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To draw a true meridian line to a map, having the variation and mag
netical meridian given. On any magnetical meridian or parallel, upon which the map is protracted, set off an angle from the north towards the east, equal to the degrees or quantity of variation if it be westerly, or from the north towards the west if it be easterly, and the line which constitutes such an angle with the magnetical meridian will be a true meridian line.
For if the variation be westerly, the magnetical meridian will be the quantity of variation of the west side of the true meridian, but if easterly, on the east side ; therefore the true meridian must be a like quantity on the east side of the magnetical one when the variation is westerly, and on the west side when it is easterly.
To lay out a true meridian line by the circumferentor. If the variation be westerly, turn the box about till the north of the needle points as many degrees from the flower-de-luce towards the east of the box, or till the south of the needle points the like number of degrees from the south towards the west, as are the number of degrees contained in the variation, and the index will be then due north and south; therefore, if a line be struck out in the direction thereof, it will be a true meridian line.
If the variation was easterly, let the north of the needle point as many degrees from the flower-de-luce towards the west of the box, or let the south of the needle point as many degrees towards the east, as are the number of degrees contained in the variation, and then the north and south of the box will coincide with the north and south points of the horizon, and consequently a line being laid out by the direction of the index will be a true meridian line.
This will be found to be very useful in setting a horizontal dial, for if you lay the edge of the index by the base of the stile of the dial, and keep the angular point of the stile towards the south of the box, and allow the variation as before, the dial will then be due north and south, and in its proper situation, provided the plane upon which it is fixed be duly horizontal, and the sun south at noon; but in places where it is north at noon the angular point of the index must be turned to the north.
How maps may be traced by the help of a true meridian line. If all maps had a true meridian line laid out upon them, it would be easy, by producing it, and drawing parallels, to make out field-notes ; and by knowing the variation, and allowing it upon every bearing, and having the distances, you would have notes sufficient for a trace. But a true meridian line is seldom to be met with; therefore we are obliged to have recourse to the foregoing method. It is therefore advised to lay out a true meridian line upon every map.
To find the difference between the present variation, and that at a time when a tract was formerly surveyed, in order to trace or run out the original lines.
If the old variation be specified in the map or writings, and the present be known, by calculation or otherwise, then the difference is immediately seen by inspection ; but as it more frequently happens that neither is certainly known, and as the variation of different instruments is not always alike at the same time, the following practical method will be found to answer every purpose.
Go to any part of the premises where any two adjacent corners are known; and if one can be seen from the other, take their bearing; which, compared with that of the same line in the former survey, shows the difference. But if trees, hills, &c. obstruct the view of the object, run the line according to the given bearing, and observe the nearest distance between the line so run and the corner, then,
As the length of the whole line moto
Suppose it be required to run a line which some years ago bore NE. 45°,
Answer, 34 minutes, or a little better than half a degree to the lefthand, is the allowance required, and the line in question bears N. 44° 26'E.
Note.--The different variations do not affect the area in the calculation, as they are similar in every part of the survey.
* 57.3 is the radius of a circle (nearly) in such parts as the circumference contains 360.