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taken be inserted on the left hand side of the fieldbook, opposite to the stations from whence they were respectively taken.
In your protraction as you proceed, let every intersection be laid off from the respective stations from whence they were taken, and let these lines be continued ; if they all converge or meet in one point, we thence conclude all is right, or so far as they do converge ; but if we find a line of intersection to diverge or fly off from the rest, we may be sure that either a mistake has happened between the station the foregoing intersection was taken at, and the station from whence the intersection line diverges, or there must be an error in the intersection; but to be assured in which of these the fault is, protract on to the next intersection, and having set it off, if it converges with the rest, though the foregoing one did not, we may conclude the fault was committed in taking the last intersection but one, and none in any station, and that so far is true as is protracted; but if this as well as the foregoing intersection diverge or fly from the point of concourse or converging point of the rest, the error must have its rise from some station or stations, at or after that, from whence the last converging intersection line was taken : so that by going to that station on the ground, and proceeding on to that where the next, or from whence the following diverging intersection was taken, we can readily and with little trouble set all to rights.
But in most tracts of land, one object cannot be seen from every station, or from perhaps one fourth of them; in this case we are under the necessity to move the pole after we begin to lose sight of it, to some other part of the land, where it may be seen from as many more stations as possible; which is easily done by viewing the boundary before it be surveyed: the pole then being fixed in an advantageous place, the first intersection to it is best to be made from the same station from whence the last one was taken, and then as often as may be thought convenient, as before ; in like manner the whole may be done by the removal of the pole.
When we here speak of stations, we do not mean such as are usually taken at every particular angle of the field: for it is to be apprehended, that every skilful surveyor, particularly such who use calculation, will take the longest distances possible, not only to lessen the number of stations, for the ease of either protraction or calculation, but with greater certainty to account for the land passed by, on the right hand or on the left, wbich is taken by off-sets : and surely it will be allowed that any measure taken on the ground, and the content thence arithmetically computed, will be much more accurate than that which is obtained from any geometrical projection.
From what has been said it is plain, that from this method any fault committed in a survey can be readily determined, and therefore must be much preferable to the present method of taking diagonals, or the bearings and lengths of lines across land, to accomplish that end; which last method is too frequently used by surveyors to proximate or arrive near the content, which will ever remain uncertain, let these diagonals be ever so many, till the station or stations wherein the error or errors were committed, be found ; and the fault or faults be corrected.
apWhere one diagonal is taken, it may perhaps close or meet with one part of the survey and not with the other; in this case, if the surveyor would discover his error, he must survey that part of the land which did not close, and this may be half or more, of the whole. And should the diagonal close with neither part, but be too long, or too short, or should it fall on either side of the assigned point it was to close with, he ought to go over the whole, and make a new survey of it in order to discover his error.
A number of diagonals are frequently taken, the sum of the lengths of which very often exceėds the circuit of the ground, and after all they are but approximations, and the content remains uncertain as before ; therefore he who returns a map, made up by the assistance of diagonals, where there remains a misclosure in any one part, runs the risque of being detected in an error, and must suffer uneasiness in his mind, as he cannot be certain of the return he makes.
The frequent misclosures which are botched up by diagonals, occasion the many and frequent scandalous broils and animosities between surveyors, which tend to the loss of character of the one or the other, and indeed often to the disrepute of both, as well as to that of the science they profess.
But these may be easily remedied by intersections, and the bearing or line to be adjusted where the fault was committed, and till this be found, nothing can be certain.
TO ENLARGE OR DIMINISH MAPS.
To enlarge or diminish a map, or to reduce a map from one scale to
another ; also the manner of uniting separate maps of lands which join each other, into one Map of any assigned size.
LAY the map you would enlarge, over the paper on which you would enlarge it, and with a fine protracting pin, prick through every angular point of your map, join these points on your paper (laying the map you copy before you) by pencilled or popped lines, and you have the copy of the map you are to enlarge : in this manner any protractiom may be copied on paper, vellum, or parchment, for a fair
map. If you would enlarge a map to a scale which is double, or treble, or quadruple to that of the map to be enlarged, the paper you must provide for its enlargement must be two, or three, or four times as long and broad as the map; for which purpose in large things you will find it necessary to join several sheets of paper, and to cement them with white wafer or paste, but the former is best,
Then pitch upon any point in your copied map for a centre ; from whence if distances be taken to its extreme points, and thence if those distances be set in a right line with (but from) the centre,
and these last points fall within your paper, the map may be increased on it to a scale as large again as its own; and if the like distances be again set outwards in right lines from the centre, and if these last points fall within your paper, it will contain a map increased to a scale three times as large as its own, &c.
PL. 12. fig. 2.
Let the pricked or popped lines represent the copy of a down or old survey, laid down by a scale of 80 perches to an inch, and let it be required to enlarge it to one laid down by 40 to an inch.
Pitch upon your centre as , from whence thro' a lay the fiducial edge of a thin ruler, with a fine pointed pair of compasses, take the distance from a to the centre o, and lay it by the ruler's edge from a to A: in the like manner take the distance from the next station b to the centre , and lay it over in a right line from bto B, and join the points A and B by the right line AB ; in the like manner set over the distance from every station to the centre, from that station outwards, and you will have every point to enlarge to; the joining of these constantly as you go on by right lines, will give you the enlarged map required.
In taking the distance from every station to the centre, set one foot of the compasses in the station, and the other very lightly over the centrepoint, so lightly as scarcely
to touch it, otherwise the centre-point will become so wide, that it may occasion several errors in the enlarged map: for