Engineering field notes on parish and railway surveying and levelling, with plans and sections, being a sequel to his Elementary text book; With ... and practice of running out curves and puttin

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1847 Excerpt: ...B, C, D, E, F, and G, draw the meridian distances, Ba, Cb, Dc, Ee, Fd, and Gf, perpendicular to this meridian, and also B, Cw, DA, and C, parallel to it; aB will be the first multiplier. Now the area of the figure, JCDEFG/J is equal to the figure JCB AG/H-the required area of the tract. And the difference of latitude and departure of the several sides will be found as in the following table. Thus Aa is the northing of AB, and aB is its easting; ab is the northing of BC, and C its easting, and so on. Also, according to the rule, aB-(-C or bC, is the E. D. D. of BC, as they "are of the same kind, and fG--aB is the W.D.D. of aB. Having obtained the double departures for the several sides, assume the multiplier aB, and find, by the rule, the several other multipliers aB &c, observing carefully, whether these multipliers are east or west. And place the areas of the product of the multipliers into their collateral northings or southings, in the columns of north or south areas, according to the proper relations between these multipliers and latitudes as given in the rule. These areas are double the required areas--being each of them double the areas of the several trapezoids into which the figure has been divided. Half the difference, therefore, of the north and south areas will be the required area. Now "dm" the multiplier last found equals Gf or the last departure. It will be perceived that all the multipliers, with the exception of the first and last, which are single, being the perpendiculars aB, fG of the triangles AaB, AfG, are double, being the sides of the trapezoids respectively, of which the other portion of the figure is made up--viz., the trapezoids Ba£C; TcbC; and &c. Answer, 9. 0. 3. CHAP. V. DIVISION OF LAND, PROBLEM I. T...