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

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Page 6

The area of a circle whose

The area of a circle whose

**diameter**is 1 , is 7854 nearly . And circles are to each other as the squares of their**diameters**. Eucl . 2. 12 , & c . Or thus - Multiply half the circumference by half the**diameter**, and the product will ... Page 7

What is the area of a circle whose

What is the area of a circle whose

**diameter**is 10 chains ? Ans . 78. 54 . Ex . 2. What is the area of an ellipsis whose**diameters**are 70 and 50 feet ? Ans . 2748. 9 . Prob . 5. To find the area of a plain triangle when the three sides ... Page 30

Hence 2RX = BO ' , and X - BO In words : the difference ( X ) between the true apparent level , is equal to the square of the distance ( BO3 ) divided by the

Hence 2RX = BO ' , and X - BO In words : the difference ( X ) between the true apparent level , is equal to the square of the distance ( BO3 ) divided by the

**diameter**of the earth , ( 2R , ) and consequently is always proportional to ... Page 67

Or 1 chain + radius , divided by the

Or 1 chain + radius , divided by the

**diameter**of the curve , will be equal the sine of the angle a BR nearly . The method of proceeding in the field : place the theodolite at the point B ; then lay off from the line B R , the angle a ... Page 68

If the point B , and the position of A B and D H are fixed , in this case the

If the point B , and the position of A B and D H are fixed , in this case the

**diameter**of the curve is fixed , or if the points B and R are fixed it will limit the**diameter**, as it must fix the point C. But if the point B be fixed and ...### What people are saying - Write a review

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### Common terms and phrases

abutments adjustment allow angle appears arch base bearing breadth bridge called canal centre chain connected consequently construction contained correct cross crown curve depression depth determine diameter difference direction distance divided division draw earth east effect engineer equal error evident fall feet figure find the area give given greater ground half height Hence horizontal inches inclination land latitude length limb lower manner mean measure meridian method middle miles move multiplied natural nearly necessary object observed parallel pass perpendicular pieces plane plate position possible practice Prob quantity radius railway refraction right angles river road rule screws side sight slope square staff station stone straight stream suppose surface survey taken telescope theodolite thickness triangle true turn upper velocity vernier vertical wedge whole

### 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.