(ACD + ADC) - (ACD - ADC) ADC = —————————————- 2

120 40' - 49 39' 46" 71 0' 14" .. ADC = ————————————- = —————— = 35 30' 7", 2 2

ACD = 180 - 35 30' 7" - 59 20' = 85 9' 53".



Now join up points C and D on the plan, and from point D set off the line D A, making an angle of 35 30' 7" with C D, and having a length of l866.15 ft, and from point C set off the angle A C D equal to 85 9' 53". Then the line A C should measure l087.6 ft long, and meet the line A D at the point A, making an angle of 59 20'. From point A draw a line A B, ll7 ft long, making an angle of 29 23' with the line A C; join B C, then the angle ABC should measure 147 17', and the angle B C A 3 20'. If the lines and angles are accurately drawn, which can be proved by checking as indicated, the line A B will represent the base line in its correct position on the plan.

The positions of the other stations can be calculated from the readings of the angles taken from such stations. Take stations E, F, G, and H as shown in Fig. 36*, the angles which are observed being marked with an arc.

It will be observed that two of the angles of each triangle are recorded, so that the third is always known. The full lines represent those sides, the lengths of which are calculated, so that the dimensions of two sides and the three angles of each triangle are known. Starting with station E,

Sin A E D: A D:: sin D A E: D E

A D sin D A E D E = ——————— sin A E D

or log D E = log A D + L sin D A E-L sin A E D.

From station F, E and G are visible, but the landmark D cannot be seen; therefore, as the latter can be seen from G, it will be necessary to fix the position of G first. Then,

sin E G D: D E :: sin E D G : E G,

D E sin E D G or EG= ———————- sin E G D

Now, sin E F G: E G :: sin F E G : F G

E G sin F E G F G = ——————- sin E F G

thus allowing the position of F to be fixed, and then

sin F H G : F G :: sin F G H : F H

F G sin F G H F H= ——————- sin F H G



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 fcal, 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.



CHAPTER XV.

HYDROGRAPHICAL SURVEYING.

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.



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."



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.



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.



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:—



"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.



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

THE END