85*4

THEORY AND PRACTICE OF ENGINEERING.

Book 11.

measured base 27405-6677 feet, after due correction made for temperature, &c. Theradius R being taken at 7,002,667 yards; the length of this line at the level of the sea isthus found : —

A, the measured base, is equal to 27405-6677 feet

h , the height, ------ 102

R, the radius of the earth, - 21008001

2i405 6677 x 10-. __ Hence the reduced base will be 27405-6677 — 0-133 =

2100800127 105*5347 feet.

Before a base is reduced to its length at the level of the sea, it is necessary to considerits horizontal value, as all lines measured over the earth’s surface must be treated as con-centric, and are more or less inclined to the horizon.

Signals, and their Construction. — When the base has been set out, permanent signalsmust be established; they should be constructed in a durable manner, and have perfectsteadiness.

In ordinary surveys straight poles fixed in trees or firmly in the ground may servesufficiently for all purposes, and when greater security is required, they may be held in avertical position by ropes, in the same manner as a ship’s mast, and such an arrangementmay be easily rendered more lofty by means of an additional mast, and the help of guysand stays. These masts have each a bunting flag, usually either red or white when pro-jected against^ a dark ground, and green and red when against the sky ; sometimes a cir-cular disk of sheet-iron is found a better substitute for the flag, and may be attached to thetop of the pole.

The parabolic reflector has been successfully employed in Ireland , and for the illuminatingpower, a ball of chalk lime was submitted to a stream of oxygen directed through theflame of alcohol; the light was estimated at 83 times the intensity of the brightest part ofthe flame of an Argand burner of the best construction, supplied with the finest oil. Thedirection of this light was marked by placing a guiding light at the distance of every15 miles, which was a 15-inch parabolic reflector illumined by an Argand lamp: by thismeans the former light, though 66 miles distant, was perceived, larger and brighter thanthe guiding lights. Plano-convex lenses, 2 or more feet feet in diameter, illumined by anArgand burner, with four concentric wicks, the lens composed of a series of concentricrings reduced in thickness and cemented together at the edges, are often used, and their ap-pearance at a distance of 48 miles is stated to resemble a star of the first magnitude.

Summits of mountains are usually selected for stations, and the signals constructed uponthem are built either pyramidically or conical, with a pillar in the centre. The selectionof stations depends much upon the nature of the country to be surveyed; they ought to beplaced in such positions as to be visible from each other, that the errors of observationmay have as little effect as possible on the distances measured: the triangles should beequilateral ; the smallest errors are likely to occur when the angle opposite to themeasured side is less than a right angle, and the angles adjacent to that angle are nearlyequal: in general no angle should be less than 30 degrees, and then the calculated sides ina series of triangles will not be very different from those obtained by actual measurement.

When a great survey is undertaken, the sides of the first triangles should be of greaterlength than the original measured base, and which is readily accomplished ; triangles whosesides were from 70 to 90 miles in length were adopted in Ireland , though in Englandthose whose sides were from 12 to 18 miles were considered preferable.

Calculation of the sides of Triangles. — Ail the angles and the triangles which are takenin a trigonometrical survey by the theodolite are spherical, as they form a part of thesurface of a spheroid : it is evident that as every object used for pointing the telescope ofa theodolite has some certain elevation not only above the soil, but above the level of thesea, and as these elevations differ in every instance, a reduction to the horizon at all themeasured angles is necessary ; but by the construction of the theodolite, this reduction ismade by reading off the horizontal angles. Ramsden’s large instrument, 3 feet in diameter,was the first by which this spherical excess was observed ; it is in all trigonometrical ob-servations small, not exceeding 4 or 5 seconds in the largest triangles employed : if theearth’s surface was a plane, the sum of the three angles would be exactly 180°, and theexcess above 180° is so far from being a proof of incorrectness in the work, that it isessential to its accuracy, whilst it offers at the same time another proof of the earth’ssphericity. The true way to judge of a trigonometrical survey is to consider the net workof triangles as the bases of so many pyramids converging to the centre of the sphere : thetheodolite accurately measures the angles included by the planes of these pyramids, and thesurface of an imaginary sphere at the level of the sea intersects them in an assemblage ofspherical triangles, above whose angles in the radii prolonged, the real stations of the ob-servations are raised by the superficial inequalities of mountain and valley. When thetviangles are so large as to make the difference between the chords and their arcs perceptible,the condition of the sphericity must be ascertained, or else, when all the triangles are laid