Chap. VIII.

GEOMETRY.

851

Fig. 1075.

between the observer and the coast, in such a position that one additional station can heseen from it: at the time of a given signal, angles are observed from the assistant boat to

three objects on shore, and to the distant boat; and from the latter, angles at the same

time measured to the two stations on shore, and to the assistant boat: suppose I) to bethe distant station, from whence A and B can be seen, and E the position of the assistantboat from whence A, B, and C can be seen; then at the samemoment of time, the angles are observed from E and from D ;their mean show the position of D ; for the point E is fixed in

position by the observed angles C E A, A E B, and it becomes

therefore a fixed station with reference to D, from which twoangles are observed to three stations fixed in position. Breakersand currents must also be observed at that time when the tideis favourable, or when a perfect calm allows them to be re-cognised.

To reduce soundings after they have been taken consists indeducting from the depths, as noted down, proportionate quantitiesvarying with the time, so that all may agree with the lowestlevel of the tide; the whole are then written on the chart infathoms and quarter fathoms.

Maritime Surveying without the aid of Triangulation on Shore,is not in its results so accurate as that where they can be adopted ;hut where- free access to a country is not attainable, this methodis resorted to as the nearest approaching to the excellence of thefirst: instead of commencing with the measurement of a shortbase, and a series of triangles spread over a great area, a muchlonger base is established; sometimes one of 50 miles or more:upon this all the observations are made, and the details laid downas quickly as they are taken, and all errors corrected during theprogress of the work. On the choice of direction for this base line much of the successdepends: elevated land, or some mountain or conspicuous object, should terminate eachextremity; and the more numerous the intermediate objects that can be sben from the endsof this base line, the greater will be the correctness of the survey. The latitude andlongitude of the first station being taken and determined by astronomical observations, andthe bearing of the several objects by the compass, the same is to be done at the chiefstations along the line selected for the base. The stations are determined by the chrono-meter and measurement of the rate of sailing ; from them the observations are made whichare to be laid down on the chart: the distance between the primary stations, whose lati-tudes and longitudes have been determined, is obtained by supposing P to represent thepole of the earth : the angle P is known by the difference oflongitude between the twostations B and A; the sides PA and PB are also given, being the respective co-latitudesof the two stations. In the spherical triangle A B P are two sides and the contained angle,from which we may obtain the length of the opposite side A B: a line joining any twoof these stations is the arc of a circle on the surface of the earth, and must therefore be re-duced to its chord, which is equal to twice the sine of half the arc. When a survey of acoast is made at night, and intersections cannot be obtained, observationmust be taken within a few miles from the shore by anchoring the vesselat one or more intermediate stations : the position of the vessel is deter-mined by a careful observation of the angles subtended between the sun andprimary stations, noting the time also when the observation is made : thetime gives the sun’s azimuth, and from it is deduced the azimuth of thetwo primary stations from the vessel; those intermediate are obtainedby the intersection of their lines of direction as observed at the differentstations. The details and soundings are then to be taken, with the filling-in as it can be obtained; by this means a very accurate map may belaid down: it is often necessary to make a survey of the coast when aship is under sail, and although the system adopted may vary in itsdetails, the general principles are the same. The angular distancesbetween prominent points of land as observed from the vessel, should betaken when at anchor, and the outline of the coast sketched: astronomicalobservations must be made at the same time to determine the position ofthe vessel, and the bearing by the compass noted: continuing a series of such observationsin sailing from one point to another, and having special care not to lose sight of the pointsto which angles have been observed, as this would lead to confusion and great difficultywhen the whole is to be laid down on paper. A reckoning of the ship’s rate ofsailing must be carefully noted by the log line; though much reliance cannot beplaced upon it, it may help, in some degree, to check any error arising from the astro-nomical observations: when sailing, care must be paid that the vessel has all its bearings

3 i 2

Fig.1070.