Page:The Construction of the Wonderful Canon of Logarithms.djvu/120

96 Notes. translation of the passage is given in the ‘Edinburgh New Philosophical Journal’ for April 1836, p. 285:—

It has been said, and Delambre repeats the remark, that the last figures of his [Napier’s] numbers are inaccurate: this is a truth, but it would have been a truth of more value to have ascertained whether the inaccuracy resulted from the method, or from some error of calculation in its applications. This I have done, and thereby have detected that there is in fact a slight error of this kind, a very slight error, in the last term of the second progression which he forms preparatory to the calculation of his table. Now all the subsequent steps are deduced from that, which infuses those slight errors that have been remarked. I corrected the error; and then, using his method, but abridging the operations by our more rapid processes of development, calculated the logarithm of 5000000, which is the last in Napier’s table, and consequently that upon which all the errors accumulate; I found for its value 6931471.808942, whereas by the modern series, it ought to be 6931471.805599; thus the difference commences with the tenth figure.

It has been shown in the foregoing pages that the difference referred to does not really commence until the fifteenth figure.

Numerical errata in the text—In consequence of what is mentioned above, the figures in the text are in many places more or less inaccurate, but after careful consideration it is thought that the course least open to objection is to give them as in the original.

Different