SCALE, a mathematical instrument, consisting of several lines drawn on wood, brass, silver, &c. and variously divided, according to the purposes it is intended to serve whence it acquires various de nominations, as the plain scale, diagonal scale, plotting scale, Gunter's scale, &c.
See MATIMIATICAL INSTRUWErrS.
diagonal, is projected thus: first draw eleven parallel lines at equal distances, the whole length of which be ing divided into a certain number of equal parts, according to the length of the scale, by perpendicular parallels, let the first division be again subdivided into ten equal parts, both above and below; then drawing the oblique lines from the first perpendicular below to the first subdi vision above, and from the first subdi vision below to the second subdivision above, &c. the first space shall thereby be exactly divided into one hundred equal parts ; for as each of these subdivisions is one tenth part of the whole first space or division, so each parallel above it is one tenth of such subdivision, and con sequently one hundredth part of the whole first space; and if there be ten of the larger divisions, one thousandth part of the whole scale. If therefore the larger
divisions be accounted units, the first sub divisions will be tenth parts of an unit ; and the second subdivisions, marked by the diagonals on the parallels, hundredth parts of an unit. Again, if the larger divisions be reckoned tens, the first sub divisions will be units, and the second subdivisions tenth parts ; and if the larger divisions be accounted hundredths, the first subdivisions will be tens, and the second units : and so on.