OFFSETS. Let AEF....B....D....0 be a field with very irregular sides; take the points A, 0, M, Cat or as near the corners as convenient, the object being to inclose as much of the field as possible within the quadrilateral AOMC; and for this pose, it is sometimes necessary, as in the present case, to include a corner (as SHQ) which is outside the field. The area AOCD is found by means of the diagonal AM, and the pendiculars'on it from C and 0. The area AEEG....BL is found by dividing it into angles and trapezoids by means of lars (to which the term offsets was originally applied, though it now denotes the irregular area before mentioned) from the corners E, G, H, etc. (see THIANDLE and TRAPEZOID), and adding together the areas of the separate ures AEF, FGg, GlIgh, etc. Similarly the areas of OLN....D and MDUW are found. To the sum of these must be added the areas of the triangles ATS, QPC, diminished by the area of SIN, and the result is the whole area of the field. If the offset have no distinct corners as (fig. 2) ABLITIN....0K, then the base AK is divided into equal parts by perpendiculars ABLI, Max, Nn, etc., and the area of the offset is found approximately as follows: the whole offset = ABU+ LiMes Mm + etc. +PpOK = Al X -IT (AB Li) ins X -HI,/ Mm) vin X (Mm Na) • • • • -E-pK x (pP OK) = (since the divisions of the base are equal) Al X AB + 223M-1-2Nn + 2p P OK = Al X AR OK Li + ?elm Na Pp }-; i.e., the area of an offset is found approximately by adding the
intermediate perpendiculars to the semi-sum of the first and last mid multiplying the sum total by the length of a division of the base, the divisions being equal; and the greater the number of perpendiculars, • the nearer the result is to the true area.
OG, an Amoritish king of Bastian. He reigned ever 60 cities, of which the chief were Aslitaroth and Edrei, at the time of the entrance of the Israelites into Canaan, n.c. 1618. Ile and his people were defeated and destroyed at Edrei immediately after the conquest of Sihon, his friend and ally. His walled cities were taken, and his kingdom, with its capital, transferred to the tribes east of the Jordan. He was one of the last of the race of the giants, and Scripture records the size of his iron liedstead preserved in " Rabbath of the children of Ammon," which was shout 15 ft. long and 6 broad. This is supposed to have been one of the common flat beds used on the house-tops of eastern cities, but made of iron instead of palm-branches.