## 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 16

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**radius**= perpendicular of such polygon ; therefore , half the circumference by half the diameter will give the area . ) - Note . The ratio of the diameter to circumference is as 7 is to 22 , or 1 to 3. 1416 , & c . Hence it is easy to ... Page 7

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**radius**ON , describe the circle meeting MO in Q , which must pass through R , because a right angle , and through S , because NS is parallel to BC , and NO = OS . Now , it is evident that AO is = sum of the two sides AC and AB , and QO ... Page 8

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**radius**, and let fall the perpendicular MN , which is the natural sine of the angle C. Similar trian- gles , we get CN : NM :: CA : AP , and ( 16. 6. ) CN . AP = BC BC NM . CA. Multiply off by , and AP . = BC CA , NM . BC . MN . But AP ... Page 13

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**Radius**. Let fall the perpendiculars CO , DP , and MN . Now per similar triangles MN = AB ÷ 100 . In this case it is plain AB must always be a decimal , and = MN the natural sine of half the proposed angle . Prob . 15. To take an ... Page 30

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**radius**AO , which is the excess of the ap- parent above the true level . Then R + X ' R ' + BII ' , that is R2 + 2RX + X ' = R ' + BH ' , whence 2RX + X2 = BH2 = X + ( 2R + X ) . But now as X is so small , when com- pared with the**radius**...### 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.