Part 3 out of 3
In triangles such as E F G and F G H all three angles can be
directly read, so that any inaccuracy in the readings is at once
apparent. The station H and further stations along the coast being:
out of sight of landmark D, it will be as well to connect the survey
up with another landmark K, which can be utilised in the forward work;
the line K H being equal to
F H sin K F H
-------------
sin F K H
The distance between C and D in Fig. 35 is calculated in a
similar manner, because sin A C D : A D:: sin CAD : CD,
AD sin CAD 1866.15 sin 59 20'
or CD = ---------- = -------------------
sin SCD sin 85 9' 53"
or log CD = log 1866.15 + L sin 59 20' - L sin 85 9' 53"
= 3.2709456 + 9.9345738 - 9.9984516
= 3.2070678. ' . CD = 1610.90 ft
The distance between any two positions of the float can be
obtained by calculation in a similar way to that in which the
length C D was obtained, but this is a lengthy process, and is
not necessary in practical work. It is desirable, of course,
that the positions of all the stations be fixed with the
greatest accuracy and plotted on the map, then the position of
the float can be located with sufficient correctness, if the
lines of sight obtained from the angles read with the
theodolites are plotted, and their point of intersection marked
on the plan. The distance between any two positions of the
float can be scaled from the plan.
The reason why close measurement is unnecessary in connection
with the positions of the float is that it represents a single
point, whereas the sewage escaping with considerable velocity
from the outfall sewer spreads itself over a wide expanse of
sea in front of the outlet, and thus has a tangible area. The
velocity of any current is greatest in the centre, and reduces
as the distance from the centre increases, until the edges of
the current are lost in comparative still water; so that
observations taken of the course of one particle, such as the
float represents, only approximately indicate the travel of the
sewage through the sea. Another point to bear in mind is that
the dilution of the sewage in the sea is so great that it is
generally only by reason of the unbroken facal, or other
matter, that it can be traced for any considerable distance
beyond the outfall. It is unlikely that such matters would
reach the outlet, except in a very finely divided state, when
they would be rapidly acted upon by the sea water, which is a
strong oxidising agent.
Hydrographical surveying is that branch of surveying which
deals with the complete preparation of charts, the survey of
coast lines, currents, soundings, etc., and it is applied in
connection with the sewerage of sea coast towns when it is
necessary to determine the course of the currents, or a float,
by observations taken from a boat to fixed points on shore, the
boat closely following the float. It has already been pointed
out that it is preferable to take the observations from the
shore rather than the boat, but circumstances may arise which
render it necessary to adopt the latter course.
In the simplest case the position of the boat may be found by
taking the compass bearings of two known objects on shore. For
example, A and B in Fig. 37 may represent the positions of two
prominent objects whose position is marked upon an ordnance map
of the neighbourhood, or they may be flagstaffs specially set
up and noted on the map; and let C represent the boat from
which the bearings of A and B are taken by a prismatic compass,
which is marked from 0 to 360 . Let the magnetic variation be
N. 15 W., and the observed bearings A 290, B 320, then the
position stands as in Fig. 38, or, correcting for magnetic
variation, as in Fig. 39, from which it will be seen that the
true bearing of C from A will be 275-180=95 East of North, or
5 below the horizontal, and the true bearing of C from B will
be 305-180=120 East of North, or 35 below the horizontal.
These directions being plotted will give the position of C
by their intersection. Fig. 40 shows the prismatic compass in
plan and section. It consists practically of an ordinary compass
box with a prism and sight-hole at one side, and a corresponding
sight-vane on the opposite side. When being used it is held
horizontally in the left hand with the prism turned up in the
position shown, and the sight-vane raised. When looking through
the sight-hole the face of the compass-card can be seen by
reflection from the back of the prism, and at the same time the
direction of any required point may be sighted with the wire in the
opposite sight vane, so that the bearing of the line between the
boat and the required point may be read. If necessary, the
compass-card may be steadied by pressing the stop at the base of
the sight vane. In recording the bearings allowance must in all
cases be made for the magnetic pole. The magnetic variation for
the year 1910 was about l5 1/2 West of North, and it is moving
nearer to true North at the rate of about seven minutes per annum.
[Illustration: FIG. 37.--POSITION OF BOAT FOUND BY COMPASS
BEARINGS.]
[Illustration: FIG. 38.--REDUCTION OF BEARINGS TO MAGNETIC NORTH.]
