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Additional Exercises with their Answers.
QUESTIONS FOR EXERCISE.
1. Given the Hypothenuse 108 and the Angle opposite the Perpendicular 25o 36; required the Base and Perpendicular.
Answer. The Base is 97.4, and the Perpendicular 46.66.
2. Given the Base 96 and its opposite Angle 710 45'; required the Perpendicular and the Hypothe
Answer. The Perpendicular is 31.66 and the Hypothenuse 101.1.
3. Given the Perpendicular 360 and its opposite Angle 586 20'; required the Base and the Hypothenuse.
Answer. The Base is 222, and the Hypothenuse 423.
4. Given the Base 720 and the Hypothenuse 980; required the Angles and the Perpendicular.
Answer. The Angles are 47° 17' and 42° 43!, and the Perpendicular 664.8
5. Given the Perpendicular 110.3 and the Hypothenuse 176.5; required the Angles and the Base.
Answer. The Angles are 38° 41' and 51° 19', and the Base 137.8.
6. Given the Base 360 and the Perpendicular 480; required the Angles and the Hypothenuse.
Answer. The Angles are 53° 8/ and 36° 52', and the Hypothenuse 600.
7. Given one Side 129, an adjacent Angle 56° 30, and the opposite Angle 81° 36' : requireil the third Angle and the remaining Sides.
Answer. The third Angle is 41° 54', and the remaining Sides are 108.7 and 87.08.
8. Given one Side 96.5, another Side 59.7, and the Angle opposite the latter Side 31° 307 : required the remaining Angles and the third Side.
Answer. This Question is ambiguous ; the given Side opposite the given Angle being less than the other given Side (see Rule I. ;) hence, if the Angle opposite the Side 96.5 be acute, it will be 570 38', the remaining Angle 90° 521, and the third Side 114.2 ; but if the Angle opposite the Side 96.5 be ohtuse, it will be 122° 22', the remaining Angle 26° 8', and the third Side 50.32.
9. Given one Side 110, another Side 102, and the contained Angle 113° 36: required the remaining Angles and the third Side.
Answer. The remaining Angles are 31° 37' and 31° 47', and the third Side is 177.5.
10 Given the three Sides respectively, 120.6, 125.5, and 146.7: required the Angles.
Answer. The Angles are 51° 53', 54° 58', and 73° 91.
The student, who has advanced thus far in this work with diligence and active curiosity, is now prepared to study, with ease and pleasure, the following part ; which comprehends all the necessary directions for the practice of Surveying.
Or the Practical Surveyor's Guide.
Containing a particular Description of the several Instruments
used in Surveying, with their respective Uses.
HE stationary distance, or merings of ground, are measured either by Gunter's chain of four poles or perches, which consists of 100 links; (and this is the most natural division) or by one of 50 links, which contains two poles or perches : but because the length of a perch differs in many places, therefore the length of chains and their respective links will differ also.
The English statute-perch is 51 yards, the twopole chain is 11 yards, and the four pole one is 22 yards; hence the length of a link in a statutechain is 7.92 inches.
There are other perches used in different parts of England, as the perch of woodland measure, which is 6 yards; that of church-land measure, which is 7 yards, and the forest measure perch, which is 8 yards.
For the more ready reckoning the links of a four-pole chain, there is a large ring, or sometimes a round piece of brass fixed at every 10 links ; and at 50 links, or in the middle, there are two large rings. In such chains as have a brass piece at every 10 links, there is the figure 1 on the first piece, 2 on the second, 3 on the third, &c. to 9. By leading therefore that end of the chain forward, which has the least nuniber next to it, he who carries the hinder end may easily determine any number of links : thus, if he has the brass piece number 8, next to him, and six links more in a distance; that distance is 86 links. After the same manner 10 may be counted for every large ring of a chain which has not brass pieces on it; and the number of links is thus readily determined.
The two-pole chain has a large ring at every 10 links, and in its middle, or at 25 links, there are 2 large rings ; so that any number of links
be the more readily counted off, as before.
The surveyer should be careful to have his chain measured before he proceeds on business, for the rings are apt to open by frequently using it, and its length is thereby increased, so that no one can be too circumspect in this point.
In measuring a stationary distance, there is an object fixed in the extreme point of the line to be measured ; this is a direction for the binder chainman to govern the foremost one by, in order that the distance may be measured in a right line; for if the binder chainman causes the other to cover the object, it is plain the foremost is then in a right
a line towards it. For this reason it is necessary to bave a person that can be relied on, at the binder
end of the chain, in order to keep the foremost man in a right line; and a surveyor who has no such person, should chain himself. The inaccuracies of most surveys arise from bad chaining, that is, from straying out of the right line, as well as from other omissions of the hinder chainman: no person, therefore, should be admitted at the hinder end of the chain, of whose abilities in this respect, the surveyor was not previously convinced; since the success of the survey, in a grest measure, depends on his care and skill.
In setting out to measure any stationary distance, the foreman of the chain carries with him 10 iron pegs pointed, each about ten inches long; and when he has stretched the chain to its full length, he at the extremity thereof sticks one of those pegs perpendicularly in the ground; and leaving it there, he draws on the chain till the hinder man checks him when he arrives at that peg: the chain being again stretched, the fore man sticks down another peg, and the hind man takes up the former; and thus they proceed at every chain's length contained in the line to be measured, counting the surplus links contained between the last peg, and the object at the termination of the line, as before: so that, the number of pegs taken up by the hinder chainman, expresses the number of chains; to which, if the odd links be annexed, the distance line required in chains and links is obtained, which must be registered in the field book, as will hereaf
ter be shewn.
If the distance exceeds 10, 20, 30, &c. chains, when the leader's pegs are all exhausted, the hinder chainman, at the extremity of the 10 chains, delivers him all the pegs; from whence they pro