GUNTER'S line, a logarithmic line, tint, ally graduated upon scales, sectors, &c. It is also called the line of lines and line of numbers ; being only the logarithms graduated upon a ruler, which therefore serves to solve problems instrumentally, in the same manner as logarithms do arithmetically. It is usually divided into an hundred parts, every tenth thereof is numbered, beginning with 1, and ending with 10 ; so that if the first great division marked 1, stand for one tenth of any in teger, the next division, marked 2, will stand for two.tenths; 3, three-tenths, and soon ; and the intermediate divisions, will in like manner represent 100th parts of the same integer. If each of the great divisions represent 10 integers, then will the lesser divisions stand for integers ; and if the great divisions be supposed each 100, the subdivisions will be each 10.
Guxxsa's line, use of 1. find the product of two numbers." From 1 ex- tend the compasses to the multiplier ; and the same extent, applied the same way from the multiplicand, will reach to the proillict. Thus, if the product of 4 and 8 be required, extend the compasses from 1 to 4, and that extent, laid from 8 the same way, will reach to 32, their pro duct. 2. " To divide one number by another." The extent from the divisor to unity will reach from the dividend to the quotient ; thus, to divide 36 by 4, ex tend the compasses from 4 to 1, and the tame extent will reach from 36 to 9, the quotient sought. 3. " To three given
numbers, to find a fourth proportional." Suppose the numbers 6, 8, 9; extend the compasses from 6 to 8, and this extent, laid from 9 the same way, will reach to 12. the fourth proportional required. 4. " To find a mean proportional between any two given numbers." Suppose 8 and 32 : extend the compasses from 8 in the left-hand part of the line to 32 in the right ; then bisecting this distance, its half will reach from 8 forward, or from 32 backward, to 16, the mean propor tional sought. 5. " To extract the square root of any number." Suppose 25: bisect the distance between one on the scale and the point representing 25 ; then the half of this distance, set off from 1, will give the point representing the root 5. In the same manner the cube root, or that of any higher power, may be found, by dividing the distance on the line, be tween 1 and the given number, into as many equal parts as the index of the power expresses ; then one of those parts, set from 1, will find the point represent ing the root required.
Guszxa'a quadrant, one made of wood, brass, &c. containing a kind of stereo graphic projection of the sphere, on the plane of the equinoctial; the eye being supposed placed in one of the poles. Be sides the use of this quadrant in finding heights and distances, it serves also to find the hour of the day, the sun's azimuth, and other problems of the globe.