- | PREFACE. v. Section the ninth treats of Levelling, adapted to the surveying of roads and hilly ground, with Promiscuous Questions. Section the first (Part the Third) contains the Astronomical methods of finding the Latitude, Variation of the Compass, &c. with a description of the instruments used in these operations. Section the second contains a description of the instruments requisite in Astronomical Observations. Section the third shows how to find the Latitude by the Meridian Altitude of the Sun. as Section the fourth shows how to find the Variation of the Compass, with a description of the Azimuth Compass, and its use. In this Edition is introduced a new set of accurate Mathematical Tables. ... Truth calls upon me to acknowledge, that the methods of calculation herein set forth, got their rise from those of the late Thomas Burgh, Esq.” who first discovered an universal method for determining the Areas of right-lined figures, and for which he obtained a parliamentary reward. I hope, therefore, it cannot be construed as an intention in me to take from his great merit, when I say, that the methods herein contained are much more concise and ready than his. * This method, with very little alteration and improvement, in this coun." try, is usually called the Pennsylvania Method of Calculation. Aldo. CONTENTS. **Goo- * 4. Elements of Geo- 9. Levelling 316 . Tri - Sect. 1. The Chain 145 ciples 330 The Circumfe- 2. Description of In- The Theodolite 170 3. To find the Lati- - The Semicircle 175 tude by the Angles by these tude of the Sun 348 Instruments 180 4. Variation of the - The Protractor 182 Compass 352 - heights 190 - Areas 215|Logarithms of Numbers 1 General Method 252 Sines, Tangents, and Se- Of computing the Points of the Compass 82 Area of a Sur- Traverse Table 3 vey, Geometri- Mean Refraction 174 cally considered Sun's Parallax and demonstra- Dip of the Horizon 175 - ted 271 | Dip for Dif. Dist. of land 5. Method of survey- 6.Changing the scale 289 * . EXPLANATION of the Mathematical Characters used in this Work. f + signifies plus, or addition. : ... proportion. - r known which is the greater. 5 + 3, denotes that 3 is to be added to 5. 6 — 2, denotes that 2 is to be taken from 6. 7 x 3, or 7.3, denotes that 7 is to be multiplied by 3. 3 -i-4, denotes that 8 is to be divided by 4. 2 : 3 ; ; 4 : 6, shows that 2 is to 3 as 4 is to 6. 6 + 4 = 10, shows that the sum of 6 and 4 is equal to 10. A/ 3, or 3}, denotes the square root of the number 3. 3/5, or 5}, denotes the cube root of the number 5. &c. THE * THEORY AND PRACTICE OF SURVEYING. HE word surveying, in the mathematics, signifies the art of measuring land, and of . delineating its boundaries on a map. The Surveyor, in the practice of this art, directs his attention, at first to the tracing and measuring of lines; secondly, to the position of these lines in respect to each other, or the angles formed by them; thirdly, to the plan, or representation of the field, or tract, which he surveys; and fourthly, to the calculation of its area, or superficial content. When this art is employed in observing and delineating Coasts and Harbours, in determining their variation of the Compass, their Latitude, Longitude and soundings, together with the bearings of their most remarkable places from each other, it is usually denominated Mari time Surveying. This branch of Surveying, how ever, demands no other qualifications than those, which should be thoroughly acquired by every Land-Surveyor, who aspires to the character of . an accomplished and skilful practitioner. Surveying, therefore, requires an intimate acquaintance with the several parts of the Mathematics which are here inserted as an introduction to this treatise. |