EXAMPLES. 1. How many acres are in a circle of a mile diamter? Answer, 502A. 2R. 25P. · 2. A. gentleman, knowing that the area of a circle is greater than that of any other figure of equal perimeter, walls in a circular deer-park of 100 perches diaméter, in which he makes an elliptical fish pond 10 perches long by 5 wide; required the length of his wall, content of his park, and area of his pond? Answer, the wall 314.16 perches, inclosing 49A. 14P. of which 39 perches, or of an acre nearly is appropriated to the pond. 3. What is the area of an elliptical pond whose diameters are 15 and 28 perches? 1 A. R. P. Answer 1. 2. 11. PROB. XIII. The area of a circle given to find its diameter. RULE. To the logarithm of the area add 0.10491, and half the sum will be the logarithm of the diameter. Or divide the area by .7854 and the square root of the EXAMPLE. A horse in the midst of a meadow suppose, Answer, 7.13865 per.=117F. 1In. PROB. XIV. To make the proper allowance for roads. It is customary to deduct 6 acres out of 106 for roads; the land before the deduction is made may be termed the gross, and that remaining after such deduction, the neat. 1. How much land must I enclose to have 850A. 2R. 20. neat. A. R. P. Answer, 901. 2. 26. 2. How much neat land is there in a tract of 901A. PROB. XV. To find the area of a piece of ground, be it ever so irregular, by dividing it into triangles and trape We here admit the survey to be taken, and protracted; by having therefore the map, and knowing the scale by which it was laid down, the content may be thus obtained. Dispose the given map into triangles, by fine pencilled lines, such as are here represented by popp'd lines in the scheme, and number the triangles with 1, 2, 3, 4, &c. Your map being thus prepared, rule a table with four columns; the first of which is for the number of the triangle, the second for the base of it, the third for the perpendicular, and the fourth for the content in perches. Then proceed to measure the base of number 1, place that in the second column of the table under the word base; and from the angle opposite to the base, open your compasses so, as when one foot is in the angular point, the other being moved backwards, and forwards may just touch the base line, and neither go the least above or beneath it; that distance in the compasses, measured from the same scale, is the length of that perpendicular, which placed in the third column, under the word perpendicular. If the perpendiculars of two triangles fall on one and the same base, it is unnecessary to put down the base twice, but insert the second perpendicular opposite to the number of the triangles in the table, and join it with the other perpendicular by a brace, as No. 1 & 2, 4 & 5, 6 & 7, 9 & 10, &c. Proceed after this manner, till you have measured all the triangles; and then by prob. 6. find the content in perches of each respective triangle which severally place in the table opposite to the number of the triangle, in the fourth column, under the word content. But where two perpendiculars are joined together in the table, by a brace, having both one and the same base; find the content of each (being a trapezium) in perches, by prob. 11. which place opposite the middle of those perpendiculars, in the fourth column, under the word content. Having thus obtained the content of each respective triangle and trapezium, which the map contains, add them all together, and their sum will be the content of the map in perches; which being divided by 160, gives the content in acres. Thus, for This being divided by 160, will give 25A. 3R. 22P. the content of the map. Let your map be laid down by the largest scale your paper will admit, for then the bases and perpendiculars can be measured with greater accuracy than when laid down by a smaller scale; and if possible measure from scales divided diagonally. If the bases and perpendiculars were measured by |