[Illustration: FIG. 39.--REDUCTION OF BEARINGS TO TRUE NORTH.]
There are three of Euclid's propositions that bear very closely
upon the problems involved in locating the position of a
floating object with regard to the coast, by observations taken
from the object. They are Euclid I. (32), "The three interior
angles of every triangle are together equal to two right
angles"; Euclid III. (20),
"The angle at the centre of a circle is double that of the
angle at the circumference upon the same base--that is, upon
the same part of the circumference,"
or in other words, on a given chord the angle subtended by it
at the centre of the circle is double the angle subtended by it
at the circumference; and Euclid III. (21),
"The angles in the same segment of a circle are equal to one
another."
[Illustration: Fig. 40.--Section and Plan of Prismatic
Compass.]
Having regard to this last proposition (Euclid III., 21), it
will be observed that in the case of Fig. 37 it would not have
been possible to locate the point C by reading the angle A C B
alone, as such point might be amywhere on the circumference of
a circle of which A B was the chord. The usual and more
accurate method of determining the position of a floating
object from the object, itself, or from a boat alongside, is by
taking angles with a sextant, or box-sextant, between three
fixed points on shore in two operations. Let A B C, Fig. 41, be
the three fixed points on shore, the positions of which are
measured and recorded upon an ordnance map, or checked if they
are already there. Let D be the floating object, the position
of which is required to be located, and let the observed angles
from the object be A D B 30 and B D C 45 . Then on the map
join A B and B C, from A and B set off angles = 90 - 30 = 60 ,
and they will intersect at point E, which will be the centre of
a circle, which must be drawn, with radius E A. The circle will
pass through A B, and the point D will be somewhere on its
circumference. Then from B and C set off angles = 90-45 = 45 ,
which will intersect at point F, which will be the centre of a
circle of radius F B, which will pass through points
B C, and point D will be somewhere on the circumference of this
circle also; therefore the intersection of the two circles at D
fixes that point on the map. It will be observed that the three
interior angles in the triangle A B E are together equal to two
right angles (Euclid I. 32), therefore the angle A E B = 180 -
2 x (90 - 30) = 600, so that the angle A E B is double the
angle A D B (Euclid III., 20), and that as the angles
subtending a given chord from any point of the circumference
are equal (Euclid III, 21), the point that is common to the two
circumferences is the required point. When point D is inked in,
the construction lines are rubbed out ready for plotting the
observations from the next position. When the floating point is
out of range of A, a new fixed point will be required on shore
beyond C, so that B, C, and the new point will be used
together. Another approximate method which may sometimes be
employed is to take a point on a piece of tracing paper and
draw from it three lines of unlimited length, which shall form
the two observed angles. If, now, this piece of paper is moved
about on top of the ordnance map until each of the three lines
passes through the corresponding fixed points on shore, then the
point from which the lines radiate will represent the position of
the boat.
[Illustration: Fig. 41. Geometrical Diagram for Locating
Observation Point Afloat.]
The general appearance of a box-sextant is as shown in Fig. 42,
and an enlarged diagrammatic plan of it is shown in Fig. 43. It
is about 3 in in diameter, and is made with or without the
telescope; it is used for measuring approximately the angle
between any two lines by observing poles at their extremities
from the point of intersection. In Fig. 43, A is the sight-
hole, B is a fixed mirror having one-half silvered and the
other half plain; C is a mirror attached to the same pivot as
the vernier arm D. The side of the case is open to admit rays
of light from the observed objects. In making an observation of
the angle formed by lines to two poles, one pole would be seen
through the clear part of mirror B, and at the same time rays
of light from the other pole would fall on to mirror C, which
should be moved until the pole is reflected on the silvered
part of mirror B, exactly in line, vertically, with the pole
seen by direct vision, then the angle between the two poles
would be indicated on the vernier. Take the case of a single
pole, then the angle indicated should be zero, but whether it
would actually be so depends upon circumstances which may be
explained as follows: Suppose the pole to be fixed at E, which
is extremely close, it will be found that the arrow on the vernier
arm falls short of the zero of the scale owing to what may be
called the width of the base line of the instrument. If the pole
is placed farther off, as at F, the rays of light from the pole will
take the course of the stroke-and-dot line, and the vernier arm will
require to be shifted nearer the zero of the scale. After a distance
of two chains between the pole and sextant is reached, the rays of
light from the pole to B and C are so nearly parallel that the
error is under one minute, and the instrument can be used under
such conditions without difficulty occurring by reason of
error. To adjust the box-sextant the smoked glass slide should
be drawn over the eyepiece, and then, if the sun is sighted, it
should appear as a perfect sphere when the vernier is at zero,
in whatever position the sextant may be held. When reading the
angle formed by the lines from two stations, the nearer station
should be sighted through the plain glass, which may
necessitate holding the instrument upside down. When the angle
to be read between two stations exceeds 90 , an intermediate
station should be fixed, and the angle taken in two parts, as
in viewing large angles the mirror C is turned round to such an
extent that its own reflection, and that of the image upon it,
is viewed almost edgeways in the mirror B.
