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This intersection comes
differences of the two given radii. in the point G, fig. 4 (pages 222, 223). The problem, therefore, algebraically resolves itself into the following:
If A = the angle FCE=ACH=NCK (fig. 5),
r = radius of new curve,
then NC=R cos. A,
N KR sin. A,
K G2 = (R − r)2
K P2 (NC-M C)2= (R cos. A − r)2
.:. GP = √(R − r)2 – (R cos. A − r)2
√ R2 − 2Rr + r2 – R2 cos. 2A + 2 Rr cos. Ar2
.. MG=R sin. A - R2 sin.3A - (4 Rrsin.24)
IN Marine Surveying, the use of two theodolites upon the
TAKEN WITH THE BOX SEXTANT
and the angles bear upon the stations D and E, and between
A good form of book for recording soundings consists of pages of ruled line paper with the addition of vertical lines dividing a page into five columns so as to enter when taking a section along a line, sav between H and G
as shown in the figure. (Page 226.) The records give : (1) distance from H obtained by tallies fixed to a stranded copper wire attached to the shore at H, and attached round a reel in the centre of the boat, the wire being pulled taut by the man who winds the reel by means of a crab handle and by the oarsman rowing the boat so as to render the wire in tension; (2) a column to enter the time, which it will be sufficient to enter every five minutes; (3) the record of a gauge to show height of water, an operation meanwhile performed by another man at some fixed station near at hand, who enters the readings in an independent book, so as to be subsequently repeated in the sounding book; (4) the sounding read in feet and inches off a sounding chain usually 80 feet long, in which the links measure an inch; (5) the reduced sounding for plotting. This operation requires a man at H to sight a mark at G, and to direct the boat in line or preferably to fix a back station at E, so that the men in the boat can place themselves in line with H and E, and in the boat besides the surveyor, two men at the oars, one man at the sounding, and one man to wind the reel or let out the stranded wire as directed. The columns of a book suitable for a section are further explained in the form given on page 229. The soundings upon the Admiralty Charts are expressed in feet for the mean low-water of spring tides, and reference should be made to the diagram of the compass card on these maps, showing the magnetic variation of the direction of north from the true north. The surveyor should also make himself familiar with the readings of the compass-card, so as to feel quite at home with the boatmen whose language involves the continual use of such descriptions of wind and direction.
By means of a current meter, the rate of flow in any river or stream, or in a tidal current, can be readily and accurately ascertained, either at or below the surface, as may be required. The meter shown on page 228 is a considerable improvement upon instruments of this kind hitherto in use, the parts most exposed to wear being thoroughly strengthened, and the indication of flowing being at once shown upon the dial. It consists of an axis carrying two screw blades, and having
an endless screw, which works a differential disc in two parts, the front part showing the number of feet run, from 0 to 330; and the back part, miles and furlongs, from o to 12 miles. The arm carrying this disc is so attached to the frame that the disc, when not in use, is kept free of the endless screw by a coiled spring, but can be instantly brought into working contact with it, either by a cord held by the operator, or by a nut on the vertical screw at one end of the arm. A flat vane, clamped to the frame, serves to keep the instrument with its screw properly facing the current. The mode of using the current meter is as follows:The meter is to be well fitted, and securely clamped to the end of a stout stick-preferably a cane-the flat
vane to be fixed in place, and a cord attached to the eyehole of the vertical screw. The differential disc is then to be set to zero of each graduated circle, in which position it will be held by a point projecting on the inside of the bottom of the frame. The meter is then to be lowered into the water, the screw or turbine being held facing the current, and when the intended depth is reached, the differential disc is to be brought into contact with the endless screw or shaft by tightening the cord, the time being carefully noted at the moment of contact, and again on releasing the disc. The distance registered on the graduated circles,
being divided by the time, gives the rate of flow per minute or per second, as required.
If, however, time can be given for a long run, and especially in a rapid current, the disc may be brought into contact by screwing up the small nut under the eye-hole before immersion, the time being taken at the moments of entering and leaving the water.
In a rapid current the vibration caused by the screw is considerable; precaution must, therefore, be taken to hold the instrument firmly in its true position, and when the observation is taken at some depth it will be found useful to have a tie head at the top of the staff for this purpose.
It is also advisable to attach a line to the eye-hole of the vertical screw, whether contact be made before entering, or in the water, in case of the instrument becoming by any accident detached from the stick, mentioned above.
The Station Pointer (page 81) is used for plotting the position of any soundings A, B, C, shown in the figure, and such position is fixed by simultaneously taking the bearings of three known objects on shore D, E, F, or in the case of a river section upon the line E G, the bearing of two objects D and F right and left of that line. The position of the point may be found by means of tracing paper, on which observed angles are plotted, in which case the draughtsman shifts the tracing paper, with the angle plotted thereon, over the plan until the point falls on to the only spot from which the lines containing the observed angles will intersect the three fixed stations. (See illustration, page 226.) Section Line No.........