CALCULATING QUANTITIES GENERALLY FOR To measure an angle from the meridian 230

LAND AND ENGINEERING SURVEYING.

PART I.

INTRODUCTION.

PREVIOUS authors have disagreed as to the origin of Land Surveying it has been attributed to the annual inundation of the Nile, the deposit from which destroyed the landmarks; it therefore called forth some accurate method of ascertaining the original boundary of individual property.

This object was carried into effect in the most efficient manner by Euclid, a mathematician, who flourished three hundred and eight years before the birth of Christ; he was so highly respected in his lifetime, that King Ptolemy became one of his pupils, and from that time no mathematician was found who had not studied in the school established by him at Alexandria; even in the present day Euclid's elements are the foundation to our greatest mathematicians. Whoever considers the whole extent of geometry, will find that the main design of all its speculation is mensuration; to this the elements of Euclid are almost entirely devoted.

The latter part of this century has been remarkable for its wonderful march of scientific improvements, and has opened a

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vast field for talent and enterprise in the art of land surveying, by the introduction of railroads, forming part of the duties of the civil engineer and architect.

To be a perfect surveyor, he should be well qualified in the knowledge of arithmetic, geometry, mensuration, algebra, logarithms, and decimals, and be thoroughly acquainted with the most eminent authors on mathematics.

The duties of a surveyor frequently extend beyond making a plan and giving the superficial area: such as disputed boundaries, manorial rights, exchange or the division of land, diversion and improvement of roads, measuring stone, quarries, drainage, and building materials.

Land surveying may be considered to be divided into three classes:

First, by the chain only; second, by the chain and the use of the theodolite, or other instruments for measuring angles; third, by trigonometry, which is chiefly performed by the theodolite and logarithmic tables. This branch is seldom required in ordinary surveying; it is applied to the survey of counties, kingdoms, maritime surveying, and inaccessible distances.

In all cases, whether it be a single field, estate, parish, or county, the triangle is the only figure adopted to lay down the foundation of a survey. Now, let it be remembered, a triangle itself has no proof of accuracy where the chain only is used, a fourth line must be measured from either of the two sides, or from one of its angles to its opposite side; this will also apply to the second case, or by measuring all the three angles with the instrument; the same also in the third case.

A figure of four unequal sides, called a trapezium, could not be plotted unless a line was measured from the opposite corners or angles, dividing it into two triangles. This would also require another line from either its two opposite sides, or the two opposite angles, to prove its accuracy.

To obtain the accurate quantities of fields, all the irregular fences are reduced to straight lines, and then to triangles.

Those who have not received a preparatory knowledge of geometry and the higher branches of mathematics, are recommended to apply their leisure hours to the works of any of the following authors: Hutton, Bonycastle, Keith, &c., as only such portions of geometry, mensuration, and logarithms will be here introduced as are immediately connected with the subject.

In computing the areas or contents of fields, in addition to the system shown by mensuration, another system will be described by means of a sliding scale, and will be found to be truly accurate and expeditious, particularly on very irregular boundaries.

In order that the student may more readily comprehend the system of surveying by the chain only, and by the chain and instrument, the same field will be adopted to both.

It is an erroneous opinion amongst many, that a straight line cannot be polled out, or a survey correctly made, without the use of a theodolite; the student should first make himself thoroughly master of the chain by laying out his work by large intersecting triangles. There are certain cases where a theodolite is indispensable-such as a town or village, hilly and woody country, &c.

The theodolite is the most perfect instrument for surveying; a box sextant will be found a most valuable auxiliary in filling up the details of a survey. To accompany these must be provided a protractor, to plot the angles that are taken by the instrument. These are all the instruments required for surveying-for a description of which see Part V.

The treatise of logarithms, decimal fractions, and the roots, are extended to a greater length than was intended for this work; the value of it to the surveyor will amply remunerate him for perseverance in obtaining a perfect knowledge of them from the authors before recommended.