second for the occupiers; the third for the number in the map; the fourth for a description of cultivation; the fifth for the quantity of statute acres in each field; the sixth for the name of each field; and the seventh for observations.

The foregoing plan being only part of a larger survey, whose greatest length lay in the direction of the base line AB, the direction on the original plan has been retained. This direction, however, does not range with the greatest length of the portion here laid down, which does not accord with the instructions given in the commencement of this survey. The direction of the original base line is retained, in order to take advantage of the field book of that part which is taken to illustrate the rules.

The area of the foregoing survey may be found, independently of its graphic representation, by the following method for finding the area of a triangle. Add the three sides together, and take half the sum ; from this half sum deduct each side separately; then to the logarithm of the half sum, add the logarithm of the three remainders, and the natural number answering to half the sum of the four logarithms will be the area of the triangle.

In laying out the large or primary triangles, most surveyors make use of some distant object to chain to, such as the chimney of a large building, the spire of a church, or such like conspicuous object. This practice, no doubt, has one thing to recommend it, namely, that such objects can be distinctly seen at a great distance; but the difficulty, nay the impossibility in most cases, in measuring exactly to the point directly under the object

approached, renders the practice by no means desirable, an error being invariably the result, except in cases where you can measure to the point directly under the elevated object towards which you chain; therefore, such stations should be taken with due caution. The corner of a house, or a lofty tree, are often chosen as stations, as they can be measured to without much difficulty.

In no case does the surveyor show more judgment than in the choice of his stations. It does not very unfrequently happen that an inexperienced one takes it in a situation so limited in its view, as to make it a matter of great difficulty to extend his triangulation much farther. Therefore, before fixing upon any spot for a station, he should take a prospective as well as retrospective view, that he may have no difficulty after in extending the work.

Long poles, with flags of some colour easily distinguished, placed on an eminence commanding as extensive a view as the ground would permit, are preferable to any clumsy object difficult of access.

When the view is intercepted by a hedge, a clump of trees, or such like, the obstruction should be removed by opening a passage through it, thus extending your view without doing more damage than is absolutely necessary for the prosecution of the work. For this purpose, and for the purpose of pointing stakes to drive into the ground at the different stations, a hatchet would be found a most useful implement.

It is a question often discussed, whether the absolute surface should be measured, or the diminished quantity which would result, had the whole been reduced to a

horizontal plane. This last quantity is, and ought to be, the computed and delineated contents of every survey, whether large or small; allowance being made in very extensive surveys for the curvature of the earth, but none for hilly grounds, the hypothenusal distances being invariably reduced to their horizontal lengths, before the work is plotted or the calculation begun. This preference to the horizontal quantity is founded on the obvious principle, that as plants shoot up vertically, the vegetable produce of hilly ground can never exceed what would have grown on its level base. In the case of a plantation of large trees, the thing appears self-evident. Hence the necessity of paying due attention to the reduction of hypothenusal measurement to horizontal, which can only be effected by proper instruments constructed for the purpose.

To find the area of a survey bounded by curved, or very irregular lines, by equating the portions excluded from, and included in the figure, requires both judgment and practice. This method reduces the curved or irregular boundaries of the survey to straight lines, which shall inclose the same or equal area as those crooked sides, and so obtain the area of the original irregular figure by means of the right-lined one of less complicated form.

Let it be required, for example, to find the contents of the annexed figure, which we shall suppose is plotted to a scale of 4 chains to an inch.

First, draw the four dotted lines AB, BC, CD, and AD, excluding as much of the original figure as you included of ground which lies outside the boundary of the farm or field; then draw the diagonal BD, and

from the points A and C demit the perpendiculars AF, CE, which, with the diagonal, will afford sufficient data

D

B

to find the area. When the scale is applied to BD, it measures 1256, to AF, it measures 456, and to CE, it measures 428. Hence

In this case the trapezium is made as nearly equal to the original figure as the eye can judge, and its area found as above, which is equal to that of the farm or field.

Mr. Brough, in his treatise on survey, introduces a method of surveying by taking angles with the chain. This method should never be practised, it being impossible, by it, to approach the truth with any reasonable degree of certainty.

TRIGONOMETRICAL SURVEYING.

Trigonometrical surveying shows how to survey large tracts of land by means of a series of triangles connected together, so as to inclose the entire. The principal difference between this method and that by the chain only, is, that when the chain only is used, the three sides of every triangle must be measured, whereas in the method which we are now about to describe, only one side of the first triangle is measured with the chain, and two angles with the theodolite; then having one side and two angles of a triangle given, the other two sides can be found by trigonometry. By taking two angles at the extremities of the sides of this triangle, whose sides are now given, all the parts of the adjacent triangles may be found without using the chain, by which the error of chainage is avoided.

The only instrument to be depended on in trigonometrical surveying, is the theodolite; and the best and most convenient for general use, is Jones' or Troughton and Simms' five-inch instrument, which reads to one minute.