronometers.

BABBAGE’S DIFFERENCE MACHINE.

In the wonderful versatility of the human mind, the improvement, when made, will very probably be made by paths where it is least expected.  The great inducement to Mr. Babbage to attempt the construction of an engine by which astronomical tables could be calculated, and even printed, by mechanical means and with entire accuracy, was the errors in the requisite tables.  Nineteen such errors, in point of fact, were discovered in an edition of Taylor’s Logarithms printed in 1796; some of which might have led to the most dangerous results in calculating a ship’s place.  These nineteen errors, (of which one only was an error of the press), were pointed out in the Nautical Almanac for 1832.  In one of these errata the seat of the error was stated to be in cosine of 14 degrees 18 minutes 3 seconds.  Subsequent examination showed that there was an error of one second in this correction; and, accordingly, in the Nautical Almanac of the next year a new correction was necessary.  But in making the new correction of one second, a new error was committed of ten degrees.  Instead of cosine 14 degrees 18 minutes 2 seconds the correction was printed cosine 4 degrees 18 minutes 2 seconds making it still necessary, in some future edition of the Nautical Almanac, to insert an erratum in an erratum of the errata in Taylor’s logarithms.[A]

[Footnote A:  Edinburgh Review, Vol.  LIX., 282.]

In the hope of obviating the possibility of such errors, Mr. Babbage projected his calculating, or, as he prefers to call it, his difference machine.  Although this extraordinary undertaking has been arrested, in consequence of the enormous expense attending its execution, enough has been achieved to show the mechanical possibility of constructing an engine of this kind, and even one of far higher powers, of which Mr. Babbage has matured the conception, devised the notation, and executed the drawings—­themselves an imperishable monument of the genius of the author.