and as the same may be shown for any figure whatever, we may regard the rule as demonstrated for all cases.

We will now make the calculations in numbers. Having balanced the work, we can place it in the following table.

Observing in the field notes that station 2 is the most westerly point of the land, we assume the meridian which passes through this point, as the one from which the meridian distances are calculated. We mark the principal station with a star.

Opposite station 2, we enter, in the column of double meridian distances, headed D. M. D., the departure of the course from 2 to 3, which is the double meridian distance of that course, and plus. To this we add the departure of the course, and also the departure of the next course their sum is the double meridian distance of the course from 3 to 4.

To the last sum add the departure opposite station 3, and the minus departure opposite station 4: their algebraic sum is the double meridian distance from 4 to 1.

To the last sum add the last departure, which is minus, also the next departure which is likewise minus: this will give the double meridian distance of the course from 1 to 2, which is also equal to its departure.

Then forming the products, adding them together, taking their difference, and dividing it by 2, according to the rule, we

For this purpose, draw any line, B as NS, to represent the meridian. passing through the principal station, on which take any point, as B, to represent that station.

D

S

FIRST METHOD OF PLOTTING.

A

Having fixed upon the scale on which the plot is to be made, lay off from B on the meridian, a distance Bs equal to the difference of latitude of the first course, and at s erect a perpendicular to the meridian, and make it equal to the departure of the first course: then draw BC, which will be the first course.

Through C draw a meridian, and make Cf equal to the difference of latitude of the second course, and through f draw a perpendicular fD, and make it equal to the departure of the second course: draw CD, and it will be the second course.

Lay down, in the same manner, the courses DA and AB, and the entire plot will be completed.

SECOND METHOD OF PLOTTING.

At

The work may be plotted in another manner, thus. the principal station B, lay off an angle equal to the bearing from B to C, which will give the direction of BC. Then, from the scale of equal parts, make BC equal to the first course this will give the station C.

Through C draw a meridian, and lay off an angle equal to the bearing from C to D, and then lay off the course CD. Do the same for the bearing at D and the course DA; also, for the bearing at A and the course AB, and a complete plot of the ground will thus be obtained. If the work is all right, the last line AB will exactly close the figure. This plot is made on a scale of 40 chains to an inch.

2. It is required to determine the content and plot of a piece of land, of which the following are the field notes, viz.

REMARK. When a bearing is due east or west, the error

the sum of the courses, before balancing the columns of lati tude. In the last example; the 3d bearing is due east, and the first term of the several proportions for error in latitude,

was 132.40-21.25=111.15.

In like manner, if a bearing is due north or south, the error in departure is nothing; and the sum of the courses must be diminished by this course, before balancing the columns of departure.

3. Required the content and plot of a piece of land, of which the following are the field notes.

4. Required the content and plot of a piece of land, from the following field notes.

5. Required the content and plot of a piece of land, from the following field notes.

To determine the content and boundary of a piece of land, by means of offsets from the principal lines.

145. An offset is a line drawn perpendicular to a course, and may lie either on the right or left of it.

146. Let ABCDE be a piece of ground to be surveyed. Let us suppose it to be bounded on the west and north by a fence and road, and on the cast and south by a creek or river.

Place stations at the principal points, as A, B, C, D and E. Take, with the compass, the bearings from A to B, from B to C, from C to D, from D to E, and from E to A; and measure the distances AB, BC, CD, DE, and EA.

N

At convenient points of the course AB, as a, c and f, make the offsets ab, cd, fg. Then, having measured these lines, as also the distances Aa, ac, ef and fB, enough will be