to mention here. After that work had been for several years in circulation in every part of Europe, it was discovered that the commencement of the table of co-tangents and co-secants was vitiated by an error of considerable magnitude. In the first co-tangent the last nine places of figures were incorrect; but from the manner in which the numbers of the table were computed, the error was gradually, though slowly, diminished, until at length it became extinguished in the eighty-sixth page. After the detection of this extensive error, Pitiscus undertook the recomputation of the eighty-six erroneous pages. His corrected calculation was printed, and the erroneous part of the remaining copies of the Opus Palatinum was cancelled. But as the corrected table of Pitiscus was not published until 1607,—thirteen years after the original work,—the erroneous part of the volume was cancelled in comparatively few copies, and consequently correct copies of the work are now exceedingly rare. Thus, in the collection of tables published by M. Schulze,11 the whole of the erroneous part of the Opus Palatinum has been adopted; he having used the copy of that work which exists in the library of the Academy of Berlin, and which is one of those copies in which the incorrect part was not cancelled. The corrected copies of this work may be very easily distinguished at present from the erroneous ones: it happened that the former were printed with a very bad and worn-out type, and upon paper of a quality inferior to that of the original work. On comparing the first eighty-six pages of the volume with the succeeding ones, they are, therefore, immediately distinguishable in the corrected copies. Besides this test, there is another, which it may not be uninteresting to point out:—At the bottom of page 7 in the corrected copies, there is an error in the position of the words basis and hypothenusa, their places being interchanged. In the original uncorrected work this error does not exist.
At the time when the calculation and publication of Taylor's Logarithms were undertaken, it so happened that a similar work was in progress in France; and it was not until the calculation of the French work was completed, that its author was informed of the publication of the English work. This circumstance caused the French calculator to relinquish the publication of his tables. The manuscript subsequently passed into the library of Delambre, and, after his death, was purchased at the sale of his books, by Mr Babbage, in whose possession it now is. Some years ago it was thought advisable to compare these manuscript tables with Taylor's Logarithms, with a view to ascertain the errors in each, but especially in Taylor. The two works were peculiarly well suited for the attainment of this end; as the circumstances under which they were produced, rendered it quite certain that they were computed independently of each other. The comparison was conducted under the direction of the late Dr Young, and the result was the detection of the following nineteen errors in Taylor's Logarithms. To enable those who used Taylor's Logarithms to make the necessary corrections in them, the corrections of the detected errors appeared as follows in the Nautical Almanac for 1832.
ERRATA, detected in Taylor's Logarithms. London: 4to, 1792.