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SURVEYING is the art of measuring, laying out, and dividing land.
Preliminary Definitions, Observations, &c.
The instrument used for measuring the sides of fields, or plantations, is a GUNTER'S CHAIN, which is 4 poles or 66 feet in length, and is divided into 100 equal parts or links; consequently the length of each link is 7.92 inches: also 1 square chain is equal to 16 square perches, and 10 square chains make an acre.
When the land is uneven or hilly, a four-pole chain is too long to be convenient, and the measures cannot be taken with it as accurately as with one that is shorter. Surveyors therefore generally make use of a chain that is two poles in length and divided into 50 links. The measures thus taken are, for the sake of ease in the calculation, reduced either to four-pole chains or to perches. The following rules shew the method of making these, and some other reductions.
To reduce two-pole chains and links to four-pole chains
1. If the number of chains be even, divide them by 2, and to the quotient annex the given number of links. Thus, in 16 two-pole chains and 37 links, there are 8 four-pole chains and 37 links. Or because each link is the hundredth part of a four-pole chain, the four-pole chains and links may be written thus 8.37 four-pole chains.
2. If the number of chains be odd, divide by 2 as before, and for the 1 that is to carry, add 50 to the given number of links. Thus in 17 two-pole chains and 42 links, there are 8 four-pole chains and 92 links, or 8.92 four-pole chains.
To reduce two-pole chains and links, to perches and decimals of a perch.
Multiply the links by 4 and the chains by 2. If the links when multiplied by 4, exceed a hundred set down the excess and carry 1 to the chains. Thus 17 two-pole chains and 21 links 34.84 perches; also 15 two-pole chains and 38 links = 31.52 perches.
To reduce four-pole chains and links, to perches and decimals of a perch.
Multiply the chains and links by 4. Thus 13.64 four
To reduce square four-pole chains to acres.
Divide by 10, and the quotient will be acres. If there be decimals in the quotient, multiply by 4 and by 40 to obtain the roods and perches.
EXAMPLE. In 523.2791 square chains, how many
Ans. 52A. 1R. 12P.
Observation on Chaining. All slant or inclined surfaces, as the sides of a hill, should be measured horizontally and not on the plane or surface of the hill. To effect this the hind end of the chain, in ascending a hill, should be raised from the ground, till it is on a level with the fore end, and by means of a plummet and line, should be held perpendicularly above the termination of the preceding chain. In descending a hill the fore end of the chain should be raised in the same manner, and the plummet being suspended from it, will shew the commencement of the succeeding chain.
The bearing or course of a line is its situation in re
A line running due north and south is called a meridian line.
The bearing of a line is expressed by the angle contained between it, and a meridian line passing through one of its ends, and is said to be north so many degrees east or west, or south so many degrees east or west, according as the line runs between the north and east or north and west, or between the south and east or south and
The bearings of lines are generally taken with an instrument called a Circumferentor, or more commonly a Surveyor's Compass. A description of this instrument or of the method of using it, is deemed unnecessary, as it will be better understood from a few minutes inspection of the instrument itself, and an explanation from a person acquainted with the manner of using it, than from a detailed description in writing.
The bearing of a line taken at one end, is the reverse of the bearing of the same line taken at the other end:* thus, if the bearing of a line AB taken at the end A, be north 35° east, its bearing taken at the end B, will be south 35° west.
When the bearings of two lines, running from the same point, are given, the angle contained between them may be found by the following rules.
RULE 1. When the bearings of both lines are between the north and east or north and west, or between the south and east or south and west, subtract the less bear
*Note. This is not, except in a few cases, strictly true; but the difference is too small to be observed in practice. In the latitude of 40° the greatest difference between the bearing and the reverse bearing
ing from the greater; the remainder will be the angle contained between them: thus if AB bear N. 34° E. and AD, N. 589 E. the angle BAD will be = 24°. Fig. 67.
RULE 2. When the bearing of one of the lines is between the north and east and the other between the north and west, or when one is between the south and east and the other between the south and west, add them together; the sum will be the angle contained between them: thus if BA bear S. 34°W. and BC, S. 35° E., the angle ABC will be 69°. Fig. 67.
RULE 3. When the bearing of one of the lines is between the north and east and the other between the south and east, or when one is between the north and west and the other between the south and west, add them together and subtract the sum from 180°; the remainder will be the angle contained between them: thus if CB bear N. 35° W., and CD, S. 87°W., the angle BCD will be = 58°. Fig. 67.
RULE 4. When the bearing of one of the lines is between the north and east, and the other between the south and west, or when one is between the north and west and the other between the south and east, add 180 to the less bearing, and from the sum subtract the greater; the remainder will be the angle contained between them: thus if DC bear N. 87° E. and DA, S. 58°W. the angle ADC will be 151°. Fig. 67.