[Illustration: Fig. 42.--Box-Sextant.]
It should be noted that the box-sextant only reads angles in
the plane of the instrument, so that if one object sighted is
lower than the other, the angle read will be the direct angle
between them, and not the horizontal angle, as given by a
theodolite.
The same principles may be adopted for locating the position of
an object in the water when the observations have to be taken
at some distance from it. To illustrate this, use may be made
of an examination question in hydrographical surveying given at
the Royal Naval College, Incidentally, it shows one method of
recording the observations. The question was as follows:--
[Illustration: Fig. 43.--Diagram Showing Principle of Box-
Sextant]
"From Coastguard, Mound bore N. 77 W. (true) 0.45 of a mile,
and Mill bore, N. 88 E, 0.56 of a mile, the following stations
were taken to fix a shoal on which the sea breaks too heavily to
risk the boat near:--
Mound 60 C.G. 47 Mill.
[Greek: phi]
Centre of shoal
Mound 55 C.G. 57 30' Mill.
[Greek: phi]
Centre of shoal.
Project the positions on a scale of 5 in = a mile, giving the
centre of the shoal." It should be noted that the sign [Greek:
phi] signifies stations in one line or "in transit," and C G
indicates coastguard station. The order of lettering in Fig. 44
shows the order of working.
[Illustration: Fig. 44.--Method of Locating Point in Water
When Observations Have to Be Taken Beyond It.]
The base lines A B and A C are set out from the lengths and
directions given; then, when the boat at D is "in transit" with
the centre of the shoal and the coastguard station, the angle
formed at D by lines from that point to B and A is 60 , and the
angle formed by lines to A and C is 47 . If angles of 90 - 60
are set up at A and B, their intersection at E will, as has
already been explained, give the centre of a circle which will
pass through points A, B, and D. Similarly, by setting up
angles of 90 -47 at A and C, a circle is found which will pass
through A C and D. The intersection of these circles gives the
position of the boat D, and it is known that the shoal is
situated somewhere in the straight line from D to A. The boat
was then moved to G, so as to be "in transit" with the centre
of the shoal and the mound, and the angle B G A was found to be
55 , and the angle A G C 57 30'. By a similar construction to
that just described, the intersection of the circles will give
the position of G, and as the shoal is situated somewhere in
the line G B and also in the line A D, the intersection of
these two lines at K will give its exact position.
