104 52 6.24 4 .96 Ans. 146 ft. 6 in. nearly. 10 ASCERTAIN THE NUMBER OF INCHES IN A LINK. As it will not increase 66 by multiplying it by 1, multiply 66 by 12, and the product will be 7.92 inches. TO REDUCE INCHES TO THE DECIMAL OF A FOOT. RULE. Annex two ciphers to the inches and divide that sum by 12, and the quotient will be the decimal required. EXAMPLE. What part of a foot is 9 inches? 12)900(.75 60 60 Ans. 75 or 75-100. TO REDUCE FEET AND INCHES TO CHAINS AND LINKS. RULE. Reduce the inches to the decimal of a foot, and annex that to the feet; or if there are no inches, annex two ciphers to the feet, and divide that sum by 66, and the quotient will be chains and links. EXAMPLE. In 440 feet 3 inches, how many chains and links? 66)440.25(6.67 396 442 396 465 462 3 Ans. 6 ch. 67 links. When a piece of land is calculated by chains and links, and the contents stand in acres and decimal parts of an acre, it may be multiplied by the price of an acre, and the product will be the amount. EXAMPLE. A piece of land 16 chains and 75 links in length, and 12 chains and 25 links in breadth, is sold for $25.25 per acre, what is the price of it? What is the length of a side of a square which contains 6040 acres? 6040 24160 40 Logarithm of 966400 15.985157 2.992578. Answer, 983.06 rods. What is the length of a side of a square which contains Logarithms of 640 12.806180 1.403090. Answer, 25.3 rods. A four sided figure, described by the following courses and distances, is divided, into two triangles to find arithmetically the contents of each, and the amount of both, viz. A, B. N. 100 E. 55 rods, B, C. S. 85° E. 65 rods, C, D. S. 8° W. 60 rods, D, A. N. 80° 35′ W. 66.85 rods. The supplement of the angle contained between the two first sides is 85o, what is the area of the triangle? The angle contained between the two last sides is 88° 35', Perhaps the above is as short and as certain a method to calculate the contents of an oblique angled, four sided figure, as can be taken.* Any polygon may be reduced to triangles, and the contents cal The method of calculating areas of such figures by multiplying together half the sum of the two opposite sides, is incorrect, or the only certainty there is in it, is that of making, in a greater or less degree, an excess of quantity. In cities, it is the practice to measure lots by feet and inches. To calculate the areas of such lots, reduce the inches to the decimal of a foot, annex such decimals to the feet to which they belong, and calculate, as by other measure, which will give the areas in square feet. When it is required to give the areas of such lots in square rods, and the contents stand in square feet, divide the feet by 272.25, the number of square feet in a rod, and the quotient will be the answer; or the feet and inches given in the distances, may be reduced to chains and links, or to rods and decimal parts of a rod, and the calculations made as in other cases. In measuring city lots, as step-stones and other obstructions may be in the way, extend a rope across the front. Let it be level, drawn tight, and made fast at each end. Measure on the rope; also, measure the other sides with equal accuracy, if necessary. In the two first editions of this work, a rule was inserted to prove the correctness of the courses in a survey, but it was afterwards discovered by Mr. Flint, and by others, that the rule will prove courses to be correctly taken when they are incor rect. The same rule has recently made its appearance in the American Journal of Science and Arts, and it may take a second tour among surveyors, under the character of an unerring rule. FORM OF A FIELD BOOK. Beginning at a mere-stone at the south-west corner. On account of the diurnal motion of the magnetic needle, in the warm season of the year, the courses in all surveys, if practicable, should be taken before 9 o'clock in the morn ing. Let this matter be investigated. A survey is commenced at seven o'clock in the morning, but is not completed until three o'clock in the afternoon. The course of the first line is N. 5o E., and the distance is 70 rods. The departure on this course and distance is 6.10 rods. When the survey is completed, the bearing of this line is again taken, and the course is N. 5° 10' E. The departure is now 6.30 rods, five links more than it was in the morning. Every compass which is in such order as it ought to be, will generally find in the summer, from morning to one o'clock, as great a change as this, often greater, but seldom less. The writer knows not who invented the following rules for finding contained angles, but they have been extensively adopted into practice. N. 62° E. Į S. 720 E. S. 25° E. N. 64° E. N. 570 W. S. 250 E. When the first letters are alike, and the last unlike, add the courses. When the first letters are alike, and the last also, substract the less course from the greater. When the first letters are unlike and the last alike, add the courses, and substract their sum from 180°. When the first and the last letters are unlike, substract the less course from the greater, and the remainder from 180°. To find the quantity of an angle, reverse the preceding course, then both courses will run from the same point. These rules are applied only when the first course is reversed. EXAMPLE. Two courses are given, viz. S. 62° W., and N. 44° W. to find their contained angle. Suppose yourself standing at the point where these courses meet. Reverse the letters of the first course, and they will stand thus: The following figures were prepared for the sixth edition of this treatise, by Mr. Barnard.* There is nothing in the rules to which they are applied, different in principle from the preceding ones, but they do not require the first course to be reversed. |