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Sail round the coast to be surveyed, and fix station staves on the principal points where there are no remarkable objects to distinguish them; at the same time make a rough sketch of the harbour, on which denote the positions of the objects and station staves by the letters a, b, c, d, etc.; seek for a proper place on the shore on which a base line may be measured ; and as there is no part of the coast that commands a view of all the stations, it will be necessary to measure two base lines. The base line A B is first fixed upon, the ground being level and a considerable number of the stations being visible from each extremity; its length, as measured by a chain, is 8 cables, and the bearing of B from A is 50° (N. 50° E.) true.
From each end of the base measure the angles contained between the base line and the several stations within sight, which are as follows
The above are all the stations that are visible from each of the stations A and B, hence it is necessary to fix upon a place where another base line may be measured from each end of which the remaining stations can be seen. The most convenient spot is between D and E; let D E be the second base line, its length being 6.6 cables, and the bearing of E from D 293° (N. 67° W.) true ; but as its southern extremity D can be seen only from one end of the first base line, the LDCD is to be observed from station C (on the island) in order to ascertain the position of the second base with regard to the first; this angle is found to be 45° 40'. Now observe the angles formed by lines drawn from each end of this base line to each of the station staves or other objects, which are as followFrom Station D
From Station E
Angle D Eg = 22° 0'
72 15 „ fDg = 77
fEk = 69 10 In sounding for depths of water, a shoal was discovered in the western entrance, and in order to fix its extremities, buoys were placed at i and h, and the following true bearings takenFrom Station D
From Station E i bore S. 77° W.
i bore S. 44o E. h „ S. 16° W.
S. 34° E.
When c (on the mainland) bears N. 14° E. and the angle between c and bis 81°, the vessel is on the anchorage ground for large vessels in Sandy Bay; and when D bears N. 76° W. and the angle between Town church and D is 82°, the vessel is on the anchorage ground in Town Bay.
The above angles and bearings being laid off will give the positions of all the stations relative to the base lines. If it be desired to fix the geographical positions, it will be necessary to fix the latitude and longitude of some prominent place, as in Example II., by astronomical observations, from whence the geographical position of any other point can be found. The latitude will be determined by meridian and ex-meridian altitudes of sun and stars, and the longitude by sun and star chronometers taken on or near the prime vertical, and observed in an artificial horizon. The true direction of the base line must be found by reference to the true meridian, the direction of which will have been determined from the sun's true bearing, either computed or taken from the azimuth tables.
In order to plot the observations in the three examples just given, proceed as follows:
Mount the paper on a drawing-board. Select a convenient position on the paper and make a dot and enclose it in a circle ; this will represent the observatory station. Through the observatory station draw the true meridian. The spot chosen should admit of all the stations being got on the plan.
From the observatory station draw the base line in the true direction on the required scale, and at the other extremity make a clear mark.
From each end of the base line lay off the angles or bearings observed by means of a protractor or Field's parallel rulers, and where the several lines intersect each other will be the position of each station relative to the base line.
In these examples only the prominent points have been fixed, so that the work could be easily followed and the method of carrying out the work clearly seen.
For the purpose of cutting in the coast line a sufficient number of stations must be selected to enable the work to be done with accuracy, and, in all probability, it will be necessary to use other base lines for this purpose, remembering that it is better to cut inwards from a long base than outwards from a short base. Any of the sides of the triangles can be computed and used as new base lines, and the work of fixing the stations carried out exactly in the same manner as explained above.