Aberdeen Sea Outfall
Admiralty, Diving Regulations of
--Charts, Datums for Soundings on
--Main Currents Shown on
Age of Tide
Air Pressure on Tides, Effect of
Almanac, Nautical
Analysis of Cement
--Sea Water
Anchor Bolts for Sea Outfalls
Anemometer for Measuring Wind
Aphelion
Apogee
Atlantic Ocean, Tides in
Autumnal Equinox
Barometric Pressure, Effect on Tides of
Beach Material, Use in Concrete of
Beaufort Scale for Wind
Bench Mark for Tide Gauge
"Bird" Tides
Board of Trade, Approval of Outfall by
Bolts for Sea Outfall Pipes
Box Sextant
Bristol Channel
--Datum for Tides at
Buoy for Marking Position of Outfall
Can Buoy to Mark Position of Outfall
Cast Iron, Resistance to Sea Water of
Cement, Action of Sea Water on
--Analysis of
--Characteristics Causing Hardening of
--Setting of
--Effect of Saline Matters on Strength of
--Sea Water on Setting Time of
--Physical Changes Due to Action of Sea Water on
--Precautions in Marine Use of
--Retardation of Setting Time of
--Tests for Marine Use of
Centrifugal Force, Effect on Tides of
Centripetal Force, Effect on Tides of
--Variations in Intensity of
Charts, Datum for Soundings on
--Main Currents Shown on
Chepstow, Greatest Tide at
Clifton, Tides at
Compass, Magnetic Variation
--Marine
--Prismatic
Concentration of Storm Water in Sewers
Concrete, Action of Sea Water on
--Composition to Withstand Sea Water
--Destruction in Sea Water of
Crown, Foreshore owned by
Currents and Tides. Lack of co-ordination in change of
--Formation of
--in Rivers, 30
--Observations of
--Variation of Surface and Deep
--Variations in Velocity of
Current Observations by Marine Compass
--Theodolites
--Floats for
--Hydrographical Surveying for
--Method of making
--Plotting on Plans, The
--Selecting Stations for
--Special points for consideration in making
--Suitable Boat for
--Trigonometrical Surveying for
Datum Levels for Tides
Declination of Sun and Moon
Decompression after Diving
Density of Sea Water
Derivative Waves
Design of Schemes, Conditions governing
Diffusion of Sewage in Sea
Discharge from Sea Outfalls, Calculations for
--Precautions necessary for
--Time of
Disposal of Sewage by Diffusion
--dependent on time of Discharge
Diurnal Inequality of Tides
Diverting-plate Storm Overflow
Diving
--Illnesses caused by
--Instruction in
--Medical Examination previous to
--Physical Principles involved in
--Equipment
Diving Equipment, Weight of
Dublin, Datum for Tides at
Earth, Distance from Moon
--Sun
--Orbit around Sun of
--Size of
--Time and Speed of Revolution of
Equinox
Erosion of Shore caused by Sea Outfalls
Establishment
Flap Valves on Sea Outfall Pipes
Floats, Deep and Surface
--to govern Pumping Plant
Foreshore owned by Crown
Gauges, Measuring flow over Weirs by
Gauging flow of Sewage
--, Formula: for
Gradient, Effect on Currents of Surface
--Tides of Barometric
Gravity, Specific, of Sea Water
--Tides caused by
Great Crosby Sea Outfall
Harbour and Fisheries Dept., Approval of Outfall by
Harwich, Mean Level of Sea at
High Water Mark of Ordinary Tides
Hook-Gauge, for Measuring flow over Weirs
Hull, Mean Level of Sea at
Hydrographical Surveying Problems in Current Observations
Impermeable Areas, Flow of Rain off
--Percentage of
--per Head of Population
Indian Ocean, Tides in
Infiltration Water
Irish Channel, Analysis of Water in
Iron, Effect of Sea Water on Cast
June, Low Spring: Tides in
Kelvin's Tide Predicting Machine
Land, Area of Globe Occupied by
Leap-weir Storm Overflow
Liverpool, Datum for Tides at
--Soundings on Charts of
--Tide Tables
Lloyd-Davies, Investigations by
Local Government Board, Current Observations Required for
London, Datum for Port of
Low Water Mark of Ordinary Tides
Lunar Month
Lunation
Magnetic Variation of Compass
Marine Compass
Mean High Water
Mersey, Soundings on Charts of
Mixing Action of Sewage and Water
Moon, Declination of
--Distance from Earth of
--Effect on Tides of
--Mass of
--Minor Movements of
--Orbit around Earth of
--Perigee and Apogee
Morse Code for Signalling
Nautical Almanac
Neap Tides
--Average Rise of
Orbit of Earth around Sun
--Moon around Earth
Ordinary Tides, lines on Ordnance Maps of
Ordnance Datum for England
--Ireland, 17
--Records made to fix
--Maps, lines of High and Low Water on
Outfall Sewers, Approval by Board of Trade of
--Calculations for Discharge of
