The correction may also be found as follows:- Set the length upon c against 12 upon D, and against half the excess of the breadth over the thickness upon D will be found upon o the required correction in cubic feet. As the error of the result obtained with the rule may amount to theth part of the whole, the correction given above may always be neglected, whenever the excess of the breadth over the thickness does not exceed the 4th part of the breadth, or 11⁄2 inch for each 12 inches of breadth, and the result may be depended upon to as great an accuracy as can be obtained by the rule. When, however, the excess is more than two inches for each 12 inches of breadth, either the correction should be applied or the first method be used. Example 1.-Required the content of a piece of timber 10 inches broad, 8 inches thick, and 18 feet long. 10 8 Since X 80 144' = set 80 on B against 144 on A, and against 18 on A will be found 10 on B, and the content required is 10 cubic feet. Example 2.-Required the content of a piece of timber 15 inches broad, 10 inches thick, and 24 feet long. Set 24 on c against 12 on D, and against 12.5, of 121, the quarter girt on D, will be found on c 26.04, the approximate content. The excess of 15 over 10 being 3rd of 15, Table I. shows the required correction to th of 26.04. Set then 25 on в against 26.04 on ▲, and against 1 on B will be found 1.04 on A, which subtracted from 26.04 cubic feet leaves 25 cubic feet, the true content. Problem 10. To find the Content of a Piece of Square Timber, which tapers from end to end.-Set the length in feet upon c against 12 upon D, and against half the sum in inches of the quarter girts at the two ends upon D will be found a content in cubic feet upon c. Again, set one-third of the length in feet upon c against 12 upon D, and against half the difference, in inches, of the quarter girts at the two ends upon D will be found a second content in cubic feet upon c. Add together the two contents thus found for the content required. If the breadth exceed the thickness considerably, the same part of the result must be subtracted, as in Problem 9. Example. The quarter girts at the ends of a piece of timber 21 feet long, being 22 inches and 10 inches respectively, and the breadth not much exceeding the thickness, required the content. Set 21 upon c against 12 on D, and against 16 upon D will be found 37 or 37.3 upon c. Again, set 7 upon c against 12 upon D, and against 6 upon D will be 14 or 175 upon c. The sum of 37 cubic feet and 12 cubic foot is then 39 or 39.1 cubic feet, the whole content required. Problem 11. To find the Content of a Round Piece of Timber of the same Size throughout its entire Length.—Set the length in feet upon c against 10.63* upon D, and against the quarter girt in inches upon D will be found the content upon c. Example.-Required the content of a round piece of timber 32 feet long, the quarter girt being 11 inches. Set 32 upon c against 10.63 upon D, and against 11 upon D will be found upon c 34 25 or 324, the content required. Problem 12. To find the Content of a Round Piece of Timber, which tapers from end to end.-Set the length in feet upon c against 10.63 upon D, and against half the sum in inches of the quarter girts at the two ends upon D will be found a content in cubic feet upon c. Again, set one third of the length in feet upon c against 10.63 upon D, and against half the difference in inches of the quarter girts at the two A mark is placed upon the rule at this point, 10.63 being the quarter girt in inches of the circle, whose area is a square foot.. ends upon D will be found a second content in cubic feet upon Add together the two contents thus found for the content required. C. Note. In buying rough or unsquared timber, an allowance of about th should be made for the bark. A further allowance should also be made for the loss in squaring down the tree to make useful shaped timber. The whole amount of timber to be taken off to make a square piece from a round piece of timber will be 36 per cent., or more than a third of the whole. The timber so taken off must not, however, be considered completely valueless. If the length upon o be set against 12 upon D, instead of upon 10.63 in the two preceding problems, this will be equivalent to an allowance of about 21 per cent., which may be considered a just allowance. Example 1.-A piece of round tapering timber measures 23 feet in length, the quarter girt at the larger end is 231⁄2 inches, and at the smaller end the quarter girt is 15 inches. Required the true content. Set 23 upon c against 10.63 upon D, and against 19 or 19.5 upon D will be found 77·5 upon c. Again, set 7 or 7.66 upon c against 10.63 upon D, and against 8 upon D will be found 4:3 upon c. Then the sum of 77.5 cubic feet and 4.3 cubic feet is 81.8 cubic feet, the content required. Example 2.-Required the content of a piece of unsquared timber of the same dimensions as in the preceding example, making allowance of 21 per cent. for loss in squaring down into a useful shape. Set 23 upon c against 12 upon D, and against 19, or 19.5, upon D will be found 60-75 upon c. Again, set 7 or 7.66 upon c against 12 upon D, and against 8 upon D will be found 34 upon c. Then the sum of 60.75 cubic feet and 34 cubic feet is 64.15 cubic feet, the content required. Problem 13. To find the Content of a Cylindrical Vessel in Gallons.