Page:Philosophical Transactions - Volume 096.djvu/383

examining parts taken at random, we may in some cases satisfy ourselves of its accuracy, as well as by examining the whole.^[1]

Among the various methods of computing logarithms, none, that I know of, possesses this advantage of forming them with tolerable ease independently of each other by means of a few easy bases. This desideratum, I trust, the following method will supply, while at the same time it is peculiarly easy of application, requiring no division, multiplication, or extraction of roots, and has its relative advantages highly increased by

The chief part of the working consists in merely setting down a number under itself removed one or more places to the right, and subtracting, and repeating this operation; and consequently is very little liable to mistake. Moreover, from e commodious manner in which the work stands, it may be revised with extreme rapidity. It may be performed after a few minutes instruction by any one who is competent to subtract. It is as easy for large numbers as for small; and on an average about 27 subtractions will furnish a logarithm acccurately to 10 places of decimals. In general $9\times {\frac {n+1}{2}}$ subtractions will be accurate to $2n$ places of decimals.

In computing hyperbolic logarithms by this method it is necessary to have previously establised the h. logs. of ${\frac {10}{9}},{\frac {100}{99}},{\frac {1000}{999}},$ &c. of 2 and of 10.

1. For example, we may wish to know whether the editor of a table has been careless. We examine detached portions here and there to a certain extent; if we find no errors, we have a moral certainty that the editor was careful, and consequently a moral certainty that the edition is accurate.