Let AB-820 BC=434 When the irregularities of the boundaries of a field are numerous, it may not be improper to recommend a field-book, in which the several measures are to be recorded, to prevent confufion. But when the field is not very irregular, all the meafures may, with equal advantage, be marked upon an eyedraught of the field, each against the corresponding parts of the figure. And either of these methods may be practised, whether the survey be large or small. There is no particular form for the field-book ; every one rules and contrives as he judges most proper for himself; but, to avoid perplexity, the fimpleft form is the best. The follow, ing is a specimen of a method generally practised. It is divi. ded into three columns; in the middle is marked the stations, bearing, and distances measured. On the right hand, the offsets are marked against their corresponding distances in the middle column, together with such other remarks as occur in measuring, such as houses, hedges, ponds, roads, &c. In the left hand column are marked the inlets against their corresponding distances in the middle column, and remarks, as above. N. B. The inlets are perpendiculars dropt from such irregularities as fall within the station-line. The area of which is to be subtracted from the general content of the field. The measures of the preceding figure may be arranged in a field-book as follows: THE The bearings, distances, off-sets, &c. ought to be recorded in the field-book immediately when taken, otherwise material mistakes may be committed. The field-book may be made up thus : Suppose A the first station, and AB the first line measureda In the middle column mark .1 for the first station ; next find by the theodolite the quantity of the angle BAE, which insert in the middle column. Then write a cypher below to denote the station, and another in the right hand column to signify that at the station A there is no off-set; and at the distance of 100 links from A, in the direction AB, is an off-set of 40 links. Register the distance 100 in the middle column; and against this distance, in the middle column, write the off-set 40 in the right hand column. Again, at the distance of 135 links from A, in the direction AB, is an off-set of 60 links; mark the diftance 135 in the middle column; and right opposite to 135 in the middle column, write the off-set 60 in the right hand column. At the distance of 470 from A, in the direction AB, the crooked boundary touches the station-line AB; in which case the distance 470 is marked in the middle column, and a cypher in the right hand column, there being no off-let. At the distance 680 from A, the irregular boundary again deviates from the station-line AB. The distance 680 is marked in the middle column, and the cypher at the right-hand side, as above. At the distance of 700 links from A, is an off-set of 30 links ; mark these as above. Lastly, Mark the whole length of the line AB 850, then draw a ftroke. In like manner mark B .2' also the angle ABC; and proceed to measure BC as above ; and so on, till all the boundaries are measured. If, in planning the field, the direction EA does not pass through the point A with the measuted distance EA, fome er. ror has been committed, and the work must be revifed over again. It may fave much trouble to know whether the mistake has arisen from the angles or from the distances : If the angles are right, the distances alone are to be measured. To To know if thé angles have been accurately taken, add all the inward angles into one sum; and when the work is right, their sum is equal to twice as many right angles as the figure has fides, wanting 4 right angles, (Euclid 31. 1. Cor. 1.) Or, instead of the inward angles, their supplements may be added into one sum ; and if it is equal to 360°, the angles have been taken right, (Euclid 31. 1. Cor. 2.) becaufe all the exterior angles of any, rectilineal figure are together equal to 4 tight angles. Few directions for planning may serve for any one who has studied and understands the use of his instruments. It may, indeed, be necessary to mention, that all plans of surveys ought to be laid down so, as the north side may ly towards the top of the paper, the east towards the right hand side, the west to the left, and the south to the bottom. Likewise it is customary to draw a meridian line, with a flower-de-luce directed to the top of the map or plan, to point out the north. When the plan of tising-ground is to be made out, the hypothenusal lines must be reduced to a level, otherwise the plani will be distorted; and when å mountain is to be represented on a plan, the base only is taken ; and in computing its content, as well as in planning it, this should be considered, that the base of the mountain will contain as many growing trees as its surface',- We shall subjoin a table for making the necessary deductions to reduce hypothenusal lines to a level; and these allowances may be made immediately when measured, before the measures are recorded in the field-book, or when the plan is to be protracted. • This may appear a paradox to fome, who perhaps never observed, that trees grow perpendicular to the horizon, or parallel to each other. |