SURVEYING. This important art, however difficult its attainment may ap pear, is nevertheless to be comprised within a very few general rules. The ac curacy of the work must depend entirely on the correctness of the instruments em ployed, the steadiness of the hand and eye of the operator, and the faithfully tracing the given lines and angles on the paper designed to exhibit the estate, or premises, under examination. The fol lowing leading principles will give an in sight into the %ode of displaying the re sults, whatever' may be the means em ployed for their computation. First. We are to reject the actual curvaty,fie of our globe, in all land surveirs ; thatilt, where no current of water, Mk the level of any fluid, is under consideration : such curva ture amounts to about eight inches in every mile, either of latitude or of longi tude. In brief, we consider the earth to be flat, instead of spherical. Secondly. We must ever carry in mind, that every triangle is equal to half a parallelogram of equal base and altitude ; as shown un der the head of GEOMETRY. Thirdly. That wherever there is a deviation from the horizontal, there will be a greater ex tent of sirface displayed on a scite than if the same were horizontal. To illustrate this, let an orange be cut through in the middle, and the flat part, i. e. the section, be placed bn a level table : it is evident that the round surface of the half orange will offer more surface than:the flat section which lays upon the table : but, if it were required to build on the semi-spherical surface, it would be found that no more houses, &c. could be raised thereon, than would stand on the extent of the flat sec tion. The reason of which is, that no more perpendiculars can be raised on one than on the other. This shows how fallacious is the mode of purchasing what is called side-long, or hanging, land by the acre. The greater the deviation from the horizontal, the -more is the base di minished. Fourthly. The surveyor must recollect, that all planes, of whatever ex tent or form; may be divided into, and be represented by, triangles of various forms and dimensions, whose aggregate will amount to the measurement of the area thus partitioned off: for, asEuclid justly observes, "All the parts, taken together, are equal to the whole." It will be fur
ther seen, that every figure may, either directly or circuitously, be commuted into a triangle, of corresponding area : but it may be necessary, at the same time, to observe, that the squaring of the circle has not hitherto been per fected ; though we have arrived so near ly to the completion of that object, as to leave no room for regret at • the want of absolute precision.
These points being completely under stood, the learner may proceed to the ru diments of surveying ; suppasing him to be grounded in the few preliminary prob lems which enable him to describe the ordinary figures : should he not have ob tained any previous information on that subject, we recommend that lie turn back to the heads of GEOMETRY and MATHE. MATICAL instruments ; under which he will find various items indispensable to wards his progress.
We shall submit a few propositions which the student may work with his compasses, plain scale, and protractor : when able to do all that may be need ful on paper, he may then try his hand with one or other of the various instill ments in use among surveyors.
Proposition I. " To ascertain the con tents of the square field ABCD, fig. 1. Plate XV. Miscel." Here little is to be clone ; one of the sides being measured, say 70 yards, and multiplied by itself, will give 4,900 square yards for the area ; or oue acre (i. e. 4,800 square yards) and 100 square yards.
Proposition II. ". To survey the field ABCD, fig. 2." This figure having the sides AB and CD parallel, and at right angles to All, add the lengths of those parallels, say 70 and 90 yards, together ; divide half their sum (i. e. 80) and multi ply that half by the depth of AD, say 70; which being multiplied by the medium length, GE, gives an area of 5,600 square yards. The parallelogram, ABED, might have been computed by simply multiply ing its length by its breadth ; and the triangle, BCE, might be taken separate ly, thus : the depth, (or altitude) BE, 70 yards, to be multiplied by half CE, (1. e. 10 yards) this would give 700; and the produce of AB, which is 70, by BE, which is also 70, would be 4,900; making in all 5,600, as above shown.