tances from those two lines; for example, taking their arithmetical mean, if the required place is midway between them; if it be twice. as near one as the other, dividing the sum of twice the change of the nearest line, and once the change of the other, by three; and so in other cases; i. e. giving the change at each place, a "weight" inversely as its distance from the place at which the change is to be found.

(319) Determination of the change, by old lines. When the former Bearing of any old line, such as a farm-fence, &c. is recorded, the change in the Variation from the date of the original observation to the present time can be at once found by setting the compass at one end of the line and sighting to the other. The difference of the two Bearings is the required change.

If one end of the old line cannot be seen from the other, as is often the case when the line is fixed only by a "corner" at each end of it, proceed thus. Run a line from one corner with the old Bearing and with its distance. Measure the distance from the end of this line to the other corner, to which it will be opposite. Multiply this distance by 57.3, and divide by the length of the line. The quotient will be the change of variation in degrees.*

For example, a line 63 chains long, in 1827 had a Bearing of North 10 East. In 1847 a trial line was run from one end of the former line with the same Bearing and distance, and its other end was found to be 125 links to the West of the true corner.

The

10.137 = 1° 8'

Fig. 208.

вс
AB

× 57.3; or more precisely 57.29578.

B

will now bear N. 3° E. and S. 3° W; the line AB, which before was N. 40° E. will now bear N. 43° E; the line DF which before was N. 40° W. will now bear N. 37° W; and the line WE, which before was due East and West, will now bear S. 87° E. and N. 87° W. Any line is similarly changed. The proof of this is apparent on inspecting the figure.

Suppose now that a surveyor, ignorant or neglectful of this change, should attempt to run out a

farm by the old Bearings of the deed, none of the old fences or corners remaining. The full lines in the figure represent the original bounds of the farm, and the dotted lines those of the new piece of land which, starting from A, he would unwittingly run out. It would be of

the same size and the same shape as the true one, but it would be in the wrong place. None of its lines. would agree with the true ones, and in some places it would encroach on one neighbor, and in other places

1

Fig. 210.

would leave a gore which belongs to it, between itself and another neighbor. Yet this is often done, and is the source of a great part of the litigation among farmers respecting their "lines."

-F

E

(321) To run out old lines. To succeed in retracing old lines, proper allowance must be made for the change in the variation since the date of the original survey. That date must first be accurately ascertained; for the survey may be much older than the deed, into which its bearings may have been copied from an older one. The amount and direction of the change is then to be ascertained by the methods of Arts. (318) or (319). ings may then be corrected by the following RULES.

The bear

When the North end of the needle has been moving Westerly, (as it has for about forty years), the present Bearings will be the sums of the change and the old Bearings which were North-Easterly or South-Westerly, and the differences of the change and the old Bearings which were North-Westerly or South-Easterly.

If the change have been Easterly, reverse the preceding rules, subtracting where it is directed to add, and adding where it is directed to subtract.

Run out the lines with the Bearings thus corrected.

It will be noticed that the process is precisely the reverse of that in Art. (311). The rules there given in more detail, may therefore be used; RULE 1, "when the Variation is West," being employed when the change has been a movement of the N. end of the needle to the East; and RULE 2, "when the Variation is East," being employed when the N. end of the needle has been moving to the West.

If the compass has a Vernier, it can be set for the change, once for all, precisely as directed in Art. (312), and then the courses can be run out as given in the deed, the correction being made by the instrument.

(322) Example. The following is a remarkable case which recently came before the Supreme Court of New-York. The North line of a large Estate was fixed by a royal grant, dated in 1704, as a due East and West line. It was run out in 1715, by a surveyor, whom we will call Mr. A. It was again surveyed in 1765, by Mr. B. who ran a course N. 87° 30′ E. It was run out for a third time in 1789, by Mr. C. who adopted the course N. 86° 18' E. In 1845 it was surveyed for the fourth time by

Mr. D. with a course of N. 88° 30′ E. He found old " corners,” and “blazes” of a former survey, on his line. They are also found on another line, South of his. Which of the preceding courses were correct, and where does the true line lie?

The question was investigated as follows. There were no old records of variation at the precise locality, but it lies between the lines of equal variation which pass through New-York and Boston, its distance from the Boston line being about twice its distance from the New-York line. The records of those two cities (referred to in Art. (317)) could therefore be used in the manner explained in Art. (318). For the later dates, observations at New-Haven could serve as a check. Combining all these, the author inferred the variation at the desired place to have been as follows: In 1715, Variation 8° 02' West.

We are now prepared to examine the correctness of the allowances

made by the old surveyors.

The course run by Mr. B. in 1765, N. 87° 30′ E. made an allowance of 2° 30' as the decrease of variation, agreeing precisely with our calculation. The course of Mr. C. in 1789, N. 86° 18' E., allowed a change of 1° 12', which was wrong by our calculation, which gives only about 27', and was deduced from three different records. Mr. D. in 1845, ran a course of N. 88° 30′ E, calling the increase of variation since 1789, 2° 12'. Our estimate was 2° 18′, the difference being comparatively small. Our conclusion then is this: the second surveyor retraced correctly the line of the first: the third surveyor ran out a new and incorrect line: and the fourth surveyor correctly retraced the line of the third, and found his marks, but this line was wrong originally and therefore wrong now. All the surveyors ran their lines on the supposition that the original "due East and West line" meant East and West as the needle pointed at that time.

The preponderance of the testimony as to old land marks agreed with the results of the above reasoning, and the decision of the court was in accordance therewith.

N

Fig. 211

C,1789. D,1845
A,1715. B,1765

E

In the above figure the horizontal and vertical lines represent true East and North lines; and the two upper lines running from left to right represent the two lines set out by the surveyors and in the years, there named.

(323) Remedy for the evils of the Secular change. The only complete remedy for the disputes, and the uncertainty of bounds, resulting from the continued change in the variation, is this. Let a Meridian, i. e. a true North and South line, be established in every town or county, by the authority of the State; monuments, such as stones set deep in the ground, being placed at each end of it. Let every surveyor be obliged by law to test hist compass by this line, at least once in each year. This he could do as easily as in taking the Bearing of a fence, by setting his instrument on one monument, and sighting to a staff held on the other. Let the variation thus ascertained be inserted in the notes of the survey and recorded in the deed. Another surveyor, years or centuries afterwards, could test his compass by taking the Bearing of the same monuments, and the difference between this and the former Bearing would be the change of variation. He could thus determine with entire certainty the proper allowance to be made (as in Art. (321)) in order to retrace the original line, no matter how much, or how irregularly, the variation may have changed, or how badly adjusted was the compass of the original survey. Any permanent line employed in the same manner as the meridian line, would answer the same purpose, though less conveniently, and every surveyor should have such a line at least, for his own use.*

* This remedy seems to have been first suggested by Rittenhouse. It has since been recommended by T. Sopwith, in 1822; by E. F. Johnson, in 1831, and by W. Roberts, of Troy, in 1839. The errors of re-surveys, in which the change is neglected, were noticed in the "Philosophical Transactions," as long ago as 1679.