But for the affiftance of those who do not understand decimal arithmetic, I have inferted the following table. C. C. L. P. - I 5 53 3 ,0 33 33 02 The Ufe of the Table. If the length or breadth be given in chains, links, &c. the other may be found by inspection, viz. if the length be even chains, look on the contrary dimenfions and you will fee how many ,50 chains, links, &c. must be measured for an acre. ,0 EXAMPLE. Suppofe the length of a field was 5 chains, how much in breadth will make an acre ? 42,28 against 5 chains in the table you will find 2 chains; 25 ,o the breadth required to make an acre; and fo of I II ,11 the reft. 4 2 2 Length PROB. 9. I I To Reduce a large plot of land or map into a lesser compass, or, on the contrary, to enlarge it. RULE. If it be a field or two it is the best way to plot it over again by a greater or leffer scale; but if it be large, as the map of a county or manor, &c. the readiest way is to circumfcribe it with a geometric square, and divide that square into several other leffer fquares, and by this means every field, house, &c. in one will fall in the fame fquare in the other. PROB. 10. To find the exact diftance to any visible object without any inftrument, or actually measuring the fame. RULE. Firft, get four straight sticks, of any length you please, then let it be required to find the diftance A B upon level ground, at B put down one of your sticks, there stand and order an affiftant to put down another at F; fo that standing at B you may fee the staff F and the object at A, both in a straight line (now it matters not at what distance the ftaff B is from the staff F, but if your distance required be far, then the further F is from B the better,) then take a third staff and go from F any number of yards, chains, or any other measure to D, fo that the line F D be at right angles with B A, and at D put down the third staff. Laftly, take the other ftaff, and go from B (fquare-wife, as before) fo far till you can see the staff D and the object A in a right line; which fuppofe at C; here make a mark, and measure the distance C G, 25 feet, &c. and G B 39,1; then C G 25+ G B 39,1 = B C, 64,1 feet; by measuring F D BG 39,1; the truth of this problem grounded upon fimilar triangles, for the triangle C G D is fimilar to the triangle CB A. Therefore it will always hold. may As As C As C G 25 is to G D 39, fo is C B 64,1 to B A 100 the answer. As 25 39 64,1 39 5769 1923 The work at Length. 25)2499,9(99,9 = 1oo nearly, the distance required. N. B. As the narrow limits of this treatife would not admit of room to give the whole art of furveying, I have given fuch examples as I thought would be the most useful to the young Tyro, as well as the farmer and grazier, which examples carefully confidered and duly regarded, will enable the learner to find the content, and plan a single field, or estate with certainty and expedition. LXXVII. SPECIFIC GRAVITY. HE fpecific gravity of a body, is the relation that the weight of a body of one kind hath to the weight of an equal magnitude of a body of another kind; the knowledge of which is of great ufe, not only in natural philosophy, but also in common life, in computing the weights of fuch bodies as are too unweildy to have their weights discovered by other means. The following table fhews the fpecific gravity to rain water, of metals, and other bodies; and the weight of a cubic inch of each, in parts of a pound avoirdupoife and of ounces troy. N. B. If the fpecific gravity of any folid in the table be lefs than 1000, it will swim in water; but if greater than 1000 it will fink, 3 ķ Bodies Note. If you take away the points from the numbers, in the secondcolumn, and reckon them to be whole numbers, they will fhew how many avoirdupoife ounces are contained in a cubic foot of each of the above bodies in the table. CASE I. The dimenfions, or folidity of any body being given to find its weight. RULE. Multiply the cubic inches contained in that body, by the tabular weight correfponding, and it will give the weight in pounds avoirdupoife, or ounces troy. EXAMPLE I. What is the weight of a piece of oak, of a rectangu. lar form, whofe folidity is 11880 cubic inches? ,0330946 26475680 330945 330946 112)393,1638480(3,5104 cwt. the answer. E. 2. There is a bar of iron, in length 156 inches, and 1 inch fquare; I defire to know how many pounds avoirdupoise it doth weigh? ,2808159 16848954 14040795 43,8072804 lb. the answer. E. 3. What is the weight of a piece of fir, whofe girt is 20 inches and length 40 feet? First, 2054, alfo 4×4=16 square of girt. And 40 feet =480 inches. Then 480 X 2 X 16 inches (per rule 2. Sect. 73.) 960 X 16 = 15360 cubic Therefore 0237630 E. 4. What is the weight of an iron fhot, of 8 inches diameter ? Firft, 8X8X8X,5236=268,0832 Solid inches, (per PROB. 10, Sect. 68,) E. 5, What is the diameter of an iron fhot, weighing 69,18281058304lb. avoirdupoife? First, 2580647)69, 18281058304(268,0832 Solid inches. 1 Then,5236)268,0832(=512 Cube of the diameter. 3 Therefore √512-8 The diameter fought. E. 6. What is the weight of an iron bomb fhell, of 3 inches thick, the greatest diameter being 14 inches? First, 14—6—8, Diameter of the concavity. Then 14X14X14X,5236=1436,7584 Content of the whole. And 8x 8X 8X,5256= 268,0832 Ditto of the concavity. Solidity of the fhell 1168,6752 Inches. Therefore 1168,6752×,2580647=301,59381488544 lb. the weight required. E. 7. In the walls of Balbeck, in Turkey, there are three ftones laid end to end, now in fight, that measure in length 61 yards; one of which, in particular, is 63 feet long, 12 feet thick, and 4 yards over now, if this ftone was marble, what power would ballance it, so as to prepare for moving? First, 63X12X12=9072 Solid feet. Therefore 15676416 it ,0977286 2240)1532034, 1886976(683,9438=638 tons, 18 cwt. 97 lb. the ans. CASE 2, |