-Set the length of the cylinder in inches upon c against the gauge mark at 18.79, marked &, upon D, and against the diameter of the cylinder in inches upon D will be found the required content in gallons upon c. If the number of inches in the diameter lie beyond c, or if this number be greater than 40, so as not to be contained upon D, the th part, or any part that may be convenient, of the number of inches in the diameter may be taken, and the result thus obtained, multiplied by 100, or the square of the divisor made use of, will give the content required. Example.-A circular vat 5 feet in diameter being filled to the depth of four feet, required the quantity of liquor in it. Set 48 upon c against the gauge mark at 18.79 upon D, and against 6, the th part of the diameter in inches, upon D will be found upon c 49; and consequently 4.9 x 100 or 490 gallons is the quantity of liquor in the vat. PRACTICAL HINTS, ETC.* ON THE MANAGEMENT OF DRAWING PAPER THE first thing to be done, preparatory to the commencement of a drawing, is to stretch the paper evenly upon the smooth and flat surface of a drawing board. The edges of the paper should first be cut straight, and, as nearly as possible, at right angles with each other; also the sheet should be so much larger than the intended drawing and its margin, as to admit of being afterwards cut from the board, leaving the border by which it is attached thereto by glue or paste, as we shall next explain. The paper must first be thoroughly and equally damped with a sponge and clean water, on the opposite side from that on which the drawing is to be made. When the paper absorbs the water, which may be seen by the wetted side becoming dim, as its surface is viewed slantwise against the light, it is to be laid on the drawing board with the wetted side downwards, and placed so that its edges may be nearly parallel with those of the board; otherwise, in using a T square, an inconvenience may be experienced. This done, lay a straight flat ruler on the paper, with its edge parallel to, and about half an inch from, one of its edges. The ruler must now be held firm, while the said projecting half inch of paper is turned up along its edge; then, a piece of solid glue (common glue will answer the purpose), having its edge partially dissolved by holding it in boiling water for a few seconds, must be passed once or twice along the turned edge of the paper, after which, this glued border must be again laid flat by sliding the rule over it, and, the ruler being pressed down upon it, the edge of the paper will adhere to the board. If sufficient glue has been applied, the ruler may be removed directly, and the edge finally rubbed down by an ivory bookknife, or any clean polished substance at hand, which will then firmly cement the paper to the board. Another but adjoining edge of the paper must, next, be acted upon in like manner, and then the remaining edges in succession; we say the adjoining edges, because we have occasionally observed that, when the opposite and parallel edges have been laid down first, without continuing the process progressively round the board, a greater degree of care is required to prevent undulations in the paper as it dries. *Extracted from a Treatise on Drawing Instruments by F. W. Simms, Civil Engineer and Surveyor. Sometimes strong paste is used instead of glue; but, as this takes a longer time to set, it is usual to wet the paper also on the upper surface to within an inch of the paste mark, care being taken not to rub or injure the surface in the process. The wetting of the paper in either case is for the purpose of expanding it; and the edges being fixed to the board in its enlarged state, act as stretchers upon the paper, while it contracts in drying, which it should be allowed to do gradually. All creases or undulations by this means disappear from the surface, and it forms a smooth plane to receive the drawing. MOUNTING PAPER AND DRAWINGS, VARNISHING, ETC. In mounting paper upon canvas, the latter should be well stretched upon a smooth flat surface, being damped for that purpose, and its edges glued down as was recommended in stretching drawing paper. Then with a brush spread strong paste upon the canvas, beating it in till the grain of the canvas be all filled up; for this, when dry, will prevent the canvas from shrinking when subsequently removed; and, having cut the edges of the paper straight, paste one side of every sheet, and lay them upon the canvas, sheet by sheet, overlapping each other a small quantity. If the drawing paper is strong, it is best to let every sheet lie five or six minutes after the paste is put on it; for, as the paste soaks in, the paper will stretch, and may be better spread smooth upon the canvas; whereas, if it be laid on before the paste has moistened the paper, it will stretch afterwards and rise in blisters when laid upon the canvas. The paper should not be cut off from its extended position till thoroughly dry; and the drying should not be hastened, but gradually take place in a dry room, if time permit; if not, the paper may be exposed to the sun, unless in the winter season, when the help of a fire is necessary, care being had that it is not placed too near a scorching heat. In joining two sheets of paper together by overlapping, it |