inch, taking for every foot one of those divisions, and for every inch one of the subdivisions into twelfths; and proceed in like manner in proportioning a drawing to any of the other divisions of the scale. An instrument in the form of a semi-circle, called a protractor, and used for laying down and measuring angles, is of much service to surveyors, but not much to carpenters. 11. In drawing parallel lines, when they are to be parallel to either side of the board, use the T-square; but when it is required to draw lines parallel to a line which is drawn in a direction oblique to either side of the board, the set-square must be used. Let a b, (Fig. 2,) be a line, parallel to which it is desired to draw one or more lines. Place any edge, as c d, of the set-square even with said line; then place the ruler, gh, against one of the other sides, as c e, and hold it firmly; slide the set-square along the edge of the ruler as far as it is desired, as at f; and a line drawn by the edge, if, will be parallel to a b. 12.—To draw a line, as k 1, (Fig. 3,) perpendicular to another, as a b, set the shortest edge of the set-square at the line, a b; place the ruler against the longest side, (the hypothenuse of the right-angled triangle ;) hold the ruler firmly, and slide the setsquare along until the side, e d touches the point, k; then the line, lk, drawn by it, will be perpendicular to a b. In like manner the drawing of other problems may be facilitated, as will be discovered in using the instruments. 13.-In drawing a problem, proceed, with the pencil sharpened to a point, to lay down the several lines until the whole figure is completed; observing to let the lines cross each other at the several angles, instead of merely meeting. By this, the length of every line will be clearly defined. With a drop or two of vater, rub one end of the cake of ink upon a plate or saucer, until a sufficiency adheres to it. Be careful to dry the cake of ink; because if it is left wet, it will crack and crumble in pieces. With an inferior camel's-hair pencil, add a little water to the ink that was rubbed on the plate, and mix it well. It should be diluted sufficiently to flow freely from the pen, and yet be thick enough to make a black line. With the hair pencil, place a little of the ink between the nibs of the drawing-pen, and screw the nibs together until the pen makes a fine line. Beginning with the curved lines, proceed to ink all the lines of the figure; being careful now to make every line of its requisite length. It they are a trifle too short or too long, the drawing will have a ragged appearance; and this is opposed to that neatness and accuracy which is indispensable to a good drawing. When the ink is dry, efface the pencil-marks with the india-rubber. If the pencil is used lightly, they will all rub off, leaving those lines only that were inked. 14. In problems, all auxiliary lines are drawn light; while the lines given and those sought, in order to be distinguished at a glance, are made much heavier. The heavy lines are made so, by passing over them a second time, having the nibs of the pen separated far enough to make the lines as heavy as desired. If the heavy lines are made before the drawing is cleaned with. the rubber, they will not appear so black and neat; because the india-rubber takes away part of the ink. If the drawing is a ground-plan or elevation of a house, the shade-lines, as they are termed, should not be put in until the drawing is shaded; as there is danger of the heavy lines spreading, when the brush, in shading or coloring, passes over them. If the lines are inked. with common writing-ink, they will, however fine they may be made, be subject to the same evil; for which reason, india-ink is the only kind to be used. THE AMERICAN HOUSE-CARPENTER. SECTION 1.-PRACTICAL GEOMETRY. DEFINITIONS. 15. - Geometry treats of the properties of magnitudes, 16.-A point has neither length, breadth, nor thickness. 17. —A line has length only. 18.-Superficies has length and breadth only. 19.-A plane is a surface, perfectly straight and even in every direction; as the face of a panel when not warped nor winding. 20. A solid has length, breadth and thickness. 21.-A right, or straight, line is the shortest that can be drawn between two points. 22.-Parallel lines are equi-distant throughout their length. 23.-An angle is the inclination of two lines towards one another. (Fig. 4.) 24.--A right angle has one line perpendicular to the other. (Fig. 5.) 25.-An oblique angle is either greater or less than a right angle. (Fig. 4 and 6.) 26. An acute angle is less than a right angle. (Fig. 4.) (Fig. 6.) When an angle is denoted by three letters, the middle one, in the order they stand, denotes the angular point, and the other two the sides containing the angle; thus, let a bc, (Fig. 4,) be the angle, then b will be the angular point, and a b and b c will be the two sides containing that angle. 28.—A triangle is a superficies having three sides and angles, (Fig. 7, 8, 9 and 10.) 29.-An equi-lateral triangle has its three sides equal. (Fig. 7.) 30.-An isosceles triangle has only two sides equal. (Fig. 8.) 31.-A scalene triangle has all its sides unequal. (Fig. 9) 32.--A right-angled triangle has one right angle. (Fig. 10.) 33. An acute-angled triangle has all its angles acute. (Fig. 7 and 8.) 34.-An obtuse-angled triangle has one obtuse angle, (Fig. 9.) 35.- A quadrangle has four sides and four angles. (Fig. 11 to 16.) |