Chap. VIII.

GEOMETRY.

817

the remaining figures; the decimal figures cut off arc multiplied by 4, to bring them intoroods, and the decimal part of the last product multiplied by 40 gives the poles or perches.The chain now in use is of 100 feet, and divided into as many links: whichever chainis adopted for the measurement of distances, it is divided every ten links by brass marksnotched in a manner to distinguish them, and to enable the number of links at anypart of the chain to be read oft' conveniently: ten arrows accompany this chain, and whenused two persons arc employed, one of whom leads and takes the ten arrows with him :when the chain has been stretched in the proper direction, an arrow is stuck in theground where the chain terminates; and these are collected by the follower as heproceeds, and when ten have been taken up, they arc given to the leader to be used again,care being taken to notice each exchange from the follower to the leader; for whenthe line is entirely measured, the number of changes added to the number of arrows inthe follower’s hand, and to the number of links or feet extending from the last arrow putdown to the extremity of the line, gives the entire length : the only care to ensure correct-ness is, that the line so measured is perfectly straight, and that the ends of the chain aremade to coincide with the arrows placed in the ground as accurately as possible. Thelinks of the chain being pliable, and united by rings that are not welded, render it extremelyliable to get out of order; therefore, it is essential that it should during an extensive mea-surement be frequently applied to some standard, to examine and test its correctness: thisis very important, more particularly so, as it has been advised that no person should headmitted to give evidence in any court of justice with any other than a stamped measure:when the chain is used in wet weather, it often becomes shorter from the collection ofparticles of dirt getting into the joints or rings, and defective by the bending of thelinks. When the survey is made with a chain of 100 feet, and it is required to plot it toa scale of five chains to an inch, the scale must be divided into the 330 parts of an inch,there being that number of feet contained in five chains, making 33 divisions, eacli re-presenting 10. A scale double tbe length of Gunter’s, divided into 100 links, is foundboth correct and convenient, each link being double the ordinary length.

The Offset Staff is a rod ten links in length, marked at each link by a notch or bybrass nails; the follower carries this, and is employed by the surveyor for taking oftsets,but where these offsets are considerable, a tape 100 feet in length is the most con-venient: they should always he taken at right angles to the main line, and formerlythe cross staff was employed; at present, an instrument called the optical square isfound the most convenient for this purpose, it is a small circular box about 2 inchesin diameter, which makes a right angle with both accuracy and expedition; it has twoglasses fixed at an angle of 45° from each other, and one of them acts .as a mirror; theother is half silvered, so as to admit direct vision of one object and reflected vision of theother; so placed at right angles to a line passing from the observer to the first object, theimage of the second is reflected from the first mirror: the principle is, that the anglemade by the first and last direction of a ray of light which has suffered two reflections inone plane, is equal to twice the angle of inclination of the reflecting surfaces. Withthis little instrument right angles may be accurately set out, by the observer simplystanding over the given point and looking through it along the line, having some one witha marking rod in the direction where the perpendicular is to be set out, and by motioninghim to the right or left, until the rod he holds is seen by reflection to coincide with a stairfixed on the line where the observer is looking; when this is the case the rod is fixed inthe ground : a perpendicular line is often set out by the use of the chain only, by measuringon the base line a distance of 40 feet; then at the extremities of this distance measuringas an hypotenuse 50, and as a perpendicular 30: when the sides of a triangle are in theproportions of 30, 40, and 50, it is a right angle, and has the two short sides perpendicularto each other.

To survey a Plot of Ground with the Chain , we are confined to the use of the triangle,it being the only figure the sides of which cannot be altered. The field to be measuredis then divided into a series of triangles of as large a description as can well be obtained ;much of the judgment of the surveyor is called into play upon the adoption of the triangle,or laying out the sides of the figure, which should approach as nearly as possible that ofthe equilateral: the sides of the triangles are then measured, also a line from one ofthe points to the middle of its opposite sides which enables the surveyor to detect anyerror that may have been committed in the measurement of the three sides: the generalcombination of these triangles must be laid down so that the largest come as nearlyto the boundary of the spot as possible; and when their figure is determined, pickets areplaced on the ground at their angles; these are called station points, and are measuredto and from, and all the lines connecting them are denominated station lines, which areto be distinguished from the simple offset lines.

The Field Book should commence with a rough sketch made of the land to be plotted,and which should be the result of a careful walk over the ground previous to the measure-ments being taken : it is ruled into three columns; in the middle one is to be set down