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Thomas Baker Digitized by Google EUDB1ENTABY TEEATISE MENSURATION, EOE THE USE OE SCHOOLS AND PEACTICAL MEN: MODERN ENGINEERING. E., Author of "Theodolite Survejjn K, Labelling, lie." in the Ninth Edition of h*. 95 Planning Surveys— The- Field Book 9S To Survey with the Chain and Croa B — Tables and fito Problems, with numerous Esam plea 97 IV CONTENTS. From any angle A draw diagonals to the other angles ; take A 6 a side of the figure required ; then draw S c parallel to B C, and c d to C D, and rfeto DE, &c. Set two sides A B, B C, of the given squares, perpendicular to each other ; join their extremities A C ; so shall the squars* R, constructed on A C, be equal to the two P and Q taken together. (See the last figure.) On the side A C of the greater square, as a diameter, describe a semicircle ; in which apply A B the side of the less square ; join B C, will be the side of a square equal to the differ- ence between the two P and R as required. To make a square equal to the sum of any number of squares taken together. Required the content of an oblate spheroid, the axes of which are 50 and 30 inches.

t ECfje Mitt] ffiliiiion, fottfj Sfo Sittans oirt Corttttions. '■ - ■ " " iihvi Ly Fiigiincring ; '' " Li-.d mi,: ] 'i :u-l : hjfr ! To Survey witli the Chain only — Four Problems and n amplea, with the method of Surveying a Large Estate . Draw two indefinite lines A m, A n, perpendicular to each other at the point A.

If the radii C F, C E be drawn, the space, hounded by these radii and the arc F E, will be the sector of a circle. The circumference of every circle 13 supposed to he divided into 360 equal parts, called degrees, and each degree into 60 minutes, each minute into 60 seconds, &c. What are the superficies and solidity of the octahedron, the linear side of which is 2 feet ?

Let the angle be required to \*7 contain 41 degrees. Draw A o and B o making the angles A and B each equal to half j the angle of the polygon, by Prob. The angle of any polygon, of which the angles o A B and o B A are each one half, is found thus : divide the whole 360 degrees by (he number of sides, and the quotient will be the angle at the centre o ; then subtract that from 1HO degrees, mid the remainder will be the angle of the polygon, and is double of o A B or of o B A. Find the points m, n, p, &c, as in the last problem ; to which draw radii m o, n o, &c, to fie centre of the circle ; then through these points m, n, &c, and per- pendicular to these radii, draw the sides of the polygon. Let the radius of the given circle be five feet; then, having described a regular pentagon round it, the side of the figure Olgilir M By Coogl PRACTICAL GEOMETRY. Bisect any two sides with the per- pendiculars m o, no, and their intersec- tion will be the centre ; then with the centre o, and the distance o m, describe the inscribed circle ; or with the distance to one of the angles as A, describe the circumscribing circle. square or a Draw two diameters A B, CD, perpen- dicular to each other; then connect their extremities, and that will give the inscribed square A C D B. Rule.- — Multiply the square of the diameter of the base by the height or axis, and the product again by -3927 for the content. What is the content of the parabolic conoid, the height of which ia 42, and the dinmeter of its base 24 ? C B = 3 yards; describe another arc cutting the former arc in C:— draw AC and CB; then ABC is the triangle required. Given the base and perpendicular, witlt the place of the latter on the base, to con- C struct the triangle. From any scale of equal parts lay off the base A B = 5 yard9 ; with the centre A and radius A C = 4 yards, de- scribe an arc ; with centre B and radius . ■ 108 La TOUMO— Definition— Levelling Instruments 115 The Y Level ibid. On the one of these set off A B the side a of one of the given squares, and on the other A C the side of another of them ; join B C, and it will be the side of a square equal to the two together. Leveling Staves (Gravatfa) 118 Correction fur Curvature . Then take A D equal to B C, and A E equal to the side of the third given square. "What is the content of n ring, the thickness of which is 4, and inner diameter 1 6 feet ?

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is well as the following one, is usually performed by an "1 infer. Through a given point r, to draw a straight line CD parallel to a given straight line A B. * D the distance nr, describe the arc rm: — from centre r, with the same radius, describe the / '\ / arc ns: — take the arc mr in the compasses, A«t an( j a pp]y it f rom n to s : — through r and s draw C D, which is the parallel required. From a given point P in a straight Una A B to erect a per- pendicular. With the centre P, and any radius, de- scribe the arc nrs; — from the point n, with the same radius, turn the compasses twice on the arc, as at r and s : — again, with centres r and s, describe arcs inter- secting in C :— draw C P, and it will bo / the perpendicular required. Tbis problem imd the following one are usually done with an insiru- ment called tie square. From a given point C to let fall a perpendicular to a given line.

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