(316) The Annual change. If the observations be continued throughout an entire year, it will be found that the Diurnal changes vary with the seasons, being about twice as great in Summer as in Winter. The period of this change being a year, it is called the Annual Variation.

(317) The Secular change. When accurate observations on the Variation of the needle in the same place are continued for several years, it is found that there is a continual and tolerably regular increase or decrease of the Variation, continuing to proceed in the same direction for so long a period, that it may be called the Secular change of Variation.*

The most ancient observations are those taken in Paris. In the year 1541 the needle pointed 7° East of North; in 1580 the Variation had increased to 1110 East, being its maximum; the needle then began to move Westward, and in 1666, it had returned to the Meridian; the Variation then became West, and continued to increase till in 1814 it attained its maximum, being 22° 34′ West of North. It is now decreasing, and in 1853 was 20° 17′ W. In London, the Variation in 1576 was 11° 15' E.; in 1662, 0°; in 1700, 9° 40′ W.; in 1778, 22° 11' W.; in 1815, 24° 27′ W.; and in 1843, 23° 8' W.

In this country the north end of the needle was moving Eastward at the earliest recorded observations, and continued to do so till about the year 1810 (variously recorded as from 1793 to 1819), when it began to move Westward which it has ever since continued to do. Thus, in Boston, from 1708 to 1807 the Varia tion changed from 9° W. to 6° 5' W., and from 1807 to 1840, it changed from 6° 5' W. to 9° 18′ W.

Valuable Tables of the Secular changes of the Variation in var ous parts of the United States have been published by Prof. Loomis in Silliman's "American Journal of Science," Vol. 34, July, 1838, p. 301; Vol. 39, Oct. 1849, p. 42; and Vol. 43, Oct. 1842, p. 107. An abstract of the most reliable of them is here given. Troy and Schenectady are from other sources.

*If the term "Declination of the Needle" could be restored to its proper use his "Change of Variation' would be properly called the "Variation of the De clination."

From these and other observations it appears that at present the lines of equal variation are moving Westward, producing an annual change of variation (increasing the Westerly and lessening the Easterly) which is different in different parts of the country, and is about five or six minutes in the North-Eastern States, three or four minutes in the Middle States, and two minutes in the Southern States.

(318) Determination of the change, by Interpolation. To determine the change at any place and for any interval not found in the recorded observations, an approximation, sufficient for most purposes of the surveyor, may be obtained by interpolation (by a simple proportion) between the places given in the Tables, assuming the movements to have been uniform between the given dates; and also assuming the change at any place not found in the Tables, to have been intermediate between those of the lines of equal variation, which pass through the places of recorded observations on each side of it, and to have been in the ratio of its respective dis

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.

When

(319) Determination of the change, by old lines. 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 1.25 x 57.3 63

change of Variation was therefore Westerly.

= 10.137 = 128'

Fig. 208.

BC

=

× 57.3 or more precisely 57.29578. AB

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 appa rent 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

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.

(321) To run out old lines. To succeed in retracing old lines, proper allowance must be made for the change in the varia tion 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). The bearings may then be corrected by the following RULES.

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