Then, for determining the area of the east field,

we have the following lines, viz.

The area comprehended within these lines, computed according to the foregoing universal theorem, is

There are no offsets to be added in this field, the areas of the offsets to be subtracted, computed as in the last example, are

Remains the area of the east field, Acres.....

A 22.91936

2.22052

20.69884

For ascertaining the area of the west field, we have

The area comprehended within these lines, computed according to the foregoing universal theorem, is..

. A. 22.18048

The areas of the offsets to be added, computed as in the last example

Sum....

The areas of the offsets to be subtracted..

0.62287

22.80335

1.15900

For ascertaining the area of the north field, we have the following lines, viz.

The area comprehended within these lines, computed according to the following universal theorem, is.....

.. A. 21.81422

The areas of the offsets to be added, computed as in the last example ...

Sum.....

1.25030

23.06452

The areas of the offsets to be subtracted......

0.50080

Remains the area of the north field, Acres ....

22.56372

4

The agreement of this total with the area of the whole, as first ascertained, shews the work to be right. We must not, however, in actual practice expect to find so perfect an agreement as the above. A difference of a few perches, in actual practice, is no impeachment either of the field work, or of the computations.*+

OF THE NEW MAP-METER OR PLAN-MEASUrer.

This is a small but very useful instrument to surveyors, engineers, officers, &c. for enabling them in a very easy and expeditious manner, to measure the periphery of circles, the lengths of curves, and all other irregular lines upon maps or plans, in order to ascertain correctly distances, lengths of roads, boundaries, &c. &c., which cannot readily be done by compasses or scales.

Plate 20, fig. 2, is a representation of the machine of its real size, which is in thickness not half that of a common watch: it consists of a dial plate resembling that of a watch, with two similar moving hands or indices: by the proportion of the wheels within its case, the short index in one revolution points out 16 miles upon a scale of a map of one inch to a mile, and the long index moves round once to a mile.

The following are the circles graduated on the plate: The outer circle is a centesimal scale, which adapts the instrument to any scale of a map or plan different from one inch to a mile, by decimating any line measured by the instrument; the next inner circle is divided into 12 equal parts, which is useful in giving the distances into 12ths or duodecimally: the next circle is a scale

For other methods of surveying, and a new plan of a field book, see the Addenda to this work.

of 80 chains; the next, the same scale divided into eight furlongs, both being the distance of one mile, upon a map drawn on a scale of one inch to a mile.

a represents the small side wheel which gives motion to the wheel work and indices when it is moved over the line to be measured; it is so proportioned to the teeth of the inner wheels, that an inch of its circumference is pointed out as a mile by one revolution of the long index, or the 1-16th part by the short index: b is an ivory handle the instrument is held by, when you run the wheel a upon the line of the map: there is an index pointer on the wheel a to set off by with precision: before use, the wheel a must be turned round till the two indices coincide at the 100 or 16; then, placing the wheel on the map with the brass index exactly over the point to be measured from, run the wheel along the map; if you have occasion to turn an acute angle, lift up the wheel and set it down again in the new direction with the pointer precisely over the point.

By the decimal divisions, a scale on a map of 5 miles to an inch will be shewn by the long index pointing to 20 for one mile, 40 for 2 miles, &c. which will shew to the reader the application for any other scale of a map.

1

In the complete instruments, the wheel a is contrived to shift upon the axis of another contiguous wheel which is so proportioned as to point out distances upon a map, upon a scale of an inch to a mile, in which case the figures of the divisions must be doubled.

A back steel finger spring is also sometimes applied to keep the wheel a immoveable after use. EDIT.

† TO PLOT ELEVATED OR HILLY PIECES OF ground. In many instances, elevated ground may be of that value that a surveyor will be required to measure its whole surface to obtain its area or content, but the planning or plotting of it afterwards will require a reduction of the hypothenuse to the base, which may in many cases be sufficiently effected at the time of the survey by King's Quadrant already described at page 197. In great eminences and large surveys it is a more accurate method to take the angles of elevation or depressions with the theodolite, and with this angle, referred to the table for shortening the hy pothenuse at the end of this work, to obtain the requisite reduction of links, and to illustrate which, the following_examples have been extracted from Mr. Crocker's Elements of Land Surveying, 12mo. 1806.

OF

MARITIME SURVEYING.

Ir was not my intention at first to say any thing concerning maritime surveying, as that subject had

Case 1. Where only part of one side of a hill is required, as represented by the section A B C DE, fig. 1.

Example. Given the line of surface, or the side A C, or DE=600. The A or acclivity of the hill = 29° 30′. Required the base or plotting line AB. By the table it appears, that when the of B acclivity is 29° 30′, each

A 560

chain's length must, for plotting, be reduced 13 links. Then, 6 chains x 13 links 78 links, to be deducted out of 600, will leave 522 for the plotting line A B; which, on the measured surface, will extend no further than a b.

In comparing the computed areas of the elevated surface and base, the latter will in square measures be less than the former by 2 roods 5 perches, a difference more than a 6th part of the whole

surface.

Case 2. When the land ascends a hill on one side, occupies the plain on the top, and descends on the other side; in the manner represented by the section A B C D E F.

is the length of the whole plotting line AD? By the table the length of the line A E must be shortened 4 links in every chain; in the whole 31 links, which taken from 790 leaves for the line AB 759 links, BC the plain remains as EF = 620; and by the table, FD is to be shortened 6 links in every chain, in the whole 31 links; leaving for CD 489, total 1868.