ferences of latitude and the departures, computed to different courses and distances.

13. The Area or Content of a tract of land is the horizontal surface included within its boundaries, expressed in known measures, as Acres, Roods, and Perches.

14. In going round a tract of land and returning to the place of beginning, it is evident that the whole northing which has been made, must be equal to the southing, and the easting to the westing; or in other words, that the sum of all the northings must be equal to that of the southings, and the sum of the eastings, to that of the westings.

This principle enables us to judge of the accuracy of a survey, when the bearings and distances of all the sides have been taken. If the sums of the computed northings and southings are equal, and also those of the eastings and westings; or, if, though not exactly equal, they are very nearly so, we may conclude that the survey has been correctly made; as very small differences in these sums may be imputed to little, unavoidable errors in taking the bearings and measuring the distances. But when the sum of the northings differs considerably from that of the southings, or that of the eastings from that of the westings, we must infer that an error has been made, too great to be admitted. In this case a re-survey should be taken.

It is a rule with some of our best practical surveyors, that when the difference between the sums of the northings and southings, called the error in latitude, or that between the sums of the eastings and westings, called the error in departure, exceeds one link for every five chains in the sum of the distances, a re-survey ought to

When the errors in latitude and departure fall within the limits just mentioned, they should be properly apportioned among the several latitudes* and departures; we shall thus obtain what are called the corrected latitudes and departures. The method of doing this will be given in one of the following problems.

PROBLEM I.

To reduce two-pole chains and links to four-pole chains and links.

RULE.

1. If the number of chains is even, divide it by 2, and to the quotient annex the given number of links.

2. If the number of chains is odd, divide by 2 as before, for the chains; and for the 1 that is off, add 50 to the given number of links.

EXAMPLES.

1. In 16 two-pole chains and 37 links, how many fourpole chains and links? Ans. 8 ch. 37 links, or 8.37 ch.

2. How many four-pole chains and links are there in 17 two-pole chains and 42 links? Ans. 8.92 ch.

3. How many four-pole chains and links are there in 22 two-pole chains and 7 links? Ans. 11.07 ch.

* In order to conciseness of expression, difference of latitude is frequently

PROBLEM II.

To reduce two-pole chains and links to perches and hundredths of a perch.

RULE.

Multiply the links by 4, for the hundredths, and the chains by 2, for the perches. If the hundredths exceed 100, set down the excess, and add 1 to the perches.

Note.

This rule

vided into 50 links.

supposes the two-pole chain to be di

EXAMPLES.

1. Reduce 17 two-pole chains and 21 links to perches and hundredths. Ans. 34.84 per.

2. Reduce 15 two-pole chains and 38 links to perches and hundredths. Ans. 31.52 per.

3. Reduce 57 two-pole chains and 49 links to perches and hundredths. Ans. 115.96 per.

PROBLEM III.

To reduce square four-pole chains to acres.

RULE.

Divide by 10, and the quotient will be the acres. If there is a decimal in the quotient, multiply it by 4, for the roods; and the detimal of these by 40, for the

To reduce acres, roods and perches to square chains.

RULE.

Divide the perches by 40 and prefix the roods; divide the result by 4 and prefix the acres; then this latter result, multiplied by 10, will give the square chains.

Or reduce the given quantity to perches and divide by 16.

EXAMPLES.

1. Reduce 13 ac. 1 r. 10 p. to square chains.

40)10

4)1.25

2. Reduce 127 ac. 3r. 23 p. to square chains.

Ans. 1278.9375 sq. ch.

3. Reduce 35 ac. 0 r. 20 p. to square chains.

PROBLEM V.

Ans. 351.25 sq. ch

To find the bearing of a line.

1. Let a stake of six or eight feet in length be set up perpendicularly, at the far end of the line. Set up the compass staff perpendicularly, at the beginning of the line, and placing the compass on the staff, adjust it to a horizontal position; the ball and socket admitting a motion for that purpose. This position can be determined with sufficient accuracy, by observing whether, when the compass is turned round, the ends of the needle remain at the same height above the face of the instrument.

2. Turn the compass round so as to bring the south end of it towards the stake at the far end of the line. Then applying the eye to the sight at the north end, move the compass gently round till the stake can be seen through the fine slits in both sights, and let it remain in this position.

3. When the needle has settled, observe the number of degrees and parts of a degree, that are intercepted between the south end of the needle and the north or south point of the compass, to whichever it is nearest ; which will be the bearing, reckoning it from that point, towards the east if the south end of the needle is to the right hand, but towards the west if it is to the left hand.

Note 1.-The bearing thus obtained may be, and should be, verified by going to the far end of the ne,