been very well digested by Mr. Murdock Mackenzie, whose treatise on Maritime Surveying ought to be

Case 3. When the profile of a hill as A B, fig. 3, is shewn, the angles of acclivities, and lengths of ascending lines are given to find how the plotting-lines are to be shortened, that the plan thereof may not extend beyond its proper limits.

Example. Suppose the line ab is 1920 links, and that its angle of acclivity= 12° 30'. The line cd is 1900 links, and its angle 8° 0'. The line ef is 1800 links, and its angle = 7° 0'. Required the length of those lines to plot by.

=

By the table, the line ab (being 12° 30' acclivity) must be shortened about 24 links per chain, in the whole 47 links. The line c d its angle being 8° 0', must be shortened 1 link per chain, or 19 links on the whole; leaving the plotting line 1881 links. And the line ef (its angle of acclivity being 7° 0'), must be shortened about 1 link to a chain, or 18 links in the whole, leaving the plotting-line 1782 links.

3

Case 4. When a hill is circular, or approaching to that form, or the abrupt termination of a long hill, as fig. 4, of a rounded form presents itself, to shew how the same may be plotted within its proper limits.

Here ab 240 links (being 9° 45′ declivity) must by the table be shortened, for plotting, about 5 links; a c, 245 (being 12° 0′)

in every person's hands who is engaged in this branch of surveying, a branch which has been hi therto too much neglected. A few general prin

must be shortened about 5 links; ad 263 (being 13° 0') must be shortened 6 links; a e 285 (being 12° 0') must be shortened 7 links; and al 335 (being 10° 0) must be shortened about 6 links. The area of the surface may be found from the foregoing dimensions, as may also the superficial plan in its true bearing from the meridian. Globular surfaces must be projected by their chords found by trigonometry, by the rule that the square of the sine added to the square of versed sine is equal to the chord, and the root extracted gives the chord: the versed sine is the difference between the natural radius (1) and the nat. cosine of the angle.

ciples only can be laid down in this work; these, however, it is presumed, will be found sufficient for most purposes; when the practice is seen to be easy, and the knowledge thereof readily attained, it is to be hoped, that it will constitute a part of every seaman's education, and the more so, as it is a subject in which the safety of shipping and sailors is very much concerned.

1. Make a rough sketch of the coast or harbour, and mark every point of land, or particular variation of the coast, with some letter of the alphabet; either walk or sail round the coast, and fix a staff with a white rag at the top at each of the places marked with the letters of the alphabet. If there be a tree, house, white cliff, or other remarkable object at any of these places, it may serve instead of a station staff.*

2. Choose some level spot of ground upon which a right line, called a fundamental base, may be measured either by a chain, a measuring pole, or a piece of log-line marked into feet; generally speaking, the longer this line is, the better; its situation must be such, that the whole, or most part of the station-staves may be seen from both ends thereof; and its length and direction must, if possible, be such, that the bearing of any station-staff, taken from one of its ends, may differ at least ten degrees from the bearing of the same staff taken from the

Example. Suppose in fig. 5, the measured line

650 links, and its angle of declivity 18° 20′

a b
c d = 1650
ef= 1700
gh = 1200

ik = 700

What must be the length of each plotting line?

20 0

18 0

18 30

12 10

By the table, ab must be shortened 5 links on each chain; c d 6 links on each chain; ef5 links; gh 5 links; ik 2 links. The lengths of the plotting-lines will therefore be: ab 618; cd 1551; ef 1615; g h 1125; and ik 683.

* See Nicholson's Navigator's Assistant

other end; station-staves must be set at each end of the fundamental base.

If a convenient right line cannot be had, two lines and the interjacent angles may be measured, and the distance of their extremes found by construction, may be taken as the fundamental base.

If the sand measured has a sensible and gradual declivity, as from high-water mark to low-water, then the length measured may be reduced to the horizontal distance, which is the proper distance, by making the perpendicular rise of the tide one side of a right-angled triangle; the distance measured along the sand, the hypothenuse; and from thence finding the other side trigonometrically, or by protraction, on paper; which will be the true length of the base line. If the plane measured be on the dry land, and there is a sensible declivity there, the height of the descent must be taken by a spirit-level, or by a quadrant, and that made the perpendicular side of the triangle.

If in a bay one straight line of a sufficient length cannot be measured, let two or three lines, forming angles with each other, like the sides of a polygon, be measured on the sand along the circuit of the bay; these angles carefully taken with the theodolite, and exactly protracted and calculated, will give the straight distance between the two farthest extremities of the first and last line.

3. Find the bearing of the fundamental base by the compass, as accurately as possible, with Hadley's quadrant, or any other instrument equally exact; take the angles formed at one end of the base, between the base line and lines drawn to each of the station-staves; take likewise the angles formed between the base line and lines drawn to every remarkable object near the shore, as houses, trees, windmills, churches, &c. which may be supposed useful as pilot marks; from the other end of the base, take the angles formed between the base and

lines drawn to every one of the station staves and objects; if any angle be greater than the arc of the quadrant, measure it at twice, by taking the angular distance of some intermediate object from each extreme object; enter all these angles in a book as they are taken.

4. Draw the fundamental base upon paper from a scale of equal parts, and from its ends respectively draw unlimited lines, forming with it the angles taken in the survey, and mark the extreme of each line with the letter of the station to which its angle corresponds. The intersection of every two lines, whose extremes are marked with the same letter, will denote the situation of the station or object to which, in the rough draught, that letter belongs; through, or near all the points of intersection which represent station-staves draw a waving line with a pencil to represent the coast.

5. At low water sail about the harbour, and take the soundings, observing whether the ground be rocky, sandy, shelly, &c. These soundings may be entered by small numeral figures in the chart, by taking at the same time the bearings of two remarkable objects; in this excursion, be particular in examining the ground off points of land which project out into the sea, or where the water is remarkably smooth, without a visible cause, or in the vicinity of a small island, &c. observe the set and velocity of the tide of flood, by heaving the log while at anchor, and denote the same in the chart by small darts. The time of high water is denoted by Roman numeral letters; rocks are denoted by small crosses; sands, by dotted shading, the figures upon which usually shew the depth at low water in fect; good anchoring places are marked by a small anchor. Upon coming near the shore, care must be taken to examine and correct the outline of the chart, by observing the inflections, creeks, &c.. more minutely.