Observe that in travelling along X Y Z the hills A B C can be mapped for at X, or thereabouts; the bearing of B from C can be determined at Y; that of A from B; and at Z that of A from C, and so on, for any number of hills. And it is very important to recollect that it is not necessary to catch these lines of sight precisely, for by taking bearings twice, and the intermediate course approximately, there are sufficient data for protracting out upon paper the required bearing.
Thus, as soon as the peak of a distant hill is about to be occulted by the shoulder of a nearer one, a bearing should be taken, and again another as soon as it has reappeared on the other side, and the intermediate course noted.
The advantage of this method of filling up a field sketch will become more apparent as experience is gained. A third and accurate method of fixing the position is in general use among marine surveyors, but has hitherto been but little resorted to by land travellers, viz., by the angles subtended between three known objects. The instrument called the station-pointer is generally used for this purpose, but the position may also be found with a pair of compasses and a protractor, or more simply as follows by means of a protractor and a sheet of tracing paper. Draw a line through the centre of the paper, place the protractor on it, near to the bottom of the sheet, lay off the right hand angle to the right, and the left hand angle to the left of the centre line; rule pencil lines, radiating from the point over which the centre of the protractor had been placed, to the points that had been laid off, then place the paper on the plan or map, and move it about until the three lines coincide with the objects taken, prick through the points that lay beneath the centre of the protractor, and the observer’s position is transferred to the plan. When possible the centre object should be the nearest.
To construct a Map on Mercator’s Projection.
On a sheet of cartridge paper, 38in. by 20in., it is proposed to construct a map on Mercator’s projection, on a scale of ten miles to an inch equatorial, i.e. 6in. to a degree of longitude.
| Lat. | 31° to 33° N. |
| Long. | 34° to 36° E. |
Draw a base line, find its centre, and erect a perpendicular to the top of the paper; the extremes of longitude 34° and 36°, added together and divided by 2°, give 35°, the central meridian, and which is represented by the perpendicular. On each side of it lay off 6in., and erect perpendiculars for the meridians 34° and 36°; divide the base line into ten mile divisions, and the part from 35° 50´ to 36° into miles for the latitude scale. From Table A take the following quantities:—
| ° | ° | ° | ´ | ° | ° | ||
| Lat. | 31 | to 32 | = 1 | 10·4 | = the distance between parallels | 31 | and 32 |
| Lat. | 32 | to 33 | = 1 | 11·1 | ” ” | 32 | and 33 |
| = 2 | 21·5 | ” ” | 31 | and 33 |
Having thus obtained the distance between the required parallels, divide the map into squares of ten miles each way, and the map is ready for the projection of the route.