Insert as much topographical detail as is necessary, also lines of soundings with the nature of the bottom, using for this purpose the conventional signs and abbreviations. The scales of latitude and distance, and longitude, should always be drawn on the plan, so that any alteration, owing to atmospheric changes, will affect each in the same manner
In Plate III. there are some shallow patches at the eastern entrance, some of which dry at low water. A vessel entering or leaving the harbour will clear the danger by keeping an angle of 35° on the sextant between the two beacons at the eastern entrance. For example : the dotted line at the eastern extremity represents a vessel approaching from the eastward ; at the point of contact with the circle the church and eastern beacon are in transit, and the horizontal angle between the beacons is 35° ; by maintaining this angle on the sextant the vessel cannot get into danger, and when the eastern beacon and the farmhouse are in transit the vessel is clear of all danger, and can shape courses for the anchorage. 'A vessel leaving the harbour and bound to the eastward would be clear of all danger when the eastern beacon and the church were in transit and the angle between the beacons was 35o.
Any student wishing to prove that the ship is on the circle so long as the angle is 35o, can do so by taking a piece of tracing paper and drawing an angle of 35° on it; then place the angular point on any part of the circle seaward of the two beacons, and the legs forming the angle will lie over the two beacons ; now move the angular point round the circle, and the legs will continue to lie over the two beacons, but it will be observed that one leg shortens as the other lengthens, the angle remaining the same. A vessel striking any part of the circle seaward of the two beacons would have an angle of 35 between them.
CHART CONSTRUCTION Before commencing chart construction it is necessary, for the proper understanding of a chart, to have a thorough knowledge of what is meant by the expression “ Natural Scale,” which is found in the title of a chart or plan expressed as a fraction. The “Natural Scale,” when properly understood, conveys an idea of how much detail can be shown on a chart or plan.
DEF. --The natural scale is the ratio which the length of a certain unit on the chart bears to the real length of that unit on the earth's surface ; for example, natural scale means that i inch on the chart represents
72960 72,960 inches on the earth's surface, or I nautical mile of 6,080 feet equal to 72,960 inches. In the following examples the mean length of a minute of latitude is used, but it must be distinctly understood that in constructing a plan the real length of a mile for that particular geographical position for which the plan is constructed must always be used.
The following natural scales, fully explained, will make the subject clear. The numerator represents i inch and the denominator the number of inches on the earth's surface equivalent to it.
= 1 inch to i mile, because I inch represents 72,960 inches 72960
on the earth's surface, equal to a mile of 6,080 feet. I = 1 inch to 2 miles, because 145,920 inches
= 2 miles. 145920
It will be observed that as the denominator increases the scale of the chart or plan decreases, and as the denominator decreases the scale increases.
If the scale of inches per mile be given to find the natural scale, divide the number of inches in a mile by the scale of inches per mile, and the result is the natural scale required.
Example.--If 3 inches represent one mile, what is the natural scale ?
If the natural scale be given to find the number of inches which represent I mile, divide the number of inches in a mile by the given natural scale and the result is the number of inches required.
If the natural scale be given to find the number of miles to 1 inch, divide the given natural scale by the number of inches in a mile and the result is the number of miles to 1 inch.
Example I.-Given the natural scale to find the number of miles
12160 represented by 1 inch.
Example II.-Given the natural scale
to find the number of
145920 miles represented by 1 inch.
Given the longitude scale 6 inches to one degree, find the length between 47° N. and 48° N.; that is, the latitude scale.
Lat. scale long. scale X sec. of middle latitude.
Long scale 6 inches log. 0-778151
8.881 log. 0.948468 Ans. Latitude scale = 8881 inches.
Given 6 inches to a degree of middle latitude, to find the longitude scale, the middle latitude being 47° 30' N.
Long. scale = middle lat. scale x cosine middle lat.
Middle lat. scale 6 inches log. 0.778151
47° 30' cos. 9.829683
4.054 log. 0.607834 Ans. Longitude scale
Let it be required to find the length of the meridian between lat. 50° N. and 50° 40' N., when the longitude scale is 6 inches to i degree.
Lat. 50° mer. pts. 3474:47 The mer. parts between lat. 50° Lat. 50° 40' mer. pts. 3537-14 and lat. 50° 40' N. are 62'67, and
this distance, taken in the compasses, Mer. parts between 50° and 50° 40' = 62:67 will reach from lat. 50° to 50° 40' N.