--Construction of
--Detail Designs for
--Details of cast-iron Pipe Joints for
--Flap Valves on end of
--Inspection during Construction of
--Marking position by Buoy of
--Selection of Site for
Overflows for Storm Water
Pacific Ocean, Tides in
Parliament, Current Observations Required for
Perigee
Perihelion
Piling for Sea Outfalls
Pipes, Joints of Cast Iron
--Steel
Plymouth, Mean Sea Level at
Predicting Tides
Primary Waves
Prismatic Compass
Pumping
--Cost of
--Plant
--Management of
--Utilisation of Windmills for
Pumps for Use with Windmills
Quantity of Rainfall to Provide for
--Sewage to Provide for
Rainfall
--at Times of Light Winds
--Frequency of Heavy
--in Sewers
--Intensity of
--Storage Capacity to be Provided for
--To Provide for
Range of Tides
Rise of Tides
Screening Sewage before Discharge
--Storm Water before Overflow
Sea, Mean Level of
Sea Outfalls, Calculations for Discharge of
--Construction of
--Design of
--Lights and Buoy to mark position of
--Selection of Site for
Seashore Material used in Concrete
Sea, Variation around Coast in level of
--Water, Analysis of
--Effect on Cast-Iron of
--Effect on Cement
--Galvanic action in
--Weight of
Secondary Waves
Separate System of Sewerage
Sewage, Effect of Sea Water on
--Gauging flow of
--Calculations for
--Hourly and daily variation in flow of, 42
--Quantity to provide for
Sewers, Economic considerations in provision of Surface Water
--Effect on Design of Scheme of Subsidiary
--Storm Water in
Sextant, Box
Signalling, Flags for
--Morse Code for
Solstice, Summer and Winter
Soundings on Charts, Datum for
Southampton, Tides at
Southern Ocean, High Water in
--Origin of Tides in
--Width and Length of
Specific Gravity of Sea Water
Spring Tides
--Average Rise of
--Variation in Height of
Storage Tanks, Automatic High Water Alarms for
--Determination of Capacity of
--For Windmill Pumps
Storm Water in Sewers
--Overflows
Subsidiary Sewers, Effect on Design of Scheme of
Summer Solstice
Sun, Aphelion and Perihelion
--Declination of
--Distance from Earth
--Effect on Tides of
--Mass of
--Minor Movements of
Surface Water Sewers, Average Cost of
--Economic Considerations in Provision of
Surveying, Problems in Hydrographical
--Trigonometrical
Thames Conservancy Datum
--Flow of Sewage in
Tidal Action in Crust of Earth
--Attraction
--Day, Length of
--Flap Valves on Sea Outfall Pipes
--Observations, Best Time to Make
--Records, Diagram of
--Rivers, Tides and Currents in
--Waves, Length of Primary
--Secondary or Derivative
--Speed of Primary
--Velocity of
Tide Gauge, Method of Erecting
--Selecting Position of
Tide, Observations of Rise and Fall of
Tide-Predicting Machine
--Recording Instrument
--Tables
Tides, Abnormally High
--Age of
Tides and Currents, Lack of Co-ordination in Change of
--Diagrammatic Representation of Principal
--Diurnal Inequality
--Double, 9
--Effect of Barometric Pressure on
--Centripetal and Centrifugal Force
--Storms on,
--Extraordinary High
--Formation of
--in Rivers
--lines on Ordnance Maps of High and Low Water of
--Propagation to Branch Oceans of
--Proportionate Effect of Sun and Moon on
--Range of
--Rate of Rise and Fall of
--Rise of
--Spring and Neap
--Variations in Height of
Towers for Windmills
Trade Wastes, Effect on flow of Sewage of
Trass in Cement for Marine Vork
Trigonometrical Surveying for Cuirent Observations
Trinity High Water Mark
Upland Water, Effect on Rivers of
Valves on Sea Outfall Pipes
Velocity of Currents
Vernal Equinox
Visitors, Quantity of Sewage from
Volume of Sewage
Water, Area of Globe occupied by
--Fittings, Leakage from
--Power for Pumping
--Supply, Quantity per Head for
--Weight of
Waterloo Sea Outfall
Waves, Horizontal Movement of
--Motion of
--Primary and Secondary
--Tidal
--Wind
Weight of Fresh Water
--Sea Water
--Sewage
Weirs for Gauging Sewage, Design of
--Storm Overflow by Parallel
Weymouth, Mean Level of Sea at
Wind
--Beaufort Scale for
Wind, Mean Hourly Velocity of
--Measuring Velocity of
--Monthly Analysis of
--Power of Windmills According to Velocity of
--Rainfall at Time of Light
--Velocity and Pressure of
--Waves
Windmills
--Comparative Cost of
--Details of Construction of
--Effective Duty of
--Efficient Sizes of
--For Pumping Sewage
--Height of Towers for
--Power in Varying Winds of
Winter Solstice