found, nearly, by comparison with other places where such observations have been made.

When any well-established marks can be found, the change may be determined by taking the bearings of these and comparing them with the records. The difference will give the change that has taken place between the dates of the two surveys.

If the two marks are not on the same line, they may still be used for this purpose. Thus, according to an old deed, the bearings of three adjacent sides of a tract were as follows,-viz.: 1. Beginning at a marked locust, N. 60° E. 200 perches to a chestnut; 2. N. 251° E. 183 perches to a post; 3. N. 45° E. 105.3 perches to a white-oak. The locust is gone, but the stump remains, and the white-oak is still standing. The intermediate corners are entirely lost. Setting the instrument over the stump, run N. 601⁄2° E. 200 perches; thence N. 251° E. 183 perches; and thence N. 45° E. 105.3 perches.

If no change had taken place in the variation, and both surveys had been accurately made, the last distance would have been terminated at the white-oak. Instead of this, however, the tree bears S. 54° 25′ E. 2.93 perches. Fig. 200 is a draft of the above.

From the bearings of AB, BC, and CD, calculate that of AD, which (Art. A 350) will be found to be N. 43° 59′ E. 470.38 perches. This, therefore, was the bearing and distance of AD at the

Fig. 200.

B

D'

time of the former survey. It is now the bearing and distance of AD'.

With the latitude and departure of AD' and that of DD', calculate the present bearing and distance of AD (Art. 350.) It will be found to be N. 47° 54′ E. 476.25 perches. The change of variation has therefore been 3° 55′ W. There is likewise a variation of 5.87 perches in the measurement, from which it is inferred that the chain used in the former survey was 101.25 links in length, or 14 links too long.

In order, therefore, correctly to trace the lines of the tract, the vernier of the compass must be set 3° 55′ W., and all the distances be increased 14 links per chain, or 11 perches per hundred. The magnetic bearings and the distances of the three sides are now,-1. N. 64° 25′ E. 202.5 perches; 2. N. 29° 10′ E. 185.3 perches; 3. N. 48° 55′ E. 106.6 perches.

445. Diurnal Change. If the position of the needle be accurately noted at sunrise on a clear summer day, and the observation be repeated at intervals, it will be found that the north pole will gradually be deflected to the west, attaining its maximum deviation about 2 or 3 o'clock. During the afternoon it will gradually return towards its former position, which it will regain about 8 or 9 o'clock in the evening. This deviation from the normal position is known as the diurnal change. It amounts sometimes to as much as a quarter of a degree, being greater in a clear day than when the sky is overcast, and not being perceptible if the day is entirely cloudy. It is likewise greater in summer than in winter.

In consequence of this diurnal change, it is evident that a line run in the morning cannot be retraced with the same bearings at noon. The surveyor should therefore record not merely the date at which a survey is made, but also the time of day at which any important line was run, and also the state of the weather, whether clear or otherwise.

446. Irregular Changes. Besides the secular and diurnal changes, the needle is subject to disturbance from the passage of thunder storms, or from the occurrence of aurora boreali. It is likewise sometimes violently agitated when no apparent cause exists. Such disturbances probably result from the occurrence of a distant magnetic storm, which would otherwise be unperceived, or from the passage of electric currents through the atmosphere.

447. From the preceding articles it will be apparent that

the needle, though an invaluable instrument for many purposes, is little to be depended on where precision is required. It would be very desirable that prominent marks, the bearings of which were fully known, were established over the country, and that all important lines should be determined, by triangulation, from these. The true bearings should always be recorded. There would then be no difficulty in retracing old lines. In the State of Pennsylvania, and perhaps in some others, this is now required by law, though it is very doubtful whether the law is yet carried out in a way to be of much practical benefit, owing to the want of scientific knowledge on the part of much the larger number of those who undertake the business of surveying.

Until there is a more general diffusion of theoretical as well as practical science among those whose business it is to settle the boundaries of estates, cases will continually occur in which confusing lines will be found to exist. This could never occur if all the bearings were made to the true meridian, the surveyor being careful to determine the local attraction and to allow for it in making his record. In no instance should a station be left before the back-sight has been taken, since, even in those regions where but little such influence exists, it will sometimes be found at particular points. It sometimes likewise extends, without any change, over a considerable space, and thus may deflect the needle similarly at a number of stations. An instance of this kind was related to the author, a short time since, by a surveyor of great practical experience.

A line was in dispute. One of the parties called in a surveyor, whom we shall call A., who ran the line, coming out at a stone. The other party, not being satisfied, called upon B., who traced a line agreeing exactly with the one run by A. until he came to a certain point: he then deviated from the former line some 4° to the west. He likewise arrived at a stone. Both parties were now dissatisfied. The first called on A. again, who retraced his line, following exactly his former course. B. was again employed. His course deviated at the same point as before from A.'s. It was then

concluded to have them together. B., being the older hand, went ahead. When they arrived at the point at which their lines separated, B. called on A. to look through the sights, saying, "Is not this right, Mr. A. ?" "It looks very well," he replied: "but look back, Mr. B." On doing so, he found he was really running 4° to the west of his former course. The attraction was first manifest at that point, and continued, without change, at all the subsequent stations along the line he had traversed.

APPENDIX.

THE following demonstration of the rule for finding the area of a triangle when three sides are given is more concise than that given in Art. 251. As the former, however, develops some important properties respecting the centre of the inscribed circle, it was thought best to retain it :

Now, from similar triangles, ADE and AFB, we have