SLIDING

, in Mechanics, is when the same point of a body, moving along a surface, describes a line on | that surface. Such is the motion of a parallelopipedon moved along a plane.

From Sliding arises friction.

Sliding Rule, a mathematical instrument serving to perform computations in gauging, measuring, &c, without the use of compasses; merely by the sliding of the parts of the instrument one by another, the lines and divisions of which give the answer or amount by inspection.

This instrument is variously contrived and applied by different authors, particularly Gunter, Partridge, Hunt, Everard, and Coggeshall; but the most usual and useful ones are those of the two latter.

Everard's Sliding Rule is chiefly used in cask gauging. It is commonly made of box, 12 inches long, 1 inch broad, and (6/10) of an inch thick. It consists of three parts; viz, the stock just mentioned, and two thin slips, of the same length, sliding in small grooves in two opposite sides of the stock: consequently, when both these pieces are drawn out to their full extent, the instrument is 3 feet long.

On the first broad face of the instrument are four logarithmic lines of numbers; for the properties &c, of which, see Gunter's Line. The first, marked A, consisting of two radii numbered 1, 2, 3, 4, 5, 6, 7, 8, 9, 1; and then 2, 3, 4, 5, &c, to 10. On this line are four brass centre-pins, two in each radius; one in each of them being marked MB, for malt-bushel, is set at 2150.42 the number of cubic inches in a maltbushel; the other two are marked with A, for ale-gallon, at 282, the number of cubic inches in an ale gallon. The 2d and 3d lines of numbers are on the sliding pieces, and are exactly the same with the first; but they are distinguished by the letter B. In the first radius is a dot, marked Si, at .707, the side of a square inscribed in a circle whose diameter is 1. Another dot, marked Se. stands at .886, the side of a square equal to the area of the same circle. A third dot, marked W, is at 231, the cubic inches in a wine gallon. And a fourth, marked C, at 3.14, the circumference of the same circle whose diameter is 1. The fourth line of numbers, marked MD, to signify malt-depth, is a broken line of two radii, numbered 2, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, &c; the number 1 being set directly against MB on the first radius.

On the second broad face, marked cd, are several lines: as 1st, a line marked D, and numbered 1, 2, 3, &c, to 10. On this line are four centre pins: the first, marked WG, for wine-gauge, is at 17.15, the gaugepoint for wine gallons, being the diameter of a cylinder whose height is one inch, and content 231 cubic inches, or a wine gallon: the second centre-pin, marked AG, for ale-gauge, is at 18.95, the like diameter for an ale gallon: the 3d, marked MS, for malt square, is at 46.3, the square root of 2150.42, or the side of a square whose content is equal to the number of inches in a solid bushel: and the fourth, marked MR, for malt-round, is at 52.32, the diameter of a cylinder, or bushel, the area of whose base is the same 2150.42, the inches in a bushel. 2dly, Two lines of numbers on the sliding piece, on the other side, marked C. On these are two dots; the one, marked c, at .0795, the area of a circle whose circumference is 1; and the other, marked d, at .785, the area of the circle whose diame- ter is 1. 3dly, Two lines of segments, each numbered 1, 2, 3, to 100; the first for finding the ullage of a cask, taken as the middle frustum of a spheroid, lying with its axis parallel to the horizon; and the other for finding the ullage of a cask standing.

Again, on one of the narrow sides, noted c, are, 1st, a line of inches, numbered 1, 2, 3, &c to 12, each subdivided into 10 equal parts. 2dly, A line by which, with that of inches, we find a mean diameter for a cask, in the figure of the middle frustum of a spheroid: it is marked Spheroid, and numbered 1, 2, 3, &c to 7. 3dly, A line for finding the mean diameter of a cask, in the form of the middle frustum of a parabolic spindle, which gaugers call the second variety of casks; it is therefore marked Second Variety, and is numbered 1, 2, 3, &c.

4thly, A line by which is found the mean diameter of a cask of the third variety, consisting of the frustums of two parabolic conoids, abutting on a common base; it is therefore marked Third Variety, and is numbered 1, 2, 3, &c.

On the other narrow face, marked f, are 1st, a line of a foot divided into 100 equal parts, marked FM. 2dly, A line of inches, like that before mentioned, marked IM. 3dly, A line for finding the mean diameter of the fourth variety of casks, which is formed of the frustums of two cones, abutting on a common base. It is numbered 1, 2, 3, &c; and marked EC, for frustum of a cone.

On the backside of the two sliding pieces is a line of inches, from 12 to 36, for the whole extent of the 3 feet, when the pieces are put endwise, and against that, the correspondent gallons, and 100th parts, that any small tub, or the like open vessel, will contain at 1 inch deep.

For the various uses of this instrument, see the authors mentioned above, and most other writers on Gauging.

Coggeshall's Sliding Rule is chiefly used in measuring the superficies and solidity of timber, masonry, brickwork, &c.

This consists of two rulers, each a foot long, which are united together in various ways. Sometimes they are made to slide by one another, like glaziers' rules: sometimes a groove is made in the sideof a common twofoot joint rule, and a thin sliding piece in one side, and Coggeshall's lines added on that side; thus forming the common or Carpenter's rule: and sometimes one of the two rulers is made to slide in a groove made in the side of the other.

On the Sliding side of the rule are four lines of numbers, three of which are double, that is, are lines to two radii, and the fourth is a single broken line of numbers. The first three, marked A, B, C, are sigured 1, 2, 3, &c to 9; then 1, 2, 3, &c to 10; the construction and use of them being the same as those on Everard's Sliding rule. The single line, called the girt line, and marked D, whose radius is equal to the two radii of any of the other lines, is broken for the easier measuring of timber, and figured 4, 5, 6, 7, 8, 9, 10, 20, 30, &c. From 4 to 5 it is divided into 10 parts, and each 10th subdivided into 2; and so on from 5 to 10, &c.

On the backside of the rule are, 1st, a line of inch measure, from 1 to 12; each inch being divided and subdivided. 2dly, A line of foot measure, consisting | of one foot divided into 100 equal parts, and figured 10, 20, 30, &c.

The backside of the sliding piece is divided into inches, halves, &c, and figured from 12 to 24; so that when the slide is out, there may be a measure of 2 feet.

In the Carpenter's rule, the inch measure is on one side, continued all the way from 1 to 24, when the rule is unfolded, and subdivided into 8ths or half-quarters: on this side are also some diagonal scales of equal parts. And upon the edge, the whole length of 2 feet is divided into 200 equal parts, or 100ths of a foot.