To survey a Farm-General Directions. To determine the Bearing by a Station near the Middle of the Line...... 174 If the Line and the Point both be inaccessible. Prolongation and Interpolation of Lines........ To determine the Distance to the Intersection of two Lines.............. To determine the Distance between two inaccesible Points......... The Bearing, Distance, Latitude, and Departure,—any two being given, To determine the Latitude and Departure by the Traverse Table.. By the Table of Natural Sines and Cosines................................ 197 To determine the Deflection between two Courses. To determine the Angle between two Lines......... The Angles and one Side of a Triangle being given, to find the Area..... 225 To determine the Area of a Trapezium, three Sides and the two included To lay out a given Quantity of Land in the form of a Square.............. 251 To lay out a given Quantity of Land in the form of a Rectangle, one Side To lay out a given quantity of Land in the form of a Triangle or Paral- By a Division line drawn from one of the Angles. By a Line running a given Course............................................................. By a Line through a given Point in the old Line......... By a Line through a given Point in one of the Adjacent Sides....... 283 To divide a Trapezium into two parts having a given Ratio. By a Line through any Point... By a Line running a given Course.. By an Altitude of the Sun or a Star not in the Meridian....... A TREATISE ON SURVEYING. CHAPTER I. ON THE NATURE AND USE OF LOGARITHMS. SECTION I. ON THE NATURE OF LOGARITHMS. 1. Definition. LOGARITHMS are a series of numbers, by the aid of which the operations of multiplication, division, the raising of powers, and the extraction of roots, may, respectively, be performed by addition, subtraction, multiplication, and division. Such a series may be thus constructed. Above a geometric series, the first term of which is 1, place a corresponding arithmetic series, the first term of which is 0; thus:Arithmetical series, 0 1 2 3 4 5 6 7 8 Geometrical series, 1 2 4 8 16 32 64 32 64 128 256 To determine the product of any two terms of the geometric series, it is evidently only necessary to add the corresponding terms of the arithmetic series, and to notice the term of the geometric series agreeing to their sum; which term is the product required. Thus, to find the product of 4 and 32, we add the corresponding terms, 2 and 5, in the arithmetic series. Their sum, 7, corresponds to 128, the product required. 2. In a table of logarithms, the terms of the geometrical series are called the numbers; the ratio in this series is denominated the base of the table; and the terms of the arithmetical series are called the logarithms of the corresponding |