1. _In Squares._--Extract the square root of the desired content, reduced to square chains (ten square chains equal one acre). The result will be the length of the required side in chains. Thus if we wish to find the side of a square block containing 25 acres, we first reduce the acres to square chains: 25 × 10 = 250, the square root of which is 15·81, or 15 chains 81 links; the side required. By reference to the tables of square roots on page 189, the required sides of square block for a large number of acres can be read off at once. _One acre_ laid out as a square must have its side made 316¼ links, or 208-71/100 feet, or 69-57/100 yards, 70 paces being a near approximation. 2. _In Rectangles._--Divide the content by the length or breadth, according to which factor is known, and the result will be the required side. Thus 5 acres, or 50 square chains, if 10 chains long, will require to be 5 chains wide. If the content only is given, and the length is to be a certain number of times the breadth, the content in square chains divided by the ratio of the length to the breadth, and the square root of the quotient, will give the length of the shorter side. Thus, if we wish to lay out 72 acres as a rectangle twice as long as broad: 72 acres = 720 square chains, divided by 2, the ratio given, = 360, the square root of which is 18·97 chains, the length of the shorter side. The length of the other side is therefore 18·97 × 2 = 37·94 chains, or 3794 links. MENSURATION. =TO FIND THE AREA OF A TRIANGLE WHEN THE BASE AND PERPENDICULAR HEIGHT ARE GIVEN=: Multiply the base by half the height, or _vice versâ_. =TO FIND THE AREA OF A TRIANGLE WHEN THE THREE SIDES ARE GIVEN=: Take half the sum of the sides, subtract each severally from this sum, then multiply this and the three remainders together, and take the square root for the area. =TO FIND THE AREA OF A RECTANGULAR FIGURE=: Multiply the length by the breadth, the product will be the area. =TO FIND THE AREA OF A TRAPEZOID=: Multiply half the sum of the two parallel sides by the distance between them. =TO FIND THE AREA OF A PARALLELOGRAM WHOSE ANGLES ARE NOT RIGHT ANGLES=: Multiply the length of any one of the sides by the perpendicular. =TO FIND THE AREA OF A TRAPEZIUM=: Divide it into two triangles and find the areas of the latter by the first rule. =TO FIND THE AREA OF AN IRREGULAR POLYGON=: Divide the polygon into triangles and find the area of the latter. =TO FIND THE AREA OF AN IRREGULAR FIGURE=: Draw the figure on fine cardboard or thin sheet metal, cut the same carefully out and weigh with an accurate balance. Then this weight, compared with the weight of a piece of the cardboard or metal of a definite size, say one square inch, gives at once the area required. MINE SURVEYING PROBLEMS.