## A Treatise on Surveying and Civil Engineering, Wherein Everything that is Useful and Curious is Demonstrated from Its First Principles1848 - 98 pages |

### From inside the book

Results 1-5 of 17

Page 5

...

...

**Multiply**the length by the perpendicular breadth , the product will be the area . ( The truth of this rule is evi- dent from ( 36-1 . ) Ex . .1 . Required the area of a plantation , in the form of a rhombus , whose length is 64 chains ... Page 6

...

...

**Multiply**the base by the perpendicular and half the product will be the area . ( This rule is plain , as the triangle is half the paralleo- gram upon the same base and altitude 41. 1. ) Ex . What is the area of a field , in the form of ... Page 7

...

...

**Multiply**the half sum and the three remainders continually together , the square root of the product will be the area . Demonstration . - Let ABC figure 1 , be the given tri- angle . Draw the parallels CP and BX , meeting the two sides ... Page 8

...

...

**multiply**these two numbers together and one - fourth the square root will be the area of the triangle . Demonstration . - Let ABC figure 2 , be the proposed triangle . Let fall the perpendicular AP , and bisect BC in O. Take AC = b , AB ... Page 9

...

...

**Multiply**the square of the side , by the rectangle of the two natural sines of said angles divided by 2 sine of the third angle , for the area . Demonstration . - Look to the last figure . Now , CA. NM . 2 -the area . And sine A : BC ...### Common terms and phrases

50 feet abutments adjacent angles adjustment altitude angle of friction arch bearing breadth bridge bubble canal centre chain circumferentor correct cross-wires crown curvature curve depression depth diameter difference of level direction divided division Dumpy Level ellipsis embankments engineer equal error evident extrados fall find the area give the area given ground half height horizontal inches inclination inclined plane instrument intersection land latitude and departure length limb line of collimation mean velocity measure method middle miles miles per hour multiplied natural sine necessary object parallel plate-screws piers plane plate position prismoid Prob quired radius railway refraction right angles road screws secants shafts side similar triangles slope square staff station stone straight line stream suppose surface survey tangent telescope theodolite thickness trapezium triangle tube tunnel vernier vertical arc voussoirs wedge whole width wires

### Popular passages

Page 7 - ... and 48° 15'? Ans. 6 A. 3 R. 18 P. PROBLEM V. To find the area of a triangle when the three sides are given. RULE. From half the sum of the three sides...

Page 23 - ... perfect in both positions of the telescope, the line of collimation in altitude or depression is correct, but if not, the operation must be repeated carefully, until the adjustment is satisfactory. A similar proceeding will also put the vertical line correct, or rather, the point of intersection, when there are two oblique lines instead of a vertical one. The second adjustment is that which puts the level attached to the telescope parallel to the rectified line of collimation. The clips...

Page 54 - The middle 18 feet of pavement is to be coated with hard stones to the depth of 6 inches. Four of these 6 iuches to be first put on and worked in by carriages and horses, care being taken to rake in the ruts until the surface becomes firm and consolidated, after which the remaining 2 inches are to be put on.

Page 54 - All the irregularities of the upper part of the said pavement are to be broken off by the hammer, and all the interstices to be filled with stone chips firmly wedged or packed by hand with a light hammer, so that when the whole pavement is finished there shall be a convexity of four inches in the breadth of fifteen feet from the centre.

Page 54 - Upon the level bed prepared for the road materials, a bottom course, or layer of stones, is to be set by hand, in form of a close firm pavement ; the stones set in the middle of the road are to be 7 inches in depth ; at 9 feet from the centre, 5 inches ; at 12 feet from the centre, 4 inches ; and at 15 feet, 3 inches.

Page 68 - RULE.* To the sum of the areas of the two ends add four times the area of a section parallel to and equally distant from both ends, and this last sum multiplied by £ of the height will give the solidity.

Page 84 - ... the practical architect to adopt his visions, raised another system, which is said to secure a perfectly equilibrated structure, by making an equality at every point of the curve. The deduction from this theory consists in making the height of the wall incumbent on any point of the intrados, directly as the cube of the secant of the curve's inclination to the horizon at that point, or inversely as the radius of curvature there. It must be added, that this theory expects the joints of the voissoirs...

Page 23 - First, make the centre of the horizontal wire coincide with some well-defined part of a distant object; then turn the telescope half round in its Y's till the level lies above it, and observe if the same point is again cut by the centre of the wire ; if not, move the wire...

Page 24 - P; which done, reverse the telescope in its Y's, that is, turn it end for end, which must be done carefully, that it may not disturb the vertical arc, and if the bubble resume its former situation in the middle of the tube, all is right; but if it retires to one end, bring it back one half, by the screw...

Page 25 - ... determined by repeating the observation of an altitude or depression in the reversed positions, both of the telescope and the vernier plate : the two readings will have equal and opposite errors, one half of their difference being the index error.