3d. By Günter's Scale. The first proportion is extended on the line of numbers; and it is no matter whether you extend from the first to the third, or to the second term, since they are all of the same kind : If you extend to the second, that distance applied to the third, will give the fourth ; but if you extend from the first to the third, that extent will reach from the second to the fourth. The methods of extending the other proportions have been already fully treated of. 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. nuse. 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. PART II, Or the Practical Surveyor's Guide. SECT. I. Containing a particular Description of the several Instruments used in Surveying, with their respective Uses. THE CHAIN. THE 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 may 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 |