Proper deductions are to be made for chimneys, doors, &c. But 'the windows are seldom deducted, as the plastered returns at the top and sides are allowed to compensate for the window opening. 3 hundred of lime, 4 loads of sand, and 10 bushels of hair to 200 yards of render set; 4 hundreds of lime, 6 loads of sand, 15 bushels of hair, and 2 loads of laths and nails, to 270 feet of lath plaster work. 1 bundle of laths, and 5 hundred of nails, will cover 4 yards superficial. PAINTERS' WORK. Painters' work is computed in square yards. Every part is measured where the color lies; and the measuring line is forced into all the moldings and corners. Windows are done at so much a piece; and it is usual to allow double measure for carved moldings, &c. GLAZIERS' WORK. Glaziers' work is done at so much per light, that is, computed at a given price for putting in each pane of glass, according to the size. (See article on Paints, Lockers &c., under Miscellaneous Notes.) ENGINEERING. HINTS ABOUT LAYING OUT CURVES. In laying out curves, the following method has the advantages of great accuracy and expedition over that of angles taken by an instru ment. The stations are supposed to be 100 feet apart. B In the cut, the chord A C, is divided into four equal parts: the middle ordinate, y, is expressed by 2 × 2=4, and ≈ and z are expressed by 1×3=3; Measure at the intersection the angle, A O B, in the above figure, of the two straight lines to be joined, by observing the quantity of deflection in 100 feet; that is, the length of the arc, as of a circle comprehended between the angular lines, the radius of the arc being 100 feet. When the angle is small, the length of the chord is sufficiently 10000 D R triangle You accurate. Divide this quantity by the number of stations you propose to give the curve. The quotient is D hereafter mentioned. 10000 is R, radius of the curve, or reciprocally, is D deflection. Produce the tangent, 100 feet beyond the commencement o the curve, and set off so as to form an isosceles have then obtained the first station on the curve. chord 100 feet beyond this station, and set off D. Proceed in like manner, setting off D at each station. Having completed the curve, produce the last chord 100 feet, and set off. The point thus obtained, and the end of the curve, form the line of the tangent. Produce the first Having completed a curve as above, if you do not arrive at the destined point, measure the variation, v, and divide it among the stations in proportion to the square of the distance from the point of com mencement. To find what difference of direction will be obtained for the tangent by making the offset of the above-mentioned variation, v, divide twice the variation by the number of stations. The quotient, is the dif ference of direction for one station. 9 14 17 18 7 8 1 4 In running a curve for laying of track upon a finished grading, if, both ends being adjusted, the curve varies at intermediate points from the grading, measure the variation v, at the point g, where it is greatest, or assume some quantity v, that shall be a judicious average of variations. In making the change, it will not be proper to occupy less than 4 stations on each side of the point g, making 8 stations in all. If 8 stations are occupied, set off on each side of g, at the 3d station therefrom, v; then, proceeding towards g, set off successively at the stations, 4, , v. If 12 stations are to be occupied, set off at 5 stations from g, v; then successively toward g, 18, 189 189 189 18 V. These fractions can always be obtained as follows: Decide upon some even number of stations, to be used on each side of g. The denominator is the square of the number, n, of stations on one side of g, and the numerators are found by deducting from the denominators successively the square numbers 1, 4, 9, 16, 25, &c., till the remainder is a perfect square, which will be one-half the denominators, and consequently the square of n. It will also be arrived at inn from g. Thus, if 14 be decided upon as the number of stations on each side g, 98 will be the denominator, and the numerators will be, successively, 98, 97, 94, 89, 82, 73, 62, 49. This last No. is the denominator, and 7 stations from g. It is likewise 73. The remaining numerators are, inversely, the succession of square numbers previously deducted from the numerators. Thus, continuing the above example from 49, we have 36, 25, 16, 9, 4, 1. If necessary, the numerator may be preserved equal to the denominator on either side of g, for an indefinite period before diminishing. For distances not exceeding 200 in length on curves, the offsets from a tangent are (sufficiently near for practice) in proportion to the squares of the distances from the commencement. It is proper in laying out a curve by this rule to measure the distances, both on the curve and on the tangent. For approximation in the field, this rule is valuable for a distance of 400; after which it is rather unsafe, and for 900 absolutely useless. It will be found serviceable for calculating vertical curves in a profile of grades, measuring the angle of the two planes, as of the lines in horizontal curves. The calculation by this rule always exceeds the true offset. The excess for 200 on a 10 curve (radius 5730), is 1.14 feet; for 300, 5·86 feet; for 600, 94 feet; and for 90°, 490 feet. For 100, the variation is scarcely perceptible. To obtain ordinates from a chord, observe the three following rules: 1. The deflection D for chords is in proportion to the square o their lengths. 2. The ordinate at the middle of a chord is always D. 3. All the ordinates of a chord are in proportion to the rectangle of the two parts into which they divide the chord. Thus, divide the chord into 10 parts; equal; the middle ordinate will be expressed by 5×5 25; and the others will be successively expressed by 4×6=24; 3×7=21; 2×8=16; and 1×9=9. Where R is 5000, and the chord 100, D is 2, or middle ordinate is 25; the others are 24, 21, 16, and 09, on each side the center. B In the cut, the chord A C, is divided into four equal parts: the middle ordinate, y, is expressed by 2×2=4, and a and z are expressed by 1×3=3; and x z are therefore each of y. The 1st and 2d of these rules will be found useful for springing rails of any length, or any radius of curvature. Thus, for 100 feet chord, the middle ordinate is 25; for an 18 feet rail, the middle ordinate 25 as 18 x 18=324; 100 × 100=10000; or 03240324×250081 feet; or 0972 inch, or for practice inch. The difference in length, between the inner and the outer rail, may be determined as follows: Where R is radius, C the length of the CW inner rail, and W the width of the track, the difference is R Where 5 feet is the width, is the difference for 100 feet, and R 20 500 is the length required to gain 3 inches. This formula will be found convenient for distributing overlength iron for curves. |