On the carpenter's and engineer's eliding-rule are engraved a number of numerals in columns with headings, of which the following is a specimen:— These divisors (called gauge-points) are intended to convert into pounds the weight of a rectangular prism, cylinder, or globe, of cast iron ; the first, on three suppositions, namely, all dimensions in feet, one in feet and two in inches, and all in inches ; the second, ou the auppositiona that the length is in feet and the diameter in inches, and that both are in inches ; the third, on the supposition that tho llamasr is either in feet or in inches. We shall here content ourselves with verifying one of these, say the first of those marked " cylinder," which will show the nature of the divisor.
The specific gravity of cast-iron is 7'207, and the content of a cylinder of D inches diameter and a feet of length is /854 x divided by 144, .n cubic feet. A cubic foot of water weighs pounds avoirdupois : me of cast-iron, therefore, weighs 62.321 x 7•207; whence the weight if the cylinder is, in pounds, mar enough. to .411 to illustrate our object, but showing that the !omputer of this divisor used a specific gravity slightly differing from he above. The rule in all tho cases is to multiply the three dimensions egether, diameters or lengths, and to divide by the divisor given in he table. The term gauge-point, which properly belongs to the part of the scale on which the divisor is marked, has passed to the divisor Itself.
The following list of sliding.rules contains all, or nearly all, which can be useful to any one :— 1. Common Engineer's Rule, or Carpenter's Rule in its beet form. A double 12.inch rule, a slide of two radii with the mine scale on one side, and a scale of one radius of double length ou the other, with divieors. (Sold by all rule makers.) There is a description In Kentish 's ' Treatise on a Box of Instruments,' &c., London, 1839.
2. Ilevan's Engineer's Rule, 12 indica. Has slides on both faces (which may be exchanged), and serves for squares, cubes, square roots of cubes, he There are scales on the backs of the slides and in the grooves, for sines, tangents, inverted numbers, compound interest and annuities et 5 per cent. (Cary, Strand, with an explanatory treatise.) Ilenderson's Double-Slide Rule, 12 inches. Hu two parallel con tiguous slides, with scales of numbers fixed above and below, and solves at one operation must sets of multiplications and divisions not exceeding five operations. At the back are tables of divisors for Solids.
4. 1Voollgar's l'ocket Calculator, 8 inches. The two slides work in
either of the grooves : the backs and the grooves have scales of sines, tangents, areas of polygons, circular segments ; iuterest, annuities, certain and for lives, at several rates of interest. An addition may be made by a metal slip, giving the solution of the same questions as the Last rule.
5. Woollgar's Pocket-Book Rule, 6 and 8 Riches. Two radii, one under the other, as described in the preceding part • of the article; a line for sines aud duplicate proportions at the back of the elide, At the bottom of the groove arc sometimes inserted lines for finding the relations of right-angled triangles, for cask-gauging, and for cuttings and embankments.
6. Excise Officer's Sliding Rule, modern form. Sold at the Excise Store-office, and by some of the instrument-makers. The old Excise rule was a thick block, with a slide on each face.
7. Bayley's Rule, (Elliot, Strand) has a scale of numbers, squares, and cubes, and a scale of equal parts, of the length of the line of squares, from which the logarithm of a number can be approximately read. This line is of considerable use in operations connected with higher powers : it is found also in Bevan's rules. The constructor of this scale, which is well divided and convenient, has a full treatise on the whole subject in the press.
Among separate treatises not yet noted are Flower's, Svo., London, 1763; 31ackay's, tiro., 2nd edit., London, 1811 ; do. Leith, 1812 ; ' Instruction sur la lklanilire de se scrvir do Is Regle h Calcul.,' petit-in 8vo., Paris et Dijon, 1825; The Universal Ready-Reckoner,' by an Idle Gentleman, 12mo., London, 1839 ; and there is a good deal on the subject in Ingram's ' Concise System of Mathematics,' 12mo., Edin burgh ; and Bateman's Excise Officer's Manual,' 12mo., London.
Between the sliding-rule and the book of logarithms comes the card of four-figure logarithms, published by Messrs. Taylor and Walton (explained in the 'Companion to the Almanac ' for 1841), to which has been added a similar card for sines and tangents. A sliding-rule, which would in et/ parts compete with these tables in accuracy must have a radios of from 8 to 10 feet, and would be unmanageable. At what length the card begins to be more easily used than the rule we cannot determine, but we should suspect that the former would be preferable to a rule of four feet radius. We have found the rule of 24 inches extremely useful in checking the material figures of more minute cal culations, particularly when there are many divisions by the same divisor.