## A Treatise on Land-surveying: Comprising the Theory Developed from Five Elementary Principles; and the Practice with the Chain Alone, the Compass, the Transit, the Theodolite, the Plane Table, &c. Illustrated by Four Hundred Engravings, and a Magnetic Chart |

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acres angle base Bearing calculated called centre chains CHAPTER circle compass corner correct Cosine Cotang course Departure desired determined difference direction distance divided division draw drawn East equal equivalent Example explained expression feet field figure fixed four give given ground half inch intersection known land Latitude latter length marked means measured meeting Meridian method mile move needle North noted object observed obtained opposite parallel passing perpendicular plat plate position preceding precisely problem proportion quadrilateral radius reading represent scale seen side sight similar Sine South square station straight Surveying Table taken Tang Tangent telescope Theorem third township Transit triangle true turn usually Variation Vernier West whence

### Popular passages

Page 153 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 365 - ... in all cases where the exterior lines of the townships thus to be subdivided into sections or half sections, shall exceed, or shall not extend six miles, the excess or deficiency shall be specially noted, and added to or deducted from the western or northern ranges of sections or half sections in such township, according as the error may be in running the lines from east to west, or from south to north...

Page 169 - Longitudes of points are measured, or reckoned. The distance which one end of a line is due North or South of the other end, is called the Difference of Latitude of the two ends of the line ; or its Northing or Southing ; or simply its Latitude.

Page 379 - Every circumference of a. circle, whether the circle be large or small, is supposed to be divided into 360 equal parts called degrees. Each degree is divided into 60 equal parts called minutes, and each minute into 60 equal parts called seconds.

Page 370 - President may prescribe, to cause the lands thus situated to be surveyed in tracts of two acres in width, fronting on any river, bayou, lake, or watercourse, and running back the depth of forty acres...

Page 385 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.

Page 372 - The precise relative position of islands, in a township made fractional by the river in which the same are situated, is to be determined trigonometrically — sighting to a flag or other fixed object on the island, from a special and carefully measured base line, connected with the surveyed lines, on or near the river bank, you are to form connection between the meander corners on the river to points corresponding thereto, in direct line, on the bank of the island, and there establish the proper...

Page 369 - ... to No. 18, the established corner to sections 1, 2, 11, and 12, taking care to establish the quarter.section corner on the true line, at the distance of 40 chains from said section corner, so as to throw the excess or deficiency on the northern half. mile, according to law. Proceed in like manner through all the intervening tiers of sections to No. 73, the corner to sections 31, 32, 5, and 6 ; thence north, on a true meridian line, to No.

Page 366 - ... (either of which would indicate an important error in the surveying,) the lines must be retraced, even if found necessary to remeasure the meridional boundaries of the township, (especially the western boundary,) so as to discover and correct the error ; in doing which, the true corners must be established and marked, and the false ones destroyed and obliterated to prevent confusion in future ; and all the facts must be distinctly

Page 372 - A sufficient number of other trees standing within 50 links of the line, on either side of it, are to be blazed on two sides diagonally, or quartering toward the line, in order to render the line conspicuous, and readily to be traced, the blazes to be opposite each other, coinciding in direction with the line where the trees stand very near it, and to approach nearer each other the farther the line passes from the blazed trees. Due care must ever be taken to have the lines so well marked as to be...